42
STEREOTYPES Pedro Bordalo Katherine Coffman Nicola Gennaioli Andrei Shleifer We present a model of stereotypes based on Kahneman and Tversky’s representativeness heuristic. A decision maker assesses a target group by over- weighting its representative types, defined as the types that occur more fre- quently in that group than in a baseline reference group. Stereotypes formed this way contain a ‘‘kernel of truth’’: they are rooted in true differences between groups. Because stereotypes focus on differences, they cause belief distortions, particularly when groups are similar. Stereotypes are also con- text dependent: beliefs about a group depend on the characteristics of the ref- erence group. In line with our predictions, beliefs in the lab about abstract groups and beliefs in the field about political groups are context dependent and distorted in the direction of representative types. JEL Codes: D03, D83, D84, C91. I. Introduction The Oxford English Dictionary defines a stereotype as a ‘‘widely held but fixed and oversimplified image or idea of a par- ticular type of person or thing.’’ Stereotypes are ubiquitous. Among other things, they cover racial groups (‘‘Asians are good at math’’), political groups (‘‘Republicans are rich’’), genders (‘‘Women are bad at math’’), demographic groups (‘‘Florida resi- dents are elderly’’), and situations (‘‘Tel Aviv is dangerous’’). As these and other examples illustrate, some stereotypes are roughly accurate (‘‘the Dutch are tall’’), while others much less so (‘‘Irish are red-headed’’; only 10% are). Moreover, stereotypes change: in the United States, Jews were stereotyped as religious and We are grateful to Nick Barberis, Roland Be ´nabou, Dan Benjamin, Tom Cunningham, Matthew Gentzkow, Emir Kamenica, Larry Katz, Eliana La Ferrara, David Laibson, Sendhil Mullainathan, Josh Schwartzstein, Jesse Shapiro, Alp Simsek, Neil Thakral, and four anonymous referees for extremely helpful comments and Jesse Graham, Jonathan Haidt, and Brian Nosek for sharing the Moral Foundations Questionnaire data. We thank the Pershing Square Venture Fund for Research on the Foundations of Human Behavior for support of this research, and Maik Wehmeyer, Laura Freitag, and Aaron Englander for re- search assistance. ! The Author(s) 2016. Published by Oxford University Press, on behalf of President and Fellows of Harvard College. All rights reserved. For Permissions, please email: [email protected] The Quarterly Journal of Economics (2016), 1753–1794. doi:10.1093/qje/qjw029. Advance Access publication on July 19, 2016. 1753 at Harvard Library on October 28, 2016 http://qje.oxfordjournals.org/ Downloaded from

I. Introduction · uneducated at the beginning of the 20th century, and as high achievers at the beginning of the 21st (Madon et al. 2001). Social science has produced three broad

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Page 1: I. Introduction · uneducated at the beginning of the 20th century, and as high achievers at the beginning of the 21st (Madon et al. 2001). Social science has produced three broad

STEREOTYPES

Pedro Bordalo

Katherine Coffman

Nicola Gennaioli

Andrei Shleifer

We present a model of stereotypes based on Kahneman and Tverskyrsquosrepresentativeness heuristic A decision maker assesses a target group by over-weighting its representative types defined as the types that occur more fre-quently in that group than in a baseline reference group Stereotypesformed this way contain a lsquolsquokernel of truthrsquorsquo they are rooted in true differencesbetween groups Because stereotypes focus on differences they cause beliefdistortions particularly when groups are similar Stereotypes are also con-text dependent beliefs about a group depend on the characteristics of the ref-erence group In line with our predictions beliefs in the lab about abstractgroups and beliefs in the field about political groups are context dependentand distorted in the direction of representative types JEL Codes D03 D83D84 C91

I Introduction

The Oxford English Dictionary defines a stereotype as alsquolsquowidely held but fixed and oversimplified image or idea of a par-ticular type of person or thingrsquorsquo Stereotypes are ubiquitousAmong other things they cover racial groups (lsquolsquoAsians are goodat mathrsquorsquo) political groups (lsquolsquoRepublicans are richrsquorsquo) genders(lsquolsquoWomen are bad at mathrsquorsquo) demographic groups (lsquolsquoFlorida resi-dents are elderlyrsquorsquo) and situations (lsquolsquoTel Aviv is dangerousrsquorsquo) Asthese and other examples illustrate some stereotypes are roughlyaccurate (lsquolsquothe Dutch are tallrsquorsquo) while others much less so (lsquolsquoIrishare red-headedrsquorsquo only 10 are) Moreover stereotypes change inthe United States Jews were stereotyped as religious and

We are grateful to Nick Barberis Roland Benabou Dan Benjamin TomCunningham Matthew Gentzkow Emir Kamenica Larry Katz Eliana LaFerrara David Laibson Sendhil Mullainathan Josh Schwartzstein JesseShapiro Alp Simsek Neil Thakral and four anonymous referees for extremelyhelpful comments and Jesse Graham Jonathan Haidt and Brian Nosek for sharingthe Moral Foundations Questionnaire data We thank the Pershing SquareVenture Fund for Research on the Foundations of Human Behavior for support ofthis research and Maik Wehmeyer Laura Freitag and Aaron Englander for re-search assistance

The Author(s) 2016 Published by Oxford University Press on behalf of Presidentand Fellows of Harvard College All rights reserved For Permissions please emailjournalspermissionsoupcomThe Quarterly Journal of Economics (2016) 1753ndash1794 doi101093qjeqjw029Advance Access publication on July 19 2016

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uneducated at the beginning of the 20th century and as highachievers at the beginning of the 21st (Madon et al 2001)

Social science has produced three broad approaches to ste-reotypes The economic approach of Phelps (1972) and Arrow(1973) sees stereotypes as a manifestation of statistical discrim-ination rational formation of beliefs about a group member interms of the aggregate distribution of group traits Statisticaldiscrimination may affect actual group characteristics in equilib-rium (Arrow 1973) but even so stereotypes are based on rationalexpectations1 As such these models do not address the centralproblem that stereotypes are often inaccurate The vast majorityof Florida residents are not elderly the vast majority of the Irishare not red-headed and Tel Aviv is really pretty safe

The sociological approach to stereotyping pertains only tosocial groups It views stereotypes as fundamentally incorrectand derogatory generalizations of group traits reflective of thestereotyperrsquos underlying prejudices (Adorno et al 1950) or otherinternal motivations (Schneider 2004) Social groups that havebeen historically mistreated such as racial and ethnic minoritiescontinue to suffer through bad stereotyping perhaps because thegroups in power want to perpetuate false beliefs about them(Glaeser 2005 Steele 2010) The stereotypes against blacks arethus rooted in the history of slavery and continuing discrimina-tion This approach might be relevant in some important in-stances but it leaves a lot out While some stereotypes areinaccurate many are quite fair (lsquolsquoDutch are tallrsquorsquo lsquolsquoSwedes areblondrsquorsquo) Moreover many stereotypes are flattering to the groupin question rather than pejorative (lsquolsquoAsians are good at mathrsquorsquo)Finally stereotypes change so they are at least in part respon-sive to reality rather than entirely rooted in the past (Madon et al2001)

The third approach to stereotypesmdashand the one we followmdashisthe lsquolsquosocial cognition approachrsquorsquo rooted in social psychology(Schneider 2004) This approach gained ground in the 1980s

1 More recent work explores under what conditions stereotypes are self-ful-filling Assuming that freely available information is used correctly minorities caninvest in visible signals of quality that offset preconceptions (Lundberg and Startz1983) Glover Pallais and Pariente (2015) present evidence on self-fulfilling as-pects of stereotypes in labor markets

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and views social stereotypes as special cases of cognitive schemasor theories (Schneider Hastorf and Ellsworth 1979) These the-ories are intuitive generalizations that individuals routinely usein their everyday life and they entail savings on cognitive re-sources Hilton and Von Hippel (1996) define stereotypes aslsquolsquomental representations of real differences between groups [ ]allowing easier and more efficient processing of informationStereotypes are selective however in that they are localizedaround group features that are the most distinctive that providethe greatest differentiation between groups and that show theleast within-group variationrsquorsquo A related lsquolsquokernel-of-truth hypoth-esisrsquorsquo holds that stereotypes are based on some empirical realityas such they are useful but may entail exaggerations (Judd andPark 1993)

We show that this approach to stereotypes is intimately re-lated to another idea from psychology the use of heuristics inprobability judgments (Kahneman and Tversky 1972) Justas heuristics simplify the assessment of complex probabilistichypotheses they also simplify the representation of heteroge-neous groups sometimes causing errors in judgment We for-mally explore this idea by modeling stereotype formation as aconsequence of Kahneman and Tverskyrsquos representativenessheuristic Tversky and Kahneman (1983) write that lsquolsquoan attributeis representative of a class if it is very diagnostic that is therelative frequency of this attribute is much higher in that classthan in the relevant reference classrsquorsquo Following Gennaioli andShleifer (GS 2010) we assume that a type t is representativefor group G relative to a comparison group ndashG if it scores highon the likelihood ratio

Pr ethtjGTHORN

Pr ethtj GTHORNeth1THORN

The most representative types come to mind first and so areoverweighted in judgments Predictions about G are then madeunder a distorted distribution or stereotype that overweightsrepresentative types Our results obtain with minimal assump-tions on such overweighting We describe a number of weightingspecifications and explore their properties

To illustrate the logic of the model consider the stereotypelsquolsquoFlorida residents are elderlyrsquorsquo The proportion of elderly people

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in Florida and in the overall United States population isshown here2

The table shows that the age distributions in Florida and in therest of the United States are very similar Yet someone over 65 ishighly representative of a Florida resident because this age bracket

maximizes the likelihood ratio Pr ethtjFloridaTHORNPr ethtjUSTHORN When thinking about the

age of Floridians then the 65+ type immediately comes to mindbecause in this age bracket Florida is most different from the rest ofthe United States in the precise sense of representativenessRepresentativeness-based recall induces an observer to overweightthe 65+ type in their assessment of the average age of Floridians

This example also illustrates how stereotypes can be inaccu-rate Indeed and perhaps surprisingly only about 17 of Floridaresidents are elderly The largest share of Florida residentsnearly as many as in the overall US population are in the agebracket 19ndash44 which maximizes PrethtjFloridaTHORN Being elderly isnot the most likely age bracket for Florida residents but ratherthe age bracket that occurs with the highest relative frequencyA stereotype-based prediction that a Florida resident is elderlyhas very little validity

The same logic of representativeness suggests that the reasonpeople stereotype the Irish as red-headed is that red hair is morecommon among the Irish than among other groups even though itis not that common in absolute terms The reason people stereo-type Republicans as wealthy is that the wealthy are more commonamong Republicans than Democrats3 In both cases the represen-tation entails judgment errors people overestimate the proportionof red-haired among the Irish or of the wealthy among theRepublicans

2 Data from the 2010 US Census see httpfactfindercensusgovfacestableservicesjsfpagesproductview xhtmlpid=DEC_10_DP_DPDP1ampsrc=pt

3 See httpwwwnytimescompackagespdfpolitics20041107_px_ELECTORATExls

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We find that representativeness often generates fairly accu-rate stereotypes but sometimes causes stereotypes to be inaccu-rate particularly when groups have similar distributions thatdiffer most in unlikely types More generally our model high-lights two critical properties

Stereotypes amplify systematic differences betweengroups even if these differences are in reality verysmall When groups differ by a shift in means stereotyp-ing exaggerates differences in means and when groupsdiffer by an increase in variance stereotyping exagger-ates the differences in variances In these cases (but notalways) representativeness yields stereotypes that con-tain a lsquolsquokernel of truthrsquorsquo in the sense that they differen-tiate groups along existing and highly diagnosticcharacteristics exactly as Hilton Von Hippel andSchneider define them

Stereotypes are context dependent The assessment of agiven target group depends on the reference group towhich it is compared

In line with the social cognition approach to stereotypes asignificant body of psychological research on beliefs about genderrace age and political groups finds that stereotypes broadly re-flect reality but display biases Social psychologists have exploredthe extent to which stereotypes exaggerate real differences thuspossessing a kernel of truth Evidence on exaggeration varies bydomain For race and gender many studies have reportedroughly accurate beliefs whereas others have found underesti-mation or exaggeration of true differences (Jussim et al 2015)4

For age and political stereotypes evidence points more stronglytoward exaggeration5 Schneider (2004 337) summarizes the

4 For evidence of roughly accurate beliefs for race see for example Ashtonand Esses (1999) on beliefs of academic ability Kaplowitz Fisher and Broman(2003) on income poverty rates and out-of-wedlock births and Wolsko et al(2000) on a array of positive and negative attributes Ryan (1996) and Gilens(1996) find evidence of exaggeration of race stereotypes on personal attributesand poverty rates respectively Some studies have found roughly accurate beliefson gender (McCauley Thangavelu and Rozin 1988 Briton and Hall 1995Diekman Eagly and Kulesa 2002) while others find evidence of exaggeration(Martin 1987 Bayer 1999)

5 See Chan et al (2012) on age We discuss evidence on political stereotypes inSection IV

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existing empirical work on stereotype accuracy as follows lsquolsquothebest we can do by way of general summary is to say that somestereotypes held by some people for some groups are sometimesaccuratersquorsquo Our empirical investigation explores the connectionbetween stereotype accuracy and representativeness which wemeasure using the previously defined likelihood ratio

We first assess the role of representativeness and contextdependence in the lab We construct a group of mundane objectsG and present it to participants next to a comparison group ndashGIn our baseline condition the comparison group is chosen so thatno type is particularly representative of group G In our treat-ment we change the comparison group ndashG while leaving thetarget group G unchanged The new comparison group givesrise to highly representative types within G In line with thekey prediction of our model participants in the treatment condi-tion shift their assessment of G toward the representative types

We test the model using two data sets on political preferencesand beliefs about political preferences in the United States Heregroups are political constituencies (Democrats and Republicans)and types are their positions on a number of issues Holding fixedthe groups and the set of types and varying the groupsrsquo true dis-tributions across issues the data allow us to test whether beliefsabout political preferences are shaped by representativeness Wefirst show that such beliefs depart from the truth by exaggerating(mean) differences as per the kernel of truth logic We then ex-plore how the extent of exaggeration varies across issuesConsistent with the model we find that beliefs systematicallydepart from rational expectations and that the degree to whichthey exaggerate true differences is a function of representative-ness While representativeness is not the only heuristic thatshapes recall (availability driven by recency or frequency of ex-posure also plays a role) it explains the fact that in the datastated beliefs indeed exaggerate differences among groups

Since Kahneman and Tverskyrsquos (1972 1973) work on heuris-tics and biases several studies have formally modeled heuristicsabout probabilistic judgments and incorporated them into eco-nomic models Work on the confirmation bias (Rabin andSchrag 1999) and on probabilistic extrapolation (Grether 1980Barberis Shleifer and Vishny 1998 Rabin 2002 Rabin andVayanos 2010 Benjamin Rabin and Raymond 2015) assumesthat the decision maker has an incorrect model in mind or incor-rectly processes available data Our approach is instead based on

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the assumption that representative information comes foremostto mind when making judgments The mental operation that liesat the heart of our modelmdashgenerating a prediction for the distri-bution of types in a group based on data stored in memorymdashalsocaptures base rate neglect and overreaction to diagnostic infor-mation The underweighting or neglect of information in ourmodel simplifies judgment problems in a way related to modelsof categorization (Mullainathan 2002 Fryer and Jackson 2008)In these models however decision makers use coarse categoriesorganized according to likelihood not representativeness Thisapproach generates imprecision but does not create a systematicbias for overestimating unlikely events nor does it allow for con-text-dependent beliefs In our empirical analysis of political be-liefs we explicitly compare the predictions of representativeness-based recall to those of likelihood-based models and find that theevidence supports the former

In modeling representativeness we follow the specification ofGS (2010) but investigate a new set of questions GS (2010) ex-amine how representativeness distorts the assessed probabilitiesof alternative hypotheses but not how the probability of a givenhypothesis or group is distributed across its constituent elementsIn the context of the current setting GS (2010) ask how imperfectrecall affects the assessed probability that a randomly drawnmember from a universe belongs to group G The current arti-cle in contrast asks which type t we expect to draw once we knowthat we are facing group G GS (2010) show how representative-ness generates biased probabilistic assessments such as conjunc-tion and disjunction fallacies This article deals with perhaps abroader and more ubiquitous problem of stereotype formationextensively studied by other social scientists but largely ne-glected by economists

Section II describes our model In Section III we examine theproperties of stereotypes including the forces that shape stereo-type accuracy and illustrate these properties with examples InSection IV we bring the model to the data performing a lab ex-periment and analyzing existing surveys of political beliefsSection V concludes The Online Appendix presents proofs anumber of extensions of the model and additional results forthe experiments and field evidence

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II A Model of Representativeness and Stereotypes

IIA The Model

A decision maker (DM) faces a prediction problem such asassessing the ability of a job candidate from a certain ethnicgroup the future performance of a firm belonging to a certainsector or future earnings based on own gender

Formally there is a set of types of interest T and an overallpopulation of which group G is a subset The set of typesT can be unordered (eg occupations) or ordered (and typi-cally cardinal eg earnings levels) When T is ordered wewrite T frac14 ft1 tTg with t1 lt t2 lt lt tT6 There is a probabil-ity or frequency distribution 2 ethT THORN that induces a condi-tional distribution PrethT frac14 tjGTHORN when restricted to G7 In whatfollows we denote by tG frac14 PrethT frac14 tjGTHORN the probability of typet in group G and by G the vector ethtGTHORNt2T containing the condi-tional distribution

The DMrsquos goal is to assess the distribution of the types ofinterest in a particular group G Although the DM has stored inmemory the full distribution he retrieves from memory a dis-torted version of G that overweights the probability of thosetypes that are most representative of G relative to a comparisongroup ndashG Generically ndashG is a group in that is distinct from Gnamely G7 nG although in some cases it can coincide withthe complement of G

According to Tversky and Kahneman (1983) a type t is rep-resentative of G if it is relatively more likely to occur in G thanin ndashG Definitions 1 and 2 formalize this representativeness-based recall following GS (2010)

6 For simplicity we also use T to denote the number of types jTj The modelapplies also to cases in which types (i) are multidimensional capturing a bundle ofattributes such as occupation and nationality or (ii) are continuous We considerthese cases in Online Appendixes C and D respectively Also G may represent anycategory of interest such as the historical performance of a firm or industry actionsavailable to a decision maker (T = set of payoffs G = occupations) or categories inthe natural world (T = ability to fly G = birds)

7 In many applications each individual in is characterized by a determin-istic type (eg age hair color) As a result ethtTHORN frac14 1

jj For instance each Floridian

has a single age type (at the finest temporal resolution) When types are stochasticinstead such as when estimating future earnings of a person or a firm each indi-vidual is described by a nondegenerate distribution

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DEFINITION 1 The representativeness of type t for group G givencomparison group ndashG is defined as the likelihood ratio

RethtGGTHORN tG

tGeth2THORN

Definition 1 implies that DMs are attuned to log differencesin probabilities representativeness depends on the percentageprobability increase of a type from ndashG to G This captures aform of diminishing sensitivity whereby for a fixed probabilitydifference a type is more likely to be overweighed if it is unlikelyin the comparison group8 Thus the representative age of aFloridian is 65+ because people in this age bracket are morecommon in Florida than in the rest of the United StatesStatistically representative types are also diagnostic of thetarget group G Indeed the higher is RethtGGTHORN the more confi-dent is a Bayesian DM observing t that t belongs to G rather thanto ndashG9

The ease of recall of highly representative types affectsjudgments because more easily recalled types are overweighted

We model distorted recall as follows Denote by RethtGGTHORN

tG

tG

t2T

the vector of representativeness of all types in G

We then have

8 Our definition of representativeness links to Weberrsquos law of sensory percep-tion see Section IIB It also links to our previous work on salience in which wepostulated that log differences in payoffs determine the attention to lottery payoffs(Bordalo Gennaioli and Shleifer 2012) and to goodsrsquo attributes (BordaloGennaioli and Shleifer 2013) Equation (2) establishes the same principle for thedomain of probabilities

9 This insight led Tenenbaum and Griffiths (2001) to define representative-ness as individualsrsquo sense as intuitive Bayesians of updating in reaction to dataTheir definition like ours is in terms of the likelihood ratio However Tenenbaumand Griffiths interpret representativeness as a mechanism that affects intuitivejudgments of similarity rather than beliefs (eg it accounts well for lab evidencewhere subjects are asked to rank types in terms of representativeness or ofstrength of association with a group) Accordingly they do not consider the possi-bility of systematically distorted and context dependent beliefs

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DEFINITION 2 The DM attaches to each type t 2 T in group G adistorted probability

sttG frac14 tG

htethRethtGGTHORNTHORNPs2T sGhsethRethtGGTHORNTHORN

eth3THORN

where ht RTthornRthorn is a weighting function such that

(i) The weight ht is a symmetric function of the representa-

tiveness of types s 6frac14 t Formally ht frac14 h tG

tG

sG

sG

s2Tn tf g

where h Rthorn RT1thorn Rthorn is a function that is invariant to

a permutation of the last T ndash 1 arguments(ii) Weighing of a type increases in own representativeness

and decreases in the representativeness of other typesFormally the function hethTHORN is weakly increasing in itsfirst argument and weakly decreasing in the other T 1arguments

We call the distribution ethsttGTHORNt2T the stereotype for G If a type

t is objectively more likely namely tG is higher then the ste-reotype attaches higher probability to it By property i distor-tions are due exclusively to the fact that a type is more or lessrepresentative than the others In particular if all types areequally representative the DM equally weighs all of them ath(1) and holds rational expectations about G If instead the rep-resentativeness of different types differs property ii implies thatthe stereotype ceteris paribus overweights the probability of morerepresentative types

Most of the results we explore in this article hold for a gen-eral weighing function htethTHORN Specific functional forms captureadded assumptions about the psychology of representativeness-based recall and are useful in applications We outline a few spe-cifications and their properties

Rank-based stereotypes the ranking of the representa-tiveness of different types shapes distortions Denote byrethtTHORN 2 f1 Tg the representativeness ranking of type tWhen r(t) = 1 type t is the most representative one (po-tentially with ties) We can specify two ways in which atypersquos representativeness ranking distorts its probability

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(i) Rank-based truncation the DM only recalls the typesthat have representativeness ranking of at most dnamely ft 2 TjrethtTHORN dg Zero probability is attachedto the remaining types10 Denote by IethrethtTHORN dTHORN an in-dicator function taking the value 1 if the representa-tiveness ranking of t is at most d Then theweighting function is ht frac14 IethrethtTHORN dTHORN so that

sttG frac14 tG

IethrethtTHORN dTHORNPs2T sGIethrethsTHORN dTHORN

which is the true conditional probability within re-called types This assumption is used in Gennaioliand Shleifer (2010)11

(ii) Rank-based discounting the DM discounts by a con-stant factor 2 frac1201 the odds of type t relative to itsimmediate predecessors in the representativenessranking Lower implies stronger discounting ofless representative types Formally the weightingfunction is ht frac14

rethtTHORN so that

sttG frac14 tG

rethtTHORNPs2T sG

rethsTHORN

Representativness-based discounting all else equal theweight attached by the DM to type t increases continuouslywith its representativeness One convenient formulation is

ht frac14tG

tG

so that

10 These neglected types are not viewed as impossible they are just assignedzero probability in the DMrsquos current thinking This formulation allows us to modelsurprise and reactions to unforeseen contingencies which have proved useful in-gredients in modeling probabilistic judgments (GS 2010) as well as neglect of risk infinancial crises (Gennaioli Shleifer and Vishny 2012)

11 Specifically in GS (2010) the assessed probability that a certain hypothesisG is true is equal to

Pr ethGTHORN frac14

Pt tGIethrethtTHORN dTHORNP

t tGIethrethtTHORN dTHORN thornP

t t=GIethrethtTHORN dTHORN

which increases in the ratio between the total probability mass recalled for Gand that recalled for G frac14 nG

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sttG frac14 tG

tG

tG

P

s2T sGsG

sG

where 0 captures the extent to which representative-ness distorts beliefs This formulation is particularly con-venient when dealing with continuous distributions ofthe exponential or power classes

These functional forms all embody the main idea of our modelthat the stereotype overweights the probability of more represen-tative types Rank-based truncation captures a central manifes-tation of limited memory forgetting unrepresentative typesSmoother discounting (based on ranking or on representative-ness) may be more appropriate when the type space is smalland smooth discounting can be more tractable in certain settings

Section III characterizes the general properties of stereotypesIn particular it shows their ability to account for social psycholo-gistsrsquo kernel of truth hypothesis under the general weighting func-tion of Definition 2 To bring the model to the data in Section IVBwe derive linear approximations of stereotypical beliefs by assum-ing that the weighting function is differentiable with respect to atypersquos representativeness This assumption excludes rank-basedweighting but allows for many possibilities

IIB Discussion of Assumptions

Before moving to the formal analysis we discuss some prop-erties and limitations of our approach Representativeness-basedrecall the idea that individuals recall distinctive group types canbe viewed as an instance of what Kahneman and Tversky calllsquolsquoattribute substitutionrsquorsquo When dealing with the difficult questionlsquolsquowhat is the distribution of hair color among the Irishrsquorsquo peopleintuitively answer to the simpler question lsquolsquowhich hair color dis-tinguishes the Irish peoplersquorsquo Critically as discussed byKahneman and Tversky attribute substitution does not occurbecause people misunderstand the original question or mechan-ically confuse the assessment of PrethtjGTHORN with that of PrethGjtTHORNRather it occurs because the distinctive or representative typesimmediately come to mind and individuals anchor their overallprobability judgment to them As a consequence subjects do notonly make mistakes in judging the probability that a Floridian is

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over age 65 They also give too high an answer to the questionlsquolsquowhat is the average age of a Floridianrsquorsquo12

One interesting question is whether the process of stereotyp-ing we describe is optimal in some sense Focusing mental repre-sentations on a few types can be justified by the costs of thinkingor retrieval This approach however is not enough to explainwhy individuals should focus on representative rather thanlikely types We do not formally analyze the optimality of repre-sentativeness here but we mention some relevant considerationsfrom cognitive psychology Kahneman and Tversky (1979) stressthe similarity between many perceptual and cognitive operationsFor instance the highlight of contrastmdasha key principle of visualperceptionmdashis invoked to justify the prospect theory assumptionthat the carriers of utility are changes relative to a referencepoint The same logic applies to our model in which stereotypesprecisely highlight the contrast between groups

In visual perception assessing properties such as brightnesscolor size or distance to an object by comparing them to otherproximate objects has been shown to be optimal in the presence ofmultiplicative background noise (Kersten Mamassian andYuille 2004 Cunningham 2013) Our formulation of representa-tiveness is related to the same idea in the sense that individualsestimating properties of one group stress differences from an-other group In a noisy world in which attention is limited thisprocess may optimally allow for swift reactions to changes ingroup characteristics even if errors are sometimes made13

12 Indeed in many cases mere confusion of PrethtjGTHORNwith PrethGjtTHORNwould not yieldthe phenomenon of stereotyping In the Irish hair color example the probability ofbeing Irish conditional on having red hair is

PrethIrishjredTHORN frac14PrethredjIrishTHORNPrethIrishTHORN

PrethredjIrishTHORNPrethIrishTHORN thorn PrethredjNonIrishTHORNPrethNonIrishTHORN

This probability is clearly very small given that the Irish population is a tinyfraction of the world population Confusion of PrethtjGTHORN with PrethGjtTHORN in this casewould lead to an understatement of the probability of the red-haired Irish

13 To give a simple example suppose thatmdashas in the case of Proposition 3mdashthevariance in the environment increases in the sense that extreme tail events becomemore likely Then a likelihood-based stereotype would detect no change whereas arepresentativeness-based stereotype would focus on the heightened probability ofthe tails In particular an asymmetric increase in tail probabilities that shifts themean would be detected by a representativeness-based stereotype even if the dis-tributionrsquos mode does not change

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Exploring this idea formally is an interesting avenue for futurework

Consider some limitations of our model First representa-tiveness is not the only heuristic that shapes recall Decisionmakers may for instance find it easier to recall types that aresufficiently likely Another potentially important mechanism isavailability understood by Kahneman and Tversky (1972) as thelsquolsquoeasersquorsquo with which information comes to mind (because of actualfrequency or repetition) In Online Appendix E we present a trun-cation-based recall mechanism in which distortions are driven bya combination of representativeness and likelihood of types(which is equivalent to relaxing property i in Definition 2) Thismodel can offer a useful starting point to capture availability aswell even though a full model of availability is beyond the scopeof this article Even in this more general setting the influence ofrepresentativeness on recall is the driving force of stereotypesthat in line with the social psychology perspective are basedon underlying differences among groups As we show in SectionIV this feature is critical in accounting for the evidence

The second set of model-related issues concerns how to spe-cify the elements of Definition 1 in applications group G the typespace T and the reference group ndashG Take the specification of thegroup G and of the type space T Often the problem itself pro-vides a natural specification of these features This is the case inthe empirically important class of lsquolsquoclosedrsquorsquo questions such asthose used in surveys which provide respondents with a set ofalternatives as in the data we use in Section IV More generallythe problem solved by the DMmdashsuch as evaluating the resume ofa job applicant coming from a certain ethnic groupmdashprimes agroup a dimension of interest and a set of types (eg the appli-cantrsquos qualification or skill levels) When types have a naturalorder such as income age or education the granularity of T isalso naturally given by the problem (income age and years ofschooling brackets) When the set of types is not specified by theproblem DMs spontaneously generate one14 It would be useful tohave a model of which dimensions and types come to mind par-ticularly for more open-ended problems Psychologists have

14 For example suppose a person is asked to guess the typical occupation of ademocratic voter in an lsquolsquoopen-endedrsquorsquo format (without being provided a set of alter-natives) Here the level of granularity at which types are defined is not obvious (egteacher versus a university teacher vs a professor of comparative literature)

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sought to construct a theory of natural types and dimensions(Rosch 1973) We do not make a contribution to this problembut we note that in many problems of interest in economics thedimension as well as the set of types is naturally givenFurthermore in our model details of the type space can be impor-tant under rank-based truncation but they matter less undersmooth discounting

Consider finally the role of the comparison group ndashG Thisgroup captures the context in which a stereotype is formed andagain is often implied by the problem when G = Floridians ndashG =rest of US population when G = African Americans ndashG = whiteAmericans A distinctive prediction of our model confirmed byour experiments in Section IVA is that the stereotype for agiven group G depends on the comparison group ndashG15 WhenndashG is not pinned down by the problem itself to derive testablepredictions from representativeness we set G frac14 nG where

is the natural population over which the unconditional distribu-tion of types is measured

III Properties of Stereotypes

We now study stereotypical beliefs and their accuracy Toillustrate the role of representativeness we first ask to whatextent the most representative type is a good fit for the groupnamely whether it is modal Next we assess the accuracy of theentire stereotypical distribution To do so we focus on a cardinaltypes and compare the stereotypersquos mean and variance to the trueones

15 Some empirical papers have taken a similar approach exogenously varyingthe natural comparison group through priming Benjamin Choi and Strickland(2010) show that priming racial or ethnic identity can affect the risk preferences ofparticipants Chen et al (2014) find that Asian students cooperate less with out-group members when primed with their ethnic identity rather than their universityidentity Shih Pittinsky and Ambady (1999) show that Asian American womenstereotype themselves as better or worse in math with corresponding impact onperformance when their ethnicity or gender respectively is primed ShihPittinsky and Trahan (2006) replicate this effect using a verbal task documentingthat Asian American women performed better when their gender rather than theirethnicity was primed Although the generalizability and replicability of priminghas been doubted (Klein et al 2014) this body of evidence is consistent with contextdependence

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IIIA Likely versus Unlikely Exemplars

The most representative type for a group is the one thatagents most easily recall and associate with the group itself forinstance a red-haired Irishman or a 65+-year-old FloridianSocial psychologists call this type the exemplar of the groupAccordingly we define

DEFINITION 3 A type t is an exemplar for G given comparisongroup ndashG when

t 2 arg maxt

tG

tG

Under any specification of the weighting function ht inDefinition 2 overweighting (weakly) increases as we movetoward more representative types so the exemplar is also thetype whose probability is overweighted the most16 By analyzingthe exemplar then we can gauge whether representativenessinduces the DM to overweight a likely type (as happens in stan-dard models of categorical thinking) or an unlikely type Whenoverweighting occurs in unlikely and extreme types the biases ofstereotypes can be particularly severe17

Equation (2) yields the following characterization

PROPOSITION 1 Suppose the conditional distributions G and G

are not identical Consider two extreme cases

(i) If for all t t0

2 T we have that tG gt t0 G if and only iftG gt t0 G then the modal type is not an exemplar forat least one group

(ii) If for all t t0

2 T we have that tG gt t0 G if and only iftG lt t0 G then for each group the modal type is theexemplar

16 Consider the function hethTHORN from Definition 2 When applied to more repre-sentative types the first argument of the function increases while one of the otherT ndash 1 arguments decreases As a result the weighting factor ht (and thus overweigh-ing

sttG

tG) increases as well

17 In the rank-based truncation model the frequency of the exemplar providesa measure of stereotype accuracy By accuracy we mean the extent to which thestereotype minimizes the distance

Pt eth

sttG tGTHORN

2 When d = 1 and only one type isrecalled (there are no ties) accuracy is maximized if the exemplar is the most likelytype and minimized if the exemplar is the least likely type

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Case i says that when groups have similar distributions inthe sense of having the same likelihood ranking the most repre-sentative type is unlikely for at least one group potentially bothRepresentativeness draws the DMrsquos attention to group differ-ences neglecting the fact that the groups are similar and havethe same mode This mechanism generates inaccurate stereo-types and is illustrated by the Florida example This resultholds under any measure of representativeness that differenti-ates the two groups (eg the difference tG tG)

Case ii says that the most representative type tends to belikely for both groups when the distributions are very differentIn this case groups differ the most around their modes so repre-sentativeness and likelihood coincide Thinking of Swedes aslsquolsquoblondrsquorsquo and Europeans as lsquolsquodark hairedrsquorsquo is accurate precisely be-cause these are majority traits of the Swedish and European pop-ulations respectively In these cases stereotyping yields fairlyreliable models Of course there is still some inaccuracy Evenin the case of likely exemplars judgment errors can be signifi-cant For instance voters in some US states are perceived aslsquolsquobluersquorsquo or lsquolsquoredrsquorsquo because a majority of the population votesDemocrat or Republican In reality even in lsquolsquobluersquorsquo states farfrom everyone votes Democrat In the 2012 presidential electionvote shares of either candidate in most states ranged from 40 to6018

When DMs strongly overweight representative types themost severe biases occur when those types are unlikely and ex-treme This is true both under rank based truncations and undersmooth discounting functions (see Section IIIB) Ethnic stereo-types based on crime or terrorism exhibit this error they neglectthe fact that by far the most common types in all groups arehonest and peaceful

IIIB Stereotypical Moments

We now characterize how the first two moments of a distri-bution are distorted by the process of stereotyping To do so wemust restrict our analysis to cardinal ordered types The follow-ing results hold for any weighting function htethTHORN satisfyingDefinition 2 We consider two canonical cases that prove usefulin illustrating the predictions of the model

18 Presidential Election Results NBCNewscom see httpelectionsnbcnewscomnspolitics2012allpresident (accessed 5 September 2016)

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In the first case groups G and ndashG are such that the likelihoodratio tG

tGis monotonic in t The monotone likelihood ratio prop-

erty (MLRP) holds to a first approximation in many empiricalsettings and is also assumed in many economic models such asstandard agency models19 If tG

tGis monotonically increasing (de-

creasing) in t then group G is associated with higher (lower)values of t relative to the comparison group ndashG Formally

PROPOSITION 2 Suppose that MLRP holds and assume wlogthat the likelihood ratio tG

tGis strictly increasing in t Then

for any weighting function htethTHORN that is not constant in therelevant range

EstethtjGTHORN gt EethtjGTHORN gt EethtjGTHORN gt E

stethtjGTHORN

Under MLRP the most representative part of the distribu-tion for G is the right tail if tG

tGincreases in t or the left tail if tG

tG

decreases in t The representative tail is then overweighted whilethe nonrepresentative tail is underweighted As a consequencethe assessed mean E

stethtjGTHORN is too extreme in the direction of therepresentative tail

Critically in line with the social cognition perspective the ste-reotype contains a kernel of truth the DM overestimates the meanof G if this group has a higher mean than the comparison groupnamely EethtjGTHORN gt EethtjGTHORN and conversely if EethtjGTHORN lt EethtjGTHORN TheDM exaggerates this true difference because he inflates the asso-ciation of G with its most representative types20 For instancewhen judging an asset manager who performs well we tend to

19 Examples include the binomial and the Poisson families of distributionswith different parameters The characterization of distributions satisfying MLRPis easier in the case of continuous distributions (see Online Appendix D) two dis-tributions f(x) f ethx THORN that differ only in their mean satisfy MLRP if and only if thedistribution f(x) is log-concave Examples include the exponential and normal dis-tributions To the extent that discrete distributions sufficiently approximate thesedistributions (as the Poisson distribution PoisethTHORN approximates the normal distri-bution Neth THORN for large l) they will also satisfy MLRP

20 Depending on the distribution and the weighing function the DMrsquos assess-ment of the variance VarethtjGTHORNmay also be dampened relative to the truth This isoften true under the truncation weighing function In this case stereotyping effec-tively leads to a form of overconfidence in which the DM holds extreme views andoverestimates the precision of his assessment That extreme views and overconfi-dence (in the sense of over precision) go together has been documented in the settingof political ideology among others (Ortoleva and Snowberg 2015)

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overemphasize skill relative to luck because higher skill levels arerelatively more associated with higher performance This occurseven if for both skilled and unskilled managers high performanceis mostly due to luck

In the second case for which we characterize the stereotypi-cal distributions groups G and ndashG have the same mean EethtjGTHORNfrac14 EethtjGTHORN frac14 EethtTHORN but differ in their variance We abstract fromskewness and higher moments by considering distributionsethtGTHORNt2T and ethtGTHORNt2T that share the same support and are sym-metric around the medianmean EethtTHORN

PROPOSITION 3 Suppose that in G more extreme types are rela-tively more frequent than in ndashG Formally the likelihoodratio tG

tGis U-shaped in t around EethtTHORN Then for any weight-

ing function htethTHORN that is not constant in the relevant rangestereotypical beliefs satisfy

VarstethtjGTHORN gt VarethtjGTHORN gt VarethtjGTHORN gt VarstethtjGTHORN

EstethtjGTHORN frac14 E

stethtjGTHORN frac14 EethtTHORN

When group G has a higher relative prevalence of extremetypes its representative types are located at both extremes of thedistribution The DMrsquos beliefs about G are then formed by over-weighting both tails while underweighting the unrepresentativemiddle The overweighting of Grsquos tails causes the assessment ofits variance VarstethtjGTHORN to be too high For example the skill dis-tribution of immigrants to the United States may be perceived ashaving very fat tails or even bimodal with immigrants beingperceived as either unskilled or very skilled relative to the resi-dent population The mean of the group in contrast is assessedcorrectly because the stereotypical distribution remains symmet-ric around EethtTHORN As before the stereotype contains a kernel oftruth It induces the agent to exaggerate the true differences be-tween groups namely the higher variance of G relative to itscounterpart

We present a number of extensions of the model in the OnlineAppendix We first consider multidimensional type spaces andshow that stereotypes center around the dimension wheregroups differ the most in line with the kernel of truth logic(Online Appendix C) Multidimensional stereotypes imply thatthe dimension we think about is influenced by context For

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example the Irish are stereotyped as red-haired when comparedwith the European population However when compared withthe Scots a more plausible stereotype for the Irish is lsquolsquoCatholicrsquorsquobecause religion is the dimension along which Irish and Scotsdiffer the most

In Online Appendix D we extend the model to continuoustype spaces Many settings of interest in economics can be use-fully described by continuous probability distributions and weshow our model is particularly tractable in this case In OnlineAppendix E we relax Definition 2 and allow weighting of types toalso be influenced by their likelihood We show that the basicinsight that stereotypes contain a kernel of truth carries throughto these cases as well

To summarize the psychology of representativeness yieldsstereotypes that are consistent with the social cognition approachin which individuals assess groups by recalling and focusing ondistinctive group traits When there are systematic differencesbetween groups stereotypes get the direction right but exagger-ate differences

IIIC Some Examples

A growing body of field and experimental evidence points to awidespread belief that women are worse than men at mathemat-ics (Eccles Jacobs and Harold 1990 Guiso et al 2008 CarrellPage and West 2010) This belief persists despite the fact that fordecades women have been gaining ground in average schoolgrades including mathematics and have recently surpassedmen in overall school performance (Goldin Katz and Kuziemko2006 Hyde et al 2008) This belief shared by men and women(Reuben Sapienza and Zingales 2014) may help account for thegender gap in the choices of high school tracks college degreesand careers with women disproportionately choosing humanitiesand health-related areas (Weinberger 2005 Buser Niederle andOosterbeek 2014) and forgoing significant wage premiums toquantitative skills (Bertrand 2011)

Gender stereotypes in mathematics particularly beliefs thatexaggerate the extent of average differences are consistent withthe predictions of our model The fact that men are overrepre-sented at the very highest performance levels leads a stereotyp-ical thinker to exaggerate the magnitude of mean differencesFigure I shows the score distributions from the mathematics

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section of 2013rsquos Scholastic Aptitude Test (SAT) for men andwomen21 The distributions are very similar with averagescores slightly higher for men (531 versus 499 out of 800)However scores for men have a heavier right tail with mentwice as likely to have a perfect SAT math score than women22

In light of such data the stereotypical male performance in math-ematics is high while the stereotypical female performance ispoor Predictions based on such stereotypes are inaccurate exag-gerating true differences Consistent with this prediction exper-imental evidence shows that both genders underestimatewomenrsquos ability in simple math tasks even controlling for pastperformance (Reuben Sapienza and Zingales 2014) Coffman(2014) shows a similar pattern extends to confidence about ownability in other male-typed domains with women reporting sig-nificantly less confidence in gender-incongruent than gender-congruent tasks Our model suggests that these patterns mightcome from stereotypes based on gender differences in the righttail of the distribution While differences in the right tail of thedistribution are unlikely to be relevant for most decisions stereo-typical thinking driven by these differences has the potential toimpact economically important decisions whether through self-stereotyping (ie choice of careers or majors as in BuserNiederle and Oosterbeek 2014) or through discrimination (iehiring decisions as in Bohnet van Geen and Bazerman 2016)

The logic of exaggerated yet directionally correct stereotypesalso sheds light on the well-documented phenomenon of base rateneglect (Kahneman and Tversky 1973) Indeed Proposition 2implies that the DM overreacts to information that assigns

21 Standardized test performance measures not only innate ability but alsoeffort and investment by third parties (Hyde et al 2008) The mapping of test per-formance into inferences about innate ability is an issue not addressed by ourmodel

22 For 2013 SAT Mathematics scores see httpmediacollegeboardcomdigitalServicespdfresearchSAT-Percentile-Ranks-By-Gender-Ethnicity-2013pdf Results are similar for the National Assessment of Educational Progress(NAEP) which are more representative of the overall population For 2012NAEP scores for 17-year-olds in mathematics see httpnationsreportcardgovltt_2012age17maspx See Hyde et al (2008) Fryer and Levitt (2010) and Popeand Sydnor (2010) for in-depth empirical analyses of the gender gap inmathematics

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people to groups precisely because such information generatesextreme stereotypes Consider the classic example in which amedical test for a particular disease with a 5 prevalence has a90 rate of true positives and a 5 rate of false positives The testassigns each person to one of two groups + (positive test) or ndash(negative test) The DM estimates the frequency of the sick type(s) and the healthy type (h) in each group The test is informativea positive result increases the relative likelihood of sickness anda negative result increases the relative likelihood of health forany prior Formally

PreththornjsTHORN

PreththornjhTHORNgt 1 gt

PrethjsTHORN

PrethjhTHORNeth4THORN

This condition has clear implications the representative personwho tests positive is sick while the representative person whotests negative is healthy Following Proposition 2 the DMreacts to the test by moving his priors too far in the right di-rection generating extreme stereotypes He greatly boosts hisassessment that a positively tested person is sick but also thata negatively tested person is healthy Because most people arehealthy the DMrsquos assessment about the group that tested neg-ative is fairly accurate but is severely biased for the group that

FIGURE I

SAT Mathematics Scores by Gender (2013)

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tested positive This analysis formalizes Tversky andKahnemanrsquos (1983) verbal account of base rate neglect23

The same mechanism may underlie several other instanceswhere DMs overweight diagnostic information When assessingan employeersquos skill level an employer attributes high perfor-mance to high skill because high performance is the distinctivemark of a talented employee Because he neglects the possibilitythat some talented employees perform poorly and that somenontalented ones perform well (perhaps due to stochasticity inthe environment) the employer has too much faith in skill andneglects the role of luck in accounting for the output Similarlywhen assessing the performance of firms in a hot sector of theeconomy (eg G = internet) an investor recalls highly successfulfirms in that sector (t = return of Google Amazon etc) He ne-glects the possibility of firms being unsuccessful because lack ofsuccess is statistically nondiagnostic and psychologically nonrep-resentative of a growing sectormdasheven if it is likely This causesexcessive optimism (in that the expectation of growth is unrea-sonably high) and overconfidence (in that the variability in earn-ings growth considered possible is truncated) True the hot sectormay have better growth opportunities on average but represen-tativeness exaggerates this feature and induces the investor toneglect a significant risk of failure

IV Evidence on Representativeness and Stereotypes

Testing our model requires evaluating the beliefs individualshold about a target group against the true distribution of thattarget group over an attribute space An ideal data set would

23 Our account is distinct from a mechanical underweighting of base rates inBayes rule as in Grether (1980) and Bodoh-Creed Benjamin and Rabin (2013) Inthose models upon receiving the test results the DM can update his beliefs in thewrong direction he can be less confident that a person is healthy after a negativetest than under his prior which cannot happen in our model Although this predic-tion of our model seems consistent with introspection we are not aware of experi-mental evidence on this point Griffin and Tversky (1992) present evidenceconsistent with pure neglect of base rates but in a significantly different tasknamely inferring the bias of a coin from a history of coin flips Such experimentsare hard to compare with the predictions of our model because subjects are asked togenerate distributions of different numbers of coin flips in their minds which is amuch more involved task than to recall types of a given distribution Their assess-ments then might be wrong for other reasons See Bodoh-Creed Benjamin andRabin (2013) for a detailed discussion

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consist of naturally defined groups with known distributions overa given space of types and a corresponding set of beliefs about thedistribution of each group over that space of types This wouldallow us to test for exaggeration of true differences betweengroups and to ask whether this exaggeration is well predictedby overweighting representative types To identify a causal rolefor representativeness or context dependence we would need ex-ogenous variation in either the comparison group ndashG or in thedistributions over the type spaces This is unavailable in existingdata sets Accordingly we take a two-pronged approach First wecreate a controlled laboratory environment that allows us toinduce the exogenous variation in representative types that weneed to test causality then we reanalyze existing field evidence tocheck for consistency with our predictions

In testing our model we focus on the two main implicationsof representativeness-based stereotypes

Context dependence the stereotype of a target group de-pends on the characteristics of the reference group it iscompared to

Kernel of truth stereotypes depend on group character-istics andmdashin most (precisely characterized) settingsmdashare slanted toward representative types

We test the first property with a lab experiment (SectionIVA) We then turn to survey data on beliefs about US politicalgroups (Section IVB) for an empirical analysis that explores thesecond property The survey data are more tightly linked to ourinterest in social stereotypes The laboratory experiment allowsus to directly test the role of representativeness in generatingcontext dependent beliefs Online Appendixes F and G provideall details and additional results for the experiments and fieldevidence

IVA Lab Evidence on Representativeness and ContextDependence

The influence of the representativeness heuristic on recalland on beliefs has been extensively documented in the lab(Kahneman and Tversky 1972 1973) Our goal is to considerhow representativeness as formalized in equation (2) gives riseto context-dependent beliefs To our knowledge the possibility

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that representativeness may generate context dependence hasnot been tested before

To assess this prediction we perform a controlled laboratoryexperiment that allows us to isolate representativeness frommany confounding factorsmdashhistorical sociological or other-wisemdashthat may affect stereotype formation in the real worldWe construct our own groups of ordinary objects creating atarget group G and a comparison group ndashG We hold thetarget group G fixed and explore how participant impressions ofit change as we change the comparison group ndashG and thusrepresentativeness

We conducted several experiments in the laboratory and onAmazon Mechanical Turk Each involves a basic three-stepdesign First participants are shown the target group and a ran-domly assigned comparison group for 15 seconds In this timedifferences between groups can be noticed but the groupsrsquo precisecompositions cannot be memorized The second step consists of afew filler questions which briefly draw the participantsrsquo cognitivebandwidth away from their observation Finally participants areasked to assess the groups they saw Participants are incentiv-ized to provide accurate answers

We randomly assign participants to either the Control or theRepresentativeness condition In the Control condition G and ndashGhave nearly identical distributions so that all types are similarlyrepresentative for each group In the Representativeness condi-tion ndashG is changed in such a way that a certain type becomes veryrepresentative for G Context dependence implies that the assess-ment of G should now overweight this representative type eventhough the distribution of G itself has not changed

We ran six experiments of this form with design changesfocused on reducing participant confusion and removing con-founds We describe the final and most refined version of theseexperiments here In an attempt to provide a overview of the re-sults while remaining concise we provide the results from pooledspecifications that use all data collected In Online Appendix Fwe offer additional details and report all experiments conductedWe also give instructions and materials for each experiment thefull data set is available by request

Consider first the experiment illustrated in Figure II Agroup of 25 cartoon girls is presented next to a group of 25 cartoonboys in T-shirts of different colors blue green or purple In theControl condition (Figure II Panel a) the groups have identical

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color distributions (13 purple 12 green) so no color is represen-tative of either group The Representativeness condition (Panel b)compares the same group of girls with a different group of boysfor whom green shirts are replaced with blue shirts Now onlygirls wear green and only boys wear blue These colors althoughstill not the most frequent for either group are now most repre-sentative For each group girls and boys participants are asked anumber of questions concerning the frequency of T-shirts of dif-ferent colors worn by that group

Applying our model in the control condition the type space isT frac14 fgreen purpleg and the groups are G = girls and ndashG = boysGiven that the color distributions are identical across groups both

types are equally representativegreengirls

greenboysfrac14 1 frac14

purplegirls

purpleboys As a result

assessment of G should be correct on average stcontrolgreengirls frac14 greengirls

and stcontrolpurplegirls frac14 purplegirls for any weighing function (the same is

true about assessments of ndashG)In the treatment condition the distribution of shirt colors re-

mains the same for girls For boys green shirts are changed intoblue Thus the type space changes to T frac14 fgreen purple bluegand the representative color for girls becomes greengreengirls

greenboysfrac14 1 gt 1 frac14

purplegirls

purpleboys while that for boys becomes blue As

a result in the treatment condition subjects should inflate the

frequency of green shirts relative to the truth sttreatmentgreengirls

gt greengirls (the same should happen to assessments of blueshirts for boys) We also expect the assessed frequency of greenshirts to go up relative to the control condition namely

sttreatmentgreengirls gt stcontrol

greengirls Critically the only factor that varies

across treatments is the representativeness of the 12-colorshirt Thus if we see differences across conditions the causalrole of representativeness-based recall in shaping group judg-ments is clear24

24 We vary which colors are used in which roles across participants Someparticipants saw this particular color distribution while others see for examplegreen as the modal color and purple as the diagnostic color for boys in theRepresentativeness condition and blue as the diagnostic color for girls in theRepresentativeness condition We vary the colors across the roles to avoid con-founding the characteristics of any particular color with its diagnosticity

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FIG

UR

EII

T-S

hir

tsE

xp

erim

ent

Fig

ure

sap

pea

red

inco

lor

top

art

icip

an

tsin

the

exp

erim

ent

For

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ty

we

have

ad

ded

ale

tter

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chT

-sh

irt

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enti

fyth

eco

lor

for

the

read

er

lsquolsquoGrsquorsquo

ind

icate

sgre

en

lsquolsquoPrsquorsquo

ind

icate

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urp

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ind

icate

sblu

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icip

an

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for

read

erre

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P

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onli

ne

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sion

ofp

ubli

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icle

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We collected data from 301 participants using this T-shirtsdesign25 Since the number of green and purple shirts is verysimilar we first ask each participant the simplest question ofwhich shirt color is modal Next we ask participants to assessthe share of green and purple shirts

Consistent with the role of representativeness participantsassigned to the Representativeness condition are 105 percentagepoints more likely to recall the less frequent color (green for girlsor blue for boys) as the modal color when it is representative of agroup (35 of participants guess the less frequent color is modalin the Control condition this proportion increases to 46 in theRepresentativeness condition p = 01 estimated from a probitregression reported in Online Appendix F)

We now turn to subjectsrsquo estimates of how many T-shirts ofeach color they saw in each group In both conditions the truedifference in counts is 1 (13 purple shirts 12 green or blue shirts)In the Control condition participants on average believe they saw054 more purple shirts than green or blue shirts In theRepresentativeness condition participants believe they saw072 fewer purple shirts than green or blue shirts (the acrosstreatment difference is significant with p = 01 from OLS regres-sion reported in Online Appendix F)

In total we collected data for six experiments of this generalstructure gathering evidence from more than 1000 participantsAs we describe in Online Appendix F although there is substan-tial variation across experiments when we pool all of the data wefind significant aggregate treatment effects in line with a role ofrepresentativeness in judgment We employ four different unor-dered types designs similar to the T-shirts experiment using sixsamples (four online and two in the laboratory) with 741 partic-ipants We find effects in the predicted direction for five of the sixsamples Using a probit regression that pools the data for theseunordered type experiments we find that participants are 93 per-centage points more likely to guess that the less frequent type ismodal when it is representative than when it is not (p = 002) Wealso run a family of ordered types experiments (two designs fivesamples 402 participants) Unlike the simpler T-shirts style

25 Throughout our analysis we exclude any participant who participated in aprevious version of the experiment and any participant who self-identified as color-blind In Online Appendix F we show that our results are unchanged if we includethese additional observations

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design the theoretical predictions for the ordered types designsare more sensitive to the specific assumptions one makes aboutthe weighting function of the DM26 We find effects in the pre-dicted direction for three of the five samples As we discuss inmore detail in Online Appendix F the ordered types resultsvary by platform with consistently stronger results on AmazonMechanical Turk than in the laboratory samples Pooling all or-dered types experiments participants are 93 percentage pointsmore likely to guess that the group of interest has a greater av-erage than the comparison group when the right tail is represen-tative (p = 062) Given our simple experimental setting withgroups of mundane objects we interpret our resultsmdasha signifi-cant and reasonably sized impact on average beliefsmdashas an im-portant proof of concept the presence of representative typesbiases ex post assessment

IVB Empirical Evidence on Political Stereotypes

We examine two data sets on political preferences and be-liefs about political preferences in the United States We inves-tigate the roles of representativeness and context dependence byseparately testing for hypotheses that allow us to assess the lead-ing theories of stereotypes

First we test whether beliefs are correct or depart systemat-ically from the truth The statistical discrimination approachbuilds on the assumption that people hold rational expectationsof group traits Comparing beliefs to the truth allows us to assessthe validity of this assumption in our data

Second we test if beliefs depart from the truth by exagger-ating (mean) differences among groups per the kernel of truthhypothesis This is an implicit test of context dependence be-cause it implies that beliefs about the target groups are shapednot only by that grouprsquos characteristics but also by those of thereference group27

Third we test if distortions in beliefs can be accounted for bythe overweighting of highly representative types (defined astypes that are relatively more frequent in the target relative to

26 This is due in part to our choice to not study MLRP distributions We moti-vate and discuss this design decision in Online Appendix F

27 Of course unlike in the laboratory experiment in this setting we cannot testfor context dependence by exogenously varying the reference group

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the reference group) The second and third tests address the keypredictions of our model

1 The Data We have two data sets on political preferences andbeliefs about political preferences The first data set from GrahamNosek and Haidt (GNH 2012) contains data from the MoralFoundations Questionnaire Respondents (1174 self-identified lib-erals and 500 self-identified conservatives) answer questions abouttheir position on a subset of 45 issues 20 moral relevance state-ments (eg lsquolsquowhen you decide whether something is right orwrong to what extent are the following considerations relevantto your thinkingrsquorsquo) and 25 moral judgments (eg lsquolsquoindicate theextent to which you would agree or disagreersquorsquo) For each issue arandomly determined subset of participants states their own posi-tion another subset states their belief on the position of a lsquolsquotypicalliberalrsquorsquo and a third subset states their belief on the position of alsquolsquotypical conservativersquorsquo The data thus include the distribution overpositions for both liberal and conservatives as well as the averagebelieved typical position of liberals and of conservatives on the 45issues Each position is elicited on 1ndash6 scale

The second data set comes from the American NationalElection Survey (ANES) and contains data from more than20000 respondents between 1964 and 201228 The surveycovers political issues of the day such as the optimal amount ofgovernment spending and service provision (1984ndash2000) or theplace of women in society (1972ndash1998) We focus on the 10 issuesthat ask participants to respond on a 1ndash7 scale (rather than justindicate binary agreement or disagreement) all 10 issues areasked in multiple years Participants are asked to provide theirown position on the scale and their believed position of theDemocratic and Republican parties (lsquolsquoWhere would you placethe Democratic [Republican] party on this scalersquorsquo) The data in-clude for each issue-year observation the distribution of partic-ipant positions for self-identified liberals and self-identifiedconservatives as well as the distribution of believed typical posi-tions of the Democratic and Republican parties

28 These data are publicly available at httpwwwelectionstudiesorgstudy-pagesanes_timeseries_cdfanes_timeseries_cdfhtm

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2 Empirical Strategy Our analysis focuses on beliefs abouttwo groups Conservatives and Liberals The types are the possi-ble positions for each issue (1 2 6 7) For the GNH data weinterpret beliefs about the lsquolsquotypicalrsquorsquo element of a group to coincidewith the believed average position in that group Similarly forthe ANES data we use the believed party positions as a proxy forbelieved mean of each group29 We then take as a benchmark thehypothesis that individuals hold accurate beliefs about eachgroup and in particular that believed mean position shouldequal true mean position at least on average across subjectsThe accurate beliefs hypothesis underlies the most common eco-nomic model of stereotyping statistical discrimination

To assess our representativeness-based model we perform aregression exercise To test our model in a linear regressionframework we rely on linear approximations of the weightingfunction Our model then yields two regression specifications

PROPOSITION 4 Let G 2 fconservative liberal g and assume

ht h tG

tG

be a differentiable and strictly increasing weight-

ing function as in Definition 2 The following hold as a first-order approximation around identical distributions G

Gfrac14 1

(i) Kernel of truth regression There exists a constant gt 0such that

EstethtjGTHORN frac14 EethtjGTHORNeth1thorn THORN EethtjGTHORNeth5THORN

(ii) Representativeness regression Denote H frac14 fT 2 Tg

the right tail of types and RconsH frac14

PHtconsPHtlib

as the average

representativeness of right tail types for conservatives

29 This assumption is consistent with the authorsrsquo interpretation of the GNHdata (GNH 2012) and with previous studies using ANES (eg Westfall et al 2015)Furthermore to the extent that this assumption holds equally well for most issueswithin a data set our focus on cross-issue differences should allow us to test thepredictions of our model even with an imperfect proxy for beliefs of mean positionsFinally the data provide some insight into whether subjects are reporting (per-ceived) modal or mean types As we show the modal type is a poor prediction ofstated beliefs while a distorted mean slanted toward representative types is anaccurate prediction of stated beliefs

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Under the further approximation where tcons

tlibampRcons

H for

t 2 H

EstethtjconsTHORN frac14 EethtjconsTHORN thorn consethR

consH 1THORNeth6THORN

EstethtjlibTHORN frac14 EethtjlibTHORN libethR

consH 1THORNeth7THORN

where lcons and llib are positive constants

The first regression allows us to test for the kernel of truthhypothesis and the second set of regressions allows us to test forthe role of representativeness

Equation (5) says that respondents in our model inflate theaverage position of a group say the conservatives if and only ifthe group has a higher average position than the other groupnamely the liberals Formally EstethtjconsTHORN gt EethtjconsTHORN if and onlyif EethtjconsTHORN gt EethtjlibTHORN Because in our measurement scale highertypes mean lsquolsquomore conservativersquorsquo we expect (i) believed conserva-tive average to be higher than the truth and (ii) the extent ofoverstatement to decrease in the average liberal position EethtjlibTHORNConversely we expect the average liberal position to be lowerthan the truth the more so the higher the average conservativeposition EethtjconsTHORN

As previously discussed the basis of these predictions is con-text dependence information about the distribution of ndashG is rel-evant for the beliefs about G This context dependence isinconsistent with rational expectations in which only thegrouprsquos own means should affect beliefs We test the hypothesisthat the true mean EethtjGTHORN is a significant predictor of the believedmean E

stethtjGTHORN with a positive sign and the other grouprsquos truemean EethtjGTHORN is a predictor of the believed mean with a negativesign

Equations (6) and (7) say that repondentsrsquo assessment bias isshaped by representativeness When the right tail is more repre-sentative for conservatives (Rcons

H 1 positive and large) partici-pants should inflate the average conservative position more(higher E

stethtjconsTHORN EethtjconsTHORN) and deflate the average liberal po-sition more (lower E

stethtjlibTHORN EethtjlibTHORN) We test the hypothesisthat the inflation in conservative positions is positively associatedwith the representativeness of the right tail for the conservativesand the inflation in liberal positions is negatively associated with

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it Once again the representativeness of the right tail is com-puted using the true distribution of positions

In equations (6) and (7) in many cases the representative tailis also the most likely one As a consequence these tests cannotdistinguish a representativeness-based from a likelihood-basedmodel of distorted beliefs We perform two additional testsFirst we run versions of equations (6) and (7) in which we controlfor the likelihood of tails (see Table A4 in Online Appendix G)Second we compute numerically the predictions of a representa-tiveness-based model of stereotypes and a likelihood-based modelof stereotypes We then assess which of these two is better able tomatch the data on beliefs

3 Empirical Results To begin we illustrate the structure ofthe data and the nature of our predictions with two simple exam-ples from the GNH data set focusing on beliefs about conserva-tives In example 1 participants are asked about their agreementwith the statement lsquolsquoIt can never be right to kill a human beingrsquorsquoIn example 2 participants are asked about the moral relevance oflsquolsquowhether or not someone cared for someone weak or vulnerablersquorsquoAs can be seen in Figure III in example 1 the modal position(strongly disagree (1)) and most representative positions(strongly disagree (1)) coincide for conservatives In contrast inexample 2 in Figure III the most representative types (slightlyrelevant (3) not at all relevant (1)) are not most likely for theconservative group Following Proposition 1 we predict that be-liefs will be distorted in the direction of the most representativetypes Thus we expect more exaggeration in example 2 than inexample 1 since in example 2 the most representative types (inthe left tail) are far from the modal type whereas in example 1they coincide This is what we find the conservative position isexaggerated by only 009 positions in Example 1 (true mean 299believed mean 290) but by 106 positions in Example 2 (truemean 421 believed mean 315)

In the full data sets we treat each (issue year) pair as anobservation and we cluster standard errors at the issue level Forthe GNH data we have 45 observations 45 issues measured inthe same year For the ANES data we have 66 observations 10issues measured in multiple years To begin we simply docu-ment systematic exaggeration in both data sets This is a primaryfocus of the original analysis in GNH (2012) and also in Westfall

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FIGURE III

Two Examples

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et al (2015)rsquos analysis of the ANES data30 Figure IV shows thatthe believed difference between typical conservative and typicalliberal positions is larger than the true difference in mean posi-tions for 109 of the 111 observations The data for both GNH(squares) and ANES (triangles) lie above the 45-degree line(dashed)31 Average exaggeration is 062 positions on the scale(066 in the GNH data 059 in the ANES data)32

The systematic and significant exaggeration of mean differ-ences suggests that the benchmark model of accurate beliefs ismissing something important Indeed this exaggeration reflectsthe fact that believed means are typically more extreme than truemeans First note that the kernel of truth regression (equation(5)) generates exaggeration of mean differences just as docu-mented in Figure IV

EstethtjGTHORN E

stethtjGTHORN frac14 eth1thorn 2THORN frac12EethtjGTHORN EethtjGTHORN

To bring this prediction to the data we regress the believedmean position for each group EBethtjGTHORN on the true mean of thegroup EethtjGTHORN and the true mean of the comparison groupEethtjGTHORN across issues We do this for each group (liberals con-servatives) in each data set separately We also present pooledspecifications that combine the data sets to make a prediction fora given group (liberals conservatives) In these pooled specifica-tions we include a dummy variable indicating whether theobservation came from the ANES data set For all specificationswe cluster observations at the issue level33 The results from re-gression are shown in Table I In every specification we find thatEethtjGTHORN is a significant predictor of EBethtjGTHORN with the predicted pos-itive sign Crucially for five of the six specifications the mean of

30 Chambers and Melnyk (2006) also find evidence of exaggeration of truedifferences in beliefs about political positions

31 For convenience we recode all issues so that the high end of the scale (67)represents the stereotypically more conservative position

32 A natural question to ask is how beliefs vary across liberals and conserva-tives That is do beliefs about a group G depend on membership in G versus ndashG Ourmodel does not speak to this issue However in Online Appendix G we show thatthe results we document below hold for both beliefs held by conservatives and be-liefs held by liberals see Tables A9 A10 and A11

33 In general the results presented below for the ANES data are not largelyimpacted by the decision to cluster at the issue level Similar results are obtained ifthe data are not clustered

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the comparison group EethtjGTHORN is also a significant predictor ofE

BethtjGTHORN with the predicted negative signAlthough these results provide strong evidence of context

dependence and are consistent with our model they do not pindown a role for representativeness of types Our next test relatesthe magnitude of representativeness of tail types to the magni-tude of belief distortions

To this end we implement the regressions in equations (6)and (7) Following Proposition 4 we compute the average repre-

sentativeness of tail types for conservatives RconsH frac14

PtT2tconsPtT2tlib

We

again test the hypothesis that RconsH is a significant predictor of Est

ethtjconsTHORN with a positive sign and a predictor of EstethtjlibTHORN with a

negative sign Table II shows that conditional on true mean RconsH

predicts believed mean for each group G as expected The firstthree specifications display the results for predicting beliefs heldabout conservatives In both data sets the average representa-tiveness of tail types for conservatives is a significant positivepredictor of beliefs held about conservatives The final three spe-cifications display the results for predicting beliefs held about

FIGURE IV

Exaggeration of Differences

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liberals We find that the average representativeness of tail typesfor conservatives is a negative predictor of beliefs held about lib-erals This effect is significant in the GNH data and marginallysignificant in the ANES data

We present several additional results in Online Appendix GTo further examine the role of representativeness in driving be-liefs we first show the results of Table II carry through when we

TABLE II

AVERAGE REPRESENTATIVENESS OF TAIL POSITIONS PREDICTS BELIEFS

OLS Predicting Believed Mean of Group G for Each Issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position

of group G for issue

078 024 051 072 018 041

(006) (008) (009) (005) (005) (010)

Avg rep of tail types for

conservatives RconsH

019 055 025 014 012 024

(007) (022) (008) (006) (007) (005)

Constant 101 260 184 093 271 201

(026) (045) (029) (022) (025) (032)

R2 082 048 060 091 031 070

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

TABLE I

INFORMATION ABOUT ndashG PREDICTS BELIEFS ABOUT G

OLS predicting believed mean of group G for each issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position of

conservatives for issue

102 098 096 021 019 025

(0097) (0133) (0076) (0060) (0116) (0060)

True mean position of

liberals for issue

035 086 058 0987 039 073

(0106) (0134) (0131) (0066) (0106) (0135)

Constant 151 335 235 069 258 156

(0195) (0269) (0279) (0122) (0249) (0270)

R2 083 053 066 092 032 068

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

STEREOTYPES 1789

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control for the average likelihood on the tail positions (see Table A4in Online Appendix G) Most tellingly we use the model to predictbeliefs across issues and compare those to the data For simplicitywe use the rank-based truncation specification to predict mean be-liefs when stereotypes include the d most representative types ford frac14 1 T We compare these predictions to those of a model inwhich beliefs are obtained by restricting the distribution to the dmost likely types Our benchmark for both models is predicting thebelieved mean from the entire distribution where d = T We showthat the predictions of the rank-based truncation model with d = 4or 5 compare favorably to both a likelihood-based truncation model(with any d) and the accurate beliefs benchmark Interestingly thisresult suggests that stereotypical beliefs are well approximated byneglecting the least representative types (as opposed to focusingonly on the most representative types) and so represent a moderatethough systematic departure from the standard benchmarkFinally we show that the results we document above hold forboth beliefs held by conservatives and beliefs held by liberals (seeTables A9 A10 and A11 in Online Appendix G)

V Conclusion

We present a model of stereotypical thinking in which DMsmaking predictions about a group overweight the grouprsquos mostdistinctive types These overweighted types are not the mostlikely ones given the DMrsquos data but the most representativeones in the sense of being the most diagnostic of the group rela-tive to other groups Representativeness implies that what ismost distinctive of a group depends on what group it is comparedwith We present experimental evidence that confirms this con-text dependence in recall-based assessments of groups Finallywe evaluated the predictions of the model using political data fromexisting large-scale surveys We find context dependence to be akey feature of beliefs Given the richness of the political data wecan go a step further and identify a role for representativeness inparticular As the representativeness of tail types increases beliefsof a group are distorted in the direction of that tail

Our approach provides a parsimonious and psychologicallyfounded account of how DMs generate simplified representationsof reality from social groups to stock returns and offers a unifiedaccount of disparate pieces of evidence relating to this type of

QUARTERLY JOURNAL OF ECONOMICS1790

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uncertainty The model captures the central fact that stereotypeshighlight the greatest difference between groups thus explainingwhy some stereotypes are very accurate while others lack valid-ity Still stereotypes often have a kernel of truth when they arebased on systematicmdasheven if smallmdashdifferences between groupsThis logic allows us to describe a number of heuristics and psy-chological biases many of which arise in the context of predictionproblems Generically our model generates overreaction to diag-nostic information

Our model is based on representativeness and does not cap-ture all the features of stereotypical thinking However it cap-tures perhaps the central feature when we think of a group wefocus on what is most distinctive about it and neglect or under-weight the rest

Saeuroıd Business School University of Oxford

Ohio State University and Harvard Business School

Universita Bocconi and Innocenzo Gasparini Institute

for Economic Research

Harvard University

Supplementary Material

An Online Appendix for this article can be found at QJEonline (qjeoxfordjournalorg)

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Arrow Kenneth lsquolsquoThe Theory of Discriminationrsquorsquo in Discrimination in LaborMarkets Orley Ashenfelter and Albert Rees eds (Princeton NJPrinceton University Press 1973)

Ashton Michael and Victoria Esses lsquolsquoStereotype Accuracy Estimating theAcademic Performance of Ethnic Groupsrsquorsquo Personality and SocialPsychology Bulletin 25 (1999) 225ndash236

Barberis Nicholas Andrei Shleifer and Robert Vishny lsquolsquoA Model of InvestorSentimentrsquorsquo Journal of Financial Economics 49 (1998) 307ndash343

Bayer Sylvia lsquolsquoThe Accuracy of Academic Gender Stereotypesrsquorsquo Sex Roles 40(1999) 787ndash813

Benjamin Dan James Choi and Joshua Strickland lsquolsquoSocial Identity andPreferencesrsquorsquo American Economic Review 100 (2010) 1913ndash1928

Benjamin Dan Matthew Rabin and Collin Raymond lsquolsquoA Model of Non-Belief inthe Law of Large Numbersrsquorsquo Journal of the European Economic Association15 (2015) 515ndash544

Bertrand Marianne lsquolsquoNew Perspectives on Genderrsquorsquo Handbook of LaborEconomics 4 (2011) 1543ndash1590

Bodoh-Creed Aaron Dan Benjamin and Matthew Rabin lsquolsquoThe Dynamics of Base-Rate Neglectrsquorsquo mimeo Haas Business School 2013

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Bohnet Iris Alexandra van Geen and Max Bazerman lsquolsquoWhen PerformanceTrumps Gender Bias Joint versus Separate Evaluationrsquorsquo ManagementScience 5 (2016) 1225ndash1234

Bordalo Pedro Nicola Gennaioli and Andrei Shleifer lsquolsquoSalience Theory of Choiceunder Riskrsquorsquo Quarterly Journal of Economics 127 (2012) 1243ndash1285

mdashmdashmdash lsquolsquoSalience and Consumer Choicersquorsquo Journal of Political Economy 121(2013) 803ndash843

Briton Nancy and Judith Hall lsquolsquoBeliefs about Female and Male NonverbalCommunicationrsquorsquo Sex Roles 32 (1995) 79ndash90

Buser Thomas Muriel Niederle and Hessel Oosterbeek lsquolsquoGenderCompetitiveness and Career Choicesrsquorsquo Quarterly Journal of Economics 129(2014) 1409ndash1447

Carrell Scott Marianne Page and James West lsquolsquoSex and Science How ProfessorGender Perpetuates the Gender Gaprsquorsquo Quarterly Journal of Economics 125(2010) 1101ndash1144

Chambers John and Darya Melnyk lsquolsquoWhy Do I Hate Thee ConflictMisperceptions and Intergroup Mistrustrsquorsquo Personality and SocialPsychology Bulletin 32 (2006) 1295ndash1311

Chan Wayne Robert R McCrae Filip De Fruyt Lee Jussim CorinnaE Lockenhoff Marleen De Bolle Paul T Costa Jr Angelina R SutinAnu Realo Juri Allik Katsuharu Nakazato Yoshiko ShimonakaMartina Hrebıckova Sylvie Graf Michelle Yik Marina Brunner-SciarraNora Leibovich De Figueora Vanina Schmidt Chang-kyo Ahn Hyun-nie Ahn Maria E Aguilar-Vafaie Jerzy Siuta Barbara SzmigielskaThomas R Cain Janet T Crawford Khairul Anwar Mastor Jean-Pierre Rolland Florence Nansubuga Daniel R MiramontezVeronica Benet-Martınez Jerome Rossier Denis Bratko Iris MarusicJamin Halberstadt Mami Yamaguchi Goran Knezevic Thomas A MartinMirona Gheorghiu Peter B Smith Claudio Barbaranelli Lei WangJane Shakespeare-Finch Margarida P Lima Waldemar KlinkoszAndrzej Sekowski Lidia Alcalay Franco Simonetti Tatyana V AvdeyevaV S Pramila and Antonio Terracciano lsquolsquoStereotypes of Age Differences inPersonality Traits Universal and Accuratersquorsquo Journal of Personality andSocial Psychology 103 (2012) 1050ndash1066

Chen Yan Sherry Xin Liu Tracy Xiao and Margaret Shih lsquolsquoWhich Hat to WearImpact of Natural Identities on Coordination and Cooperationrsquorsquo Games andEconomic Behavior 84 (2014) 58ndash86

Coffman Katherine lsquolsquoEvidence on Self-Stereotyping and the Contribution ofIdeasrsquorsquo Quarterly Journal of Economics 129 (2014) 1625ndash1660

Cunningham Tom lsquolsquoComparisons and Choicersquorsquo mimeo Stockholm University2013

Diekman Amanda Alice Eagly and Patrick Kulesa lsquolsquoAccuracy and Bias in theStereotypes about the Social and Political Attitudes of Women and MenrsquorsquoJournal of Experimental Social Psychology 38 (2002) 268ndash282

Eccles Jacquelynne S Janis E Jacobs and Rena D Harold lsquolsquoGender RoleStereotypes Expectancy Effects and Parentsrsquo Socialization of GenderDifferencesrsquorsquo Journal of Social Issues 46 (1990) 183ndash201

Fryer Roland and Matthew Jackson lsquolsquoA Categorical Model of Cognition andBiased Decision-Makingrsquorsquo BE Journal of Theoretical Economics 8 (2008)1ndash42

Fryer Roland and Steven Levitt lsquolsquoAn Empirical Analysis of the Gender Gap inMathematicsrsquorsquo American Economic Journal Applied Economics 2 (2010)210ndash240

Gennaioli Nicola and Andrei Shleifer lsquolsquoWhat Comes to Mindrsquorsquo Quarterly Journalof Economics 125 (2010) 1399ndash1433

Gennaioli Nicola Andrei Shleifer and Robert Vishny lsquolsquoNeglected RisksFinancial Innovation and Financial Fragilityrsquorsquo Journal of FinancialEconomics 104 (2012) 452ndash468

Gilens Martin lsquolsquoRace and Poverty in America Public Misperceptions and theAmerican News Mediarsquorsquo Public Opinion Quarterly 60 (1996) 515ndash541

Glaeser Edward lsquolsquoThe Political Economy of Hatredrsquorsquo Quarterly Journal ofEconomics 120 (2005) 45ndash86

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Glover Dyland Amanda Pallais and William Pariente lsquolsquoDiscrimination as a Self-Fulfilling Prophecy Evidence from French Grocery Storesrsquorsquo mimeo HarvardUniversity 2015

Goldin Claudia Lawrence Katz and Ilyana Kuziemko lsquolsquoThe Homecoming ofAmerican College Women The Reversal of the College Gender GaprsquorsquoJournal of Economic Perspectives 20 (2006) 133ndash156

Graham Jesse Brian Nosek and Jonathan Haidt lsquolsquoThe Moral Stereotypes ofLiberals and Conservatives Exaggeration of Differences across thePolitical Spectrumrsquorsquo PLoS One 7 (2012) 1ndash13

Grether David lsquolsquoBayes Rule as a Descriptive Model The RepresentativenessHeuristicrsquorsquo Quarterly Journal of Economics 95 (1980) 537ndash557

Griffin Dale and Amos Tversky lsquolsquoThe Weighing of Evidence and theDeterminants of Confidencersquorsquo Cognitive Psychology 24 (1992) 411ndash435

Guiso Luigi Ferdinando Monte Paola Sapienza and Luigi Zingales lsquolsquoCultureGender and Mathrsquorsquo Science 320 (2008) 1164ndash1165

Hilton James and William Von Hippel lsquolsquoStereotypesrsquorsquo Annual Review ofPsychology 47 (1996) 237ndash271

Hyde Janet Sara Lindberg Marcia Linn Amy Ellis and Caroline WilliamslsquolsquoGender Similarities Characterize Math Performancersquorsquo Science 321 (2008)494ndash495

Judd Charles and Bernardette Park lsquolsquoDefinition and Assessment of Accuracy inSocial Stereotypesrsquorsquo Psychological Review 100 (1993) 109ndash128

Jussim Lee Jarret Crawford Stephanie Anglin John Chambers Sean Stevensand Florette Cohen lsquolsquoStereotype Accuracy One of the Largest and MostReplicable Effects in All of Social Psychologyrsquorsquo in The Handbook ofPrejudice Stereotyping and Discrimination Todd Nelson ed (MahwahNJ Lawrence Erlbaum 2015)

Kahneman Daniel and Amos Tversky lsquolsquoSubjective Probability A Judgment ofRepresentativenessrsquorsquo Cognitive Psychology 3 (1972) 430ndash454

mdashmdashmdash lsquolsquoOn the Psychology of Predictionrsquorsquo Psychological Review 80 (1973) 237ndash251

Kaplowitz Stan Bradley Fisher and Clifford Broman lsquolsquoHow Accurate ArePerceptions of Social Statistics about Blacks and Whitesrsquorsquo Public OpinionQuarterly 67 (2003) 237ndash243

Kersten Daniel Pascal Mamassian and Alan Yuille lsquolsquoObject Perception asBayesian Inferencersquorsquo Annual Review of Psychology 55 (2004) 271ndash304

Klein Richard Kate A Ratliff Michelangelo Vianello Reginald B Adams JrStepan Bahnik Michael J Bernstein Konrad Bocian Mark J BrandtBeach Brooks Claudia Chloe Brumbaugh Zeynep CemalcilarJesse Chandler Winnee Cheong William E Davis Thierry DevosMatthew Eisner Natalia Frankowska David Furrow Elisa Maria GallianiFred Hasselman Joshua A Hicks James F Hovermale S Jane HuntJeffrey R Huntsinger Hans IJzerman Melissa-Sue John Jennifer A Joy-Gaba Heather Barry Kappes Lacy E Krueger Jaime Kurtz CarmelA Levitan Robyn Mallett Wendy L Morris Anthony J Nelson JasonA Nier Grant Packard Ronaldo Pilati Abraham M RutchickKathleen Schmidt Jeanine L Skorinko Robert Smith Troy G SteinerJustin Storbeck Lyn M Van Swol Donna Thompson Anna van rsquot VeerLeigh Ann Vaughn Marek Vranka Aaron Wichman Julie A Woodzickaand Brian A Nosek lsquolsquoInvestigating Variation in Replicability A ManyLabs Replication Projectrsquorsquo Social Psychology 45 (2014) 142ndash152

Lundberg Shelly and Richard Startz lsquolsquoPrivate Discrimination and SocialIntervention in Competitive Labor Marketsrsquorsquo American Economic Review73 (1983) 340ndash347

Madon Stephanie Max Guyll Kathy Aboufadel Eulices Montiel Alison SmithPolly Palumbo and Lee Jussim lsquolsquoEthnic and National Stereotypes ThePrinceton Trilogy Revisited and Revisedrsquorsquo Personality and SocialPsychological Bulletin 27 (2001) 996ndash1010

Martin Carol lsquolsquoA Ratio Measure of Sex Stereotypingrsquorsquo Journal of Personality andSocial Psychology 52 (1987) 489ndash499

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McCauley Clark Krishna Thangavelu and Paul Rozin lsquolsquoSex Stereotyping ofOccupations in Relation to Television Representations and Census FactsrsquorsquoBasic and Applied Social Psychology 9 (1988) 197ndash212

Mullainathan Sendhil lsquolsquoThinking through Categoriesrsquorsquo mimeo HarvardUniversity 2002

Ortoleva Pietro and Erik Snowberg lsquolsquoOverconfidence in Political BehaviorrsquorsquoAmerican Economic Review 105 (2015) 504ndash535

Phelps Edmund lsquolsquoThe Statistical Theory of Racism and Sexismrsquorsquo AmericanEconomic Review 62 (1972) 659ndash661

Pope Devin and Justin Sydnor lsquolsquoGeographic Variation in the Gender Differencesin Test Scoresrsquorsquo Journal of Economic Perspectives 24 (2010) 95ndash108

Rabin Matthew lsquolsquoInference by Believers in the Law of Small NumbersrsquorsquoQuarterly Journal of Economics 117 (2002) 775ndash816

Rabin Matthew and Joel Schrag lsquolsquoFirst Impressions Matter A Model ofConfirmatory Biasrsquorsquo Quarterly Journal of Economics 114 (1999) 37ndash82

Rabin Matthew and Dimitri Vayanos lsquolsquoThe Gamblerrsquos and Hot-Hand FallaciesTheory and Applicationsrsquorsquo Review of Economic Studies 77 (2010) 730ndash778

Reuben Ernesto Paola Sapienza and Luigi Zingales lsquolsquoHow Stereotypes ImpairWomenrsquos Careers in Sciencersquorsquo Proceedings of the National Academy ofSciences 111 (2014) 4403ndash4408

Rosch Eleanor lsquolsquoNatural Categoriesrsquorsquo Cognitive Psychology 4 (1973) 328ndash350Ryan Carey S lsquolsquoAccuracy of Black and White College Studentsrsquo In-Group and

Out-Group Stereotypesrsquorsquo Personality and Social Psychology Bulletin 22(1996) 1114ndash1127

Schneider David The Psychology of Stereotyping (New York Guilford Press2004)

Schneider David Albert Hastorf and Phoebe Ellsworth Person Perception(Reading MA Addison-Wesley 1979)

Shih Margaret Todd Pittinsky and Nalini Ambady lsquolsquoStereotype SusceptibilityIdentity Salience and Shifts in Quantitative Performancersquorsquo PsychologicalScience 10 (1999) 80ndash83

Shih Margaret Todd Pittinsky and Amy Trahan lsquolsquoDomain-Specific Effects ofStereotypes on Performancersquorsquo Self and Identity 5 (2006) 1ndash14

Steele Claude Whistling Vivaldi How Stereotypes Affect Us and What We CanDo (New York Norton 2010)

Tenenbaum Joshua and Thomas Griffiths lsquolsquoThe Rational Basis ofRepresentativenessrsquorsquo 23rd Annual Conference of the Cognitive ScienceSociety (2001) 1036ndash1041

Tversky Amos and Daniel Kahneman lsquolsquoExtensional versus Intuitive ReasoningThe Conjunction Fallacy in Probability Judgmentrsquorsquo Psychological Review 90(1983) 293ndash315

Weinberger Catherin lsquolsquoIs the Science and Engineering Workforce Drawn fromthe Far Upper Tail of the Math Ability Distributionrsquorsquo mimeo UCSB 2005

Westfall Jacob Leaf Van Boven John Chambers and Charles Judd lsquolsquoPerceivingPolitical Polarization in the United States Party Identity Strength andAttitude Extremity Exacerbate the Perceived Partisan DividersquorsquoPsychological Science 10 (2015) 145ndash158

Wolsko Christopher Bernadette Park Charles Judd and Bernd WittenbrinklsquolsquoFraming Interethnic Ideology Effects of Multicultural and Color-BlindPerspectives on Judgments of Groups and Individualsrsquorsquo Journal ofPersonality and Social Psychology 78 (2000) 635ndash654

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Page 2: I. Introduction · uneducated at the beginning of the 20th century, and as high achievers at the beginning of the 21st (Madon et al. 2001). Social science has produced three broad

uneducated at the beginning of the 20th century and as highachievers at the beginning of the 21st (Madon et al 2001)

Social science has produced three broad approaches to ste-reotypes The economic approach of Phelps (1972) and Arrow(1973) sees stereotypes as a manifestation of statistical discrim-ination rational formation of beliefs about a group member interms of the aggregate distribution of group traits Statisticaldiscrimination may affect actual group characteristics in equilib-rium (Arrow 1973) but even so stereotypes are based on rationalexpectations1 As such these models do not address the centralproblem that stereotypes are often inaccurate The vast majorityof Florida residents are not elderly the vast majority of the Irishare not red-headed and Tel Aviv is really pretty safe

The sociological approach to stereotyping pertains only tosocial groups It views stereotypes as fundamentally incorrectand derogatory generalizations of group traits reflective of thestereotyperrsquos underlying prejudices (Adorno et al 1950) or otherinternal motivations (Schneider 2004) Social groups that havebeen historically mistreated such as racial and ethnic minoritiescontinue to suffer through bad stereotyping perhaps because thegroups in power want to perpetuate false beliefs about them(Glaeser 2005 Steele 2010) The stereotypes against blacks arethus rooted in the history of slavery and continuing discrimina-tion This approach might be relevant in some important in-stances but it leaves a lot out While some stereotypes areinaccurate many are quite fair (lsquolsquoDutch are tallrsquorsquo lsquolsquoSwedes areblondrsquorsquo) Moreover many stereotypes are flattering to the groupin question rather than pejorative (lsquolsquoAsians are good at mathrsquorsquo)Finally stereotypes change so they are at least in part respon-sive to reality rather than entirely rooted in the past (Madon et al2001)

The third approach to stereotypesmdashand the one we followmdashisthe lsquolsquosocial cognition approachrsquorsquo rooted in social psychology(Schneider 2004) This approach gained ground in the 1980s

1 More recent work explores under what conditions stereotypes are self-ful-filling Assuming that freely available information is used correctly minorities caninvest in visible signals of quality that offset preconceptions (Lundberg and Startz1983) Glover Pallais and Pariente (2015) present evidence on self-fulfilling as-pects of stereotypes in labor markets

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and views social stereotypes as special cases of cognitive schemasor theories (Schneider Hastorf and Ellsworth 1979) These the-ories are intuitive generalizations that individuals routinely usein their everyday life and they entail savings on cognitive re-sources Hilton and Von Hippel (1996) define stereotypes aslsquolsquomental representations of real differences between groups [ ]allowing easier and more efficient processing of informationStereotypes are selective however in that they are localizedaround group features that are the most distinctive that providethe greatest differentiation between groups and that show theleast within-group variationrsquorsquo A related lsquolsquokernel-of-truth hypoth-esisrsquorsquo holds that stereotypes are based on some empirical realityas such they are useful but may entail exaggerations (Judd andPark 1993)

We show that this approach to stereotypes is intimately re-lated to another idea from psychology the use of heuristics inprobability judgments (Kahneman and Tversky 1972) Justas heuristics simplify the assessment of complex probabilistichypotheses they also simplify the representation of heteroge-neous groups sometimes causing errors in judgment We for-mally explore this idea by modeling stereotype formation as aconsequence of Kahneman and Tverskyrsquos representativenessheuristic Tversky and Kahneman (1983) write that lsquolsquoan attributeis representative of a class if it is very diagnostic that is therelative frequency of this attribute is much higher in that classthan in the relevant reference classrsquorsquo Following Gennaioli andShleifer (GS 2010) we assume that a type t is representativefor group G relative to a comparison group ndashG if it scores highon the likelihood ratio

Pr ethtjGTHORN

Pr ethtj GTHORNeth1THORN

The most representative types come to mind first and so areoverweighted in judgments Predictions about G are then madeunder a distorted distribution or stereotype that overweightsrepresentative types Our results obtain with minimal assump-tions on such overweighting We describe a number of weightingspecifications and explore their properties

To illustrate the logic of the model consider the stereotypelsquolsquoFlorida residents are elderlyrsquorsquo The proportion of elderly people

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in Florida and in the overall United States population isshown here2

The table shows that the age distributions in Florida and in therest of the United States are very similar Yet someone over 65 ishighly representative of a Florida resident because this age bracket

maximizes the likelihood ratio Pr ethtjFloridaTHORNPr ethtjUSTHORN When thinking about the

age of Floridians then the 65+ type immediately comes to mindbecause in this age bracket Florida is most different from the rest ofthe United States in the precise sense of representativenessRepresentativeness-based recall induces an observer to overweightthe 65+ type in their assessment of the average age of Floridians

This example also illustrates how stereotypes can be inaccu-rate Indeed and perhaps surprisingly only about 17 of Floridaresidents are elderly The largest share of Florida residentsnearly as many as in the overall US population are in the agebracket 19ndash44 which maximizes PrethtjFloridaTHORN Being elderly isnot the most likely age bracket for Florida residents but ratherthe age bracket that occurs with the highest relative frequencyA stereotype-based prediction that a Florida resident is elderlyhas very little validity

The same logic of representativeness suggests that the reasonpeople stereotype the Irish as red-headed is that red hair is morecommon among the Irish than among other groups even though itis not that common in absolute terms The reason people stereo-type Republicans as wealthy is that the wealthy are more commonamong Republicans than Democrats3 In both cases the represen-tation entails judgment errors people overestimate the proportionof red-haired among the Irish or of the wealthy among theRepublicans

2 Data from the 2010 US Census see httpfactfindercensusgovfacestableservicesjsfpagesproductview xhtmlpid=DEC_10_DP_DPDP1ampsrc=pt

3 See httpwwwnytimescompackagespdfpolitics20041107_px_ELECTORATExls

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We find that representativeness often generates fairly accu-rate stereotypes but sometimes causes stereotypes to be inaccu-rate particularly when groups have similar distributions thatdiffer most in unlikely types More generally our model high-lights two critical properties

Stereotypes amplify systematic differences betweengroups even if these differences are in reality verysmall When groups differ by a shift in means stereotyp-ing exaggerates differences in means and when groupsdiffer by an increase in variance stereotyping exagger-ates the differences in variances In these cases (but notalways) representativeness yields stereotypes that con-tain a lsquolsquokernel of truthrsquorsquo in the sense that they differen-tiate groups along existing and highly diagnosticcharacteristics exactly as Hilton Von Hippel andSchneider define them

Stereotypes are context dependent The assessment of agiven target group depends on the reference group towhich it is compared

In line with the social cognition approach to stereotypes asignificant body of psychological research on beliefs about genderrace age and political groups finds that stereotypes broadly re-flect reality but display biases Social psychologists have exploredthe extent to which stereotypes exaggerate real differences thuspossessing a kernel of truth Evidence on exaggeration varies bydomain For race and gender many studies have reportedroughly accurate beliefs whereas others have found underesti-mation or exaggeration of true differences (Jussim et al 2015)4

For age and political stereotypes evidence points more stronglytoward exaggeration5 Schneider (2004 337) summarizes the

4 For evidence of roughly accurate beliefs for race see for example Ashtonand Esses (1999) on beliefs of academic ability Kaplowitz Fisher and Broman(2003) on income poverty rates and out-of-wedlock births and Wolsko et al(2000) on a array of positive and negative attributes Ryan (1996) and Gilens(1996) find evidence of exaggeration of race stereotypes on personal attributesand poverty rates respectively Some studies have found roughly accurate beliefson gender (McCauley Thangavelu and Rozin 1988 Briton and Hall 1995Diekman Eagly and Kulesa 2002) while others find evidence of exaggeration(Martin 1987 Bayer 1999)

5 See Chan et al (2012) on age We discuss evidence on political stereotypes inSection IV

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existing empirical work on stereotype accuracy as follows lsquolsquothebest we can do by way of general summary is to say that somestereotypes held by some people for some groups are sometimesaccuratersquorsquo Our empirical investigation explores the connectionbetween stereotype accuracy and representativeness which wemeasure using the previously defined likelihood ratio

We first assess the role of representativeness and contextdependence in the lab We construct a group of mundane objectsG and present it to participants next to a comparison group ndashGIn our baseline condition the comparison group is chosen so thatno type is particularly representative of group G In our treat-ment we change the comparison group ndashG while leaving thetarget group G unchanged The new comparison group givesrise to highly representative types within G In line with thekey prediction of our model participants in the treatment condi-tion shift their assessment of G toward the representative types

We test the model using two data sets on political preferencesand beliefs about political preferences in the United States Heregroups are political constituencies (Democrats and Republicans)and types are their positions on a number of issues Holding fixedthe groups and the set of types and varying the groupsrsquo true dis-tributions across issues the data allow us to test whether beliefsabout political preferences are shaped by representativeness Wefirst show that such beliefs depart from the truth by exaggerating(mean) differences as per the kernel of truth logic We then ex-plore how the extent of exaggeration varies across issuesConsistent with the model we find that beliefs systematicallydepart from rational expectations and that the degree to whichthey exaggerate true differences is a function of representative-ness While representativeness is not the only heuristic thatshapes recall (availability driven by recency or frequency of ex-posure also plays a role) it explains the fact that in the datastated beliefs indeed exaggerate differences among groups

Since Kahneman and Tverskyrsquos (1972 1973) work on heuris-tics and biases several studies have formally modeled heuristicsabout probabilistic judgments and incorporated them into eco-nomic models Work on the confirmation bias (Rabin andSchrag 1999) and on probabilistic extrapolation (Grether 1980Barberis Shleifer and Vishny 1998 Rabin 2002 Rabin andVayanos 2010 Benjamin Rabin and Raymond 2015) assumesthat the decision maker has an incorrect model in mind or incor-rectly processes available data Our approach is instead based on

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the assumption that representative information comes foremostto mind when making judgments The mental operation that liesat the heart of our modelmdashgenerating a prediction for the distri-bution of types in a group based on data stored in memorymdashalsocaptures base rate neglect and overreaction to diagnostic infor-mation The underweighting or neglect of information in ourmodel simplifies judgment problems in a way related to modelsof categorization (Mullainathan 2002 Fryer and Jackson 2008)In these models however decision makers use coarse categoriesorganized according to likelihood not representativeness Thisapproach generates imprecision but does not create a systematicbias for overestimating unlikely events nor does it allow for con-text-dependent beliefs In our empirical analysis of political be-liefs we explicitly compare the predictions of representativeness-based recall to those of likelihood-based models and find that theevidence supports the former

In modeling representativeness we follow the specification ofGS (2010) but investigate a new set of questions GS (2010) ex-amine how representativeness distorts the assessed probabilitiesof alternative hypotheses but not how the probability of a givenhypothesis or group is distributed across its constituent elementsIn the context of the current setting GS (2010) ask how imperfectrecall affects the assessed probability that a randomly drawnmember from a universe belongs to group G The current arti-cle in contrast asks which type t we expect to draw once we knowthat we are facing group G GS (2010) show how representative-ness generates biased probabilistic assessments such as conjunc-tion and disjunction fallacies This article deals with perhaps abroader and more ubiquitous problem of stereotype formationextensively studied by other social scientists but largely ne-glected by economists

Section II describes our model In Section III we examine theproperties of stereotypes including the forces that shape stereo-type accuracy and illustrate these properties with examples InSection IV we bring the model to the data performing a lab ex-periment and analyzing existing surveys of political beliefsSection V concludes The Online Appendix presents proofs anumber of extensions of the model and additional results forthe experiments and field evidence

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II A Model of Representativeness and Stereotypes

IIA The Model

A decision maker (DM) faces a prediction problem such asassessing the ability of a job candidate from a certain ethnicgroup the future performance of a firm belonging to a certainsector or future earnings based on own gender

Formally there is a set of types of interest T and an overallpopulation of which group G is a subset The set of typesT can be unordered (eg occupations) or ordered (and typi-cally cardinal eg earnings levels) When T is ordered wewrite T frac14 ft1 tTg with t1 lt t2 lt lt tT6 There is a probabil-ity or frequency distribution 2 ethT THORN that induces a condi-tional distribution PrethT frac14 tjGTHORN when restricted to G7 In whatfollows we denote by tG frac14 PrethT frac14 tjGTHORN the probability of typet in group G and by G the vector ethtGTHORNt2T containing the condi-tional distribution

The DMrsquos goal is to assess the distribution of the types ofinterest in a particular group G Although the DM has stored inmemory the full distribution he retrieves from memory a dis-torted version of G that overweights the probability of thosetypes that are most representative of G relative to a comparisongroup ndashG Generically ndashG is a group in that is distinct from Gnamely G7 nG although in some cases it can coincide withthe complement of G

According to Tversky and Kahneman (1983) a type t is rep-resentative of G if it is relatively more likely to occur in G thanin ndashG Definitions 1 and 2 formalize this representativeness-based recall following GS (2010)

6 For simplicity we also use T to denote the number of types jTj The modelapplies also to cases in which types (i) are multidimensional capturing a bundle ofattributes such as occupation and nationality or (ii) are continuous We considerthese cases in Online Appendixes C and D respectively Also G may represent anycategory of interest such as the historical performance of a firm or industry actionsavailable to a decision maker (T = set of payoffs G = occupations) or categories inthe natural world (T = ability to fly G = birds)

7 In many applications each individual in is characterized by a determin-istic type (eg age hair color) As a result ethtTHORN frac14 1

jj For instance each Floridian

has a single age type (at the finest temporal resolution) When types are stochasticinstead such as when estimating future earnings of a person or a firm each indi-vidual is described by a nondegenerate distribution

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DEFINITION 1 The representativeness of type t for group G givencomparison group ndashG is defined as the likelihood ratio

RethtGGTHORN tG

tGeth2THORN

Definition 1 implies that DMs are attuned to log differencesin probabilities representativeness depends on the percentageprobability increase of a type from ndashG to G This captures aform of diminishing sensitivity whereby for a fixed probabilitydifference a type is more likely to be overweighed if it is unlikelyin the comparison group8 Thus the representative age of aFloridian is 65+ because people in this age bracket are morecommon in Florida than in the rest of the United StatesStatistically representative types are also diagnostic of thetarget group G Indeed the higher is RethtGGTHORN the more confi-dent is a Bayesian DM observing t that t belongs to G rather thanto ndashG9

The ease of recall of highly representative types affectsjudgments because more easily recalled types are overweighted

We model distorted recall as follows Denote by RethtGGTHORN

tG

tG

t2T

the vector of representativeness of all types in G

We then have

8 Our definition of representativeness links to Weberrsquos law of sensory percep-tion see Section IIB It also links to our previous work on salience in which wepostulated that log differences in payoffs determine the attention to lottery payoffs(Bordalo Gennaioli and Shleifer 2012) and to goodsrsquo attributes (BordaloGennaioli and Shleifer 2013) Equation (2) establishes the same principle for thedomain of probabilities

9 This insight led Tenenbaum and Griffiths (2001) to define representative-ness as individualsrsquo sense as intuitive Bayesians of updating in reaction to dataTheir definition like ours is in terms of the likelihood ratio However Tenenbaumand Griffiths interpret representativeness as a mechanism that affects intuitivejudgments of similarity rather than beliefs (eg it accounts well for lab evidencewhere subjects are asked to rank types in terms of representativeness or ofstrength of association with a group) Accordingly they do not consider the possi-bility of systematically distorted and context dependent beliefs

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DEFINITION 2 The DM attaches to each type t 2 T in group G adistorted probability

sttG frac14 tG

htethRethtGGTHORNTHORNPs2T sGhsethRethtGGTHORNTHORN

eth3THORN

where ht RTthornRthorn is a weighting function such that

(i) The weight ht is a symmetric function of the representa-

tiveness of types s 6frac14 t Formally ht frac14 h tG

tG

sG

sG

s2Tn tf g

where h Rthorn RT1thorn Rthorn is a function that is invariant to

a permutation of the last T ndash 1 arguments(ii) Weighing of a type increases in own representativeness

and decreases in the representativeness of other typesFormally the function hethTHORN is weakly increasing in itsfirst argument and weakly decreasing in the other T 1arguments

We call the distribution ethsttGTHORNt2T the stereotype for G If a type

t is objectively more likely namely tG is higher then the ste-reotype attaches higher probability to it By property i distor-tions are due exclusively to the fact that a type is more or lessrepresentative than the others In particular if all types areequally representative the DM equally weighs all of them ath(1) and holds rational expectations about G If instead the rep-resentativeness of different types differs property ii implies thatthe stereotype ceteris paribus overweights the probability of morerepresentative types

Most of the results we explore in this article hold for a gen-eral weighing function htethTHORN Specific functional forms captureadded assumptions about the psychology of representativeness-based recall and are useful in applications We outline a few spe-cifications and their properties

Rank-based stereotypes the ranking of the representa-tiveness of different types shapes distortions Denote byrethtTHORN 2 f1 Tg the representativeness ranking of type tWhen r(t) = 1 type t is the most representative one (po-tentially with ties) We can specify two ways in which atypersquos representativeness ranking distorts its probability

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(i) Rank-based truncation the DM only recalls the typesthat have representativeness ranking of at most dnamely ft 2 TjrethtTHORN dg Zero probability is attachedto the remaining types10 Denote by IethrethtTHORN dTHORN an in-dicator function taking the value 1 if the representa-tiveness ranking of t is at most d Then theweighting function is ht frac14 IethrethtTHORN dTHORN so that

sttG frac14 tG

IethrethtTHORN dTHORNPs2T sGIethrethsTHORN dTHORN

which is the true conditional probability within re-called types This assumption is used in Gennaioliand Shleifer (2010)11

(ii) Rank-based discounting the DM discounts by a con-stant factor 2 frac1201 the odds of type t relative to itsimmediate predecessors in the representativenessranking Lower implies stronger discounting ofless representative types Formally the weightingfunction is ht frac14

rethtTHORN so that

sttG frac14 tG

rethtTHORNPs2T sG

rethsTHORN

Representativness-based discounting all else equal theweight attached by the DM to type t increases continuouslywith its representativeness One convenient formulation is

ht frac14tG

tG

so that

10 These neglected types are not viewed as impossible they are just assignedzero probability in the DMrsquos current thinking This formulation allows us to modelsurprise and reactions to unforeseen contingencies which have proved useful in-gredients in modeling probabilistic judgments (GS 2010) as well as neglect of risk infinancial crises (Gennaioli Shleifer and Vishny 2012)

11 Specifically in GS (2010) the assessed probability that a certain hypothesisG is true is equal to

Pr ethGTHORN frac14

Pt tGIethrethtTHORN dTHORNP

t tGIethrethtTHORN dTHORN thornP

t t=GIethrethtTHORN dTHORN

which increases in the ratio between the total probability mass recalled for Gand that recalled for G frac14 nG

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sttG frac14 tG

tG

tG

P

s2T sGsG

sG

where 0 captures the extent to which representative-ness distorts beliefs This formulation is particularly con-venient when dealing with continuous distributions ofthe exponential or power classes

These functional forms all embody the main idea of our modelthat the stereotype overweights the probability of more represen-tative types Rank-based truncation captures a central manifes-tation of limited memory forgetting unrepresentative typesSmoother discounting (based on ranking or on representative-ness) may be more appropriate when the type space is smalland smooth discounting can be more tractable in certain settings

Section III characterizes the general properties of stereotypesIn particular it shows their ability to account for social psycholo-gistsrsquo kernel of truth hypothesis under the general weighting func-tion of Definition 2 To bring the model to the data in Section IVBwe derive linear approximations of stereotypical beliefs by assum-ing that the weighting function is differentiable with respect to atypersquos representativeness This assumption excludes rank-basedweighting but allows for many possibilities

IIB Discussion of Assumptions

Before moving to the formal analysis we discuss some prop-erties and limitations of our approach Representativeness-basedrecall the idea that individuals recall distinctive group types canbe viewed as an instance of what Kahneman and Tversky calllsquolsquoattribute substitutionrsquorsquo When dealing with the difficult questionlsquolsquowhat is the distribution of hair color among the Irishrsquorsquo peopleintuitively answer to the simpler question lsquolsquowhich hair color dis-tinguishes the Irish peoplersquorsquo Critically as discussed byKahneman and Tversky attribute substitution does not occurbecause people misunderstand the original question or mechan-ically confuse the assessment of PrethtjGTHORN with that of PrethGjtTHORNRather it occurs because the distinctive or representative typesimmediately come to mind and individuals anchor their overallprobability judgment to them As a consequence subjects do notonly make mistakes in judging the probability that a Floridian is

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over age 65 They also give too high an answer to the questionlsquolsquowhat is the average age of a Floridianrsquorsquo12

One interesting question is whether the process of stereotyp-ing we describe is optimal in some sense Focusing mental repre-sentations on a few types can be justified by the costs of thinkingor retrieval This approach however is not enough to explainwhy individuals should focus on representative rather thanlikely types We do not formally analyze the optimality of repre-sentativeness here but we mention some relevant considerationsfrom cognitive psychology Kahneman and Tversky (1979) stressthe similarity between many perceptual and cognitive operationsFor instance the highlight of contrastmdasha key principle of visualperceptionmdashis invoked to justify the prospect theory assumptionthat the carriers of utility are changes relative to a referencepoint The same logic applies to our model in which stereotypesprecisely highlight the contrast between groups

In visual perception assessing properties such as brightnesscolor size or distance to an object by comparing them to otherproximate objects has been shown to be optimal in the presence ofmultiplicative background noise (Kersten Mamassian andYuille 2004 Cunningham 2013) Our formulation of representa-tiveness is related to the same idea in the sense that individualsestimating properties of one group stress differences from an-other group In a noisy world in which attention is limited thisprocess may optimally allow for swift reactions to changes ingroup characteristics even if errors are sometimes made13

12 Indeed in many cases mere confusion of PrethtjGTHORNwith PrethGjtTHORNwould not yieldthe phenomenon of stereotyping In the Irish hair color example the probability ofbeing Irish conditional on having red hair is

PrethIrishjredTHORN frac14PrethredjIrishTHORNPrethIrishTHORN

PrethredjIrishTHORNPrethIrishTHORN thorn PrethredjNonIrishTHORNPrethNonIrishTHORN

This probability is clearly very small given that the Irish population is a tinyfraction of the world population Confusion of PrethtjGTHORN with PrethGjtTHORN in this casewould lead to an understatement of the probability of the red-haired Irish

13 To give a simple example suppose thatmdashas in the case of Proposition 3mdashthevariance in the environment increases in the sense that extreme tail events becomemore likely Then a likelihood-based stereotype would detect no change whereas arepresentativeness-based stereotype would focus on the heightened probability ofthe tails In particular an asymmetric increase in tail probabilities that shifts themean would be detected by a representativeness-based stereotype even if the dis-tributionrsquos mode does not change

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Exploring this idea formally is an interesting avenue for futurework

Consider some limitations of our model First representa-tiveness is not the only heuristic that shapes recall Decisionmakers may for instance find it easier to recall types that aresufficiently likely Another potentially important mechanism isavailability understood by Kahneman and Tversky (1972) as thelsquolsquoeasersquorsquo with which information comes to mind (because of actualfrequency or repetition) In Online Appendix E we present a trun-cation-based recall mechanism in which distortions are driven bya combination of representativeness and likelihood of types(which is equivalent to relaxing property i in Definition 2) Thismodel can offer a useful starting point to capture availability aswell even though a full model of availability is beyond the scopeof this article Even in this more general setting the influence ofrepresentativeness on recall is the driving force of stereotypesthat in line with the social psychology perspective are basedon underlying differences among groups As we show in SectionIV this feature is critical in accounting for the evidence

The second set of model-related issues concerns how to spe-cify the elements of Definition 1 in applications group G the typespace T and the reference group ndashG Take the specification of thegroup G and of the type space T Often the problem itself pro-vides a natural specification of these features This is the case inthe empirically important class of lsquolsquoclosedrsquorsquo questions such asthose used in surveys which provide respondents with a set ofalternatives as in the data we use in Section IV More generallythe problem solved by the DMmdashsuch as evaluating the resume ofa job applicant coming from a certain ethnic groupmdashprimes agroup a dimension of interest and a set of types (eg the appli-cantrsquos qualification or skill levels) When types have a naturalorder such as income age or education the granularity of T isalso naturally given by the problem (income age and years ofschooling brackets) When the set of types is not specified by theproblem DMs spontaneously generate one14 It would be useful tohave a model of which dimensions and types come to mind par-ticularly for more open-ended problems Psychologists have

14 For example suppose a person is asked to guess the typical occupation of ademocratic voter in an lsquolsquoopen-endedrsquorsquo format (without being provided a set of alter-natives) Here the level of granularity at which types are defined is not obvious (egteacher versus a university teacher vs a professor of comparative literature)

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sought to construct a theory of natural types and dimensions(Rosch 1973) We do not make a contribution to this problembut we note that in many problems of interest in economics thedimension as well as the set of types is naturally givenFurthermore in our model details of the type space can be impor-tant under rank-based truncation but they matter less undersmooth discounting

Consider finally the role of the comparison group ndashG Thisgroup captures the context in which a stereotype is formed andagain is often implied by the problem when G = Floridians ndashG =rest of US population when G = African Americans ndashG = whiteAmericans A distinctive prediction of our model confirmed byour experiments in Section IVA is that the stereotype for agiven group G depends on the comparison group ndashG15 WhenndashG is not pinned down by the problem itself to derive testablepredictions from representativeness we set G frac14 nG where

is the natural population over which the unconditional distribu-tion of types is measured

III Properties of Stereotypes

We now study stereotypical beliefs and their accuracy Toillustrate the role of representativeness we first ask to whatextent the most representative type is a good fit for the groupnamely whether it is modal Next we assess the accuracy of theentire stereotypical distribution To do so we focus on a cardinaltypes and compare the stereotypersquos mean and variance to the trueones

15 Some empirical papers have taken a similar approach exogenously varyingthe natural comparison group through priming Benjamin Choi and Strickland(2010) show that priming racial or ethnic identity can affect the risk preferences ofparticipants Chen et al (2014) find that Asian students cooperate less with out-group members when primed with their ethnic identity rather than their universityidentity Shih Pittinsky and Ambady (1999) show that Asian American womenstereotype themselves as better or worse in math with corresponding impact onperformance when their ethnicity or gender respectively is primed ShihPittinsky and Trahan (2006) replicate this effect using a verbal task documentingthat Asian American women performed better when their gender rather than theirethnicity was primed Although the generalizability and replicability of priminghas been doubted (Klein et al 2014) this body of evidence is consistent with contextdependence

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IIIA Likely versus Unlikely Exemplars

The most representative type for a group is the one thatagents most easily recall and associate with the group itself forinstance a red-haired Irishman or a 65+-year-old FloridianSocial psychologists call this type the exemplar of the groupAccordingly we define

DEFINITION 3 A type t is an exemplar for G given comparisongroup ndashG when

t 2 arg maxt

tG

tG

Under any specification of the weighting function ht inDefinition 2 overweighting (weakly) increases as we movetoward more representative types so the exemplar is also thetype whose probability is overweighted the most16 By analyzingthe exemplar then we can gauge whether representativenessinduces the DM to overweight a likely type (as happens in stan-dard models of categorical thinking) or an unlikely type Whenoverweighting occurs in unlikely and extreme types the biases ofstereotypes can be particularly severe17

Equation (2) yields the following characterization

PROPOSITION 1 Suppose the conditional distributions G and G

are not identical Consider two extreme cases

(i) If for all t t0

2 T we have that tG gt t0 G if and only iftG gt t0 G then the modal type is not an exemplar forat least one group

(ii) If for all t t0

2 T we have that tG gt t0 G if and only iftG lt t0 G then for each group the modal type is theexemplar

16 Consider the function hethTHORN from Definition 2 When applied to more repre-sentative types the first argument of the function increases while one of the otherT ndash 1 arguments decreases As a result the weighting factor ht (and thus overweigh-ing

sttG

tG) increases as well

17 In the rank-based truncation model the frequency of the exemplar providesa measure of stereotype accuracy By accuracy we mean the extent to which thestereotype minimizes the distance

Pt eth

sttG tGTHORN

2 When d = 1 and only one type isrecalled (there are no ties) accuracy is maximized if the exemplar is the most likelytype and minimized if the exemplar is the least likely type

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Case i says that when groups have similar distributions inthe sense of having the same likelihood ranking the most repre-sentative type is unlikely for at least one group potentially bothRepresentativeness draws the DMrsquos attention to group differ-ences neglecting the fact that the groups are similar and havethe same mode This mechanism generates inaccurate stereo-types and is illustrated by the Florida example This resultholds under any measure of representativeness that differenti-ates the two groups (eg the difference tG tG)

Case ii says that the most representative type tends to belikely for both groups when the distributions are very differentIn this case groups differ the most around their modes so repre-sentativeness and likelihood coincide Thinking of Swedes aslsquolsquoblondrsquorsquo and Europeans as lsquolsquodark hairedrsquorsquo is accurate precisely be-cause these are majority traits of the Swedish and European pop-ulations respectively In these cases stereotyping yields fairlyreliable models Of course there is still some inaccuracy Evenin the case of likely exemplars judgment errors can be signifi-cant For instance voters in some US states are perceived aslsquolsquobluersquorsquo or lsquolsquoredrsquorsquo because a majority of the population votesDemocrat or Republican In reality even in lsquolsquobluersquorsquo states farfrom everyone votes Democrat In the 2012 presidential electionvote shares of either candidate in most states ranged from 40 to6018

When DMs strongly overweight representative types themost severe biases occur when those types are unlikely and ex-treme This is true both under rank based truncations and undersmooth discounting functions (see Section IIIB) Ethnic stereo-types based on crime or terrorism exhibit this error they neglectthe fact that by far the most common types in all groups arehonest and peaceful

IIIB Stereotypical Moments

We now characterize how the first two moments of a distri-bution are distorted by the process of stereotyping To do so wemust restrict our analysis to cardinal ordered types The follow-ing results hold for any weighting function htethTHORN satisfyingDefinition 2 We consider two canonical cases that prove usefulin illustrating the predictions of the model

18 Presidential Election Results NBCNewscom see httpelectionsnbcnewscomnspolitics2012allpresident (accessed 5 September 2016)

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In the first case groups G and ndashG are such that the likelihoodratio tG

tGis monotonic in t The monotone likelihood ratio prop-

erty (MLRP) holds to a first approximation in many empiricalsettings and is also assumed in many economic models such asstandard agency models19 If tG

tGis monotonically increasing (de-

creasing) in t then group G is associated with higher (lower)values of t relative to the comparison group ndashG Formally

PROPOSITION 2 Suppose that MLRP holds and assume wlogthat the likelihood ratio tG

tGis strictly increasing in t Then

for any weighting function htethTHORN that is not constant in therelevant range

EstethtjGTHORN gt EethtjGTHORN gt EethtjGTHORN gt E

stethtjGTHORN

Under MLRP the most representative part of the distribu-tion for G is the right tail if tG

tGincreases in t or the left tail if tG

tG

decreases in t The representative tail is then overweighted whilethe nonrepresentative tail is underweighted As a consequencethe assessed mean E

stethtjGTHORN is too extreme in the direction of therepresentative tail

Critically in line with the social cognition perspective the ste-reotype contains a kernel of truth the DM overestimates the meanof G if this group has a higher mean than the comparison groupnamely EethtjGTHORN gt EethtjGTHORN and conversely if EethtjGTHORN lt EethtjGTHORN TheDM exaggerates this true difference because he inflates the asso-ciation of G with its most representative types20 For instancewhen judging an asset manager who performs well we tend to

19 Examples include the binomial and the Poisson families of distributionswith different parameters The characterization of distributions satisfying MLRPis easier in the case of continuous distributions (see Online Appendix D) two dis-tributions f(x) f ethx THORN that differ only in their mean satisfy MLRP if and only if thedistribution f(x) is log-concave Examples include the exponential and normal dis-tributions To the extent that discrete distributions sufficiently approximate thesedistributions (as the Poisson distribution PoisethTHORN approximates the normal distri-bution Neth THORN for large l) they will also satisfy MLRP

20 Depending on the distribution and the weighing function the DMrsquos assess-ment of the variance VarethtjGTHORNmay also be dampened relative to the truth This isoften true under the truncation weighing function In this case stereotyping effec-tively leads to a form of overconfidence in which the DM holds extreme views andoverestimates the precision of his assessment That extreme views and overconfi-dence (in the sense of over precision) go together has been documented in the settingof political ideology among others (Ortoleva and Snowberg 2015)

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overemphasize skill relative to luck because higher skill levels arerelatively more associated with higher performance This occurseven if for both skilled and unskilled managers high performanceis mostly due to luck

In the second case for which we characterize the stereotypi-cal distributions groups G and ndashG have the same mean EethtjGTHORNfrac14 EethtjGTHORN frac14 EethtTHORN but differ in their variance We abstract fromskewness and higher moments by considering distributionsethtGTHORNt2T and ethtGTHORNt2T that share the same support and are sym-metric around the medianmean EethtTHORN

PROPOSITION 3 Suppose that in G more extreme types are rela-tively more frequent than in ndashG Formally the likelihoodratio tG

tGis U-shaped in t around EethtTHORN Then for any weight-

ing function htethTHORN that is not constant in the relevant rangestereotypical beliefs satisfy

VarstethtjGTHORN gt VarethtjGTHORN gt VarethtjGTHORN gt VarstethtjGTHORN

EstethtjGTHORN frac14 E

stethtjGTHORN frac14 EethtTHORN

When group G has a higher relative prevalence of extremetypes its representative types are located at both extremes of thedistribution The DMrsquos beliefs about G are then formed by over-weighting both tails while underweighting the unrepresentativemiddle The overweighting of Grsquos tails causes the assessment ofits variance VarstethtjGTHORN to be too high For example the skill dis-tribution of immigrants to the United States may be perceived ashaving very fat tails or even bimodal with immigrants beingperceived as either unskilled or very skilled relative to the resi-dent population The mean of the group in contrast is assessedcorrectly because the stereotypical distribution remains symmet-ric around EethtTHORN As before the stereotype contains a kernel oftruth It induces the agent to exaggerate the true differences be-tween groups namely the higher variance of G relative to itscounterpart

We present a number of extensions of the model in the OnlineAppendix We first consider multidimensional type spaces andshow that stereotypes center around the dimension wheregroups differ the most in line with the kernel of truth logic(Online Appendix C) Multidimensional stereotypes imply thatthe dimension we think about is influenced by context For

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example the Irish are stereotyped as red-haired when comparedwith the European population However when compared withthe Scots a more plausible stereotype for the Irish is lsquolsquoCatholicrsquorsquobecause religion is the dimension along which Irish and Scotsdiffer the most

In Online Appendix D we extend the model to continuoustype spaces Many settings of interest in economics can be use-fully described by continuous probability distributions and weshow our model is particularly tractable in this case In OnlineAppendix E we relax Definition 2 and allow weighting of types toalso be influenced by their likelihood We show that the basicinsight that stereotypes contain a kernel of truth carries throughto these cases as well

To summarize the psychology of representativeness yieldsstereotypes that are consistent with the social cognition approachin which individuals assess groups by recalling and focusing ondistinctive group traits When there are systematic differencesbetween groups stereotypes get the direction right but exagger-ate differences

IIIC Some Examples

A growing body of field and experimental evidence points to awidespread belief that women are worse than men at mathemat-ics (Eccles Jacobs and Harold 1990 Guiso et al 2008 CarrellPage and West 2010) This belief persists despite the fact that fordecades women have been gaining ground in average schoolgrades including mathematics and have recently surpassedmen in overall school performance (Goldin Katz and Kuziemko2006 Hyde et al 2008) This belief shared by men and women(Reuben Sapienza and Zingales 2014) may help account for thegender gap in the choices of high school tracks college degreesand careers with women disproportionately choosing humanitiesand health-related areas (Weinberger 2005 Buser Niederle andOosterbeek 2014) and forgoing significant wage premiums toquantitative skills (Bertrand 2011)

Gender stereotypes in mathematics particularly beliefs thatexaggerate the extent of average differences are consistent withthe predictions of our model The fact that men are overrepre-sented at the very highest performance levels leads a stereotyp-ical thinker to exaggerate the magnitude of mean differencesFigure I shows the score distributions from the mathematics

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section of 2013rsquos Scholastic Aptitude Test (SAT) for men andwomen21 The distributions are very similar with averagescores slightly higher for men (531 versus 499 out of 800)However scores for men have a heavier right tail with mentwice as likely to have a perfect SAT math score than women22

In light of such data the stereotypical male performance in math-ematics is high while the stereotypical female performance ispoor Predictions based on such stereotypes are inaccurate exag-gerating true differences Consistent with this prediction exper-imental evidence shows that both genders underestimatewomenrsquos ability in simple math tasks even controlling for pastperformance (Reuben Sapienza and Zingales 2014) Coffman(2014) shows a similar pattern extends to confidence about ownability in other male-typed domains with women reporting sig-nificantly less confidence in gender-incongruent than gender-congruent tasks Our model suggests that these patterns mightcome from stereotypes based on gender differences in the righttail of the distribution While differences in the right tail of thedistribution are unlikely to be relevant for most decisions stereo-typical thinking driven by these differences has the potential toimpact economically important decisions whether through self-stereotyping (ie choice of careers or majors as in BuserNiederle and Oosterbeek 2014) or through discrimination (iehiring decisions as in Bohnet van Geen and Bazerman 2016)

The logic of exaggerated yet directionally correct stereotypesalso sheds light on the well-documented phenomenon of base rateneglect (Kahneman and Tversky 1973) Indeed Proposition 2implies that the DM overreacts to information that assigns

21 Standardized test performance measures not only innate ability but alsoeffort and investment by third parties (Hyde et al 2008) The mapping of test per-formance into inferences about innate ability is an issue not addressed by ourmodel

22 For 2013 SAT Mathematics scores see httpmediacollegeboardcomdigitalServicespdfresearchSAT-Percentile-Ranks-By-Gender-Ethnicity-2013pdf Results are similar for the National Assessment of Educational Progress(NAEP) which are more representative of the overall population For 2012NAEP scores for 17-year-olds in mathematics see httpnationsreportcardgovltt_2012age17maspx See Hyde et al (2008) Fryer and Levitt (2010) and Popeand Sydnor (2010) for in-depth empirical analyses of the gender gap inmathematics

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people to groups precisely because such information generatesextreme stereotypes Consider the classic example in which amedical test for a particular disease with a 5 prevalence has a90 rate of true positives and a 5 rate of false positives The testassigns each person to one of two groups + (positive test) or ndash(negative test) The DM estimates the frequency of the sick type(s) and the healthy type (h) in each group The test is informativea positive result increases the relative likelihood of sickness anda negative result increases the relative likelihood of health forany prior Formally

PreththornjsTHORN

PreththornjhTHORNgt 1 gt

PrethjsTHORN

PrethjhTHORNeth4THORN

This condition has clear implications the representative personwho tests positive is sick while the representative person whotests negative is healthy Following Proposition 2 the DMreacts to the test by moving his priors too far in the right di-rection generating extreme stereotypes He greatly boosts hisassessment that a positively tested person is sick but also thata negatively tested person is healthy Because most people arehealthy the DMrsquos assessment about the group that tested neg-ative is fairly accurate but is severely biased for the group that

FIGURE I

SAT Mathematics Scores by Gender (2013)

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tested positive This analysis formalizes Tversky andKahnemanrsquos (1983) verbal account of base rate neglect23

The same mechanism may underlie several other instanceswhere DMs overweight diagnostic information When assessingan employeersquos skill level an employer attributes high perfor-mance to high skill because high performance is the distinctivemark of a talented employee Because he neglects the possibilitythat some talented employees perform poorly and that somenontalented ones perform well (perhaps due to stochasticity inthe environment) the employer has too much faith in skill andneglects the role of luck in accounting for the output Similarlywhen assessing the performance of firms in a hot sector of theeconomy (eg G = internet) an investor recalls highly successfulfirms in that sector (t = return of Google Amazon etc) He ne-glects the possibility of firms being unsuccessful because lack ofsuccess is statistically nondiagnostic and psychologically nonrep-resentative of a growing sectormdasheven if it is likely This causesexcessive optimism (in that the expectation of growth is unrea-sonably high) and overconfidence (in that the variability in earn-ings growth considered possible is truncated) True the hot sectormay have better growth opportunities on average but represen-tativeness exaggerates this feature and induces the investor toneglect a significant risk of failure

IV Evidence on Representativeness and Stereotypes

Testing our model requires evaluating the beliefs individualshold about a target group against the true distribution of thattarget group over an attribute space An ideal data set would

23 Our account is distinct from a mechanical underweighting of base rates inBayes rule as in Grether (1980) and Bodoh-Creed Benjamin and Rabin (2013) Inthose models upon receiving the test results the DM can update his beliefs in thewrong direction he can be less confident that a person is healthy after a negativetest than under his prior which cannot happen in our model Although this predic-tion of our model seems consistent with introspection we are not aware of experi-mental evidence on this point Griffin and Tversky (1992) present evidenceconsistent with pure neglect of base rates but in a significantly different tasknamely inferring the bias of a coin from a history of coin flips Such experimentsare hard to compare with the predictions of our model because subjects are asked togenerate distributions of different numbers of coin flips in their minds which is amuch more involved task than to recall types of a given distribution Their assess-ments then might be wrong for other reasons See Bodoh-Creed Benjamin andRabin (2013) for a detailed discussion

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consist of naturally defined groups with known distributions overa given space of types and a corresponding set of beliefs about thedistribution of each group over that space of types This wouldallow us to test for exaggeration of true differences betweengroups and to ask whether this exaggeration is well predictedby overweighting representative types To identify a causal rolefor representativeness or context dependence we would need ex-ogenous variation in either the comparison group ndashG or in thedistributions over the type spaces This is unavailable in existingdata sets Accordingly we take a two-pronged approach First wecreate a controlled laboratory environment that allows us toinduce the exogenous variation in representative types that weneed to test causality then we reanalyze existing field evidence tocheck for consistency with our predictions

In testing our model we focus on the two main implicationsof representativeness-based stereotypes

Context dependence the stereotype of a target group de-pends on the characteristics of the reference group it iscompared to

Kernel of truth stereotypes depend on group character-istics andmdashin most (precisely characterized) settingsmdashare slanted toward representative types

We test the first property with a lab experiment (SectionIVA) We then turn to survey data on beliefs about US politicalgroups (Section IVB) for an empirical analysis that explores thesecond property The survey data are more tightly linked to ourinterest in social stereotypes The laboratory experiment allowsus to directly test the role of representativeness in generatingcontext dependent beliefs Online Appendixes F and G provideall details and additional results for the experiments and fieldevidence

IVA Lab Evidence on Representativeness and ContextDependence

The influence of the representativeness heuristic on recalland on beliefs has been extensively documented in the lab(Kahneman and Tversky 1972 1973) Our goal is to considerhow representativeness as formalized in equation (2) gives riseto context-dependent beliefs To our knowledge the possibility

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that representativeness may generate context dependence hasnot been tested before

To assess this prediction we perform a controlled laboratoryexperiment that allows us to isolate representativeness frommany confounding factorsmdashhistorical sociological or other-wisemdashthat may affect stereotype formation in the real worldWe construct our own groups of ordinary objects creating atarget group G and a comparison group ndashG We hold thetarget group G fixed and explore how participant impressions ofit change as we change the comparison group ndashG and thusrepresentativeness

We conducted several experiments in the laboratory and onAmazon Mechanical Turk Each involves a basic three-stepdesign First participants are shown the target group and a ran-domly assigned comparison group for 15 seconds In this timedifferences between groups can be noticed but the groupsrsquo precisecompositions cannot be memorized The second step consists of afew filler questions which briefly draw the participantsrsquo cognitivebandwidth away from their observation Finally participants areasked to assess the groups they saw Participants are incentiv-ized to provide accurate answers

We randomly assign participants to either the Control or theRepresentativeness condition In the Control condition G and ndashGhave nearly identical distributions so that all types are similarlyrepresentative for each group In the Representativeness condi-tion ndashG is changed in such a way that a certain type becomes veryrepresentative for G Context dependence implies that the assess-ment of G should now overweight this representative type eventhough the distribution of G itself has not changed

We ran six experiments of this form with design changesfocused on reducing participant confusion and removing con-founds We describe the final and most refined version of theseexperiments here In an attempt to provide a overview of the re-sults while remaining concise we provide the results from pooledspecifications that use all data collected In Online Appendix Fwe offer additional details and report all experiments conductedWe also give instructions and materials for each experiment thefull data set is available by request

Consider first the experiment illustrated in Figure II Agroup of 25 cartoon girls is presented next to a group of 25 cartoonboys in T-shirts of different colors blue green or purple In theControl condition (Figure II Panel a) the groups have identical

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color distributions (13 purple 12 green) so no color is represen-tative of either group The Representativeness condition (Panel b)compares the same group of girls with a different group of boysfor whom green shirts are replaced with blue shirts Now onlygirls wear green and only boys wear blue These colors althoughstill not the most frequent for either group are now most repre-sentative For each group girls and boys participants are asked anumber of questions concerning the frequency of T-shirts of dif-ferent colors worn by that group

Applying our model in the control condition the type space isT frac14 fgreen purpleg and the groups are G = girls and ndashG = boysGiven that the color distributions are identical across groups both

types are equally representativegreengirls

greenboysfrac14 1 frac14

purplegirls

purpleboys As a result

assessment of G should be correct on average stcontrolgreengirls frac14 greengirls

and stcontrolpurplegirls frac14 purplegirls for any weighing function (the same is

true about assessments of ndashG)In the treatment condition the distribution of shirt colors re-

mains the same for girls For boys green shirts are changed intoblue Thus the type space changes to T frac14 fgreen purple bluegand the representative color for girls becomes greengreengirls

greenboysfrac14 1 gt 1 frac14

purplegirls

purpleboys while that for boys becomes blue As

a result in the treatment condition subjects should inflate the

frequency of green shirts relative to the truth sttreatmentgreengirls

gt greengirls (the same should happen to assessments of blueshirts for boys) We also expect the assessed frequency of greenshirts to go up relative to the control condition namely

sttreatmentgreengirls gt stcontrol

greengirls Critically the only factor that varies

across treatments is the representativeness of the 12-colorshirt Thus if we see differences across conditions the causalrole of representativeness-based recall in shaping group judg-ments is clear24

24 We vary which colors are used in which roles across participants Someparticipants saw this particular color distribution while others see for examplegreen as the modal color and purple as the diagnostic color for boys in theRepresentativeness condition and blue as the diagnostic color for girls in theRepresentativeness condition We vary the colors across the roles to avoid con-founding the characteristics of any particular color with its diagnosticity

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FIG

UR

EII

T-S

hir

tsE

xp

erim

ent

Fig

ure

sap

pea

red

inco

lor

top

art

icip

an

tsin

the

exp

erim

ent

For

clari

ty

we

have

ad

ded

ale

tter

toea

chT

-sh

irt

toid

enti

fyth

eco

lor

for

the

read

er

lsquolsquoGrsquorsquo

ind

icate

sgre

en

lsquolsquoPrsquorsquo

ind

icate

sp

urp

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lsquolsquoBrsquorsquo

ind

icate

sblu

eT

hes

ele

tter

sd

idn

otap

pea

rto

part

icip

an

tsan

dare

for

read

erre

fere

nce

only

P

lease

see

onli

ne

ver

sion

ofp

ubli

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icle

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pea

red

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icip

an

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We collected data from 301 participants using this T-shirtsdesign25 Since the number of green and purple shirts is verysimilar we first ask each participant the simplest question ofwhich shirt color is modal Next we ask participants to assessthe share of green and purple shirts

Consistent with the role of representativeness participantsassigned to the Representativeness condition are 105 percentagepoints more likely to recall the less frequent color (green for girlsor blue for boys) as the modal color when it is representative of agroup (35 of participants guess the less frequent color is modalin the Control condition this proportion increases to 46 in theRepresentativeness condition p = 01 estimated from a probitregression reported in Online Appendix F)

We now turn to subjectsrsquo estimates of how many T-shirts ofeach color they saw in each group In both conditions the truedifference in counts is 1 (13 purple shirts 12 green or blue shirts)In the Control condition participants on average believe they saw054 more purple shirts than green or blue shirts In theRepresentativeness condition participants believe they saw072 fewer purple shirts than green or blue shirts (the acrosstreatment difference is significant with p = 01 from OLS regres-sion reported in Online Appendix F)

In total we collected data for six experiments of this generalstructure gathering evidence from more than 1000 participantsAs we describe in Online Appendix F although there is substan-tial variation across experiments when we pool all of the data wefind significant aggregate treatment effects in line with a role ofrepresentativeness in judgment We employ four different unor-dered types designs similar to the T-shirts experiment using sixsamples (four online and two in the laboratory) with 741 partic-ipants We find effects in the predicted direction for five of the sixsamples Using a probit regression that pools the data for theseunordered type experiments we find that participants are 93 per-centage points more likely to guess that the less frequent type ismodal when it is representative than when it is not (p = 002) Wealso run a family of ordered types experiments (two designs fivesamples 402 participants) Unlike the simpler T-shirts style

25 Throughout our analysis we exclude any participant who participated in aprevious version of the experiment and any participant who self-identified as color-blind In Online Appendix F we show that our results are unchanged if we includethese additional observations

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design the theoretical predictions for the ordered types designsare more sensitive to the specific assumptions one makes aboutthe weighting function of the DM26 We find effects in the pre-dicted direction for three of the five samples As we discuss inmore detail in Online Appendix F the ordered types resultsvary by platform with consistently stronger results on AmazonMechanical Turk than in the laboratory samples Pooling all or-dered types experiments participants are 93 percentage pointsmore likely to guess that the group of interest has a greater av-erage than the comparison group when the right tail is represen-tative (p = 062) Given our simple experimental setting withgroups of mundane objects we interpret our resultsmdasha signifi-cant and reasonably sized impact on average beliefsmdashas an im-portant proof of concept the presence of representative typesbiases ex post assessment

IVB Empirical Evidence on Political Stereotypes

We examine two data sets on political preferences and be-liefs about political preferences in the United States We inves-tigate the roles of representativeness and context dependence byseparately testing for hypotheses that allow us to assess the lead-ing theories of stereotypes

First we test whether beliefs are correct or depart systemat-ically from the truth The statistical discrimination approachbuilds on the assumption that people hold rational expectationsof group traits Comparing beliefs to the truth allows us to assessthe validity of this assumption in our data

Second we test if beliefs depart from the truth by exagger-ating (mean) differences among groups per the kernel of truthhypothesis This is an implicit test of context dependence be-cause it implies that beliefs about the target groups are shapednot only by that grouprsquos characteristics but also by those of thereference group27

Third we test if distortions in beliefs can be accounted for bythe overweighting of highly representative types (defined astypes that are relatively more frequent in the target relative to

26 This is due in part to our choice to not study MLRP distributions We moti-vate and discuss this design decision in Online Appendix F

27 Of course unlike in the laboratory experiment in this setting we cannot testfor context dependence by exogenously varying the reference group

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the reference group) The second and third tests address the keypredictions of our model

1 The Data We have two data sets on political preferences andbeliefs about political preferences The first data set from GrahamNosek and Haidt (GNH 2012) contains data from the MoralFoundations Questionnaire Respondents (1174 self-identified lib-erals and 500 self-identified conservatives) answer questions abouttheir position on a subset of 45 issues 20 moral relevance state-ments (eg lsquolsquowhen you decide whether something is right orwrong to what extent are the following considerations relevantto your thinkingrsquorsquo) and 25 moral judgments (eg lsquolsquoindicate theextent to which you would agree or disagreersquorsquo) For each issue arandomly determined subset of participants states their own posi-tion another subset states their belief on the position of a lsquolsquotypicalliberalrsquorsquo and a third subset states their belief on the position of alsquolsquotypical conservativersquorsquo The data thus include the distribution overpositions for both liberal and conservatives as well as the averagebelieved typical position of liberals and of conservatives on the 45issues Each position is elicited on 1ndash6 scale

The second data set comes from the American NationalElection Survey (ANES) and contains data from more than20000 respondents between 1964 and 201228 The surveycovers political issues of the day such as the optimal amount ofgovernment spending and service provision (1984ndash2000) or theplace of women in society (1972ndash1998) We focus on the 10 issuesthat ask participants to respond on a 1ndash7 scale (rather than justindicate binary agreement or disagreement) all 10 issues areasked in multiple years Participants are asked to provide theirown position on the scale and their believed position of theDemocratic and Republican parties (lsquolsquoWhere would you placethe Democratic [Republican] party on this scalersquorsquo) The data in-clude for each issue-year observation the distribution of partic-ipant positions for self-identified liberals and self-identifiedconservatives as well as the distribution of believed typical posi-tions of the Democratic and Republican parties

28 These data are publicly available at httpwwwelectionstudiesorgstudy-pagesanes_timeseries_cdfanes_timeseries_cdfhtm

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2 Empirical Strategy Our analysis focuses on beliefs abouttwo groups Conservatives and Liberals The types are the possi-ble positions for each issue (1 2 6 7) For the GNH data weinterpret beliefs about the lsquolsquotypicalrsquorsquo element of a group to coincidewith the believed average position in that group Similarly forthe ANES data we use the believed party positions as a proxy forbelieved mean of each group29 We then take as a benchmark thehypothesis that individuals hold accurate beliefs about eachgroup and in particular that believed mean position shouldequal true mean position at least on average across subjectsThe accurate beliefs hypothesis underlies the most common eco-nomic model of stereotyping statistical discrimination

To assess our representativeness-based model we perform aregression exercise To test our model in a linear regressionframework we rely on linear approximations of the weightingfunction Our model then yields two regression specifications

PROPOSITION 4 Let G 2 fconservative liberal g and assume

ht h tG

tG

be a differentiable and strictly increasing weight-

ing function as in Definition 2 The following hold as a first-order approximation around identical distributions G

Gfrac14 1

(i) Kernel of truth regression There exists a constant gt 0such that

EstethtjGTHORN frac14 EethtjGTHORNeth1thorn THORN EethtjGTHORNeth5THORN

(ii) Representativeness regression Denote H frac14 fT 2 Tg

the right tail of types and RconsH frac14

PHtconsPHtlib

as the average

representativeness of right tail types for conservatives

29 This assumption is consistent with the authorsrsquo interpretation of the GNHdata (GNH 2012) and with previous studies using ANES (eg Westfall et al 2015)Furthermore to the extent that this assumption holds equally well for most issueswithin a data set our focus on cross-issue differences should allow us to test thepredictions of our model even with an imperfect proxy for beliefs of mean positionsFinally the data provide some insight into whether subjects are reporting (per-ceived) modal or mean types As we show the modal type is a poor prediction ofstated beliefs while a distorted mean slanted toward representative types is anaccurate prediction of stated beliefs

STEREOTYPES 1783

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Under the further approximation where tcons

tlibampRcons

H for

t 2 H

EstethtjconsTHORN frac14 EethtjconsTHORN thorn consethR

consH 1THORNeth6THORN

EstethtjlibTHORN frac14 EethtjlibTHORN libethR

consH 1THORNeth7THORN

where lcons and llib are positive constants

The first regression allows us to test for the kernel of truthhypothesis and the second set of regressions allows us to test forthe role of representativeness

Equation (5) says that respondents in our model inflate theaverage position of a group say the conservatives if and only ifthe group has a higher average position than the other groupnamely the liberals Formally EstethtjconsTHORN gt EethtjconsTHORN if and onlyif EethtjconsTHORN gt EethtjlibTHORN Because in our measurement scale highertypes mean lsquolsquomore conservativersquorsquo we expect (i) believed conserva-tive average to be higher than the truth and (ii) the extent ofoverstatement to decrease in the average liberal position EethtjlibTHORNConversely we expect the average liberal position to be lowerthan the truth the more so the higher the average conservativeposition EethtjconsTHORN

As previously discussed the basis of these predictions is con-text dependence information about the distribution of ndashG is rel-evant for the beliefs about G This context dependence isinconsistent with rational expectations in which only thegrouprsquos own means should affect beliefs We test the hypothesisthat the true mean EethtjGTHORN is a significant predictor of the believedmean E

stethtjGTHORN with a positive sign and the other grouprsquos truemean EethtjGTHORN is a predictor of the believed mean with a negativesign

Equations (6) and (7) say that repondentsrsquo assessment bias isshaped by representativeness When the right tail is more repre-sentative for conservatives (Rcons

H 1 positive and large) partici-pants should inflate the average conservative position more(higher E

stethtjconsTHORN EethtjconsTHORN) and deflate the average liberal po-sition more (lower E

stethtjlibTHORN EethtjlibTHORN) We test the hypothesisthat the inflation in conservative positions is positively associatedwith the representativeness of the right tail for the conservativesand the inflation in liberal positions is negatively associated with

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it Once again the representativeness of the right tail is com-puted using the true distribution of positions

In equations (6) and (7) in many cases the representative tailis also the most likely one As a consequence these tests cannotdistinguish a representativeness-based from a likelihood-basedmodel of distorted beliefs We perform two additional testsFirst we run versions of equations (6) and (7) in which we controlfor the likelihood of tails (see Table A4 in Online Appendix G)Second we compute numerically the predictions of a representa-tiveness-based model of stereotypes and a likelihood-based modelof stereotypes We then assess which of these two is better able tomatch the data on beliefs

3 Empirical Results To begin we illustrate the structure ofthe data and the nature of our predictions with two simple exam-ples from the GNH data set focusing on beliefs about conserva-tives In example 1 participants are asked about their agreementwith the statement lsquolsquoIt can never be right to kill a human beingrsquorsquoIn example 2 participants are asked about the moral relevance oflsquolsquowhether or not someone cared for someone weak or vulnerablersquorsquoAs can be seen in Figure III in example 1 the modal position(strongly disagree (1)) and most representative positions(strongly disagree (1)) coincide for conservatives In contrast inexample 2 in Figure III the most representative types (slightlyrelevant (3) not at all relevant (1)) are not most likely for theconservative group Following Proposition 1 we predict that be-liefs will be distorted in the direction of the most representativetypes Thus we expect more exaggeration in example 2 than inexample 1 since in example 2 the most representative types (inthe left tail) are far from the modal type whereas in example 1they coincide This is what we find the conservative position isexaggerated by only 009 positions in Example 1 (true mean 299believed mean 290) but by 106 positions in Example 2 (truemean 421 believed mean 315)

In the full data sets we treat each (issue year) pair as anobservation and we cluster standard errors at the issue level Forthe GNH data we have 45 observations 45 issues measured inthe same year For the ANES data we have 66 observations 10issues measured in multiple years To begin we simply docu-ment systematic exaggeration in both data sets This is a primaryfocus of the original analysis in GNH (2012) and also in Westfall

STEREOTYPES 1785

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FIGURE III

Two Examples

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et al (2015)rsquos analysis of the ANES data30 Figure IV shows thatthe believed difference between typical conservative and typicalliberal positions is larger than the true difference in mean posi-tions for 109 of the 111 observations The data for both GNH(squares) and ANES (triangles) lie above the 45-degree line(dashed)31 Average exaggeration is 062 positions on the scale(066 in the GNH data 059 in the ANES data)32

The systematic and significant exaggeration of mean differ-ences suggests that the benchmark model of accurate beliefs ismissing something important Indeed this exaggeration reflectsthe fact that believed means are typically more extreme than truemeans First note that the kernel of truth regression (equation(5)) generates exaggeration of mean differences just as docu-mented in Figure IV

EstethtjGTHORN E

stethtjGTHORN frac14 eth1thorn 2THORN frac12EethtjGTHORN EethtjGTHORN

To bring this prediction to the data we regress the believedmean position for each group EBethtjGTHORN on the true mean of thegroup EethtjGTHORN and the true mean of the comparison groupEethtjGTHORN across issues We do this for each group (liberals con-servatives) in each data set separately We also present pooledspecifications that combine the data sets to make a prediction fora given group (liberals conservatives) In these pooled specifica-tions we include a dummy variable indicating whether theobservation came from the ANES data set For all specificationswe cluster observations at the issue level33 The results from re-gression are shown in Table I In every specification we find thatEethtjGTHORN is a significant predictor of EBethtjGTHORN with the predicted pos-itive sign Crucially for five of the six specifications the mean of

30 Chambers and Melnyk (2006) also find evidence of exaggeration of truedifferences in beliefs about political positions

31 For convenience we recode all issues so that the high end of the scale (67)represents the stereotypically more conservative position

32 A natural question to ask is how beliefs vary across liberals and conserva-tives That is do beliefs about a group G depend on membership in G versus ndashG Ourmodel does not speak to this issue However in Online Appendix G we show thatthe results we document below hold for both beliefs held by conservatives and be-liefs held by liberals see Tables A9 A10 and A11

33 In general the results presented below for the ANES data are not largelyimpacted by the decision to cluster at the issue level Similar results are obtained ifthe data are not clustered

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the comparison group EethtjGTHORN is also a significant predictor ofE

BethtjGTHORN with the predicted negative signAlthough these results provide strong evidence of context

dependence and are consistent with our model they do not pindown a role for representativeness of types Our next test relatesthe magnitude of representativeness of tail types to the magni-tude of belief distortions

To this end we implement the regressions in equations (6)and (7) Following Proposition 4 we compute the average repre-

sentativeness of tail types for conservatives RconsH frac14

PtT2tconsPtT2tlib

We

again test the hypothesis that RconsH is a significant predictor of Est

ethtjconsTHORN with a positive sign and a predictor of EstethtjlibTHORN with a

negative sign Table II shows that conditional on true mean RconsH

predicts believed mean for each group G as expected The firstthree specifications display the results for predicting beliefs heldabout conservatives In both data sets the average representa-tiveness of tail types for conservatives is a significant positivepredictor of beliefs held about conservatives The final three spe-cifications display the results for predicting beliefs held about

FIGURE IV

Exaggeration of Differences

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liberals We find that the average representativeness of tail typesfor conservatives is a negative predictor of beliefs held about lib-erals This effect is significant in the GNH data and marginallysignificant in the ANES data

We present several additional results in Online Appendix GTo further examine the role of representativeness in driving be-liefs we first show the results of Table II carry through when we

TABLE II

AVERAGE REPRESENTATIVENESS OF TAIL POSITIONS PREDICTS BELIEFS

OLS Predicting Believed Mean of Group G for Each Issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position

of group G for issue

078 024 051 072 018 041

(006) (008) (009) (005) (005) (010)

Avg rep of tail types for

conservatives RconsH

019 055 025 014 012 024

(007) (022) (008) (006) (007) (005)

Constant 101 260 184 093 271 201

(026) (045) (029) (022) (025) (032)

R2 082 048 060 091 031 070

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

TABLE I

INFORMATION ABOUT ndashG PREDICTS BELIEFS ABOUT G

OLS predicting believed mean of group G for each issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position of

conservatives for issue

102 098 096 021 019 025

(0097) (0133) (0076) (0060) (0116) (0060)

True mean position of

liberals for issue

035 086 058 0987 039 073

(0106) (0134) (0131) (0066) (0106) (0135)

Constant 151 335 235 069 258 156

(0195) (0269) (0279) (0122) (0249) (0270)

R2 083 053 066 092 032 068

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

STEREOTYPES 1789

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control for the average likelihood on the tail positions (see Table A4in Online Appendix G) Most tellingly we use the model to predictbeliefs across issues and compare those to the data For simplicitywe use the rank-based truncation specification to predict mean be-liefs when stereotypes include the d most representative types ford frac14 1 T We compare these predictions to those of a model inwhich beliefs are obtained by restricting the distribution to the dmost likely types Our benchmark for both models is predicting thebelieved mean from the entire distribution where d = T We showthat the predictions of the rank-based truncation model with d = 4or 5 compare favorably to both a likelihood-based truncation model(with any d) and the accurate beliefs benchmark Interestingly thisresult suggests that stereotypical beliefs are well approximated byneglecting the least representative types (as opposed to focusingonly on the most representative types) and so represent a moderatethough systematic departure from the standard benchmarkFinally we show that the results we document above hold forboth beliefs held by conservatives and beliefs held by liberals (seeTables A9 A10 and A11 in Online Appendix G)

V Conclusion

We present a model of stereotypical thinking in which DMsmaking predictions about a group overweight the grouprsquos mostdistinctive types These overweighted types are not the mostlikely ones given the DMrsquos data but the most representativeones in the sense of being the most diagnostic of the group rela-tive to other groups Representativeness implies that what ismost distinctive of a group depends on what group it is comparedwith We present experimental evidence that confirms this con-text dependence in recall-based assessments of groups Finallywe evaluated the predictions of the model using political data fromexisting large-scale surveys We find context dependence to be akey feature of beliefs Given the richness of the political data wecan go a step further and identify a role for representativeness inparticular As the representativeness of tail types increases beliefsof a group are distorted in the direction of that tail

Our approach provides a parsimonious and psychologicallyfounded account of how DMs generate simplified representationsof reality from social groups to stock returns and offers a unifiedaccount of disparate pieces of evidence relating to this type of

QUARTERLY JOURNAL OF ECONOMICS1790

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uncertainty The model captures the central fact that stereotypeshighlight the greatest difference between groups thus explainingwhy some stereotypes are very accurate while others lack valid-ity Still stereotypes often have a kernel of truth when they arebased on systematicmdasheven if smallmdashdifferences between groupsThis logic allows us to describe a number of heuristics and psy-chological biases many of which arise in the context of predictionproblems Generically our model generates overreaction to diag-nostic information

Our model is based on representativeness and does not cap-ture all the features of stereotypical thinking However it cap-tures perhaps the central feature when we think of a group wefocus on what is most distinctive about it and neglect or under-weight the rest

Saeuroıd Business School University of Oxford

Ohio State University and Harvard Business School

Universita Bocconi and Innocenzo Gasparini Institute

for Economic Research

Harvard University

Supplementary Material

An Online Appendix for this article can be found at QJEonline (qjeoxfordjournalorg)

References

Adorno Theodor Else Frenkel-Brunswik Daniel Levinson and Nevitt SanfordThe Authoritarian Personality (New York Harper amp Row 1950)

Arrow Kenneth lsquolsquoThe Theory of Discriminationrsquorsquo in Discrimination in LaborMarkets Orley Ashenfelter and Albert Rees eds (Princeton NJPrinceton University Press 1973)

Ashton Michael and Victoria Esses lsquolsquoStereotype Accuracy Estimating theAcademic Performance of Ethnic Groupsrsquorsquo Personality and SocialPsychology Bulletin 25 (1999) 225ndash236

Barberis Nicholas Andrei Shleifer and Robert Vishny lsquolsquoA Model of InvestorSentimentrsquorsquo Journal of Financial Economics 49 (1998) 307ndash343

Bayer Sylvia lsquolsquoThe Accuracy of Academic Gender Stereotypesrsquorsquo Sex Roles 40(1999) 787ndash813

Benjamin Dan James Choi and Joshua Strickland lsquolsquoSocial Identity andPreferencesrsquorsquo American Economic Review 100 (2010) 1913ndash1928

Benjamin Dan Matthew Rabin and Collin Raymond lsquolsquoA Model of Non-Belief inthe Law of Large Numbersrsquorsquo Journal of the European Economic Association15 (2015) 515ndash544

Bertrand Marianne lsquolsquoNew Perspectives on Genderrsquorsquo Handbook of LaborEconomics 4 (2011) 1543ndash1590

Bodoh-Creed Aaron Dan Benjamin and Matthew Rabin lsquolsquoThe Dynamics of Base-Rate Neglectrsquorsquo mimeo Haas Business School 2013

STEREOTYPES 1791

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

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Bohnet Iris Alexandra van Geen and Max Bazerman lsquolsquoWhen PerformanceTrumps Gender Bias Joint versus Separate Evaluationrsquorsquo ManagementScience 5 (2016) 1225ndash1234

Bordalo Pedro Nicola Gennaioli and Andrei Shleifer lsquolsquoSalience Theory of Choiceunder Riskrsquorsquo Quarterly Journal of Economics 127 (2012) 1243ndash1285

mdashmdashmdash lsquolsquoSalience and Consumer Choicersquorsquo Journal of Political Economy 121(2013) 803ndash843

Briton Nancy and Judith Hall lsquolsquoBeliefs about Female and Male NonverbalCommunicationrsquorsquo Sex Roles 32 (1995) 79ndash90

Buser Thomas Muriel Niederle and Hessel Oosterbeek lsquolsquoGenderCompetitiveness and Career Choicesrsquorsquo Quarterly Journal of Economics 129(2014) 1409ndash1447

Carrell Scott Marianne Page and James West lsquolsquoSex and Science How ProfessorGender Perpetuates the Gender Gaprsquorsquo Quarterly Journal of Economics 125(2010) 1101ndash1144

Chambers John and Darya Melnyk lsquolsquoWhy Do I Hate Thee ConflictMisperceptions and Intergroup Mistrustrsquorsquo Personality and SocialPsychology Bulletin 32 (2006) 1295ndash1311

Chan Wayne Robert R McCrae Filip De Fruyt Lee Jussim CorinnaE Lockenhoff Marleen De Bolle Paul T Costa Jr Angelina R SutinAnu Realo Juri Allik Katsuharu Nakazato Yoshiko ShimonakaMartina Hrebıckova Sylvie Graf Michelle Yik Marina Brunner-SciarraNora Leibovich De Figueora Vanina Schmidt Chang-kyo Ahn Hyun-nie Ahn Maria E Aguilar-Vafaie Jerzy Siuta Barbara SzmigielskaThomas R Cain Janet T Crawford Khairul Anwar Mastor Jean-Pierre Rolland Florence Nansubuga Daniel R MiramontezVeronica Benet-Martınez Jerome Rossier Denis Bratko Iris MarusicJamin Halberstadt Mami Yamaguchi Goran Knezevic Thomas A MartinMirona Gheorghiu Peter B Smith Claudio Barbaranelli Lei WangJane Shakespeare-Finch Margarida P Lima Waldemar KlinkoszAndrzej Sekowski Lidia Alcalay Franco Simonetti Tatyana V AvdeyevaV S Pramila and Antonio Terracciano lsquolsquoStereotypes of Age Differences inPersonality Traits Universal and Accuratersquorsquo Journal of Personality andSocial Psychology 103 (2012) 1050ndash1066

Chen Yan Sherry Xin Liu Tracy Xiao and Margaret Shih lsquolsquoWhich Hat to WearImpact of Natural Identities on Coordination and Cooperationrsquorsquo Games andEconomic Behavior 84 (2014) 58ndash86

Coffman Katherine lsquolsquoEvidence on Self-Stereotyping and the Contribution ofIdeasrsquorsquo Quarterly Journal of Economics 129 (2014) 1625ndash1660

Cunningham Tom lsquolsquoComparisons and Choicersquorsquo mimeo Stockholm University2013

Diekman Amanda Alice Eagly and Patrick Kulesa lsquolsquoAccuracy and Bias in theStereotypes about the Social and Political Attitudes of Women and MenrsquorsquoJournal of Experimental Social Psychology 38 (2002) 268ndash282

Eccles Jacquelynne S Janis E Jacobs and Rena D Harold lsquolsquoGender RoleStereotypes Expectancy Effects and Parentsrsquo Socialization of GenderDifferencesrsquorsquo Journal of Social Issues 46 (1990) 183ndash201

Fryer Roland and Matthew Jackson lsquolsquoA Categorical Model of Cognition andBiased Decision-Makingrsquorsquo BE Journal of Theoretical Economics 8 (2008)1ndash42

Fryer Roland and Steven Levitt lsquolsquoAn Empirical Analysis of the Gender Gap inMathematicsrsquorsquo American Economic Journal Applied Economics 2 (2010)210ndash240

Gennaioli Nicola and Andrei Shleifer lsquolsquoWhat Comes to Mindrsquorsquo Quarterly Journalof Economics 125 (2010) 1399ndash1433

Gennaioli Nicola Andrei Shleifer and Robert Vishny lsquolsquoNeglected RisksFinancial Innovation and Financial Fragilityrsquorsquo Journal of FinancialEconomics 104 (2012) 452ndash468

Gilens Martin lsquolsquoRace and Poverty in America Public Misperceptions and theAmerican News Mediarsquorsquo Public Opinion Quarterly 60 (1996) 515ndash541

Glaeser Edward lsquolsquoThe Political Economy of Hatredrsquorsquo Quarterly Journal ofEconomics 120 (2005) 45ndash86

QUARTERLY JOURNAL OF ECONOMICS1792

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Glover Dyland Amanda Pallais and William Pariente lsquolsquoDiscrimination as a Self-Fulfilling Prophecy Evidence from French Grocery Storesrsquorsquo mimeo HarvardUniversity 2015

Goldin Claudia Lawrence Katz and Ilyana Kuziemko lsquolsquoThe Homecoming ofAmerican College Women The Reversal of the College Gender GaprsquorsquoJournal of Economic Perspectives 20 (2006) 133ndash156

Graham Jesse Brian Nosek and Jonathan Haidt lsquolsquoThe Moral Stereotypes ofLiberals and Conservatives Exaggeration of Differences across thePolitical Spectrumrsquorsquo PLoS One 7 (2012) 1ndash13

Grether David lsquolsquoBayes Rule as a Descriptive Model The RepresentativenessHeuristicrsquorsquo Quarterly Journal of Economics 95 (1980) 537ndash557

Griffin Dale and Amos Tversky lsquolsquoThe Weighing of Evidence and theDeterminants of Confidencersquorsquo Cognitive Psychology 24 (1992) 411ndash435

Guiso Luigi Ferdinando Monte Paola Sapienza and Luigi Zingales lsquolsquoCultureGender and Mathrsquorsquo Science 320 (2008) 1164ndash1165

Hilton James and William Von Hippel lsquolsquoStereotypesrsquorsquo Annual Review ofPsychology 47 (1996) 237ndash271

Hyde Janet Sara Lindberg Marcia Linn Amy Ellis and Caroline WilliamslsquolsquoGender Similarities Characterize Math Performancersquorsquo Science 321 (2008)494ndash495

Judd Charles and Bernardette Park lsquolsquoDefinition and Assessment of Accuracy inSocial Stereotypesrsquorsquo Psychological Review 100 (1993) 109ndash128

Jussim Lee Jarret Crawford Stephanie Anglin John Chambers Sean Stevensand Florette Cohen lsquolsquoStereotype Accuracy One of the Largest and MostReplicable Effects in All of Social Psychologyrsquorsquo in The Handbook ofPrejudice Stereotyping and Discrimination Todd Nelson ed (MahwahNJ Lawrence Erlbaum 2015)

Kahneman Daniel and Amos Tversky lsquolsquoSubjective Probability A Judgment ofRepresentativenessrsquorsquo Cognitive Psychology 3 (1972) 430ndash454

mdashmdashmdash lsquolsquoOn the Psychology of Predictionrsquorsquo Psychological Review 80 (1973) 237ndash251

Kaplowitz Stan Bradley Fisher and Clifford Broman lsquolsquoHow Accurate ArePerceptions of Social Statistics about Blacks and Whitesrsquorsquo Public OpinionQuarterly 67 (2003) 237ndash243

Kersten Daniel Pascal Mamassian and Alan Yuille lsquolsquoObject Perception asBayesian Inferencersquorsquo Annual Review of Psychology 55 (2004) 271ndash304

Klein Richard Kate A Ratliff Michelangelo Vianello Reginald B Adams JrStepan Bahnik Michael J Bernstein Konrad Bocian Mark J BrandtBeach Brooks Claudia Chloe Brumbaugh Zeynep CemalcilarJesse Chandler Winnee Cheong William E Davis Thierry DevosMatthew Eisner Natalia Frankowska David Furrow Elisa Maria GallianiFred Hasselman Joshua A Hicks James F Hovermale S Jane HuntJeffrey R Huntsinger Hans IJzerman Melissa-Sue John Jennifer A Joy-Gaba Heather Barry Kappes Lacy E Krueger Jaime Kurtz CarmelA Levitan Robyn Mallett Wendy L Morris Anthony J Nelson JasonA Nier Grant Packard Ronaldo Pilati Abraham M RutchickKathleen Schmidt Jeanine L Skorinko Robert Smith Troy G SteinerJustin Storbeck Lyn M Van Swol Donna Thompson Anna van rsquot VeerLeigh Ann Vaughn Marek Vranka Aaron Wichman Julie A Woodzickaand Brian A Nosek lsquolsquoInvestigating Variation in Replicability A ManyLabs Replication Projectrsquorsquo Social Psychology 45 (2014) 142ndash152

Lundberg Shelly and Richard Startz lsquolsquoPrivate Discrimination and SocialIntervention in Competitive Labor Marketsrsquorsquo American Economic Review73 (1983) 340ndash347

Madon Stephanie Max Guyll Kathy Aboufadel Eulices Montiel Alison SmithPolly Palumbo and Lee Jussim lsquolsquoEthnic and National Stereotypes ThePrinceton Trilogy Revisited and Revisedrsquorsquo Personality and SocialPsychological Bulletin 27 (2001) 996ndash1010

Martin Carol lsquolsquoA Ratio Measure of Sex Stereotypingrsquorsquo Journal of Personality andSocial Psychology 52 (1987) 489ndash499

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ibrary on October 28 2016

httpqjeoxfordjournalsorgD

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McCauley Clark Krishna Thangavelu and Paul Rozin lsquolsquoSex Stereotyping ofOccupations in Relation to Television Representations and Census FactsrsquorsquoBasic and Applied Social Psychology 9 (1988) 197ndash212

Mullainathan Sendhil lsquolsquoThinking through Categoriesrsquorsquo mimeo HarvardUniversity 2002

Ortoleva Pietro and Erik Snowberg lsquolsquoOverconfidence in Political BehaviorrsquorsquoAmerican Economic Review 105 (2015) 504ndash535

Phelps Edmund lsquolsquoThe Statistical Theory of Racism and Sexismrsquorsquo AmericanEconomic Review 62 (1972) 659ndash661

Pope Devin and Justin Sydnor lsquolsquoGeographic Variation in the Gender Differencesin Test Scoresrsquorsquo Journal of Economic Perspectives 24 (2010) 95ndash108

Rabin Matthew lsquolsquoInference by Believers in the Law of Small NumbersrsquorsquoQuarterly Journal of Economics 117 (2002) 775ndash816

Rabin Matthew and Joel Schrag lsquolsquoFirst Impressions Matter A Model ofConfirmatory Biasrsquorsquo Quarterly Journal of Economics 114 (1999) 37ndash82

Rabin Matthew and Dimitri Vayanos lsquolsquoThe Gamblerrsquos and Hot-Hand FallaciesTheory and Applicationsrsquorsquo Review of Economic Studies 77 (2010) 730ndash778

Reuben Ernesto Paola Sapienza and Luigi Zingales lsquolsquoHow Stereotypes ImpairWomenrsquos Careers in Sciencersquorsquo Proceedings of the National Academy ofSciences 111 (2014) 4403ndash4408

Rosch Eleanor lsquolsquoNatural Categoriesrsquorsquo Cognitive Psychology 4 (1973) 328ndash350Ryan Carey S lsquolsquoAccuracy of Black and White College Studentsrsquo In-Group and

Out-Group Stereotypesrsquorsquo Personality and Social Psychology Bulletin 22(1996) 1114ndash1127

Schneider David The Psychology of Stereotyping (New York Guilford Press2004)

Schneider David Albert Hastorf and Phoebe Ellsworth Person Perception(Reading MA Addison-Wesley 1979)

Shih Margaret Todd Pittinsky and Nalini Ambady lsquolsquoStereotype SusceptibilityIdentity Salience and Shifts in Quantitative Performancersquorsquo PsychologicalScience 10 (1999) 80ndash83

Shih Margaret Todd Pittinsky and Amy Trahan lsquolsquoDomain-Specific Effects ofStereotypes on Performancersquorsquo Self and Identity 5 (2006) 1ndash14

Steele Claude Whistling Vivaldi How Stereotypes Affect Us and What We CanDo (New York Norton 2010)

Tenenbaum Joshua and Thomas Griffiths lsquolsquoThe Rational Basis ofRepresentativenessrsquorsquo 23rd Annual Conference of the Cognitive ScienceSociety (2001) 1036ndash1041

Tversky Amos and Daniel Kahneman lsquolsquoExtensional versus Intuitive ReasoningThe Conjunction Fallacy in Probability Judgmentrsquorsquo Psychological Review 90(1983) 293ndash315

Weinberger Catherin lsquolsquoIs the Science and Engineering Workforce Drawn fromthe Far Upper Tail of the Math Ability Distributionrsquorsquo mimeo UCSB 2005

Westfall Jacob Leaf Van Boven John Chambers and Charles Judd lsquolsquoPerceivingPolitical Polarization in the United States Party Identity Strength andAttitude Extremity Exacerbate the Perceived Partisan DividersquorsquoPsychological Science 10 (2015) 145ndash158

Wolsko Christopher Bernadette Park Charles Judd and Bernd WittenbrinklsquolsquoFraming Interethnic Ideology Effects of Multicultural and Color-BlindPerspectives on Judgments of Groups and Individualsrsquorsquo Journal ofPersonality and Social Psychology 78 (2000) 635ndash654

QUARTERLY JOURNAL OF ECONOMICS1794

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ibrary on October 28 2016

httpqjeoxfordjournalsorgD

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Page 3: I. Introduction · uneducated at the beginning of the 20th century, and as high achievers at the beginning of the 21st (Madon et al. 2001). Social science has produced three broad

and views social stereotypes as special cases of cognitive schemasor theories (Schneider Hastorf and Ellsworth 1979) These the-ories are intuitive generalizations that individuals routinely usein their everyday life and they entail savings on cognitive re-sources Hilton and Von Hippel (1996) define stereotypes aslsquolsquomental representations of real differences between groups [ ]allowing easier and more efficient processing of informationStereotypes are selective however in that they are localizedaround group features that are the most distinctive that providethe greatest differentiation between groups and that show theleast within-group variationrsquorsquo A related lsquolsquokernel-of-truth hypoth-esisrsquorsquo holds that stereotypes are based on some empirical realityas such they are useful but may entail exaggerations (Judd andPark 1993)

We show that this approach to stereotypes is intimately re-lated to another idea from psychology the use of heuristics inprobability judgments (Kahneman and Tversky 1972) Justas heuristics simplify the assessment of complex probabilistichypotheses they also simplify the representation of heteroge-neous groups sometimes causing errors in judgment We for-mally explore this idea by modeling stereotype formation as aconsequence of Kahneman and Tverskyrsquos representativenessheuristic Tversky and Kahneman (1983) write that lsquolsquoan attributeis representative of a class if it is very diagnostic that is therelative frequency of this attribute is much higher in that classthan in the relevant reference classrsquorsquo Following Gennaioli andShleifer (GS 2010) we assume that a type t is representativefor group G relative to a comparison group ndashG if it scores highon the likelihood ratio

Pr ethtjGTHORN

Pr ethtj GTHORNeth1THORN

The most representative types come to mind first and so areoverweighted in judgments Predictions about G are then madeunder a distorted distribution or stereotype that overweightsrepresentative types Our results obtain with minimal assump-tions on such overweighting We describe a number of weightingspecifications and explore their properties

To illustrate the logic of the model consider the stereotypelsquolsquoFlorida residents are elderlyrsquorsquo The proportion of elderly people

STEREOTYPES 1755

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in Florida and in the overall United States population isshown here2

The table shows that the age distributions in Florida and in therest of the United States are very similar Yet someone over 65 ishighly representative of a Florida resident because this age bracket

maximizes the likelihood ratio Pr ethtjFloridaTHORNPr ethtjUSTHORN When thinking about the

age of Floridians then the 65+ type immediately comes to mindbecause in this age bracket Florida is most different from the rest ofthe United States in the precise sense of representativenessRepresentativeness-based recall induces an observer to overweightthe 65+ type in their assessment of the average age of Floridians

This example also illustrates how stereotypes can be inaccu-rate Indeed and perhaps surprisingly only about 17 of Floridaresidents are elderly The largest share of Florida residentsnearly as many as in the overall US population are in the agebracket 19ndash44 which maximizes PrethtjFloridaTHORN Being elderly isnot the most likely age bracket for Florida residents but ratherthe age bracket that occurs with the highest relative frequencyA stereotype-based prediction that a Florida resident is elderlyhas very little validity

The same logic of representativeness suggests that the reasonpeople stereotype the Irish as red-headed is that red hair is morecommon among the Irish than among other groups even though itis not that common in absolute terms The reason people stereo-type Republicans as wealthy is that the wealthy are more commonamong Republicans than Democrats3 In both cases the represen-tation entails judgment errors people overestimate the proportionof red-haired among the Irish or of the wealthy among theRepublicans

2 Data from the 2010 US Census see httpfactfindercensusgovfacestableservicesjsfpagesproductview xhtmlpid=DEC_10_DP_DPDP1ampsrc=pt

3 See httpwwwnytimescompackagespdfpolitics20041107_px_ELECTORATExls

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We find that representativeness often generates fairly accu-rate stereotypes but sometimes causes stereotypes to be inaccu-rate particularly when groups have similar distributions thatdiffer most in unlikely types More generally our model high-lights two critical properties

Stereotypes amplify systematic differences betweengroups even if these differences are in reality verysmall When groups differ by a shift in means stereotyp-ing exaggerates differences in means and when groupsdiffer by an increase in variance stereotyping exagger-ates the differences in variances In these cases (but notalways) representativeness yields stereotypes that con-tain a lsquolsquokernel of truthrsquorsquo in the sense that they differen-tiate groups along existing and highly diagnosticcharacteristics exactly as Hilton Von Hippel andSchneider define them

Stereotypes are context dependent The assessment of agiven target group depends on the reference group towhich it is compared

In line with the social cognition approach to stereotypes asignificant body of psychological research on beliefs about genderrace age and political groups finds that stereotypes broadly re-flect reality but display biases Social psychologists have exploredthe extent to which stereotypes exaggerate real differences thuspossessing a kernel of truth Evidence on exaggeration varies bydomain For race and gender many studies have reportedroughly accurate beliefs whereas others have found underesti-mation or exaggeration of true differences (Jussim et al 2015)4

For age and political stereotypes evidence points more stronglytoward exaggeration5 Schneider (2004 337) summarizes the

4 For evidence of roughly accurate beliefs for race see for example Ashtonand Esses (1999) on beliefs of academic ability Kaplowitz Fisher and Broman(2003) on income poverty rates and out-of-wedlock births and Wolsko et al(2000) on a array of positive and negative attributes Ryan (1996) and Gilens(1996) find evidence of exaggeration of race stereotypes on personal attributesand poverty rates respectively Some studies have found roughly accurate beliefson gender (McCauley Thangavelu and Rozin 1988 Briton and Hall 1995Diekman Eagly and Kulesa 2002) while others find evidence of exaggeration(Martin 1987 Bayer 1999)

5 See Chan et al (2012) on age We discuss evidence on political stereotypes inSection IV

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existing empirical work on stereotype accuracy as follows lsquolsquothebest we can do by way of general summary is to say that somestereotypes held by some people for some groups are sometimesaccuratersquorsquo Our empirical investigation explores the connectionbetween stereotype accuracy and representativeness which wemeasure using the previously defined likelihood ratio

We first assess the role of representativeness and contextdependence in the lab We construct a group of mundane objectsG and present it to participants next to a comparison group ndashGIn our baseline condition the comparison group is chosen so thatno type is particularly representative of group G In our treat-ment we change the comparison group ndashG while leaving thetarget group G unchanged The new comparison group givesrise to highly representative types within G In line with thekey prediction of our model participants in the treatment condi-tion shift their assessment of G toward the representative types

We test the model using two data sets on political preferencesand beliefs about political preferences in the United States Heregroups are political constituencies (Democrats and Republicans)and types are their positions on a number of issues Holding fixedthe groups and the set of types and varying the groupsrsquo true dis-tributions across issues the data allow us to test whether beliefsabout political preferences are shaped by representativeness Wefirst show that such beliefs depart from the truth by exaggerating(mean) differences as per the kernel of truth logic We then ex-plore how the extent of exaggeration varies across issuesConsistent with the model we find that beliefs systematicallydepart from rational expectations and that the degree to whichthey exaggerate true differences is a function of representative-ness While representativeness is not the only heuristic thatshapes recall (availability driven by recency or frequency of ex-posure also plays a role) it explains the fact that in the datastated beliefs indeed exaggerate differences among groups

Since Kahneman and Tverskyrsquos (1972 1973) work on heuris-tics and biases several studies have formally modeled heuristicsabout probabilistic judgments and incorporated them into eco-nomic models Work on the confirmation bias (Rabin andSchrag 1999) and on probabilistic extrapolation (Grether 1980Barberis Shleifer and Vishny 1998 Rabin 2002 Rabin andVayanos 2010 Benjamin Rabin and Raymond 2015) assumesthat the decision maker has an incorrect model in mind or incor-rectly processes available data Our approach is instead based on

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the assumption that representative information comes foremostto mind when making judgments The mental operation that liesat the heart of our modelmdashgenerating a prediction for the distri-bution of types in a group based on data stored in memorymdashalsocaptures base rate neglect and overreaction to diagnostic infor-mation The underweighting or neglect of information in ourmodel simplifies judgment problems in a way related to modelsof categorization (Mullainathan 2002 Fryer and Jackson 2008)In these models however decision makers use coarse categoriesorganized according to likelihood not representativeness Thisapproach generates imprecision but does not create a systematicbias for overestimating unlikely events nor does it allow for con-text-dependent beliefs In our empirical analysis of political be-liefs we explicitly compare the predictions of representativeness-based recall to those of likelihood-based models and find that theevidence supports the former

In modeling representativeness we follow the specification ofGS (2010) but investigate a new set of questions GS (2010) ex-amine how representativeness distorts the assessed probabilitiesof alternative hypotheses but not how the probability of a givenhypothesis or group is distributed across its constituent elementsIn the context of the current setting GS (2010) ask how imperfectrecall affects the assessed probability that a randomly drawnmember from a universe belongs to group G The current arti-cle in contrast asks which type t we expect to draw once we knowthat we are facing group G GS (2010) show how representative-ness generates biased probabilistic assessments such as conjunc-tion and disjunction fallacies This article deals with perhaps abroader and more ubiquitous problem of stereotype formationextensively studied by other social scientists but largely ne-glected by economists

Section II describes our model In Section III we examine theproperties of stereotypes including the forces that shape stereo-type accuracy and illustrate these properties with examples InSection IV we bring the model to the data performing a lab ex-periment and analyzing existing surveys of political beliefsSection V concludes The Online Appendix presents proofs anumber of extensions of the model and additional results forthe experiments and field evidence

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II A Model of Representativeness and Stereotypes

IIA The Model

A decision maker (DM) faces a prediction problem such asassessing the ability of a job candidate from a certain ethnicgroup the future performance of a firm belonging to a certainsector or future earnings based on own gender

Formally there is a set of types of interest T and an overallpopulation of which group G is a subset The set of typesT can be unordered (eg occupations) or ordered (and typi-cally cardinal eg earnings levels) When T is ordered wewrite T frac14 ft1 tTg with t1 lt t2 lt lt tT6 There is a probabil-ity or frequency distribution 2 ethT THORN that induces a condi-tional distribution PrethT frac14 tjGTHORN when restricted to G7 In whatfollows we denote by tG frac14 PrethT frac14 tjGTHORN the probability of typet in group G and by G the vector ethtGTHORNt2T containing the condi-tional distribution

The DMrsquos goal is to assess the distribution of the types ofinterest in a particular group G Although the DM has stored inmemory the full distribution he retrieves from memory a dis-torted version of G that overweights the probability of thosetypes that are most representative of G relative to a comparisongroup ndashG Generically ndashG is a group in that is distinct from Gnamely G7 nG although in some cases it can coincide withthe complement of G

According to Tversky and Kahneman (1983) a type t is rep-resentative of G if it is relatively more likely to occur in G thanin ndashG Definitions 1 and 2 formalize this representativeness-based recall following GS (2010)

6 For simplicity we also use T to denote the number of types jTj The modelapplies also to cases in which types (i) are multidimensional capturing a bundle ofattributes such as occupation and nationality or (ii) are continuous We considerthese cases in Online Appendixes C and D respectively Also G may represent anycategory of interest such as the historical performance of a firm or industry actionsavailable to a decision maker (T = set of payoffs G = occupations) or categories inthe natural world (T = ability to fly G = birds)

7 In many applications each individual in is characterized by a determin-istic type (eg age hair color) As a result ethtTHORN frac14 1

jj For instance each Floridian

has a single age type (at the finest temporal resolution) When types are stochasticinstead such as when estimating future earnings of a person or a firm each indi-vidual is described by a nondegenerate distribution

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DEFINITION 1 The representativeness of type t for group G givencomparison group ndashG is defined as the likelihood ratio

RethtGGTHORN tG

tGeth2THORN

Definition 1 implies that DMs are attuned to log differencesin probabilities representativeness depends on the percentageprobability increase of a type from ndashG to G This captures aform of diminishing sensitivity whereby for a fixed probabilitydifference a type is more likely to be overweighed if it is unlikelyin the comparison group8 Thus the representative age of aFloridian is 65+ because people in this age bracket are morecommon in Florida than in the rest of the United StatesStatistically representative types are also diagnostic of thetarget group G Indeed the higher is RethtGGTHORN the more confi-dent is a Bayesian DM observing t that t belongs to G rather thanto ndashG9

The ease of recall of highly representative types affectsjudgments because more easily recalled types are overweighted

We model distorted recall as follows Denote by RethtGGTHORN

tG

tG

t2T

the vector of representativeness of all types in G

We then have

8 Our definition of representativeness links to Weberrsquos law of sensory percep-tion see Section IIB It also links to our previous work on salience in which wepostulated that log differences in payoffs determine the attention to lottery payoffs(Bordalo Gennaioli and Shleifer 2012) and to goodsrsquo attributes (BordaloGennaioli and Shleifer 2013) Equation (2) establishes the same principle for thedomain of probabilities

9 This insight led Tenenbaum and Griffiths (2001) to define representative-ness as individualsrsquo sense as intuitive Bayesians of updating in reaction to dataTheir definition like ours is in terms of the likelihood ratio However Tenenbaumand Griffiths interpret representativeness as a mechanism that affects intuitivejudgments of similarity rather than beliefs (eg it accounts well for lab evidencewhere subjects are asked to rank types in terms of representativeness or ofstrength of association with a group) Accordingly they do not consider the possi-bility of systematically distorted and context dependent beliefs

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DEFINITION 2 The DM attaches to each type t 2 T in group G adistorted probability

sttG frac14 tG

htethRethtGGTHORNTHORNPs2T sGhsethRethtGGTHORNTHORN

eth3THORN

where ht RTthornRthorn is a weighting function such that

(i) The weight ht is a symmetric function of the representa-

tiveness of types s 6frac14 t Formally ht frac14 h tG

tG

sG

sG

s2Tn tf g

where h Rthorn RT1thorn Rthorn is a function that is invariant to

a permutation of the last T ndash 1 arguments(ii) Weighing of a type increases in own representativeness

and decreases in the representativeness of other typesFormally the function hethTHORN is weakly increasing in itsfirst argument and weakly decreasing in the other T 1arguments

We call the distribution ethsttGTHORNt2T the stereotype for G If a type

t is objectively more likely namely tG is higher then the ste-reotype attaches higher probability to it By property i distor-tions are due exclusively to the fact that a type is more or lessrepresentative than the others In particular if all types areequally representative the DM equally weighs all of them ath(1) and holds rational expectations about G If instead the rep-resentativeness of different types differs property ii implies thatthe stereotype ceteris paribus overweights the probability of morerepresentative types

Most of the results we explore in this article hold for a gen-eral weighing function htethTHORN Specific functional forms captureadded assumptions about the psychology of representativeness-based recall and are useful in applications We outline a few spe-cifications and their properties

Rank-based stereotypes the ranking of the representa-tiveness of different types shapes distortions Denote byrethtTHORN 2 f1 Tg the representativeness ranking of type tWhen r(t) = 1 type t is the most representative one (po-tentially with ties) We can specify two ways in which atypersquos representativeness ranking distorts its probability

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(i) Rank-based truncation the DM only recalls the typesthat have representativeness ranking of at most dnamely ft 2 TjrethtTHORN dg Zero probability is attachedto the remaining types10 Denote by IethrethtTHORN dTHORN an in-dicator function taking the value 1 if the representa-tiveness ranking of t is at most d Then theweighting function is ht frac14 IethrethtTHORN dTHORN so that

sttG frac14 tG

IethrethtTHORN dTHORNPs2T sGIethrethsTHORN dTHORN

which is the true conditional probability within re-called types This assumption is used in Gennaioliand Shleifer (2010)11

(ii) Rank-based discounting the DM discounts by a con-stant factor 2 frac1201 the odds of type t relative to itsimmediate predecessors in the representativenessranking Lower implies stronger discounting ofless representative types Formally the weightingfunction is ht frac14

rethtTHORN so that

sttG frac14 tG

rethtTHORNPs2T sG

rethsTHORN

Representativness-based discounting all else equal theweight attached by the DM to type t increases continuouslywith its representativeness One convenient formulation is

ht frac14tG

tG

so that

10 These neglected types are not viewed as impossible they are just assignedzero probability in the DMrsquos current thinking This formulation allows us to modelsurprise and reactions to unforeseen contingencies which have proved useful in-gredients in modeling probabilistic judgments (GS 2010) as well as neglect of risk infinancial crises (Gennaioli Shleifer and Vishny 2012)

11 Specifically in GS (2010) the assessed probability that a certain hypothesisG is true is equal to

Pr ethGTHORN frac14

Pt tGIethrethtTHORN dTHORNP

t tGIethrethtTHORN dTHORN thornP

t t=GIethrethtTHORN dTHORN

which increases in the ratio between the total probability mass recalled for Gand that recalled for G frac14 nG

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sttG frac14 tG

tG

tG

P

s2T sGsG

sG

where 0 captures the extent to which representative-ness distorts beliefs This formulation is particularly con-venient when dealing with continuous distributions ofthe exponential or power classes

These functional forms all embody the main idea of our modelthat the stereotype overweights the probability of more represen-tative types Rank-based truncation captures a central manifes-tation of limited memory forgetting unrepresentative typesSmoother discounting (based on ranking or on representative-ness) may be more appropriate when the type space is smalland smooth discounting can be more tractable in certain settings

Section III characterizes the general properties of stereotypesIn particular it shows their ability to account for social psycholo-gistsrsquo kernel of truth hypothesis under the general weighting func-tion of Definition 2 To bring the model to the data in Section IVBwe derive linear approximations of stereotypical beliefs by assum-ing that the weighting function is differentiable with respect to atypersquos representativeness This assumption excludes rank-basedweighting but allows for many possibilities

IIB Discussion of Assumptions

Before moving to the formal analysis we discuss some prop-erties and limitations of our approach Representativeness-basedrecall the idea that individuals recall distinctive group types canbe viewed as an instance of what Kahneman and Tversky calllsquolsquoattribute substitutionrsquorsquo When dealing with the difficult questionlsquolsquowhat is the distribution of hair color among the Irishrsquorsquo peopleintuitively answer to the simpler question lsquolsquowhich hair color dis-tinguishes the Irish peoplersquorsquo Critically as discussed byKahneman and Tversky attribute substitution does not occurbecause people misunderstand the original question or mechan-ically confuse the assessment of PrethtjGTHORN with that of PrethGjtTHORNRather it occurs because the distinctive or representative typesimmediately come to mind and individuals anchor their overallprobability judgment to them As a consequence subjects do notonly make mistakes in judging the probability that a Floridian is

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over age 65 They also give too high an answer to the questionlsquolsquowhat is the average age of a Floridianrsquorsquo12

One interesting question is whether the process of stereotyp-ing we describe is optimal in some sense Focusing mental repre-sentations on a few types can be justified by the costs of thinkingor retrieval This approach however is not enough to explainwhy individuals should focus on representative rather thanlikely types We do not formally analyze the optimality of repre-sentativeness here but we mention some relevant considerationsfrom cognitive psychology Kahneman and Tversky (1979) stressthe similarity between many perceptual and cognitive operationsFor instance the highlight of contrastmdasha key principle of visualperceptionmdashis invoked to justify the prospect theory assumptionthat the carriers of utility are changes relative to a referencepoint The same logic applies to our model in which stereotypesprecisely highlight the contrast between groups

In visual perception assessing properties such as brightnesscolor size or distance to an object by comparing them to otherproximate objects has been shown to be optimal in the presence ofmultiplicative background noise (Kersten Mamassian andYuille 2004 Cunningham 2013) Our formulation of representa-tiveness is related to the same idea in the sense that individualsestimating properties of one group stress differences from an-other group In a noisy world in which attention is limited thisprocess may optimally allow for swift reactions to changes ingroup characteristics even if errors are sometimes made13

12 Indeed in many cases mere confusion of PrethtjGTHORNwith PrethGjtTHORNwould not yieldthe phenomenon of stereotyping In the Irish hair color example the probability ofbeing Irish conditional on having red hair is

PrethIrishjredTHORN frac14PrethredjIrishTHORNPrethIrishTHORN

PrethredjIrishTHORNPrethIrishTHORN thorn PrethredjNonIrishTHORNPrethNonIrishTHORN

This probability is clearly very small given that the Irish population is a tinyfraction of the world population Confusion of PrethtjGTHORN with PrethGjtTHORN in this casewould lead to an understatement of the probability of the red-haired Irish

13 To give a simple example suppose thatmdashas in the case of Proposition 3mdashthevariance in the environment increases in the sense that extreme tail events becomemore likely Then a likelihood-based stereotype would detect no change whereas arepresentativeness-based stereotype would focus on the heightened probability ofthe tails In particular an asymmetric increase in tail probabilities that shifts themean would be detected by a representativeness-based stereotype even if the dis-tributionrsquos mode does not change

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Exploring this idea formally is an interesting avenue for futurework

Consider some limitations of our model First representa-tiveness is not the only heuristic that shapes recall Decisionmakers may for instance find it easier to recall types that aresufficiently likely Another potentially important mechanism isavailability understood by Kahneman and Tversky (1972) as thelsquolsquoeasersquorsquo with which information comes to mind (because of actualfrequency or repetition) In Online Appendix E we present a trun-cation-based recall mechanism in which distortions are driven bya combination of representativeness and likelihood of types(which is equivalent to relaxing property i in Definition 2) Thismodel can offer a useful starting point to capture availability aswell even though a full model of availability is beyond the scopeof this article Even in this more general setting the influence ofrepresentativeness on recall is the driving force of stereotypesthat in line with the social psychology perspective are basedon underlying differences among groups As we show in SectionIV this feature is critical in accounting for the evidence

The second set of model-related issues concerns how to spe-cify the elements of Definition 1 in applications group G the typespace T and the reference group ndashG Take the specification of thegroup G and of the type space T Often the problem itself pro-vides a natural specification of these features This is the case inthe empirically important class of lsquolsquoclosedrsquorsquo questions such asthose used in surveys which provide respondents with a set ofalternatives as in the data we use in Section IV More generallythe problem solved by the DMmdashsuch as evaluating the resume ofa job applicant coming from a certain ethnic groupmdashprimes agroup a dimension of interest and a set of types (eg the appli-cantrsquos qualification or skill levels) When types have a naturalorder such as income age or education the granularity of T isalso naturally given by the problem (income age and years ofschooling brackets) When the set of types is not specified by theproblem DMs spontaneously generate one14 It would be useful tohave a model of which dimensions and types come to mind par-ticularly for more open-ended problems Psychologists have

14 For example suppose a person is asked to guess the typical occupation of ademocratic voter in an lsquolsquoopen-endedrsquorsquo format (without being provided a set of alter-natives) Here the level of granularity at which types are defined is not obvious (egteacher versus a university teacher vs a professor of comparative literature)

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sought to construct a theory of natural types and dimensions(Rosch 1973) We do not make a contribution to this problembut we note that in many problems of interest in economics thedimension as well as the set of types is naturally givenFurthermore in our model details of the type space can be impor-tant under rank-based truncation but they matter less undersmooth discounting

Consider finally the role of the comparison group ndashG Thisgroup captures the context in which a stereotype is formed andagain is often implied by the problem when G = Floridians ndashG =rest of US population when G = African Americans ndashG = whiteAmericans A distinctive prediction of our model confirmed byour experiments in Section IVA is that the stereotype for agiven group G depends on the comparison group ndashG15 WhenndashG is not pinned down by the problem itself to derive testablepredictions from representativeness we set G frac14 nG where

is the natural population over which the unconditional distribu-tion of types is measured

III Properties of Stereotypes

We now study stereotypical beliefs and their accuracy Toillustrate the role of representativeness we first ask to whatextent the most representative type is a good fit for the groupnamely whether it is modal Next we assess the accuracy of theentire stereotypical distribution To do so we focus on a cardinaltypes and compare the stereotypersquos mean and variance to the trueones

15 Some empirical papers have taken a similar approach exogenously varyingthe natural comparison group through priming Benjamin Choi and Strickland(2010) show that priming racial or ethnic identity can affect the risk preferences ofparticipants Chen et al (2014) find that Asian students cooperate less with out-group members when primed with their ethnic identity rather than their universityidentity Shih Pittinsky and Ambady (1999) show that Asian American womenstereotype themselves as better or worse in math with corresponding impact onperformance when their ethnicity or gender respectively is primed ShihPittinsky and Trahan (2006) replicate this effect using a verbal task documentingthat Asian American women performed better when their gender rather than theirethnicity was primed Although the generalizability and replicability of priminghas been doubted (Klein et al 2014) this body of evidence is consistent with contextdependence

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IIIA Likely versus Unlikely Exemplars

The most representative type for a group is the one thatagents most easily recall and associate with the group itself forinstance a red-haired Irishman or a 65+-year-old FloridianSocial psychologists call this type the exemplar of the groupAccordingly we define

DEFINITION 3 A type t is an exemplar for G given comparisongroup ndashG when

t 2 arg maxt

tG

tG

Under any specification of the weighting function ht inDefinition 2 overweighting (weakly) increases as we movetoward more representative types so the exemplar is also thetype whose probability is overweighted the most16 By analyzingthe exemplar then we can gauge whether representativenessinduces the DM to overweight a likely type (as happens in stan-dard models of categorical thinking) or an unlikely type Whenoverweighting occurs in unlikely and extreme types the biases ofstereotypes can be particularly severe17

Equation (2) yields the following characterization

PROPOSITION 1 Suppose the conditional distributions G and G

are not identical Consider two extreme cases

(i) If for all t t0

2 T we have that tG gt t0 G if and only iftG gt t0 G then the modal type is not an exemplar forat least one group

(ii) If for all t t0

2 T we have that tG gt t0 G if and only iftG lt t0 G then for each group the modal type is theexemplar

16 Consider the function hethTHORN from Definition 2 When applied to more repre-sentative types the first argument of the function increases while one of the otherT ndash 1 arguments decreases As a result the weighting factor ht (and thus overweigh-ing

sttG

tG) increases as well

17 In the rank-based truncation model the frequency of the exemplar providesa measure of stereotype accuracy By accuracy we mean the extent to which thestereotype minimizes the distance

Pt eth

sttG tGTHORN

2 When d = 1 and only one type isrecalled (there are no ties) accuracy is maximized if the exemplar is the most likelytype and minimized if the exemplar is the least likely type

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Case i says that when groups have similar distributions inthe sense of having the same likelihood ranking the most repre-sentative type is unlikely for at least one group potentially bothRepresentativeness draws the DMrsquos attention to group differ-ences neglecting the fact that the groups are similar and havethe same mode This mechanism generates inaccurate stereo-types and is illustrated by the Florida example This resultholds under any measure of representativeness that differenti-ates the two groups (eg the difference tG tG)

Case ii says that the most representative type tends to belikely for both groups when the distributions are very differentIn this case groups differ the most around their modes so repre-sentativeness and likelihood coincide Thinking of Swedes aslsquolsquoblondrsquorsquo and Europeans as lsquolsquodark hairedrsquorsquo is accurate precisely be-cause these are majority traits of the Swedish and European pop-ulations respectively In these cases stereotyping yields fairlyreliable models Of course there is still some inaccuracy Evenin the case of likely exemplars judgment errors can be signifi-cant For instance voters in some US states are perceived aslsquolsquobluersquorsquo or lsquolsquoredrsquorsquo because a majority of the population votesDemocrat or Republican In reality even in lsquolsquobluersquorsquo states farfrom everyone votes Democrat In the 2012 presidential electionvote shares of either candidate in most states ranged from 40 to6018

When DMs strongly overweight representative types themost severe biases occur when those types are unlikely and ex-treme This is true both under rank based truncations and undersmooth discounting functions (see Section IIIB) Ethnic stereo-types based on crime or terrorism exhibit this error they neglectthe fact that by far the most common types in all groups arehonest and peaceful

IIIB Stereotypical Moments

We now characterize how the first two moments of a distri-bution are distorted by the process of stereotyping To do so wemust restrict our analysis to cardinal ordered types The follow-ing results hold for any weighting function htethTHORN satisfyingDefinition 2 We consider two canonical cases that prove usefulin illustrating the predictions of the model

18 Presidential Election Results NBCNewscom see httpelectionsnbcnewscomnspolitics2012allpresident (accessed 5 September 2016)

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In the first case groups G and ndashG are such that the likelihoodratio tG

tGis monotonic in t The monotone likelihood ratio prop-

erty (MLRP) holds to a first approximation in many empiricalsettings and is also assumed in many economic models such asstandard agency models19 If tG

tGis monotonically increasing (de-

creasing) in t then group G is associated with higher (lower)values of t relative to the comparison group ndashG Formally

PROPOSITION 2 Suppose that MLRP holds and assume wlogthat the likelihood ratio tG

tGis strictly increasing in t Then

for any weighting function htethTHORN that is not constant in therelevant range

EstethtjGTHORN gt EethtjGTHORN gt EethtjGTHORN gt E

stethtjGTHORN

Under MLRP the most representative part of the distribu-tion for G is the right tail if tG

tGincreases in t or the left tail if tG

tG

decreases in t The representative tail is then overweighted whilethe nonrepresentative tail is underweighted As a consequencethe assessed mean E

stethtjGTHORN is too extreme in the direction of therepresentative tail

Critically in line with the social cognition perspective the ste-reotype contains a kernel of truth the DM overestimates the meanof G if this group has a higher mean than the comparison groupnamely EethtjGTHORN gt EethtjGTHORN and conversely if EethtjGTHORN lt EethtjGTHORN TheDM exaggerates this true difference because he inflates the asso-ciation of G with its most representative types20 For instancewhen judging an asset manager who performs well we tend to

19 Examples include the binomial and the Poisson families of distributionswith different parameters The characterization of distributions satisfying MLRPis easier in the case of continuous distributions (see Online Appendix D) two dis-tributions f(x) f ethx THORN that differ only in their mean satisfy MLRP if and only if thedistribution f(x) is log-concave Examples include the exponential and normal dis-tributions To the extent that discrete distributions sufficiently approximate thesedistributions (as the Poisson distribution PoisethTHORN approximates the normal distri-bution Neth THORN for large l) they will also satisfy MLRP

20 Depending on the distribution and the weighing function the DMrsquos assess-ment of the variance VarethtjGTHORNmay also be dampened relative to the truth This isoften true under the truncation weighing function In this case stereotyping effec-tively leads to a form of overconfidence in which the DM holds extreme views andoverestimates the precision of his assessment That extreme views and overconfi-dence (in the sense of over precision) go together has been documented in the settingof political ideology among others (Ortoleva and Snowberg 2015)

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overemphasize skill relative to luck because higher skill levels arerelatively more associated with higher performance This occurseven if for both skilled and unskilled managers high performanceis mostly due to luck

In the second case for which we characterize the stereotypi-cal distributions groups G and ndashG have the same mean EethtjGTHORNfrac14 EethtjGTHORN frac14 EethtTHORN but differ in their variance We abstract fromskewness and higher moments by considering distributionsethtGTHORNt2T and ethtGTHORNt2T that share the same support and are sym-metric around the medianmean EethtTHORN

PROPOSITION 3 Suppose that in G more extreme types are rela-tively more frequent than in ndashG Formally the likelihoodratio tG

tGis U-shaped in t around EethtTHORN Then for any weight-

ing function htethTHORN that is not constant in the relevant rangestereotypical beliefs satisfy

VarstethtjGTHORN gt VarethtjGTHORN gt VarethtjGTHORN gt VarstethtjGTHORN

EstethtjGTHORN frac14 E

stethtjGTHORN frac14 EethtTHORN

When group G has a higher relative prevalence of extremetypes its representative types are located at both extremes of thedistribution The DMrsquos beliefs about G are then formed by over-weighting both tails while underweighting the unrepresentativemiddle The overweighting of Grsquos tails causes the assessment ofits variance VarstethtjGTHORN to be too high For example the skill dis-tribution of immigrants to the United States may be perceived ashaving very fat tails or even bimodal with immigrants beingperceived as either unskilled or very skilled relative to the resi-dent population The mean of the group in contrast is assessedcorrectly because the stereotypical distribution remains symmet-ric around EethtTHORN As before the stereotype contains a kernel oftruth It induces the agent to exaggerate the true differences be-tween groups namely the higher variance of G relative to itscounterpart

We present a number of extensions of the model in the OnlineAppendix We first consider multidimensional type spaces andshow that stereotypes center around the dimension wheregroups differ the most in line with the kernel of truth logic(Online Appendix C) Multidimensional stereotypes imply thatthe dimension we think about is influenced by context For

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example the Irish are stereotyped as red-haired when comparedwith the European population However when compared withthe Scots a more plausible stereotype for the Irish is lsquolsquoCatholicrsquorsquobecause religion is the dimension along which Irish and Scotsdiffer the most

In Online Appendix D we extend the model to continuoustype spaces Many settings of interest in economics can be use-fully described by continuous probability distributions and weshow our model is particularly tractable in this case In OnlineAppendix E we relax Definition 2 and allow weighting of types toalso be influenced by their likelihood We show that the basicinsight that stereotypes contain a kernel of truth carries throughto these cases as well

To summarize the psychology of representativeness yieldsstereotypes that are consistent with the social cognition approachin which individuals assess groups by recalling and focusing ondistinctive group traits When there are systematic differencesbetween groups stereotypes get the direction right but exagger-ate differences

IIIC Some Examples

A growing body of field and experimental evidence points to awidespread belief that women are worse than men at mathemat-ics (Eccles Jacobs and Harold 1990 Guiso et al 2008 CarrellPage and West 2010) This belief persists despite the fact that fordecades women have been gaining ground in average schoolgrades including mathematics and have recently surpassedmen in overall school performance (Goldin Katz and Kuziemko2006 Hyde et al 2008) This belief shared by men and women(Reuben Sapienza and Zingales 2014) may help account for thegender gap in the choices of high school tracks college degreesand careers with women disproportionately choosing humanitiesand health-related areas (Weinberger 2005 Buser Niederle andOosterbeek 2014) and forgoing significant wage premiums toquantitative skills (Bertrand 2011)

Gender stereotypes in mathematics particularly beliefs thatexaggerate the extent of average differences are consistent withthe predictions of our model The fact that men are overrepre-sented at the very highest performance levels leads a stereotyp-ical thinker to exaggerate the magnitude of mean differencesFigure I shows the score distributions from the mathematics

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section of 2013rsquos Scholastic Aptitude Test (SAT) for men andwomen21 The distributions are very similar with averagescores slightly higher for men (531 versus 499 out of 800)However scores for men have a heavier right tail with mentwice as likely to have a perfect SAT math score than women22

In light of such data the stereotypical male performance in math-ematics is high while the stereotypical female performance ispoor Predictions based on such stereotypes are inaccurate exag-gerating true differences Consistent with this prediction exper-imental evidence shows that both genders underestimatewomenrsquos ability in simple math tasks even controlling for pastperformance (Reuben Sapienza and Zingales 2014) Coffman(2014) shows a similar pattern extends to confidence about ownability in other male-typed domains with women reporting sig-nificantly less confidence in gender-incongruent than gender-congruent tasks Our model suggests that these patterns mightcome from stereotypes based on gender differences in the righttail of the distribution While differences in the right tail of thedistribution are unlikely to be relevant for most decisions stereo-typical thinking driven by these differences has the potential toimpact economically important decisions whether through self-stereotyping (ie choice of careers or majors as in BuserNiederle and Oosterbeek 2014) or through discrimination (iehiring decisions as in Bohnet van Geen and Bazerman 2016)

The logic of exaggerated yet directionally correct stereotypesalso sheds light on the well-documented phenomenon of base rateneglect (Kahneman and Tversky 1973) Indeed Proposition 2implies that the DM overreacts to information that assigns

21 Standardized test performance measures not only innate ability but alsoeffort and investment by third parties (Hyde et al 2008) The mapping of test per-formance into inferences about innate ability is an issue not addressed by ourmodel

22 For 2013 SAT Mathematics scores see httpmediacollegeboardcomdigitalServicespdfresearchSAT-Percentile-Ranks-By-Gender-Ethnicity-2013pdf Results are similar for the National Assessment of Educational Progress(NAEP) which are more representative of the overall population For 2012NAEP scores for 17-year-olds in mathematics see httpnationsreportcardgovltt_2012age17maspx See Hyde et al (2008) Fryer and Levitt (2010) and Popeand Sydnor (2010) for in-depth empirical analyses of the gender gap inmathematics

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people to groups precisely because such information generatesextreme stereotypes Consider the classic example in which amedical test for a particular disease with a 5 prevalence has a90 rate of true positives and a 5 rate of false positives The testassigns each person to one of two groups + (positive test) or ndash(negative test) The DM estimates the frequency of the sick type(s) and the healthy type (h) in each group The test is informativea positive result increases the relative likelihood of sickness anda negative result increases the relative likelihood of health forany prior Formally

PreththornjsTHORN

PreththornjhTHORNgt 1 gt

PrethjsTHORN

PrethjhTHORNeth4THORN

This condition has clear implications the representative personwho tests positive is sick while the representative person whotests negative is healthy Following Proposition 2 the DMreacts to the test by moving his priors too far in the right di-rection generating extreme stereotypes He greatly boosts hisassessment that a positively tested person is sick but also thata negatively tested person is healthy Because most people arehealthy the DMrsquos assessment about the group that tested neg-ative is fairly accurate but is severely biased for the group that

FIGURE I

SAT Mathematics Scores by Gender (2013)

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tested positive This analysis formalizes Tversky andKahnemanrsquos (1983) verbal account of base rate neglect23

The same mechanism may underlie several other instanceswhere DMs overweight diagnostic information When assessingan employeersquos skill level an employer attributes high perfor-mance to high skill because high performance is the distinctivemark of a talented employee Because he neglects the possibilitythat some talented employees perform poorly and that somenontalented ones perform well (perhaps due to stochasticity inthe environment) the employer has too much faith in skill andneglects the role of luck in accounting for the output Similarlywhen assessing the performance of firms in a hot sector of theeconomy (eg G = internet) an investor recalls highly successfulfirms in that sector (t = return of Google Amazon etc) He ne-glects the possibility of firms being unsuccessful because lack ofsuccess is statistically nondiagnostic and psychologically nonrep-resentative of a growing sectormdasheven if it is likely This causesexcessive optimism (in that the expectation of growth is unrea-sonably high) and overconfidence (in that the variability in earn-ings growth considered possible is truncated) True the hot sectormay have better growth opportunities on average but represen-tativeness exaggerates this feature and induces the investor toneglect a significant risk of failure

IV Evidence on Representativeness and Stereotypes

Testing our model requires evaluating the beliefs individualshold about a target group against the true distribution of thattarget group over an attribute space An ideal data set would

23 Our account is distinct from a mechanical underweighting of base rates inBayes rule as in Grether (1980) and Bodoh-Creed Benjamin and Rabin (2013) Inthose models upon receiving the test results the DM can update his beliefs in thewrong direction he can be less confident that a person is healthy after a negativetest than under his prior which cannot happen in our model Although this predic-tion of our model seems consistent with introspection we are not aware of experi-mental evidence on this point Griffin and Tversky (1992) present evidenceconsistent with pure neglect of base rates but in a significantly different tasknamely inferring the bias of a coin from a history of coin flips Such experimentsare hard to compare with the predictions of our model because subjects are asked togenerate distributions of different numbers of coin flips in their minds which is amuch more involved task than to recall types of a given distribution Their assess-ments then might be wrong for other reasons See Bodoh-Creed Benjamin andRabin (2013) for a detailed discussion

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consist of naturally defined groups with known distributions overa given space of types and a corresponding set of beliefs about thedistribution of each group over that space of types This wouldallow us to test for exaggeration of true differences betweengroups and to ask whether this exaggeration is well predictedby overweighting representative types To identify a causal rolefor representativeness or context dependence we would need ex-ogenous variation in either the comparison group ndashG or in thedistributions over the type spaces This is unavailable in existingdata sets Accordingly we take a two-pronged approach First wecreate a controlled laboratory environment that allows us toinduce the exogenous variation in representative types that weneed to test causality then we reanalyze existing field evidence tocheck for consistency with our predictions

In testing our model we focus on the two main implicationsof representativeness-based stereotypes

Context dependence the stereotype of a target group de-pends on the characteristics of the reference group it iscompared to

Kernel of truth stereotypes depend on group character-istics andmdashin most (precisely characterized) settingsmdashare slanted toward representative types

We test the first property with a lab experiment (SectionIVA) We then turn to survey data on beliefs about US politicalgroups (Section IVB) for an empirical analysis that explores thesecond property The survey data are more tightly linked to ourinterest in social stereotypes The laboratory experiment allowsus to directly test the role of representativeness in generatingcontext dependent beliefs Online Appendixes F and G provideall details and additional results for the experiments and fieldevidence

IVA Lab Evidence on Representativeness and ContextDependence

The influence of the representativeness heuristic on recalland on beliefs has been extensively documented in the lab(Kahneman and Tversky 1972 1973) Our goal is to considerhow representativeness as formalized in equation (2) gives riseto context-dependent beliefs To our knowledge the possibility

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that representativeness may generate context dependence hasnot been tested before

To assess this prediction we perform a controlled laboratoryexperiment that allows us to isolate representativeness frommany confounding factorsmdashhistorical sociological or other-wisemdashthat may affect stereotype formation in the real worldWe construct our own groups of ordinary objects creating atarget group G and a comparison group ndashG We hold thetarget group G fixed and explore how participant impressions ofit change as we change the comparison group ndashG and thusrepresentativeness

We conducted several experiments in the laboratory and onAmazon Mechanical Turk Each involves a basic three-stepdesign First participants are shown the target group and a ran-domly assigned comparison group for 15 seconds In this timedifferences between groups can be noticed but the groupsrsquo precisecompositions cannot be memorized The second step consists of afew filler questions which briefly draw the participantsrsquo cognitivebandwidth away from their observation Finally participants areasked to assess the groups they saw Participants are incentiv-ized to provide accurate answers

We randomly assign participants to either the Control or theRepresentativeness condition In the Control condition G and ndashGhave nearly identical distributions so that all types are similarlyrepresentative for each group In the Representativeness condi-tion ndashG is changed in such a way that a certain type becomes veryrepresentative for G Context dependence implies that the assess-ment of G should now overweight this representative type eventhough the distribution of G itself has not changed

We ran six experiments of this form with design changesfocused on reducing participant confusion and removing con-founds We describe the final and most refined version of theseexperiments here In an attempt to provide a overview of the re-sults while remaining concise we provide the results from pooledspecifications that use all data collected In Online Appendix Fwe offer additional details and report all experiments conductedWe also give instructions and materials for each experiment thefull data set is available by request

Consider first the experiment illustrated in Figure II Agroup of 25 cartoon girls is presented next to a group of 25 cartoonboys in T-shirts of different colors blue green or purple In theControl condition (Figure II Panel a) the groups have identical

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color distributions (13 purple 12 green) so no color is represen-tative of either group The Representativeness condition (Panel b)compares the same group of girls with a different group of boysfor whom green shirts are replaced with blue shirts Now onlygirls wear green and only boys wear blue These colors althoughstill not the most frequent for either group are now most repre-sentative For each group girls and boys participants are asked anumber of questions concerning the frequency of T-shirts of dif-ferent colors worn by that group

Applying our model in the control condition the type space isT frac14 fgreen purpleg and the groups are G = girls and ndashG = boysGiven that the color distributions are identical across groups both

types are equally representativegreengirls

greenboysfrac14 1 frac14

purplegirls

purpleboys As a result

assessment of G should be correct on average stcontrolgreengirls frac14 greengirls

and stcontrolpurplegirls frac14 purplegirls for any weighing function (the same is

true about assessments of ndashG)In the treatment condition the distribution of shirt colors re-

mains the same for girls For boys green shirts are changed intoblue Thus the type space changes to T frac14 fgreen purple bluegand the representative color for girls becomes greengreengirls

greenboysfrac14 1 gt 1 frac14

purplegirls

purpleboys while that for boys becomes blue As

a result in the treatment condition subjects should inflate the

frequency of green shirts relative to the truth sttreatmentgreengirls

gt greengirls (the same should happen to assessments of blueshirts for boys) We also expect the assessed frequency of greenshirts to go up relative to the control condition namely

sttreatmentgreengirls gt stcontrol

greengirls Critically the only factor that varies

across treatments is the representativeness of the 12-colorshirt Thus if we see differences across conditions the causalrole of representativeness-based recall in shaping group judg-ments is clear24

24 We vary which colors are used in which roles across participants Someparticipants saw this particular color distribution while others see for examplegreen as the modal color and purple as the diagnostic color for boys in theRepresentativeness condition and blue as the diagnostic color for girls in theRepresentativeness condition We vary the colors across the roles to avoid con-founding the characteristics of any particular color with its diagnosticity

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FIG

UR

EII

T-S

hir

tsE

xp

erim

ent

Fig

ure

sap

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red

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lor

top

art

icip

an

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the

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ent

For

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ty

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ded

ale

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irt

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er

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ind

icate

sgre

en

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icate

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icate

sblu

eT

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tter

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otap

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icip

an

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dare

for

read

erre

fere

nce

only

P

lease

see

onli

ne

ver

sion

ofp

ubli

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icle

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rfi

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pea

red

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icip

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We collected data from 301 participants using this T-shirtsdesign25 Since the number of green and purple shirts is verysimilar we first ask each participant the simplest question ofwhich shirt color is modal Next we ask participants to assessthe share of green and purple shirts

Consistent with the role of representativeness participantsassigned to the Representativeness condition are 105 percentagepoints more likely to recall the less frequent color (green for girlsor blue for boys) as the modal color when it is representative of agroup (35 of participants guess the less frequent color is modalin the Control condition this proportion increases to 46 in theRepresentativeness condition p = 01 estimated from a probitregression reported in Online Appendix F)

We now turn to subjectsrsquo estimates of how many T-shirts ofeach color they saw in each group In both conditions the truedifference in counts is 1 (13 purple shirts 12 green or blue shirts)In the Control condition participants on average believe they saw054 more purple shirts than green or blue shirts In theRepresentativeness condition participants believe they saw072 fewer purple shirts than green or blue shirts (the acrosstreatment difference is significant with p = 01 from OLS regres-sion reported in Online Appendix F)

In total we collected data for six experiments of this generalstructure gathering evidence from more than 1000 participantsAs we describe in Online Appendix F although there is substan-tial variation across experiments when we pool all of the data wefind significant aggregate treatment effects in line with a role ofrepresentativeness in judgment We employ four different unor-dered types designs similar to the T-shirts experiment using sixsamples (four online and two in the laboratory) with 741 partic-ipants We find effects in the predicted direction for five of the sixsamples Using a probit regression that pools the data for theseunordered type experiments we find that participants are 93 per-centage points more likely to guess that the less frequent type ismodal when it is representative than when it is not (p = 002) Wealso run a family of ordered types experiments (two designs fivesamples 402 participants) Unlike the simpler T-shirts style

25 Throughout our analysis we exclude any participant who participated in aprevious version of the experiment and any participant who self-identified as color-blind In Online Appendix F we show that our results are unchanged if we includethese additional observations

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design the theoretical predictions for the ordered types designsare more sensitive to the specific assumptions one makes aboutthe weighting function of the DM26 We find effects in the pre-dicted direction for three of the five samples As we discuss inmore detail in Online Appendix F the ordered types resultsvary by platform with consistently stronger results on AmazonMechanical Turk than in the laboratory samples Pooling all or-dered types experiments participants are 93 percentage pointsmore likely to guess that the group of interest has a greater av-erage than the comparison group when the right tail is represen-tative (p = 062) Given our simple experimental setting withgroups of mundane objects we interpret our resultsmdasha signifi-cant and reasonably sized impact on average beliefsmdashas an im-portant proof of concept the presence of representative typesbiases ex post assessment

IVB Empirical Evidence on Political Stereotypes

We examine two data sets on political preferences and be-liefs about political preferences in the United States We inves-tigate the roles of representativeness and context dependence byseparately testing for hypotheses that allow us to assess the lead-ing theories of stereotypes

First we test whether beliefs are correct or depart systemat-ically from the truth The statistical discrimination approachbuilds on the assumption that people hold rational expectationsof group traits Comparing beliefs to the truth allows us to assessthe validity of this assumption in our data

Second we test if beliefs depart from the truth by exagger-ating (mean) differences among groups per the kernel of truthhypothesis This is an implicit test of context dependence be-cause it implies that beliefs about the target groups are shapednot only by that grouprsquos characteristics but also by those of thereference group27

Third we test if distortions in beliefs can be accounted for bythe overweighting of highly representative types (defined astypes that are relatively more frequent in the target relative to

26 This is due in part to our choice to not study MLRP distributions We moti-vate and discuss this design decision in Online Appendix F

27 Of course unlike in the laboratory experiment in this setting we cannot testfor context dependence by exogenously varying the reference group

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the reference group) The second and third tests address the keypredictions of our model

1 The Data We have two data sets on political preferences andbeliefs about political preferences The first data set from GrahamNosek and Haidt (GNH 2012) contains data from the MoralFoundations Questionnaire Respondents (1174 self-identified lib-erals and 500 self-identified conservatives) answer questions abouttheir position on a subset of 45 issues 20 moral relevance state-ments (eg lsquolsquowhen you decide whether something is right orwrong to what extent are the following considerations relevantto your thinkingrsquorsquo) and 25 moral judgments (eg lsquolsquoindicate theextent to which you would agree or disagreersquorsquo) For each issue arandomly determined subset of participants states their own posi-tion another subset states their belief on the position of a lsquolsquotypicalliberalrsquorsquo and a third subset states their belief on the position of alsquolsquotypical conservativersquorsquo The data thus include the distribution overpositions for both liberal and conservatives as well as the averagebelieved typical position of liberals and of conservatives on the 45issues Each position is elicited on 1ndash6 scale

The second data set comes from the American NationalElection Survey (ANES) and contains data from more than20000 respondents between 1964 and 201228 The surveycovers political issues of the day such as the optimal amount ofgovernment spending and service provision (1984ndash2000) or theplace of women in society (1972ndash1998) We focus on the 10 issuesthat ask participants to respond on a 1ndash7 scale (rather than justindicate binary agreement or disagreement) all 10 issues areasked in multiple years Participants are asked to provide theirown position on the scale and their believed position of theDemocratic and Republican parties (lsquolsquoWhere would you placethe Democratic [Republican] party on this scalersquorsquo) The data in-clude for each issue-year observation the distribution of partic-ipant positions for self-identified liberals and self-identifiedconservatives as well as the distribution of believed typical posi-tions of the Democratic and Republican parties

28 These data are publicly available at httpwwwelectionstudiesorgstudy-pagesanes_timeseries_cdfanes_timeseries_cdfhtm

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2 Empirical Strategy Our analysis focuses on beliefs abouttwo groups Conservatives and Liberals The types are the possi-ble positions for each issue (1 2 6 7) For the GNH data weinterpret beliefs about the lsquolsquotypicalrsquorsquo element of a group to coincidewith the believed average position in that group Similarly forthe ANES data we use the believed party positions as a proxy forbelieved mean of each group29 We then take as a benchmark thehypothesis that individuals hold accurate beliefs about eachgroup and in particular that believed mean position shouldequal true mean position at least on average across subjectsThe accurate beliefs hypothesis underlies the most common eco-nomic model of stereotyping statistical discrimination

To assess our representativeness-based model we perform aregression exercise To test our model in a linear regressionframework we rely on linear approximations of the weightingfunction Our model then yields two regression specifications

PROPOSITION 4 Let G 2 fconservative liberal g and assume

ht h tG

tG

be a differentiable and strictly increasing weight-

ing function as in Definition 2 The following hold as a first-order approximation around identical distributions G

Gfrac14 1

(i) Kernel of truth regression There exists a constant gt 0such that

EstethtjGTHORN frac14 EethtjGTHORNeth1thorn THORN EethtjGTHORNeth5THORN

(ii) Representativeness regression Denote H frac14 fT 2 Tg

the right tail of types and RconsH frac14

PHtconsPHtlib

as the average

representativeness of right tail types for conservatives

29 This assumption is consistent with the authorsrsquo interpretation of the GNHdata (GNH 2012) and with previous studies using ANES (eg Westfall et al 2015)Furthermore to the extent that this assumption holds equally well for most issueswithin a data set our focus on cross-issue differences should allow us to test thepredictions of our model even with an imperfect proxy for beliefs of mean positionsFinally the data provide some insight into whether subjects are reporting (per-ceived) modal or mean types As we show the modal type is a poor prediction ofstated beliefs while a distorted mean slanted toward representative types is anaccurate prediction of stated beliefs

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Under the further approximation where tcons

tlibampRcons

H for

t 2 H

EstethtjconsTHORN frac14 EethtjconsTHORN thorn consethR

consH 1THORNeth6THORN

EstethtjlibTHORN frac14 EethtjlibTHORN libethR

consH 1THORNeth7THORN

where lcons and llib are positive constants

The first regression allows us to test for the kernel of truthhypothesis and the second set of regressions allows us to test forthe role of representativeness

Equation (5) says that respondents in our model inflate theaverage position of a group say the conservatives if and only ifthe group has a higher average position than the other groupnamely the liberals Formally EstethtjconsTHORN gt EethtjconsTHORN if and onlyif EethtjconsTHORN gt EethtjlibTHORN Because in our measurement scale highertypes mean lsquolsquomore conservativersquorsquo we expect (i) believed conserva-tive average to be higher than the truth and (ii) the extent ofoverstatement to decrease in the average liberal position EethtjlibTHORNConversely we expect the average liberal position to be lowerthan the truth the more so the higher the average conservativeposition EethtjconsTHORN

As previously discussed the basis of these predictions is con-text dependence information about the distribution of ndashG is rel-evant for the beliefs about G This context dependence isinconsistent with rational expectations in which only thegrouprsquos own means should affect beliefs We test the hypothesisthat the true mean EethtjGTHORN is a significant predictor of the believedmean E

stethtjGTHORN with a positive sign and the other grouprsquos truemean EethtjGTHORN is a predictor of the believed mean with a negativesign

Equations (6) and (7) say that repondentsrsquo assessment bias isshaped by representativeness When the right tail is more repre-sentative for conservatives (Rcons

H 1 positive and large) partici-pants should inflate the average conservative position more(higher E

stethtjconsTHORN EethtjconsTHORN) and deflate the average liberal po-sition more (lower E

stethtjlibTHORN EethtjlibTHORN) We test the hypothesisthat the inflation in conservative positions is positively associatedwith the representativeness of the right tail for the conservativesand the inflation in liberal positions is negatively associated with

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it Once again the representativeness of the right tail is com-puted using the true distribution of positions

In equations (6) and (7) in many cases the representative tailis also the most likely one As a consequence these tests cannotdistinguish a representativeness-based from a likelihood-basedmodel of distorted beliefs We perform two additional testsFirst we run versions of equations (6) and (7) in which we controlfor the likelihood of tails (see Table A4 in Online Appendix G)Second we compute numerically the predictions of a representa-tiveness-based model of stereotypes and a likelihood-based modelof stereotypes We then assess which of these two is better able tomatch the data on beliefs

3 Empirical Results To begin we illustrate the structure ofthe data and the nature of our predictions with two simple exam-ples from the GNH data set focusing on beliefs about conserva-tives In example 1 participants are asked about their agreementwith the statement lsquolsquoIt can never be right to kill a human beingrsquorsquoIn example 2 participants are asked about the moral relevance oflsquolsquowhether or not someone cared for someone weak or vulnerablersquorsquoAs can be seen in Figure III in example 1 the modal position(strongly disagree (1)) and most representative positions(strongly disagree (1)) coincide for conservatives In contrast inexample 2 in Figure III the most representative types (slightlyrelevant (3) not at all relevant (1)) are not most likely for theconservative group Following Proposition 1 we predict that be-liefs will be distorted in the direction of the most representativetypes Thus we expect more exaggeration in example 2 than inexample 1 since in example 2 the most representative types (inthe left tail) are far from the modal type whereas in example 1they coincide This is what we find the conservative position isexaggerated by only 009 positions in Example 1 (true mean 299believed mean 290) but by 106 positions in Example 2 (truemean 421 believed mean 315)

In the full data sets we treat each (issue year) pair as anobservation and we cluster standard errors at the issue level Forthe GNH data we have 45 observations 45 issues measured inthe same year For the ANES data we have 66 observations 10issues measured in multiple years To begin we simply docu-ment systematic exaggeration in both data sets This is a primaryfocus of the original analysis in GNH (2012) and also in Westfall

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FIGURE III

Two Examples

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et al (2015)rsquos analysis of the ANES data30 Figure IV shows thatthe believed difference between typical conservative and typicalliberal positions is larger than the true difference in mean posi-tions for 109 of the 111 observations The data for both GNH(squares) and ANES (triangles) lie above the 45-degree line(dashed)31 Average exaggeration is 062 positions on the scale(066 in the GNH data 059 in the ANES data)32

The systematic and significant exaggeration of mean differ-ences suggests that the benchmark model of accurate beliefs ismissing something important Indeed this exaggeration reflectsthe fact that believed means are typically more extreme than truemeans First note that the kernel of truth regression (equation(5)) generates exaggeration of mean differences just as docu-mented in Figure IV

EstethtjGTHORN E

stethtjGTHORN frac14 eth1thorn 2THORN frac12EethtjGTHORN EethtjGTHORN

To bring this prediction to the data we regress the believedmean position for each group EBethtjGTHORN on the true mean of thegroup EethtjGTHORN and the true mean of the comparison groupEethtjGTHORN across issues We do this for each group (liberals con-servatives) in each data set separately We also present pooledspecifications that combine the data sets to make a prediction fora given group (liberals conservatives) In these pooled specifica-tions we include a dummy variable indicating whether theobservation came from the ANES data set For all specificationswe cluster observations at the issue level33 The results from re-gression are shown in Table I In every specification we find thatEethtjGTHORN is a significant predictor of EBethtjGTHORN with the predicted pos-itive sign Crucially for five of the six specifications the mean of

30 Chambers and Melnyk (2006) also find evidence of exaggeration of truedifferences in beliefs about political positions

31 For convenience we recode all issues so that the high end of the scale (67)represents the stereotypically more conservative position

32 A natural question to ask is how beliefs vary across liberals and conserva-tives That is do beliefs about a group G depend on membership in G versus ndashG Ourmodel does not speak to this issue However in Online Appendix G we show thatthe results we document below hold for both beliefs held by conservatives and be-liefs held by liberals see Tables A9 A10 and A11

33 In general the results presented below for the ANES data are not largelyimpacted by the decision to cluster at the issue level Similar results are obtained ifthe data are not clustered

STEREOTYPES 1787

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the comparison group EethtjGTHORN is also a significant predictor ofE

BethtjGTHORN with the predicted negative signAlthough these results provide strong evidence of context

dependence and are consistent with our model they do not pindown a role for representativeness of types Our next test relatesthe magnitude of representativeness of tail types to the magni-tude of belief distortions

To this end we implement the regressions in equations (6)and (7) Following Proposition 4 we compute the average repre-

sentativeness of tail types for conservatives RconsH frac14

PtT2tconsPtT2tlib

We

again test the hypothesis that RconsH is a significant predictor of Est

ethtjconsTHORN with a positive sign and a predictor of EstethtjlibTHORN with a

negative sign Table II shows that conditional on true mean RconsH

predicts believed mean for each group G as expected The firstthree specifications display the results for predicting beliefs heldabout conservatives In both data sets the average representa-tiveness of tail types for conservatives is a significant positivepredictor of beliefs held about conservatives The final three spe-cifications display the results for predicting beliefs held about

FIGURE IV

Exaggeration of Differences

QUARTERLY JOURNAL OF ECONOMICS1788

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liberals We find that the average representativeness of tail typesfor conservatives is a negative predictor of beliefs held about lib-erals This effect is significant in the GNH data and marginallysignificant in the ANES data

We present several additional results in Online Appendix GTo further examine the role of representativeness in driving be-liefs we first show the results of Table II carry through when we

TABLE II

AVERAGE REPRESENTATIVENESS OF TAIL POSITIONS PREDICTS BELIEFS

OLS Predicting Believed Mean of Group G for Each Issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position

of group G for issue

078 024 051 072 018 041

(006) (008) (009) (005) (005) (010)

Avg rep of tail types for

conservatives RconsH

019 055 025 014 012 024

(007) (022) (008) (006) (007) (005)

Constant 101 260 184 093 271 201

(026) (045) (029) (022) (025) (032)

R2 082 048 060 091 031 070

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

TABLE I

INFORMATION ABOUT ndashG PREDICTS BELIEFS ABOUT G

OLS predicting believed mean of group G for each issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position of

conservatives for issue

102 098 096 021 019 025

(0097) (0133) (0076) (0060) (0116) (0060)

True mean position of

liberals for issue

035 086 058 0987 039 073

(0106) (0134) (0131) (0066) (0106) (0135)

Constant 151 335 235 069 258 156

(0195) (0269) (0279) (0122) (0249) (0270)

R2 083 053 066 092 032 068

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

STEREOTYPES 1789

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control for the average likelihood on the tail positions (see Table A4in Online Appendix G) Most tellingly we use the model to predictbeliefs across issues and compare those to the data For simplicitywe use the rank-based truncation specification to predict mean be-liefs when stereotypes include the d most representative types ford frac14 1 T We compare these predictions to those of a model inwhich beliefs are obtained by restricting the distribution to the dmost likely types Our benchmark for both models is predicting thebelieved mean from the entire distribution where d = T We showthat the predictions of the rank-based truncation model with d = 4or 5 compare favorably to both a likelihood-based truncation model(with any d) and the accurate beliefs benchmark Interestingly thisresult suggests that stereotypical beliefs are well approximated byneglecting the least representative types (as opposed to focusingonly on the most representative types) and so represent a moderatethough systematic departure from the standard benchmarkFinally we show that the results we document above hold forboth beliefs held by conservatives and beliefs held by liberals (seeTables A9 A10 and A11 in Online Appendix G)

V Conclusion

We present a model of stereotypical thinking in which DMsmaking predictions about a group overweight the grouprsquos mostdistinctive types These overweighted types are not the mostlikely ones given the DMrsquos data but the most representativeones in the sense of being the most diagnostic of the group rela-tive to other groups Representativeness implies that what ismost distinctive of a group depends on what group it is comparedwith We present experimental evidence that confirms this con-text dependence in recall-based assessments of groups Finallywe evaluated the predictions of the model using political data fromexisting large-scale surveys We find context dependence to be akey feature of beliefs Given the richness of the political data wecan go a step further and identify a role for representativeness inparticular As the representativeness of tail types increases beliefsof a group are distorted in the direction of that tail

Our approach provides a parsimonious and psychologicallyfounded account of how DMs generate simplified representationsof reality from social groups to stock returns and offers a unifiedaccount of disparate pieces of evidence relating to this type of

QUARTERLY JOURNAL OF ECONOMICS1790

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uncertainty The model captures the central fact that stereotypeshighlight the greatest difference between groups thus explainingwhy some stereotypes are very accurate while others lack valid-ity Still stereotypes often have a kernel of truth when they arebased on systematicmdasheven if smallmdashdifferences between groupsThis logic allows us to describe a number of heuristics and psy-chological biases many of which arise in the context of predictionproblems Generically our model generates overreaction to diag-nostic information

Our model is based on representativeness and does not cap-ture all the features of stereotypical thinking However it cap-tures perhaps the central feature when we think of a group wefocus on what is most distinctive about it and neglect or under-weight the rest

Saeuroıd Business School University of Oxford

Ohio State University and Harvard Business School

Universita Bocconi and Innocenzo Gasparini Institute

for Economic Research

Harvard University

Supplementary Material

An Online Appendix for this article can be found at QJEonline (qjeoxfordjournalorg)

References

Adorno Theodor Else Frenkel-Brunswik Daniel Levinson and Nevitt SanfordThe Authoritarian Personality (New York Harper amp Row 1950)

Arrow Kenneth lsquolsquoThe Theory of Discriminationrsquorsquo in Discrimination in LaborMarkets Orley Ashenfelter and Albert Rees eds (Princeton NJPrinceton University Press 1973)

Ashton Michael and Victoria Esses lsquolsquoStereotype Accuracy Estimating theAcademic Performance of Ethnic Groupsrsquorsquo Personality and SocialPsychology Bulletin 25 (1999) 225ndash236

Barberis Nicholas Andrei Shleifer and Robert Vishny lsquolsquoA Model of InvestorSentimentrsquorsquo Journal of Financial Economics 49 (1998) 307ndash343

Bayer Sylvia lsquolsquoThe Accuracy of Academic Gender Stereotypesrsquorsquo Sex Roles 40(1999) 787ndash813

Benjamin Dan James Choi and Joshua Strickland lsquolsquoSocial Identity andPreferencesrsquorsquo American Economic Review 100 (2010) 1913ndash1928

Benjamin Dan Matthew Rabin and Collin Raymond lsquolsquoA Model of Non-Belief inthe Law of Large Numbersrsquorsquo Journal of the European Economic Association15 (2015) 515ndash544

Bertrand Marianne lsquolsquoNew Perspectives on Genderrsquorsquo Handbook of LaborEconomics 4 (2011) 1543ndash1590

Bodoh-Creed Aaron Dan Benjamin and Matthew Rabin lsquolsquoThe Dynamics of Base-Rate Neglectrsquorsquo mimeo Haas Business School 2013

STEREOTYPES 1791

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

Bohnet Iris Alexandra van Geen and Max Bazerman lsquolsquoWhen PerformanceTrumps Gender Bias Joint versus Separate Evaluationrsquorsquo ManagementScience 5 (2016) 1225ndash1234

Bordalo Pedro Nicola Gennaioli and Andrei Shleifer lsquolsquoSalience Theory of Choiceunder Riskrsquorsquo Quarterly Journal of Economics 127 (2012) 1243ndash1285

mdashmdashmdash lsquolsquoSalience and Consumer Choicersquorsquo Journal of Political Economy 121(2013) 803ndash843

Briton Nancy and Judith Hall lsquolsquoBeliefs about Female and Male NonverbalCommunicationrsquorsquo Sex Roles 32 (1995) 79ndash90

Buser Thomas Muriel Niederle and Hessel Oosterbeek lsquolsquoGenderCompetitiveness and Career Choicesrsquorsquo Quarterly Journal of Economics 129(2014) 1409ndash1447

Carrell Scott Marianne Page and James West lsquolsquoSex and Science How ProfessorGender Perpetuates the Gender Gaprsquorsquo Quarterly Journal of Economics 125(2010) 1101ndash1144

Chambers John and Darya Melnyk lsquolsquoWhy Do I Hate Thee ConflictMisperceptions and Intergroup Mistrustrsquorsquo Personality and SocialPsychology Bulletin 32 (2006) 1295ndash1311

Chan Wayne Robert R McCrae Filip De Fruyt Lee Jussim CorinnaE Lockenhoff Marleen De Bolle Paul T Costa Jr Angelina R SutinAnu Realo Juri Allik Katsuharu Nakazato Yoshiko ShimonakaMartina Hrebıckova Sylvie Graf Michelle Yik Marina Brunner-SciarraNora Leibovich De Figueora Vanina Schmidt Chang-kyo Ahn Hyun-nie Ahn Maria E Aguilar-Vafaie Jerzy Siuta Barbara SzmigielskaThomas R Cain Janet T Crawford Khairul Anwar Mastor Jean-Pierre Rolland Florence Nansubuga Daniel R MiramontezVeronica Benet-Martınez Jerome Rossier Denis Bratko Iris MarusicJamin Halberstadt Mami Yamaguchi Goran Knezevic Thomas A MartinMirona Gheorghiu Peter B Smith Claudio Barbaranelli Lei WangJane Shakespeare-Finch Margarida P Lima Waldemar KlinkoszAndrzej Sekowski Lidia Alcalay Franco Simonetti Tatyana V AvdeyevaV S Pramila and Antonio Terracciano lsquolsquoStereotypes of Age Differences inPersonality Traits Universal and Accuratersquorsquo Journal of Personality andSocial Psychology 103 (2012) 1050ndash1066

Chen Yan Sherry Xin Liu Tracy Xiao and Margaret Shih lsquolsquoWhich Hat to WearImpact of Natural Identities on Coordination and Cooperationrsquorsquo Games andEconomic Behavior 84 (2014) 58ndash86

Coffman Katherine lsquolsquoEvidence on Self-Stereotyping and the Contribution ofIdeasrsquorsquo Quarterly Journal of Economics 129 (2014) 1625ndash1660

Cunningham Tom lsquolsquoComparisons and Choicersquorsquo mimeo Stockholm University2013

Diekman Amanda Alice Eagly and Patrick Kulesa lsquolsquoAccuracy and Bias in theStereotypes about the Social and Political Attitudes of Women and MenrsquorsquoJournal of Experimental Social Psychology 38 (2002) 268ndash282

Eccles Jacquelynne S Janis E Jacobs and Rena D Harold lsquolsquoGender RoleStereotypes Expectancy Effects and Parentsrsquo Socialization of GenderDifferencesrsquorsquo Journal of Social Issues 46 (1990) 183ndash201

Fryer Roland and Matthew Jackson lsquolsquoA Categorical Model of Cognition andBiased Decision-Makingrsquorsquo BE Journal of Theoretical Economics 8 (2008)1ndash42

Fryer Roland and Steven Levitt lsquolsquoAn Empirical Analysis of the Gender Gap inMathematicsrsquorsquo American Economic Journal Applied Economics 2 (2010)210ndash240

Gennaioli Nicola and Andrei Shleifer lsquolsquoWhat Comes to Mindrsquorsquo Quarterly Journalof Economics 125 (2010) 1399ndash1433

Gennaioli Nicola Andrei Shleifer and Robert Vishny lsquolsquoNeglected RisksFinancial Innovation and Financial Fragilityrsquorsquo Journal of FinancialEconomics 104 (2012) 452ndash468

Gilens Martin lsquolsquoRace and Poverty in America Public Misperceptions and theAmerican News Mediarsquorsquo Public Opinion Quarterly 60 (1996) 515ndash541

Glaeser Edward lsquolsquoThe Political Economy of Hatredrsquorsquo Quarterly Journal ofEconomics 120 (2005) 45ndash86

QUARTERLY JOURNAL OF ECONOMICS1792

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Glover Dyland Amanda Pallais and William Pariente lsquolsquoDiscrimination as a Self-Fulfilling Prophecy Evidence from French Grocery Storesrsquorsquo mimeo HarvardUniversity 2015

Goldin Claudia Lawrence Katz and Ilyana Kuziemko lsquolsquoThe Homecoming ofAmerican College Women The Reversal of the College Gender GaprsquorsquoJournal of Economic Perspectives 20 (2006) 133ndash156

Graham Jesse Brian Nosek and Jonathan Haidt lsquolsquoThe Moral Stereotypes ofLiberals and Conservatives Exaggeration of Differences across thePolitical Spectrumrsquorsquo PLoS One 7 (2012) 1ndash13

Grether David lsquolsquoBayes Rule as a Descriptive Model The RepresentativenessHeuristicrsquorsquo Quarterly Journal of Economics 95 (1980) 537ndash557

Griffin Dale and Amos Tversky lsquolsquoThe Weighing of Evidence and theDeterminants of Confidencersquorsquo Cognitive Psychology 24 (1992) 411ndash435

Guiso Luigi Ferdinando Monte Paola Sapienza and Luigi Zingales lsquolsquoCultureGender and Mathrsquorsquo Science 320 (2008) 1164ndash1165

Hilton James and William Von Hippel lsquolsquoStereotypesrsquorsquo Annual Review ofPsychology 47 (1996) 237ndash271

Hyde Janet Sara Lindberg Marcia Linn Amy Ellis and Caroline WilliamslsquolsquoGender Similarities Characterize Math Performancersquorsquo Science 321 (2008)494ndash495

Judd Charles and Bernardette Park lsquolsquoDefinition and Assessment of Accuracy inSocial Stereotypesrsquorsquo Psychological Review 100 (1993) 109ndash128

Jussim Lee Jarret Crawford Stephanie Anglin John Chambers Sean Stevensand Florette Cohen lsquolsquoStereotype Accuracy One of the Largest and MostReplicable Effects in All of Social Psychologyrsquorsquo in The Handbook ofPrejudice Stereotyping and Discrimination Todd Nelson ed (MahwahNJ Lawrence Erlbaum 2015)

Kahneman Daniel and Amos Tversky lsquolsquoSubjective Probability A Judgment ofRepresentativenessrsquorsquo Cognitive Psychology 3 (1972) 430ndash454

mdashmdashmdash lsquolsquoOn the Psychology of Predictionrsquorsquo Psychological Review 80 (1973) 237ndash251

Kaplowitz Stan Bradley Fisher and Clifford Broman lsquolsquoHow Accurate ArePerceptions of Social Statistics about Blacks and Whitesrsquorsquo Public OpinionQuarterly 67 (2003) 237ndash243

Kersten Daniel Pascal Mamassian and Alan Yuille lsquolsquoObject Perception asBayesian Inferencersquorsquo Annual Review of Psychology 55 (2004) 271ndash304

Klein Richard Kate A Ratliff Michelangelo Vianello Reginald B Adams JrStepan Bahnik Michael J Bernstein Konrad Bocian Mark J BrandtBeach Brooks Claudia Chloe Brumbaugh Zeynep CemalcilarJesse Chandler Winnee Cheong William E Davis Thierry DevosMatthew Eisner Natalia Frankowska David Furrow Elisa Maria GallianiFred Hasselman Joshua A Hicks James F Hovermale S Jane HuntJeffrey R Huntsinger Hans IJzerman Melissa-Sue John Jennifer A Joy-Gaba Heather Barry Kappes Lacy E Krueger Jaime Kurtz CarmelA Levitan Robyn Mallett Wendy L Morris Anthony J Nelson JasonA Nier Grant Packard Ronaldo Pilati Abraham M RutchickKathleen Schmidt Jeanine L Skorinko Robert Smith Troy G SteinerJustin Storbeck Lyn M Van Swol Donna Thompson Anna van rsquot VeerLeigh Ann Vaughn Marek Vranka Aaron Wichman Julie A Woodzickaand Brian A Nosek lsquolsquoInvestigating Variation in Replicability A ManyLabs Replication Projectrsquorsquo Social Psychology 45 (2014) 142ndash152

Lundberg Shelly and Richard Startz lsquolsquoPrivate Discrimination and SocialIntervention in Competitive Labor Marketsrsquorsquo American Economic Review73 (1983) 340ndash347

Madon Stephanie Max Guyll Kathy Aboufadel Eulices Montiel Alison SmithPolly Palumbo and Lee Jussim lsquolsquoEthnic and National Stereotypes ThePrinceton Trilogy Revisited and Revisedrsquorsquo Personality and SocialPsychological Bulletin 27 (2001) 996ndash1010

Martin Carol lsquolsquoA Ratio Measure of Sex Stereotypingrsquorsquo Journal of Personality andSocial Psychology 52 (1987) 489ndash499

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ibrary on October 28 2016

httpqjeoxfordjournalsorgD

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McCauley Clark Krishna Thangavelu and Paul Rozin lsquolsquoSex Stereotyping ofOccupations in Relation to Television Representations and Census FactsrsquorsquoBasic and Applied Social Psychology 9 (1988) 197ndash212

Mullainathan Sendhil lsquolsquoThinking through Categoriesrsquorsquo mimeo HarvardUniversity 2002

Ortoleva Pietro and Erik Snowberg lsquolsquoOverconfidence in Political BehaviorrsquorsquoAmerican Economic Review 105 (2015) 504ndash535

Phelps Edmund lsquolsquoThe Statistical Theory of Racism and Sexismrsquorsquo AmericanEconomic Review 62 (1972) 659ndash661

Pope Devin and Justin Sydnor lsquolsquoGeographic Variation in the Gender Differencesin Test Scoresrsquorsquo Journal of Economic Perspectives 24 (2010) 95ndash108

Rabin Matthew lsquolsquoInference by Believers in the Law of Small NumbersrsquorsquoQuarterly Journal of Economics 117 (2002) 775ndash816

Rabin Matthew and Joel Schrag lsquolsquoFirst Impressions Matter A Model ofConfirmatory Biasrsquorsquo Quarterly Journal of Economics 114 (1999) 37ndash82

Rabin Matthew and Dimitri Vayanos lsquolsquoThe Gamblerrsquos and Hot-Hand FallaciesTheory and Applicationsrsquorsquo Review of Economic Studies 77 (2010) 730ndash778

Reuben Ernesto Paola Sapienza and Luigi Zingales lsquolsquoHow Stereotypes ImpairWomenrsquos Careers in Sciencersquorsquo Proceedings of the National Academy ofSciences 111 (2014) 4403ndash4408

Rosch Eleanor lsquolsquoNatural Categoriesrsquorsquo Cognitive Psychology 4 (1973) 328ndash350Ryan Carey S lsquolsquoAccuracy of Black and White College Studentsrsquo In-Group and

Out-Group Stereotypesrsquorsquo Personality and Social Psychology Bulletin 22(1996) 1114ndash1127

Schneider David The Psychology of Stereotyping (New York Guilford Press2004)

Schneider David Albert Hastorf and Phoebe Ellsworth Person Perception(Reading MA Addison-Wesley 1979)

Shih Margaret Todd Pittinsky and Nalini Ambady lsquolsquoStereotype SusceptibilityIdentity Salience and Shifts in Quantitative Performancersquorsquo PsychologicalScience 10 (1999) 80ndash83

Shih Margaret Todd Pittinsky and Amy Trahan lsquolsquoDomain-Specific Effects ofStereotypes on Performancersquorsquo Self and Identity 5 (2006) 1ndash14

Steele Claude Whistling Vivaldi How Stereotypes Affect Us and What We CanDo (New York Norton 2010)

Tenenbaum Joshua and Thomas Griffiths lsquolsquoThe Rational Basis ofRepresentativenessrsquorsquo 23rd Annual Conference of the Cognitive ScienceSociety (2001) 1036ndash1041

Tversky Amos and Daniel Kahneman lsquolsquoExtensional versus Intuitive ReasoningThe Conjunction Fallacy in Probability Judgmentrsquorsquo Psychological Review 90(1983) 293ndash315

Weinberger Catherin lsquolsquoIs the Science and Engineering Workforce Drawn fromthe Far Upper Tail of the Math Ability Distributionrsquorsquo mimeo UCSB 2005

Westfall Jacob Leaf Van Boven John Chambers and Charles Judd lsquolsquoPerceivingPolitical Polarization in the United States Party Identity Strength andAttitude Extremity Exacerbate the Perceived Partisan DividersquorsquoPsychological Science 10 (2015) 145ndash158

Wolsko Christopher Bernadette Park Charles Judd and Bernd WittenbrinklsquolsquoFraming Interethnic Ideology Effects of Multicultural and Color-BlindPerspectives on Judgments of Groups and Individualsrsquorsquo Journal ofPersonality and Social Psychology 78 (2000) 635ndash654

QUARTERLY JOURNAL OF ECONOMICS1794

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

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Page 4: I. Introduction · uneducated at the beginning of the 20th century, and as high achievers at the beginning of the 21st (Madon et al. 2001). Social science has produced three broad

in Florida and in the overall United States population isshown here2

The table shows that the age distributions in Florida and in therest of the United States are very similar Yet someone over 65 ishighly representative of a Florida resident because this age bracket

maximizes the likelihood ratio Pr ethtjFloridaTHORNPr ethtjUSTHORN When thinking about the

age of Floridians then the 65+ type immediately comes to mindbecause in this age bracket Florida is most different from the rest ofthe United States in the precise sense of representativenessRepresentativeness-based recall induces an observer to overweightthe 65+ type in their assessment of the average age of Floridians

This example also illustrates how stereotypes can be inaccu-rate Indeed and perhaps surprisingly only about 17 of Floridaresidents are elderly The largest share of Florida residentsnearly as many as in the overall US population are in the agebracket 19ndash44 which maximizes PrethtjFloridaTHORN Being elderly isnot the most likely age bracket for Florida residents but ratherthe age bracket that occurs with the highest relative frequencyA stereotype-based prediction that a Florida resident is elderlyhas very little validity

The same logic of representativeness suggests that the reasonpeople stereotype the Irish as red-headed is that red hair is morecommon among the Irish than among other groups even though itis not that common in absolute terms The reason people stereo-type Republicans as wealthy is that the wealthy are more commonamong Republicans than Democrats3 In both cases the represen-tation entails judgment errors people overestimate the proportionof red-haired among the Irish or of the wealthy among theRepublicans

2 Data from the 2010 US Census see httpfactfindercensusgovfacestableservicesjsfpagesproductview xhtmlpid=DEC_10_DP_DPDP1ampsrc=pt

3 See httpwwwnytimescompackagespdfpolitics20041107_px_ELECTORATExls

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We find that representativeness often generates fairly accu-rate stereotypes but sometimes causes stereotypes to be inaccu-rate particularly when groups have similar distributions thatdiffer most in unlikely types More generally our model high-lights two critical properties

Stereotypes amplify systematic differences betweengroups even if these differences are in reality verysmall When groups differ by a shift in means stereotyp-ing exaggerates differences in means and when groupsdiffer by an increase in variance stereotyping exagger-ates the differences in variances In these cases (but notalways) representativeness yields stereotypes that con-tain a lsquolsquokernel of truthrsquorsquo in the sense that they differen-tiate groups along existing and highly diagnosticcharacteristics exactly as Hilton Von Hippel andSchneider define them

Stereotypes are context dependent The assessment of agiven target group depends on the reference group towhich it is compared

In line with the social cognition approach to stereotypes asignificant body of psychological research on beliefs about genderrace age and political groups finds that stereotypes broadly re-flect reality but display biases Social psychologists have exploredthe extent to which stereotypes exaggerate real differences thuspossessing a kernel of truth Evidence on exaggeration varies bydomain For race and gender many studies have reportedroughly accurate beliefs whereas others have found underesti-mation or exaggeration of true differences (Jussim et al 2015)4

For age and political stereotypes evidence points more stronglytoward exaggeration5 Schneider (2004 337) summarizes the

4 For evidence of roughly accurate beliefs for race see for example Ashtonand Esses (1999) on beliefs of academic ability Kaplowitz Fisher and Broman(2003) on income poverty rates and out-of-wedlock births and Wolsko et al(2000) on a array of positive and negative attributes Ryan (1996) and Gilens(1996) find evidence of exaggeration of race stereotypes on personal attributesand poverty rates respectively Some studies have found roughly accurate beliefson gender (McCauley Thangavelu and Rozin 1988 Briton and Hall 1995Diekman Eagly and Kulesa 2002) while others find evidence of exaggeration(Martin 1987 Bayer 1999)

5 See Chan et al (2012) on age We discuss evidence on political stereotypes inSection IV

STEREOTYPES 1757

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existing empirical work on stereotype accuracy as follows lsquolsquothebest we can do by way of general summary is to say that somestereotypes held by some people for some groups are sometimesaccuratersquorsquo Our empirical investigation explores the connectionbetween stereotype accuracy and representativeness which wemeasure using the previously defined likelihood ratio

We first assess the role of representativeness and contextdependence in the lab We construct a group of mundane objectsG and present it to participants next to a comparison group ndashGIn our baseline condition the comparison group is chosen so thatno type is particularly representative of group G In our treat-ment we change the comparison group ndashG while leaving thetarget group G unchanged The new comparison group givesrise to highly representative types within G In line with thekey prediction of our model participants in the treatment condi-tion shift their assessment of G toward the representative types

We test the model using two data sets on political preferencesand beliefs about political preferences in the United States Heregroups are political constituencies (Democrats and Republicans)and types are their positions on a number of issues Holding fixedthe groups and the set of types and varying the groupsrsquo true dis-tributions across issues the data allow us to test whether beliefsabout political preferences are shaped by representativeness Wefirst show that such beliefs depart from the truth by exaggerating(mean) differences as per the kernel of truth logic We then ex-plore how the extent of exaggeration varies across issuesConsistent with the model we find that beliefs systematicallydepart from rational expectations and that the degree to whichthey exaggerate true differences is a function of representative-ness While representativeness is not the only heuristic thatshapes recall (availability driven by recency or frequency of ex-posure also plays a role) it explains the fact that in the datastated beliefs indeed exaggerate differences among groups

Since Kahneman and Tverskyrsquos (1972 1973) work on heuris-tics and biases several studies have formally modeled heuristicsabout probabilistic judgments and incorporated them into eco-nomic models Work on the confirmation bias (Rabin andSchrag 1999) and on probabilistic extrapolation (Grether 1980Barberis Shleifer and Vishny 1998 Rabin 2002 Rabin andVayanos 2010 Benjamin Rabin and Raymond 2015) assumesthat the decision maker has an incorrect model in mind or incor-rectly processes available data Our approach is instead based on

QUARTERLY JOURNAL OF ECONOMICS1758

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the assumption that representative information comes foremostto mind when making judgments The mental operation that liesat the heart of our modelmdashgenerating a prediction for the distri-bution of types in a group based on data stored in memorymdashalsocaptures base rate neglect and overreaction to diagnostic infor-mation The underweighting or neglect of information in ourmodel simplifies judgment problems in a way related to modelsof categorization (Mullainathan 2002 Fryer and Jackson 2008)In these models however decision makers use coarse categoriesorganized according to likelihood not representativeness Thisapproach generates imprecision but does not create a systematicbias for overestimating unlikely events nor does it allow for con-text-dependent beliefs In our empirical analysis of political be-liefs we explicitly compare the predictions of representativeness-based recall to those of likelihood-based models and find that theevidence supports the former

In modeling representativeness we follow the specification ofGS (2010) but investigate a new set of questions GS (2010) ex-amine how representativeness distorts the assessed probabilitiesof alternative hypotheses but not how the probability of a givenhypothesis or group is distributed across its constituent elementsIn the context of the current setting GS (2010) ask how imperfectrecall affects the assessed probability that a randomly drawnmember from a universe belongs to group G The current arti-cle in contrast asks which type t we expect to draw once we knowthat we are facing group G GS (2010) show how representative-ness generates biased probabilistic assessments such as conjunc-tion and disjunction fallacies This article deals with perhaps abroader and more ubiquitous problem of stereotype formationextensively studied by other social scientists but largely ne-glected by economists

Section II describes our model In Section III we examine theproperties of stereotypes including the forces that shape stereo-type accuracy and illustrate these properties with examples InSection IV we bring the model to the data performing a lab ex-periment and analyzing existing surveys of political beliefsSection V concludes The Online Appendix presents proofs anumber of extensions of the model and additional results forthe experiments and field evidence

STEREOTYPES 1759

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II A Model of Representativeness and Stereotypes

IIA The Model

A decision maker (DM) faces a prediction problem such asassessing the ability of a job candidate from a certain ethnicgroup the future performance of a firm belonging to a certainsector or future earnings based on own gender

Formally there is a set of types of interest T and an overallpopulation of which group G is a subset The set of typesT can be unordered (eg occupations) or ordered (and typi-cally cardinal eg earnings levels) When T is ordered wewrite T frac14 ft1 tTg with t1 lt t2 lt lt tT6 There is a probabil-ity or frequency distribution 2 ethT THORN that induces a condi-tional distribution PrethT frac14 tjGTHORN when restricted to G7 In whatfollows we denote by tG frac14 PrethT frac14 tjGTHORN the probability of typet in group G and by G the vector ethtGTHORNt2T containing the condi-tional distribution

The DMrsquos goal is to assess the distribution of the types ofinterest in a particular group G Although the DM has stored inmemory the full distribution he retrieves from memory a dis-torted version of G that overweights the probability of thosetypes that are most representative of G relative to a comparisongroup ndashG Generically ndashG is a group in that is distinct from Gnamely G7 nG although in some cases it can coincide withthe complement of G

According to Tversky and Kahneman (1983) a type t is rep-resentative of G if it is relatively more likely to occur in G thanin ndashG Definitions 1 and 2 formalize this representativeness-based recall following GS (2010)

6 For simplicity we also use T to denote the number of types jTj The modelapplies also to cases in which types (i) are multidimensional capturing a bundle ofattributes such as occupation and nationality or (ii) are continuous We considerthese cases in Online Appendixes C and D respectively Also G may represent anycategory of interest such as the historical performance of a firm or industry actionsavailable to a decision maker (T = set of payoffs G = occupations) or categories inthe natural world (T = ability to fly G = birds)

7 In many applications each individual in is characterized by a determin-istic type (eg age hair color) As a result ethtTHORN frac14 1

jj For instance each Floridian

has a single age type (at the finest temporal resolution) When types are stochasticinstead such as when estimating future earnings of a person or a firm each indi-vidual is described by a nondegenerate distribution

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DEFINITION 1 The representativeness of type t for group G givencomparison group ndashG is defined as the likelihood ratio

RethtGGTHORN tG

tGeth2THORN

Definition 1 implies that DMs are attuned to log differencesin probabilities representativeness depends on the percentageprobability increase of a type from ndashG to G This captures aform of diminishing sensitivity whereby for a fixed probabilitydifference a type is more likely to be overweighed if it is unlikelyin the comparison group8 Thus the representative age of aFloridian is 65+ because people in this age bracket are morecommon in Florida than in the rest of the United StatesStatistically representative types are also diagnostic of thetarget group G Indeed the higher is RethtGGTHORN the more confi-dent is a Bayesian DM observing t that t belongs to G rather thanto ndashG9

The ease of recall of highly representative types affectsjudgments because more easily recalled types are overweighted

We model distorted recall as follows Denote by RethtGGTHORN

tG

tG

t2T

the vector of representativeness of all types in G

We then have

8 Our definition of representativeness links to Weberrsquos law of sensory percep-tion see Section IIB It also links to our previous work on salience in which wepostulated that log differences in payoffs determine the attention to lottery payoffs(Bordalo Gennaioli and Shleifer 2012) and to goodsrsquo attributes (BordaloGennaioli and Shleifer 2013) Equation (2) establishes the same principle for thedomain of probabilities

9 This insight led Tenenbaum and Griffiths (2001) to define representative-ness as individualsrsquo sense as intuitive Bayesians of updating in reaction to dataTheir definition like ours is in terms of the likelihood ratio However Tenenbaumand Griffiths interpret representativeness as a mechanism that affects intuitivejudgments of similarity rather than beliefs (eg it accounts well for lab evidencewhere subjects are asked to rank types in terms of representativeness or ofstrength of association with a group) Accordingly they do not consider the possi-bility of systematically distorted and context dependent beliefs

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DEFINITION 2 The DM attaches to each type t 2 T in group G adistorted probability

sttG frac14 tG

htethRethtGGTHORNTHORNPs2T sGhsethRethtGGTHORNTHORN

eth3THORN

where ht RTthornRthorn is a weighting function such that

(i) The weight ht is a symmetric function of the representa-

tiveness of types s 6frac14 t Formally ht frac14 h tG

tG

sG

sG

s2Tn tf g

where h Rthorn RT1thorn Rthorn is a function that is invariant to

a permutation of the last T ndash 1 arguments(ii) Weighing of a type increases in own representativeness

and decreases in the representativeness of other typesFormally the function hethTHORN is weakly increasing in itsfirst argument and weakly decreasing in the other T 1arguments

We call the distribution ethsttGTHORNt2T the stereotype for G If a type

t is objectively more likely namely tG is higher then the ste-reotype attaches higher probability to it By property i distor-tions are due exclusively to the fact that a type is more or lessrepresentative than the others In particular if all types areequally representative the DM equally weighs all of them ath(1) and holds rational expectations about G If instead the rep-resentativeness of different types differs property ii implies thatthe stereotype ceteris paribus overweights the probability of morerepresentative types

Most of the results we explore in this article hold for a gen-eral weighing function htethTHORN Specific functional forms captureadded assumptions about the psychology of representativeness-based recall and are useful in applications We outline a few spe-cifications and their properties

Rank-based stereotypes the ranking of the representa-tiveness of different types shapes distortions Denote byrethtTHORN 2 f1 Tg the representativeness ranking of type tWhen r(t) = 1 type t is the most representative one (po-tentially with ties) We can specify two ways in which atypersquos representativeness ranking distorts its probability

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(i) Rank-based truncation the DM only recalls the typesthat have representativeness ranking of at most dnamely ft 2 TjrethtTHORN dg Zero probability is attachedto the remaining types10 Denote by IethrethtTHORN dTHORN an in-dicator function taking the value 1 if the representa-tiveness ranking of t is at most d Then theweighting function is ht frac14 IethrethtTHORN dTHORN so that

sttG frac14 tG

IethrethtTHORN dTHORNPs2T sGIethrethsTHORN dTHORN

which is the true conditional probability within re-called types This assumption is used in Gennaioliand Shleifer (2010)11

(ii) Rank-based discounting the DM discounts by a con-stant factor 2 frac1201 the odds of type t relative to itsimmediate predecessors in the representativenessranking Lower implies stronger discounting ofless representative types Formally the weightingfunction is ht frac14

rethtTHORN so that

sttG frac14 tG

rethtTHORNPs2T sG

rethsTHORN

Representativness-based discounting all else equal theweight attached by the DM to type t increases continuouslywith its representativeness One convenient formulation is

ht frac14tG

tG

so that

10 These neglected types are not viewed as impossible they are just assignedzero probability in the DMrsquos current thinking This formulation allows us to modelsurprise and reactions to unforeseen contingencies which have proved useful in-gredients in modeling probabilistic judgments (GS 2010) as well as neglect of risk infinancial crises (Gennaioli Shleifer and Vishny 2012)

11 Specifically in GS (2010) the assessed probability that a certain hypothesisG is true is equal to

Pr ethGTHORN frac14

Pt tGIethrethtTHORN dTHORNP

t tGIethrethtTHORN dTHORN thornP

t t=GIethrethtTHORN dTHORN

which increases in the ratio between the total probability mass recalled for Gand that recalled for G frac14 nG

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sttG frac14 tG

tG

tG

P

s2T sGsG

sG

where 0 captures the extent to which representative-ness distorts beliefs This formulation is particularly con-venient when dealing with continuous distributions ofthe exponential or power classes

These functional forms all embody the main idea of our modelthat the stereotype overweights the probability of more represen-tative types Rank-based truncation captures a central manifes-tation of limited memory forgetting unrepresentative typesSmoother discounting (based on ranking or on representative-ness) may be more appropriate when the type space is smalland smooth discounting can be more tractable in certain settings

Section III characterizes the general properties of stereotypesIn particular it shows their ability to account for social psycholo-gistsrsquo kernel of truth hypothesis under the general weighting func-tion of Definition 2 To bring the model to the data in Section IVBwe derive linear approximations of stereotypical beliefs by assum-ing that the weighting function is differentiable with respect to atypersquos representativeness This assumption excludes rank-basedweighting but allows for many possibilities

IIB Discussion of Assumptions

Before moving to the formal analysis we discuss some prop-erties and limitations of our approach Representativeness-basedrecall the idea that individuals recall distinctive group types canbe viewed as an instance of what Kahneman and Tversky calllsquolsquoattribute substitutionrsquorsquo When dealing with the difficult questionlsquolsquowhat is the distribution of hair color among the Irishrsquorsquo peopleintuitively answer to the simpler question lsquolsquowhich hair color dis-tinguishes the Irish peoplersquorsquo Critically as discussed byKahneman and Tversky attribute substitution does not occurbecause people misunderstand the original question or mechan-ically confuse the assessment of PrethtjGTHORN with that of PrethGjtTHORNRather it occurs because the distinctive or representative typesimmediately come to mind and individuals anchor their overallprobability judgment to them As a consequence subjects do notonly make mistakes in judging the probability that a Floridian is

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over age 65 They also give too high an answer to the questionlsquolsquowhat is the average age of a Floridianrsquorsquo12

One interesting question is whether the process of stereotyp-ing we describe is optimal in some sense Focusing mental repre-sentations on a few types can be justified by the costs of thinkingor retrieval This approach however is not enough to explainwhy individuals should focus on representative rather thanlikely types We do not formally analyze the optimality of repre-sentativeness here but we mention some relevant considerationsfrom cognitive psychology Kahneman and Tversky (1979) stressthe similarity between many perceptual and cognitive operationsFor instance the highlight of contrastmdasha key principle of visualperceptionmdashis invoked to justify the prospect theory assumptionthat the carriers of utility are changes relative to a referencepoint The same logic applies to our model in which stereotypesprecisely highlight the contrast between groups

In visual perception assessing properties such as brightnesscolor size or distance to an object by comparing them to otherproximate objects has been shown to be optimal in the presence ofmultiplicative background noise (Kersten Mamassian andYuille 2004 Cunningham 2013) Our formulation of representa-tiveness is related to the same idea in the sense that individualsestimating properties of one group stress differences from an-other group In a noisy world in which attention is limited thisprocess may optimally allow for swift reactions to changes ingroup characteristics even if errors are sometimes made13

12 Indeed in many cases mere confusion of PrethtjGTHORNwith PrethGjtTHORNwould not yieldthe phenomenon of stereotyping In the Irish hair color example the probability ofbeing Irish conditional on having red hair is

PrethIrishjredTHORN frac14PrethredjIrishTHORNPrethIrishTHORN

PrethredjIrishTHORNPrethIrishTHORN thorn PrethredjNonIrishTHORNPrethNonIrishTHORN

This probability is clearly very small given that the Irish population is a tinyfraction of the world population Confusion of PrethtjGTHORN with PrethGjtTHORN in this casewould lead to an understatement of the probability of the red-haired Irish

13 To give a simple example suppose thatmdashas in the case of Proposition 3mdashthevariance in the environment increases in the sense that extreme tail events becomemore likely Then a likelihood-based stereotype would detect no change whereas arepresentativeness-based stereotype would focus on the heightened probability ofthe tails In particular an asymmetric increase in tail probabilities that shifts themean would be detected by a representativeness-based stereotype even if the dis-tributionrsquos mode does not change

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Exploring this idea formally is an interesting avenue for futurework

Consider some limitations of our model First representa-tiveness is not the only heuristic that shapes recall Decisionmakers may for instance find it easier to recall types that aresufficiently likely Another potentially important mechanism isavailability understood by Kahneman and Tversky (1972) as thelsquolsquoeasersquorsquo with which information comes to mind (because of actualfrequency or repetition) In Online Appendix E we present a trun-cation-based recall mechanism in which distortions are driven bya combination of representativeness and likelihood of types(which is equivalent to relaxing property i in Definition 2) Thismodel can offer a useful starting point to capture availability aswell even though a full model of availability is beyond the scopeof this article Even in this more general setting the influence ofrepresentativeness on recall is the driving force of stereotypesthat in line with the social psychology perspective are basedon underlying differences among groups As we show in SectionIV this feature is critical in accounting for the evidence

The second set of model-related issues concerns how to spe-cify the elements of Definition 1 in applications group G the typespace T and the reference group ndashG Take the specification of thegroup G and of the type space T Often the problem itself pro-vides a natural specification of these features This is the case inthe empirically important class of lsquolsquoclosedrsquorsquo questions such asthose used in surveys which provide respondents with a set ofalternatives as in the data we use in Section IV More generallythe problem solved by the DMmdashsuch as evaluating the resume ofa job applicant coming from a certain ethnic groupmdashprimes agroup a dimension of interest and a set of types (eg the appli-cantrsquos qualification or skill levels) When types have a naturalorder such as income age or education the granularity of T isalso naturally given by the problem (income age and years ofschooling brackets) When the set of types is not specified by theproblem DMs spontaneously generate one14 It would be useful tohave a model of which dimensions and types come to mind par-ticularly for more open-ended problems Psychologists have

14 For example suppose a person is asked to guess the typical occupation of ademocratic voter in an lsquolsquoopen-endedrsquorsquo format (without being provided a set of alter-natives) Here the level of granularity at which types are defined is not obvious (egteacher versus a university teacher vs a professor of comparative literature)

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sought to construct a theory of natural types and dimensions(Rosch 1973) We do not make a contribution to this problembut we note that in many problems of interest in economics thedimension as well as the set of types is naturally givenFurthermore in our model details of the type space can be impor-tant under rank-based truncation but they matter less undersmooth discounting

Consider finally the role of the comparison group ndashG Thisgroup captures the context in which a stereotype is formed andagain is often implied by the problem when G = Floridians ndashG =rest of US population when G = African Americans ndashG = whiteAmericans A distinctive prediction of our model confirmed byour experiments in Section IVA is that the stereotype for agiven group G depends on the comparison group ndashG15 WhenndashG is not pinned down by the problem itself to derive testablepredictions from representativeness we set G frac14 nG where

is the natural population over which the unconditional distribu-tion of types is measured

III Properties of Stereotypes

We now study stereotypical beliefs and their accuracy Toillustrate the role of representativeness we first ask to whatextent the most representative type is a good fit for the groupnamely whether it is modal Next we assess the accuracy of theentire stereotypical distribution To do so we focus on a cardinaltypes and compare the stereotypersquos mean and variance to the trueones

15 Some empirical papers have taken a similar approach exogenously varyingthe natural comparison group through priming Benjamin Choi and Strickland(2010) show that priming racial or ethnic identity can affect the risk preferences ofparticipants Chen et al (2014) find that Asian students cooperate less with out-group members when primed with their ethnic identity rather than their universityidentity Shih Pittinsky and Ambady (1999) show that Asian American womenstereotype themselves as better or worse in math with corresponding impact onperformance when their ethnicity or gender respectively is primed ShihPittinsky and Trahan (2006) replicate this effect using a verbal task documentingthat Asian American women performed better when their gender rather than theirethnicity was primed Although the generalizability and replicability of priminghas been doubted (Klein et al 2014) this body of evidence is consistent with contextdependence

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IIIA Likely versus Unlikely Exemplars

The most representative type for a group is the one thatagents most easily recall and associate with the group itself forinstance a red-haired Irishman or a 65+-year-old FloridianSocial psychologists call this type the exemplar of the groupAccordingly we define

DEFINITION 3 A type t is an exemplar for G given comparisongroup ndashG when

t 2 arg maxt

tG

tG

Under any specification of the weighting function ht inDefinition 2 overweighting (weakly) increases as we movetoward more representative types so the exemplar is also thetype whose probability is overweighted the most16 By analyzingthe exemplar then we can gauge whether representativenessinduces the DM to overweight a likely type (as happens in stan-dard models of categorical thinking) or an unlikely type Whenoverweighting occurs in unlikely and extreme types the biases ofstereotypes can be particularly severe17

Equation (2) yields the following characterization

PROPOSITION 1 Suppose the conditional distributions G and G

are not identical Consider two extreme cases

(i) If for all t t0

2 T we have that tG gt t0 G if and only iftG gt t0 G then the modal type is not an exemplar forat least one group

(ii) If for all t t0

2 T we have that tG gt t0 G if and only iftG lt t0 G then for each group the modal type is theexemplar

16 Consider the function hethTHORN from Definition 2 When applied to more repre-sentative types the first argument of the function increases while one of the otherT ndash 1 arguments decreases As a result the weighting factor ht (and thus overweigh-ing

sttG

tG) increases as well

17 In the rank-based truncation model the frequency of the exemplar providesa measure of stereotype accuracy By accuracy we mean the extent to which thestereotype minimizes the distance

Pt eth

sttG tGTHORN

2 When d = 1 and only one type isrecalled (there are no ties) accuracy is maximized if the exemplar is the most likelytype and minimized if the exemplar is the least likely type

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Case i says that when groups have similar distributions inthe sense of having the same likelihood ranking the most repre-sentative type is unlikely for at least one group potentially bothRepresentativeness draws the DMrsquos attention to group differ-ences neglecting the fact that the groups are similar and havethe same mode This mechanism generates inaccurate stereo-types and is illustrated by the Florida example This resultholds under any measure of representativeness that differenti-ates the two groups (eg the difference tG tG)

Case ii says that the most representative type tends to belikely for both groups when the distributions are very differentIn this case groups differ the most around their modes so repre-sentativeness and likelihood coincide Thinking of Swedes aslsquolsquoblondrsquorsquo and Europeans as lsquolsquodark hairedrsquorsquo is accurate precisely be-cause these are majority traits of the Swedish and European pop-ulations respectively In these cases stereotyping yields fairlyreliable models Of course there is still some inaccuracy Evenin the case of likely exemplars judgment errors can be signifi-cant For instance voters in some US states are perceived aslsquolsquobluersquorsquo or lsquolsquoredrsquorsquo because a majority of the population votesDemocrat or Republican In reality even in lsquolsquobluersquorsquo states farfrom everyone votes Democrat In the 2012 presidential electionvote shares of either candidate in most states ranged from 40 to6018

When DMs strongly overweight representative types themost severe biases occur when those types are unlikely and ex-treme This is true both under rank based truncations and undersmooth discounting functions (see Section IIIB) Ethnic stereo-types based on crime or terrorism exhibit this error they neglectthe fact that by far the most common types in all groups arehonest and peaceful

IIIB Stereotypical Moments

We now characterize how the first two moments of a distri-bution are distorted by the process of stereotyping To do so wemust restrict our analysis to cardinal ordered types The follow-ing results hold for any weighting function htethTHORN satisfyingDefinition 2 We consider two canonical cases that prove usefulin illustrating the predictions of the model

18 Presidential Election Results NBCNewscom see httpelectionsnbcnewscomnspolitics2012allpresident (accessed 5 September 2016)

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In the first case groups G and ndashG are such that the likelihoodratio tG

tGis monotonic in t The monotone likelihood ratio prop-

erty (MLRP) holds to a first approximation in many empiricalsettings and is also assumed in many economic models such asstandard agency models19 If tG

tGis monotonically increasing (de-

creasing) in t then group G is associated with higher (lower)values of t relative to the comparison group ndashG Formally

PROPOSITION 2 Suppose that MLRP holds and assume wlogthat the likelihood ratio tG

tGis strictly increasing in t Then

for any weighting function htethTHORN that is not constant in therelevant range

EstethtjGTHORN gt EethtjGTHORN gt EethtjGTHORN gt E

stethtjGTHORN

Under MLRP the most representative part of the distribu-tion for G is the right tail if tG

tGincreases in t or the left tail if tG

tG

decreases in t The representative tail is then overweighted whilethe nonrepresentative tail is underweighted As a consequencethe assessed mean E

stethtjGTHORN is too extreme in the direction of therepresentative tail

Critically in line with the social cognition perspective the ste-reotype contains a kernel of truth the DM overestimates the meanof G if this group has a higher mean than the comparison groupnamely EethtjGTHORN gt EethtjGTHORN and conversely if EethtjGTHORN lt EethtjGTHORN TheDM exaggerates this true difference because he inflates the asso-ciation of G with its most representative types20 For instancewhen judging an asset manager who performs well we tend to

19 Examples include the binomial and the Poisson families of distributionswith different parameters The characterization of distributions satisfying MLRPis easier in the case of continuous distributions (see Online Appendix D) two dis-tributions f(x) f ethx THORN that differ only in their mean satisfy MLRP if and only if thedistribution f(x) is log-concave Examples include the exponential and normal dis-tributions To the extent that discrete distributions sufficiently approximate thesedistributions (as the Poisson distribution PoisethTHORN approximates the normal distri-bution Neth THORN for large l) they will also satisfy MLRP

20 Depending on the distribution and the weighing function the DMrsquos assess-ment of the variance VarethtjGTHORNmay also be dampened relative to the truth This isoften true under the truncation weighing function In this case stereotyping effec-tively leads to a form of overconfidence in which the DM holds extreme views andoverestimates the precision of his assessment That extreme views and overconfi-dence (in the sense of over precision) go together has been documented in the settingof political ideology among others (Ortoleva and Snowberg 2015)

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overemphasize skill relative to luck because higher skill levels arerelatively more associated with higher performance This occurseven if for both skilled and unskilled managers high performanceis mostly due to luck

In the second case for which we characterize the stereotypi-cal distributions groups G and ndashG have the same mean EethtjGTHORNfrac14 EethtjGTHORN frac14 EethtTHORN but differ in their variance We abstract fromskewness and higher moments by considering distributionsethtGTHORNt2T and ethtGTHORNt2T that share the same support and are sym-metric around the medianmean EethtTHORN

PROPOSITION 3 Suppose that in G more extreme types are rela-tively more frequent than in ndashG Formally the likelihoodratio tG

tGis U-shaped in t around EethtTHORN Then for any weight-

ing function htethTHORN that is not constant in the relevant rangestereotypical beliefs satisfy

VarstethtjGTHORN gt VarethtjGTHORN gt VarethtjGTHORN gt VarstethtjGTHORN

EstethtjGTHORN frac14 E

stethtjGTHORN frac14 EethtTHORN

When group G has a higher relative prevalence of extremetypes its representative types are located at both extremes of thedistribution The DMrsquos beliefs about G are then formed by over-weighting both tails while underweighting the unrepresentativemiddle The overweighting of Grsquos tails causes the assessment ofits variance VarstethtjGTHORN to be too high For example the skill dis-tribution of immigrants to the United States may be perceived ashaving very fat tails or even bimodal with immigrants beingperceived as either unskilled or very skilled relative to the resi-dent population The mean of the group in contrast is assessedcorrectly because the stereotypical distribution remains symmet-ric around EethtTHORN As before the stereotype contains a kernel oftruth It induces the agent to exaggerate the true differences be-tween groups namely the higher variance of G relative to itscounterpart

We present a number of extensions of the model in the OnlineAppendix We first consider multidimensional type spaces andshow that stereotypes center around the dimension wheregroups differ the most in line with the kernel of truth logic(Online Appendix C) Multidimensional stereotypes imply thatthe dimension we think about is influenced by context For

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example the Irish are stereotyped as red-haired when comparedwith the European population However when compared withthe Scots a more plausible stereotype for the Irish is lsquolsquoCatholicrsquorsquobecause religion is the dimension along which Irish and Scotsdiffer the most

In Online Appendix D we extend the model to continuoustype spaces Many settings of interest in economics can be use-fully described by continuous probability distributions and weshow our model is particularly tractable in this case In OnlineAppendix E we relax Definition 2 and allow weighting of types toalso be influenced by their likelihood We show that the basicinsight that stereotypes contain a kernel of truth carries throughto these cases as well

To summarize the psychology of representativeness yieldsstereotypes that are consistent with the social cognition approachin which individuals assess groups by recalling and focusing ondistinctive group traits When there are systematic differencesbetween groups stereotypes get the direction right but exagger-ate differences

IIIC Some Examples

A growing body of field and experimental evidence points to awidespread belief that women are worse than men at mathemat-ics (Eccles Jacobs and Harold 1990 Guiso et al 2008 CarrellPage and West 2010) This belief persists despite the fact that fordecades women have been gaining ground in average schoolgrades including mathematics and have recently surpassedmen in overall school performance (Goldin Katz and Kuziemko2006 Hyde et al 2008) This belief shared by men and women(Reuben Sapienza and Zingales 2014) may help account for thegender gap in the choices of high school tracks college degreesand careers with women disproportionately choosing humanitiesand health-related areas (Weinberger 2005 Buser Niederle andOosterbeek 2014) and forgoing significant wage premiums toquantitative skills (Bertrand 2011)

Gender stereotypes in mathematics particularly beliefs thatexaggerate the extent of average differences are consistent withthe predictions of our model The fact that men are overrepre-sented at the very highest performance levels leads a stereotyp-ical thinker to exaggerate the magnitude of mean differencesFigure I shows the score distributions from the mathematics

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section of 2013rsquos Scholastic Aptitude Test (SAT) for men andwomen21 The distributions are very similar with averagescores slightly higher for men (531 versus 499 out of 800)However scores for men have a heavier right tail with mentwice as likely to have a perfect SAT math score than women22

In light of such data the stereotypical male performance in math-ematics is high while the stereotypical female performance ispoor Predictions based on such stereotypes are inaccurate exag-gerating true differences Consistent with this prediction exper-imental evidence shows that both genders underestimatewomenrsquos ability in simple math tasks even controlling for pastperformance (Reuben Sapienza and Zingales 2014) Coffman(2014) shows a similar pattern extends to confidence about ownability in other male-typed domains with women reporting sig-nificantly less confidence in gender-incongruent than gender-congruent tasks Our model suggests that these patterns mightcome from stereotypes based on gender differences in the righttail of the distribution While differences in the right tail of thedistribution are unlikely to be relevant for most decisions stereo-typical thinking driven by these differences has the potential toimpact economically important decisions whether through self-stereotyping (ie choice of careers or majors as in BuserNiederle and Oosterbeek 2014) or through discrimination (iehiring decisions as in Bohnet van Geen and Bazerman 2016)

The logic of exaggerated yet directionally correct stereotypesalso sheds light on the well-documented phenomenon of base rateneglect (Kahneman and Tversky 1973) Indeed Proposition 2implies that the DM overreacts to information that assigns

21 Standardized test performance measures not only innate ability but alsoeffort and investment by third parties (Hyde et al 2008) The mapping of test per-formance into inferences about innate ability is an issue not addressed by ourmodel

22 For 2013 SAT Mathematics scores see httpmediacollegeboardcomdigitalServicespdfresearchSAT-Percentile-Ranks-By-Gender-Ethnicity-2013pdf Results are similar for the National Assessment of Educational Progress(NAEP) which are more representative of the overall population For 2012NAEP scores for 17-year-olds in mathematics see httpnationsreportcardgovltt_2012age17maspx See Hyde et al (2008) Fryer and Levitt (2010) and Popeand Sydnor (2010) for in-depth empirical analyses of the gender gap inmathematics

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people to groups precisely because such information generatesextreme stereotypes Consider the classic example in which amedical test for a particular disease with a 5 prevalence has a90 rate of true positives and a 5 rate of false positives The testassigns each person to one of two groups + (positive test) or ndash(negative test) The DM estimates the frequency of the sick type(s) and the healthy type (h) in each group The test is informativea positive result increases the relative likelihood of sickness anda negative result increases the relative likelihood of health forany prior Formally

PreththornjsTHORN

PreththornjhTHORNgt 1 gt

PrethjsTHORN

PrethjhTHORNeth4THORN

This condition has clear implications the representative personwho tests positive is sick while the representative person whotests negative is healthy Following Proposition 2 the DMreacts to the test by moving his priors too far in the right di-rection generating extreme stereotypes He greatly boosts hisassessment that a positively tested person is sick but also thata negatively tested person is healthy Because most people arehealthy the DMrsquos assessment about the group that tested neg-ative is fairly accurate but is severely biased for the group that

FIGURE I

SAT Mathematics Scores by Gender (2013)

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tested positive This analysis formalizes Tversky andKahnemanrsquos (1983) verbal account of base rate neglect23

The same mechanism may underlie several other instanceswhere DMs overweight diagnostic information When assessingan employeersquos skill level an employer attributes high perfor-mance to high skill because high performance is the distinctivemark of a talented employee Because he neglects the possibilitythat some talented employees perform poorly and that somenontalented ones perform well (perhaps due to stochasticity inthe environment) the employer has too much faith in skill andneglects the role of luck in accounting for the output Similarlywhen assessing the performance of firms in a hot sector of theeconomy (eg G = internet) an investor recalls highly successfulfirms in that sector (t = return of Google Amazon etc) He ne-glects the possibility of firms being unsuccessful because lack ofsuccess is statistically nondiagnostic and psychologically nonrep-resentative of a growing sectormdasheven if it is likely This causesexcessive optimism (in that the expectation of growth is unrea-sonably high) and overconfidence (in that the variability in earn-ings growth considered possible is truncated) True the hot sectormay have better growth opportunities on average but represen-tativeness exaggerates this feature and induces the investor toneglect a significant risk of failure

IV Evidence on Representativeness and Stereotypes

Testing our model requires evaluating the beliefs individualshold about a target group against the true distribution of thattarget group over an attribute space An ideal data set would

23 Our account is distinct from a mechanical underweighting of base rates inBayes rule as in Grether (1980) and Bodoh-Creed Benjamin and Rabin (2013) Inthose models upon receiving the test results the DM can update his beliefs in thewrong direction he can be less confident that a person is healthy after a negativetest than under his prior which cannot happen in our model Although this predic-tion of our model seems consistent with introspection we are not aware of experi-mental evidence on this point Griffin and Tversky (1992) present evidenceconsistent with pure neglect of base rates but in a significantly different tasknamely inferring the bias of a coin from a history of coin flips Such experimentsare hard to compare with the predictions of our model because subjects are asked togenerate distributions of different numbers of coin flips in their minds which is amuch more involved task than to recall types of a given distribution Their assess-ments then might be wrong for other reasons See Bodoh-Creed Benjamin andRabin (2013) for a detailed discussion

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consist of naturally defined groups with known distributions overa given space of types and a corresponding set of beliefs about thedistribution of each group over that space of types This wouldallow us to test for exaggeration of true differences betweengroups and to ask whether this exaggeration is well predictedby overweighting representative types To identify a causal rolefor representativeness or context dependence we would need ex-ogenous variation in either the comparison group ndashG or in thedistributions over the type spaces This is unavailable in existingdata sets Accordingly we take a two-pronged approach First wecreate a controlled laboratory environment that allows us toinduce the exogenous variation in representative types that weneed to test causality then we reanalyze existing field evidence tocheck for consistency with our predictions

In testing our model we focus on the two main implicationsof representativeness-based stereotypes

Context dependence the stereotype of a target group de-pends on the characteristics of the reference group it iscompared to

Kernel of truth stereotypes depend on group character-istics andmdashin most (precisely characterized) settingsmdashare slanted toward representative types

We test the first property with a lab experiment (SectionIVA) We then turn to survey data on beliefs about US politicalgroups (Section IVB) for an empirical analysis that explores thesecond property The survey data are more tightly linked to ourinterest in social stereotypes The laboratory experiment allowsus to directly test the role of representativeness in generatingcontext dependent beliefs Online Appendixes F and G provideall details and additional results for the experiments and fieldevidence

IVA Lab Evidence on Representativeness and ContextDependence

The influence of the representativeness heuristic on recalland on beliefs has been extensively documented in the lab(Kahneman and Tversky 1972 1973) Our goal is to considerhow representativeness as formalized in equation (2) gives riseto context-dependent beliefs To our knowledge the possibility

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that representativeness may generate context dependence hasnot been tested before

To assess this prediction we perform a controlled laboratoryexperiment that allows us to isolate representativeness frommany confounding factorsmdashhistorical sociological or other-wisemdashthat may affect stereotype formation in the real worldWe construct our own groups of ordinary objects creating atarget group G and a comparison group ndashG We hold thetarget group G fixed and explore how participant impressions ofit change as we change the comparison group ndashG and thusrepresentativeness

We conducted several experiments in the laboratory and onAmazon Mechanical Turk Each involves a basic three-stepdesign First participants are shown the target group and a ran-domly assigned comparison group for 15 seconds In this timedifferences between groups can be noticed but the groupsrsquo precisecompositions cannot be memorized The second step consists of afew filler questions which briefly draw the participantsrsquo cognitivebandwidth away from their observation Finally participants areasked to assess the groups they saw Participants are incentiv-ized to provide accurate answers

We randomly assign participants to either the Control or theRepresentativeness condition In the Control condition G and ndashGhave nearly identical distributions so that all types are similarlyrepresentative for each group In the Representativeness condi-tion ndashG is changed in such a way that a certain type becomes veryrepresentative for G Context dependence implies that the assess-ment of G should now overweight this representative type eventhough the distribution of G itself has not changed

We ran six experiments of this form with design changesfocused on reducing participant confusion and removing con-founds We describe the final and most refined version of theseexperiments here In an attempt to provide a overview of the re-sults while remaining concise we provide the results from pooledspecifications that use all data collected In Online Appendix Fwe offer additional details and report all experiments conductedWe also give instructions and materials for each experiment thefull data set is available by request

Consider first the experiment illustrated in Figure II Agroup of 25 cartoon girls is presented next to a group of 25 cartoonboys in T-shirts of different colors blue green or purple In theControl condition (Figure II Panel a) the groups have identical

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color distributions (13 purple 12 green) so no color is represen-tative of either group The Representativeness condition (Panel b)compares the same group of girls with a different group of boysfor whom green shirts are replaced with blue shirts Now onlygirls wear green and only boys wear blue These colors althoughstill not the most frequent for either group are now most repre-sentative For each group girls and boys participants are asked anumber of questions concerning the frequency of T-shirts of dif-ferent colors worn by that group

Applying our model in the control condition the type space isT frac14 fgreen purpleg and the groups are G = girls and ndashG = boysGiven that the color distributions are identical across groups both

types are equally representativegreengirls

greenboysfrac14 1 frac14

purplegirls

purpleboys As a result

assessment of G should be correct on average stcontrolgreengirls frac14 greengirls

and stcontrolpurplegirls frac14 purplegirls for any weighing function (the same is

true about assessments of ndashG)In the treatment condition the distribution of shirt colors re-

mains the same for girls For boys green shirts are changed intoblue Thus the type space changes to T frac14 fgreen purple bluegand the representative color for girls becomes greengreengirls

greenboysfrac14 1 gt 1 frac14

purplegirls

purpleboys while that for boys becomes blue As

a result in the treatment condition subjects should inflate the

frequency of green shirts relative to the truth sttreatmentgreengirls

gt greengirls (the same should happen to assessments of blueshirts for boys) We also expect the assessed frequency of greenshirts to go up relative to the control condition namely

sttreatmentgreengirls gt stcontrol

greengirls Critically the only factor that varies

across treatments is the representativeness of the 12-colorshirt Thus if we see differences across conditions the causalrole of representativeness-based recall in shaping group judg-ments is clear24

24 We vary which colors are used in which roles across participants Someparticipants saw this particular color distribution while others see for examplegreen as the modal color and purple as the diagnostic color for boys in theRepresentativeness condition and blue as the diagnostic color for girls in theRepresentativeness condition We vary the colors across the roles to avoid con-founding the characteristics of any particular color with its diagnosticity

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FIG

UR

EII

T-S

hir

tsE

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ent

Fig

ure

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red

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lor

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icip

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ty

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irt

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er

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icate

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en

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icate

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icate

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icip

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read

erre

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nce

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sion

ofp

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icle

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red

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We collected data from 301 participants using this T-shirtsdesign25 Since the number of green and purple shirts is verysimilar we first ask each participant the simplest question ofwhich shirt color is modal Next we ask participants to assessthe share of green and purple shirts

Consistent with the role of representativeness participantsassigned to the Representativeness condition are 105 percentagepoints more likely to recall the less frequent color (green for girlsor blue for boys) as the modal color when it is representative of agroup (35 of participants guess the less frequent color is modalin the Control condition this proportion increases to 46 in theRepresentativeness condition p = 01 estimated from a probitregression reported in Online Appendix F)

We now turn to subjectsrsquo estimates of how many T-shirts ofeach color they saw in each group In both conditions the truedifference in counts is 1 (13 purple shirts 12 green or blue shirts)In the Control condition participants on average believe they saw054 more purple shirts than green or blue shirts In theRepresentativeness condition participants believe they saw072 fewer purple shirts than green or blue shirts (the acrosstreatment difference is significant with p = 01 from OLS regres-sion reported in Online Appendix F)

In total we collected data for six experiments of this generalstructure gathering evidence from more than 1000 participantsAs we describe in Online Appendix F although there is substan-tial variation across experiments when we pool all of the data wefind significant aggregate treatment effects in line with a role ofrepresentativeness in judgment We employ four different unor-dered types designs similar to the T-shirts experiment using sixsamples (four online and two in the laboratory) with 741 partic-ipants We find effects in the predicted direction for five of the sixsamples Using a probit regression that pools the data for theseunordered type experiments we find that participants are 93 per-centage points more likely to guess that the less frequent type ismodal when it is representative than when it is not (p = 002) Wealso run a family of ordered types experiments (two designs fivesamples 402 participants) Unlike the simpler T-shirts style

25 Throughout our analysis we exclude any participant who participated in aprevious version of the experiment and any participant who self-identified as color-blind In Online Appendix F we show that our results are unchanged if we includethese additional observations

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design the theoretical predictions for the ordered types designsare more sensitive to the specific assumptions one makes aboutthe weighting function of the DM26 We find effects in the pre-dicted direction for three of the five samples As we discuss inmore detail in Online Appendix F the ordered types resultsvary by platform with consistently stronger results on AmazonMechanical Turk than in the laboratory samples Pooling all or-dered types experiments participants are 93 percentage pointsmore likely to guess that the group of interest has a greater av-erage than the comparison group when the right tail is represen-tative (p = 062) Given our simple experimental setting withgroups of mundane objects we interpret our resultsmdasha signifi-cant and reasonably sized impact on average beliefsmdashas an im-portant proof of concept the presence of representative typesbiases ex post assessment

IVB Empirical Evidence on Political Stereotypes

We examine two data sets on political preferences and be-liefs about political preferences in the United States We inves-tigate the roles of representativeness and context dependence byseparately testing for hypotheses that allow us to assess the lead-ing theories of stereotypes

First we test whether beliefs are correct or depart systemat-ically from the truth The statistical discrimination approachbuilds on the assumption that people hold rational expectationsof group traits Comparing beliefs to the truth allows us to assessthe validity of this assumption in our data

Second we test if beliefs depart from the truth by exagger-ating (mean) differences among groups per the kernel of truthhypothesis This is an implicit test of context dependence be-cause it implies that beliefs about the target groups are shapednot only by that grouprsquos characteristics but also by those of thereference group27

Third we test if distortions in beliefs can be accounted for bythe overweighting of highly representative types (defined astypes that are relatively more frequent in the target relative to

26 This is due in part to our choice to not study MLRP distributions We moti-vate and discuss this design decision in Online Appendix F

27 Of course unlike in the laboratory experiment in this setting we cannot testfor context dependence by exogenously varying the reference group

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the reference group) The second and third tests address the keypredictions of our model

1 The Data We have two data sets on political preferences andbeliefs about political preferences The first data set from GrahamNosek and Haidt (GNH 2012) contains data from the MoralFoundations Questionnaire Respondents (1174 self-identified lib-erals and 500 self-identified conservatives) answer questions abouttheir position on a subset of 45 issues 20 moral relevance state-ments (eg lsquolsquowhen you decide whether something is right orwrong to what extent are the following considerations relevantto your thinkingrsquorsquo) and 25 moral judgments (eg lsquolsquoindicate theextent to which you would agree or disagreersquorsquo) For each issue arandomly determined subset of participants states their own posi-tion another subset states their belief on the position of a lsquolsquotypicalliberalrsquorsquo and a third subset states their belief on the position of alsquolsquotypical conservativersquorsquo The data thus include the distribution overpositions for both liberal and conservatives as well as the averagebelieved typical position of liberals and of conservatives on the 45issues Each position is elicited on 1ndash6 scale

The second data set comes from the American NationalElection Survey (ANES) and contains data from more than20000 respondents between 1964 and 201228 The surveycovers political issues of the day such as the optimal amount ofgovernment spending and service provision (1984ndash2000) or theplace of women in society (1972ndash1998) We focus on the 10 issuesthat ask participants to respond on a 1ndash7 scale (rather than justindicate binary agreement or disagreement) all 10 issues areasked in multiple years Participants are asked to provide theirown position on the scale and their believed position of theDemocratic and Republican parties (lsquolsquoWhere would you placethe Democratic [Republican] party on this scalersquorsquo) The data in-clude for each issue-year observation the distribution of partic-ipant positions for self-identified liberals and self-identifiedconservatives as well as the distribution of believed typical posi-tions of the Democratic and Republican parties

28 These data are publicly available at httpwwwelectionstudiesorgstudy-pagesanes_timeseries_cdfanes_timeseries_cdfhtm

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2 Empirical Strategy Our analysis focuses on beliefs abouttwo groups Conservatives and Liberals The types are the possi-ble positions for each issue (1 2 6 7) For the GNH data weinterpret beliefs about the lsquolsquotypicalrsquorsquo element of a group to coincidewith the believed average position in that group Similarly forthe ANES data we use the believed party positions as a proxy forbelieved mean of each group29 We then take as a benchmark thehypothesis that individuals hold accurate beliefs about eachgroup and in particular that believed mean position shouldequal true mean position at least on average across subjectsThe accurate beliefs hypothesis underlies the most common eco-nomic model of stereotyping statistical discrimination

To assess our representativeness-based model we perform aregression exercise To test our model in a linear regressionframework we rely on linear approximations of the weightingfunction Our model then yields two regression specifications

PROPOSITION 4 Let G 2 fconservative liberal g and assume

ht h tG

tG

be a differentiable and strictly increasing weight-

ing function as in Definition 2 The following hold as a first-order approximation around identical distributions G

Gfrac14 1

(i) Kernel of truth regression There exists a constant gt 0such that

EstethtjGTHORN frac14 EethtjGTHORNeth1thorn THORN EethtjGTHORNeth5THORN

(ii) Representativeness regression Denote H frac14 fT 2 Tg

the right tail of types and RconsH frac14

PHtconsPHtlib

as the average

representativeness of right tail types for conservatives

29 This assumption is consistent with the authorsrsquo interpretation of the GNHdata (GNH 2012) and with previous studies using ANES (eg Westfall et al 2015)Furthermore to the extent that this assumption holds equally well for most issueswithin a data set our focus on cross-issue differences should allow us to test thepredictions of our model even with an imperfect proxy for beliefs of mean positionsFinally the data provide some insight into whether subjects are reporting (per-ceived) modal or mean types As we show the modal type is a poor prediction ofstated beliefs while a distorted mean slanted toward representative types is anaccurate prediction of stated beliefs

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Under the further approximation where tcons

tlibampRcons

H for

t 2 H

EstethtjconsTHORN frac14 EethtjconsTHORN thorn consethR

consH 1THORNeth6THORN

EstethtjlibTHORN frac14 EethtjlibTHORN libethR

consH 1THORNeth7THORN

where lcons and llib are positive constants

The first regression allows us to test for the kernel of truthhypothesis and the second set of regressions allows us to test forthe role of representativeness

Equation (5) says that respondents in our model inflate theaverage position of a group say the conservatives if and only ifthe group has a higher average position than the other groupnamely the liberals Formally EstethtjconsTHORN gt EethtjconsTHORN if and onlyif EethtjconsTHORN gt EethtjlibTHORN Because in our measurement scale highertypes mean lsquolsquomore conservativersquorsquo we expect (i) believed conserva-tive average to be higher than the truth and (ii) the extent ofoverstatement to decrease in the average liberal position EethtjlibTHORNConversely we expect the average liberal position to be lowerthan the truth the more so the higher the average conservativeposition EethtjconsTHORN

As previously discussed the basis of these predictions is con-text dependence information about the distribution of ndashG is rel-evant for the beliefs about G This context dependence isinconsistent with rational expectations in which only thegrouprsquos own means should affect beliefs We test the hypothesisthat the true mean EethtjGTHORN is a significant predictor of the believedmean E

stethtjGTHORN with a positive sign and the other grouprsquos truemean EethtjGTHORN is a predictor of the believed mean with a negativesign

Equations (6) and (7) say that repondentsrsquo assessment bias isshaped by representativeness When the right tail is more repre-sentative for conservatives (Rcons

H 1 positive and large) partici-pants should inflate the average conservative position more(higher E

stethtjconsTHORN EethtjconsTHORN) and deflate the average liberal po-sition more (lower E

stethtjlibTHORN EethtjlibTHORN) We test the hypothesisthat the inflation in conservative positions is positively associatedwith the representativeness of the right tail for the conservativesand the inflation in liberal positions is negatively associated with

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it Once again the representativeness of the right tail is com-puted using the true distribution of positions

In equations (6) and (7) in many cases the representative tailis also the most likely one As a consequence these tests cannotdistinguish a representativeness-based from a likelihood-basedmodel of distorted beliefs We perform two additional testsFirst we run versions of equations (6) and (7) in which we controlfor the likelihood of tails (see Table A4 in Online Appendix G)Second we compute numerically the predictions of a representa-tiveness-based model of stereotypes and a likelihood-based modelof stereotypes We then assess which of these two is better able tomatch the data on beliefs

3 Empirical Results To begin we illustrate the structure ofthe data and the nature of our predictions with two simple exam-ples from the GNH data set focusing on beliefs about conserva-tives In example 1 participants are asked about their agreementwith the statement lsquolsquoIt can never be right to kill a human beingrsquorsquoIn example 2 participants are asked about the moral relevance oflsquolsquowhether or not someone cared for someone weak or vulnerablersquorsquoAs can be seen in Figure III in example 1 the modal position(strongly disagree (1)) and most representative positions(strongly disagree (1)) coincide for conservatives In contrast inexample 2 in Figure III the most representative types (slightlyrelevant (3) not at all relevant (1)) are not most likely for theconservative group Following Proposition 1 we predict that be-liefs will be distorted in the direction of the most representativetypes Thus we expect more exaggeration in example 2 than inexample 1 since in example 2 the most representative types (inthe left tail) are far from the modal type whereas in example 1they coincide This is what we find the conservative position isexaggerated by only 009 positions in Example 1 (true mean 299believed mean 290) but by 106 positions in Example 2 (truemean 421 believed mean 315)

In the full data sets we treat each (issue year) pair as anobservation and we cluster standard errors at the issue level Forthe GNH data we have 45 observations 45 issues measured inthe same year For the ANES data we have 66 observations 10issues measured in multiple years To begin we simply docu-ment systematic exaggeration in both data sets This is a primaryfocus of the original analysis in GNH (2012) and also in Westfall

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FIGURE III

Two Examples

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et al (2015)rsquos analysis of the ANES data30 Figure IV shows thatthe believed difference between typical conservative and typicalliberal positions is larger than the true difference in mean posi-tions for 109 of the 111 observations The data for both GNH(squares) and ANES (triangles) lie above the 45-degree line(dashed)31 Average exaggeration is 062 positions on the scale(066 in the GNH data 059 in the ANES data)32

The systematic and significant exaggeration of mean differ-ences suggests that the benchmark model of accurate beliefs ismissing something important Indeed this exaggeration reflectsthe fact that believed means are typically more extreme than truemeans First note that the kernel of truth regression (equation(5)) generates exaggeration of mean differences just as docu-mented in Figure IV

EstethtjGTHORN E

stethtjGTHORN frac14 eth1thorn 2THORN frac12EethtjGTHORN EethtjGTHORN

To bring this prediction to the data we regress the believedmean position for each group EBethtjGTHORN on the true mean of thegroup EethtjGTHORN and the true mean of the comparison groupEethtjGTHORN across issues We do this for each group (liberals con-servatives) in each data set separately We also present pooledspecifications that combine the data sets to make a prediction fora given group (liberals conservatives) In these pooled specifica-tions we include a dummy variable indicating whether theobservation came from the ANES data set For all specificationswe cluster observations at the issue level33 The results from re-gression are shown in Table I In every specification we find thatEethtjGTHORN is a significant predictor of EBethtjGTHORN with the predicted pos-itive sign Crucially for five of the six specifications the mean of

30 Chambers and Melnyk (2006) also find evidence of exaggeration of truedifferences in beliefs about political positions

31 For convenience we recode all issues so that the high end of the scale (67)represents the stereotypically more conservative position

32 A natural question to ask is how beliefs vary across liberals and conserva-tives That is do beliefs about a group G depend on membership in G versus ndashG Ourmodel does not speak to this issue However in Online Appendix G we show thatthe results we document below hold for both beliefs held by conservatives and be-liefs held by liberals see Tables A9 A10 and A11

33 In general the results presented below for the ANES data are not largelyimpacted by the decision to cluster at the issue level Similar results are obtained ifthe data are not clustered

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the comparison group EethtjGTHORN is also a significant predictor ofE

BethtjGTHORN with the predicted negative signAlthough these results provide strong evidence of context

dependence and are consistent with our model they do not pindown a role for representativeness of types Our next test relatesthe magnitude of representativeness of tail types to the magni-tude of belief distortions

To this end we implement the regressions in equations (6)and (7) Following Proposition 4 we compute the average repre-

sentativeness of tail types for conservatives RconsH frac14

PtT2tconsPtT2tlib

We

again test the hypothesis that RconsH is a significant predictor of Est

ethtjconsTHORN with a positive sign and a predictor of EstethtjlibTHORN with a

negative sign Table II shows that conditional on true mean RconsH

predicts believed mean for each group G as expected The firstthree specifications display the results for predicting beliefs heldabout conservatives In both data sets the average representa-tiveness of tail types for conservatives is a significant positivepredictor of beliefs held about conservatives The final three spe-cifications display the results for predicting beliefs held about

FIGURE IV

Exaggeration of Differences

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liberals We find that the average representativeness of tail typesfor conservatives is a negative predictor of beliefs held about lib-erals This effect is significant in the GNH data and marginallysignificant in the ANES data

We present several additional results in Online Appendix GTo further examine the role of representativeness in driving be-liefs we first show the results of Table II carry through when we

TABLE II

AVERAGE REPRESENTATIVENESS OF TAIL POSITIONS PREDICTS BELIEFS

OLS Predicting Believed Mean of Group G for Each Issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position

of group G for issue

078 024 051 072 018 041

(006) (008) (009) (005) (005) (010)

Avg rep of tail types for

conservatives RconsH

019 055 025 014 012 024

(007) (022) (008) (006) (007) (005)

Constant 101 260 184 093 271 201

(026) (045) (029) (022) (025) (032)

R2 082 048 060 091 031 070

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

TABLE I

INFORMATION ABOUT ndashG PREDICTS BELIEFS ABOUT G

OLS predicting believed mean of group G for each issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position of

conservatives for issue

102 098 096 021 019 025

(0097) (0133) (0076) (0060) (0116) (0060)

True mean position of

liberals for issue

035 086 058 0987 039 073

(0106) (0134) (0131) (0066) (0106) (0135)

Constant 151 335 235 069 258 156

(0195) (0269) (0279) (0122) (0249) (0270)

R2 083 053 066 092 032 068

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

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control for the average likelihood on the tail positions (see Table A4in Online Appendix G) Most tellingly we use the model to predictbeliefs across issues and compare those to the data For simplicitywe use the rank-based truncation specification to predict mean be-liefs when stereotypes include the d most representative types ford frac14 1 T We compare these predictions to those of a model inwhich beliefs are obtained by restricting the distribution to the dmost likely types Our benchmark for both models is predicting thebelieved mean from the entire distribution where d = T We showthat the predictions of the rank-based truncation model with d = 4or 5 compare favorably to both a likelihood-based truncation model(with any d) and the accurate beliefs benchmark Interestingly thisresult suggests that stereotypical beliefs are well approximated byneglecting the least representative types (as opposed to focusingonly on the most representative types) and so represent a moderatethough systematic departure from the standard benchmarkFinally we show that the results we document above hold forboth beliefs held by conservatives and beliefs held by liberals (seeTables A9 A10 and A11 in Online Appendix G)

V Conclusion

We present a model of stereotypical thinking in which DMsmaking predictions about a group overweight the grouprsquos mostdistinctive types These overweighted types are not the mostlikely ones given the DMrsquos data but the most representativeones in the sense of being the most diagnostic of the group rela-tive to other groups Representativeness implies that what ismost distinctive of a group depends on what group it is comparedwith We present experimental evidence that confirms this con-text dependence in recall-based assessments of groups Finallywe evaluated the predictions of the model using political data fromexisting large-scale surveys We find context dependence to be akey feature of beliefs Given the richness of the political data wecan go a step further and identify a role for representativeness inparticular As the representativeness of tail types increases beliefsof a group are distorted in the direction of that tail

Our approach provides a parsimonious and psychologicallyfounded account of how DMs generate simplified representationsof reality from social groups to stock returns and offers a unifiedaccount of disparate pieces of evidence relating to this type of

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uncertainty The model captures the central fact that stereotypeshighlight the greatest difference between groups thus explainingwhy some stereotypes are very accurate while others lack valid-ity Still stereotypes often have a kernel of truth when they arebased on systematicmdasheven if smallmdashdifferences between groupsThis logic allows us to describe a number of heuristics and psy-chological biases many of which arise in the context of predictionproblems Generically our model generates overreaction to diag-nostic information

Our model is based on representativeness and does not cap-ture all the features of stereotypical thinking However it cap-tures perhaps the central feature when we think of a group wefocus on what is most distinctive about it and neglect or under-weight the rest

Saeuroıd Business School University of Oxford

Ohio State University and Harvard Business School

Universita Bocconi and Innocenzo Gasparini Institute

for Economic Research

Harvard University

Supplementary Material

An Online Appendix for this article can be found at QJEonline (qjeoxfordjournalorg)

References

Adorno Theodor Else Frenkel-Brunswik Daniel Levinson and Nevitt SanfordThe Authoritarian Personality (New York Harper amp Row 1950)

Arrow Kenneth lsquolsquoThe Theory of Discriminationrsquorsquo in Discrimination in LaborMarkets Orley Ashenfelter and Albert Rees eds (Princeton NJPrinceton University Press 1973)

Ashton Michael and Victoria Esses lsquolsquoStereotype Accuracy Estimating theAcademic Performance of Ethnic Groupsrsquorsquo Personality and SocialPsychology Bulletin 25 (1999) 225ndash236

Barberis Nicholas Andrei Shleifer and Robert Vishny lsquolsquoA Model of InvestorSentimentrsquorsquo Journal of Financial Economics 49 (1998) 307ndash343

Bayer Sylvia lsquolsquoThe Accuracy of Academic Gender Stereotypesrsquorsquo Sex Roles 40(1999) 787ndash813

Benjamin Dan James Choi and Joshua Strickland lsquolsquoSocial Identity andPreferencesrsquorsquo American Economic Review 100 (2010) 1913ndash1928

Benjamin Dan Matthew Rabin and Collin Raymond lsquolsquoA Model of Non-Belief inthe Law of Large Numbersrsquorsquo Journal of the European Economic Association15 (2015) 515ndash544

Bertrand Marianne lsquolsquoNew Perspectives on Genderrsquorsquo Handbook of LaborEconomics 4 (2011) 1543ndash1590

Bodoh-Creed Aaron Dan Benjamin and Matthew Rabin lsquolsquoThe Dynamics of Base-Rate Neglectrsquorsquo mimeo Haas Business School 2013

STEREOTYPES 1791

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

Bohnet Iris Alexandra van Geen and Max Bazerman lsquolsquoWhen PerformanceTrumps Gender Bias Joint versus Separate Evaluationrsquorsquo ManagementScience 5 (2016) 1225ndash1234

Bordalo Pedro Nicola Gennaioli and Andrei Shleifer lsquolsquoSalience Theory of Choiceunder Riskrsquorsquo Quarterly Journal of Economics 127 (2012) 1243ndash1285

mdashmdashmdash lsquolsquoSalience and Consumer Choicersquorsquo Journal of Political Economy 121(2013) 803ndash843

Briton Nancy and Judith Hall lsquolsquoBeliefs about Female and Male NonverbalCommunicationrsquorsquo Sex Roles 32 (1995) 79ndash90

Buser Thomas Muriel Niederle and Hessel Oosterbeek lsquolsquoGenderCompetitiveness and Career Choicesrsquorsquo Quarterly Journal of Economics 129(2014) 1409ndash1447

Carrell Scott Marianne Page and James West lsquolsquoSex and Science How ProfessorGender Perpetuates the Gender Gaprsquorsquo Quarterly Journal of Economics 125(2010) 1101ndash1144

Chambers John and Darya Melnyk lsquolsquoWhy Do I Hate Thee ConflictMisperceptions and Intergroup Mistrustrsquorsquo Personality and SocialPsychology Bulletin 32 (2006) 1295ndash1311

Chan Wayne Robert R McCrae Filip De Fruyt Lee Jussim CorinnaE Lockenhoff Marleen De Bolle Paul T Costa Jr Angelina R SutinAnu Realo Juri Allik Katsuharu Nakazato Yoshiko ShimonakaMartina Hrebıckova Sylvie Graf Michelle Yik Marina Brunner-SciarraNora Leibovich De Figueora Vanina Schmidt Chang-kyo Ahn Hyun-nie Ahn Maria E Aguilar-Vafaie Jerzy Siuta Barbara SzmigielskaThomas R Cain Janet T Crawford Khairul Anwar Mastor Jean-Pierre Rolland Florence Nansubuga Daniel R MiramontezVeronica Benet-Martınez Jerome Rossier Denis Bratko Iris MarusicJamin Halberstadt Mami Yamaguchi Goran Knezevic Thomas A MartinMirona Gheorghiu Peter B Smith Claudio Barbaranelli Lei WangJane Shakespeare-Finch Margarida P Lima Waldemar KlinkoszAndrzej Sekowski Lidia Alcalay Franco Simonetti Tatyana V AvdeyevaV S Pramila and Antonio Terracciano lsquolsquoStereotypes of Age Differences inPersonality Traits Universal and Accuratersquorsquo Journal of Personality andSocial Psychology 103 (2012) 1050ndash1066

Chen Yan Sherry Xin Liu Tracy Xiao and Margaret Shih lsquolsquoWhich Hat to WearImpact of Natural Identities on Coordination and Cooperationrsquorsquo Games andEconomic Behavior 84 (2014) 58ndash86

Coffman Katherine lsquolsquoEvidence on Self-Stereotyping and the Contribution ofIdeasrsquorsquo Quarterly Journal of Economics 129 (2014) 1625ndash1660

Cunningham Tom lsquolsquoComparisons and Choicersquorsquo mimeo Stockholm University2013

Diekman Amanda Alice Eagly and Patrick Kulesa lsquolsquoAccuracy and Bias in theStereotypes about the Social and Political Attitudes of Women and MenrsquorsquoJournal of Experimental Social Psychology 38 (2002) 268ndash282

Eccles Jacquelynne S Janis E Jacobs and Rena D Harold lsquolsquoGender RoleStereotypes Expectancy Effects and Parentsrsquo Socialization of GenderDifferencesrsquorsquo Journal of Social Issues 46 (1990) 183ndash201

Fryer Roland and Matthew Jackson lsquolsquoA Categorical Model of Cognition andBiased Decision-Makingrsquorsquo BE Journal of Theoretical Economics 8 (2008)1ndash42

Fryer Roland and Steven Levitt lsquolsquoAn Empirical Analysis of the Gender Gap inMathematicsrsquorsquo American Economic Journal Applied Economics 2 (2010)210ndash240

Gennaioli Nicola and Andrei Shleifer lsquolsquoWhat Comes to Mindrsquorsquo Quarterly Journalof Economics 125 (2010) 1399ndash1433

Gennaioli Nicola Andrei Shleifer and Robert Vishny lsquolsquoNeglected RisksFinancial Innovation and Financial Fragilityrsquorsquo Journal of FinancialEconomics 104 (2012) 452ndash468

Gilens Martin lsquolsquoRace and Poverty in America Public Misperceptions and theAmerican News Mediarsquorsquo Public Opinion Quarterly 60 (1996) 515ndash541

Glaeser Edward lsquolsquoThe Political Economy of Hatredrsquorsquo Quarterly Journal ofEconomics 120 (2005) 45ndash86

QUARTERLY JOURNAL OF ECONOMICS1792

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

Glover Dyland Amanda Pallais and William Pariente lsquolsquoDiscrimination as a Self-Fulfilling Prophecy Evidence from French Grocery Storesrsquorsquo mimeo HarvardUniversity 2015

Goldin Claudia Lawrence Katz and Ilyana Kuziemko lsquolsquoThe Homecoming ofAmerican College Women The Reversal of the College Gender GaprsquorsquoJournal of Economic Perspectives 20 (2006) 133ndash156

Graham Jesse Brian Nosek and Jonathan Haidt lsquolsquoThe Moral Stereotypes ofLiberals and Conservatives Exaggeration of Differences across thePolitical Spectrumrsquorsquo PLoS One 7 (2012) 1ndash13

Grether David lsquolsquoBayes Rule as a Descriptive Model The RepresentativenessHeuristicrsquorsquo Quarterly Journal of Economics 95 (1980) 537ndash557

Griffin Dale and Amos Tversky lsquolsquoThe Weighing of Evidence and theDeterminants of Confidencersquorsquo Cognitive Psychology 24 (1992) 411ndash435

Guiso Luigi Ferdinando Monte Paola Sapienza and Luigi Zingales lsquolsquoCultureGender and Mathrsquorsquo Science 320 (2008) 1164ndash1165

Hilton James and William Von Hippel lsquolsquoStereotypesrsquorsquo Annual Review ofPsychology 47 (1996) 237ndash271

Hyde Janet Sara Lindberg Marcia Linn Amy Ellis and Caroline WilliamslsquolsquoGender Similarities Characterize Math Performancersquorsquo Science 321 (2008)494ndash495

Judd Charles and Bernardette Park lsquolsquoDefinition and Assessment of Accuracy inSocial Stereotypesrsquorsquo Psychological Review 100 (1993) 109ndash128

Jussim Lee Jarret Crawford Stephanie Anglin John Chambers Sean Stevensand Florette Cohen lsquolsquoStereotype Accuracy One of the Largest and MostReplicable Effects in All of Social Psychologyrsquorsquo in The Handbook ofPrejudice Stereotyping and Discrimination Todd Nelson ed (MahwahNJ Lawrence Erlbaum 2015)

Kahneman Daniel and Amos Tversky lsquolsquoSubjective Probability A Judgment ofRepresentativenessrsquorsquo Cognitive Psychology 3 (1972) 430ndash454

mdashmdashmdash lsquolsquoOn the Psychology of Predictionrsquorsquo Psychological Review 80 (1973) 237ndash251

Kaplowitz Stan Bradley Fisher and Clifford Broman lsquolsquoHow Accurate ArePerceptions of Social Statistics about Blacks and Whitesrsquorsquo Public OpinionQuarterly 67 (2003) 237ndash243

Kersten Daniel Pascal Mamassian and Alan Yuille lsquolsquoObject Perception asBayesian Inferencersquorsquo Annual Review of Psychology 55 (2004) 271ndash304

Klein Richard Kate A Ratliff Michelangelo Vianello Reginald B Adams JrStepan Bahnik Michael J Bernstein Konrad Bocian Mark J BrandtBeach Brooks Claudia Chloe Brumbaugh Zeynep CemalcilarJesse Chandler Winnee Cheong William E Davis Thierry DevosMatthew Eisner Natalia Frankowska David Furrow Elisa Maria GallianiFred Hasselman Joshua A Hicks James F Hovermale S Jane HuntJeffrey R Huntsinger Hans IJzerman Melissa-Sue John Jennifer A Joy-Gaba Heather Barry Kappes Lacy E Krueger Jaime Kurtz CarmelA Levitan Robyn Mallett Wendy L Morris Anthony J Nelson JasonA Nier Grant Packard Ronaldo Pilati Abraham M RutchickKathleen Schmidt Jeanine L Skorinko Robert Smith Troy G SteinerJustin Storbeck Lyn M Van Swol Donna Thompson Anna van rsquot VeerLeigh Ann Vaughn Marek Vranka Aaron Wichman Julie A Woodzickaand Brian A Nosek lsquolsquoInvestigating Variation in Replicability A ManyLabs Replication Projectrsquorsquo Social Psychology 45 (2014) 142ndash152

Lundberg Shelly and Richard Startz lsquolsquoPrivate Discrimination and SocialIntervention in Competitive Labor Marketsrsquorsquo American Economic Review73 (1983) 340ndash347

Madon Stephanie Max Guyll Kathy Aboufadel Eulices Montiel Alison SmithPolly Palumbo and Lee Jussim lsquolsquoEthnic and National Stereotypes ThePrinceton Trilogy Revisited and Revisedrsquorsquo Personality and SocialPsychological Bulletin 27 (2001) 996ndash1010

Martin Carol lsquolsquoA Ratio Measure of Sex Stereotypingrsquorsquo Journal of Personality andSocial Psychology 52 (1987) 489ndash499

STEREOTYPES 1793

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

McCauley Clark Krishna Thangavelu and Paul Rozin lsquolsquoSex Stereotyping ofOccupations in Relation to Television Representations and Census FactsrsquorsquoBasic and Applied Social Psychology 9 (1988) 197ndash212

Mullainathan Sendhil lsquolsquoThinking through Categoriesrsquorsquo mimeo HarvardUniversity 2002

Ortoleva Pietro and Erik Snowberg lsquolsquoOverconfidence in Political BehaviorrsquorsquoAmerican Economic Review 105 (2015) 504ndash535

Phelps Edmund lsquolsquoThe Statistical Theory of Racism and Sexismrsquorsquo AmericanEconomic Review 62 (1972) 659ndash661

Pope Devin and Justin Sydnor lsquolsquoGeographic Variation in the Gender Differencesin Test Scoresrsquorsquo Journal of Economic Perspectives 24 (2010) 95ndash108

Rabin Matthew lsquolsquoInference by Believers in the Law of Small NumbersrsquorsquoQuarterly Journal of Economics 117 (2002) 775ndash816

Rabin Matthew and Joel Schrag lsquolsquoFirst Impressions Matter A Model ofConfirmatory Biasrsquorsquo Quarterly Journal of Economics 114 (1999) 37ndash82

Rabin Matthew and Dimitri Vayanos lsquolsquoThe Gamblerrsquos and Hot-Hand FallaciesTheory and Applicationsrsquorsquo Review of Economic Studies 77 (2010) 730ndash778

Reuben Ernesto Paola Sapienza and Luigi Zingales lsquolsquoHow Stereotypes ImpairWomenrsquos Careers in Sciencersquorsquo Proceedings of the National Academy ofSciences 111 (2014) 4403ndash4408

Rosch Eleanor lsquolsquoNatural Categoriesrsquorsquo Cognitive Psychology 4 (1973) 328ndash350Ryan Carey S lsquolsquoAccuracy of Black and White College Studentsrsquo In-Group and

Out-Group Stereotypesrsquorsquo Personality and Social Psychology Bulletin 22(1996) 1114ndash1127

Schneider David The Psychology of Stereotyping (New York Guilford Press2004)

Schneider David Albert Hastorf and Phoebe Ellsworth Person Perception(Reading MA Addison-Wesley 1979)

Shih Margaret Todd Pittinsky and Nalini Ambady lsquolsquoStereotype SusceptibilityIdentity Salience and Shifts in Quantitative Performancersquorsquo PsychologicalScience 10 (1999) 80ndash83

Shih Margaret Todd Pittinsky and Amy Trahan lsquolsquoDomain-Specific Effects ofStereotypes on Performancersquorsquo Self and Identity 5 (2006) 1ndash14

Steele Claude Whistling Vivaldi How Stereotypes Affect Us and What We CanDo (New York Norton 2010)

Tenenbaum Joshua and Thomas Griffiths lsquolsquoThe Rational Basis ofRepresentativenessrsquorsquo 23rd Annual Conference of the Cognitive ScienceSociety (2001) 1036ndash1041

Tversky Amos and Daniel Kahneman lsquolsquoExtensional versus Intuitive ReasoningThe Conjunction Fallacy in Probability Judgmentrsquorsquo Psychological Review 90(1983) 293ndash315

Weinberger Catherin lsquolsquoIs the Science and Engineering Workforce Drawn fromthe Far Upper Tail of the Math Ability Distributionrsquorsquo mimeo UCSB 2005

Westfall Jacob Leaf Van Boven John Chambers and Charles Judd lsquolsquoPerceivingPolitical Polarization in the United States Party Identity Strength andAttitude Extremity Exacerbate the Perceived Partisan DividersquorsquoPsychological Science 10 (2015) 145ndash158

Wolsko Christopher Bernadette Park Charles Judd and Bernd WittenbrinklsquolsquoFraming Interethnic Ideology Effects of Multicultural and Color-BlindPerspectives on Judgments of Groups and Individualsrsquorsquo Journal ofPersonality and Social Psychology 78 (2000) 635ndash654

QUARTERLY JOURNAL OF ECONOMICS1794

at Harvard L

ibrary on October 28 2016

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Page 5: I. Introduction · uneducated at the beginning of the 20th century, and as high achievers at the beginning of the 21st (Madon et al. 2001). Social science has produced three broad

We find that representativeness often generates fairly accu-rate stereotypes but sometimes causes stereotypes to be inaccu-rate particularly when groups have similar distributions thatdiffer most in unlikely types More generally our model high-lights two critical properties

Stereotypes amplify systematic differences betweengroups even if these differences are in reality verysmall When groups differ by a shift in means stereotyp-ing exaggerates differences in means and when groupsdiffer by an increase in variance stereotyping exagger-ates the differences in variances In these cases (but notalways) representativeness yields stereotypes that con-tain a lsquolsquokernel of truthrsquorsquo in the sense that they differen-tiate groups along existing and highly diagnosticcharacteristics exactly as Hilton Von Hippel andSchneider define them

Stereotypes are context dependent The assessment of agiven target group depends on the reference group towhich it is compared

In line with the social cognition approach to stereotypes asignificant body of psychological research on beliefs about genderrace age and political groups finds that stereotypes broadly re-flect reality but display biases Social psychologists have exploredthe extent to which stereotypes exaggerate real differences thuspossessing a kernel of truth Evidence on exaggeration varies bydomain For race and gender many studies have reportedroughly accurate beliefs whereas others have found underesti-mation or exaggeration of true differences (Jussim et al 2015)4

For age and political stereotypes evidence points more stronglytoward exaggeration5 Schneider (2004 337) summarizes the

4 For evidence of roughly accurate beliefs for race see for example Ashtonand Esses (1999) on beliefs of academic ability Kaplowitz Fisher and Broman(2003) on income poverty rates and out-of-wedlock births and Wolsko et al(2000) on a array of positive and negative attributes Ryan (1996) and Gilens(1996) find evidence of exaggeration of race stereotypes on personal attributesand poverty rates respectively Some studies have found roughly accurate beliefson gender (McCauley Thangavelu and Rozin 1988 Briton and Hall 1995Diekman Eagly and Kulesa 2002) while others find evidence of exaggeration(Martin 1987 Bayer 1999)

5 See Chan et al (2012) on age We discuss evidence on political stereotypes inSection IV

STEREOTYPES 1757

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existing empirical work on stereotype accuracy as follows lsquolsquothebest we can do by way of general summary is to say that somestereotypes held by some people for some groups are sometimesaccuratersquorsquo Our empirical investigation explores the connectionbetween stereotype accuracy and representativeness which wemeasure using the previously defined likelihood ratio

We first assess the role of representativeness and contextdependence in the lab We construct a group of mundane objectsG and present it to participants next to a comparison group ndashGIn our baseline condition the comparison group is chosen so thatno type is particularly representative of group G In our treat-ment we change the comparison group ndashG while leaving thetarget group G unchanged The new comparison group givesrise to highly representative types within G In line with thekey prediction of our model participants in the treatment condi-tion shift their assessment of G toward the representative types

We test the model using two data sets on political preferencesand beliefs about political preferences in the United States Heregroups are political constituencies (Democrats and Republicans)and types are their positions on a number of issues Holding fixedthe groups and the set of types and varying the groupsrsquo true dis-tributions across issues the data allow us to test whether beliefsabout political preferences are shaped by representativeness Wefirst show that such beliefs depart from the truth by exaggerating(mean) differences as per the kernel of truth logic We then ex-plore how the extent of exaggeration varies across issuesConsistent with the model we find that beliefs systematicallydepart from rational expectations and that the degree to whichthey exaggerate true differences is a function of representative-ness While representativeness is not the only heuristic thatshapes recall (availability driven by recency or frequency of ex-posure also plays a role) it explains the fact that in the datastated beliefs indeed exaggerate differences among groups

Since Kahneman and Tverskyrsquos (1972 1973) work on heuris-tics and biases several studies have formally modeled heuristicsabout probabilistic judgments and incorporated them into eco-nomic models Work on the confirmation bias (Rabin andSchrag 1999) and on probabilistic extrapolation (Grether 1980Barberis Shleifer and Vishny 1998 Rabin 2002 Rabin andVayanos 2010 Benjamin Rabin and Raymond 2015) assumesthat the decision maker has an incorrect model in mind or incor-rectly processes available data Our approach is instead based on

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the assumption that representative information comes foremostto mind when making judgments The mental operation that liesat the heart of our modelmdashgenerating a prediction for the distri-bution of types in a group based on data stored in memorymdashalsocaptures base rate neglect and overreaction to diagnostic infor-mation The underweighting or neglect of information in ourmodel simplifies judgment problems in a way related to modelsof categorization (Mullainathan 2002 Fryer and Jackson 2008)In these models however decision makers use coarse categoriesorganized according to likelihood not representativeness Thisapproach generates imprecision but does not create a systematicbias for overestimating unlikely events nor does it allow for con-text-dependent beliefs In our empirical analysis of political be-liefs we explicitly compare the predictions of representativeness-based recall to those of likelihood-based models and find that theevidence supports the former

In modeling representativeness we follow the specification ofGS (2010) but investigate a new set of questions GS (2010) ex-amine how representativeness distorts the assessed probabilitiesof alternative hypotheses but not how the probability of a givenhypothesis or group is distributed across its constituent elementsIn the context of the current setting GS (2010) ask how imperfectrecall affects the assessed probability that a randomly drawnmember from a universe belongs to group G The current arti-cle in contrast asks which type t we expect to draw once we knowthat we are facing group G GS (2010) show how representative-ness generates biased probabilistic assessments such as conjunc-tion and disjunction fallacies This article deals with perhaps abroader and more ubiquitous problem of stereotype formationextensively studied by other social scientists but largely ne-glected by economists

Section II describes our model In Section III we examine theproperties of stereotypes including the forces that shape stereo-type accuracy and illustrate these properties with examples InSection IV we bring the model to the data performing a lab ex-periment and analyzing existing surveys of political beliefsSection V concludes The Online Appendix presents proofs anumber of extensions of the model and additional results forthe experiments and field evidence

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II A Model of Representativeness and Stereotypes

IIA The Model

A decision maker (DM) faces a prediction problem such asassessing the ability of a job candidate from a certain ethnicgroup the future performance of a firm belonging to a certainsector or future earnings based on own gender

Formally there is a set of types of interest T and an overallpopulation of which group G is a subset The set of typesT can be unordered (eg occupations) or ordered (and typi-cally cardinal eg earnings levels) When T is ordered wewrite T frac14 ft1 tTg with t1 lt t2 lt lt tT6 There is a probabil-ity or frequency distribution 2 ethT THORN that induces a condi-tional distribution PrethT frac14 tjGTHORN when restricted to G7 In whatfollows we denote by tG frac14 PrethT frac14 tjGTHORN the probability of typet in group G and by G the vector ethtGTHORNt2T containing the condi-tional distribution

The DMrsquos goal is to assess the distribution of the types ofinterest in a particular group G Although the DM has stored inmemory the full distribution he retrieves from memory a dis-torted version of G that overweights the probability of thosetypes that are most representative of G relative to a comparisongroup ndashG Generically ndashG is a group in that is distinct from Gnamely G7 nG although in some cases it can coincide withthe complement of G

According to Tversky and Kahneman (1983) a type t is rep-resentative of G if it is relatively more likely to occur in G thanin ndashG Definitions 1 and 2 formalize this representativeness-based recall following GS (2010)

6 For simplicity we also use T to denote the number of types jTj The modelapplies also to cases in which types (i) are multidimensional capturing a bundle ofattributes such as occupation and nationality or (ii) are continuous We considerthese cases in Online Appendixes C and D respectively Also G may represent anycategory of interest such as the historical performance of a firm or industry actionsavailable to a decision maker (T = set of payoffs G = occupations) or categories inthe natural world (T = ability to fly G = birds)

7 In many applications each individual in is characterized by a determin-istic type (eg age hair color) As a result ethtTHORN frac14 1

jj For instance each Floridian

has a single age type (at the finest temporal resolution) When types are stochasticinstead such as when estimating future earnings of a person or a firm each indi-vidual is described by a nondegenerate distribution

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DEFINITION 1 The representativeness of type t for group G givencomparison group ndashG is defined as the likelihood ratio

RethtGGTHORN tG

tGeth2THORN

Definition 1 implies that DMs are attuned to log differencesin probabilities representativeness depends on the percentageprobability increase of a type from ndashG to G This captures aform of diminishing sensitivity whereby for a fixed probabilitydifference a type is more likely to be overweighed if it is unlikelyin the comparison group8 Thus the representative age of aFloridian is 65+ because people in this age bracket are morecommon in Florida than in the rest of the United StatesStatistically representative types are also diagnostic of thetarget group G Indeed the higher is RethtGGTHORN the more confi-dent is a Bayesian DM observing t that t belongs to G rather thanto ndashG9

The ease of recall of highly representative types affectsjudgments because more easily recalled types are overweighted

We model distorted recall as follows Denote by RethtGGTHORN

tG

tG

t2T

the vector of representativeness of all types in G

We then have

8 Our definition of representativeness links to Weberrsquos law of sensory percep-tion see Section IIB It also links to our previous work on salience in which wepostulated that log differences in payoffs determine the attention to lottery payoffs(Bordalo Gennaioli and Shleifer 2012) and to goodsrsquo attributes (BordaloGennaioli and Shleifer 2013) Equation (2) establishes the same principle for thedomain of probabilities

9 This insight led Tenenbaum and Griffiths (2001) to define representative-ness as individualsrsquo sense as intuitive Bayesians of updating in reaction to dataTheir definition like ours is in terms of the likelihood ratio However Tenenbaumand Griffiths interpret representativeness as a mechanism that affects intuitivejudgments of similarity rather than beliefs (eg it accounts well for lab evidencewhere subjects are asked to rank types in terms of representativeness or ofstrength of association with a group) Accordingly they do not consider the possi-bility of systematically distorted and context dependent beliefs

STEREOTYPES 1761

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DEFINITION 2 The DM attaches to each type t 2 T in group G adistorted probability

sttG frac14 tG

htethRethtGGTHORNTHORNPs2T sGhsethRethtGGTHORNTHORN

eth3THORN

where ht RTthornRthorn is a weighting function such that

(i) The weight ht is a symmetric function of the representa-

tiveness of types s 6frac14 t Formally ht frac14 h tG

tG

sG

sG

s2Tn tf g

where h Rthorn RT1thorn Rthorn is a function that is invariant to

a permutation of the last T ndash 1 arguments(ii) Weighing of a type increases in own representativeness

and decreases in the representativeness of other typesFormally the function hethTHORN is weakly increasing in itsfirst argument and weakly decreasing in the other T 1arguments

We call the distribution ethsttGTHORNt2T the stereotype for G If a type

t is objectively more likely namely tG is higher then the ste-reotype attaches higher probability to it By property i distor-tions are due exclusively to the fact that a type is more or lessrepresentative than the others In particular if all types areequally representative the DM equally weighs all of them ath(1) and holds rational expectations about G If instead the rep-resentativeness of different types differs property ii implies thatthe stereotype ceteris paribus overweights the probability of morerepresentative types

Most of the results we explore in this article hold for a gen-eral weighing function htethTHORN Specific functional forms captureadded assumptions about the psychology of representativeness-based recall and are useful in applications We outline a few spe-cifications and their properties

Rank-based stereotypes the ranking of the representa-tiveness of different types shapes distortions Denote byrethtTHORN 2 f1 Tg the representativeness ranking of type tWhen r(t) = 1 type t is the most representative one (po-tentially with ties) We can specify two ways in which atypersquos representativeness ranking distorts its probability

QUARTERLY JOURNAL OF ECONOMICS1762

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(i) Rank-based truncation the DM only recalls the typesthat have representativeness ranking of at most dnamely ft 2 TjrethtTHORN dg Zero probability is attachedto the remaining types10 Denote by IethrethtTHORN dTHORN an in-dicator function taking the value 1 if the representa-tiveness ranking of t is at most d Then theweighting function is ht frac14 IethrethtTHORN dTHORN so that

sttG frac14 tG

IethrethtTHORN dTHORNPs2T sGIethrethsTHORN dTHORN

which is the true conditional probability within re-called types This assumption is used in Gennaioliand Shleifer (2010)11

(ii) Rank-based discounting the DM discounts by a con-stant factor 2 frac1201 the odds of type t relative to itsimmediate predecessors in the representativenessranking Lower implies stronger discounting ofless representative types Formally the weightingfunction is ht frac14

rethtTHORN so that

sttG frac14 tG

rethtTHORNPs2T sG

rethsTHORN

Representativness-based discounting all else equal theweight attached by the DM to type t increases continuouslywith its representativeness One convenient formulation is

ht frac14tG

tG

so that

10 These neglected types are not viewed as impossible they are just assignedzero probability in the DMrsquos current thinking This formulation allows us to modelsurprise and reactions to unforeseen contingencies which have proved useful in-gredients in modeling probabilistic judgments (GS 2010) as well as neglect of risk infinancial crises (Gennaioli Shleifer and Vishny 2012)

11 Specifically in GS (2010) the assessed probability that a certain hypothesisG is true is equal to

Pr ethGTHORN frac14

Pt tGIethrethtTHORN dTHORNP

t tGIethrethtTHORN dTHORN thornP

t t=GIethrethtTHORN dTHORN

which increases in the ratio between the total probability mass recalled for Gand that recalled for G frac14 nG

STEREOTYPES 1763

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sttG frac14 tG

tG

tG

P

s2T sGsG

sG

where 0 captures the extent to which representative-ness distorts beliefs This formulation is particularly con-venient when dealing with continuous distributions ofthe exponential or power classes

These functional forms all embody the main idea of our modelthat the stereotype overweights the probability of more represen-tative types Rank-based truncation captures a central manifes-tation of limited memory forgetting unrepresentative typesSmoother discounting (based on ranking or on representative-ness) may be more appropriate when the type space is smalland smooth discounting can be more tractable in certain settings

Section III characterizes the general properties of stereotypesIn particular it shows their ability to account for social psycholo-gistsrsquo kernel of truth hypothesis under the general weighting func-tion of Definition 2 To bring the model to the data in Section IVBwe derive linear approximations of stereotypical beliefs by assum-ing that the weighting function is differentiable with respect to atypersquos representativeness This assumption excludes rank-basedweighting but allows for many possibilities

IIB Discussion of Assumptions

Before moving to the formal analysis we discuss some prop-erties and limitations of our approach Representativeness-basedrecall the idea that individuals recall distinctive group types canbe viewed as an instance of what Kahneman and Tversky calllsquolsquoattribute substitutionrsquorsquo When dealing with the difficult questionlsquolsquowhat is the distribution of hair color among the Irishrsquorsquo peopleintuitively answer to the simpler question lsquolsquowhich hair color dis-tinguishes the Irish peoplersquorsquo Critically as discussed byKahneman and Tversky attribute substitution does not occurbecause people misunderstand the original question or mechan-ically confuse the assessment of PrethtjGTHORN with that of PrethGjtTHORNRather it occurs because the distinctive or representative typesimmediately come to mind and individuals anchor their overallprobability judgment to them As a consequence subjects do notonly make mistakes in judging the probability that a Floridian is

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over age 65 They also give too high an answer to the questionlsquolsquowhat is the average age of a Floridianrsquorsquo12

One interesting question is whether the process of stereotyp-ing we describe is optimal in some sense Focusing mental repre-sentations on a few types can be justified by the costs of thinkingor retrieval This approach however is not enough to explainwhy individuals should focus on representative rather thanlikely types We do not formally analyze the optimality of repre-sentativeness here but we mention some relevant considerationsfrom cognitive psychology Kahneman and Tversky (1979) stressthe similarity between many perceptual and cognitive operationsFor instance the highlight of contrastmdasha key principle of visualperceptionmdashis invoked to justify the prospect theory assumptionthat the carriers of utility are changes relative to a referencepoint The same logic applies to our model in which stereotypesprecisely highlight the contrast between groups

In visual perception assessing properties such as brightnesscolor size or distance to an object by comparing them to otherproximate objects has been shown to be optimal in the presence ofmultiplicative background noise (Kersten Mamassian andYuille 2004 Cunningham 2013) Our formulation of representa-tiveness is related to the same idea in the sense that individualsestimating properties of one group stress differences from an-other group In a noisy world in which attention is limited thisprocess may optimally allow for swift reactions to changes ingroup characteristics even if errors are sometimes made13

12 Indeed in many cases mere confusion of PrethtjGTHORNwith PrethGjtTHORNwould not yieldthe phenomenon of stereotyping In the Irish hair color example the probability ofbeing Irish conditional on having red hair is

PrethIrishjredTHORN frac14PrethredjIrishTHORNPrethIrishTHORN

PrethredjIrishTHORNPrethIrishTHORN thorn PrethredjNonIrishTHORNPrethNonIrishTHORN

This probability is clearly very small given that the Irish population is a tinyfraction of the world population Confusion of PrethtjGTHORN with PrethGjtTHORN in this casewould lead to an understatement of the probability of the red-haired Irish

13 To give a simple example suppose thatmdashas in the case of Proposition 3mdashthevariance in the environment increases in the sense that extreme tail events becomemore likely Then a likelihood-based stereotype would detect no change whereas arepresentativeness-based stereotype would focus on the heightened probability ofthe tails In particular an asymmetric increase in tail probabilities that shifts themean would be detected by a representativeness-based stereotype even if the dis-tributionrsquos mode does not change

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Exploring this idea formally is an interesting avenue for futurework

Consider some limitations of our model First representa-tiveness is not the only heuristic that shapes recall Decisionmakers may for instance find it easier to recall types that aresufficiently likely Another potentially important mechanism isavailability understood by Kahneman and Tversky (1972) as thelsquolsquoeasersquorsquo with which information comes to mind (because of actualfrequency or repetition) In Online Appendix E we present a trun-cation-based recall mechanism in which distortions are driven bya combination of representativeness and likelihood of types(which is equivalent to relaxing property i in Definition 2) Thismodel can offer a useful starting point to capture availability aswell even though a full model of availability is beyond the scopeof this article Even in this more general setting the influence ofrepresentativeness on recall is the driving force of stereotypesthat in line with the social psychology perspective are basedon underlying differences among groups As we show in SectionIV this feature is critical in accounting for the evidence

The second set of model-related issues concerns how to spe-cify the elements of Definition 1 in applications group G the typespace T and the reference group ndashG Take the specification of thegroup G and of the type space T Often the problem itself pro-vides a natural specification of these features This is the case inthe empirically important class of lsquolsquoclosedrsquorsquo questions such asthose used in surveys which provide respondents with a set ofalternatives as in the data we use in Section IV More generallythe problem solved by the DMmdashsuch as evaluating the resume ofa job applicant coming from a certain ethnic groupmdashprimes agroup a dimension of interest and a set of types (eg the appli-cantrsquos qualification or skill levels) When types have a naturalorder such as income age or education the granularity of T isalso naturally given by the problem (income age and years ofschooling brackets) When the set of types is not specified by theproblem DMs spontaneously generate one14 It would be useful tohave a model of which dimensions and types come to mind par-ticularly for more open-ended problems Psychologists have

14 For example suppose a person is asked to guess the typical occupation of ademocratic voter in an lsquolsquoopen-endedrsquorsquo format (without being provided a set of alter-natives) Here the level of granularity at which types are defined is not obvious (egteacher versus a university teacher vs a professor of comparative literature)

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sought to construct a theory of natural types and dimensions(Rosch 1973) We do not make a contribution to this problembut we note that in many problems of interest in economics thedimension as well as the set of types is naturally givenFurthermore in our model details of the type space can be impor-tant under rank-based truncation but they matter less undersmooth discounting

Consider finally the role of the comparison group ndashG Thisgroup captures the context in which a stereotype is formed andagain is often implied by the problem when G = Floridians ndashG =rest of US population when G = African Americans ndashG = whiteAmericans A distinctive prediction of our model confirmed byour experiments in Section IVA is that the stereotype for agiven group G depends on the comparison group ndashG15 WhenndashG is not pinned down by the problem itself to derive testablepredictions from representativeness we set G frac14 nG where

is the natural population over which the unconditional distribu-tion of types is measured

III Properties of Stereotypes

We now study stereotypical beliefs and their accuracy Toillustrate the role of representativeness we first ask to whatextent the most representative type is a good fit for the groupnamely whether it is modal Next we assess the accuracy of theentire stereotypical distribution To do so we focus on a cardinaltypes and compare the stereotypersquos mean and variance to the trueones

15 Some empirical papers have taken a similar approach exogenously varyingthe natural comparison group through priming Benjamin Choi and Strickland(2010) show that priming racial or ethnic identity can affect the risk preferences ofparticipants Chen et al (2014) find that Asian students cooperate less with out-group members when primed with their ethnic identity rather than their universityidentity Shih Pittinsky and Ambady (1999) show that Asian American womenstereotype themselves as better or worse in math with corresponding impact onperformance when their ethnicity or gender respectively is primed ShihPittinsky and Trahan (2006) replicate this effect using a verbal task documentingthat Asian American women performed better when their gender rather than theirethnicity was primed Although the generalizability and replicability of priminghas been doubted (Klein et al 2014) this body of evidence is consistent with contextdependence

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IIIA Likely versus Unlikely Exemplars

The most representative type for a group is the one thatagents most easily recall and associate with the group itself forinstance a red-haired Irishman or a 65+-year-old FloridianSocial psychologists call this type the exemplar of the groupAccordingly we define

DEFINITION 3 A type t is an exemplar for G given comparisongroup ndashG when

t 2 arg maxt

tG

tG

Under any specification of the weighting function ht inDefinition 2 overweighting (weakly) increases as we movetoward more representative types so the exemplar is also thetype whose probability is overweighted the most16 By analyzingthe exemplar then we can gauge whether representativenessinduces the DM to overweight a likely type (as happens in stan-dard models of categorical thinking) or an unlikely type Whenoverweighting occurs in unlikely and extreme types the biases ofstereotypes can be particularly severe17

Equation (2) yields the following characterization

PROPOSITION 1 Suppose the conditional distributions G and G

are not identical Consider two extreme cases

(i) If for all t t0

2 T we have that tG gt t0 G if and only iftG gt t0 G then the modal type is not an exemplar forat least one group

(ii) If for all t t0

2 T we have that tG gt t0 G if and only iftG lt t0 G then for each group the modal type is theexemplar

16 Consider the function hethTHORN from Definition 2 When applied to more repre-sentative types the first argument of the function increases while one of the otherT ndash 1 arguments decreases As a result the weighting factor ht (and thus overweigh-ing

sttG

tG) increases as well

17 In the rank-based truncation model the frequency of the exemplar providesa measure of stereotype accuracy By accuracy we mean the extent to which thestereotype minimizes the distance

Pt eth

sttG tGTHORN

2 When d = 1 and only one type isrecalled (there are no ties) accuracy is maximized if the exemplar is the most likelytype and minimized if the exemplar is the least likely type

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Case i says that when groups have similar distributions inthe sense of having the same likelihood ranking the most repre-sentative type is unlikely for at least one group potentially bothRepresentativeness draws the DMrsquos attention to group differ-ences neglecting the fact that the groups are similar and havethe same mode This mechanism generates inaccurate stereo-types and is illustrated by the Florida example This resultholds under any measure of representativeness that differenti-ates the two groups (eg the difference tG tG)

Case ii says that the most representative type tends to belikely for both groups when the distributions are very differentIn this case groups differ the most around their modes so repre-sentativeness and likelihood coincide Thinking of Swedes aslsquolsquoblondrsquorsquo and Europeans as lsquolsquodark hairedrsquorsquo is accurate precisely be-cause these are majority traits of the Swedish and European pop-ulations respectively In these cases stereotyping yields fairlyreliable models Of course there is still some inaccuracy Evenin the case of likely exemplars judgment errors can be signifi-cant For instance voters in some US states are perceived aslsquolsquobluersquorsquo or lsquolsquoredrsquorsquo because a majority of the population votesDemocrat or Republican In reality even in lsquolsquobluersquorsquo states farfrom everyone votes Democrat In the 2012 presidential electionvote shares of either candidate in most states ranged from 40 to6018

When DMs strongly overweight representative types themost severe biases occur when those types are unlikely and ex-treme This is true both under rank based truncations and undersmooth discounting functions (see Section IIIB) Ethnic stereo-types based on crime or terrorism exhibit this error they neglectthe fact that by far the most common types in all groups arehonest and peaceful

IIIB Stereotypical Moments

We now characterize how the first two moments of a distri-bution are distorted by the process of stereotyping To do so wemust restrict our analysis to cardinal ordered types The follow-ing results hold for any weighting function htethTHORN satisfyingDefinition 2 We consider two canonical cases that prove usefulin illustrating the predictions of the model

18 Presidential Election Results NBCNewscom see httpelectionsnbcnewscomnspolitics2012allpresident (accessed 5 September 2016)

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In the first case groups G and ndashG are such that the likelihoodratio tG

tGis monotonic in t The monotone likelihood ratio prop-

erty (MLRP) holds to a first approximation in many empiricalsettings and is also assumed in many economic models such asstandard agency models19 If tG

tGis monotonically increasing (de-

creasing) in t then group G is associated with higher (lower)values of t relative to the comparison group ndashG Formally

PROPOSITION 2 Suppose that MLRP holds and assume wlogthat the likelihood ratio tG

tGis strictly increasing in t Then

for any weighting function htethTHORN that is not constant in therelevant range

EstethtjGTHORN gt EethtjGTHORN gt EethtjGTHORN gt E

stethtjGTHORN

Under MLRP the most representative part of the distribu-tion for G is the right tail if tG

tGincreases in t or the left tail if tG

tG

decreases in t The representative tail is then overweighted whilethe nonrepresentative tail is underweighted As a consequencethe assessed mean E

stethtjGTHORN is too extreme in the direction of therepresentative tail

Critically in line with the social cognition perspective the ste-reotype contains a kernel of truth the DM overestimates the meanof G if this group has a higher mean than the comparison groupnamely EethtjGTHORN gt EethtjGTHORN and conversely if EethtjGTHORN lt EethtjGTHORN TheDM exaggerates this true difference because he inflates the asso-ciation of G with its most representative types20 For instancewhen judging an asset manager who performs well we tend to

19 Examples include the binomial and the Poisson families of distributionswith different parameters The characterization of distributions satisfying MLRPis easier in the case of continuous distributions (see Online Appendix D) two dis-tributions f(x) f ethx THORN that differ only in their mean satisfy MLRP if and only if thedistribution f(x) is log-concave Examples include the exponential and normal dis-tributions To the extent that discrete distributions sufficiently approximate thesedistributions (as the Poisson distribution PoisethTHORN approximates the normal distri-bution Neth THORN for large l) they will also satisfy MLRP

20 Depending on the distribution and the weighing function the DMrsquos assess-ment of the variance VarethtjGTHORNmay also be dampened relative to the truth This isoften true under the truncation weighing function In this case stereotyping effec-tively leads to a form of overconfidence in which the DM holds extreme views andoverestimates the precision of his assessment That extreme views and overconfi-dence (in the sense of over precision) go together has been documented in the settingof political ideology among others (Ortoleva and Snowberg 2015)

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overemphasize skill relative to luck because higher skill levels arerelatively more associated with higher performance This occurseven if for both skilled and unskilled managers high performanceis mostly due to luck

In the second case for which we characterize the stereotypi-cal distributions groups G and ndashG have the same mean EethtjGTHORNfrac14 EethtjGTHORN frac14 EethtTHORN but differ in their variance We abstract fromskewness and higher moments by considering distributionsethtGTHORNt2T and ethtGTHORNt2T that share the same support and are sym-metric around the medianmean EethtTHORN

PROPOSITION 3 Suppose that in G more extreme types are rela-tively more frequent than in ndashG Formally the likelihoodratio tG

tGis U-shaped in t around EethtTHORN Then for any weight-

ing function htethTHORN that is not constant in the relevant rangestereotypical beliefs satisfy

VarstethtjGTHORN gt VarethtjGTHORN gt VarethtjGTHORN gt VarstethtjGTHORN

EstethtjGTHORN frac14 E

stethtjGTHORN frac14 EethtTHORN

When group G has a higher relative prevalence of extremetypes its representative types are located at both extremes of thedistribution The DMrsquos beliefs about G are then formed by over-weighting both tails while underweighting the unrepresentativemiddle The overweighting of Grsquos tails causes the assessment ofits variance VarstethtjGTHORN to be too high For example the skill dis-tribution of immigrants to the United States may be perceived ashaving very fat tails or even bimodal with immigrants beingperceived as either unskilled or very skilled relative to the resi-dent population The mean of the group in contrast is assessedcorrectly because the stereotypical distribution remains symmet-ric around EethtTHORN As before the stereotype contains a kernel oftruth It induces the agent to exaggerate the true differences be-tween groups namely the higher variance of G relative to itscounterpart

We present a number of extensions of the model in the OnlineAppendix We first consider multidimensional type spaces andshow that stereotypes center around the dimension wheregroups differ the most in line with the kernel of truth logic(Online Appendix C) Multidimensional stereotypes imply thatthe dimension we think about is influenced by context For

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example the Irish are stereotyped as red-haired when comparedwith the European population However when compared withthe Scots a more plausible stereotype for the Irish is lsquolsquoCatholicrsquorsquobecause religion is the dimension along which Irish and Scotsdiffer the most

In Online Appendix D we extend the model to continuoustype spaces Many settings of interest in economics can be use-fully described by continuous probability distributions and weshow our model is particularly tractable in this case In OnlineAppendix E we relax Definition 2 and allow weighting of types toalso be influenced by their likelihood We show that the basicinsight that stereotypes contain a kernel of truth carries throughto these cases as well

To summarize the psychology of representativeness yieldsstereotypes that are consistent with the social cognition approachin which individuals assess groups by recalling and focusing ondistinctive group traits When there are systematic differencesbetween groups stereotypes get the direction right but exagger-ate differences

IIIC Some Examples

A growing body of field and experimental evidence points to awidespread belief that women are worse than men at mathemat-ics (Eccles Jacobs and Harold 1990 Guiso et al 2008 CarrellPage and West 2010) This belief persists despite the fact that fordecades women have been gaining ground in average schoolgrades including mathematics and have recently surpassedmen in overall school performance (Goldin Katz and Kuziemko2006 Hyde et al 2008) This belief shared by men and women(Reuben Sapienza and Zingales 2014) may help account for thegender gap in the choices of high school tracks college degreesand careers with women disproportionately choosing humanitiesand health-related areas (Weinberger 2005 Buser Niederle andOosterbeek 2014) and forgoing significant wage premiums toquantitative skills (Bertrand 2011)

Gender stereotypes in mathematics particularly beliefs thatexaggerate the extent of average differences are consistent withthe predictions of our model The fact that men are overrepre-sented at the very highest performance levels leads a stereotyp-ical thinker to exaggerate the magnitude of mean differencesFigure I shows the score distributions from the mathematics

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section of 2013rsquos Scholastic Aptitude Test (SAT) for men andwomen21 The distributions are very similar with averagescores slightly higher for men (531 versus 499 out of 800)However scores for men have a heavier right tail with mentwice as likely to have a perfect SAT math score than women22

In light of such data the stereotypical male performance in math-ematics is high while the stereotypical female performance ispoor Predictions based on such stereotypes are inaccurate exag-gerating true differences Consistent with this prediction exper-imental evidence shows that both genders underestimatewomenrsquos ability in simple math tasks even controlling for pastperformance (Reuben Sapienza and Zingales 2014) Coffman(2014) shows a similar pattern extends to confidence about ownability in other male-typed domains with women reporting sig-nificantly less confidence in gender-incongruent than gender-congruent tasks Our model suggests that these patterns mightcome from stereotypes based on gender differences in the righttail of the distribution While differences in the right tail of thedistribution are unlikely to be relevant for most decisions stereo-typical thinking driven by these differences has the potential toimpact economically important decisions whether through self-stereotyping (ie choice of careers or majors as in BuserNiederle and Oosterbeek 2014) or through discrimination (iehiring decisions as in Bohnet van Geen and Bazerman 2016)

The logic of exaggerated yet directionally correct stereotypesalso sheds light on the well-documented phenomenon of base rateneglect (Kahneman and Tversky 1973) Indeed Proposition 2implies that the DM overreacts to information that assigns

21 Standardized test performance measures not only innate ability but alsoeffort and investment by third parties (Hyde et al 2008) The mapping of test per-formance into inferences about innate ability is an issue not addressed by ourmodel

22 For 2013 SAT Mathematics scores see httpmediacollegeboardcomdigitalServicespdfresearchSAT-Percentile-Ranks-By-Gender-Ethnicity-2013pdf Results are similar for the National Assessment of Educational Progress(NAEP) which are more representative of the overall population For 2012NAEP scores for 17-year-olds in mathematics see httpnationsreportcardgovltt_2012age17maspx See Hyde et al (2008) Fryer and Levitt (2010) and Popeand Sydnor (2010) for in-depth empirical analyses of the gender gap inmathematics

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people to groups precisely because such information generatesextreme stereotypes Consider the classic example in which amedical test for a particular disease with a 5 prevalence has a90 rate of true positives and a 5 rate of false positives The testassigns each person to one of two groups + (positive test) or ndash(negative test) The DM estimates the frequency of the sick type(s) and the healthy type (h) in each group The test is informativea positive result increases the relative likelihood of sickness anda negative result increases the relative likelihood of health forany prior Formally

PreththornjsTHORN

PreththornjhTHORNgt 1 gt

PrethjsTHORN

PrethjhTHORNeth4THORN

This condition has clear implications the representative personwho tests positive is sick while the representative person whotests negative is healthy Following Proposition 2 the DMreacts to the test by moving his priors too far in the right di-rection generating extreme stereotypes He greatly boosts hisassessment that a positively tested person is sick but also thata negatively tested person is healthy Because most people arehealthy the DMrsquos assessment about the group that tested neg-ative is fairly accurate but is severely biased for the group that

FIGURE I

SAT Mathematics Scores by Gender (2013)

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tested positive This analysis formalizes Tversky andKahnemanrsquos (1983) verbal account of base rate neglect23

The same mechanism may underlie several other instanceswhere DMs overweight diagnostic information When assessingan employeersquos skill level an employer attributes high perfor-mance to high skill because high performance is the distinctivemark of a talented employee Because he neglects the possibilitythat some talented employees perform poorly and that somenontalented ones perform well (perhaps due to stochasticity inthe environment) the employer has too much faith in skill andneglects the role of luck in accounting for the output Similarlywhen assessing the performance of firms in a hot sector of theeconomy (eg G = internet) an investor recalls highly successfulfirms in that sector (t = return of Google Amazon etc) He ne-glects the possibility of firms being unsuccessful because lack ofsuccess is statistically nondiagnostic and psychologically nonrep-resentative of a growing sectormdasheven if it is likely This causesexcessive optimism (in that the expectation of growth is unrea-sonably high) and overconfidence (in that the variability in earn-ings growth considered possible is truncated) True the hot sectormay have better growth opportunities on average but represen-tativeness exaggerates this feature and induces the investor toneglect a significant risk of failure

IV Evidence on Representativeness and Stereotypes

Testing our model requires evaluating the beliefs individualshold about a target group against the true distribution of thattarget group over an attribute space An ideal data set would

23 Our account is distinct from a mechanical underweighting of base rates inBayes rule as in Grether (1980) and Bodoh-Creed Benjamin and Rabin (2013) Inthose models upon receiving the test results the DM can update his beliefs in thewrong direction he can be less confident that a person is healthy after a negativetest than under his prior which cannot happen in our model Although this predic-tion of our model seems consistent with introspection we are not aware of experi-mental evidence on this point Griffin and Tversky (1992) present evidenceconsistent with pure neglect of base rates but in a significantly different tasknamely inferring the bias of a coin from a history of coin flips Such experimentsare hard to compare with the predictions of our model because subjects are asked togenerate distributions of different numbers of coin flips in their minds which is amuch more involved task than to recall types of a given distribution Their assess-ments then might be wrong for other reasons See Bodoh-Creed Benjamin andRabin (2013) for a detailed discussion

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consist of naturally defined groups with known distributions overa given space of types and a corresponding set of beliefs about thedistribution of each group over that space of types This wouldallow us to test for exaggeration of true differences betweengroups and to ask whether this exaggeration is well predictedby overweighting representative types To identify a causal rolefor representativeness or context dependence we would need ex-ogenous variation in either the comparison group ndashG or in thedistributions over the type spaces This is unavailable in existingdata sets Accordingly we take a two-pronged approach First wecreate a controlled laboratory environment that allows us toinduce the exogenous variation in representative types that weneed to test causality then we reanalyze existing field evidence tocheck for consistency with our predictions

In testing our model we focus on the two main implicationsof representativeness-based stereotypes

Context dependence the stereotype of a target group de-pends on the characteristics of the reference group it iscompared to

Kernel of truth stereotypes depend on group character-istics andmdashin most (precisely characterized) settingsmdashare slanted toward representative types

We test the first property with a lab experiment (SectionIVA) We then turn to survey data on beliefs about US politicalgroups (Section IVB) for an empirical analysis that explores thesecond property The survey data are more tightly linked to ourinterest in social stereotypes The laboratory experiment allowsus to directly test the role of representativeness in generatingcontext dependent beliefs Online Appendixes F and G provideall details and additional results for the experiments and fieldevidence

IVA Lab Evidence on Representativeness and ContextDependence

The influence of the representativeness heuristic on recalland on beliefs has been extensively documented in the lab(Kahneman and Tversky 1972 1973) Our goal is to considerhow representativeness as formalized in equation (2) gives riseto context-dependent beliefs To our knowledge the possibility

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that representativeness may generate context dependence hasnot been tested before

To assess this prediction we perform a controlled laboratoryexperiment that allows us to isolate representativeness frommany confounding factorsmdashhistorical sociological or other-wisemdashthat may affect stereotype formation in the real worldWe construct our own groups of ordinary objects creating atarget group G and a comparison group ndashG We hold thetarget group G fixed and explore how participant impressions ofit change as we change the comparison group ndashG and thusrepresentativeness

We conducted several experiments in the laboratory and onAmazon Mechanical Turk Each involves a basic three-stepdesign First participants are shown the target group and a ran-domly assigned comparison group for 15 seconds In this timedifferences between groups can be noticed but the groupsrsquo precisecompositions cannot be memorized The second step consists of afew filler questions which briefly draw the participantsrsquo cognitivebandwidth away from their observation Finally participants areasked to assess the groups they saw Participants are incentiv-ized to provide accurate answers

We randomly assign participants to either the Control or theRepresentativeness condition In the Control condition G and ndashGhave nearly identical distributions so that all types are similarlyrepresentative for each group In the Representativeness condi-tion ndashG is changed in such a way that a certain type becomes veryrepresentative for G Context dependence implies that the assess-ment of G should now overweight this representative type eventhough the distribution of G itself has not changed

We ran six experiments of this form with design changesfocused on reducing participant confusion and removing con-founds We describe the final and most refined version of theseexperiments here In an attempt to provide a overview of the re-sults while remaining concise we provide the results from pooledspecifications that use all data collected In Online Appendix Fwe offer additional details and report all experiments conductedWe also give instructions and materials for each experiment thefull data set is available by request

Consider first the experiment illustrated in Figure II Agroup of 25 cartoon girls is presented next to a group of 25 cartoonboys in T-shirts of different colors blue green or purple In theControl condition (Figure II Panel a) the groups have identical

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color distributions (13 purple 12 green) so no color is represen-tative of either group The Representativeness condition (Panel b)compares the same group of girls with a different group of boysfor whom green shirts are replaced with blue shirts Now onlygirls wear green and only boys wear blue These colors althoughstill not the most frequent for either group are now most repre-sentative For each group girls and boys participants are asked anumber of questions concerning the frequency of T-shirts of dif-ferent colors worn by that group

Applying our model in the control condition the type space isT frac14 fgreen purpleg and the groups are G = girls and ndashG = boysGiven that the color distributions are identical across groups both

types are equally representativegreengirls

greenboysfrac14 1 frac14

purplegirls

purpleboys As a result

assessment of G should be correct on average stcontrolgreengirls frac14 greengirls

and stcontrolpurplegirls frac14 purplegirls for any weighing function (the same is

true about assessments of ndashG)In the treatment condition the distribution of shirt colors re-

mains the same for girls For boys green shirts are changed intoblue Thus the type space changes to T frac14 fgreen purple bluegand the representative color for girls becomes greengreengirls

greenboysfrac14 1 gt 1 frac14

purplegirls

purpleboys while that for boys becomes blue As

a result in the treatment condition subjects should inflate the

frequency of green shirts relative to the truth sttreatmentgreengirls

gt greengirls (the same should happen to assessments of blueshirts for boys) We also expect the assessed frequency of greenshirts to go up relative to the control condition namely

sttreatmentgreengirls gt stcontrol

greengirls Critically the only factor that varies

across treatments is the representativeness of the 12-colorshirt Thus if we see differences across conditions the causalrole of representativeness-based recall in shaping group judg-ments is clear24

24 We vary which colors are used in which roles across participants Someparticipants saw this particular color distribution while others see for examplegreen as the modal color and purple as the diagnostic color for boys in theRepresentativeness condition and blue as the diagnostic color for girls in theRepresentativeness condition We vary the colors across the roles to avoid con-founding the characteristics of any particular color with its diagnosticity

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FIG

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We collected data from 301 participants using this T-shirtsdesign25 Since the number of green and purple shirts is verysimilar we first ask each participant the simplest question ofwhich shirt color is modal Next we ask participants to assessthe share of green and purple shirts

Consistent with the role of representativeness participantsassigned to the Representativeness condition are 105 percentagepoints more likely to recall the less frequent color (green for girlsor blue for boys) as the modal color when it is representative of agroup (35 of participants guess the less frequent color is modalin the Control condition this proportion increases to 46 in theRepresentativeness condition p = 01 estimated from a probitregression reported in Online Appendix F)

We now turn to subjectsrsquo estimates of how many T-shirts ofeach color they saw in each group In both conditions the truedifference in counts is 1 (13 purple shirts 12 green or blue shirts)In the Control condition participants on average believe they saw054 more purple shirts than green or blue shirts In theRepresentativeness condition participants believe they saw072 fewer purple shirts than green or blue shirts (the acrosstreatment difference is significant with p = 01 from OLS regres-sion reported in Online Appendix F)

In total we collected data for six experiments of this generalstructure gathering evidence from more than 1000 participantsAs we describe in Online Appendix F although there is substan-tial variation across experiments when we pool all of the data wefind significant aggregate treatment effects in line with a role ofrepresentativeness in judgment We employ four different unor-dered types designs similar to the T-shirts experiment using sixsamples (four online and two in the laboratory) with 741 partic-ipants We find effects in the predicted direction for five of the sixsamples Using a probit regression that pools the data for theseunordered type experiments we find that participants are 93 per-centage points more likely to guess that the less frequent type ismodal when it is representative than when it is not (p = 002) Wealso run a family of ordered types experiments (two designs fivesamples 402 participants) Unlike the simpler T-shirts style

25 Throughout our analysis we exclude any participant who participated in aprevious version of the experiment and any participant who self-identified as color-blind In Online Appendix F we show that our results are unchanged if we includethese additional observations

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design the theoretical predictions for the ordered types designsare more sensitive to the specific assumptions one makes aboutthe weighting function of the DM26 We find effects in the pre-dicted direction for three of the five samples As we discuss inmore detail in Online Appendix F the ordered types resultsvary by platform with consistently stronger results on AmazonMechanical Turk than in the laboratory samples Pooling all or-dered types experiments participants are 93 percentage pointsmore likely to guess that the group of interest has a greater av-erage than the comparison group when the right tail is represen-tative (p = 062) Given our simple experimental setting withgroups of mundane objects we interpret our resultsmdasha signifi-cant and reasonably sized impact on average beliefsmdashas an im-portant proof of concept the presence of representative typesbiases ex post assessment

IVB Empirical Evidence on Political Stereotypes

We examine two data sets on political preferences and be-liefs about political preferences in the United States We inves-tigate the roles of representativeness and context dependence byseparately testing for hypotheses that allow us to assess the lead-ing theories of stereotypes

First we test whether beliefs are correct or depart systemat-ically from the truth The statistical discrimination approachbuilds on the assumption that people hold rational expectationsof group traits Comparing beliefs to the truth allows us to assessthe validity of this assumption in our data

Second we test if beliefs depart from the truth by exagger-ating (mean) differences among groups per the kernel of truthhypothesis This is an implicit test of context dependence be-cause it implies that beliefs about the target groups are shapednot only by that grouprsquos characteristics but also by those of thereference group27

Third we test if distortions in beliefs can be accounted for bythe overweighting of highly representative types (defined astypes that are relatively more frequent in the target relative to

26 This is due in part to our choice to not study MLRP distributions We moti-vate and discuss this design decision in Online Appendix F

27 Of course unlike in the laboratory experiment in this setting we cannot testfor context dependence by exogenously varying the reference group

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the reference group) The second and third tests address the keypredictions of our model

1 The Data We have two data sets on political preferences andbeliefs about political preferences The first data set from GrahamNosek and Haidt (GNH 2012) contains data from the MoralFoundations Questionnaire Respondents (1174 self-identified lib-erals and 500 self-identified conservatives) answer questions abouttheir position on a subset of 45 issues 20 moral relevance state-ments (eg lsquolsquowhen you decide whether something is right orwrong to what extent are the following considerations relevantto your thinkingrsquorsquo) and 25 moral judgments (eg lsquolsquoindicate theextent to which you would agree or disagreersquorsquo) For each issue arandomly determined subset of participants states their own posi-tion another subset states their belief on the position of a lsquolsquotypicalliberalrsquorsquo and a third subset states their belief on the position of alsquolsquotypical conservativersquorsquo The data thus include the distribution overpositions for both liberal and conservatives as well as the averagebelieved typical position of liberals and of conservatives on the 45issues Each position is elicited on 1ndash6 scale

The second data set comes from the American NationalElection Survey (ANES) and contains data from more than20000 respondents between 1964 and 201228 The surveycovers political issues of the day such as the optimal amount ofgovernment spending and service provision (1984ndash2000) or theplace of women in society (1972ndash1998) We focus on the 10 issuesthat ask participants to respond on a 1ndash7 scale (rather than justindicate binary agreement or disagreement) all 10 issues areasked in multiple years Participants are asked to provide theirown position on the scale and their believed position of theDemocratic and Republican parties (lsquolsquoWhere would you placethe Democratic [Republican] party on this scalersquorsquo) The data in-clude for each issue-year observation the distribution of partic-ipant positions for self-identified liberals and self-identifiedconservatives as well as the distribution of believed typical posi-tions of the Democratic and Republican parties

28 These data are publicly available at httpwwwelectionstudiesorgstudy-pagesanes_timeseries_cdfanes_timeseries_cdfhtm

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2 Empirical Strategy Our analysis focuses on beliefs abouttwo groups Conservatives and Liberals The types are the possi-ble positions for each issue (1 2 6 7) For the GNH data weinterpret beliefs about the lsquolsquotypicalrsquorsquo element of a group to coincidewith the believed average position in that group Similarly forthe ANES data we use the believed party positions as a proxy forbelieved mean of each group29 We then take as a benchmark thehypothesis that individuals hold accurate beliefs about eachgroup and in particular that believed mean position shouldequal true mean position at least on average across subjectsThe accurate beliefs hypothesis underlies the most common eco-nomic model of stereotyping statistical discrimination

To assess our representativeness-based model we perform aregression exercise To test our model in a linear regressionframework we rely on linear approximations of the weightingfunction Our model then yields two regression specifications

PROPOSITION 4 Let G 2 fconservative liberal g and assume

ht h tG

tG

be a differentiable and strictly increasing weight-

ing function as in Definition 2 The following hold as a first-order approximation around identical distributions G

Gfrac14 1

(i) Kernel of truth regression There exists a constant gt 0such that

EstethtjGTHORN frac14 EethtjGTHORNeth1thorn THORN EethtjGTHORNeth5THORN

(ii) Representativeness regression Denote H frac14 fT 2 Tg

the right tail of types and RconsH frac14

PHtconsPHtlib

as the average

representativeness of right tail types for conservatives

29 This assumption is consistent with the authorsrsquo interpretation of the GNHdata (GNH 2012) and with previous studies using ANES (eg Westfall et al 2015)Furthermore to the extent that this assumption holds equally well for most issueswithin a data set our focus on cross-issue differences should allow us to test thepredictions of our model even with an imperfect proxy for beliefs of mean positionsFinally the data provide some insight into whether subjects are reporting (per-ceived) modal or mean types As we show the modal type is a poor prediction ofstated beliefs while a distorted mean slanted toward representative types is anaccurate prediction of stated beliefs

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Under the further approximation where tcons

tlibampRcons

H for

t 2 H

EstethtjconsTHORN frac14 EethtjconsTHORN thorn consethR

consH 1THORNeth6THORN

EstethtjlibTHORN frac14 EethtjlibTHORN libethR

consH 1THORNeth7THORN

where lcons and llib are positive constants

The first regression allows us to test for the kernel of truthhypothesis and the second set of regressions allows us to test forthe role of representativeness

Equation (5) says that respondents in our model inflate theaverage position of a group say the conservatives if and only ifthe group has a higher average position than the other groupnamely the liberals Formally EstethtjconsTHORN gt EethtjconsTHORN if and onlyif EethtjconsTHORN gt EethtjlibTHORN Because in our measurement scale highertypes mean lsquolsquomore conservativersquorsquo we expect (i) believed conserva-tive average to be higher than the truth and (ii) the extent ofoverstatement to decrease in the average liberal position EethtjlibTHORNConversely we expect the average liberal position to be lowerthan the truth the more so the higher the average conservativeposition EethtjconsTHORN

As previously discussed the basis of these predictions is con-text dependence information about the distribution of ndashG is rel-evant for the beliefs about G This context dependence isinconsistent with rational expectations in which only thegrouprsquos own means should affect beliefs We test the hypothesisthat the true mean EethtjGTHORN is a significant predictor of the believedmean E

stethtjGTHORN with a positive sign and the other grouprsquos truemean EethtjGTHORN is a predictor of the believed mean with a negativesign

Equations (6) and (7) say that repondentsrsquo assessment bias isshaped by representativeness When the right tail is more repre-sentative for conservatives (Rcons

H 1 positive and large) partici-pants should inflate the average conservative position more(higher E

stethtjconsTHORN EethtjconsTHORN) and deflate the average liberal po-sition more (lower E

stethtjlibTHORN EethtjlibTHORN) We test the hypothesisthat the inflation in conservative positions is positively associatedwith the representativeness of the right tail for the conservativesand the inflation in liberal positions is negatively associated with

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it Once again the representativeness of the right tail is com-puted using the true distribution of positions

In equations (6) and (7) in many cases the representative tailis also the most likely one As a consequence these tests cannotdistinguish a representativeness-based from a likelihood-basedmodel of distorted beliefs We perform two additional testsFirst we run versions of equations (6) and (7) in which we controlfor the likelihood of tails (see Table A4 in Online Appendix G)Second we compute numerically the predictions of a representa-tiveness-based model of stereotypes and a likelihood-based modelof stereotypes We then assess which of these two is better able tomatch the data on beliefs

3 Empirical Results To begin we illustrate the structure ofthe data and the nature of our predictions with two simple exam-ples from the GNH data set focusing on beliefs about conserva-tives In example 1 participants are asked about their agreementwith the statement lsquolsquoIt can never be right to kill a human beingrsquorsquoIn example 2 participants are asked about the moral relevance oflsquolsquowhether or not someone cared for someone weak or vulnerablersquorsquoAs can be seen in Figure III in example 1 the modal position(strongly disagree (1)) and most representative positions(strongly disagree (1)) coincide for conservatives In contrast inexample 2 in Figure III the most representative types (slightlyrelevant (3) not at all relevant (1)) are not most likely for theconservative group Following Proposition 1 we predict that be-liefs will be distorted in the direction of the most representativetypes Thus we expect more exaggeration in example 2 than inexample 1 since in example 2 the most representative types (inthe left tail) are far from the modal type whereas in example 1they coincide This is what we find the conservative position isexaggerated by only 009 positions in Example 1 (true mean 299believed mean 290) but by 106 positions in Example 2 (truemean 421 believed mean 315)

In the full data sets we treat each (issue year) pair as anobservation and we cluster standard errors at the issue level Forthe GNH data we have 45 observations 45 issues measured inthe same year For the ANES data we have 66 observations 10issues measured in multiple years To begin we simply docu-ment systematic exaggeration in both data sets This is a primaryfocus of the original analysis in GNH (2012) and also in Westfall

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FIGURE III

Two Examples

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et al (2015)rsquos analysis of the ANES data30 Figure IV shows thatthe believed difference between typical conservative and typicalliberal positions is larger than the true difference in mean posi-tions for 109 of the 111 observations The data for both GNH(squares) and ANES (triangles) lie above the 45-degree line(dashed)31 Average exaggeration is 062 positions on the scale(066 in the GNH data 059 in the ANES data)32

The systematic and significant exaggeration of mean differ-ences suggests that the benchmark model of accurate beliefs ismissing something important Indeed this exaggeration reflectsthe fact that believed means are typically more extreme than truemeans First note that the kernel of truth regression (equation(5)) generates exaggeration of mean differences just as docu-mented in Figure IV

EstethtjGTHORN E

stethtjGTHORN frac14 eth1thorn 2THORN frac12EethtjGTHORN EethtjGTHORN

To bring this prediction to the data we regress the believedmean position for each group EBethtjGTHORN on the true mean of thegroup EethtjGTHORN and the true mean of the comparison groupEethtjGTHORN across issues We do this for each group (liberals con-servatives) in each data set separately We also present pooledspecifications that combine the data sets to make a prediction fora given group (liberals conservatives) In these pooled specifica-tions we include a dummy variable indicating whether theobservation came from the ANES data set For all specificationswe cluster observations at the issue level33 The results from re-gression are shown in Table I In every specification we find thatEethtjGTHORN is a significant predictor of EBethtjGTHORN with the predicted pos-itive sign Crucially for five of the six specifications the mean of

30 Chambers and Melnyk (2006) also find evidence of exaggeration of truedifferences in beliefs about political positions

31 For convenience we recode all issues so that the high end of the scale (67)represents the stereotypically more conservative position

32 A natural question to ask is how beliefs vary across liberals and conserva-tives That is do beliefs about a group G depend on membership in G versus ndashG Ourmodel does not speak to this issue However in Online Appendix G we show thatthe results we document below hold for both beliefs held by conservatives and be-liefs held by liberals see Tables A9 A10 and A11

33 In general the results presented below for the ANES data are not largelyimpacted by the decision to cluster at the issue level Similar results are obtained ifthe data are not clustered

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the comparison group EethtjGTHORN is also a significant predictor ofE

BethtjGTHORN with the predicted negative signAlthough these results provide strong evidence of context

dependence and are consistent with our model they do not pindown a role for representativeness of types Our next test relatesthe magnitude of representativeness of tail types to the magni-tude of belief distortions

To this end we implement the regressions in equations (6)and (7) Following Proposition 4 we compute the average repre-

sentativeness of tail types for conservatives RconsH frac14

PtT2tconsPtT2tlib

We

again test the hypothesis that RconsH is a significant predictor of Est

ethtjconsTHORN with a positive sign and a predictor of EstethtjlibTHORN with a

negative sign Table II shows that conditional on true mean RconsH

predicts believed mean for each group G as expected The firstthree specifications display the results for predicting beliefs heldabout conservatives In both data sets the average representa-tiveness of tail types for conservatives is a significant positivepredictor of beliefs held about conservatives The final three spe-cifications display the results for predicting beliefs held about

FIGURE IV

Exaggeration of Differences

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liberals We find that the average representativeness of tail typesfor conservatives is a negative predictor of beliefs held about lib-erals This effect is significant in the GNH data and marginallysignificant in the ANES data

We present several additional results in Online Appendix GTo further examine the role of representativeness in driving be-liefs we first show the results of Table II carry through when we

TABLE II

AVERAGE REPRESENTATIVENESS OF TAIL POSITIONS PREDICTS BELIEFS

OLS Predicting Believed Mean of Group G for Each Issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position

of group G for issue

078 024 051 072 018 041

(006) (008) (009) (005) (005) (010)

Avg rep of tail types for

conservatives RconsH

019 055 025 014 012 024

(007) (022) (008) (006) (007) (005)

Constant 101 260 184 093 271 201

(026) (045) (029) (022) (025) (032)

R2 082 048 060 091 031 070

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

TABLE I

INFORMATION ABOUT ndashG PREDICTS BELIEFS ABOUT G

OLS predicting believed mean of group G for each issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position of

conservatives for issue

102 098 096 021 019 025

(0097) (0133) (0076) (0060) (0116) (0060)

True mean position of

liberals for issue

035 086 058 0987 039 073

(0106) (0134) (0131) (0066) (0106) (0135)

Constant 151 335 235 069 258 156

(0195) (0269) (0279) (0122) (0249) (0270)

R2 083 053 066 092 032 068

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

STEREOTYPES 1789

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control for the average likelihood on the tail positions (see Table A4in Online Appendix G) Most tellingly we use the model to predictbeliefs across issues and compare those to the data For simplicitywe use the rank-based truncation specification to predict mean be-liefs when stereotypes include the d most representative types ford frac14 1 T We compare these predictions to those of a model inwhich beliefs are obtained by restricting the distribution to the dmost likely types Our benchmark for both models is predicting thebelieved mean from the entire distribution where d = T We showthat the predictions of the rank-based truncation model with d = 4or 5 compare favorably to both a likelihood-based truncation model(with any d) and the accurate beliefs benchmark Interestingly thisresult suggests that stereotypical beliefs are well approximated byneglecting the least representative types (as opposed to focusingonly on the most representative types) and so represent a moderatethough systematic departure from the standard benchmarkFinally we show that the results we document above hold forboth beliefs held by conservatives and beliefs held by liberals (seeTables A9 A10 and A11 in Online Appendix G)

V Conclusion

We present a model of stereotypical thinking in which DMsmaking predictions about a group overweight the grouprsquos mostdistinctive types These overweighted types are not the mostlikely ones given the DMrsquos data but the most representativeones in the sense of being the most diagnostic of the group rela-tive to other groups Representativeness implies that what ismost distinctive of a group depends on what group it is comparedwith We present experimental evidence that confirms this con-text dependence in recall-based assessments of groups Finallywe evaluated the predictions of the model using political data fromexisting large-scale surveys We find context dependence to be akey feature of beliefs Given the richness of the political data wecan go a step further and identify a role for representativeness inparticular As the representativeness of tail types increases beliefsof a group are distorted in the direction of that tail

Our approach provides a parsimonious and psychologicallyfounded account of how DMs generate simplified representationsof reality from social groups to stock returns and offers a unifiedaccount of disparate pieces of evidence relating to this type of

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uncertainty The model captures the central fact that stereotypeshighlight the greatest difference between groups thus explainingwhy some stereotypes are very accurate while others lack valid-ity Still stereotypes often have a kernel of truth when they arebased on systematicmdasheven if smallmdashdifferences between groupsThis logic allows us to describe a number of heuristics and psy-chological biases many of which arise in the context of predictionproblems Generically our model generates overreaction to diag-nostic information

Our model is based on representativeness and does not cap-ture all the features of stereotypical thinking However it cap-tures perhaps the central feature when we think of a group wefocus on what is most distinctive about it and neglect or under-weight the rest

Saeuroıd Business School University of Oxford

Ohio State University and Harvard Business School

Universita Bocconi and Innocenzo Gasparini Institute

for Economic Research

Harvard University

Supplementary Material

An Online Appendix for this article can be found at QJEonline (qjeoxfordjournalorg)

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Arrow Kenneth lsquolsquoThe Theory of Discriminationrsquorsquo in Discrimination in LaborMarkets Orley Ashenfelter and Albert Rees eds (Princeton NJPrinceton University Press 1973)

Ashton Michael and Victoria Esses lsquolsquoStereotype Accuracy Estimating theAcademic Performance of Ethnic Groupsrsquorsquo Personality and SocialPsychology Bulletin 25 (1999) 225ndash236

Barberis Nicholas Andrei Shleifer and Robert Vishny lsquolsquoA Model of InvestorSentimentrsquorsquo Journal of Financial Economics 49 (1998) 307ndash343

Bayer Sylvia lsquolsquoThe Accuracy of Academic Gender Stereotypesrsquorsquo Sex Roles 40(1999) 787ndash813

Benjamin Dan James Choi and Joshua Strickland lsquolsquoSocial Identity andPreferencesrsquorsquo American Economic Review 100 (2010) 1913ndash1928

Benjamin Dan Matthew Rabin and Collin Raymond lsquolsquoA Model of Non-Belief inthe Law of Large Numbersrsquorsquo Journal of the European Economic Association15 (2015) 515ndash544

Bertrand Marianne lsquolsquoNew Perspectives on Genderrsquorsquo Handbook of LaborEconomics 4 (2011) 1543ndash1590

Bodoh-Creed Aaron Dan Benjamin and Matthew Rabin lsquolsquoThe Dynamics of Base-Rate Neglectrsquorsquo mimeo Haas Business School 2013

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Bohnet Iris Alexandra van Geen and Max Bazerman lsquolsquoWhen PerformanceTrumps Gender Bias Joint versus Separate Evaluationrsquorsquo ManagementScience 5 (2016) 1225ndash1234

Bordalo Pedro Nicola Gennaioli and Andrei Shleifer lsquolsquoSalience Theory of Choiceunder Riskrsquorsquo Quarterly Journal of Economics 127 (2012) 1243ndash1285

mdashmdashmdash lsquolsquoSalience and Consumer Choicersquorsquo Journal of Political Economy 121(2013) 803ndash843

Briton Nancy and Judith Hall lsquolsquoBeliefs about Female and Male NonverbalCommunicationrsquorsquo Sex Roles 32 (1995) 79ndash90

Buser Thomas Muriel Niederle and Hessel Oosterbeek lsquolsquoGenderCompetitiveness and Career Choicesrsquorsquo Quarterly Journal of Economics 129(2014) 1409ndash1447

Carrell Scott Marianne Page and James West lsquolsquoSex and Science How ProfessorGender Perpetuates the Gender Gaprsquorsquo Quarterly Journal of Economics 125(2010) 1101ndash1144

Chambers John and Darya Melnyk lsquolsquoWhy Do I Hate Thee ConflictMisperceptions and Intergroup Mistrustrsquorsquo Personality and SocialPsychology Bulletin 32 (2006) 1295ndash1311

Chan Wayne Robert R McCrae Filip De Fruyt Lee Jussim CorinnaE Lockenhoff Marleen De Bolle Paul T Costa Jr Angelina R SutinAnu Realo Juri Allik Katsuharu Nakazato Yoshiko ShimonakaMartina Hrebıckova Sylvie Graf Michelle Yik Marina Brunner-SciarraNora Leibovich De Figueora Vanina Schmidt Chang-kyo Ahn Hyun-nie Ahn Maria E Aguilar-Vafaie Jerzy Siuta Barbara SzmigielskaThomas R Cain Janet T Crawford Khairul Anwar Mastor Jean-Pierre Rolland Florence Nansubuga Daniel R MiramontezVeronica Benet-Martınez Jerome Rossier Denis Bratko Iris MarusicJamin Halberstadt Mami Yamaguchi Goran Knezevic Thomas A MartinMirona Gheorghiu Peter B Smith Claudio Barbaranelli Lei WangJane Shakespeare-Finch Margarida P Lima Waldemar KlinkoszAndrzej Sekowski Lidia Alcalay Franco Simonetti Tatyana V AvdeyevaV S Pramila and Antonio Terracciano lsquolsquoStereotypes of Age Differences inPersonality Traits Universal and Accuratersquorsquo Journal of Personality andSocial Psychology 103 (2012) 1050ndash1066

Chen Yan Sherry Xin Liu Tracy Xiao and Margaret Shih lsquolsquoWhich Hat to WearImpact of Natural Identities on Coordination and Cooperationrsquorsquo Games andEconomic Behavior 84 (2014) 58ndash86

Coffman Katherine lsquolsquoEvidence on Self-Stereotyping and the Contribution ofIdeasrsquorsquo Quarterly Journal of Economics 129 (2014) 1625ndash1660

Cunningham Tom lsquolsquoComparisons and Choicersquorsquo mimeo Stockholm University2013

Diekman Amanda Alice Eagly and Patrick Kulesa lsquolsquoAccuracy and Bias in theStereotypes about the Social and Political Attitudes of Women and MenrsquorsquoJournal of Experimental Social Psychology 38 (2002) 268ndash282

Eccles Jacquelynne S Janis E Jacobs and Rena D Harold lsquolsquoGender RoleStereotypes Expectancy Effects and Parentsrsquo Socialization of GenderDifferencesrsquorsquo Journal of Social Issues 46 (1990) 183ndash201

Fryer Roland and Matthew Jackson lsquolsquoA Categorical Model of Cognition andBiased Decision-Makingrsquorsquo BE Journal of Theoretical Economics 8 (2008)1ndash42

Fryer Roland and Steven Levitt lsquolsquoAn Empirical Analysis of the Gender Gap inMathematicsrsquorsquo American Economic Journal Applied Economics 2 (2010)210ndash240

Gennaioli Nicola and Andrei Shleifer lsquolsquoWhat Comes to Mindrsquorsquo Quarterly Journalof Economics 125 (2010) 1399ndash1433

Gennaioli Nicola Andrei Shleifer and Robert Vishny lsquolsquoNeglected RisksFinancial Innovation and Financial Fragilityrsquorsquo Journal of FinancialEconomics 104 (2012) 452ndash468

Gilens Martin lsquolsquoRace and Poverty in America Public Misperceptions and theAmerican News Mediarsquorsquo Public Opinion Quarterly 60 (1996) 515ndash541

Glaeser Edward lsquolsquoThe Political Economy of Hatredrsquorsquo Quarterly Journal ofEconomics 120 (2005) 45ndash86

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Glover Dyland Amanda Pallais and William Pariente lsquolsquoDiscrimination as a Self-Fulfilling Prophecy Evidence from French Grocery Storesrsquorsquo mimeo HarvardUniversity 2015

Goldin Claudia Lawrence Katz and Ilyana Kuziemko lsquolsquoThe Homecoming ofAmerican College Women The Reversal of the College Gender GaprsquorsquoJournal of Economic Perspectives 20 (2006) 133ndash156

Graham Jesse Brian Nosek and Jonathan Haidt lsquolsquoThe Moral Stereotypes ofLiberals and Conservatives Exaggeration of Differences across thePolitical Spectrumrsquorsquo PLoS One 7 (2012) 1ndash13

Grether David lsquolsquoBayes Rule as a Descriptive Model The RepresentativenessHeuristicrsquorsquo Quarterly Journal of Economics 95 (1980) 537ndash557

Griffin Dale and Amos Tversky lsquolsquoThe Weighing of Evidence and theDeterminants of Confidencersquorsquo Cognitive Psychology 24 (1992) 411ndash435

Guiso Luigi Ferdinando Monte Paola Sapienza and Luigi Zingales lsquolsquoCultureGender and Mathrsquorsquo Science 320 (2008) 1164ndash1165

Hilton James and William Von Hippel lsquolsquoStereotypesrsquorsquo Annual Review ofPsychology 47 (1996) 237ndash271

Hyde Janet Sara Lindberg Marcia Linn Amy Ellis and Caroline WilliamslsquolsquoGender Similarities Characterize Math Performancersquorsquo Science 321 (2008)494ndash495

Judd Charles and Bernardette Park lsquolsquoDefinition and Assessment of Accuracy inSocial Stereotypesrsquorsquo Psychological Review 100 (1993) 109ndash128

Jussim Lee Jarret Crawford Stephanie Anglin John Chambers Sean Stevensand Florette Cohen lsquolsquoStereotype Accuracy One of the Largest and MostReplicable Effects in All of Social Psychologyrsquorsquo in The Handbook ofPrejudice Stereotyping and Discrimination Todd Nelson ed (MahwahNJ Lawrence Erlbaum 2015)

Kahneman Daniel and Amos Tversky lsquolsquoSubjective Probability A Judgment ofRepresentativenessrsquorsquo Cognitive Psychology 3 (1972) 430ndash454

mdashmdashmdash lsquolsquoOn the Psychology of Predictionrsquorsquo Psychological Review 80 (1973) 237ndash251

Kaplowitz Stan Bradley Fisher and Clifford Broman lsquolsquoHow Accurate ArePerceptions of Social Statistics about Blacks and Whitesrsquorsquo Public OpinionQuarterly 67 (2003) 237ndash243

Kersten Daniel Pascal Mamassian and Alan Yuille lsquolsquoObject Perception asBayesian Inferencersquorsquo Annual Review of Psychology 55 (2004) 271ndash304

Klein Richard Kate A Ratliff Michelangelo Vianello Reginald B Adams JrStepan Bahnik Michael J Bernstein Konrad Bocian Mark J BrandtBeach Brooks Claudia Chloe Brumbaugh Zeynep CemalcilarJesse Chandler Winnee Cheong William E Davis Thierry DevosMatthew Eisner Natalia Frankowska David Furrow Elisa Maria GallianiFred Hasselman Joshua A Hicks James F Hovermale S Jane HuntJeffrey R Huntsinger Hans IJzerman Melissa-Sue John Jennifer A Joy-Gaba Heather Barry Kappes Lacy E Krueger Jaime Kurtz CarmelA Levitan Robyn Mallett Wendy L Morris Anthony J Nelson JasonA Nier Grant Packard Ronaldo Pilati Abraham M RutchickKathleen Schmidt Jeanine L Skorinko Robert Smith Troy G SteinerJustin Storbeck Lyn M Van Swol Donna Thompson Anna van rsquot VeerLeigh Ann Vaughn Marek Vranka Aaron Wichman Julie A Woodzickaand Brian A Nosek lsquolsquoInvestigating Variation in Replicability A ManyLabs Replication Projectrsquorsquo Social Psychology 45 (2014) 142ndash152

Lundberg Shelly and Richard Startz lsquolsquoPrivate Discrimination and SocialIntervention in Competitive Labor Marketsrsquorsquo American Economic Review73 (1983) 340ndash347

Madon Stephanie Max Guyll Kathy Aboufadel Eulices Montiel Alison SmithPolly Palumbo and Lee Jussim lsquolsquoEthnic and National Stereotypes ThePrinceton Trilogy Revisited and Revisedrsquorsquo Personality and SocialPsychological Bulletin 27 (2001) 996ndash1010

Martin Carol lsquolsquoA Ratio Measure of Sex Stereotypingrsquorsquo Journal of Personality andSocial Psychology 52 (1987) 489ndash499

STEREOTYPES 1793

at Harvard L

ibrary on October 28 2016

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ownloaded from

McCauley Clark Krishna Thangavelu and Paul Rozin lsquolsquoSex Stereotyping ofOccupations in Relation to Television Representations and Census FactsrsquorsquoBasic and Applied Social Psychology 9 (1988) 197ndash212

Mullainathan Sendhil lsquolsquoThinking through Categoriesrsquorsquo mimeo HarvardUniversity 2002

Ortoleva Pietro and Erik Snowberg lsquolsquoOverconfidence in Political BehaviorrsquorsquoAmerican Economic Review 105 (2015) 504ndash535

Phelps Edmund lsquolsquoThe Statistical Theory of Racism and Sexismrsquorsquo AmericanEconomic Review 62 (1972) 659ndash661

Pope Devin and Justin Sydnor lsquolsquoGeographic Variation in the Gender Differencesin Test Scoresrsquorsquo Journal of Economic Perspectives 24 (2010) 95ndash108

Rabin Matthew lsquolsquoInference by Believers in the Law of Small NumbersrsquorsquoQuarterly Journal of Economics 117 (2002) 775ndash816

Rabin Matthew and Joel Schrag lsquolsquoFirst Impressions Matter A Model ofConfirmatory Biasrsquorsquo Quarterly Journal of Economics 114 (1999) 37ndash82

Rabin Matthew and Dimitri Vayanos lsquolsquoThe Gamblerrsquos and Hot-Hand FallaciesTheory and Applicationsrsquorsquo Review of Economic Studies 77 (2010) 730ndash778

Reuben Ernesto Paola Sapienza and Luigi Zingales lsquolsquoHow Stereotypes ImpairWomenrsquos Careers in Sciencersquorsquo Proceedings of the National Academy ofSciences 111 (2014) 4403ndash4408

Rosch Eleanor lsquolsquoNatural Categoriesrsquorsquo Cognitive Psychology 4 (1973) 328ndash350Ryan Carey S lsquolsquoAccuracy of Black and White College Studentsrsquo In-Group and

Out-Group Stereotypesrsquorsquo Personality and Social Psychology Bulletin 22(1996) 1114ndash1127

Schneider David The Psychology of Stereotyping (New York Guilford Press2004)

Schneider David Albert Hastorf and Phoebe Ellsworth Person Perception(Reading MA Addison-Wesley 1979)

Shih Margaret Todd Pittinsky and Nalini Ambady lsquolsquoStereotype SusceptibilityIdentity Salience and Shifts in Quantitative Performancersquorsquo PsychologicalScience 10 (1999) 80ndash83

Shih Margaret Todd Pittinsky and Amy Trahan lsquolsquoDomain-Specific Effects ofStereotypes on Performancersquorsquo Self and Identity 5 (2006) 1ndash14

Steele Claude Whistling Vivaldi How Stereotypes Affect Us and What We CanDo (New York Norton 2010)

Tenenbaum Joshua and Thomas Griffiths lsquolsquoThe Rational Basis ofRepresentativenessrsquorsquo 23rd Annual Conference of the Cognitive ScienceSociety (2001) 1036ndash1041

Tversky Amos and Daniel Kahneman lsquolsquoExtensional versus Intuitive ReasoningThe Conjunction Fallacy in Probability Judgmentrsquorsquo Psychological Review 90(1983) 293ndash315

Weinberger Catherin lsquolsquoIs the Science and Engineering Workforce Drawn fromthe Far Upper Tail of the Math Ability Distributionrsquorsquo mimeo UCSB 2005

Westfall Jacob Leaf Van Boven John Chambers and Charles Judd lsquolsquoPerceivingPolitical Polarization in the United States Party Identity Strength andAttitude Extremity Exacerbate the Perceived Partisan DividersquorsquoPsychological Science 10 (2015) 145ndash158

Wolsko Christopher Bernadette Park Charles Judd and Bernd WittenbrinklsquolsquoFraming Interethnic Ideology Effects of Multicultural and Color-BlindPerspectives on Judgments of Groups and Individualsrsquorsquo Journal ofPersonality and Social Psychology 78 (2000) 635ndash654

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Page 6: I. Introduction · uneducated at the beginning of the 20th century, and as high achievers at the beginning of the 21st (Madon et al. 2001). Social science has produced three broad

existing empirical work on stereotype accuracy as follows lsquolsquothebest we can do by way of general summary is to say that somestereotypes held by some people for some groups are sometimesaccuratersquorsquo Our empirical investigation explores the connectionbetween stereotype accuracy and representativeness which wemeasure using the previously defined likelihood ratio

We first assess the role of representativeness and contextdependence in the lab We construct a group of mundane objectsG and present it to participants next to a comparison group ndashGIn our baseline condition the comparison group is chosen so thatno type is particularly representative of group G In our treat-ment we change the comparison group ndashG while leaving thetarget group G unchanged The new comparison group givesrise to highly representative types within G In line with thekey prediction of our model participants in the treatment condi-tion shift their assessment of G toward the representative types

We test the model using two data sets on political preferencesand beliefs about political preferences in the United States Heregroups are political constituencies (Democrats and Republicans)and types are their positions on a number of issues Holding fixedthe groups and the set of types and varying the groupsrsquo true dis-tributions across issues the data allow us to test whether beliefsabout political preferences are shaped by representativeness Wefirst show that such beliefs depart from the truth by exaggerating(mean) differences as per the kernel of truth logic We then ex-plore how the extent of exaggeration varies across issuesConsistent with the model we find that beliefs systematicallydepart from rational expectations and that the degree to whichthey exaggerate true differences is a function of representative-ness While representativeness is not the only heuristic thatshapes recall (availability driven by recency or frequency of ex-posure also plays a role) it explains the fact that in the datastated beliefs indeed exaggerate differences among groups

Since Kahneman and Tverskyrsquos (1972 1973) work on heuris-tics and biases several studies have formally modeled heuristicsabout probabilistic judgments and incorporated them into eco-nomic models Work on the confirmation bias (Rabin andSchrag 1999) and on probabilistic extrapolation (Grether 1980Barberis Shleifer and Vishny 1998 Rabin 2002 Rabin andVayanos 2010 Benjamin Rabin and Raymond 2015) assumesthat the decision maker has an incorrect model in mind or incor-rectly processes available data Our approach is instead based on

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the assumption that representative information comes foremostto mind when making judgments The mental operation that liesat the heart of our modelmdashgenerating a prediction for the distri-bution of types in a group based on data stored in memorymdashalsocaptures base rate neglect and overreaction to diagnostic infor-mation The underweighting or neglect of information in ourmodel simplifies judgment problems in a way related to modelsof categorization (Mullainathan 2002 Fryer and Jackson 2008)In these models however decision makers use coarse categoriesorganized according to likelihood not representativeness Thisapproach generates imprecision but does not create a systematicbias for overestimating unlikely events nor does it allow for con-text-dependent beliefs In our empirical analysis of political be-liefs we explicitly compare the predictions of representativeness-based recall to those of likelihood-based models and find that theevidence supports the former

In modeling representativeness we follow the specification ofGS (2010) but investigate a new set of questions GS (2010) ex-amine how representativeness distorts the assessed probabilitiesof alternative hypotheses but not how the probability of a givenhypothesis or group is distributed across its constituent elementsIn the context of the current setting GS (2010) ask how imperfectrecall affects the assessed probability that a randomly drawnmember from a universe belongs to group G The current arti-cle in contrast asks which type t we expect to draw once we knowthat we are facing group G GS (2010) show how representative-ness generates biased probabilistic assessments such as conjunc-tion and disjunction fallacies This article deals with perhaps abroader and more ubiquitous problem of stereotype formationextensively studied by other social scientists but largely ne-glected by economists

Section II describes our model In Section III we examine theproperties of stereotypes including the forces that shape stereo-type accuracy and illustrate these properties with examples InSection IV we bring the model to the data performing a lab ex-periment and analyzing existing surveys of political beliefsSection V concludes The Online Appendix presents proofs anumber of extensions of the model and additional results forthe experiments and field evidence

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II A Model of Representativeness and Stereotypes

IIA The Model

A decision maker (DM) faces a prediction problem such asassessing the ability of a job candidate from a certain ethnicgroup the future performance of a firm belonging to a certainsector or future earnings based on own gender

Formally there is a set of types of interest T and an overallpopulation of which group G is a subset The set of typesT can be unordered (eg occupations) or ordered (and typi-cally cardinal eg earnings levels) When T is ordered wewrite T frac14 ft1 tTg with t1 lt t2 lt lt tT6 There is a probabil-ity or frequency distribution 2 ethT THORN that induces a condi-tional distribution PrethT frac14 tjGTHORN when restricted to G7 In whatfollows we denote by tG frac14 PrethT frac14 tjGTHORN the probability of typet in group G and by G the vector ethtGTHORNt2T containing the condi-tional distribution

The DMrsquos goal is to assess the distribution of the types ofinterest in a particular group G Although the DM has stored inmemory the full distribution he retrieves from memory a dis-torted version of G that overweights the probability of thosetypes that are most representative of G relative to a comparisongroup ndashG Generically ndashG is a group in that is distinct from Gnamely G7 nG although in some cases it can coincide withthe complement of G

According to Tversky and Kahneman (1983) a type t is rep-resentative of G if it is relatively more likely to occur in G thanin ndashG Definitions 1 and 2 formalize this representativeness-based recall following GS (2010)

6 For simplicity we also use T to denote the number of types jTj The modelapplies also to cases in which types (i) are multidimensional capturing a bundle ofattributes such as occupation and nationality or (ii) are continuous We considerthese cases in Online Appendixes C and D respectively Also G may represent anycategory of interest such as the historical performance of a firm or industry actionsavailable to a decision maker (T = set of payoffs G = occupations) or categories inthe natural world (T = ability to fly G = birds)

7 In many applications each individual in is characterized by a determin-istic type (eg age hair color) As a result ethtTHORN frac14 1

jj For instance each Floridian

has a single age type (at the finest temporal resolution) When types are stochasticinstead such as when estimating future earnings of a person or a firm each indi-vidual is described by a nondegenerate distribution

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DEFINITION 1 The representativeness of type t for group G givencomparison group ndashG is defined as the likelihood ratio

RethtGGTHORN tG

tGeth2THORN

Definition 1 implies that DMs are attuned to log differencesin probabilities representativeness depends on the percentageprobability increase of a type from ndashG to G This captures aform of diminishing sensitivity whereby for a fixed probabilitydifference a type is more likely to be overweighed if it is unlikelyin the comparison group8 Thus the representative age of aFloridian is 65+ because people in this age bracket are morecommon in Florida than in the rest of the United StatesStatistically representative types are also diagnostic of thetarget group G Indeed the higher is RethtGGTHORN the more confi-dent is a Bayesian DM observing t that t belongs to G rather thanto ndashG9

The ease of recall of highly representative types affectsjudgments because more easily recalled types are overweighted

We model distorted recall as follows Denote by RethtGGTHORN

tG

tG

t2T

the vector of representativeness of all types in G

We then have

8 Our definition of representativeness links to Weberrsquos law of sensory percep-tion see Section IIB It also links to our previous work on salience in which wepostulated that log differences in payoffs determine the attention to lottery payoffs(Bordalo Gennaioli and Shleifer 2012) and to goodsrsquo attributes (BordaloGennaioli and Shleifer 2013) Equation (2) establishes the same principle for thedomain of probabilities

9 This insight led Tenenbaum and Griffiths (2001) to define representative-ness as individualsrsquo sense as intuitive Bayesians of updating in reaction to dataTheir definition like ours is in terms of the likelihood ratio However Tenenbaumand Griffiths interpret representativeness as a mechanism that affects intuitivejudgments of similarity rather than beliefs (eg it accounts well for lab evidencewhere subjects are asked to rank types in terms of representativeness or ofstrength of association with a group) Accordingly they do not consider the possi-bility of systematically distorted and context dependent beliefs

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DEFINITION 2 The DM attaches to each type t 2 T in group G adistorted probability

sttG frac14 tG

htethRethtGGTHORNTHORNPs2T sGhsethRethtGGTHORNTHORN

eth3THORN

where ht RTthornRthorn is a weighting function such that

(i) The weight ht is a symmetric function of the representa-

tiveness of types s 6frac14 t Formally ht frac14 h tG

tG

sG

sG

s2Tn tf g

where h Rthorn RT1thorn Rthorn is a function that is invariant to

a permutation of the last T ndash 1 arguments(ii) Weighing of a type increases in own representativeness

and decreases in the representativeness of other typesFormally the function hethTHORN is weakly increasing in itsfirst argument and weakly decreasing in the other T 1arguments

We call the distribution ethsttGTHORNt2T the stereotype for G If a type

t is objectively more likely namely tG is higher then the ste-reotype attaches higher probability to it By property i distor-tions are due exclusively to the fact that a type is more or lessrepresentative than the others In particular if all types areequally representative the DM equally weighs all of them ath(1) and holds rational expectations about G If instead the rep-resentativeness of different types differs property ii implies thatthe stereotype ceteris paribus overweights the probability of morerepresentative types

Most of the results we explore in this article hold for a gen-eral weighing function htethTHORN Specific functional forms captureadded assumptions about the psychology of representativeness-based recall and are useful in applications We outline a few spe-cifications and their properties

Rank-based stereotypes the ranking of the representa-tiveness of different types shapes distortions Denote byrethtTHORN 2 f1 Tg the representativeness ranking of type tWhen r(t) = 1 type t is the most representative one (po-tentially with ties) We can specify two ways in which atypersquos representativeness ranking distorts its probability

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(i) Rank-based truncation the DM only recalls the typesthat have representativeness ranking of at most dnamely ft 2 TjrethtTHORN dg Zero probability is attachedto the remaining types10 Denote by IethrethtTHORN dTHORN an in-dicator function taking the value 1 if the representa-tiveness ranking of t is at most d Then theweighting function is ht frac14 IethrethtTHORN dTHORN so that

sttG frac14 tG

IethrethtTHORN dTHORNPs2T sGIethrethsTHORN dTHORN

which is the true conditional probability within re-called types This assumption is used in Gennaioliand Shleifer (2010)11

(ii) Rank-based discounting the DM discounts by a con-stant factor 2 frac1201 the odds of type t relative to itsimmediate predecessors in the representativenessranking Lower implies stronger discounting ofless representative types Formally the weightingfunction is ht frac14

rethtTHORN so that

sttG frac14 tG

rethtTHORNPs2T sG

rethsTHORN

Representativness-based discounting all else equal theweight attached by the DM to type t increases continuouslywith its representativeness One convenient formulation is

ht frac14tG

tG

so that

10 These neglected types are not viewed as impossible they are just assignedzero probability in the DMrsquos current thinking This formulation allows us to modelsurprise and reactions to unforeseen contingencies which have proved useful in-gredients in modeling probabilistic judgments (GS 2010) as well as neglect of risk infinancial crises (Gennaioli Shleifer and Vishny 2012)

11 Specifically in GS (2010) the assessed probability that a certain hypothesisG is true is equal to

Pr ethGTHORN frac14

Pt tGIethrethtTHORN dTHORNP

t tGIethrethtTHORN dTHORN thornP

t t=GIethrethtTHORN dTHORN

which increases in the ratio between the total probability mass recalled for Gand that recalled for G frac14 nG

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sttG frac14 tG

tG

tG

P

s2T sGsG

sG

where 0 captures the extent to which representative-ness distorts beliefs This formulation is particularly con-venient when dealing with continuous distributions ofthe exponential or power classes

These functional forms all embody the main idea of our modelthat the stereotype overweights the probability of more represen-tative types Rank-based truncation captures a central manifes-tation of limited memory forgetting unrepresentative typesSmoother discounting (based on ranking or on representative-ness) may be more appropriate when the type space is smalland smooth discounting can be more tractable in certain settings

Section III characterizes the general properties of stereotypesIn particular it shows their ability to account for social psycholo-gistsrsquo kernel of truth hypothesis under the general weighting func-tion of Definition 2 To bring the model to the data in Section IVBwe derive linear approximations of stereotypical beliefs by assum-ing that the weighting function is differentiable with respect to atypersquos representativeness This assumption excludes rank-basedweighting but allows for many possibilities

IIB Discussion of Assumptions

Before moving to the formal analysis we discuss some prop-erties and limitations of our approach Representativeness-basedrecall the idea that individuals recall distinctive group types canbe viewed as an instance of what Kahneman and Tversky calllsquolsquoattribute substitutionrsquorsquo When dealing with the difficult questionlsquolsquowhat is the distribution of hair color among the Irishrsquorsquo peopleintuitively answer to the simpler question lsquolsquowhich hair color dis-tinguishes the Irish peoplersquorsquo Critically as discussed byKahneman and Tversky attribute substitution does not occurbecause people misunderstand the original question or mechan-ically confuse the assessment of PrethtjGTHORN with that of PrethGjtTHORNRather it occurs because the distinctive or representative typesimmediately come to mind and individuals anchor their overallprobability judgment to them As a consequence subjects do notonly make mistakes in judging the probability that a Floridian is

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over age 65 They also give too high an answer to the questionlsquolsquowhat is the average age of a Floridianrsquorsquo12

One interesting question is whether the process of stereotyp-ing we describe is optimal in some sense Focusing mental repre-sentations on a few types can be justified by the costs of thinkingor retrieval This approach however is not enough to explainwhy individuals should focus on representative rather thanlikely types We do not formally analyze the optimality of repre-sentativeness here but we mention some relevant considerationsfrom cognitive psychology Kahneman and Tversky (1979) stressthe similarity between many perceptual and cognitive operationsFor instance the highlight of contrastmdasha key principle of visualperceptionmdashis invoked to justify the prospect theory assumptionthat the carriers of utility are changes relative to a referencepoint The same logic applies to our model in which stereotypesprecisely highlight the contrast between groups

In visual perception assessing properties such as brightnesscolor size or distance to an object by comparing them to otherproximate objects has been shown to be optimal in the presence ofmultiplicative background noise (Kersten Mamassian andYuille 2004 Cunningham 2013) Our formulation of representa-tiveness is related to the same idea in the sense that individualsestimating properties of one group stress differences from an-other group In a noisy world in which attention is limited thisprocess may optimally allow for swift reactions to changes ingroup characteristics even if errors are sometimes made13

12 Indeed in many cases mere confusion of PrethtjGTHORNwith PrethGjtTHORNwould not yieldthe phenomenon of stereotyping In the Irish hair color example the probability ofbeing Irish conditional on having red hair is

PrethIrishjredTHORN frac14PrethredjIrishTHORNPrethIrishTHORN

PrethredjIrishTHORNPrethIrishTHORN thorn PrethredjNonIrishTHORNPrethNonIrishTHORN

This probability is clearly very small given that the Irish population is a tinyfraction of the world population Confusion of PrethtjGTHORN with PrethGjtTHORN in this casewould lead to an understatement of the probability of the red-haired Irish

13 To give a simple example suppose thatmdashas in the case of Proposition 3mdashthevariance in the environment increases in the sense that extreme tail events becomemore likely Then a likelihood-based stereotype would detect no change whereas arepresentativeness-based stereotype would focus on the heightened probability ofthe tails In particular an asymmetric increase in tail probabilities that shifts themean would be detected by a representativeness-based stereotype even if the dis-tributionrsquos mode does not change

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Exploring this idea formally is an interesting avenue for futurework

Consider some limitations of our model First representa-tiveness is not the only heuristic that shapes recall Decisionmakers may for instance find it easier to recall types that aresufficiently likely Another potentially important mechanism isavailability understood by Kahneman and Tversky (1972) as thelsquolsquoeasersquorsquo with which information comes to mind (because of actualfrequency or repetition) In Online Appendix E we present a trun-cation-based recall mechanism in which distortions are driven bya combination of representativeness and likelihood of types(which is equivalent to relaxing property i in Definition 2) Thismodel can offer a useful starting point to capture availability aswell even though a full model of availability is beyond the scopeof this article Even in this more general setting the influence ofrepresentativeness on recall is the driving force of stereotypesthat in line with the social psychology perspective are basedon underlying differences among groups As we show in SectionIV this feature is critical in accounting for the evidence

The second set of model-related issues concerns how to spe-cify the elements of Definition 1 in applications group G the typespace T and the reference group ndashG Take the specification of thegroup G and of the type space T Often the problem itself pro-vides a natural specification of these features This is the case inthe empirically important class of lsquolsquoclosedrsquorsquo questions such asthose used in surveys which provide respondents with a set ofalternatives as in the data we use in Section IV More generallythe problem solved by the DMmdashsuch as evaluating the resume ofa job applicant coming from a certain ethnic groupmdashprimes agroup a dimension of interest and a set of types (eg the appli-cantrsquos qualification or skill levels) When types have a naturalorder such as income age or education the granularity of T isalso naturally given by the problem (income age and years ofschooling brackets) When the set of types is not specified by theproblem DMs spontaneously generate one14 It would be useful tohave a model of which dimensions and types come to mind par-ticularly for more open-ended problems Psychologists have

14 For example suppose a person is asked to guess the typical occupation of ademocratic voter in an lsquolsquoopen-endedrsquorsquo format (without being provided a set of alter-natives) Here the level of granularity at which types are defined is not obvious (egteacher versus a university teacher vs a professor of comparative literature)

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sought to construct a theory of natural types and dimensions(Rosch 1973) We do not make a contribution to this problembut we note that in many problems of interest in economics thedimension as well as the set of types is naturally givenFurthermore in our model details of the type space can be impor-tant under rank-based truncation but they matter less undersmooth discounting

Consider finally the role of the comparison group ndashG Thisgroup captures the context in which a stereotype is formed andagain is often implied by the problem when G = Floridians ndashG =rest of US population when G = African Americans ndashG = whiteAmericans A distinctive prediction of our model confirmed byour experiments in Section IVA is that the stereotype for agiven group G depends on the comparison group ndashG15 WhenndashG is not pinned down by the problem itself to derive testablepredictions from representativeness we set G frac14 nG where

is the natural population over which the unconditional distribu-tion of types is measured

III Properties of Stereotypes

We now study stereotypical beliefs and their accuracy Toillustrate the role of representativeness we first ask to whatextent the most representative type is a good fit for the groupnamely whether it is modal Next we assess the accuracy of theentire stereotypical distribution To do so we focus on a cardinaltypes and compare the stereotypersquos mean and variance to the trueones

15 Some empirical papers have taken a similar approach exogenously varyingthe natural comparison group through priming Benjamin Choi and Strickland(2010) show that priming racial or ethnic identity can affect the risk preferences ofparticipants Chen et al (2014) find that Asian students cooperate less with out-group members when primed with their ethnic identity rather than their universityidentity Shih Pittinsky and Ambady (1999) show that Asian American womenstereotype themselves as better or worse in math with corresponding impact onperformance when their ethnicity or gender respectively is primed ShihPittinsky and Trahan (2006) replicate this effect using a verbal task documentingthat Asian American women performed better when their gender rather than theirethnicity was primed Although the generalizability and replicability of priminghas been doubted (Klein et al 2014) this body of evidence is consistent with contextdependence

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IIIA Likely versus Unlikely Exemplars

The most representative type for a group is the one thatagents most easily recall and associate with the group itself forinstance a red-haired Irishman or a 65+-year-old FloridianSocial psychologists call this type the exemplar of the groupAccordingly we define

DEFINITION 3 A type t is an exemplar for G given comparisongroup ndashG when

t 2 arg maxt

tG

tG

Under any specification of the weighting function ht inDefinition 2 overweighting (weakly) increases as we movetoward more representative types so the exemplar is also thetype whose probability is overweighted the most16 By analyzingthe exemplar then we can gauge whether representativenessinduces the DM to overweight a likely type (as happens in stan-dard models of categorical thinking) or an unlikely type Whenoverweighting occurs in unlikely and extreme types the biases ofstereotypes can be particularly severe17

Equation (2) yields the following characterization

PROPOSITION 1 Suppose the conditional distributions G and G

are not identical Consider two extreme cases

(i) If for all t t0

2 T we have that tG gt t0 G if and only iftG gt t0 G then the modal type is not an exemplar forat least one group

(ii) If for all t t0

2 T we have that tG gt t0 G if and only iftG lt t0 G then for each group the modal type is theexemplar

16 Consider the function hethTHORN from Definition 2 When applied to more repre-sentative types the first argument of the function increases while one of the otherT ndash 1 arguments decreases As a result the weighting factor ht (and thus overweigh-ing

sttG

tG) increases as well

17 In the rank-based truncation model the frequency of the exemplar providesa measure of stereotype accuracy By accuracy we mean the extent to which thestereotype minimizes the distance

Pt eth

sttG tGTHORN

2 When d = 1 and only one type isrecalled (there are no ties) accuracy is maximized if the exemplar is the most likelytype and minimized if the exemplar is the least likely type

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Case i says that when groups have similar distributions inthe sense of having the same likelihood ranking the most repre-sentative type is unlikely for at least one group potentially bothRepresentativeness draws the DMrsquos attention to group differ-ences neglecting the fact that the groups are similar and havethe same mode This mechanism generates inaccurate stereo-types and is illustrated by the Florida example This resultholds under any measure of representativeness that differenti-ates the two groups (eg the difference tG tG)

Case ii says that the most representative type tends to belikely for both groups when the distributions are very differentIn this case groups differ the most around their modes so repre-sentativeness and likelihood coincide Thinking of Swedes aslsquolsquoblondrsquorsquo and Europeans as lsquolsquodark hairedrsquorsquo is accurate precisely be-cause these are majority traits of the Swedish and European pop-ulations respectively In these cases stereotyping yields fairlyreliable models Of course there is still some inaccuracy Evenin the case of likely exemplars judgment errors can be signifi-cant For instance voters in some US states are perceived aslsquolsquobluersquorsquo or lsquolsquoredrsquorsquo because a majority of the population votesDemocrat or Republican In reality even in lsquolsquobluersquorsquo states farfrom everyone votes Democrat In the 2012 presidential electionvote shares of either candidate in most states ranged from 40 to6018

When DMs strongly overweight representative types themost severe biases occur when those types are unlikely and ex-treme This is true both under rank based truncations and undersmooth discounting functions (see Section IIIB) Ethnic stereo-types based on crime or terrorism exhibit this error they neglectthe fact that by far the most common types in all groups arehonest and peaceful

IIIB Stereotypical Moments

We now characterize how the first two moments of a distri-bution are distorted by the process of stereotyping To do so wemust restrict our analysis to cardinal ordered types The follow-ing results hold for any weighting function htethTHORN satisfyingDefinition 2 We consider two canonical cases that prove usefulin illustrating the predictions of the model

18 Presidential Election Results NBCNewscom see httpelectionsnbcnewscomnspolitics2012allpresident (accessed 5 September 2016)

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In the first case groups G and ndashG are such that the likelihoodratio tG

tGis monotonic in t The monotone likelihood ratio prop-

erty (MLRP) holds to a first approximation in many empiricalsettings and is also assumed in many economic models such asstandard agency models19 If tG

tGis monotonically increasing (de-

creasing) in t then group G is associated with higher (lower)values of t relative to the comparison group ndashG Formally

PROPOSITION 2 Suppose that MLRP holds and assume wlogthat the likelihood ratio tG

tGis strictly increasing in t Then

for any weighting function htethTHORN that is not constant in therelevant range

EstethtjGTHORN gt EethtjGTHORN gt EethtjGTHORN gt E

stethtjGTHORN

Under MLRP the most representative part of the distribu-tion for G is the right tail if tG

tGincreases in t or the left tail if tG

tG

decreases in t The representative tail is then overweighted whilethe nonrepresentative tail is underweighted As a consequencethe assessed mean E

stethtjGTHORN is too extreme in the direction of therepresentative tail

Critically in line with the social cognition perspective the ste-reotype contains a kernel of truth the DM overestimates the meanof G if this group has a higher mean than the comparison groupnamely EethtjGTHORN gt EethtjGTHORN and conversely if EethtjGTHORN lt EethtjGTHORN TheDM exaggerates this true difference because he inflates the asso-ciation of G with its most representative types20 For instancewhen judging an asset manager who performs well we tend to

19 Examples include the binomial and the Poisson families of distributionswith different parameters The characterization of distributions satisfying MLRPis easier in the case of continuous distributions (see Online Appendix D) two dis-tributions f(x) f ethx THORN that differ only in their mean satisfy MLRP if and only if thedistribution f(x) is log-concave Examples include the exponential and normal dis-tributions To the extent that discrete distributions sufficiently approximate thesedistributions (as the Poisson distribution PoisethTHORN approximates the normal distri-bution Neth THORN for large l) they will also satisfy MLRP

20 Depending on the distribution and the weighing function the DMrsquos assess-ment of the variance VarethtjGTHORNmay also be dampened relative to the truth This isoften true under the truncation weighing function In this case stereotyping effec-tively leads to a form of overconfidence in which the DM holds extreme views andoverestimates the precision of his assessment That extreme views and overconfi-dence (in the sense of over precision) go together has been documented in the settingof political ideology among others (Ortoleva and Snowberg 2015)

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overemphasize skill relative to luck because higher skill levels arerelatively more associated with higher performance This occurseven if for both skilled and unskilled managers high performanceis mostly due to luck

In the second case for which we characterize the stereotypi-cal distributions groups G and ndashG have the same mean EethtjGTHORNfrac14 EethtjGTHORN frac14 EethtTHORN but differ in their variance We abstract fromskewness and higher moments by considering distributionsethtGTHORNt2T and ethtGTHORNt2T that share the same support and are sym-metric around the medianmean EethtTHORN

PROPOSITION 3 Suppose that in G more extreme types are rela-tively more frequent than in ndashG Formally the likelihoodratio tG

tGis U-shaped in t around EethtTHORN Then for any weight-

ing function htethTHORN that is not constant in the relevant rangestereotypical beliefs satisfy

VarstethtjGTHORN gt VarethtjGTHORN gt VarethtjGTHORN gt VarstethtjGTHORN

EstethtjGTHORN frac14 E

stethtjGTHORN frac14 EethtTHORN

When group G has a higher relative prevalence of extremetypes its representative types are located at both extremes of thedistribution The DMrsquos beliefs about G are then formed by over-weighting both tails while underweighting the unrepresentativemiddle The overweighting of Grsquos tails causes the assessment ofits variance VarstethtjGTHORN to be too high For example the skill dis-tribution of immigrants to the United States may be perceived ashaving very fat tails or even bimodal with immigrants beingperceived as either unskilled or very skilled relative to the resi-dent population The mean of the group in contrast is assessedcorrectly because the stereotypical distribution remains symmet-ric around EethtTHORN As before the stereotype contains a kernel oftruth It induces the agent to exaggerate the true differences be-tween groups namely the higher variance of G relative to itscounterpart

We present a number of extensions of the model in the OnlineAppendix We first consider multidimensional type spaces andshow that stereotypes center around the dimension wheregroups differ the most in line with the kernel of truth logic(Online Appendix C) Multidimensional stereotypes imply thatthe dimension we think about is influenced by context For

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example the Irish are stereotyped as red-haired when comparedwith the European population However when compared withthe Scots a more plausible stereotype for the Irish is lsquolsquoCatholicrsquorsquobecause religion is the dimension along which Irish and Scotsdiffer the most

In Online Appendix D we extend the model to continuoustype spaces Many settings of interest in economics can be use-fully described by continuous probability distributions and weshow our model is particularly tractable in this case In OnlineAppendix E we relax Definition 2 and allow weighting of types toalso be influenced by their likelihood We show that the basicinsight that stereotypes contain a kernel of truth carries throughto these cases as well

To summarize the psychology of representativeness yieldsstereotypes that are consistent with the social cognition approachin which individuals assess groups by recalling and focusing ondistinctive group traits When there are systematic differencesbetween groups stereotypes get the direction right but exagger-ate differences

IIIC Some Examples

A growing body of field and experimental evidence points to awidespread belief that women are worse than men at mathemat-ics (Eccles Jacobs and Harold 1990 Guiso et al 2008 CarrellPage and West 2010) This belief persists despite the fact that fordecades women have been gaining ground in average schoolgrades including mathematics and have recently surpassedmen in overall school performance (Goldin Katz and Kuziemko2006 Hyde et al 2008) This belief shared by men and women(Reuben Sapienza and Zingales 2014) may help account for thegender gap in the choices of high school tracks college degreesand careers with women disproportionately choosing humanitiesand health-related areas (Weinberger 2005 Buser Niederle andOosterbeek 2014) and forgoing significant wage premiums toquantitative skills (Bertrand 2011)

Gender stereotypes in mathematics particularly beliefs thatexaggerate the extent of average differences are consistent withthe predictions of our model The fact that men are overrepre-sented at the very highest performance levels leads a stereotyp-ical thinker to exaggerate the magnitude of mean differencesFigure I shows the score distributions from the mathematics

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section of 2013rsquos Scholastic Aptitude Test (SAT) for men andwomen21 The distributions are very similar with averagescores slightly higher for men (531 versus 499 out of 800)However scores for men have a heavier right tail with mentwice as likely to have a perfect SAT math score than women22

In light of such data the stereotypical male performance in math-ematics is high while the stereotypical female performance ispoor Predictions based on such stereotypes are inaccurate exag-gerating true differences Consistent with this prediction exper-imental evidence shows that both genders underestimatewomenrsquos ability in simple math tasks even controlling for pastperformance (Reuben Sapienza and Zingales 2014) Coffman(2014) shows a similar pattern extends to confidence about ownability in other male-typed domains with women reporting sig-nificantly less confidence in gender-incongruent than gender-congruent tasks Our model suggests that these patterns mightcome from stereotypes based on gender differences in the righttail of the distribution While differences in the right tail of thedistribution are unlikely to be relevant for most decisions stereo-typical thinking driven by these differences has the potential toimpact economically important decisions whether through self-stereotyping (ie choice of careers or majors as in BuserNiederle and Oosterbeek 2014) or through discrimination (iehiring decisions as in Bohnet van Geen and Bazerman 2016)

The logic of exaggerated yet directionally correct stereotypesalso sheds light on the well-documented phenomenon of base rateneglect (Kahneman and Tversky 1973) Indeed Proposition 2implies that the DM overreacts to information that assigns

21 Standardized test performance measures not only innate ability but alsoeffort and investment by third parties (Hyde et al 2008) The mapping of test per-formance into inferences about innate ability is an issue not addressed by ourmodel

22 For 2013 SAT Mathematics scores see httpmediacollegeboardcomdigitalServicespdfresearchSAT-Percentile-Ranks-By-Gender-Ethnicity-2013pdf Results are similar for the National Assessment of Educational Progress(NAEP) which are more representative of the overall population For 2012NAEP scores for 17-year-olds in mathematics see httpnationsreportcardgovltt_2012age17maspx See Hyde et al (2008) Fryer and Levitt (2010) and Popeand Sydnor (2010) for in-depth empirical analyses of the gender gap inmathematics

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people to groups precisely because such information generatesextreme stereotypes Consider the classic example in which amedical test for a particular disease with a 5 prevalence has a90 rate of true positives and a 5 rate of false positives The testassigns each person to one of two groups + (positive test) or ndash(negative test) The DM estimates the frequency of the sick type(s) and the healthy type (h) in each group The test is informativea positive result increases the relative likelihood of sickness anda negative result increases the relative likelihood of health forany prior Formally

PreththornjsTHORN

PreththornjhTHORNgt 1 gt

PrethjsTHORN

PrethjhTHORNeth4THORN

This condition has clear implications the representative personwho tests positive is sick while the representative person whotests negative is healthy Following Proposition 2 the DMreacts to the test by moving his priors too far in the right di-rection generating extreme stereotypes He greatly boosts hisassessment that a positively tested person is sick but also thata negatively tested person is healthy Because most people arehealthy the DMrsquos assessment about the group that tested neg-ative is fairly accurate but is severely biased for the group that

FIGURE I

SAT Mathematics Scores by Gender (2013)

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tested positive This analysis formalizes Tversky andKahnemanrsquos (1983) verbal account of base rate neglect23

The same mechanism may underlie several other instanceswhere DMs overweight diagnostic information When assessingan employeersquos skill level an employer attributes high perfor-mance to high skill because high performance is the distinctivemark of a talented employee Because he neglects the possibilitythat some talented employees perform poorly and that somenontalented ones perform well (perhaps due to stochasticity inthe environment) the employer has too much faith in skill andneglects the role of luck in accounting for the output Similarlywhen assessing the performance of firms in a hot sector of theeconomy (eg G = internet) an investor recalls highly successfulfirms in that sector (t = return of Google Amazon etc) He ne-glects the possibility of firms being unsuccessful because lack ofsuccess is statistically nondiagnostic and psychologically nonrep-resentative of a growing sectormdasheven if it is likely This causesexcessive optimism (in that the expectation of growth is unrea-sonably high) and overconfidence (in that the variability in earn-ings growth considered possible is truncated) True the hot sectormay have better growth opportunities on average but represen-tativeness exaggerates this feature and induces the investor toneglect a significant risk of failure

IV Evidence on Representativeness and Stereotypes

Testing our model requires evaluating the beliefs individualshold about a target group against the true distribution of thattarget group over an attribute space An ideal data set would

23 Our account is distinct from a mechanical underweighting of base rates inBayes rule as in Grether (1980) and Bodoh-Creed Benjamin and Rabin (2013) Inthose models upon receiving the test results the DM can update his beliefs in thewrong direction he can be less confident that a person is healthy after a negativetest than under his prior which cannot happen in our model Although this predic-tion of our model seems consistent with introspection we are not aware of experi-mental evidence on this point Griffin and Tversky (1992) present evidenceconsistent with pure neglect of base rates but in a significantly different tasknamely inferring the bias of a coin from a history of coin flips Such experimentsare hard to compare with the predictions of our model because subjects are asked togenerate distributions of different numbers of coin flips in their minds which is amuch more involved task than to recall types of a given distribution Their assess-ments then might be wrong for other reasons See Bodoh-Creed Benjamin andRabin (2013) for a detailed discussion

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consist of naturally defined groups with known distributions overa given space of types and a corresponding set of beliefs about thedistribution of each group over that space of types This wouldallow us to test for exaggeration of true differences betweengroups and to ask whether this exaggeration is well predictedby overweighting representative types To identify a causal rolefor representativeness or context dependence we would need ex-ogenous variation in either the comparison group ndashG or in thedistributions over the type spaces This is unavailable in existingdata sets Accordingly we take a two-pronged approach First wecreate a controlled laboratory environment that allows us toinduce the exogenous variation in representative types that weneed to test causality then we reanalyze existing field evidence tocheck for consistency with our predictions

In testing our model we focus on the two main implicationsof representativeness-based stereotypes

Context dependence the stereotype of a target group de-pends on the characteristics of the reference group it iscompared to

Kernel of truth stereotypes depend on group character-istics andmdashin most (precisely characterized) settingsmdashare slanted toward representative types

We test the first property with a lab experiment (SectionIVA) We then turn to survey data on beliefs about US politicalgroups (Section IVB) for an empirical analysis that explores thesecond property The survey data are more tightly linked to ourinterest in social stereotypes The laboratory experiment allowsus to directly test the role of representativeness in generatingcontext dependent beliefs Online Appendixes F and G provideall details and additional results for the experiments and fieldevidence

IVA Lab Evidence on Representativeness and ContextDependence

The influence of the representativeness heuristic on recalland on beliefs has been extensively documented in the lab(Kahneman and Tversky 1972 1973) Our goal is to considerhow representativeness as formalized in equation (2) gives riseto context-dependent beliefs To our knowledge the possibility

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that representativeness may generate context dependence hasnot been tested before

To assess this prediction we perform a controlled laboratoryexperiment that allows us to isolate representativeness frommany confounding factorsmdashhistorical sociological or other-wisemdashthat may affect stereotype formation in the real worldWe construct our own groups of ordinary objects creating atarget group G and a comparison group ndashG We hold thetarget group G fixed and explore how participant impressions ofit change as we change the comparison group ndashG and thusrepresentativeness

We conducted several experiments in the laboratory and onAmazon Mechanical Turk Each involves a basic three-stepdesign First participants are shown the target group and a ran-domly assigned comparison group for 15 seconds In this timedifferences between groups can be noticed but the groupsrsquo precisecompositions cannot be memorized The second step consists of afew filler questions which briefly draw the participantsrsquo cognitivebandwidth away from their observation Finally participants areasked to assess the groups they saw Participants are incentiv-ized to provide accurate answers

We randomly assign participants to either the Control or theRepresentativeness condition In the Control condition G and ndashGhave nearly identical distributions so that all types are similarlyrepresentative for each group In the Representativeness condi-tion ndashG is changed in such a way that a certain type becomes veryrepresentative for G Context dependence implies that the assess-ment of G should now overweight this representative type eventhough the distribution of G itself has not changed

We ran six experiments of this form with design changesfocused on reducing participant confusion and removing con-founds We describe the final and most refined version of theseexperiments here In an attempt to provide a overview of the re-sults while remaining concise we provide the results from pooledspecifications that use all data collected In Online Appendix Fwe offer additional details and report all experiments conductedWe also give instructions and materials for each experiment thefull data set is available by request

Consider first the experiment illustrated in Figure II Agroup of 25 cartoon girls is presented next to a group of 25 cartoonboys in T-shirts of different colors blue green or purple In theControl condition (Figure II Panel a) the groups have identical

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color distributions (13 purple 12 green) so no color is represen-tative of either group The Representativeness condition (Panel b)compares the same group of girls with a different group of boysfor whom green shirts are replaced with blue shirts Now onlygirls wear green and only boys wear blue These colors althoughstill not the most frequent for either group are now most repre-sentative For each group girls and boys participants are asked anumber of questions concerning the frequency of T-shirts of dif-ferent colors worn by that group

Applying our model in the control condition the type space isT frac14 fgreen purpleg and the groups are G = girls and ndashG = boysGiven that the color distributions are identical across groups both

types are equally representativegreengirls

greenboysfrac14 1 frac14

purplegirls

purpleboys As a result

assessment of G should be correct on average stcontrolgreengirls frac14 greengirls

and stcontrolpurplegirls frac14 purplegirls for any weighing function (the same is

true about assessments of ndashG)In the treatment condition the distribution of shirt colors re-

mains the same for girls For boys green shirts are changed intoblue Thus the type space changes to T frac14 fgreen purple bluegand the representative color for girls becomes greengreengirls

greenboysfrac14 1 gt 1 frac14

purplegirls

purpleboys while that for boys becomes blue As

a result in the treatment condition subjects should inflate the

frequency of green shirts relative to the truth sttreatmentgreengirls

gt greengirls (the same should happen to assessments of blueshirts for boys) We also expect the assessed frequency of greenshirts to go up relative to the control condition namely

sttreatmentgreengirls gt stcontrol

greengirls Critically the only factor that varies

across treatments is the representativeness of the 12-colorshirt Thus if we see differences across conditions the causalrole of representativeness-based recall in shaping group judg-ments is clear24

24 We vary which colors are used in which roles across participants Someparticipants saw this particular color distribution while others see for examplegreen as the modal color and purple as the diagnostic color for boys in theRepresentativeness condition and blue as the diagnostic color for girls in theRepresentativeness condition We vary the colors across the roles to avoid con-founding the characteristics of any particular color with its diagnosticity

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FIG

UR

EII

T-S

hir

tsE

xp

erim

ent

Fig

ure

sap

pea

red

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lor

top

art

icip

an

tsin

the

exp

erim

ent

For

clari

ty

we

have

ad

ded

ale

tter

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chT

-sh

irt

toid

enti

fyth

eco

lor

for

the

read

er

lsquolsquoGrsquorsquo

ind

icate

sgre

en

lsquolsquoPrsquorsquo

ind

icate

sp

urp

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ind

icate

sblu

eT

hes

ele

tter

sd

idn

otap

pea

rto

part

icip

an

tsan

dare

for

read

erre

fere

nce

only

P

lease

see

onli

ne

ver

sion

ofp

ubli

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art

icle

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colo

rfi

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reex

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pea

red

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We collected data from 301 participants using this T-shirtsdesign25 Since the number of green and purple shirts is verysimilar we first ask each participant the simplest question ofwhich shirt color is modal Next we ask participants to assessthe share of green and purple shirts

Consistent with the role of representativeness participantsassigned to the Representativeness condition are 105 percentagepoints more likely to recall the less frequent color (green for girlsor blue for boys) as the modal color when it is representative of agroup (35 of participants guess the less frequent color is modalin the Control condition this proportion increases to 46 in theRepresentativeness condition p = 01 estimated from a probitregression reported in Online Appendix F)

We now turn to subjectsrsquo estimates of how many T-shirts ofeach color they saw in each group In both conditions the truedifference in counts is 1 (13 purple shirts 12 green or blue shirts)In the Control condition participants on average believe they saw054 more purple shirts than green or blue shirts In theRepresentativeness condition participants believe they saw072 fewer purple shirts than green or blue shirts (the acrosstreatment difference is significant with p = 01 from OLS regres-sion reported in Online Appendix F)

In total we collected data for six experiments of this generalstructure gathering evidence from more than 1000 participantsAs we describe in Online Appendix F although there is substan-tial variation across experiments when we pool all of the data wefind significant aggregate treatment effects in line with a role ofrepresentativeness in judgment We employ four different unor-dered types designs similar to the T-shirts experiment using sixsamples (four online and two in the laboratory) with 741 partic-ipants We find effects in the predicted direction for five of the sixsamples Using a probit regression that pools the data for theseunordered type experiments we find that participants are 93 per-centage points more likely to guess that the less frequent type ismodal when it is representative than when it is not (p = 002) Wealso run a family of ordered types experiments (two designs fivesamples 402 participants) Unlike the simpler T-shirts style

25 Throughout our analysis we exclude any participant who participated in aprevious version of the experiment and any participant who self-identified as color-blind In Online Appendix F we show that our results are unchanged if we includethese additional observations

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design the theoretical predictions for the ordered types designsare more sensitive to the specific assumptions one makes aboutthe weighting function of the DM26 We find effects in the pre-dicted direction for three of the five samples As we discuss inmore detail in Online Appendix F the ordered types resultsvary by platform with consistently stronger results on AmazonMechanical Turk than in the laboratory samples Pooling all or-dered types experiments participants are 93 percentage pointsmore likely to guess that the group of interest has a greater av-erage than the comparison group when the right tail is represen-tative (p = 062) Given our simple experimental setting withgroups of mundane objects we interpret our resultsmdasha signifi-cant and reasonably sized impact on average beliefsmdashas an im-portant proof of concept the presence of representative typesbiases ex post assessment

IVB Empirical Evidence on Political Stereotypes

We examine two data sets on political preferences and be-liefs about political preferences in the United States We inves-tigate the roles of representativeness and context dependence byseparately testing for hypotheses that allow us to assess the lead-ing theories of stereotypes

First we test whether beliefs are correct or depart systemat-ically from the truth The statistical discrimination approachbuilds on the assumption that people hold rational expectationsof group traits Comparing beliefs to the truth allows us to assessthe validity of this assumption in our data

Second we test if beliefs depart from the truth by exagger-ating (mean) differences among groups per the kernel of truthhypothesis This is an implicit test of context dependence be-cause it implies that beliefs about the target groups are shapednot only by that grouprsquos characteristics but also by those of thereference group27

Third we test if distortions in beliefs can be accounted for bythe overweighting of highly representative types (defined astypes that are relatively more frequent in the target relative to

26 This is due in part to our choice to not study MLRP distributions We moti-vate and discuss this design decision in Online Appendix F

27 Of course unlike in the laboratory experiment in this setting we cannot testfor context dependence by exogenously varying the reference group

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the reference group) The second and third tests address the keypredictions of our model

1 The Data We have two data sets on political preferences andbeliefs about political preferences The first data set from GrahamNosek and Haidt (GNH 2012) contains data from the MoralFoundations Questionnaire Respondents (1174 self-identified lib-erals and 500 self-identified conservatives) answer questions abouttheir position on a subset of 45 issues 20 moral relevance state-ments (eg lsquolsquowhen you decide whether something is right orwrong to what extent are the following considerations relevantto your thinkingrsquorsquo) and 25 moral judgments (eg lsquolsquoindicate theextent to which you would agree or disagreersquorsquo) For each issue arandomly determined subset of participants states their own posi-tion another subset states their belief on the position of a lsquolsquotypicalliberalrsquorsquo and a third subset states their belief on the position of alsquolsquotypical conservativersquorsquo The data thus include the distribution overpositions for both liberal and conservatives as well as the averagebelieved typical position of liberals and of conservatives on the 45issues Each position is elicited on 1ndash6 scale

The second data set comes from the American NationalElection Survey (ANES) and contains data from more than20000 respondents between 1964 and 201228 The surveycovers political issues of the day such as the optimal amount ofgovernment spending and service provision (1984ndash2000) or theplace of women in society (1972ndash1998) We focus on the 10 issuesthat ask participants to respond on a 1ndash7 scale (rather than justindicate binary agreement or disagreement) all 10 issues areasked in multiple years Participants are asked to provide theirown position on the scale and their believed position of theDemocratic and Republican parties (lsquolsquoWhere would you placethe Democratic [Republican] party on this scalersquorsquo) The data in-clude for each issue-year observation the distribution of partic-ipant positions for self-identified liberals and self-identifiedconservatives as well as the distribution of believed typical posi-tions of the Democratic and Republican parties

28 These data are publicly available at httpwwwelectionstudiesorgstudy-pagesanes_timeseries_cdfanes_timeseries_cdfhtm

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2 Empirical Strategy Our analysis focuses on beliefs abouttwo groups Conservatives and Liberals The types are the possi-ble positions for each issue (1 2 6 7) For the GNH data weinterpret beliefs about the lsquolsquotypicalrsquorsquo element of a group to coincidewith the believed average position in that group Similarly forthe ANES data we use the believed party positions as a proxy forbelieved mean of each group29 We then take as a benchmark thehypothesis that individuals hold accurate beliefs about eachgroup and in particular that believed mean position shouldequal true mean position at least on average across subjectsThe accurate beliefs hypothesis underlies the most common eco-nomic model of stereotyping statistical discrimination

To assess our representativeness-based model we perform aregression exercise To test our model in a linear regressionframework we rely on linear approximations of the weightingfunction Our model then yields two regression specifications

PROPOSITION 4 Let G 2 fconservative liberal g and assume

ht h tG

tG

be a differentiable and strictly increasing weight-

ing function as in Definition 2 The following hold as a first-order approximation around identical distributions G

Gfrac14 1

(i) Kernel of truth regression There exists a constant gt 0such that

EstethtjGTHORN frac14 EethtjGTHORNeth1thorn THORN EethtjGTHORNeth5THORN

(ii) Representativeness regression Denote H frac14 fT 2 Tg

the right tail of types and RconsH frac14

PHtconsPHtlib

as the average

representativeness of right tail types for conservatives

29 This assumption is consistent with the authorsrsquo interpretation of the GNHdata (GNH 2012) and with previous studies using ANES (eg Westfall et al 2015)Furthermore to the extent that this assumption holds equally well for most issueswithin a data set our focus on cross-issue differences should allow us to test thepredictions of our model even with an imperfect proxy for beliefs of mean positionsFinally the data provide some insight into whether subjects are reporting (per-ceived) modal or mean types As we show the modal type is a poor prediction ofstated beliefs while a distorted mean slanted toward representative types is anaccurate prediction of stated beliefs

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Under the further approximation where tcons

tlibampRcons

H for

t 2 H

EstethtjconsTHORN frac14 EethtjconsTHORN thorn consethR

consH 1THORNeth6THORN

EstethtjlibTHORN frac14 EethtjlibTHORN libethR

consH 1THORNeth7THORN

where lcons and llib are positive constants

The first regression allows us to test for the kernel of truthhypothesis and the second set of regressions allows us to test forthe role of representativeness

Equation (5) says that respondents in our model inflate theaverage position of a group say the conservatives if and only ifthe group has a higher average position than the other groupnamely the liberals Formally EstethtjconsTHORN gt EethtjconsTHORN if and onlyif EethtjconsTHORN gt EethtjlibTHORN Because in our measurement scale highertypes mean lsquolsquomore conservativersquorsquo we expect (i) believed conserva-tive average to be higher than the truth and (ii) the extent ofoverstatement to decrease in the average liberal position EethtjlibTHORNConversely we expect the average liberal position to be lowerthan the truth the more so the higher the average conservativeposition EethtjconsTHORN

As previously discussed the basis of these predictions is con-text dependence information about the distribution of ndashG is rel-evant for the beliefs about G This context dependence isinconsistent with rational expectations in which only thegrouprsquos own means should affect beliefs We test the hypothesisthat the true mean EethtjGTHORN is a significant predictor of the believedmean E

stethtjGTHORN with a positive sign and the other grouprsquos truemean EethtjGTHORN is a predictor of the believed mean with a negativesign

Equations (6) and (7) say that repondentsrsquo assessment bias isshaped by representativeness When the right tail is more repre-sentative for conservatives (Rcons

H 1 positive and large) partici-pants should inflate the average conservative position more(higher E

stethtjconsTHORN EethtjconsTHORN) and deflate the average liberal po-sition more (lower E

stethtjlibTHORN EethtjlibTHORN) We test the hypothesisthat the inflation in conservative positions is positively associatedwith the representativeness of the right tail for the conservativesand the inflation in liberal positions is negatively associated with

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it Once again the representativeness of the right tail is com-puted using the true distribution of positions

In equations (6) and (7) in many cases the representative tailis also the most likely one As a consequence these tests cannotdistinguish a representativeness-based from a likelihood-basedmodel of distorted beliefs We perform two additional testsFirst we run versions of equations (6) and (7) in which we controlfor the likelihood of tails (see Table A4 in Online Appendix G)Second we compute numerically the predictions of a representa-tiveness-based model of stereotypes and a likelihood-based modelof stereotypes We then assess which of these two is better able tomatch the data on beliefs

3 Empirical Results To begin we illustrate the structure ofthe data and the nature of our predictions with two simple exam-ples from the GNH data set focusing on beliefs about conserva-tives In example 1 participants are asked about their agreementwith the statement lsquolsquoIt can never be right to kill a human beingrsquorsquoIn example 2 participants are asked about the moral relevance oflsquolsquowhether or not someone cared for someone weak or vulnerablersquorsquoAs can be seen in Figure III in example 1 the modal position(strongly disagree (1)) and most representative positions(strongly disagree (1)) coincide for conservatives In contrast inexample 2 in Figure III the most representative types (slightlyrelevant (3) not at all relevant (1)) are not most likely for theconservative group Following Proposition 1 we predict that be-liefs will be distorted in the direction of the most representativetypes Thus we expect more exaggeration in example 2 than inexample 1 since in example 2 the most representative types (inthe left tail) are far from the modal type whereas in example 1they coincide This is what we find the conservative position isexaggerated by only 009 positions in Example 1 (true mean 299believed mean 290) but by 106 positions in Example 2 (truemean 421 believed mean 315)

In the full data sets we treat each (issue year) pair as anobservation and we cluster standard errors at the issue level Forthe GNH data we have 45 observations 45 issues measured inthe same year For the ANES data we have 66 observations 10issues measured in multiple years To begin we simply docu-ment systematic exaggeration in both data sets This is a primaryfocus of the original analysis in GNH (2012) and also in Westfall

STEREOTYPES 1785

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FIGURE III

Two Examples

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et al (2015)rsquos analysis of the ANES data30 Figure IV shows thatthe believed difference between typical conservative and typicalliberal positions is larger than the true difference in mean posi-tions for 109 of the 111 observations The data for both GNH(squares) and ANES (triangles) lie above the 45-degree line(dashed)31 Average exaggeration is 062 positions on the scale(066 in the GNH data 059 in the ANES data)32

The systematic and significant exaggeration of mean differ-ences suggests that the benchmark model of accurate beliefs ismissing something important Indeed this exaggeration reflectsthe fact that believed means are typically more extreme than truemeans First note that the kernel of truth regression (equation(5)) generates exaggeration of mean differences just as docu-mented in Figure IV

EstethtjGTHORN E

stethtjGTHORN frac14 eth1thorn 2THORN frac12EethtjGTHORN EethtjGTHORN

To bring this prediction to the data we regress the believedmean position for each group EBethtjGTHORN on the true mean of thegroup EethtjGTHORN and the true mean of the comparison groupEethtjGTHORN across issues We do this for each group (liberals con-servatives) in each data set separately We also present pooledspecifications that combine the data sets to make a prediction fora given group (liberals conservatives) In these pooled specifica-tions we include a dummy variable indicating whether theobservation came from the ANES data set For all specificationswe cluster observations at the issue level33 The results from re-gression are shown in Table I In every specification we find thatEethtjGTHORN is a significant predictor of EBethtjGTHORN with the predicted pos-itive sign Crucially for five of the six specifications the mean of

30 Chambers and Melnyk (2006) also find evidence of exaggeration of truedifferences in beliefs about political positions

31 For convenience we recode all issues so that the high end of the scale (67)represents the stereotypically more conservative position

32 A natural question to ask is how beliefs vary across liberals and conserva-tives That is do beliefs about a group G depend on membership in G versus ndashG Ourmodel does not speak to this issue However in Online Appendix G we show thatthe results we document below hold for both beliefs held by conservatives and be-liefs held by liberals see Tables A9 A10 and A11

33 In general the results presented below for the ANES data are not largelyimpacted by the decision to cluster at the issue level Similar results are obtained ifthe data are not clustered

STEREOTYPES 1787

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the comparison group EethtjGTHORN is also a significant predictor ofE

BethtjGTHORN with the predicted negative signAlthough these results provide strong evidence of context

dependence and are consistent with our model they do not pindown a role for representativeness of types Our next test relatesthe magnitude of representativeness of tail types to the magni-tude of belief distortions

To this end we implement the regressions in equations (6)and (7) Following Proposition 4 we compute the average repre-

sentativeness of tail types for conservatives RconsH frac14

PtT2tconsPtT2tlib

We

again test the hypothesis that RconsH is a significant predictor of Est

ethtjconsTHORN with a positive sign and a predictor of EstethtjlibTHORN with a

negative sign Table II shows that conditional on true mean RconsH

predicts believed mean for each group G as expected The firstthree specifications display the results for predicting beliefs heldabout conservatives In both data sets the average representa-tiveness of tail types for conservatives is a significant positivepredictor of beliefs held about conservatives The final three spe-cifications display the results for predicting beliefs held about

FIGURE IV

Exaggeration of Differences

QUARTERLY JOURNAL OF ECONOMICS1788

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liberals We find that the average representativeness of tail typesfor conservatives is a negative predictor of beliefs held about lib-erals This effect is significant in the GNH data and marginallysignificant in the ANES data

We present several additional results in Online Appendix GTo further examine the role of representativeness in driving be-liefs we first show the results of Table II carry through when we

TABLE II

AVERAGE REPRESENTATIVENESS OF TAIL POSITIONS PREDICTS BELIEFS

OLS Predicting Believed Mean of Group G for Each Issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position

of group G for issue

078 024 051 072 018 041

(006) (008) (009) (005) (005) (010)

Avg rep of tail types for

conservatives RconsH

019 055 025 014 012 024

(007) (022) (008) (006) (007) (005)

Constant 101 260 184 093 271 201

(026) (045) (029) (022) (025) (032)

R2 082 048 060 091 031 070

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

TABLE I

INFORMATION ABOUT ndashG PREDICTS BELIEFS ABOUT G

OLS predicting believed mean of group G for each issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position of

conservatives for issue

102 098 096 021 019 025

(0097) (0133) (0076) (0060) (0116) (0060)

True mean position of

liberals for issue

035 086 058 0987 039 073

(0106) (0134) (0131) (0066) (0106) (0135)

Constant 151 335 235 069 258 156

(0195) (0269) (0279) (0122) (0249) (0270)

R2 083 053 066 092 032 068

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

STEREOTYPES 1789

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control for the average likelihood on the tail positions (see Table A4in Online Appendix G) Most tellingly we use the model to predictbeliefs across issues and compare those to the data For simplicitywe use the rank-based truncation specification to predict mean be-liefs when stereotypes include the d most representative types ford frac14 1 T We compare these predictions to those of a model inwhich beliefs are obtained by restricting the distribution to the dmost likely types Our benchmark for both models is predicting thebelieved mean from the entire distribution where d = T We showthat the predictions of the rank-based truncation model with d = 4or 5 compare favorably to both a likelihood-based truncation model(with any d) and the accurate beliefs benchmark Interestingly thisresult suggests that stereotypical beliefs are well approximated byneglecting the least representative types (as opposed to focusingonly on the most representative types) and so represent a moderatethough systematic departure from the standard benchmarkFinally we show that the results we document above hold forboth beliefs held by conservatives and beliefs held by liberals (seeTables A9 A10 and A11 in Online Appendix G)

V Conclusion

We present a model of stereotypical thinking in which DMsmaking predictions about a group overweight the grouprsquos mostdistinctive types These overweighted types are not the mostlikely ones given the DMrsquos data but the most representativeones in the sense of being the most diagnostic of the group rela-tive to other groups Representativeness implies that what ismost distinctive of a group depends on what group it is comparedwith We present experimental evidence that confirms this con-text dependence in recall-based assessments of groups Finallywe evaluated the predictions of the model using political data fromexisting large-scale surveys We find context dependence to be akey feature of beliefs Given the richness of the political data wecan go a step further and identify a role for representativeness inparticular As the representativeness of tail types increases beliefsof a group are distorted in the direction of that tail

Our approach provides a parsimonious and psychologicallyfounded account of how DMs generate simplified representationsof reality from social groups to stock returns and offers a unifiedaccount of disparate pieces of evidence relating to this type of

QUARTERLY JOURNAL OF ECONOMICS1790

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uncertainty The model captures the central fact that stereotypeshighlight the greatest difference between groups thus explainingwhy some stereotypes are very accurate while others lack valid-ity Still stereotypes often have a kernel of truth when they arebased on systematicmdasheven if smallmdashdifferences between groupsThis logic allows us to describe a number of heuristics and psy-chological biases many of which arise in the context of predictionproblems Generically our model generates overreaction to diag-nostic information

Our model is based on representativeness and does not cap-ture all the features of stereotypical thinking However it cap-tures perhaps the central feature when we think of a group wefocus on what is most distinctive about it and neglect or under-weight the rest

Saeuroıd Business School University of Oxford

Ohio State University and Harvard Business School

Universita Bocconi and Innocenzo Gasparini Institute

for Economic Research

Harvard University

Supplementary Material

An Online Appendix for this article can be found at QJEonline (qjeoxfordjournalorg)

References

Adorno Theodor Else Frenkel-Brunswik Daniel Levinson and Nevitt SanfordThe Authoritarian Personality (New York Harper amp Row 1950)

Arrow Kenneth lsquolsquoThe Theory of Discriminationrsquorsquo in Discrimination in LaborMarkets Orley Ashenfelter and Albert Rees eds (Princeton NJPrinceton University Press 1973)

Ashton Michael and Victoria Esses lsquolsquoStereotype Accuracy Estimating theAcademic Performance of Ethnic Groupsrsquorsquo Personality and SocialPsychology Bulletin 25 (1999) 225ndash236

Barberis Nicholas Andrei Shleifer and Robert Vishny lsquolsquoA Model of InvestorSentimentrsquorsquo Journal of Financial Economics 49 (1998) 307ndash343

Bayer Sylvia lsquolsquoThe Accuracy of Academic Gender Stereotypesrsquorsquo Sex Roles 40(1999) 787ndash813

Benjamin Dan James Choi and Joshua Strickland lsquolsquoSocial Identity andPreferencesrsquorsquo American Economic Review 100 (2010) 1913ndash1928

Benjamin Dan Matthew Rabin and Collin Raymond lsquolsquoA Model of Non-Belief inthe Law of Large Numbersrsquorsquo Journal of the European Economic Association15 (2015) 515ndash544

Bertrand Marianne lsquolsquoNew Perspectives on Genderrsquorsquo Handbook of LaborEconomics 4 (2011) 1543ndash1590

Bodoh-Creed Aaron Dan Benjamin and Matthew Rabin lsquolsquoThe Dynamics of Base-Rate Neglectrsquorsquo mimeo Haas Business School 2013

STEREOTYPES 1791

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

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Bohnet Iris Alexandra van Geen and Max Bazerman lsquolsquoWhen PerformanceTrumps Gender Bias Joint versus Separate Evaluationrsquorsquo ManagementScience 5 (2016) 1225ndash1234

Bordalo Pedro Nicola Gennaioli and Andrei Shleifer lsquolsquoSalience Theory of Choiceunder Riskrsquorsquo Quarterly Journal of Economics 127 (2012) 1243ndash1285

mdashmdashmdash lsquolsquoSalience and Consumer Choicersquorsquo Journal of Political Economy 121(2013) 803ndash843

Briton Nancy and Judith Hall lsquolsquoBeliefs about Female and Male NonverbalCommunicationrsquorsquo Sex Roles 32 (1995) 79ndash90

Buser Thomas Muriel Niederle and Hessel Oosterbeek lsquolsquoGenderCompetitiveness and Career Choicesrsquorsquo Quarterly Journal of Economics 129(2014) 1409ndash1447

Carrell Scott Marianne Page and James West lsquolsquoSex and Science How ProfessorGender Perpetuates the Gender Gaprsquorsquo Quarterly Journal of Economics 125(2010) 1101ndash1144

Chambers John and Darya Melnyk lsquolsquoWhy Do I Hate Thee ConflictMisperceptions and Intergroup Mistrustrsquorsquo Personality and SocialPsychology Bulletin 32 (2006) 1295ndash1311

Chan Wayne Robert R McCrae Filip De Fruyt Lee Jussim CorinnaE Lockenhoff Marleen De Bolle Paul T Costa Jr Angelina R SutinAnu Realo Juri Allik Katsuharu Nakazato Yoshiko ShimonakaMartina Hrebıckova Sylvie Graf Michelle Yik Marina Brunner-SciarraNora Leibovich De Figueora Vanina Schmidt Chang-kyo Ahn Hyun-nie Ahn Maria E Aguilar-Vafaie Jerzy Siuta Barbara SzmigielskaThomas R Cain Janet T Crawford Khairul Anwar Mastor Jean-Pierre Rolland Florence Nansubuga Daniel R MiramontezVeronica Benet-Martınez Jerome Rossier Denis Bratko Iris MarusicJamin Halberstadt Mami Yamaguchi Goran Knezevic Thomas A MartinMirona Gheorghiu Peter B Smith Claudio Barbaranelli Lei WangJane Shakespeare-Finch Margarida P Lima Waldemar KlinkoszAndrzej Sekowski Lidia Alcalay Franco Simonetti Tatyana V AvdeyevaV S Pramila and Antonio Terracciano lsquolsquoStereotypes of Age Differences inPersonality Traits Universal and Accuratersquorsquo Journal of Personality andSocial Psychology 103 (2012) 1050ndash1066

Chen Yan Sherry Xin Liu Tracy Xiao and Margaret Shih lsquolsquoWhich Hat to WearImpact of Natural Identities on Coordination and Cooperationrsquorsquo Games andEconomic Behavior 84 (2014) 58ndash86

Coffman Katherine lsquolsquoEvidence on Self-Stereotyping and the Contribution ofIdeasrsquorsquo Quarterly Journal of Economics 129 (2014) 1625ndash1660

Cunningham Tom lsquolsquoComparisons and Choicersquorsquo mimeo Stockholm University2013

Diekman Amanda Alice Eagly and Patrick Kulesa lsquolsquoAccuracy and Bias in theStereotypes about the Social and Political Attitudes of Women and MenrsquorsquoJournal of Experimental Social Psychology 38 (2002) 268ndash282

Eccles Jacquelynne S Janis E Jacobs and Rena D Harold lsquolsquoGender RoleStereotypes Expectancy Effects and Parentsrsquo Socialization of GenderDifferencesrsquorsquo Journal of Social Issues 46 (1990) 183ndash201

Fryer Roland and Matthew Jackson lsquolsquoA Categorical Model of Cognition andBiased Decision-Makingrsquorsquo BE Journal of Theoretical Economics 8 (2008)1ndash42

Fryer Roland and Steven Levitt lsquolsquoAn Empirical Analysis of the Gender Gap inMathematicsrsquorsquo American Economic Journal Applied Economics 2 (2010)210ndash240

Gennaioli Nicola and Andrei Shleifer lsquolsquoWhat Comes to Mindrsquorsquo Quarterly Journalof Economics 125 (2010) 1399ndash1433

Gennaioli Nicola Andrei Shleifer and Robert Vishny lsquolsquoNeglected RisksFinancial Innovation and Financial Fragilityrsquorsquo Journal of FinancialEconomics 104 (2012) 452ndash468

Gilens Martin lsquolsquoRace and Poverty in America Public Misperceptions and theAmerican News Mediarsquorsquo Public Opinion Quarterly 60 (1996) 515ndash541

Glaeser Edward lsquolsquoThe Political Economy of Hatredrsquorsquo Quarterly Journal ofEconomics 120 (2005) 45ndash86

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Glover Dyland Amanda Pallais and William Pariente lsquolsquoDiscrimination as a Self-Fulfilling Prophecy Evidence from French Grocery Storesrsquorsquo mimeo HarvardUniversity 2015

Goldin Claudia Lawrence Katz and Ilyana Kuziemko lsquolsquoThe Homecoming ofAmerican College Women The Reversal of the College Gender GaprsquorsquoJournal of Economic Perspectives 20 (2006) 133ndash156

Graham Jesse Brian Nosek and Jonathan Haidt lsquolsquoThe Moral Stereotypes ofLiberals and Conservatives Exaggeration of Differences across thePolitical Spectrumrsquorsquo PLoS One 7 (2012) 1ndash13

Grether David lsquolsquoBayes Rule as a Descriptive Model The RepresentativenessHeuristicrsquorsquo Quarterly Journal of Economics 95 (1980) 537ndash557

Griffin Dale and Amos Tversky lsquolsquoThe Weighing of Evidence and theDeterminants of Confidencersquorsquo Cognitive Psychology 24 (1992) 411ndash435

Guiso Luigi Ferdinando Monte Paola Sapienza and Luigi Zingales lsquolsquoCultureGender and Mathrsquorsquo Science 320 (2008) 1164ndash1165

Hilton James and William Von Hippel lsquolsquoStereotypesrsquorsquo Annual Review ofPsychology 47 (1996) 237ndash271

Hyde Janet Sara Lindberg Marcia Linn Amy Ellis and Caroline WilliamslsquolsquoGender Similarities Characterize Math Performancersquorsquo Science 321 (2008)494ndash495

Judd Charles and Bernardette Park lsquolsquoDefinition and Assessment of Accuracy inSocial Stereotypesrsquorsquo Psychological Review 100 (1993) 109ndash128

Jussim Lee Jarret Crawford Stephanie Anglin John Chambers Sean Stevensand Florette Cohen lsquolsquoStereotype Accuracy One of the Largest and MostReplicable Effects in All of Social Psychologyrsquorsquo in The Handbook ofPrejudice Stereotyping and Discrimination Todd Nelson ed (MahwahNJ Lawrence Erlbaum 2015)

Kahneman Daniel and Amos Tversky lsquolsquoSubjective Probability A Judgment ofRepresentativenessrsquorsquo Cognitive Psychology 3 (1972) 430ndash454

mdashmdashmdash lsquolsquoOn the Psychology of Predictionrsquorsquo Psychological Review 80 (1973) 237ndash251

Kaplowitz Stan Bradley Fisher and Clifford Broman lsquolsquoHow Accurate ArePerceptions of Social Statistics about Blacks and Whitesrsquorsquo Public OpinionQuarterly 67 (2003) 237ndash243

Kersten Daniel Pascal Mamassian and Alan Yuille lsquolsquoObject Perception asBayesian Inferencersquorsquo Annual Review of Psychology 55 (2004) 271ndash304

Klein Richard Kate A Ratliff Michelangelo Vianello Reginald B Adams JrStepan Bahnik Michael J Bernstein Konrad Bocian Mark J BrandtBeach Brooks Claudia Chloe Brumbaugh Zeynep CemalcilarJesse Chandler Winnee Cheong William E Davis Thierry DevosMatthew Eisner Natalia Frankowska David Furrow Elisa Maria GallianiFred Hasselman Joshua A Hicks James F Hovermale S Jane HuntJeffrey R Huntsinger Hans IJzerman Melissa-Sue John Jennifer A Joy-Gaba Heather Barry Kappes Lacy E Krueger Jaime Kurtz CarmelA Levitan Robyn Mallett Wendy L Morris Anthony J Nelson JasonA Nier Grant Packard Ronaldo Pilati Abraham M RutchickKathleen Schmidt Jeanine L Skorinko Robert Smith Troy G SteinerJustin Storbeck Lyn M Van Swol Donna Thompson Anna van rsquot VeerLeigh Ann Vaughn Marek Vranka Aaron Wichman Julie A Woodzickaand Brian A Nosek lsquolsquoInvestigating Variation in Replicability A ManyLabs Replication Projectrsquorsquo Social Psychology 45 (2014) 142ndash152

Lundberg Shelly and Richard Startz lsquolsquoPrivate Discrimination and SocialIntervention in Competitive Labor Marketsrsquorsquo American Economic Review73 (1983) 340ndash347

Madon Stephanie Max Guyll Kathy Aboufadel Eulices Montiel Alison SmithPolly Palumbo and Lee Jussim lsquolsquoEthnic and National Stereotypes ThePrinceton Trilogy Revisited and Revisedrsquorsquo Personality and SocialPsychological Bulletin 27 (2001) 996ndash1010

Martin Carol lsquolsquoA Ratio Measure of Sex Stereotypingrsquorsquo Journal of Personality andSocial Psychology 52 (1987) 489ndash499

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ibrary on October 28 2016

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McCauley Clark Krishna Thangavelu and Paul Rozin lsquolsquoSex Stereotyping ofOccupations in Relation to Television Representations and Census FactsrsquorsquoBasic and Applied Social Psychology 9 (1988) 197ndash212

Mullainathan Sendhil lsquolsquoThinking through Categoriesrsquorsquo mimeo HarvardUniversity 2002

Ortoleva Pietro and Erik Snowberg lsquolsquoOverconfidence in Political BehaviorrsquorsquoAmerican Economic Review 105 (2015) 504ndash535

Phelps Edmund lsquolsquoThe Statistical Theory of Racism and Sexismrsquorsquo AmericanEconomic Review 62 (1972) 659ndash661

Pope Devin and Justin Sydnor lsquolsquoGeographic Variation in the Gender Differencesin Test Scoresrsquorsquo Journal of Economic Perspectives 24 (2010) 95ndash108

Rabin Matthew lsquolsquoInference by Believers in the Law of Small NumbersrsquorsquoQuarterly Journal of Economics 117 (2002) 775ndash816

Rabin Matthew and Joel Schrag lsquolsquoFirst Impressions Matter A Model ofConfirmatory Biasrsquorsquo Quarterly Journal of Economics 114 (1999) 37ndash82

Rabin Matthew and Dimitri Vayanos lsquolsquoThe Gamblerrsquos and Hot-Hand FallaciesTheory and Applicationsrsquorsquo Review of Economic Studies 77 (2010) 730ndash778

Reuben Ernesto Paola Sapienza and Luigi Zingales lsquolsquoHow Stereotypes ImpairWomenrsquos Careers in Sciencersquorsquo Proceedings of the National Academy ofSciences 111 (2014) 4403ndash4408

Rosch Eleanor lsquolsquoNatural Categoriesrsquorsquo Cognitive Psychology 4 (1973) 328ndash350Ryan Carey S lsquolsquoAccuracy of Black and White College Studentsrsquo In-Group and

Out-Group Stereotypesrsquorsquo Personality and Social Psychology Bulletin 22(1996) 1114ndash1127

Schneider David The Psychology of Stereotyping (New York Guilford Press2004)

Schneider David Albert Hastorf and Phoebe Ellsworth Person Perception(Reading MA Addison-Wesley 1979)

Shih Margaret Todd Pittinsky and Nalini Ambady lsquolsquoStereotype SusceptibilityIdentity Salience and Shifts in Quantitative Performancersquorsquo PsychologicalScience 10 (1999) 80ndash83

Shih Margaret Todd Pittinsky and Amy Trahan lsquolsquoDomain-Specific Effects ofStereotypes on Performancersquorsquo Self and Identity 5 (2006) 1ndash14

Steele Claude Whistling Vivaldi How Stereotypes Affect Us and What We CanDo (New York Norton 2010)

Tenenbaum Joshua and Thomas Griffiths lsquolsquoThe Rational Basis ofRepresentativenessrsquorsquo 23rd Annual Conference of the Cognitive ScienceSociety (2001) 1036ndash1041

Tversky Amos and Daniel Kahneman lsquolsquoExtensional versus Intuitive ReasoningThe Conjunction Fallacy in Probability Judgmentrsquorsquo Psychological Review 90(1983) 293ndash315

Weinberger Catherin lsquolsquoIs the Science and Engineering Workforce Drawn fromthe Far Upper Tail of the Math Ability Distributionrsquorsquo mimeo UCSB 2005

Westfall Jacob Leaf Van Boven John Chambers and Charles Judd lsquolsquoPerceivingPolitical Polarization in the United States Party Identity Strength andAttitude Extremity Exacerbate the Perceived Partisan DividersquorsquoPsychological Science 10 (2015) 145ndash158

Wolsko Christopher Bernadette Park Charles Judd and Bernd WittenbrinklsquolsquoFraming Interethnic Ideology Effects of Multicultural and Color-BlindPerspectives on Judgments of Groups and Individualsrsquorsquo Journal ofPersonality and Social Psychology 78 (2000) 635ndash654

QUARTERLY JOURNAL OF ECONOMICS1794

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ibrary on October 28 2016

httpqjeoxfordjournalsorgD

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Page 7: I. Introduction · uneducated at the beginning of the 20th century, and as high achievers at the beginning of the 21st (Madon et al. 2001). Social science has produced three broad

the assumption that representative information comes foremostto mind when making judgments The mental operation that liesat the heart of our modelmdashgenerating a prediction for the distri-bution of types in a group based on data stored in memorymdashalsocaptures base rate neglect and overreaction to diagnostic infor-mation The underweighting or neglect of information in ourmodel simplifies judgment problems in a way related to modelsof categorization (Mullainathan 2002 Fryer and Jackson 2008)In these models however decision makers use coarse categoriesorganized according to likelihood not representativeness Thisapproach generates imprecision but does not create a systematicbias for overestimating unlikely events nor does it allow for con-text-dependent beliefs In our empirical analysis of political be-liefs we explicitly compare the predictions of representativeness-based recall to those of likelihood-based models and find that theevidence supports the former

In modeling representativeness we follow the specification ofGS (2010) but investigate a new set of questions GS (2010) ex-amine how representativeness distorts the assessed probabilitiesof alternative hypotheses but not how the probability of a givenhypothesis or group is distributed across its constituent elementsIn the context of the current setting GS (2010) ask how imperfectrecall affects the assessed probability that a randomly drawnmember from a universe belongs to group G The current arti-cle in contrast asks which type t we expect to draw once we knowthat we are facing group G GS (2010) show how representative-ness generates biased probabilistic assessments such as conjunc-tion and disjunction fallacies This article deals with perhaps abroader and more ubiquitous problem of stereotype formationextensively studied by other social scientists but largely ne-glected by economists

Section II describes our model In Section III we examine theproperties of stereotypes including the forces that shape stereo-type accuracy and illustrate these properties with examples InSection IV we bring the model to the data performing a lab ex-periment and analyzing existing surveys of political beliefsSection V concludes The Online Appendix presents proofs anumber of extensions of the model and additional results forthe experiments and field evidence

STEREOTYPES 1759

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II A Model of Representativeness and Stereotypes

IIA The Model

A decision maker (DM) faces a prediction problem such asassessing the ability of a job candidate from a certain ethnicgroup the future performance of a firm belonging to a certainsector or future earnings based on own gender

Formally there is a set of types of interest T and an overallpopulation of which group G is a subset The set of typesT can be unordered (eg occupations) or ordered (and typi-cally cardinal eg earnings levels) When T is ordered wewrite T frac14 ft1 tTg with t1 lt t2 lt lt tT6 There is a probabil-ity or frequency distribution 2 ethT THORN that induces a condi-tional distribution PrethT frac14 tjGTHORN when restricted to G7 In whatfollows we denote by tG frac14 PrethT frac14 tjGTHORN the probability of typet in group G and by G the vector ethtGTHORNt2T containing the condi-tional distribution

The DMrsquos goal is to assess the distribution of the types ofinterest in a particular group G Although the DM has stored inmemory the full distribution he retrieves from memory a dis-torted version of G that overweights the probability of thosetypes that are most representative of G relative to a comparisongroup ndashG Generically ndashG is a group in that is distinct from Gnamely G7 nG although in some cases it can coincide withthe complement of G

According to Tversky and Kahneman (1983) a type t is rep-resentative of G if it is relatively more likely to occur in G thanin ndashG Definitions 1 and 2 formalize this representativeness-based recall following GS (2010)

6 For simplicity we also use T to denote the number of types jTj The modelapplies also to cases in which types (i) are multidimensional capturing a bundle ofattributes such as occupation and nationality or (ii) are continuous We considerthese cases in Online Appendixes C and D respectively Also G may represent anycategory of interest such as the historical performance of a firm or industry actionsavailable to a decision maker (T = set of payoffs G = occupations) or categories inthe natural world (T = ability to fly G = birds)

7 In many applications each individual in is characterized by a determin-istic type (eg age hair color) As a result ethtTHORN frac14 1

jj For instance each Floridian

has a single age type (at the finest temporal resolution) When types are stochasticinstead such as when estimating future earnings of a person or a firm each indi-vidual is described by a nondegenerate distribution

QUARTERLY JOURNAL OF ECONOMICS1760

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DEFINITION 1 The representativeness of type t for group G givencomparison group ndashG is defined as the likelihood ratio

RethtGGTHORN tG

tGeth2THORN

Definition 1 implies that DMs are attuned to log differencesin probabilities representativeness depends on the percentageprobability increase of a type from ndashG to G This captures aform of diminishing sensitivity whereby for a fixed probabilitydifference a type is more likely to be overweighed if it is unlikelyin the comparison group8 Thus the representative age of aFloridian is 65+ because people in this age bracket are morecommon in Florida than in the rest of the United StatesStatistically representative types are also diagnostic of thetarget group G Indeed the higher is RethtGGTHORN the more confi-dent is a Bayesian DM observing t that t belongs to G rather thanto ndashG9

The ease of recall of highly representative types affectsjudgments because more easily recalled types are overweighted

We model distorted recall as follows Denote by RethtGGTHORN

tG

tG

t2T

the vector of representativeness of all types in G

We then have

8 Our definition of representativeness links to Weberrsquos law of sensory percep-tion see Section IIB It also links to our previous work on salience in which wepostulated that log differences in payoffs determine the attention to lottery payoffs(Bordalo Gennaioli and Shleifer 2012) and to goodsrsquo attributes (BordaloGennaioli and Shleifer 2013) Equation (2) establishes the same principle for thedomain of probabilities

9 This insight led Tenenbaum and Griffiths (2001) to define representative-ness as individualsrsquo sense as intuitive Bayesians of updating in reaction to dataTheir definition like ours is in terms of the likelihood ratio However Tenenbaumand Griffiths interpret representativeness as a mechanism that affects intuitivejudgments of similarity rather than beliefs (eg it accounts well for lab evidencewhere subjects are asked to rank types in terms of representativeness or ofstrength of association with a group) Accordingly they do not consider the possi-bility of systematically distorted and context dependent beliefs

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DEFINITION 2 The DM attaches to each type t 2 T in group G adistorted probability

sttG frac14 tG

htethRethtGGTHORNTHORNPs2T sGhsethRethtGGTHORNTHORN

eth3THORN

where ht RTthornRthorn is a weighting function such that

(i) The weight ht is a symmetric function of the representa-

tiveness of types s 6frac14 t Formally ht frac14 h tG

tG

sG

sG

s2Tn tf g

where h Rthorn RT1thorn Rthorn is a function that is invariant to

a permutation of the last T ndash 1 arguments(ii) Weighing of a type increases in own representativeness

and decreases in the representativeness of other typesFormally the function hethTHORN is weakly increasing in itsfirst argument and weakly decreasing in the other T 1arguments

We call the distribution ethsttGTHORNt2T the stereotype for G If a type

t is objectively more likely namely tG is higher then the ste-reotype attaches higher probability to it By property i distor-tions are due exclusively to the fact that a type is more or lessrepresentative than the others In particular if all types areequally representative the DM equally weighs all of them ath(1) and holds rational expectations about G If instead the rep-resentativeness of different types differs property ii implies thatthe stereotype ceteris paribus overweights the probability of morerepresentative types

Most of the results we explore in this article hold for a gen-eral weighing function htethTHORN Specific functional forms captureadded assumptions about the psychology of representativeness-based recall and are useful in applications We outline a few spe-cifications and their properties

Rank-based stereotypes the ranking of the representa-tiveness of different types shapes distortions Denote byrethtTHORN 2 f1 Tg the representativeness ranking of type tWhen r(t) = 1 type t is the most representative one (po-tentially with ties) We can specify two ways in which atypersquos representativeness ranking distorts its probability

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(i) Rank-based truncation the DM only recalls the typesthat have representativeness ranking of at most dnamely ft 2 TjrethtTHORN dg Zero probability is attachedto the remaining types10 Denote by IethrethtTHORN dTHORN an in-dicator function taking the value 1 if the representa-tiveness ranking of t is at most d Then theweighting function is ht frac14 IethrethtTHORN dTHORN so that

sttG frac14 tG

IethrethtTHORN dTHORNPs2T sGIethrethsTHORN dTHORN

which is the true conditional probability within re-called types This assumption is used in Gennaioliand Shleifer (2010)11

(ii) Rank-based discounting the DM discounts by a con-stant factor 2 frac1201 the odds of type t relative to itsimmediate predecessors in the representativenessranking Lower implies stronger discounting ofless representative types Formally the weightingfunction is ht frac14

rethtTHORN so that

sttG frac14 tG

rethtTHORNPs2T sG

rethsTHORN

Representativness-based discounting all else equal theweight attached by the DM to type t increases continuouslywith its representativeness One convenient formulation is

ht frac14tG

tG

so that

10 These neglected types are not viewed as impossible they are just assignedzero probability in the DMrsquos current thinking This formulation allows us to modelsurprise and reactions to unforeseen contingencies which have proved useful in-gredients in modeling probabilistic judgments (GS 2010) as well as neglect of risk infinancial crises (Gennaioli Shleifer and Vishny 2012)

11 Specifically in GS (2010) the assessed probability that a certain hypothesisG is true is equal to

Pr ethGTHORN frac14

Pt tGIethrethtTHORN dTHORNP

t tGIethrethtTHORN dTHORN thornP

t t=GIethrethtTHORN dTHORN

which increases in the ratio between the total probability mass recalled for Gand that recalled for G frac14 nG

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sttG frac14 tG

tG

tG

P

s2T sGsG

sG

where 0 captures the extent to which representative-ness distorts beliefs This formulation is particularly con-venient when dealing with continuous distributions ofthe exponential or power classes

These functional forms all embody the main idea of our modelthat the stereotype overweights the probability of more represen-tative types Rank-based truncation captures a central manifes-tation of limited memory forgetting unrepresentative typesSmoother discounting (based on ranking or on representative-ness) may be more appropriate when the type space is smalland smooth discounting can be more tractable in certain settings

Section III characterizes the general properties of stereotypesIn particular it shows their ability to account for social psycholo-gistsrsquo kernel of truth hypothesis under the general weighting func-tion of Definition 2 To bring the model to the data in Section IVBwe derive linear approximations of stereotypical beliefs by assum-ing that the weighting function is differentiable with respect to atypersquos representativeness This assumption excludes rank-basedweighting but allows for many possibilities

IIB Discussion of Assumptions

Before moving to the formal analysis we discuss some prop-erties and limitations of our approach Representativeness-basedrecall the idea that individuals recall distinctive group types canbe viewed as an instance of what Kahneman and Tversky calllsquolsquoattribute substitutionrsquorsquo When dealing with the difficult questionlsquolsquowhat is the distribution of hair color among the Irishrsquorsquo peopleintuitively answer to the simpler question lsquolsquowhich hair color dis-tinguishes the Irish peoplersquorsquo Critically as discussed byKahneman and Tversky attribute substitution does not occurbecause people misunderstand the original question or mechan-ically confuse the assessment of PrethtjGTHORN with that of PrethGjtTHORNRather it occurs because the distinctive or representative typesimmediately come to mind and individuals anchor their overallprobability judgment to them As a consequence subjects do notonly make mistakes in judging the probability that a Floridian is

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over age 65 They also give too high an answer to the questionlsquolsquowhat is the average age of a Floridianrsquorsquo12

One interesting question is whether the process of stereotyp-ing we describe is optimal in some sense Focusing mental repre-sentations on a few types can be justified by the costs of thinkingor retrieval This approach however is not enough to explainwhy individuals should focus on representative rather thanlikely types We do not formally analyze the optimality of repre-sentativeness here but we mention some relevant considerationsfrom cognitive psychology Kahneman and Tversky (1979) stressthe similarity between many perceptual and cognitive operationsFor instance the highlight of contrastmdasha key principle of visualperceptionmdashis invoked to justify the prospect theory assumptionthat the carriers of utility are changes relative to a referencepoint The same logic applies to our model in which stereotypesprecisely highlight the contrast between groups

In visual perception assessing properties such as brightnesscolor size or distance to an object by comparing them to otherproximate objects has been shown to be optimal in the presence ofmultiplicative background noise (Kersten Mamassian andYuille 2004 Cunningham 2013) Our formulation of representa-tiveness is related to the same idea in the sense that individualsestimating properties of one group stress differences from an-other group In a noisy world in which attention is limited thisprocess may optimally allow for swift reactions to changes ingroup characteristics even if errors are sometimes made13

12 Indeed in many cases mere confusion of PrethtjGTHORNwith PrethGjtTHORNwould not yieldthe phenomenon of stereotyping In the Irish hair color example the probability ofbeing Irish conditional on having red hair is

PrethIrishjredTHORN frac14PrethredjIrishTHORNPrethIrishTHORN

PrethredjIrishTHORNPrethIrishTHORN thorn PrethredjNonIrishTHORNPrethNonIrishTHORN

This probability is clearly very small given that the Irish population is a tinyfraction of the world population Confusion of PrethtjGTHORN with PrethGjtTHORN in this casewould lead to an understatement of the probability of the red-haired Irish

13 To give a simple example suppose thatmdashas in the case of Proposition 3mdashthevariance in the environment increases in the sense that extreme tail events becomemore likely Then a likelihood-based stereotype would detect no change whereas arepresentativeness-based stereotype would focus on the heightened probability ofthe tails In particular an asymmetric increase in tail probabilities that shifts themean would be detected by a representativeness-based stereotype even if the dis-tributionrsquos mode does not change

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Exploring this idea formally is an interesting avenue for futurework

Consider some limitations of our model First representa-tiveness is not the only heuristic that shapes recall Decisionmakers may for instance find it easier to recall types that aresufficiently likely Another potentially important mechanism isavailability understood by Kahneman and Tversky (1972) as thelsquolsquoeasersquorsquo with which information comes to mind (because of actualfrequency or repetition) In Online Appendix E we present a trun-cation-based recall mechanism in which distortions are driven bya combination of representativeness and likelihood of types(which is equivalent to relaxing property i in Definition 2) Thismodel can offer a useful starting point to capture availability aswell even though a full model of availability is beyond the scopeof this article Even in this more general setting the influence ofrepresentativeness on recall is the driving force of stereotypesthat in line with the social psychology perspective are basedon underlying differences among groups As we show in SectionIV this feature is critical in accounting for the evidence

The second set of model-related issues concerns how to spe-cify the elements of Definition 1 in applications group G the typespace T and the reference group ndashG Take the specification of thegroup G and of the type space T Often the problem itself pro-vides a natural specification of these features This is the case inthe empirically important class of lsquolsquoclosedrsquorsquo questions such asthose used in surveys which provide respondents with a set ofalternatives as in the data we use in Section IV More generallythe problem solved by the DMmdashsuch as evaluating the resume ofa job applicant coming from a certain ethnic groupmdashprimes agroup a dimension of interest and a set of types (eg the appli-cantrsquos qualification or skill levels) When types have a naturalorder such as income age or education the granularity of T isalso naturally given by the problem (income age and years ofschooling brackets) When the set of types is not specified by theproblem DMs spontaneously generate one14 It would be useful tohave a model of which dimensions and types come to mind par-ticularly for more open-ended problems Psychologists have

14 For example suppose a person is asked to guess the typical occupation of ademocratic voter in an lsquolsquoopen-endedrsquorsquo format (without being provided a set of alter-natives) Here the level of granularity at which types are defined is not obvious (egteacher versus a university teacher vs a professor of comparative literature)

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sought to construct a theory of natural types and dimensions(Rosch 1973) We do not make a contribution to this problembut we note that in many problems of interest in economics thedimension as well as the set of types is naturally givenFurthermore in our model details of the type space can be impor-tant under rank-based truncation but they matter less undersmooth discounting

Consider finally the role of the comparison group ndashG Thisgroup captures the context in which a stereotype is formed andagain is often implied by the problem when G = Floridians ndashG =rest of US population when G = African Americans ndashG = whiteAmericans A distinctive prediction of our model confirmed byour experiments in Section IVA is that the stereotype for agiven group G depends on the comparison group ndashG15 WhenndashG is not pinned down by the problem itself to derive testablepredictions from representativeness we set G frac14 nG where

is the natural population over which the unconditional distribu-tion of types is measured

III Properties of Stereotypes

We now study stereotypical beliefs and their accuracy Toillustrate the role of representativeness we first ask to whatextent the most representative type is a good fit for the groupnamely whether it is modal Next we assess the accuracy of theentire stereotypical distribution To do so we focus on a cardinaltypes and compare the stereotypersquos mean and variance to the trueones

15 Some empirical papers have taken a similar approach exogenously varyingthe natural comparison group through priming Benjamin Choi and Strickland(2010) show that priming racial or ethnic identity can affect the risk preferences ofparticipants Chen et al (2014) find that Asian students cooperate less with out-group members when primed with their ethnic identity rather than their universityidentity Shih Pittinsky and Ambady (1999) show that Asian American womenstereotype themselves as better or worse in math with corresponding impact onperformance when their ethnicity or gender respectively is primed ShihPittinsky and Trahan (2006) replicate this effect using a verbal task documentingthat Asian American women performed better when their gender rather than theirethnicity was primed Although the generalizability and replicability of priminghas been doubted (Klein et al 2014) this body of evidence is consistent with contextdependence

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IIIA Likely versus Unlikely Exemplars

The most representative type for a group is the one thatagents most easily recall and associate with the group itself forinstance a red-haired Irishman or a 65+-year-old FloridianSocial psychologists call this type the exemplar of the groupAccordingly we define

DEFINITION 3 A type t is an exemplar for G given comparisongroup ndashG when

t 2 arg maxt

tG

tG

Under any specification of the weighting function ht inDefinition 2 overweighting (weakly) increases as we movetoward more representative types so the exemplar is also thetype whose probability is overweighted the most16 By analyzingthe exemplar then we can gauge whether representativenessinduces the DM to overweight a likely type (as happens in stan-dard models of categorical thinking) or an unlikely type Whenoverweighting occurs in unlikely and extreme types the biases ofstereotypes can be particularly severe17

Equation (2) yields the following characterization

PROPOSITION 1 Suppose the conditional distributions G and G

are not identical Consider two extreme cases

(i) If for all t t0

2 T we have that tG gt t0 G if and only iftG gt t0 G then the modal type is not an exemplar forat least one group

(ii) If for all t t0

2 T we have that tG gt t0 G if and only iftG lt t0 G then for each group the modal type is theexemplar

16 Consider the function hethTHORN from Definition 2 When applied to more repre-sentative types the first argument of the function increases while one of the otherT ndash 1 arguments decreases As a result the weighting factor ht (and thus overweigh-ing

sttG

tG) increases as well

17 In the rank-based truncation model the frequency of the exemplar providesa measure of stereotype accuracy By accuracy we mean the extent to which thestereotype minimizes the distance

Pt eth

sttG tGTHORN

2 When d = 1 and only one type isrecalled (there are no ties) accuracy is maximized if the exemplar is the most likelytype and minimized if the exemplar is the least likely type

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Case i says that when groups have similar distributions inthe sense of having the same likelihood ranking the most repre-sentative type is unlikely for at least one group potentially bothRepresentativeness draws the DMrsquos attention to group differ-ences neglecting the fact that the groups are similar and havethe same mode This mechanism generates inaccurate stereo-types and is illustrated by the Florida example This resultholds under any measure of representativeness that differenti-ates the two groups (eg the difference tG tG)

Case ii says that the most representative type tends to belikely for both groups when the distributions are very differentIn this case groups differ the most around their modes so repre-sentativeness and likelihood coincide Thinking of Swedes aslsquolsquoblondrsquorsquo and Europeans as lsquolsquodark hairedrsquorsquo is accurate precisely be-cause these are majority traits of the Swedish and European pop-ulations respectively In these cases stereotyping yields fairlyreliable models Of course there is still some inaccuracy Evenin the case of likely exemplars judgment errors can be signifi-cant For instance voters in some US states are perceived aslsquolsquobluersquorsquo or lsquolsquoredrsquorsquo because a majority of the population votesDemocrat or Republican In reality even in lsquolsquobluersquorsquo states farfrom everyone votes Democrat In the 2012 presidential electionvote shares of either candidate in most states ranged from 40 to6018

When DMs strongly overweight representative types themost severe biases occur when those types are unlikely and ex-treme This is true both under rank based truncations and undersmooth discounting functions (see Section IIIB) Ethnic stereo-types based on crime or terrorism exhibit this error they neglectthe fact that by far the most common types in all groups arehonest and peaceful

IIIB Stereotypical Moments

We now characterize how the first two moments of a distri-bution are distorted by the process of stereotyping To do so wemust restrict our analysis to cardinal ordered types The follow-ing results hold for any weighting function htethTHORN satisfyingDefinition 2 We consider two canonical cases that prove usefulin illustrating the predictions of the model

18 Presidential Election Results NBCNewscom see httpelectionsnbcnewscomnspolitics2012allpresident (accessed 5 September 2016)

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In the first case groups G and ndashG are such that the likelihoodratio tG

tGis monotonic in t The monotone likelihood ratio prop-

erty (MLRP) holds to a first approximation in many empiricalsettings and is also assumed in many economic models such asstandard agency models19 If tG

tGis monotonically increasing (de-

creasing) in t then group G is associated with higher (lower)values of t relative to the comparison group ndashG Formally

PROPOSITION 2 Suppose that MLRP holds and assume wlogthat the likelihood ratio tG

tGis strictly increasing in t Then

for any weighting function htethTHORN that is not constant in therelevant range

EstethtjGTHORN gt EethtjGTHORN gt EethtjGTHORN gt E

stethtjGTHORN

Under MLRP the most representative part of the distribu-tion for G is the right tail if tG

tGincreases in t or the left tail if tG

tG

decreases in t The representative tail is then overweighted whilethe nonrepresentative tail is underweighted As a consequencethe assessed mean E

stethtjGTHORN is too extreme in the direction of therepresentative tail

Critically in line with the social cognition perspective the ste-reotype contains a kernel of truth the DM overestimates the meanof G if this group has a higher mean than the comparison groupnamely EethtjGTHORN gt EethtjGTHORN and conversely if EethtjGTHORN lt EethtjGTHORN TheDM exaggerates this true difference because he inflates the asso-ciation of G with its most representative types20 For instancewhen judging an asset manager who performs well we tend to

19 Examples include the binomial and the Poisson families of distributionswith different parameters The characterization of distributions satisfying MLRPis easier in the case of continuous distributions (see Online Appendix D) two dis-tributions f(x) f ethx THORN that differ only in their mean satisfy MLRP if and only if thedistribution f(x) is log-concave Examples include the exponential and normal dis-tributions To the extent that discrete distributions sufficiently approximate thesedistributions (as the Poisson distribution PoisethTHORN approximates the normal distri-bution Neth THORN for large l) they will also satisfy MLRP

20 Depending on the distribution and the weighing function the DMrsquos assess-ment of the variance VarethtjGTHORNmay also be dampened relative to the truth This isoften true under the truncation weighing function In this case stereotyping effec-tively leads to a form of overconfidence in which the DM holds extreme views andoverestimates the precision of his assessment That extreme views and overconfi-dence (in the sense of over precision) go together has been documented in the settingof political ideology among others (Ortoleva and Snowberg 2015)

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overemphasize skill relative to luck because higher skill levels arerelatively more associated with higher performance This occurseven if for both skilled and unskilled managers high performanceis mostly due to luck

In the second case for which we characterize the stereotypi-cal distributions groups G and ndashG have the same mean EethtjGTHORNfrac14 EethtjGTHORN frac14 EethtTHORN but differ in their variance We abstract fromskewness and higher moments by considering distributionsethtGTHORNt2T and ethtGTHORNt2T that share the same support and are sym-metric around the medianmean EethtTHORN

PROPOSITION 3 Suppose that in G more extreme types are rela-tively more frequent than in ndashG Formally the likelihoodratio tG

tGis U-shaped in t around EethtTHORN Then for any weight-

ing function htethTHORN that is not constant in the relevant rangestereotypical beliefs satisfy

VarstethtjGTHORN gt VarethtjGTHORN gt VarethtjGTHORN gt VarstethtjGTHORN

EstethtjGTHORN frac14 E

stethtjGTHORN frac14 EethtTHORN

When group G has a higher relative prevalence of extremetypes its representative types are located at both extremes of thedistribution The DMrsquos beliefs about G are then formed by over-weighting both tails while underweighting the unrepresentativemiddle The overweighting of Grsquos tails causes the assessment ofits variance VarstethtjGTHORN to be too high For example the skill dis-tribution of immigrants to the United States may be perceived ashaving very fat tails or even bimodal with immigrants beingperceived as either unskilled or very skilled relative to the resi-dent population The mean of the group in contrast is assessedcorrectly because the stereotypical distribution remains symmet-ric around EethtTHORN As before the stereotype contains a kernel oftruth It induces the agent to exaggerate the true differences be-tween groups namely the higher variance of G relative to itscounterpart

We present a number of extensions of the model in the OnlineAppendix We first consider multidimensional type spaces andshow that stereotypes center around the dimension wheregroups differ the most in line with the kernel of truth logic(Online Appendix C) Multidimensional stereotypes imply thatthe dimension we think about is influenced by context For

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example the Irish are stereotyped as red-haired when comparedwith the European population However when compared withthe Scots a more plausible stereotype for the Irish is lsquolsquoCatholicrsquorsquobecause religion is the dimension along which Irish and Scotsdiffer the most

In Online Appendix D we extend the model to continuoustype spaces Many settings of interest in economics can be use-fully described by continuous probability distributions and weshow our model is particularly tractable in this case In OnlineAppendix E we relax Definition 2 and allow weighting of types toalso be influenced by their likelihood We show that the basicinsight that stereotypes contain a kernel of truth carries throughto these cases as well

To summarize the psychology of representativeness yieldsstereotypes that are consistent with the social cognition approachin which individuals assess groups by recalling and focusing ondistinctive group traits When there are systematic differencesbetween groups stereotypes get the direction right but exagger-ate differences

IIIC Some Examples

A growing body of field and experimental evidence points to awidespread belief that women are worse than men at mathemat-ics (Eccles Jacobs and Harold 1990 Guiso et al 2008 CarrellPage and West 2010) This belief persists despite the fact that fordecades women have been gaining ground in average schoolgrades including mathematics and have recently surpassedmen in overall school performance (Goldin Katz and Kuziemko2006 Hyde et al 2008) This belief shared by men and women(Reuben Sapienza and Zingales 2014) may help account for thegender gap in the choices of high school tracks college degreesand careers with women disproportionately choosing humanitiesand health-related areas (Weinberger 2005 Buser Niederle andOosterbeek 2014) and forgoing significant wage premiums toquantitative skills (Bertrand 2011)

Gender stereotypes in mathematics particularly beliefs thatexaggerate the extent of average differences are consistent withthe predictions of our model The fact that men are overrepre-sented at the very highest performance levels leads a stereotyp-ical thinker to exaggerate the magnitude of mean differencesFigure I shows the score distributions from the mathematics

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section of 2013rsquos Scholastic Aptitude Test (SAT) for men andwomen21 The distributions are very similar with averagescores slightly higher for men (531 versus 499 out of 800)However scores for men have a heavier right tail with mentwice as likely to have a perfect SAT math score than women22

In light of such data the stereotypical male performance in math-ematics is high while the stereotypical female performance ispoor Predictions based on such stereotypes are inaccurate exag-gerating true differences Consistent with this prediction exper-imental evidence shows that both genders underestimatewomenrsquos ability in simple math tasks even controlling for pastperformance (Reuben Sapienza and Zingales 2014) Coffman(2014) shows a similar pattern extends to confidence about ownability in other male-typed domains with women reporting sig-nificantly less confidence in gender-incongruent than gender-congruent tasks Our model suggests that these patterns mightcome from stereotypes based on gender differences in the righttail of the distribution While differences in the right tail of thedistribution are unlikely to be relevant for most decisions stereo-typical thinking driven by these differences has the potential toimpact economically important decisions whether through self-stereotyping (ie choice of careers or majors as in BuserNiederle and Oosterbeek 2014) or through discrimination (iehiring decisions as in Bohnet van Geen and Bazerman 2016)

The logic of exaggerated yet directionally correct stereotypesalso sheds light on the well-documented phenomenon of base rateneglect (Kahneman and Tversky 1973) Indeed Proposition 2implies that the DM overreacts to information that assigns

21 Standardized test performance measures not only innate ability but alsoeffort and investment by third parties (Hyde et al 2008) The mapping of test per-formance into inferences about innate ability is an issue not addressed by ourmodel

22 For 2013 SAT Mathematics scores see httpmediacollegeboardcomdigitalServicespdfresearchSAT-Percentile-Ranks-By-Gender-Ethnicity-2013pdf Results are similar for the National Assessment of Educational Progress(NAEP) which are more representative of the overall population For 2012NAEP scores for 17-year-olds in mathematics see httpnationsreportcardgovltt_2012age17maspx See Hyde et al (2008) Fryer and Levitt (2010) and Popeand Sydnor (2010) for in-depth empirical analyses of the gender gap inmathematics

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people to groups precisely because such information generatesextreme stereotypes Consider the classic example in which amedical test for a particular disease with a 5 prevalence has a90 rate of true positives and a 5 rate of false positives The testassigns each person to one of two groups + (positive test) or ndash(negative test) The DM estimates the frequency of the sick type(s) and the healthy type (h) in each group The test is informativea positive result increases the relative likelihood of sickness anda negative result increases the relative likelihood of health forany prior Formally

PreththornjsTHORN

PreththornjhTHORNgt 1 gt

PrethjsTHORN

PrethjhTHORNeth4THORN

This condition has clear implications the representative personwho tests positive is sick while the representative person whotests negative is healthy Following Proposition 2 the DMreacts to the test by moving his priors too far in the right di-rection generating extreme stereotypes He greatly boosts hisassessment that a positively tested person is sick but also thata negatively tested person is healthy Because most people arehealthy the DMrsquos assessment about the group that tested neg-ative is fairly accurate but is severely biased for the group that

FIGURE I

SAT Mathematics Scores by Gender (2013)

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tested positive This analysis formalizes Tversky andKahnemanrsquos (1983) verbal account of base rate neglect23

The same mechanism may underlie several other instanceswhere DMs overweight diagnostic information When assessingan employeersquos skill level an employer attributes high perfor-mance to high skill because high performance is the distinctivemark of a talented employee Because he neglects the possibilitythat some talented employees perform poorly and that somenontalented ones perform well (perhaps due to stochasticity inthe environment) the employer has too much faith in skill andneglects the role of luck in accounting for the output Similarlywhen assessing the performance of firms in a hot sector of theeconomy (eg G = internet) an investor recalls highly successfulfirms in that sector (t = return of Google Amazon etc) He ne-glects the possibility of firms being unsuccessful because lack ofsuccess is statistically nondiagnostic and psychologically nonrep-resentative of a growing sectormdasheven if it is likely This causesexcessive optimism (in that the expectation of growth is unrea-sonably high) and overconfidence (in that the variability in earn-ings growth considered possible is truncated) True the hot sectormay have better growth opportunities on average but represen-tativeness exaggerates this feature and induces the investor toneglect a significant risk of failure

IV Evidence on Representativeness and Stereotypes

Testing our model requires evaluating the beliefs individualshold about a target group against the true distribution of thattarget group over an attribute space An ideal data set would

23 Our account is distinct from a mechanical underweighting of base rates inBayes rule as in Grether (1980) and Bodoh-Creed Benjamin and Rabin (2013) Inthose models upon receiving the test results the DM can update his beliefs in thewrong direction he can be less confident that a person is healthy after a negativetest than under his prior which cannot happen in our model Although this predic-tion of our model seems consistent with introspection we are not aware of experi-mental evidence on this point Griffin and Tversky (1992) present evidenceconsistent with pure neglect of base rates but in a significantly different tasknamely inferring the bias of a coin from a history of coin flips Such experimentsare hard to compare with the predictions of our model because subjects are asked togenerate distributions of different numbers of coin flips in their minds which is amuch more involved task than to recall types of a given distribution Their assess-ments then might be wrong for other reasons See Bodoh-Creed Benjamin andRabin (2013) for a detailed discussion

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consist of naturally defined groups with known distributions overa given space of types and a corresponding set of beliefs about thedistribution of each group over that space of types This wouldallow us to test for exaggeration of true differences betweengroups and to ask whether this exaggeration is well predictedby overweighting representative types To identify a causal rolefor representativeness or context dependence we would need ex-ogenous variation in either the comparison group ndashG or in thedistributions over the type spaces This is unavailable in existingdata sets Accordingly we take a two-pronged approach First wecreate a controlled laboratory environment that allows us toinduce the exogenous variation in representative types that weneed to test causality then we reanalyze existing field evidence tocheck for consistency with our predictions

In testing our model we focus on the two main implicationsof representativeness-based stereotypes

Context dependence the stereotype of a target group de-pends on the characteristics of the reference group it iscompared to

Kernel of truth stereotypes depend on group character-istics andmdashin most (precisely characterized) settingsmdashare slanted toward representative types

We test the first property with a lab experiment (SectionIVA) We then turn to survey data on beliefs about US politicalgroups (Section IVB) for an empirical analysis that explores thesecond property The survey data are more tightly linked to ourinterest in social stereotypes The laboratory experiment allowsus to directly test the role of representativeness in generatingcontext dependent beliefs Online Appendixes F and G provideall details and additional results for the experiments and fieldevidence

IVA Lab Evidence on Representativeness and ContextDependence

The influence of the representativeness heuristic on recalland on beliefs has been extensively documented in the lab(Kahneman and Tversky 1972 1973) Our goal is to considerhow representativeness as formalized in equation (2) gives riseto context-dependent beliefs To our knowledge the possibility

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that representativeness may generate context dependence hasnot been tested before

To assess this prediction we perform a controlled laboratoryexperiment that allows us to isolate representativeness frommany confounding factorsmdashhistorical sociological or other-wisemdashthat may affect stereotype formation in the real worldWe construct our own groups of ordinary objects creating atarget group G and a comparison group ndashG We hold thetarget group G fixed and explore how participant impressions ofit change as we change the comparison group ndashG and thusrepresentativeness

We conducted several experiments in the laboratory and onAmazon Mechanical Turk Each involves a basic three-stepdesign First participants are shown the target group and a ran-domly assigned comparison group for 15 seconds In this timedifferences between groups can be noticed but the groupsrsquo precisecompositions cannot be memorized The second step consists of afew filler questions which briefly draw the participantsrsquo cognitivebandwidth away from their observation Finally participants areasked to assess the groups they saw Participants are incentiv-ized to provide accurate answers

We randomly assign participants to either the Control or theRepresentativeness condition In the Control condition G and ndashGhave nearly identical distributions so that all types are similarlyrepresentative for each group In the Representativeness condi-tion ndashG is changed in such a way that a certain type becomes veryrepresentative for G Context dependence implies that the assess-ment of G should now overweight this representative type eventhough the distribution of G itself has not changed

We ran six experiments of this form with design changesfocused on reducing participant confusion and removing con-founds We describe the final and most refined version of theseexperiments here In an attempt to provide a overview of the re-sults while remaining concise we provide the results from pooledspecifications that use all data collected In Online Appendix Fwe offer additional details and report all experiments conductedWe also give instructions and materials for each experiment thefull data set is available by request

Consider first the experiment illustrated in Figure II Agroup of 25 cartoon girls is presented next to a group of 25 cartoonboys in T-shirts of different colors blue green or purple In theControl condition (Figure II Panel a) the groups have identical

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color distributions (13 purple 12 green) so no color is represen-tative of either group The Representativeness condition (Panel b)compares the same group of girls with a different group of boysfor whom green shirts are replaced with blue shirts Now onlygirls wear green and only boys wear blue These colors althoughstill not the most frequent for either group are now most repre-sentative For each group girls and boys participants are asked anumber of questions concerning the frequency of T-shirts of dif-ferent colors worn by that group

Applying our model in the control condition the type space isT frac14 fgreen purpleg and the groups are G = girls and ndashG = boysGiven that the color distributions are identical across groups both

types are equally representativegreengirls

greenboysfrac14 1 frac14

purplegirls

purpleboys As a result

assessment of G should be correct on average stcontrolgreengirls frac14 greengirls

and stcontrolpurplegirls frac14 purplegirls for any weighing function (the same is

true about assessments of ndashG)In the treatment condition the distribution of shirt colors re-

mains the same for girls For boys green shirts are changed intoblue Thus the type space changes to T frac14 fgreen purple bluegand the representative color for girls becomes greengreengirls

greenboysfrac14 1 gt 1 frac14

purplegirls

purpleboys while that for boys becomes blue As

a result in the treatment condition subjects should inflate the

frequency of green shirts relative to the truth sttreatmentgreengirls

gt greengirls (the same should happen to assessments of blueshirts for boys) We also expect the assessed frequency of greenshirts to go up relative to the control condition namely

sttreatmentgreengirls gt stcontrol

greengirls Critically the only factor that varies

across treatments is the representativeness of the 12-colorshirt Thus if we see differences across conditions the causalrole of representativeness-based recall in shaping group judg-ments is clear24

24 We vary which colors are used in which roles across participants Someparticipants saw this particular color distribution while others see for examplegreen as the modal color and purple as the diagnostic color for boys in theRepresentativeness condition and blue as the diagnostic color for girls in theRepresentativeness condition We vary the colors across the roles to avoid con-founding the characteristics of any particular color with its diagnosticity

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FIG

UR

EII

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Fig

ure

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icip

an

tsin

the

exp

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ent

For

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ty

we

have

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ded

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tter

toea

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-sh

irt

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enti

fyth

eco

lor

for

the

read

er

lsquolsquoGrsquorsquo

ind

icate

sgre

en

lsquolsquoPrsquorsquo

ind

icate

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urp

le

lsquolsquoBrsquorsquo

ind

icate

sblu

eT

hes

ele

tter

sd

idn

otap

pea

rto

part

icip

an

tsan

dare

for

read

erre

fere

nce

only

P

lease

see

onli

ne

ver

sion

ofp

ubli

shed

art

icle

for

colo

rfi

gu

reex

act

lyas

itap

pea

red

top

art

icip

an

ts

STEREOTYPES 1779

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We collected data from 301 participants using this T-shirtsdesign25 Since the number of green and purple shirts is verysimilar we first ask each participant the simplest question ofwhich shirt color is modal Next we ask participants to assessthe share of green and purple shirts

Consistent with the role of representativeness participantsassigned to the Representativeness condition are 105 percentagepoints more likely to recall the less frequent color (green for girlsor blue for boys) as the modal color when it is representative of agroup (35 of participants guess the less frequent color is modalin the Control condition this proportion increases to 46 in theRepresentativeness condition p = 01 estimated from a probitregression reported in Online Appendix F)

We now turn to subjectsrsquo estimates of how many T-shirts ofeach color they saw in each group In both conditions the truedifference in counts is 1 (13 purple shirts 12 green or blue shirts)In the Control condition participants on average believe they saw054 more purple shirts than green or blue shirts In theRepresentativeness condition participants believe they saw072 fewer purple shirts than green or blue shirts (the acrosstreatment difference is significant with p = 01 from OLS regres-sion reported in Online Appendix F)

In total we collected data for six experiments of this generalstructure gathering evidence from more than 1000 participantsAs we describe in Online Appendix F although there is substan-tial variation across experiments when we pool all of the data wefind significant aggregate treatment effects in line with a role ofrepresentativeness in judgment We employ four different unor-dered types designs similar to the T-shirts experiment using sixsamples (four online and two in the laboratory) with 741 partic-ipants We find effects in the predicted direction for five of the sixsamples Using a probit regression that pools the data for theseunordered type experiments we find that participants are 93 per-centage points more likely to guess that the less frequent type ismodal when it is representative than when it is not (p = 002) Wealso run a family of ordered types experiments (two designs fivesamples 402 participants) Unlike the simpler T-shirts style

25 Throughout our analysis we exclude any participant who participated in aprevious version of the experiment and any participant who self-identified as color-blind In Online Appendix F we show that our results are unchanged if we includethese additional observations

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design the theoretical predictions for the ordered types designsare more sensitive to the specific assumptions one makes aboutthe weighting function of the DM26 We find effects in the pre-dicted direction for three of the five samples As we discuss inmore detail in Online Appendix F the ordered types resultsvary by platform with consistently stronger results on AmazonMechanical Turk than in the laboratory samples Pooling all or-dered types experiments participants are 93 percentage pointsmore likely to guess that the group of interest has a greater av-erage than the comparison group when the right tail is represen-tative (p = 062) Given our simple experimental setting withgroups of mundane objects we interpret our resultsmdasha signifi-cant and reasonably sized impact on average beliefsmdashas an im-portant proof of concept the presence of representative typesbiases ex post assessment

IVB Empirical Evidence on Political Stereotypes

We examine two data sets on political preferences and be-liefs about political preferences in the United States We inves-tigate the roles of representativeness and context dependence byseparately testing for hypotheses that allow us to assess the lead-ing theories of stereotypes

First we test whether beliefs are correct or depart systemat-ically from the truth The statistical discrimination approachbuilds on the assumption that people hold rational expectationsof group traits Comparing beliefs to the truth allows us to assessthe validity of this assumption in our data

Second we test if beliefs depart from the truth by exagger-ating (mean) differences among groups per the kernel of truthhypothesis This is an implicit test of context dependence be-cause it implies that beliefs about the target groups are shapednot only by that grouprsquos characteristics but also by those of thereference group27

Third we test if distortions in beliefs can be accounted for bythe overweighting of highly representative types (defined astypes that are relatively more frequent in the target relative to

26 This is due in part to our choice to not study MLRP distributions We moti-vate and discuss this design decision in Online Appendix F

27 Of course unlike in the laboratory experiment in this setting we cannot testfor context dependence by exogenously varying the reference group

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the reference group) The second and third tests address the keypredictions of our model

1 The Data We have two data sets on political preferences andbeliefs about political preferences The first data set from GrahamNosek and Haidt (GNH 2012) contains data from the MoralFoundations Questionnaire Respondents (1174 self-identified lib-erals and 500 self-identified conservatives) answer questions abouttheir position on a subset of 45 issues 20 moral relevance state-ments (eg lsquolsquowhen you decide whether something is right orwrong to what extent are the following considerations relevantto your thinkingrsquorsquo) and 25 moral judgments (eg lsquolsquoindicate theextent to which you would agree or disagreersquorsquo) For each issue arandomly determined subset of participants states their own posi-tion another subset states their belief on the position of a lsquolsquotypicalliberalrsquorsquo and a third subset states their belief on the position of alsquolsquotypical conservativersquorsquo The data thus include the distribution overpositions for both liberal and conservatives as well as the averagebelieved typical position of liberals and of conservatives on the 45issues Each position is elicited on 1ndash6 scale

The second data set comes from the American NationalElection Survey (ANES) and contains data from more than20000 respondents between 1964 and 201228 The surveycovers political issues of the day such as the optimal amount ofgovernment spending and service provision (1984ndash2000) or theplace of women in society (1972ndash1998) We focus on the 10 issuesthat ask participants to respond on a 1ndash7 scale (rather than justindicate binary agreement or disagreement) all 10 issues areasked in multiple years Participants are asked to provide theirown position on the scale and their believed position of theDemocratic and Republican parties (lsquolsquoWhere would you placethe Democratic [Republican] party on this scalersquorsquo) The data in-clude for each issue-year observation the distribution of partic-ipant positions for self-identified liberals and self-identifiedconservatives as well as the distribution of believed typical posi-tions of the Democratic and Republican parties

28 These data are publicly available at httpwwwelectionstudiesorgstudy-pagesanes_timeseries_cdfanes_timeseries_cdfhtm

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2 Empirical Strategy Our analysis focuses on beliefs abouttwo groups Conservatives and Liberals The types are the possi-ble positions for each issue (1 2 6 7) For the GNH data weinterpret beliefs about the lsquolsquotypicalrsquorsquo element of a group to coincidewith the believed average position in that group Similarly forthe ANES data we use the believed party positions as a proxy forbelieved mean of each group29 We then take as a benchmark thehypothesis that individuals hold accurate beliefs about eachgroup and in particular that believed mean position shouldequal true mean position at least on average across subjectsThe accurate beliefs hypothesis underlies the most common eco-nomic model of stereotyping statistical discrimination

To assess our representativeness-based model we perform aregression exercise To test our model in a linear regressionframework we rely on linear approximations of the weightingfunction Our model then yields two regression specifications

PROPOSITION 4 Let G 2 fconservative liberal g and assume

ht h tG

tG

be a differentiable and strictly increasing weight-

ing function as in Definition 2 The following hold as a first-order approximation around identical distributions G

Gfrac14 1

(i) Kernel of truth regression There exists a constant gt 0such that

EstethtjGTHORN frac14 EethtjGTHORNeth1thorn THORN EethtjGTHORNeth5THORN

(ii) Representativeness regression Denote H frac14 fT 2 Tg

the right tail of types and RconsH frac14

PHtconsPHtlib

as the average

representativeness of right tail types for conservatives

29 This assumption is consistent with the authorsrsquo interpretation of the GNHdata (GNH 2012) and with previous studies using ANES (eg Westfall et al 2015)Furthermore to the extent that this assumption holds equally well for most issueswithin a data set our focus on cross-issue differences should allow us to test thepredictions of our model even with an imperfect proxy for beliefs of mean positionsFinally the data provide some insight into whether subjects are reporting (per-ceived) modal or mean types As we show the modal type is a poor prediction ofstated beliefs while a distorted mean slanted toward representative types is anaccurate prediction of stated beliefs

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Under the further approximation where tcons

tlibampRcons

H for

t 2 H

EstethtjconsTHORN frac14 EethtjconsTHORN thorn consethR

consH 1THORNeth6THORN

EstethtjlibTHORN frac14 EethtjlibTHORN libethR

consH 1THORNeth7THORN

where lcons and llib are positive constants

The first regression allows us to test for the kernel of truthhypothesis and the second set of regressions allows us to test forthe role of representativeness

Equation (5) says that respondents in our model inflate theaverage position of a group say the conservatives if and only ifthe group has a higher average position than the other groupnamely the liberals Formally EstethtjconsTHORN gt EethtjconsTHORN if and onlyif EethtjconsTHORN gt EethtjlibTHORN Because in our measurement scale highertypes mean lsquolsquomore conservativersquorsquo we expect (i) believed conserva-tive average to be higher than the truth and (ii) the extent ofoverstatement to decrease in the average liberal position EethtjlibTHORNConversely we expect the average liberal position to be lowerthan the truth the more so the higher the average conservativeposition EethtjconsTHORN

As previously discussed the basis of these predictions is con-text dependence information about the distribution of ndashG is rel-evant for the beliefs about G This context dependence isinconsistent with rational expectations in which only thegrouprsquos own means should affect beliefs We test the hypothesisthat the true mean EethtjGTHORN is a significant predictor of the believedmean E

stethtjGTHORN with a positive sign and the other grouprsquos truemean EethtjGTHORN is a predictor of the believed mean with a negativesign

Equations (6) and (7) say that repondentsrsquo assessment bias isshaped by representativeness When the right tail is more repre-sentative for conservatives (Rcons

H 1 positive and large) partici-pants should inflate the average conservative position more(higher E

stethtjconsTHORN EethtjconsTHORN) and deflate the average liberal po-sition more (lower E

stethtjlibTHORN EethtjlibTHORN) We test the hypothesisthat the inflation in conservative positions is positively associatedwith the representativeness of the right tail for the conservativesand the inflation in liberal positions is negatively associated with

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it Once again the representativeness of the right tail is com-puted using the true distribution of positions

In equations (6) and (7) in many cases the representative tailis also the most likely one As a consequence these tests cannotdistinguish a representativeness-based from a likelihood-basedmodel of distorted beliefs We perform two additional testsFirst we run versions of equations (6) and (7) in which we controlfor the likelihood of tails (see Table A4 in Online Appendix G)Second we compute numerically the predictions of a representa-tiveness-based model of stereotypes and a likelihood-based modelof stereotypes We then assess which of these two is better able tomatch the data on beliefs

3 Empirical Results To begin we illustrate the structure ofthe data and the nature of our predictions with two simple exam-ples from the GNH data set focusing on beliefs about conserva-tives In example 1 participants are asked about their agreementwith the statement lsquolsquoIt can never be right to kill a human beingrsquorsquoIn example 2 participants are asked about the moral relevance oflsquolsquowhether or not someone cared for someone weak or vulnerablersquorsquoAs can be seen in Figure III in example 1 the modal position(strongly disagree (1)) and most representative positions(strongly disagree (1)) coincide for conservatives In contrast inexample 2 in Figure III the most representative types (slightlyrelevant (3) not at all relevant (1)) are not most likely for theconservative group Following Proposition 1 we predict that be-liefs will be distorted in the direction of the most representativetypes Thus we expect more exaggeration in example 2 than inexample 1 since in example 2 the most representative types (inthe left tail) are far from the modal type whereas in example 1they coincide This is what we find the conservative position isexaggerated by only 009 positions in Example 1 (true mean 299believed mean 290) but by 106 positions in Example 2 (truemean 421 believed mean 315)

In the full data sets we treat each (issue year) pair as anobservation and we cluster standard errors at the issue level Forthe GNH data we have 45 observations 45 issues measured inthe same year For the ANES data we have 66 observations 10issues measured in multiple years To begin we simply docu-ment systematic exaggeration in both data sets This is a primaryfocus of the original analysis in GNH (2012) and also in Westfall

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FIGURE III

Two Examples

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et al (2015)rsquos analysis of the ANES data30 Figure IV shows thatthe believed difference between typical conservative and typicalliberal positions is larger than the true difference in mean posi-tions for 109 of the 111 observations The data for both GNH(squares) and ANES (triangles) lie above the 45-degree line(dashed)31 Average exaggeration is 062 positions on the scale(066 in the GNH data 059 in the ANES data)32

The systematic and significant exaggeration of mean differ-ences suggests that the benchmark model of accurate beliefs ismissing something important Indeed this exaggeration reflectsthe fact that believed means are typically more extreme than truemeans First note that the kernel of truth regression (equation(5)) generates exaggeration of mean differences just as docu-mented in Figure IV

EstethtjGTHORN E

stethtjGTHORN frac14 eth1thorn 2THORN frac12EethtjGTHORN EethtjGTHORN

To bring this prediction to the data we regress the believedmean position for each group EBethtjGTHORN on the true mean of thegroup EethtjGTHORN and the true mean of the comparison groupEethtjGTHORN across issues We do this for each group (liberals con-servatives) in each data set separately We also present pooledspecifications that combine the data sets to make a prediction fora given group (liberals conservatives) In these pooled specifica-tions we include a dummy variable indicating whether theobservation came from the ANES data set For all specificationswe cluster observations at the issue level33 The results from re-gression are shown in Table I In every specification we find thatEethtjGTHORN is a significant predictor of EBethtjGTHORN with the predicted pos-itive sign Crucially for five of the six specifications the mean of

30 Chambers and Melnyk (2006) also find evidence of exaggeration of truedifferences in beliefs about political positions

31 For convenience we recode all issues so that the high end of the scale (67)represents the stereotypically more conservative position

32 A natural question to ask is how beliefs vary across liberals and conserva-tives That is do beliefs about a group G depend on membership in G versus ndashG Ourmodel does not speak to this issue However in Online Appendix G we show thatthe results we document below hold for both beliefs held by conservatives and be-liefs held by liberals see Tables A9 A10 and A11

33 In general the results presented below for the ANES data are not largelyimpacted by the decision to cluster at the issue level Similar results are obtained ifthe data are not clustered

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the comparison group EethtjGTHORN is also a significant predictor ofE

BethtjGTHORN with the predicted negative signAlthough these results provide strong evidence of context

dependence and are consistent with our model they do not pindown a role for representativeness of types Our next test relatesthe magnitude of representativeness of tail types to the magni-tude of belief distortions

To this end we implement the regressions in equations (6)and (7) Following Proposition 4 we compute the average repre-

sentativeness of tail types for conservatives RconsH frac14

PtT2tconsPtT2tlib

We

again test the hypothesis that RconsH is a significant predictor of Est

ethtjconsTHORN with a positive sign and a predictor of EstethtjlibTHORN with a

negative sign Table II shows that conditional on true mean RconsH

predicts believed mean for each group G as expected The firstthree specifications display the results for predicting beliefs heldabout conservatives In both data sets the average representa-tiveness of tail types for conservatives is a significant positivepredictor of beliefs held about conservatives The final three spe-cifications display the results for predicting beliefs held about

FIGURE IV

Exaggeration of Differences

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liberals We find that the average representativeness of tail typesfor conservatives is a negative predictor of beliefs held about lib-erals This effect is significant in the GNH data and marginallysignificant in the ANES data

We present several additional results in Online Appendix GTo further examine the role of representativeness in driving be-liefs we first show the results of Table II carry through when we

TABLE II

AVERAGE REPRESENTATIVENESS OF TAIL POSITIONS PREDICTS BELIEFS

OLS Predicting Believed Mean of Group G for Each Issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position

of group G for issue

078 024 051 072 018 041

(006) (008) (009) (005) (005) (010)

Avg rep of tail types for

conservatives RconsH

019 055 025 014 012 024

(007) (022) (008) (006) (007) (005)

Constant 101 260 184 093 271 201

(026) (045) (029) (022) (025) (032)

R2 082 048 060 091 031 070

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

TABLE I

INFORMATION ABOUT ndashG PREDICTS BELIEFS ABOUT G

OLS predicting believed mean of group G for each issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position of

conservatives for issue

102 098 096 021 019 025

(0097) (0133) (0076) (0060) (0116) (0060)

True mean position of

liberals for issue

035 086 058 0987 039 073

(0106) (0134) (0131) (0066) (0106) (0135)

Constant 151 335 235 069 258 156

(0195) (0269) (0279) (0122) (0249) (0270)

R2 083 053 066 092 032 068

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

STEREOTYPES 1789

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control for the average likelihood on the tail positions (see Table A4in Online Appendix G) Most tellingly we use the model to predictbeliefs across issues and compare those to the data For simplicitywe use the rank-based truncation specification to predict mean be-liefs when stereotypes include the d most representative types ford frac14 1 T We compare these predictions to those of a model inwhich beliefs are obtained by restricting the distribution to the dmost likely types Our benchmark for both models is predicting thebelieved mean from the entire distribution where d = T We showthat the predictions of the rank-based truncation model with d = 4or 5 compare favorably to both a likelihood-based truncation model(with any d) and the accurate beliefs benchmark Interestingly thisresult suggests that stereotypical beliefs are well approximated byneglecting the least representative types (as opposed to focusingonly on the most representative types) and so represent a moderatethough systematic departure from the standard benchmarkFinally we show that the results we document above hold forboth beliefs held by conservatives and beliefs held by liberals (seeTables A9 A10 and A11 in Online Appendix G)

V Conclusion

We present a model of stereotypical thinking in which DMsmaking predictions about a group overweight the grouprsquos mostdistinctive types These overweighted types are not the mostlikely ones given the DMrsquos data but the most representativeones in the sense of being the most diagnostic of the group rela-tive to other groups Representativeness implies that what ismost distinctive of a group depends on what group it is comparedwith We present experimental evidence that confirms this con-text dependence in recall-based assessments of groups Finallywe evaluated the predictions of the model using political data fromexisting large-scale surveys We find context dependence to be akey feature of beliefs Given the richness of the political data wecan go a step further and identify a role for representativeness inparticular As the representativeness of tail types increases beliefsof a group are distorted in the direction of that tail

Our approach provides a parsimonious and psychologicallyfounded account of how DMs generate simplified representationsof reality from social groups to stock returns and offers a unifiedaccount of disparate pieces of evidence relating to this type of

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uncertainty The model captures the central fact that stereotypeshighlight the greatest difference between groups thus explainingwhy some stereotypes are very accurate while others lack valid-ity Still stereotypes often have a kernel of truth when they arebased on systematicmdasheven if smallmdashdifferences between groupsThis logic allows us to describe a number of heuristics and psy-chological biases many of which arise in the context of predictionproblems Generically our model generates overreaction to diag-nostic information

Our model is based on representativeness and does not cap-ture all the features of stereotypical thinking However it cap-tures perhaps the central feature when we think of a group wefocus on what is most distinctive about it and neglect or under-weight the rest

Saeuroıd Business School University of Oxford

Ohio State University and Harvard Business School

Universita Bocconi and Innocenzo Gasparini Institute

for Economic Research

Harvard University

Supplementary Material

An Online Appendix for this article can be found at QJEonline (qjeoxfordjournalorg)

References

Adorno Theodor Else Frenkel-Brunswik Daniel Levinson and Nevitt SanfordThe Authoritarian Personality (New York Harper amp Row 1950)

Arrow Kenneth lsquolsquoThe Theory of Discriminationrsquorsquo in Discrimination in LaborMarkets Orley Ashenfelter and Albert Rees eds (Princeton NJPrinceton University Press 1973)

Ashton Michael and Victoria Esses lsquolsquoStereotype Accuracy Estimating theAcademic Performance of Ethnic Groupsrsquorsquo Personality and SocialPsychology Bulletin 25 (1999) 225ndash236

Barberis Nicholas Andrei Shleifer and Robert Vishny lsquolsquoA Model of InvestorSentimentrsquorsquo Journal of Financial Economics 49 (1998) 307ndash343

Bayer Sylvia lsquolsquoThe Accuracy of Academic Gender Stereotypesrsquorsquo Sex Roles 40(1999) 787ndash813

Benjamin Dan James Choi and Joshua Strickland lsquolsquoSocial Identity andPreferencesrsquorsquo American Economic Review 100 (2010) 1913ndash1928

Benjamin Dan Matthew Rabin and Collin Raymond lsquolsquoA Model of Non-Belief inthe Law of Large Numbersrsquorsquo Journal of the European Economic Association15 (2015) 515ndash544

Bertrand Marianne lsquolsquoNew Perspectives on Genderrsquorsquo Handbook of LaborEconomics 4 (2011) 1543ndash1590

Bodoh-Creed Aaron Dan Benjamin and Matthew Rabin lsquolsquoThe Dynamics of Base-Rate Neglectrsquorsquo mimeo Haas Business School 2013

STEREOTYPES 1791

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ibrary on October 28 2016

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ownloaded from

Bohnet Iris Alexandra van Geen and Max Bazerman lsquolsquoWhen PerformanceTrumps Gender Bias Joint versus Separate Evaluationrsquorsquo ManagementScience 5 (2016) 1225ndash1234

Bordalo Pedro Nicola Gennaioli and Andrei Shleifer lsquolsquoSalience Theory of Choiceunder Riskrsquorsquo Quarterly Journal of Economics 127 (2012) 1243ndash1285

mdashmdashmdash lsquolsquoSalience and Consumer Choicersquorsquo Journal of Political Economy 121(2013) 803ndash843

Briton Nancy and Judith Hall lsquolsquoBeliefs about Female and Male NonverbalCommunicationrsquorsquo Sex Roles 32 (1995) 79ndash90

Buser Thomas Muriel Niederle and Hessel Oosterbeek lsquolsquoGenderCompetitiveness and Career Choicesrsquorsquo Quarterly Journal of Economics 129(2014) 1409ndash1447

Carrell Scott Marianne Page and James West lsquolsquoSex and Science How ProfessorGender Perpetuates the Gender Gaprsquorsquo Quarterly Journal of Economics 125(2010) 1101ndash1144

Chambers John and Darya Melnyk lsquolsquoWhy Do I Hate Thee ConflictMisperceptions and Intergroup Mistrustrsquorsquo Personality and SocialPsychology Bulletin 32 (2006) 1295ndash1311

Chan Wayne Robert R McCrae Filip De Fruyt Lee Jussim CorinnaE Lockenhoff Marleen De Bolle Paul T Costa Jr Angelina R SutinAnu Realo Juri Allik Katsuharu Nakazato Yoshiko ShimonakaMartina Hrebıckova Sylvie Graf Michelle Yik Marina Brunner-SciarraNora Leibovich De Figueora Vanina Schmidt Chang-kyo Ahn Hyun-nie Ahn Maria E Aguilar-Vafaie Jerzy Siuta Barbara SzmigielskaThomas R Cain Janet T Crawford Khairul Anwar Mastor Jean-Pierre Rolland Florence Nansubuga Daniel R MiramontezVeronica Benet-Martınez Jerome Rossier Denis Bratko Iris MarusicJamin Halberstadt Mami Yamaguchi Goran Knezevic Thomas A MartinMirona Gheorghiu Peter B Smith Claudio Barbaranelli Lei WangJane Shakespeare-Finch Margarida P Lima Waldemar KlinkoszAndrzej Sekowski Lidia Alcalay Franco Simonetti Tatyana V AvdeyevaV S Pramila and Antonio Terracciano lsquolsquoStereotypes of Age Differences inPersonality Traits Universal and Accuratersquorsquo Journal of Personality andSocial Psychology 103 (2012) 1050ndash1066

Chen Yan Sherry Xin Liu Tracy Xiao and Margaret Shih lsquolsquoWhich Hat to WearImpact of Natural Identities on Coordination and Cooperationrsquorsquo Games andEconomic Behavior 84 (2014) 58ndash86

Coffman Katherine lsquolsquoEvidence on Self-Stereotyping and the Contribution ofIdeasrsquorsquo Quarterly Journal of Economics 129 (2014) 1625ndash1660

Cunningham Tom lsquolsquoComparisons and Choicersquorsquo mimeo Stockholm University2013

Diekman Amanda Alice Eagly and Patrick Kulesa lsquolsquoAccuracy and Bias in theStereotypes about the Social and Political Attitudes of Women and MenrsquorsquoJournal of Experimental Social Psychology 38 (2002) 268ndash282

Eccles Jacquelynne S Janis E Jacobs and Rena D Harold lsquolsquoGender RoleStereotypes Expectancy Effects and Parentsrsquo Socialization of GenderDifferencesrsquorsquo Journal of Social Issues 46 (1990) 183ndash201

Fryer Roland and Matthew Jackson lsquolsquoA Categorical Model of Cognition andBiased Decision-Makingrsquorsquo BE Journal of Theoretical Economics 8 (2008)1ndash42

Fryer Roland and Steven Levitt lsquolsquoAn Empirical Analysis of the Gender Gap inMathematicsrsquorsquo American Economic Journal Applied Economics 2 (2010)210ndash240

Gennaioli Nicola and Andrei Shleifer lsquolsquoWhat Comes to Mindrsquorsquo Quarterly Journalof Economics 125 (2010) 1399ndash1433

Gennaioli Nicola Andrei Shleifer and Robert Vishny lsquolsquoNeglected RisksFinancial Innovation and Financial Fragilityrsquorsquo Journal of FinancialEconomics 104 (2012) 452ndash468

Gilens Martin lsquolsquoRace and Poverty in America Public Misperceptions and theAmerican News Mediarsquorsquo Public Opinion Quarterly 60 (1996) 515ndash541

Glaeser Edward lsquolsquoThe Political Economy of Hatredrsquorsquo Quarterly Journal ofEconomics 120 (2005) 45ndash86

QUARTERLY JOURNAL OF ECONOMICS1792

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

Glover Dyland Amanda Pallais and William Pariente lsquolsquoDiscrimination as a Self-Fulfilling Prophecy Evidence from French Grocery Storesrsquorsquo mimeo HarvardUniversity 2015

Goldin Claudia Lawrence Katz and Ilyana Kuziemko lsquolsquoThe Homecoming ofAmerican College Women The Reversal of the College Gender GaprsquorsquoJournal of Economic Perspectives 20 (2006) 133ndash156

Graham Jesse Brian Nosek and Jonathan Haidt lsquolsquoThe Moral Stereotypes ofLiberals and Conservatives Exaggeration of Differences across thePolitical Spectrumrsquorsquo PLoS One 7 (2012) 1ndash13

Grether David lsquolsquoBayes Rule as a Descriptive Model The RepresentativenessHeuristicrsquorsquo Quarterly Journal of Economics 95 (1980) 537ndash557

Griffin Dale and Amos Tversky lsquolsquoThe Weighing of Evidence and theDeterminants of Confidencersquorsquo Cognitive Psychology 24 (1992) 411ndash435

Guiso Luigi Ferdinando Monte Paola Sapienza and Luigi Zingales lsquolsquoCultureGender and Mathrsquorsquo Science 320 (2008) 1164ndash1165

Hilton James and William Von Hippel lsquolsquoStereotypesrsquorsquo Annual Review ofPsychology 47 (1996) 237ndash271

Hyde Janet Sara Lindberg Marcia Linn Amy Ellis and Caroline WilliamslsquolsquoGender Similarities Characterize Math Performancersquorsquo Science 321 (2008)494ndash495

Judd Charles and Bernardette Park lsquolsquoDefinition and Assessment of Accuracy inSocial Stereotypesrsquorsquo Psychological Review 100 (1993) 109ndash128

Jussim Lee Jarret Crawford Stephanie Anglin John Chambers Sean Stevensand Florette Cohen lsquolsquoStereotype Accuracy One of the Largest and MostReplicable Effects in All of Social Psychologyrsquorsquo in The Handbook ofPrejudice Stereotyping and Discrimination Todd Nelson ed (MahwahNJ Lawrence Erlbaum 2015)

Kahneman Daniel and Amos Tversky lsquolsquoSubjective Probability A Judgment ofRepresentativenessrsquorsquo Cognitive Psychology 3 (1972) 430ndash454

mdashmdashmdash lsquolsquoOn the Psychology of Predictionrsquorsquo Psychological Review 80 (1973) 237ndash251

Kaplowitz Stan Bradley Fisher and Clifford Broman lsquolsquoHow Accurate ArePerceptions of Social Statistics about Blacks and Whitesrsquorsquo Public OpinionQuarterly 67 (2003) 237ndash243

Kersten Daniel Pascal Mamassian and Alan Yuille lsquolsquoObject Perception asBayesian Inferencersquorsquo Annual Review of Psychology 55 (2004) 271ndash304

Klein Richard Kate A Ratliff Michelangelo Vianello Reginald B Adams JrStepan Bahnik Michael J Bernstein Konrad Bocian Mark J BrandtBeach Brooks Claudia Chloe Brumbaugh Zeynep CemalcilarJesse Chandler Winnee Cheong William E Davis Thierry DevosMatthew Eisner Natalia Frankowska David Furrow Elisa Maria GallianiFred Hasselman Joshua A Hicks James F Hovermale S Jane HuntJeffrey R Huntsinger Hans IJzerman Melissa-Sue John Jennifer A Joy-Gaba Heather Barry Kappes Lacy E Krueger Jaime Kurtz CarmelA Levitan Robyn Mallett Wendy L Morris Anthony J Nelson JasonA Nier Grant Packard Ronaldo Pilati Abraham M RutchickKathleen Schmidt Jeanine L Skorinko Robert Smith Troy G SteinerJustin Storbeck Lyn M Van Swol Donna Thompson Anna van rsquot VeerLeigh Ann Vaughn Marek Vranka Aaron Wichman Julie A Woodzickaand Brian A Nosek lsquolsquoInvestigating Variation in Replicability A ManyLabs Replication Projectrsquorsquo Social Psychology 45 (2014) 142ndash152

Lundberg Shelly and Richard Startz lsquolsquoPrivate Discrimination and SocialIntervention in Competitive Labor Marketsrsquorsquo American Economic Review73 (1983) 340ndash347

Madon Stephanie Max Guyll Kathy Aboufadel Eulices Montiel Alison SmithPolly Palumbo and Lee Jussim lsquolsquoEthnic and National Stereotypes ThePrinceton Trilogy Revisited and Revisedrsquorsquo Personality and SocialPsychological Bulletin 27 (2001) 996ndash1010

Martin Carol lsquolsquoA Ratio Measure of Sex Stereotypingrsquorsquo Journal of Personality andSocial Psychology 52 (1987) 489ndash499

STEREOTYPES 1793

at Harvard L

ibrary on October 28 2016

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McCauley Clark Krishna Thangavelu and Paul Rozin lsquolsquoSex Stereotyping ofOccupations in Relation to Television Representations and Census FactsrsquorsquoBasic and Applied Social Psychology 9 (1988) 197ndash212

Mullainathan Sendhil lsquolsquoThinking through Categoriesrsquorsquo mimeo HarvardUniversity 2002

Ortoleva Pietro and Erik Snowberg lsquolsquoOverconfidence in Political BehaviorrsquorsquoAmerican Economic Review 105 (2015) 504ndash535

Phelps Edmund lsquolsquoThe Statistical Theory of Racism and Sexismrsquorsquo AmericanEconomic Review 62 (1972) 659ndash661

Pope Devin and Justin Sydnor lsquolsquoGeographic Variation in the Gender Differencesin Test Scoresrsquorsquo Journal of Economic Perspectives 24 (2010) 95ndash108

Rabin Matthew lsquolsquoInference by Believers in the Law of Small NumbersrsquorsquoQuarterly Journal of Economics 117 (2002) 775ndash816

Rabin Matthew and Joel Schrag lsquolsquoFirst Impressions Matter A Model ofConfirmatory Biasrsquorsquo Quarterly Journal of Economics 114 (1999) 37ndash82

Rabin Matthew and Dimitri Vayanos lsquolsquoThe Gamblerrsquos and Hot-Hand FallaciesTheory and Applicationsrsquorsquo Review of Economic Studies 77 (2010) 730ndash778

Reuben Ernesto Paola Sapienza and Luigi Zingales lsquolsquoHow Stereotypes ImpairWomenrsquos Careers in Sciencersquorsquo Proceedings of the National Academy ofSciences 111 (2014) 4403ndash4408

Rosch Eleanor lsquolsquoNatural Categoriesrsquorsquo Cognitive Psychology 4 (1973) 328ndash350Ryan Carey S lsquolsquoAccuracy of Black and White College Studentsrsquo In-Group and

Out-Group Stereotypesrsquorsquo Personality and Social Psychology Bulletin 22(1996) 1114ndash1127

Schneider David The Psychology of Stereotyping (New York Guilford Press2004)

Schneider David Albert Hastorf and Phoebe Ellsworth Person Perception(Reading MA Addison-Wesley 1979)

Shih Margaret Todd Pittinsky and Nalini Ambady lsquolsquoStereotype SusceptibilityIdentity Salience and Shifts in Quantitative Performancersquorsquo PsychologicalScience 10 (1999) 80ndash83

Shih Margaret Todd Pittinsky and Amy Trahan lsquolsquoDomain-Specific Effects ofStereotypes on Performancersquorsquo Self and Identity 5 (2006) 1ndash14

Steele Claude Whistling Vivaldi How Stereotypes Affect Us and What We CanDo (New York Norton 2010)

Tenenbaum Joshua and Thomas Griffiths lsquolsquoThe Rational Basis ofRepresentativenessrsquorsquo 23rd Annual Conference of the Cognitive ScienceSociety (2001) 1036ndash1041

Tversky Amos and Daniel Kahneman lsquolsquoExtensional versus Intuitive ReasoningThe Conjunction Fallacy in Probability Judgmentrsquorsquo Psychological Review 90(1983) 293ndash315

Weinberger Catherin lsquolsquoIs the Science and Engineering Workforce Drawn fromthe Far Upper Tail of the Math Ability Distributionrsquorsquo mimeo UCSB 2005

Westfall Jacob Leaf Van Boven John Chambers and Charles Judd lsquolsquoPerceivingPolitical Polarization in the United States Party Identity Strength andAttitude Extremity Exacerbate the Perceived Partisan DividersquorsquoPsychological Science 10 (2015) 145ndash158

Wolsko Christopher Bernadette Park Charles Judd and Bernd WittenbrinklsquolsquoFraming Interethnic Ideology Effects of Multicultural and Color-BlindPerspectives on Judgments of Groups and Individualsrsquorsquo Journal ofPersonality and Social Psychology 78 (2000) 635ndash654

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Page 8: I. Introduction · uneducated at the beginning of the 20th century, and as high achievers at the beginning of the 21st (Madon et al. 2001). Social science has produced three broad

II A Model of Representativeness and Stereotypes

IIA The Model

A decision maker (DM) faces a prediction problem such asassessing the ability of a job candidate from a certain ethnicgroup the future performance of a firm belonging to a certainsector or future earnings based on own gender

Formally there is a set of types of interest T and an overallpopulation of which group G is a subset The set of typesT can be unordered (eg occupations) or ordered (and typi-cally cardinal eg earnings levels) When T is ordered wewrite T frac14 ft1 tTg with t1 lt t2 lt lt tT6 There is a probabil-ity or frequency distribution 2 ethT THORN that induces a condi-tional distribution PrethT frac14 tjGTHORN when restricted to G7 In whatfollows we denote by tG frac14 PrethT frac14 tjGTHORN the probability of typet in group G and by G the vector ethtGTHORNt2T containing the condi-tional distribution

The DMrsquos goal is to assess the distribution of the types ofinterest in a particular group G Although the DM has stored inmemory the full distribution he retrieves from memory a dis-torted version of G that overweights the probability of thosetypes that are most representative of G relative to a comparisongroup ndashG Generically ndashG is a group in that is distinct from Gnamely G7 nG although in some cases it can coincide withthe complement of G

According to Tversky and Kahneman (1983) a type t is rep-resentative of G if it is relatively more likely to occur in G thanin ndashG Definitions 1 and 2 formalize this representativeness-based recall following GS (2010)

6 For simplicity we also use T to denote the number of types jTj The modelapplies also to cases in which types (i) are multidimensional capturing a bundle ofattributes such as occupation and nationality or (ii) are continuous We considerthese cases in Online Appendixes C and D respectively Also G may represent anycategory of interest such as the historical performance of a firm or industry actionsavailable to a decision maker (T = set of payoffs G = occupations) or categories inthe natural world (T = ability to fly G = birds)

7 In many applications each individual in is characterized by a determin-istic type (eg age hair color) As a result ethtTHORN frac14 1

jj For instance each Floridian

has a single age type (at the finest temporal resolution) When types are stochasticinstead such as when estimating future earnings of a person or a firm each indi-vidual is described by a nondegenerate distribution

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DEFINITION 1 The representativeness of type t for group G givencomparison group ndashG is defined as the likelihood ratio

RethtGGTHORN tG

tGeth2THORN

Definition 1 implies that DMs are attuned to log differencesin probabilities representativeness depends on the percentageprobability increase of a type from ndashG to G This captures aform of diminishing sensitivity whereby for a fixed probabilitydifference a type is more likely to be overweighed if it is unlikelyin the comparison group8 Thus the representative age of aFloridian is 65+ because people in this age bracket are morecommon in Florida than in the rest of the United StatesStatistically representative types are also diagnostic of thetarget group G Indeed the higher is RethtGGTHORN the more confi-dent is a Bayesian DM observing t that t belongs to G rather thanto ndashG9

The ease of recall of highly representative types affectsjudgments because more easily recalled types are overweighted

We model distorted recall as follows Denote by RethtGGTHORN

tG

tG

t2T

the vector of representativeness of all types in G

We then have

8 Our definition of representativeness links to Weberrsquos law of sensory percep-tion see Section IIB It also links to our previous work on salience in which wepostulated that log differences in payoffs determine the attention to lottery payoffs(Bordalo Gennaioli and Shleifer 2012) and to goodsrsquo attributes (BordaloGennaioli and Shleifer 2013) Equation (2) establishes the same principle for thedomain of probabilities

9 This insight led Tenenbaum and Griffiths (2001) to define representative-ness as individualsrsquo sense as intuitive Bayesians of updating in reaction to dataTheir definition like ours is in terms of the likelihood ratio However Tenenbaumand Griffiths interpret representativeness as a mechanism that affects intuitivejudgments of similarity rather than beliefs (eg it accounts well for lab evidencewhere subjects are asked to rank types in terms of representativeness or ofstrength of association with a group) Accordingly they do not consider the possi-bility of systematically distorted and context dependent beliefs

STEREOTYPES 1761

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DEFINITION 2 The DM attaches to each type t 2 T in group G adistorted probability

sttG frac14 tG

htethRethtGGTHORNTHORNPs2T sGhsethRethtGGTHORNTHORN

eth3THORN

where ht RTthornRthorn is a weighting function such that

(i) The weight ht is a symmetric function of the representa-

tiveness of types s 6frac14 t Formally ht frac14 h tG

tG

sG

sG

s2Tn tf g

where h Rthorn RT1thorn Rthorn is a function that is invariant to

a permutation of the last T ndash 1 arguments(ii) Weighing of a type increases in own representativeness

and decreases in the representativeness of other typesFormally the function hethTHORN is weakly increasing in itsfirst argument and weakly decreasing in the other T 1arguments

We call the distribution ethsttGTHORNt2T the stereotype for G If a type

t is objectively more likely namely tG is higher then the ste-reotype attaches higher probability to it By property i distor-tions are due exclusively to the fact that a type is more or lessrepresentative than the others In particular if all types areequally representative the DM equally weighs all of them ath(1) and holds rational expectations about G If instead the rep-resentativeness of different types differs property ii implies thatthe stereotype ceteris paribus overweights the probability of morerepresentative types

Most of the results we explore in this article hold for a gen-eral weighing function htethTHORN Specific functional forms captureadded assumptions about the psychology of representativeness-based recall and are useful in applications We outline a few spe-cifications and their properties

Rank-based stereotypes the ranking of the representa-tiveness of different types shapes distortions Denote byrethtTHORN 2 f1 Tg the representativeness ranking of type tWhen r(t) = 1 type t is the most representative one (po-tentially with ties) We can specify two ways in which atypersquos representativeness ranking distorts its probability

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(i) Rank-based truncation the DM only recalls the typesthat have representativeness ranking of at most dnamely ft 2 TjrethtTHORN dg Zero probability is attachedto the remaining types10 Denote by IethrethtTHORN dTHORN an in-dicator function taking the value 1 if the representa-tiveness ranking of t is at most d Then theweighting function is ht frac14 IethrethtTHORN dTHORN so that

sttG frac14 tG

IethrethtTHORN dTHORNPs2T sGIethrethsTHORN dTHORN

which is the true conditional probability within re-called types This assumption is used in Gennaioliand Shleifer (2010)11

(ii) Rank-based discounting the DM discounts by a con-stant factor 2 frac1201 the odds of type t relative to itsimmediate predecessors in the representativenessranking Lower implies stronger discounting ofless representative types Formally the weightingfunction is ht frac14

rethtTHORN so that

sttG frac14 tG

rethtTHORNPs2T sG

rethsTHORN

Representativness-based discounting all else equal theweight attached by the DM to type t increases continuouslywith its representativeness One convenient formulation is

ht frac14tG

tG

so that

10 These neglected types are not viewed as impossible they are just assignedzero probability in the DMrsquos current thinking This formulation allows us to modelsurprise and reactions to unforeseen contingencies which have proved useful in-gredients in modeling probabilistic judgments (GS 2010) as well as neglect of risk infinancial crises (Gennaioli Shleifer and Vishny 2012)

11 Specifically in GS (2010) the assessed probability that a certain hypothesisG is true is equal to

Pr ethGTHORN frac14

Pt tGIethrethtTHORN dTHORNP

t tGIethrethtTHORN dTHORN thornP

t t=GIethrethtTHORN dTHORN

which increases in the ratio between the total probability mass recalled for Gand that recalled for G frac14 nG

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sttG frac14 tG

tG

tG

P

s2T sGsG

sG

where 0 captures the extent to which representative-ness distorts beliefs This formulation is particularly con-venient when dealing with continuous distributions ofthe exponential or power classes

These functional forms all embody the main idea of our modelthat the stereotype overweights the probability of more represen-tative types Rank-based truncation captures a central manifes-tation of limited memory forgetting unrepresentative typesSmoother discounting (based on ranking or on representative-ness) may be more appropriate when the type space is smalland smooth discounting can be more tractable in certain settings

Section III characterizes the general properties of stereotypesIn particular it shows their ability to account for social psycholo-gistsrsquo kernel of truth hypothesis under the general weighting func-tion of Definition 2 To bring the model to the data in Section IVBwe derive linear approximations of stereotypical beliefs by assum-ing that the weighting function is differentiable with respect to atypersquos representativeness This assumption excludes rank-basedweighting but allows for many possibilities

IIB Discussion of Assumptions

Before moving to the formal analysis we discuss some prop-erties and limitations of our approach Representativeness-basedrecall the idea that individuals recall distinctive group types canbe viewed as an instance of what Kahneman and Tversky calllsquolsquoattribute substitutionrsquorsquo When dealing with the difficult questionlsquolsquowhat is the distribution of hair color among the Irishrsquorsquo peopleintuitively answer to the simpler question lsquolsquowhich hair color dis-tinguishes the Irish peoplersquorsquo Critically as discussed byKahneman and Tversky attribute substitution does not occurbecause people misunderstand the original question or mechan-ically confuse the assessment of PrethtjGTHORN with that of PrethGjtTHORNRather it occurs because the distinctive or representative typesimmediately come to mind and individuals anchor their overallprobability judgment to them As a consequence subjects do notonly make mistakes in judging the probability that a Floridian is

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over age 65 They also give too high an answer to the questionlsquolsquowhat is the average age of a Floridianrsquorsquo12

One interesting question is whether the process of stereotyp-ing we describe is optimal in some sense Focusing mental repre-sentations on a few types can be justified by the costs of thinkingor retrieval This approach however is not enough to explainwhy individuals should focus on representative rather thanlikely types We do not formally analyze the optimality of repre-sentativeness here but we mention some relevant considerationsfrom cognitive psychology Kahneman and Tversky (1979) stressthe similarity between many perceptual and cognitive operationsFor instance the highlight of contrastmdasha key principle of visualperceptionmdashis invoked to justify the prospect theory assumptionthat the carriers of utility are changes relative to a referencepoint The same logic applies to our model in which stereotypesprecisely highlight the contrast between groups

In visual perception assessing properties such as brightnesscolor size or distance to an object by comparing them to otherproximate objects has been shown to be optimal in the presence ofmultiplicative background noise (Kersten Mamassian andYuille 2004 Cunningham 2013) Our formulation of representa-tiveness is related to the same idea in the sense that individualsestimating properties of one group stress differences from an-other group In a noisy world in which attention is limited thisprocess may optimally allow for swift reactions to changes ingroup characteristics even if errors are sometimes made13

12 Indeed in many cases mere confusion of PrethtjGTHORNwith PrethGjtTHORNwould not yieldthe phenomenon of stereotyping In the Irish hair color example the probability ofbeing Irish conditional on having red hair is

PrethIrishjredTHORN frac14PrethredjIrishTHORNPrethIrishTHORN

PrethredjIrishTHORNPrethIrishTHORN thorn PrethredjNonIrishTHORNPrethNonIrishTHORN

This probability is clearly very small given that the Irish population is a tinyfraction of the world population Confusion of PrethtjGTHORN with PrethGjtTHORN in this casewould lead to an understatement of the probability of the red-haired Irish

13 To give a simple example suppose thatmdashas in the case of Proposition 3mdashthevariance in the environment increases in the sense that extreme tail events becomemore likely Then a likelihood-based stereotype would detect no change whereas arepresentativeness-based stereotype would focus on the heightened probability ofthe tails In particular an asymmetric increase in tail probabilities that shifts themean would be detected by a representativeness-based stereotype even if the dis-tributionrsquos mode does not change

STEREOTYPES 1765

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Exploring this idea formally is an interesting avenue for futurework

Consider some limitations of our model First representa-tiveness is not the only heuristic that shapes recall Decisionmakers may for instance find it easier to recall types that aresufficiently likely Another potentially important mechanism isavailability understood by Kahneman and Tversky (1972) as thelsquolsquoeasersquorsquo with which information comes to mind (because of actualfrequency or repetition) In Online Appendix E we present a trun-cation-based recall mechanism in which distortions are driven bya combination of representativeness and likelihood of types(which is equivalent to relaxing property i in Definition 2) Thismodel can offer a useful starting point to capture availability aswell even though a full model of availability is beyond the scopeof this article Even in this more general setting the influence ofrepresentativeness on recall is the driving force of stereotypesthat in line with the social psychology perspective are basedon underlying differences among groups As we show in SectionIV this feature is critical in accounting for the evidence

The second set of model-related issues concerns how to spe-cify the elements of Definition 1 in applications group G the typespace T and the reference group ndashG Take the specification of thegroup G and of the type space T Often the problem itself pro-vides a natural specification of these features This is the case inthe empirically important class of lsquolsquoclosedrsquorsquo questions such asthose used in surveys which provide respondents with a set ofalternatives as in the data we use in Section IV More generallythe problem solved by the DMmdashsuch as evaluating the resume ofa job applicant coming from a certain ethnic groupmdashprimes agroup a dimension of interest and a set of types (eg the appli-cantrsquos qualification or skill levels) When types have a naturalorder such as income age or education the granularity of T isalso naturally given by the problem (income age and years ofschooling brackets) When the set of types is not specified by theproblem DMs spontaneously generate one14 It would be useful tohave a model of which dimensions and types come to mind par-ticularly for more open-ended problems Psychologists have

14 For example suppose a person is asked to guess the typical occupation of ademocratic voter in an lsquolsquoopen-endedrsquorsquo format (without being provided a set of alter-natives) Here the level of granularity at which types are defined is not obvious (egteacher versus a university teacher vs a professor of comparative literature)

QUARTERLY JOURNAL OF ECONOMICS1766

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sought to construct a theory of natural types and dimensions(Rosch 1973) We do not make a contribution to this problembut we note that in many problems of interest in economics thedimension as well as the set of types is naturally givenFurthermore in our model details of the type space can be impor-tant under rank-based truncation but they matter less undersmooth discounting

Consider finally the role of the comparison group ndashG Thisgroup captures the context in which a stereotype is formed andagain is often implied by the problem when G = Floridians ndashG =rest of US population when G = African Americans ndashG = whiteAmericans A distinctive prediction of our model confirmed byour experiments in Section IVA is that the stereotype for agiven group G depends on the comparison group ndashG15 WhenndashG is not pinned down by the problem itself to derive testablepredictions from representativeness we set G frac14 nG where

is the natural population over which the unconditional distribu-tion of types is measured

III Properties of Stereotypes

We now study stereotypical beliefs and their accuracy Toillustrate the role of representativeness we first ask to whatextent the most representative type is a good fit for the groupnamely whether it is modal Next we assess the accuracy of theentire stereotypical distribution To do so we focus on a cardinaltypes and compare the stereotypersquos mean and variance to the trueones

15 Some empirical papers have taken a similar approach exogenously varyingthe natural comparison group through priming Benjamin Choi and Strickland(2010) show that priming racial or ethnic identity can affect the risk preferences ofparticipants Chen et al (2014) find that Asian students cooperate less with out-group members when primed with their ethnic identity rather than their universityidentity Shih Pittinsky and Ambady (1999) show that Asian American womenstereotype themselves as better or worse in math with corresponding impact onperformance when their ethnicity or gender respectively is primed ShihPittinsky and Trahan (2006) replicate this effect using a verbal task documentingthat Asian American women performed better when their gender rather than theirethnicity was primed Although the generalizability and replicability of priminghas been doubted (Klein et al 2014) this body of evidence is consistent with contextdependence

STEREOTYPES 1767

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IIIA Likely versus Unlikely Exemplars

The most representative type for a group is the one thatagents most easily recall and associate with the group itself forinstance a red-haired Irishman or a 65+-year-old FloridianSocial psychologists call this type the exemplar of the groupAccordingly we define

DEFINITION 3 A type t is an exemplar for G given comparisongroup ndashG when

t 2 arg maxt

tG

tG

Under any specification of the weighting function ht inDefinition 2 overweighting (weakly) increases as we movetoward more representative types so the exemplar is also thetype whose probability is overweighted the most16 By analyzingthe exemplar then we can gauge whether representativenessinduces the DM to overweight a likely type (as happens in stan-dard models of categorical thinking) or an unlikely type Whenoverweighting occurs in unlikely and extreme types the biases ofstereotypes can be particularly severe17

Equation (2) yields the following characterization

PROPOSITION 1 Suppose the conditional distributions G and G

are not identical Consider two extreme cases

(i) If for all t t0

2 T we have that tG gt t0 G if and only iftG gt t0 G then the modal type is not an exemplar forat least one group

(ii) If for all t t0

2 T we have that tG gt t0 G if and only iftG lt t0 G then for each group the modal type is theexemplar

16 Consider the function hethTHORN from Definition 2 When applied to more repre-sentative types the first argument of the function increases while one of the otherT ndash 1 arguments decreases As a result the weighting factor ht (and thus overweigh-ing

sttG

tG) increases as well

17 In the rank-based truncation model the frequency of the exemplar providesa measure of stereotype accuracy By accuracy we mean the extent to which thestereotype minimizes the distance

Pt eth

sttG tGTHORN

2 When d = 1 and only one type isrecalled (there are no ties) accuracy is maximized if the exemplar is the most likelytype and minimized if the exemplar is the least likely type

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Case i says that when groups have similar distributions inthe sense of having the same likelihood ranking the most repre-sentative type is unlikely for at least one group potentially bothRepresentativeness draws the DMrsquos attention to group differ-ences neglecting the fact that the groups are similar and havethe same mode This mechanism generates inaccurate stereo-types and is illustrated by the Florida example This resultholds under any measure of representativeness that differenti-ates the two groups (eg the difference tG tG)

Case ii says that the most representative type tends to belikely for both groups when the distributions are very differentIn this case groups differ the most around their modes so repre-sentativeness and likelihood coincide Thinking of Swedes aslsquolsquoblondrsquorsquo and Europeans as lsquolsquodark hairedrsquorsquo is accurate precisely be-cause these are majority traits of the Swedish and European pop-ulations respectively In these cases stereotyping yields fairlyreliable models Of course there is still some inaccuracy Evenin the case of likely exemplars judgment errors can be signifi-cant For instance voters in some US states are perceived aslsquolsquobluersquorsquo or lsquolsquoredrsquorsquo because a majority of the population votesDemocrat or Republican In reality even in lsquolsquobluersquorsquo states farfrom everyone votes Democrat In the 2012 presidential electionvote shares of either candidate in most states ranged from 40 to6018

When DMs strongly overweight representative types themost severe biases occur when those types are unlikely and ex-treme This is true both under rank based truncations and undersmooth discounting functions (see Section IIIB) Ethnic stereo-types based on crime or terrorism exhibit this error they neglectthe fact that by far the most common types in all groups arehonest and peaceful

IIIB Stereotypical Moments

We now characterize how the first two moments of a distri-bution are distorted by the process of stereotyping To do so wemust restrict our analysis to cardinal ordered types The follow-ing results hold for any weighting function htethTHORN satisfyingDefinition 2 We consider two canonical cases that prove usefulin illustrating the predictions of the model

18 Presidential Election Results NBCNewscom see httpelectionsnbcnewscomnspolitics2012allpresident (accessed 5 September 2016)

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In the first case groups G and ndashG are such that the likelihoodratio tG

tGis monotonic in t The monotone likelihood ratio prop-

erty (MLRP) holds to a first approximation in many empiricalsettings and is also assumed in many economic models such asstandard agency models19 If tG

tGis monotonically increasing (de-

creasing) in t then group G is associated with higher (lower)values of t relative to the comparison group ndashG Formally

PROPOSITION 2 Suppose that MLRP holds and assume wlogthat the likelihood ratio tG

tGis strictly increasing in t Then

for any weighting function htethTHORN that is not constant in therelevant range

EstethtjGTHORN gt EethtjGTHORN gt EethtjGTHORN gt E

stethtjGTHORN

Under MLRP the most representative part of the distribu-tion for G is the right tail if tG

tGincreases in t or the left tail if tG

tG

decreases in t The representative tail is then overweighted whilethe nonrepresentative tail is underweighted As a consequencethe assessed mean E

stethtjGTHORN is too extreme in the direction of therepresentative tail

Critically in line with the social cognition perspective the ste-reotype contains a kernel of truth the DM overestimates the meanof G if this group has a higher mean than the comparison groupnamely EethtjGTHORN gt EethtjGTHORN and conversely if EethtjGTHORN lt EethtjGTHORN TheDM exaggerates this true difference because he inflates the asso-ciation of G with its most representative types20 For instancewhen judging an asset manager who performs well we tend to

19 Examples include the binomial and the Poisson families of distributionswith different parameters The characterization of distributions satisfying MLRPis easier in the case of continuous distributions (see Online Appendix D) two dis-tributions f(x) f ethx THORN that differ only in their mean satisfy MLRP if and only if thedistribution f(x) is log-concave Examples include the exponential and normal dis-tributions To the extent that discrete distributions sufficiently approximate thesedistributions (as the Poisson distribution PoisethTHORN approximates the normal distri-bution Neth THORN for large l) they will also satisfy MLRP

20 Depending on the distribution and the weighing function the DMrsquos assess-ment of the variance VarethtjGTHORNmay also be dampened relative to the truth This isoften true under the truncation weighing function In this case stereotyping effec-tively leads to a form of overconfidence in which the DM holds extreme views andoverestimates the precision of his assessment That extreme views and overconfi-dence (in the sense of over precision) go together has been documented in the settingof political ideology among others (Ortoleva and Snowberg 2015)

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overemphasize skill relative to luck because higher skill levels arerelatively more associated with higher performance This occurseven if for both skilled and unskilled managers high performanceis mostly due to luck

In the second case for which we characterize the stereotypi-cal distributions groups G and ndashG have the same mean EethtjGTHORNfrac14 EethtjGTHORN frac14 EethtTHORN but differ in their variance We abstract fromskewness and higher moments by considering distributionsethtGTHORNt2T and ethtGTHORNt2T that share the same support and are sym-metric around the medianmean EethtTHORN

PROPOSITION 3 Suppose that in G more extreme types are rela-tively more frequent than in ndashG Formally the likelihoodratio tG

tGis U-shaped in t around EethtTHORN Then for any weight-

ing function htethTHORN that is not constant in the relevant rangestereotypical beliefs satisfy

VarstethtjGTHORN gt VarethtjGTHORN gt VarethtjGTHORN gt VarstethtjGTHORN

EstethtjGTHORN frac14 E

stethtjGTHORN frac14 EethtTHORN

When group G has a higher relative prevalence of extremetypes its representative types are located at both extremes of thedistribution The DMrsquos beliefs about G are then formed by over-weighting both tails while underweighting the unrepresentativemiddle The overweighting of Grsquos tails causes the assessment ofits variance VarstethtjGTHORN to be too high For example the skill dis-tribution of immigrants to the United States may be perceived ashaving very fat tails or even bimodal with immigrants beingperceived as either unskilled or very skilled relative to the resi-dent population The mean of the group in contrast is assessedcorrectly because the stereotypical distribution remains symmet-ric around EethtTHORN As before the stereotype contains a kernel oftruth It induces the agent to exaggerate the true differences be-tween groups namely the higher variance of G relative to itscounterpart

We present a number of extensions of the model in the OnlineAppendix We first consider multidimensional type spaces andshow that stereotypes center around the dimension wheregroups differ the most in line with the kernel of truth logic(Online Appendix C) Multidimensional stereotypes imply thatthe dimension we think about is influenced by context For

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example the Irish are stereotyped as red-haired when comparedwith the European population However when compared withthe Scots a more plausible stereotype for the Irish is lsquolsquoCatholicrsquorsquobecause religion is the dimension along which Irish and Scotsdiffer the most

In Online Appendix D we extend the model to continuoustype spaces Many settings of interest in economics can be use-fully described by continuous probability distributions and weshow our model is particularly tractable in this case In OnlineAppendix E we relax Definition 2 and allow weighting of types toalso be influenced by their likelihood We show that the basicinsight that stereotypes contain a kernel of truth carries throughto these cases as well

To summarize the psychology of representativeness yieldsstereotypes that are consistent with the social cognition approachin which individuals assess groups by recalling and focusing ondistinctive group traits When there are systematic differencesbetween groups stereotypes get the direction right but exagger-ate differences

IIIC Some Examples

A growing body of field and experimental evidence points to awidespread belief that women are worse than men at mathemat-ics (Eccles Jacobs and Harold 1990 Guiso et al 2008 CarrellPage and West 2010) This belief persists despite the fact that fordecades women have been gaining ground in average schoolgrades including mathematics and have recently surpassedmen in overall school performance (Goldin Katz and Kuziemko2006 Hyde et al 2008) This belief shared by men and women(Reuben Sapienza and Zingales 2014) may help account for thegender gap in the choices of high school tracks college degreesand careers with women disproportionately choosing humanitiesand health-related areas (Weinberger 2005 Buser Niederle andOosterbeek 2014) and forgoing significant wage premiums toquantitative skills (Bertrand 2011)

Gender stereotypes in mathematics particularly beliefs thatexaggerate the extent of average differences are consistent withthe predictions of our model The fact that men are overrepre-sented at the very highest performance levels leads a stereotyp-ical thinker to exaggerate the magnitude of mean differencesFigure I shows the score distributions from the mathematics

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section of 2013rsquos Scholastic Aptitude Test (SAT) for men andwomen21 The distributions are very similar with averagescores slightly higher for men (531 versus 499 out of 800)However scores for men have a heavier right tail with mentwice as likely to have a perfect SAT math score than women22

In light of such data the stereotypical male performance in math-ematics is high while the stereotypical female performance ispoor Predictions based on such stereotypes are inaccurate exag-gerating true differences Consistent with this prediction exper-imental evidence shows that both genders underestimatewomenrsquos ability in simple math tasks even controlling for pastperformance (Reuben Sapienza and Zingales 2014) Coffman(2014) shows a similar pattern extends to confidence about ownability in other male-typed domains with women reporting sig-nificantly less confidence in gender-incongruent than gender-congruent tasks Our model suggests that these patterns mightcome from stereotypes based on gender differences in the righttail of the distribution While differences in the right tail of thedistribution are unlikely to be relevant for most decisions stereo-typical thinking driven by these differences has the potential toimpact economically important decisions whether through self-stereotyping (ie choice of careers or majors as in BuserNiederle and Oosterbeek 2014) or through discrimination (iehiring decisions as in Bohnet van Geen and Bazerman 2016)

The logic of exaggerated yet directionally correct stereotypesalso sheds light on the well-documented phenomenon of base rateneglect (Kahneman and Tversky 1973) Indeed Proposition 2implies that the DM overreacts to information that assigns

21 Standardized test performance measures not only innate ability but alsoeffort and investment by third parties (Hyde et al 2008) The mapping of test per-formance into inferences about innate ability is an issue not addressed by ourmodel

22 For 2013 SAT Mathematics scores see httpmediacollegeboardcomdigitalServicespdfresearchSAT-Percentile-Ranks-By-Gender-Ethnicity-2013pdf Results are similar for the National Assessment of Educational Progress(NAEP) which are more representative of the overall population For 2012NAEP scores for 17-year-olds in mathematics see httpnationsreportcardgovltt_2012age17maspx See Hyde et al (2008) Fryer and Levitt (2010) and Popeand Sydnor (2010) for in-depth empirical analyses of the gender gap inmathematics

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people to groups precisely because such information generatesextreme stereotypes Consider the classic example in which amedical test for a particular disease with a 5 prevalence has a90 rate of true positives and a 5 rate of false positives The testassigns each person to one of two groups + (positive test) or ndash(negative test) The DM estimates the frequency of the sick type(s) and the healthy type (h) in each group The test is informativea positive result increases the relative likelihood of sickness anda negative result increases the relative likelihood of health forany prior Formally

PreththornjsTHORN

PreththornjhTHORNgt 1 gt

PrethjsTHORN

PrethjhTHORNeth4THORN

This condition has clear implications the representative personwho tests positive is sick while the representative person whotests negative is healthy Following Proposition 2 the DMreacts to the test by moving his priors too far in the right di-rection generating extreme stereotypes He greatly boosts hisassessment that a positively tested person is sick but also thata negatively tested person is healthy Because most people arehealthy the DMrsquos assessment about the group that tested neg-ative is fairly accurate but is severely biased for the group that

FIGURE I

SAT Mathematics Scores by Gender (2013)

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tested positive This analysis formalizes Tversky andKahnemanrsquos (1983) verbal account of base rate neglect23

The same mechanism may underlie several other instanceswhere DMs overweight diagnostic information When assessingan employeersquos skill level an employer attributes high perfor-mance to high skill because high performance is the distinctivemark of a talented employee Because he neglects the possibilitythat some talented employees perform poorly and that somenontalented ones perform well (perhaps due to stochasticity inthe environment) the employer has too much faith in skill andneglects the role of luck in accounting for the output Similarlywhen assessing the performance of firms in a hot sector of theeconomy (eg G = internet) an investor recalls highly successfulfirms in that sector (t = return of Google Amazon etc) He ne-glects the possibility of firms being unsuccessful because lack ofsuccess is statistically nondiagnostic and psychologically nonrep-resentative of a growing sectormdasheven if it is likely This causesexcessive optimism (in that the expectation of growth is unrea-sonably high) and overconfidence (in that the variability in earn-ings growth considered possible is truncated) True the hot sectormay have better growth opportunities on average but represen-tativeness exaggerates this feature and induces the investor toneglect a significant risk of failure

IV Evidence on Representativeness and Stereotypes

Testing our model requires evaluating the beliefs individualshold about a target group against the true distribution of thattarget group over an attribute space An ideal data set would

23 Our account is distinct from a mechanical underweighting of base rates inBayes rule as in Grether (1980) and Bodoh-Creed Benjamin and Rabin (2013) Inthose models upon receiving the test results the DM can update his beliefs in thewrong direction he can be less confident that a person is healthy after a negativetest than under his prior which cannot happen in our model Although this predic-tion of our model seems consistent with introspection we are not aware of experi-mental evidence on this point Griffin and Tversky (1992) present evidenceconsistent with pure neglect of base rates but in a significantly different tasknamely inferring the bias of a coin from a history of coin flips Such experimentsare hard to compare with the predictions of our model because subjects are asked togenerate distributions of different numbers of coin flips in their minds which is amuch more involved task than to recall types of a given distribution Their assess-ments then might be wrong for other reasons See Bodoh-Creed Benjamin andRabin (2013) for a detailed discussion

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consist of naturally defined groups with known distributions overa given space of types and a corresponding set of beliefs about thedistribution of each group over that space of types This wouldallow us to test for exaggeration of true differences betweengroups and to ask whether this exaggeration is well predictedby overweighting representative types To identify a causal rolefor representativeness or context dependence we would need ex-ogenous variation in either the comparison group ndashG or in thedistributions over the type spaces This is unavailable in existingdata sets Accordingly we take a two-pronged approach First wecreate a controlled laboratory environment that allows us toinduce the exogenous variation in representative types that weneed to test causality then we reanalyze existing field evidence tocheck for consistency with our predictions

In testing our model we focus on the two main implicationsof representativeness-based stereotypes

Context dependence the stereotype of a target group de-pends on the characteristics of the reference group it iscompared to

Kernel of truth stereotypes depend on group character-istics andmdashin most (precisely characterized) settingsmdashare slanted toward representative types

We test the first property with a lab experiment (SectionIVA) We then turn to survey data on beliefs about US politicalgroups (Section IVB) for an empirical analysis that explores thesecond property The survey data are more tightly linked to ourinterest in social stereotypes The laboratory experiment allowsus to directly test the role of representativeness in generatingcontext dependent beliefs Online Appendixes F and G provideall details and additional results for the experiments and fieldevidence

IVA Lab Evidence on Representativeness and ContextDependence

The influence of the representativeness heuristic on recalland on beliefs has been extensively documented in the lab(Kahneman and Tversky 1972 1973) Our goal is to considerhow representativeness as formalized in equation (2) gives riseto context-dependent beliefs To our knowledge the possibility

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that representativeness may generate context dependence hasnot been tested before

To assess this prediction we perform a controlled laboratoryexperiment that allows us to isolate representativeness frommany confounding factorsmdashhistorical sociological or other-wisemdashthat may affect stereotype formation in the real worldWe construct our own groups of ordinary objects creating atarget group G and a comparison group ndashG We hold thetarget group G fixed and explore how participant impressions ofit change as we change the comparison group ndashG and thusrepresentativeness

We conducted several experiments in the laboratory and onAmazon Mechanical Turk Each involves a basic three-stepdesign First participants are shown the target group and a ran-domly assigned comparison group for 15 seconds In this timedifferences between groups can be noticed but the groupsrsquo precisecompositions cannot be memorized The second step consists of afew filler questions which briefly draw the participantsrsquo cognitivebandwidth away from their observation Finally participants areasked to assess the groups they saw Participants are incentiv-ized to provide accurate answers

We randomly assign participants to either the Control or theRepresentativeness condition In the Control condition G and ndashGhave nearly identical distributions so that all types are similarlyrepresentative for each group In the Representativeness condi-tion ndashG is changed in such a way that a certain type becomes veryrepresentative for G Context dependence implies that the assess-ment of G should now overweight this representative type eventhough the distribution of G itself has not changed

We ran six experiments of this form with design changesfocused on reducing participant confusion and removing con-founds We describe the final and most refined version of theseexperiments here In an attempt to provide a overview of the re-sults while remaining concise we provide the results from pooledspecifications that use all data collected In Online Appendix Fwe offer additional details and report all experiments conductedWe also give instructions and materials for each experiment thefull data set is available by request

Consider first the experiment illustrated in Figure II Agroup of 25 cartoon girls is presented next to a group of 25 cartoonboys in T-shirts of different colors blue green or purple In theControl condition (Figure II Panel a) the groups have identical

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color distributions (13 purple 12 green) so no color is represen-tative of either group The Representativeness condition (Panel b)compares the same group of girls with a different group of boysfor whom green shirts are replaced with blue shirts Now onlygirls wear green and only boys wear blue These colors althoughstill not the most frequent for either group are now most repre-sentative For each group girls and boys participants are asked anumber of questions concerning the frequency of T-shirts of dif-ferent colors worn by that group

Applying our model in the control condition the type space isT frac14 fgreen purpleg and the groups are G = girls and ndashG = boysGiven that the color distributions are identical across groups both

types are equally representativegreengirls

greenboysfrac14 1 frac14

purplegirls

purpleboys As a result

assessment of G should be correct on average stcontrolgreengirls frac14 greengirls

and stcontrolpurplegirls frac14 purplegirls for any weighing function (the same is

true about assessments of ndashG)In the treatment condition the distribution of shirt colors re-

mains the same for girls For boys green shirts are changed intoblue Thus the type space changes to T frac14 fgreen purple bluegand the representative color for girls becomes greengreengirls

greenboysfrac14 1 gt 1 frac14

purplegirls

purpleboys while that for boys becomes blue As

a result in the treatment condition subjects should inflate the

frequency of green shirts relative to the truth sttreatmentgreengirls

gt greengirls (the same should happen to assessments of blueshirts for boys) We also expect the assessed frequency of greenshirts to go up relative to the control condition namely

sttreatmentgreengirls gt stcontrol

greengirls Critically the only factor that varies

across treatments is the representativeness of the 12-colorshirt Thus if we see differences across conditions the causalrole of representativeness-based recall in shaping group judg-ments is clear24

24 We vary which colors are used in which roles across participants Someparticipants saw this particular color distribution while others see for examplegreen as the modal color and purple as the diagnostic color for boys in theRepresentativeness condition and blue as the diagnostic color for girls in theRepresentativeness condition We vary the colors across the roles to avoid con-founding the characteristics of any particular color with its diagnosticity

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FIG

UR

EII

T-S

hir

tsE

xp

erim

ent

Fig

ure

sap

pea

red

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lor

top

art

icip

an

tsin

the

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ent

For

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ty

we

have

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ded

ale

tter

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-sh

irt

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enti

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lor

for

the

read

er

lsquolsquoGrsquorsquo

ind

icate

sgre

en

lsquolsquoPrsquorsquo

ind

icate

sp

urp

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ind

icate

sblu

eT

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ele

tter

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rto

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icip

an

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dare

for

read

erre

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nce

only

P

lease

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onli

ne

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sion

ofp

ubli

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icle

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We collected data from 301 participants using this T-shirtsdesign25 Since the number of green and purple shirts is verysimilar we first ask each participant the simplest question ofwhich shirt color is modal Next we ask participants to assessthe share of green and purple shirts

Consistent with the role of representativeness participantsassigned to the Representativeness condition are 105 percentagepoints more likely to recall the less frequent color (green for girlsor blue for boys) as the modal color when it is representative of agroup (35 of participants guess the less frequent color is modalin the Control condition this proportion increases to 46 in theRepresentativeness condition p = 01 estimated from a probitregression reported in Online Appendix F)

We now turn to subjectsrsquo estimates of how many T-shirts ofeach color they saw in each group In both conditions the truedifference in counts is 1 (13 purple shirts 12 green or blue shirts)In the Control condition participants on average believe they saw054 more purple shirts than green or blue shirts In theRepresentativeness condition participants believe they saw072 fewer purple shirts than green or blue shirts (the acrosstreatment difference is significant with p = 01 from OLS regres-sion reported in Online Appendix F)

In total we collected data for six experiments of this generalstructure gathering evidence from more than 1000 participantsAs we describe in Online Appendix F although there is substan-tial variation across experiments when we pool all of the data wefind significant aggregate treatment effects in line with a role ofrepresentativeness in judgment We employ four different unor-dered types designs similar to the T-shirts experiment using sixsamples (four online and two in the laboratory) with 741 partic-ipants We find effects in the predicted direction for five of the sixsamples Using a probit regression that pools the data for theseunordered type experiments we find that participants are 93 per-centage points more likely to guess that the less frequent type ismodal when it is representative than when it is not (p = 002) Wealso run a family of ordered types experiments (two designs fivesamples 402 participants) Unlike the simpler T-shirts style

25 Throughout our analysis we exclude any participant who participated in aprevious version of the experiment and any participant who self-identified as color-blind In Online Appendix F we show that our results are unchanged if we includethese additional observations

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design the theoretical predictions for the ordered types designsare more sensitive to the specific assumptions one makes aboutthe weighting function of the DM26 We find effects in the pre-dicted direction for three of the five samples As we discuss inmore detail in Online Appendix F the ordered types resultsvary by platform with consistently stronger results on AmazonMechanical Turk than in the laboratory samples Pooling all or-dered types experiments participants are 93 percentage pointsmore likely to guess that the group of interest has a greater av-erage than the comparison group when the right tail is represen-tative (p = 062) Given our simple experimental setting withgroups of mundane objects we interpret our resultsmdasha signifi-cant and reasonably sized impact on average beliefsmdashas an im-portant proof of concept the presence of representative typesbiases ex post assessment

IVB Empirical Evidence on Political Stereotypes

We examine two data sets on political preferences and be-liefs about political preferences in the United States We inves-tigate the roles of representativeness and context dependence byseparately testing for hypotheses that allow us to assess the lead-ing theories of stereotypes

First we test whether beliefs are correct or depart systemat-ically from the truth The statistical discrimination approachbuilds on the assumption that people hold rational expectationsof group traits Comparing beliefs to the truth allows us to assessthe validity of this assumption in our data

Second we test if beliefs depart from the truth by exagger-ating (mean) differences among groups per the kernel of truthhypothesis This is an implicit test of context dependence be-cause it implies that beliefs about the target groups are shapednot only by that grouprsquos characteristics but also by those of thereference group27

Third we test if distortions in beliefs can be accounted for bythe overweighting of highly representative types (defined astypes that are relatively more frequent in the target relative to

26 This is due in part to our choice to not study MLRP distributions We moti-vate and discuss this design decision in Online Appendix F

27 Of course unlike in the laboratory experiment in this setting we cannot testfor context dependence by exogenously varying the reference group

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the reference group) The second and third tests address the keypredictions of our model

1 The Data We have two data sets on political preferences andbeliefs about political preferences The first data set from GrahamNosek and Haidt (GNH 2012) contains data from the MoralFoundations Questionnaire Respondents (1174 self-identified lib-erals and 500 self-identified conservatives) answer questions abouttheir position on a subset of 45 issues 20 moral relevance state-ments (eg lsquolsquowhen you decide whether something is right orwrong to what extent are the following considerations relevantto your thinkingrsquorsquo) and 25 moral judgments (eg lsquolsquoindicate theextent to which you would agree or disagreersquorsquo) For each issue arandomly determined subset of participants states their own posi-tion another subset states their belief on the position of a lsquolsquotypicalliberalrsquorsquo and a third subset states their belief on the position of alsquolsquotypical conservativersquorsquo The data thus include the distribution overpositions for both liberal and conservatives as well as the averagebelieved typical position of liberals and of conservatives on the 45issues Each position is elicited on 1ndash6 scale

The second data set comes from the American NationalElection Survey (ANES) and contains data from more than20000 respondents between 1964 and 201228 The surveycovers political issues of the day such as the optimal amount ofgovernment spending and service provision (1984ndash2000) or theplace of women in society (1972ndash1998) We focus on the 10 issuesthat ask participants to respond on a 1ndash7 scale (rather than justindicate binary agreement or disagreement) all 10 issues areasked in multiple years Participants are asked to provide theirown position on the scale and their believed position of theDemocratic and Republican parties (lsquolsquoWhere would you placethe Democratic [Republican] party on this scalersquorsquo) The data in-clude for each issue-year observation the distribution of partic-ipant positions for self-identified liberals and self-identifiedconservatives as well as the distribution of believed typical posi-tions of the Democratic and Republican parties

28 These data are publicly available at httpwwwelectionstudiesorgstudy-pagesanes_timeseries_cdfanes_timeseries_cdfhtm

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2 Empirical Strategy Our analysis focuses on beliefs abouttwo groups Conservatives and Liberals The types are the possi-ble positions for each issue (1 2 6 7) For the GNH data weinterpret beliefs about the lsquolsquotypicalrsquorsquo element of a group to coincidewith the believed average position in that group Similarly forthe ANES data we use the believed party positions as a proxy forbelieved mean of each group29 We then take as a benchmark thehypothesis that individuals hold accurate beliefs about eachgroup and in particular that believed mean position shouldequal true mean position at least on average across subjectsThe accurate beliefs hypothesis underlies the most common eco-nomic model of stereotyping statistical discrimination

To assess our representativeness-based model we perform aregression exercise To test our model in a linear regressionframework we rely on linear approximations of the weightingfunction Our model then yields two regression specifications

PROPOSITION 4 Let G 2 fconservative liberal g and assume

ht h tG

tG

be a differentiable and strictly increasing weight-

ing function as in Definition 2 The following hold as a first-order approximation around identical distributions G

Gfrac14 1

(i) Kernel of truth regression There exists a constant gt 0such that

EstethtjGTHORN frac14 EethtjGTHORNeth1thorn THORN EethtjGTHORNeth5THORN

(ii) Representativeness regression Denote H frac14 fT 2 Tg

the right tail of types and RconsH frac14

PHtconsPHtlib

as the average

representativeness of right tail types for conservatives

29 This assumption is consistent with the authorsrsquo interpretation of the GNHdata (GNH 2012) and with previous studies using ANES (eg Westfall et al 2015)Furthermore to the extent that this assumption holds equally well for most issueswithin a data set our focus on cross-issue differences should allow us to test thepredictions of our model even with an imperfect proxy for beliefs of mean positionsFinally the data provide some insight into whether subjects are reporting (per-ceived) modal or mean types As we show the modal type is a poor prediction ofstated beliefs while a distorted mean slanted toward representative types is anaccurate prediction of stated beliefs

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Under the further approximation where tcons

tlibampRcons

H for

t 2 H

EstethtjconsTHORN frac14 EethtjconsTHORN thorn consethR

consH 1THORNeth6THORN

EstethtjlibTHORN frac14 EethtjlibTHORN libethR

consH 1THORNeth7THORN

where lcons and llib are positive constants

The first regression allows us to test for the kernel of truthhypothesis and the second set of regressions allows us to test forthe role of representativeness

Equation (5) says that respondents in our model inflate theaverage position of a group say the conservatives if and only ifthe group has a higher average position than the other groupnamely the liberals Formally EstethtjconsTHORN gt EethtjconsTHORN if and onlyif EethtjconsTHORN gt EethtjlibTHORN Because in our measurement scale highertypes mean lsquolsquomore conservativersquorsquo we expect (i) believed conserva-tive average to be higher than the truth and (ii) the extent ofoverstatement to decrease in the average liberal position EethtjlibTHORNConversely we expect the average liberal position to be lowerthan the truth the more so the higher the average conservativeposition EethtjconsTHORN

As previously discussed the basis of these predictions is con-text dependence information about the distribution of ndashG is rel-evant for the beliefs about G This context dependence isinconsistent with rational expectations in which only thegrouprsquos own means should affect beliefs We test the hypothesisthat the true mean EethtjGTHORN is a significant predictor of the believedmean E

stethtjGTHORN with a positive sign and the other grouprsquos truemean EethtjGTHORN is a predictor of the believed mean with a negativesign

Equations (6) and (7) say that repondentsrsquo assessment bias isshaped by representativeness When the right tail is more repre-sentative for conservatives (Rcons

H 1 positive and large) partici-pants should inflate the average conservative position more(higher E

stethtjconsTHORN EethtjconsTHORN) and deflate the average liberal po-sition more (lower E

stethtjlibTHORN EethtjlibTHORN) We test the hypothesisthat the inflation in conservative positions is positively associatedwith the representativeness of the right tail for the conservativesand the inflation in liberal positions is negatively associated with

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it Once again the representativeness of the right tail is com-puted using the true distribution of positions

In equations (6) and (7) in many cases the representative tailis also the most likely one As a consequence these tests cannotdistinguish a representativeness-based from a likelihood-basedmodel of distorted beliefs We perform two additional testsFirst we run versions of equations (6) and (7) in which we controlfor the likelihood of tails (see Table A4 in Online Appendix G)Second we compute numerically the predictions of a representa-tiveness-based model of stereotypes and a likelihood-based modelof stereotypes We then assess which of these two is better able tomatch the data on beliefs

3 Empirical Results To begin we illustrate the structure ofthe data and the nature of our predictions with two simple exam-ples from the GNH data set focusing on beliefs about conserva-tives In example 1 participants are asked about their agreementwith the statement lsquolsquoIt can never be right to kill a human beingrsquorsquoIn example 2 participants are asked about the moral relevance oflsquolsquowhether or not someone cared for someone weak or vulnerablersquorsquoAs can be seen in Figure III in example 1 the modal position(strongly disagree (1)) and most representative positions(strongly disagree (1)) coincide for conservatives In contrast inexample 2 in Figure III the most representative types (slightlyrelevant (3) not at all relevant (1)) are not most likely for theconservative group Following Proposition 1 we predict that be-liefs will be distorted in the direction of the most representativetypes Thus we expect more exaggeration in example 2 than inexample 1 since in example 2 the most representative types (inthe left tail) are far from the modal type whereas in example 1they coincide This is what we find the conservative position isexaggerated by only 009 positions in Example 1 (true mean 299believed mean 290) but by 106 positions in Example 2 (truemean 421 believed mean 315)

In the full data sets we treat each (issue year) pair as anobservation and we cluster standard errors at the issue level Forthe GNH data we have 45 observations 45 issues measured inthe same year For the ANES data we have 66 observations 10issues measured in multiple years To begin we simply docu-ment systematic exaggeration in both data sets This is a primaryfocus of the original analysis in GNH (2012) and also in Westfall

STEREOTYPES 1785

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FIGURE III

Two Examples

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et al (2015)rsquos analysis of the ANES data30 Figure IV shows thatthe believed difference between typical conservative and typicalliberal positions is larger than the true difference in mean posi-tions for 109 of the 111 observations The data for both GNH(squares) and ANES (triangles) lie above the 45-degree line(dashed)31 Average exaggeration is 062 positions on the scale(066 in the GNH data 059 in the ANES data)32

The systematic and significant exaggeration of mean differ-ences suggests that the benchmark model of accurate beliefs ismissing something important Indeed this exaggeration reflectsthe fact that believed means are typically more extreme than truemeans First note that the kernel of truth regression (equation(5)) generates exaggeration of mean differences just as docu-mented in Figure IV

EstethtjGTHORN E

stethtjGTHORN frac14 eth1thorn 2THORN frac12EethtjGTHORN EethtjGTHORN

To bring this prediction to the data we regress the believedmean position for each group EBethtjGTHORN on the true mean of thegroup EethtjGTHORN and the true mean of the comparison groupEethtjGTHORN across issues We do this for each group (liberals con-servatives) in each data set separately We also present pooledspecifications that combine the data sets to make a prediction fora given group (liberals conservatives) In these pooled specifica-tions we include a dummy variable indicating whether theobservation came from the ANES data set For all specificationswe cluster observations at the issue level33 The results from re-gression are shown in Table I In every specification we find thatEethtjGTHORN is a significant predictor of EBethtjGTHORN with the predicted pos-itive sign Crucially for five of the six specifications the mean of

30 Chambers and Melnyk (2006) also find evidence of exaggeration of truedifferences in beliefs about political positions

31 For convenience we recode all issues so that the high end of the scale (67)represents the stereotypically more conservative position

32 A natural question to ask is how beliefs vary across liberals and conserva-tives That is do beliefs about a group G depend on membership in G versus ndashG Ourmodel does not speak to this issue However in Online Appendix G we show thatthe results we document below hold for both beliefs held by conservatives and be-liefs held by liberals see Tables A9 A10 and A11

33 In general the results presented below for the ANES data are not largelyimpacted by the decision to cluster at the issue level Similar results are obtained ifthe data are not clustered

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the comparison group EethtjGTHORN is also a significant predictor ofE

BethtjGTHORN with the predicted negative signAlthough these results provide strong evidence of context

dependence and are consistent with our model they do not pindown a role for representativeness of types Our next test relatesthe magnitude of representativeness of tail types to the magni-tude of belief distortions

To this end we implement the regressions in equations (6)and (7) Following Proposition 4 we compute the average repre-

sentativeness of tail types for conservatives RconsH frac14

PtT2tconsPtT2tlib

We

again test the hypothesis that RconsH is a significant predictor of Est

ethtjconsTHORN with a positive sign and a predictor of EstethtjlibTHORN with a

negative sign Table II shows that conditional on true mean RconsH

predicts believed mean for each group G as expected The firstthree specifications display the results for predicting beliefs heldabout conservatives In both data sets the average representa-tiveness of tail types for conservatives is a significant positivepredictor of beliefs held about conservatives The final three spe-cifications display the results for predicting beliefs held about

FIGURE IV

Exaggeration of Differences

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liberals We find that the average representativeness of tail typesfor conservatives is a negative predictor of beliefs held about lib-erals This effect is significant in the GNH data and marginallysignificant in the ANES data

We present several additional results in Online Appendix GTo further examine the role of representativeness in driving be-liefs we first show the results of Table II carry through when we

TABLE II

AVERAGE REPRESENTATIVENESS OF TAIL POSITIONS PREDICTS BELIEFS

OLS Predicting Believed Mean of Group G for Each Issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position

of group G for issue

078 024 051 072 018 041

(006) (008) (009) (005) (005) (010)

Avg rep of tail types for

conservatives RconsH

019 055 025 014 012 024

(007) (022) (008) (006) (007) (005)

Constant 101 260 184 093 271 201

(026) (045) (029) (022) (025) (032)

R2 082 048 060 091 031 070

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

TABLE I

INFORMATION ABOUT ndashG PREDICTS BELIEFS ABOUT G

OLS predicting believed mean of group G for each issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position of

conservatives for issue

102 098 096 021 019 025

(0097) (0133) (0076) (0060) (0116) (0060)

True mean position of

liberals for issue

035 086 058 0987 039 073

(0106) (0134) (0131) (0066) (0106) (0135)

Constant 151 335 235 069 258 156

(0195) (0269) (0279) (0122) (0249) (0270)

R2 083 053 066 092 032 068

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

STEREOTYPES 1789

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control for the average likelihood on the tail positions (see Table A4in Online Appendix G) Most tellingly we use the model to predictbeliefs across issues and compare those to the data For simplicitywe use the rank-based truncation specification to predict mean be-liefs when stereotypes include the d most representative types ford frac14 1 T We compare these predictions to those of a model inwhich beliefs are obtained by restricting the distribution to the dmost likely types Our benchmark for both models is predicting thebelieved mean from the entire distribution where d = T We showthat the predictions of the rank-based truncation model with d = 4or 5 compare favorably to both a likelihood-based truncation model(with any d) and the accurate beliefs benchmark Interestingly thisresult suggests that stereotypical beliefs are well approximated byneglecting the least representative types (as opposed to focusingonly on the most representative types) and so represent a moderatethough systematic departure from the standard benchmarkFinally we show that the results we document above hold forboth beliefs held by conservatives and beliefs held by liberals (seeTables A9 A10 and A11 in Online Appendix G)

V Conclusion

We present a model of stereotypical thinking in which DMsmaking predictions about a group overweight the grouprsquos mostdistinctive types These overweighted types are not the mostlikely ones given the DMrsquos data but the most representativeones in the sense of being the most diagnostic of the group rela-tive to other groups Representativeness implies that what ismost distinctive of a group depends on what group it is comparedwith We present experimental evidence that confirms this con-text dependence in recall-based assessments of groups Finallywe evaluated the predictions of the model using political data fromexisting large-scale surveys We find context dependence to be akey feature of beliefs Given the richness of the political data wecan go a step further and identify a role for representativeness inparticular As the representativeness of tail types increases beliefsof a group are distorted in the direction of that tail

Our approach provides a parsimonious and psychologicallyfounded account of how DMs generate simplified representationsof reality from social groups to stock returns and offers a unifiedaccount of disparate pieces of evidence relating to this type of

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uncertainty The model captures the central fact that stereotypeshighlight the greatest difference between groups thus explainingwhy some stereotypes are very accurate while others lack valid-ity Still stereotypes often have a kernel of truth when they arebased on systematicmdasheven if smallmdashdifferences between groupsThis logic allows us to describe a number of heuristics and psy-chological biases many of which arise in the context of predictionproblems Generically our model generates overreaction to diag-nostic information

Our model is based on representativeness and does not cap-ture all the features of stereotypical thinking However it cap-tures perhaps the central feature when we think of a group wefocus on what is most distinctive about it and neglect or under-weight the rest

Saeuroıd Business School University of Oxford

Ohio State University and Harvard Business School

Universita Bocconi and Innocenzo Gasparini Institute

for Economic Research

Harvard University

Supplementary Material

An Online Appendix for this article can be found at QJEonline (qjeoxfordjournalorg)

References

Adorno Theodor Else Frenkel-Brunswik Daniel Levinson and Nevitt SanfordThe Authoritarian Personality (New York Harper amp Row 1950)

Arrow Kenneth lsquolsquoThe Theory of Discriminationrsquorsquo in Discrimination in LaborMarkets Orley Ashenfelter and Albert Rees eds (Princeton NJPrinceton University Press 1973)

Ashton Michael and Victoria Esses lsquolsquoStereotype Accuracy Estimating theAcademic Performance of Ethnic Groupsrsquorsquo Personality and SocialPsychology Bulletin 25 (1999) 225ndash236

Barberis Nicholas Andrei Shleifer and Robert Vishny lsquolsquoA Model of InvestorSentimentrsquorsquo Journal of Financial Economics 49 (1998) 307ndash343

Bayer Sylvia lsquolsquoThe Accuracy of Academic Gender Stereotypesrsquorsquo Sex Roles 40(1999) 787ndash813

Benjamin Dan James Choi and Joshua Strickland lsquolsquoSocial Identity andPreferencesrsquorsquo American Economic Review 100 (2010) 1913ndash1928

Benjamin Dan Matthew Rabin and Collin Raymond lsquolsquoA Model of Non-Belief inthe Law of Large Numbersrsquorsquo Journal of the European Economic Association15 (2015) 515ndash544

Bertrand Marianne lsquolsquoNew Perspectives on Genderrsquorsquo Handbook of LaborEconomics 4 (2011) 1543ndash1590

Bodoh-Creed Aaron Dan Benjamin and Matthew Rabin lsquolsquoThe Dynamics of Base-Rate Neglectrsquorsquo mimeo Haas Business School 2013

STEREOTYPES 1791

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

Bohnet Iris Alexandra van Geen and Max Bazerman lsquolsquoWhen PerformanceTrumps Gender Bias Joint versus Separate Evaluationrsquorsquo ManagementScience 5 (2016) 1225ndash1234

Bordalo Pedro Nicola Gennaioli and Andrei Shleifer lsquolsquoSalience Theory of Choiceunder Riskrsquorsquo Quarterly Journal of Economics 127 (2012) 1243ndash1285

mdashmdashmdash lsquolsquoSalience and Consumer Choicersquorsquo Journal of Political Economy 121(2013) 803ndash843

Briton Nancy and Judith Hall lsquolsquoBeliefs about Female and Male NonverbalCommunicationrsquorsquo Sex Roles 32 (1995) 79ndash90

Buser Thomas Muriel Niederle and Hessel Oosterbeek lsquolsquoGenderCompetitiveness and Career Choicesrsquorsquo Quarterly Journal of Economics 129(2014) 1409ndash1447

Carrell Scott Marianne Page and James West lsquolsquoSex and Science How ProfessorGender Perpetuates the Gender Gaprsquorsquo Quarterly Journal of Economics 125(2010) 1101ndash1144

Chambers John and Darya Melnyk lsquolsquoWhy Do I Hate Thee ConflictMisperceptions and Intergroup Mistrustrsquorsquo Personality and SocialPsychology Bulletin 32 (2006) 1295ndash1311

Chan Wayne Robert R McCrae Filip De Fruyt Lee Jussim CorinnaE Lockenhoff Marleen De Bolle Paul T Costa Jr Angelina R SutinAnu Realo Juri Allik Katsuharu Nakazato Yoshiko ShimonakaMartina Hrebıckova Sylvie Graf Michelle Yik Marina Brunner-SciarraNora Leibovich De Figueora Vanina Schmidt Chang-kyo Ahn Hyun-nie Ahn Maria E Aguilar-Vafaie Jerzy Siuta Barbara SzmigielskaThomas R Cain Janet T Crawford Khairul Anwar Mastor Jean-Pierre Rolland Florence Nansubuga Daniel R MiramontezVeronica Benet-Martınez Jerome Rossier Denis Bratko Iris MarusicJamin Halberstadt Mami Yamaguchi Goran Knezevic Thomas A MartinMirona Gheorghiu Peter B Smith Claudio Barbaranelli Lei WangJane Shakespeare-Finch Margarida P Lima Waldemar KlinkoszAndrzej Sekowski Lidia Alcalay Franco Simonetti Tatyana V AvdeyevaV S Pramila and Antonio Terracciano lsquolsquoStereotypes of Age Differences inPersonality Traits Universal and Accuratersquorsquo Journal of Personality andSocial Psychology 103 (2012) 1050ndash1066

Chen Yan Sherry Xin Liu Tracy Xiao and Margaret Shih lsquolsquoWhich Hat to WearImpact of Natural Identities on Coordination and Cooperationrsquorsquo Games andEconomic Behavior 84 (2014) 58ndash86

Coffman Katherine lsquolsquoEvidence on Self-Stereotyping and the Contribution ofIdeasrsquorsquo Quarterly Journal of Economics 129 (2014) 1625ndash1660

Cunningham Tom lsquolsquoComparisons and Choicersquorsquo mimeo Stockholm University2013

Diekman Amanda Alice Eagly and Patrick Kulesa lsquolsquoAccuracy and Bias in theStereotypes about the Social and Political Attitudes of Women and MenrsquorsquoJournal of Experimental Social Psychology 38 (2002) 268ndash282

Eccles Jacquelynne S Janis E Jacobs and Rena D Harold lsquolsquoGender RoleStereotypes Expectancy Effects and Parentsrsquo Socialization of GenderDifferencesrsquorsquo Journal of Social Issues 46 (1990) 183ndash201

Fryer Roland and Matthew Jackson lsquolsquoA Categorical Model of Cognition andBiased Decision-Makingrsquorsquo BE Journal of Theoretical Economics 8 (2008)1ndash42

Fryer Roland and Steven Levitt lsquolsquoAn Empirical Analysis of the Gender Gap inMathematicsrsquorsquo American Economic Journal Applied Economics 2 (2010)210ndash240

Gennaioli Nicola and Andrei Shleifer lsquolsquoWhat Comes to Mindrsquorsquo Quarterly Journalof Economics 125 (2010) 1399ndash1433

Gennaioli Nicola Andrei Shleifer and Robert Vishny lsquolsquoNeglected RisksFinancial Innovation and Financial Fragilityrsquorsquo Journal of FinancialEconomics 104 (2012) 452ndash468

Gilens Martin lsquolsquoRace and Poverty in America Public Misperceptions and theAmerican News Mediarsquorsquo Public Opinion Quarterly 60 (1996) 515ndash541

Glaeser Edward lsquolsquoThe Political Economy of Hatredrsquorsquo Quarterly Journal ofEconomics 120 (2005) 45ndash86

QUARTERLY JOURNAL OF ECONOMICS1792

at Harvard L

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httpqjeoxfordjournalsorgD

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Glover Dyland Amanda Pallais and William Pariente lsquolsquoDiscrimination as a Self-Fulfilling Prophecy Evidence from French Grocery Storesrsquorsquo mimeo HarvardUniversity 2015

Goldin Claudia Lawrence Katz and Ilyana Kuziemko lsquolsquoThe Homecoming ofAmerican College Women The Reversal of the College Gender GaprsquorsquoJournal of Economic Perspectives 20 (2006) 133ndash156

Graham Jesse Brian Nosek and Jonathan Haidt lsquolsquoThe Moral Stereotypes ofLiberals and Conservatives Exaggeration of Differences across thePolitical Spectrumrsquorsquo PLoS One 7 (2012) 1ndash13

Grether David lsquolsquoBayes Rule as a Descriptive Model The RepresentativenessHeuristicrsquorsquo Quarterly Journal of Economics 95 (1980) 537ndash557

Griffin Dale and Amos Tversky lsquolsquoThe Weighing of Evidence and theDeterminants of Confidencersquorsquo Cognitive Psychology 24 (1992) 411ndash435

Guiso Luigi Ferdinando Monte Paola Sapienza and Luigi Zingales lsquolsquoCultureGender and Mathrsquorsquo Science 320 (2008) 1164ndash1165

Hilton James and William Von Hippel lsquolsquoStereotypesrsquorsquo Annual Review ofPsychology 47 (1996) 237ndash271

Hyde Janet Sara Lindberg Marcia Linn Amy Ellis and Caroline WilliamslsquolsquoGender Similarities Characterize Math Performancersquorsquo Science 321 (2008)494ndash495

Judd Charles and Bernardette Park lsquolsquoDefinition and Assessment of Accuracy inSocial Stereotypesrsquorsquo Psychological Review 100 (1993) 109ndash128

Jussim Lee Jarret Crawford Stephanie Anglin John Chambers Sean Stevensand Florette Cohen lsquolsquoStereotype Accuracy One of the Largest and MostReplicable Effects in All of Social Psychologyrsquorsquo in The Handbook ofPrejudice Stereotyping and Discrimination Todd Nelson ed (MahwahNJ Lawrence Erlbaum 2015)

Kahneman Daniel and Amos Tversky lsquolsquoSubjective Probability A Judgment ofRepresentativenessrsquorsquo Cognitive Psychology 3 (1972) 430ndash454

mdashmdashmdash lsquolsquoOn the Psychology of Predictionrsquorsquo Psychological Review 80 (1973) 237ndash251

Kaplowitz Stan Bradley Fisher and Clifford Broman lsquolsquoHow Accurate ArePerceptions of Social Statistics about Blacks and Whitesrsquorsquo Public OpinionQuarterly 67 (2003) 237ndash243

Kersten Daniel Pascal Mamassian and Alan Yuille lsquolsquoObject Perception asBayesian Inferencersquorsquo Annual Review of Psychology 55 (2004) 271ndash304

Klein Richard Kate A Ratliff Michelangelo Vianello Reginald B Adams JrStepan Bahnik Michael J Bernstein Konrad Bocian Mark J BrandtBeach Brooks Claudia Chloe Brumbaugh Zeynep CemalcilarJesse Chandler Winnee Cheong William E Davis Thierry DevosMatthew Eisner Natalia Frankowska David Furrow Elisa Maria GallianiFred Hasselman Joshua A Hicks James F Hovermale S Jane HuntJeffrey R Huntsinger Hans IJzerman Melissa-Sue John Jennifer A Joy-Gaba Heather Barry Kappes Lacy E Krueger Jaime Kurtz CarmelA Levitan Robyn Mallett Wendy L Morris Anthony J Nelson JasonA Nier Grant Packard Ronaldo Pilati Abraham M RutchickKathleen Schmidt Jeanine L Skorinko Robert Smith Troy G SteinerJustin Storbeck Lyn M Van Swol Donna Thompson Anna van rsquot VeerLeigh Ann Vaughn Marek Vranka Aaron Wichman Julie A Woodzickaand Brian A Nosek lsquolsquoInvestigating Variation in Replicability A ManyLabs Replication Projectrsquorsquo Social Psychology 45 (2014) 142ndash152

Lundberg Shelly and Richard Startz lsquolsquoPrivate Discrimination and SocialIntervention in Competitive Labor Marketsrsquorsquo American Economic Review73 (1983) 340ndash347

Madon Stephanie Max Guyll Kathy Aboufadel Eulices Montiel Alison SmithPolly Palumbo and Lee Jussim lsquolsquoEthnic and National Stereotypes ThePrinceton Trilogy Revisited and Revisedrsquorsquo Personality and SocialPsychological Bulletin 27 (2001) 996ndash1010

Martin Carol lsquolsquoA Ratio Measure of Sex Stereotypingrsquorsquo Journal of Personality andSocial Psychology 52 (1987) 489ndash499

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ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

McCauley Clark Krishna Thangavelu and Paul Rozin lsquolsquoSex Stereotyping ofOccupations in Relation to Television Representations and Census FactsrsquorsquoBasic and Applied Social Psychology 9 (1988) 197ndash212

Mullainathan Sendhil lsquolsquoThinking through Categoriesrsquorsquo mimeo HarvardUniversity 2002

Ortoleva Pietro and Erik Snowberg lsquolsquoOverconfidence in Political BehaviorrsquorsquoAmerican Economic Review 105 (2015) 504ndash535

Phelps Edmund lsquolsquoThe Statistical Theory of Racism and Sexismrsquorsquo AmericanEconomic Review 62 (1972) 659ndash661

Pope Devin and Justin Sydnor lsquolsquoGeographic Variation in the Gender Differencesin Test Scoresrsquorsquo Journal of Economic Perspectives 24 (2010) 95ndash108

Rabin Matthew lsquolsquoInference by Believers in the Law of Small NumbersrsquorsquoQuarterly Journal of Economics 117 (2002) 775ndash816

Rabin Matthew and Joel Schrag lsquolsquoFirst Impressions Matter A Model ofConfirmatory Biasrsquorsquo Quarterly Journal of Economics 114 (1999) 37ndash82

Rabin Matthew and Dimitri Vayanos lsquolsquoThe Gamblerrsquos and Hot-Hand FallaciesTheory and Applicationsrsquorsquo Review of Economic Studies 77 (2010) 730ndash778

Reuben Ernesto Paola Sapienza and Luigi Zingales lsquolsquoHow Stereotypes ImpairWomenrsquos Careers in Sciencersquorsquo Proceedings of the National Academy ofSciences 111 (2014) 4403ndash4408

Rosch Eleanor lsquolsquoNatural Categoriesrsquorsquo Cognitive Psychology 4 (1973) 328ndash350Ryan Carey S lsquolsquoAccuracy of Black and White College Studentsrsquo In-Group and

Out-Group Stereotypesrsquorsquo Personality and Social Psychology Bulletin 22(1996) 1114ndash1127

Schneider David The Psychology of Stereotyping (New York Guilford Press2004)

Schneider David Albert Hastorf and Phoebe Ellsworth Person Perception(Reading MA Addison-Wesley 1979)

Shih Margaret Todd Pittinsky and Nalini Ambady lsquolsquoStereotype SusceptibilityIdentity Salience and Shifts in Quantitative Performancersquorsquo PsychologicalScience 10 (1999) 80ndash83

Shih Margaret Todd Pittinsky and Amy Trahan lsquolsquoDomain-Specific Effects ofStereotypes on Performancersquorsquo Self and Identity 5 (2006) 1ndash14

Steele Claude Whistling Vivaldi How Stereotypes Affect Us and What We CanDo (New York Norton 2010)

Tenenbaum Joshua and Thomas Griffiths lsquolsquoThe Rational Basis ofRepresentativenessrsquorsquo 23rd Annual Conference of the Cognitive ScienceSociety (2001) 1036ndash1041

Tversky Amos and Daniel Kahneman lsquolsquoExtensional versus Intuitive ReasoningThe Conjunction Fallacy in Probability Judgmentrsquorsquo Psychological Review 90(1983) 293ndash315

Weinberger Catherin lsquolsquoIs the Science and Engineering Workforce Drawn fromthe Far Upper Tail of the Math Ability Distributionrsquorsquo mimeo UCSB 2005

Westfall Jacob Leaf Van Boven John Chambers and Charles Judd lsquolsquoPerceivingPolitical Polarization in the United States Party Identity Strength andAttitude Extremity Exacerbate the Perceived Partisan DividersquorsquoPsychological Science 10 (2015) 145ndash158

Wolsko Christopher Bernadette Park Charles Judd and Bernd WittenbrinklsquolsquoFraming Interethnic Ideology Effects of Multicultural and Color-BlindPerspectives on Judgments of Groups and Individualsrsquorsquo Journal ofPersonality and Social Psychology 78 (2000) 635ndash654

QUARTERLY JOURNAL OF ECONOMICS1794

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ibrary on October 28 2016

httpqjeoxfordjournalsorgD

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Page 9: I. Introduction · uneducated at the beginning of the 20th century, and as high achievers at the beginning of the 21st (Madon et al. 2001). Social science has produced three broad

DEFINITION 1 The representativeness of type t for group G givencomparison group ndashG is defined as the likelihood ratio

RethtGGTHORN tG

tGeth2THORN

Definition 1 implies that DMs are attuned to log differencesin probabilities representativeness depends on the percentageprobability increase of a type from ndashG to G This captures aform of diminishing sensitivity whereby for a fixed probabilitydifference a type is more likely to be overweighed if it is unlikelyin the comparison group8 Thus the representative age of aFloridian is 65+ because people in this age bracket are morecommon in Florida than in the rest of the United StatesStatistically representative types are also diagnostic of thetarget group G Indeed the higher is RethtGGTHORN the more confi-dent is a Bayesian DM observing t that t belongs to G rather thanto ndashG9

The ease of recall of highly representative types affectsjudgments because more easily recalled types are overweighted

We model distorted recall as follows Denote by RethtGGTHORN

tG

tG

t2T

the vector of representativeness of all types in G

We then have

8 Our definition of representativeness links to Weberrsquos law of sensory percep-tion see Section IIB It also links to our previous work on salience in which wepostulated that log differences in payoffs determine the attention to lottery payoffs(Bordalo Gennaioli and Shleifer 2012) and to goodsrsquo attributes (BordaloGennaioli and Shleifer 2013) Equation (2) establishes the same principle for thedomain of probabilities

9 This insight led Tenenbaum and Griffiths (2001) to define representative-ness as individualsrsquo sense as intuitive Bayesians of updating in reaction to dataTheir definition like ours is in terms of the likelihood ratio However Tenenbaumand Griffiths interpret representativeness as a mechanism that affects intuitivejudgments of similarity rather than beliefs (eg it accounts well for lab evidencewhere subjects are asked to rank types in terms of representativeness or ofstrength of association with a group) Accordingly they do not consider the possi-bility of systematically distorted and context dependent beliefs

STEREOTYPES 1761

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DEFINITION 2 The DM attaches to each type t 2 T in group G adistorted probability

sttG frac14 tG

htethRethtGGTHORNTHORNPs2T sGhsethRethtGGTHORNTHORN

eth3THORN

where ht RTthornRthorn is a weighting function such that

(i) The weight ht is a symmetric function of the representa-

tiveness of types s 6frac14 t Formally ht frac14 h tG

tG

sG

sG

s2Tn tf g

where h Rthorn RT1thorn Rthorn is a function that is invariant to

a permutation of the last T ndash 1 arguments(ii) Weighing of a type increases in own representativeness

and decreases in the representativeness of other typesFormally the function hethTHORN is weakly increasing in itsfirst argument and weakly decreasing in the other T 1arguments

We call the distribution ethsttGTHORNt2T the stereotype for G If a type

t is objectively more likely namely tG is higher then the ste-reotype attaches higher probability to it By property i distor-tions are due exclusively to the fact that a type is more or lessrepresentative than the others In particular if all types areequally representative the DM equally weighs all of them ath(1) and holds rational expectations about G If instead the rep-resentativeness of different types differs property ii implies thatthe stereotype ceteris paribus overweights the probability of morerepresentative types

Most of the results we explore in this article hold for a gen-eral weighing function htethTHORN Specific functional forms captureadded assumptions about the psychology of representativeness-based recall and are useful in applications We outline a few spe-cifications and their properties

Rank-based stereotypes the ranking of the representa-tiveness of different types shapes distortions Denote byrethtTHORN 2 f1 Tg the representativeness ranking of type tWhen r(t) = 1 type t is the most representative one (po-tentially with ties) We can specify two ways in which atypersquos representativeness ranking distorts its probability

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(i) Rank-based truncation the DM only recalls the typesthat have representativeness ranking of at most dnamely ft 2 TjrethtTHORN dg Zero probability is attachedto the remaining types10 Denote by IethrethtTHORN dTHORN an in-dicator function taking the value 1 if the representa-tiveness ranking of t is at most d Then theweighting function is ht frac14 IethrethtTHORN dTHORN so that

sttG frac14 tG

IethrethtTHORN dTHORNPs2T sGIethrethsTHORN dTHORN

which is the true conditional probability within re-called types This assumption is used in Gennaioliand Shleifer (2010)11

(ii) Rank-based discounting the DM discounts by a con-stant factor 2 frac1201 the odds of type t relative to itsimmediate predecessors in the representativenessranking Lower implies stronger discounting ofless representative types Formally the weightingfunction is ht frac14

rethtTHORN so that

sttG frac14 tG

rethtTHORNPs2T sG

rethsTHORN

Representativness-based discounting all else equal theweight attached by the DM to type t increases continuouslywith its representativeness One convenient formulation is

ht frac14tG

tG

so that

10 These neglected types are not viewed as impossible they are just assignedzero probability in the DMrsquos current thinking This formulation allows us to modelsurprise and reactions to unforeseen contingencies which have proved useful in-gredients in modeling probabilistic judgments (GS 2010) as well as neglect of risk infinancial crises (Gennaioli Shleifer and Vishny 2012)

11 Specifically in GS (2010) the assessed probability that a certain hypothesisG is true is equal to

Pr ethGTHORN frac14

Pt tGIethrethtTHORN dTHORNP

t tGIethrethtTHORN dTHORN thornP

t t=GIethrethtTHORN dTHORN

which increases in the ratio between the total probability mass recalled for Gand that recalled for G frac14 nG

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sttG frac14 tG

tG

tG

P

s2T sGsG

sG

where 0 captures the extent to which representative-ness distorts beliefs This formulation is particularly con-venient when dealing with continuous distributions ofthe exponential or power classes

These functional forms all embody the main idea of our modelthat the stereotype overweights the probability of more represen-tative types Rank-based truncation captures a central manifes-tation of limited memory forgetting unrepresentative typesSmoother discounting (based on ranking or on representative-ness) may be more appropriate when the type space is smalland smooth discounting can be more tractable in certain settings

Section III characterizes the general properties of stereotypesIn particular it shows their ability to account for social psycholo-gistsrsquo kernel of truth hypothesis under the general weighting func-tion of Definition 2 To bring the model to the data in Section IVBwe derive linear approximations of stereotypical beliefs by assum-ing that the weighting function is differentiable with respect to atypersquos representativeness This assumption excludes rank-basedweighting but allows for many possibilities

IIB Discussion of Assumptions

Before moving to the formal analysis we discuss some prop-erties and limitations of our approach Representativeness-basedrecall the idea that individuals recall distinctive group types canbe viewed as an instance of what Kahneman and Tversky calllsquolsquoattribute substitutionrsquorsquo When dealing with the difficult questionlsquolsquowhat is the distribution of hair color among the Irishrsquorsquo peopleintuitively answer to the simpler question lsquolsquowhich hair color dis-tinguishes the Irish peoplersquorsquo Critically as discussed byKahneman and Tversky attribute substitution does not occurbecause people misunderstand the original question or mechan-ically confuse the assessment of PrethtjGTHORN with that of PrethGjtTHORNRather it occurs because the distinctive or representative typesimmediately come to mind and individuals anchor their overallprobability judgment to them As a consequence subjects do notonly make mistakes in judging the probability that a Floridian is

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over age 65 They also give too high an answer to the questionlsquolsquowhat is the average age of a Floridianrsquorsquo12

One interesting question is whether the process of stereotyp-ing we describe is optimal in some sense Focusing mental repre-sentations on a few types can be justified by the costs of thinkingor retrieval This approach however is not enough to explainwhy individuals should focus on representative rather thanlikely types We do not formally analyze the optimality of repre-sentativeness here but we mention some relevant considerationsfrom cognitive psychology Kahneman and Tversky (1979) stressthe similarity between many perceptual and cognitive operationsFor instance the highlight of contrastmdasha key principle of visualperceptionmdashis invoked to justify the prospect theory assumptionthat the carriers of utility are changes relative to a referencepoint The same logic applies to our model in which stereotypesprecisely highlight the contrast between groups

In visual perception assessing properties such as brightnesscolor size or distance to an object by comparing them to otherproximate objects has been shown to be optimal in the presence ofmultiplicative background noise (Kersten Mamassian andYuille 2004 Cunningham 2013) Our formulation of representa-tiveness is related to the same idea in the sense that individualsestimating properties of one group stress differences from an-other group In a noisy world in which attention is limited thisprocess may optimally allow for swift reactions to changes ingroup characteristics even if errors are sometimes made13

12 Indeed in many cases mere confusion of PrethtjGTHORNwith PrethGjtTHORNwould not yieldthe phenomenon of stereotyping In the Irish hair color example the probability ofbeing Irish conditional on having red hair is

PrethIrishjredTHORN frac14PrethredjIrishTHORNPrethIrishTHORN

PrethredjIrishTHORNPrethIrishTHORN thorn PrethredjNonIrishTHORNPrethNonIrishTHORN

This probability is clearly very small given that the Irish population is a tinyfraction of the world population Confusion of PrethtjGTHORN with PrethGjtTHORN in this casewould lead to an understatement of the probability of the red-haired Irish

13 To give a simple example suppose thatmdashas in the case of Proposition 3mdashthevariance in the environment increases in the sense that extreme tail events becomemore likely Then a likelihood-based stereotype would detect no change whereas arepresentativeness-based stereotype would focus on the heightened probability ofthe tails In particular an asymmetric increase in tail probabilities that shifts themean would be detected by a representativeness-based stereotype even if the dis-tributionrsquos mode does not change

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Exploring this idea formally is an interesting avenue for futurework

Consider some limitations of our model First representa-tiveness is not the only heuristic that shapes recall Decisionmakers may for instance find it easier to recall types that aresufficiently likely Another potentially important mechanism isavailability understood by Kahneman and Tversky (1972) as thelsquolsquoeasersquorsquo with which information comes to mind (because of actualfrequency or repetition) In Online Appendix E we present a trun-cation-based recall mechanism in which distortions are driven bya combination of representativeness and likelihood of types(which is equivalent to relaxing property i in Definition 2) Thismodel can offer a useful starting point to capture availability aswell even though a full model of availability is beyond the scopeof this article Even in this more general setting the influence ofrepresentativeness on recall is the driving force of stereotypesthat in line with the social psychology perspective are basedon underlying differences among groups As we show in SectionIV this feature is critical in accounting for the evidence

The second set of model-related issues concerns how to spe-cify the elements of Definition 1 in applications group G the typespace T and the reference group ndashG Take the specification of thegroup G and of the type space T Often the problem itself pro-vides a natural specification of these features This is the case inthe empirically important class of lsquolsquoclosedrsquorsquo questions such asthose used in surveys which provide respondents with a set ofalternatives as in the data we use in Section IV More generallythe problem solved by the DMmdashsuch as evaluating the resume ofa job applicant coming from a certain ethnic groupmdashprimes agroup a dimension of interest and a set of types (eg the appli-cantrsquos qualification or skill levels) When types have a naturalorder such as income age or education the granularity of T isalso naturally given by the problem (income age and years ofschooling brackets) When the set of types is not specified by theproblem DMs spontaneously generate one14 It would be useful tohave a model of which dimensions and types come to mind par-ticularly for more open-ended problems Psychologists have

14 For example suppose a person is asked to guess the typical occupation of ademocratic voter in an lsquolsquoopen-endedrsquorsquo format (without being provided a set of alter-natives) Here the level of granularity at which types are defined is not obvious (egteacher versus a university teacher vs a professor of comparative literature)

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sought to construct a theory of natural types and dimensions(Rosch 1973) We do not make a contribution to this problembut we note that in many problems of interest in economics thedimension as well as the set of types is naturally givenFurthermore in our model details of the type space can be impor-tant under rank-based truncation but they matter less undersmooth discounting

Consider finally the role of the comparison group ndashG Thisgroup captures the context in which a stereotype is formed andagain is often implied by the problem when G = Floridians ndashG =rest of US population when G = African Americans ndashG = whiteAmericans A distinctive prediction of our model confirmed byour experiments in Section IVA is that the stereotype for agiven group G depends on the comparison group ndashG15 WhenndashG is not pinned down by the problem itself to derive testablepredictions from representativeness we set G frac14 nG where

is the natural population over which the unconditional distribu-tion of types is measured

III Properties of Stereotypes

We now study stereotypical beliefs and their accuracy Toillustrate the role of representativeness we first ask to whatextent the most representative type is a good fit for the groupnamely whether it is modal Next we assess the accuracy of theentire stereotypical distribution To do so we focus on a cardinaltypes and compare the stereotypersquos mean and variance to the trueones

15 Some empirical papers have taken a similar approach exogenously varyingthe natural comparison group through priming Benjamin Choi and Strickland(2010) show that priming racial or ethnic identity can affect the risk preferences ofparticipants Chen et al (2014) find that Asian students cooperate less with out-group members when primed with their ethnic identity rather than their universityidentity Shih Pittinsky and Ambady (1999) show that Asian American womenstereotype themselves as better or worse in math with corresponding impact onperformance when their ethnicity or gender respectively is primed ShihPittinsky and Trahan (2006) replicate this effect using a verbal task documentingthat Asian American women performed better when their gender rather than theirethnicity was primed Although the generalizability and replicability of priminghas been doubted (Klein et al 2014) this body of evidence is consistent with contextdependence

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IIIA Likely versus Unlikely Exemplars

The most representative type for a group is the one thatagents most easily recall and associate with the group itself forinstance a red-haired Irishman or a 65+-year-old FloridianSocial psychologists call this type the exemplar of the groupAccordingly we define

DEFINITION 3 A type t is an exemplar for G given comparisongroup ndashG when

t 2 arg maxt

tG

tG

Under any specification of the weighting function ht inDefinition 2 overweighting (weakly) increases as we movetoward more representative types so the exemplar is also thetype whose probability is overweighted the most16 By analyzingthe exemplar then we can gauge whether representativenessinduces the DM to overweight a likely type (as happens in stan-dard models of categorical thinking) or an unlikely type Whenoverweighting occurs in unlikely and extreme types the biases ofstereotypes can be particularly severe17

Equation (2) yields the following characterization

PROPOSITION 1 Suppose the conditional distributions G and G

are not identical Consider two extreme cases

(i) If for all t t0

2 T we have that tG gt t0 G if and only iftG gt t0 G then the modal type is not an exemplar forat least one group

(ii) If for all t t0

2 T we have that tG gt t0 G if and only iftG lt t0 G then for each group the modal type is theexemplar

16 Consider the function hethTHORN from Definition 2 When applied to more repre-sentative types the first argument of the function increases while one of the otherT ndash 1 arguments decreases As a result the weighting factor ht (and thus overweigh-ing

sttG

tG) increases as well

17 In the rank-based truncation model the frequency of the exemplar providesa measure of stereotype accuracy By accuracy we mean the extent to which thestereotype minimizes the distance

Pt eth

sttG tGTHORN

2 When d = 1 and only one type isrecalled (there are no ties) accuracy is maximized if the exemplar is the most likelytype and minimized if the exemplar is the least likely type

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Case i says that when groups have similar distributions inthe sense of having the same likelihood ranking the most repre-sentative type is unlikely for at least one group potentially bothRepresentativeness draws the DMrsquos attention to group differ-ences neglecting the fact that the groups are similar and havethe same mode This mechanism generates inaccurate stereo-types and is illustrated by the Florida example This resultholds under any measure of representativeness that differenti-ates the two groups (eg the difference tG tG)

Case ii says that the most representative type tends to belikely for both groups when the distributions are very differentIn this case groups differ the most around their modes so repre-sentativeness and likelihood coincide Thinking of Swedes aslsquolsquoblondrsquorsquo and Europeans as lsquolsquodark hairedrsquorsquo is accurate precisely be-cause these are majority traits of the Swedish and European pop-ulations respectively In these cases stereotyping yields fairlyreliable models Of course there is still some inaccuracy Evenin the case of likely exemplars judgment errors can be signifi-cant For instance voters in some US states are perceived aslsquolsquobluersquorsquo or lsquolsquoredrsquorsquo because a majority of the population votesDemocrat or Republican In reality even in lsquolsquobluersquorsquo states farfrom everyone votes Democrat In the 2012 presidential electionvote shares of either candidate in most states ranged from 40 to6018

When DMs strongly overweight representative types themost severe biases occur when those types are unlikely and ex-treme This is true both under rank based truncations and undersmooth discounting functions (see Section IIIB) Ethnic stereo-types based on crime or terrorism exhibit this error they neglectthe fact that by far the most common types in all groups arehonest and peaceful

IIIB Stereotypical Moments

We now characterize how the first two moments of a distri-bution are distorted by the process of stereotyping To do so wemust restrict our analysis to cardinal ordered types The follow-ing results hold for any weighting function htethTHORN satisfyingDefinition 2 We consider two canonical cases that prove usefulin illustrating the predictions of the model

18 Presidential Election Results NBCNewscom see httpelectionsnbcnewscomnspolitics2012allpresident (accessed 5 September 2016)

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In the first case groups G and ndashG are such that the likelihoodratio tG

tGis monotonic in t The monotone likelihood ratio prop-

erty (MLRP) holds to a first approximation in many empiricalsettings and is also assumed in many economic models such asstandard agency models19 If tG

tGis monotonically increasing (de-

creasing) in t then group G is associated with higher (lower)values of t relative to the comparison group ndashG Formally

PROPOSITION 2 Suppose that MLRP holds and assume wlogthat the likelihood ratio tG

tGis strictly increasing in t Then

for any weighting function htethTHORN that is not constant in therelevant range

EstethtjGTHORN gt EethtjGTHORN gt EethtjGTHORN gt E

stethtjGTHORN

Under MLRP the most representative part of the distribu-tion for G is the right tail if tG

tGincreases in t or the left tail if tG

tG

decreases in t The representative tail is then overweighted whilethe nonrepresentative tail is underweighted As a consequencethe assessed mean E

stethtjGTHORN is too extreme in the direction of therepresentative tail

Critically in line with the social cognition perspective the ste-reotype contains a kernel of truth the DM overestimates the meanof G if this group has a higher mean than the comparison groupnamely EethtjGTHORN gt EethtjGTHORN and conversely if EethtjGTHORN lt EethtjGTHORN TheDM exaggerates this true difference because he inflates the asso-ciation of G with its most representative types20 For instancewhen judging an asset manager who performs well we tend to

19 Examples include the binomial and the Poisson families of distributionswith different parameters The characterization of distributions satisfying MLRPis easier in the case of continuous distributions (see Online Appendix D) two dis-tributions f(x) f ethx THORN that differ only in their mean satisfy MLRP if and only if thedistribution f(x) is log-concave Examples include the exponential and normal dis-tributions To the extent that discrete distributions sufficiently approximate thesedistributions (as the Poisson distribution PoisethTHORN approximates the normal distri-bution Neth THORN for large l) they will also satisfy MLRP

20 Depending on the distribution and the weighing function the DMrsquos assess-ment of the variance VarethtjGTHORNmay also be dampened relative to the truth This isoften true under the truncation weighing function In this case stereotyping effec-tively leads to a form of overconfidence in which the DM holds extreme views andoverestimates the precision of his assessment That extreme views and overconfi-dence (in the sense of over precision) go together has been documented in the settingof political ideology among others (Ortoleva and Snowberg 2015)

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overemphasize skill relative to luck because higher skill levels arerelatively more associated with higher performance This occurseven if for both skilled and unskilled managers high performanceis mostly due to luck

In the second case for which we characterize the stereotypi-cal distributions groups G and ndashG have the same mean EethtjGTHORNfrac14 EethtjGTHORN frac14 EethtTHORN but differ in their variance We abstract fromskewness and higher moments by considering distributionsethtGTHORNt2T and ethtGTHORNt2T that share the same support and are sym-metric around the medianmean EethtTHORN

PROPOSITION 3 Suppose that in G more extreme types are rela-tively more frequent than in ndashG Formally the likelihoodratio tG

tGis U-shaped in t around EethtTHORN Then for any weight-

ing function htethTHORN that is not constant in the relevant rangestereotypical beliefs satisfy

VarstethtjGTHORN gt VarethtjGTHORN gt VarethtjGTHORN gt VarstethtjGTHORN

EstethtjGTHORN frac14 E

stethtjGTHORN frac14 EethtTHORN

When group G has a higher relative prevalence of extremetypes its representative types are located at both extremes of thedistribution The DMrsquos beliefs about G are then formed by over-weighting both tails while underweighting the unrepresentativemiddle The overweighting of Grsquos tails causes the assessment ofits variance VarstethtjGTHORN to be too high For example the skill dis-tribution of immigrants to the United States may be perceived ashaving very fat tails or even bimodal with immigrants beingperceived as either unskilled or very skilled relative to the resi-dent population The mean of the group in contrast is assessedcorrectly because the stereotypical distribution remains symmet-ric around EethtTHORN As before the stereotype contains a kernel oftruth It induces the agent to exaggerate the true differences be-tween groups namely the higher variance of G relative to itscounterpart

We present a number of extensions of the model in the OnlineAppendix We first consider multidimensional type spaces andshow that stereotypes center around the dimension wheregroups differ the most in line with the kernel of truth logic(Online Appendix C) Multidimensional stereotypes imply thatthe dimension we think about is influenced by context For

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example the Irish are stereotyped as red-haired when comparedwith the European population However when compared withthe Scots a more plausible stereotype for the Irish is lsquolsquoCatholicrsquorsquobecause religion is the dimension along which Irish and Scotsdiffer the most

In Online Appendix D we extend the model to continuoustype spaces Many settings of interest in economics can be use-fully described by continuous probability distributions and weshow our model is particularly tractable in this case In OnlineAppendix E we relax Definition 2 and allow weighting of types toalso be influenced by their likelihood We show that the basicinsight that stereotypes contain a kernel of truth carries throughto these cases as well

To summarize the psychology of representativeness yieldsstereotypes that are consistent with the social cognition approachin which individuals assess groups by recalling and focusing ondistinctive group traits When there are systematic differencesbetween groups stereotypes get the direction right but exagger-ate differences

IIIC Some Examples

A growing body of field and experimental evidence points to awidespread belief that women are worse than men at mathemat-ics (Eccles Jacobs and Harold 1990 Guiso et al 2008 CarrellPage and West 2010) This belief persists despite the fact that fordecades women have been gaining ground in average schoolgrades including mathematics and have recently surpassedmen in overall school performance (Goldin Katz and Kuziemko2006 Hyde et al 2008) This belief shared by men and women(Reuben Sapienza and Zingales 2014) may help account for thegender gap in the choices of high school tracks college degreesand careers with women disproportionately choosing humanitiesand health-related areas (Weinberger 2005 Buser Niederle andOosterbeek 2014) and forgoing significant wage premiums toquantitative skills (Bertrand 2011)

Gender stereotypes in mathematics particularly beliefs thatexaggerate the extent of average differences are consistent withthe predictions of our model The fact that men are overrepre-sented at the very highest performance levels leads a stereotyp-ical thinker to exaggerate the magnitude of mean differencesFigure I shows the score distributions from the mathematics

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section of 2013rsquos Scholastic Aptitude Test (SAT) for men andwomen21 The distributions are very similar with averagescores slightly higher for men (531 versus 499 out of 800)However scores for men have a heavier right tail with mentwice as likely to have a perfect SAT math score than women22

In light of such data the stereotypical male performance in math-ematics is high while the stereotypical female performance ispoor Predictions based on such stereotypes are inaccurate exag-gerating true differences Consistent with this prediction exper-imental evidence shows that both genders underestimatewomenrsquos ability in simple math tasks even controlling for pastperformance (Reuben Sapienza and Zingales 2014) Coffman(2014) shows a similar pattern extends to confidence about ownability in other male-typed domains with women reporting sig-nificantly less confidence in gender-incongruent than gender-congruent tasks Our model suggests that these patterns mightcome from stereotypes based on gender differences in the righttail of the distribution While differences in the right tail of thedistribution are unlikely to be relevant for most decisions stereo-typical thinking driven by these differences has the potential toimpact economically important decisions whether through self-stereotyping (ie choice of careers or majors as in BuserNiederle and Oosterbeek 2014) or through discrimination (iehiring decisions as in Bohnet van Geen and Bazerman 2016)

The logic of exaggerated yet directionally correct stereotypesalso sheds light on the well-documented phenomenon of base rateneglect (Kahneman and Tversky 1973) Indeed Proposition 2implies that the DM overreacts to information that assigns

21 Standardized test performance measures not only innate ability but alsoeffort and investment by third parties (Hyde et al 2008) The mapping of test per-formance into inferences about innate ability is an issue not addressed by ourmodel

22 For 2013 SAT Mathematics scores see httpmediacollegeboardcomdigitalServicespdfresearchSAT-Percentile-Ranks-By-Gender-Ethnicity-2013pdf Results are similar for the National Assessment of Educational Progress(NAEP) which are more representative of the overall population For 2012NAEP scores for 17-year-olds in mathematics see httpnationsreportcardgovltt_2012age17maspx See Hyde et al (2008) Fryer and Levitt (2010) and Popeand Sydnor (2010) for in-depth empirical analyses of the gender gap inmathematics

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people to groups precisely because such information generatesextreme stereotypes Consider the classic example in which amedical test for a particular disease with a 5 prevalence has a90 rate of true positives and a 5 rate of false positives The testassigns each person to one of two groups + (positive test) or ndash(negative test) The DM estimates the frequency of the sick type(s) and the healthy type (h) in each group The test is informativea positive result increases the relative likelihood of sickness anda negative result increases the relative likelihood of health forany prior Formally

PreththornjsTHORN

PreththornjhTHORNgt 1 gt

PrethjsTHORN

PrethjhTHORNeth4THORN

This condition has clear implications the representative personwho tests positive is sick while the representative person whotests negative is healthy Following Proposition 2 the DMreacts to the test by moving his priors too far in the right di-rection generating extreme stereotypes He greatly boosts hisassessment that a positively tested person is sick but also thata negatively tested person is healthy Because most people arehealthy the DMrsquos assessment about the group that tested neg-ative is fairly accurate but is severely biased for the group that

FIGURE I

SAT Mathematics Scores by Gender (2013)

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tested positive This analysis formalizes Tversky andKahnemanrsquos (1983) verbal account of base rate neglect23

The same mechanism may underlie several other instanceswhere DMs overweight diagnostic information When assessingan employeersquos skill level an employer attributes high perfor-mance to high skill because high performance is the distinctivemark of a talented employee Because he neglects the possibilitythat some talented employees perform poorly and that somenontalented ones perform well (perhaps due to stochasticity inthe environment) the employer has too much faith in skill andneglects the role of luck in accounting for the output Similarlywhen assessing the performance of firms in a hot sector of theeconomy (eg G = internet) an investor recalls highly successfulfirms in that sector (t = return of Google Amazon etc) He ne-glects the possibility of firms being unsuccessful because lack ofsuccess is statistically nondiagnostic and psychologically nonrep-resentative of a growing sectormdasheven if it is likely This causesexcessive optimism (in that the expectation of growth is unrea-sonably high) and overconfidence (in that the variability in earn-ings growth considered possible is truncated) True the hot sectormay have better growth opportunities on average but represen-tativeness exaggerates this feature and induces the investor toneglect a significant risk of failure

IV Evidence on Representativeness and Stereotypes

Testing our model requires evaluating the beliefs individualshold about a target group against the true distribution of thattarget group over an attribute space An ideal data set would

23 Our account is distinct from a mechanical underweighting of base rates inBayes rule as in Grether (1980) and Bodoh-Creed Benjamin and Rabin (2013) Inthose models upon receiving the test results the DM can update his beliefs in thewrong direction he can be less confident that a person is healthy after a negativetest than under his prior which cannot happen in our model Although this predic-tion of our model seems consistent with introspection we are not aware of experi-mental evidence on this point Griffin and Tversky (1992) present evidenceconsistent with pure neglect of base rates but in a significantly different tasknamely inferring the bias of a coin from a history of coin flips Such experimentsare hard to compare with the predictions of our model because subjects are asked togenerate distributions of different numbers of coin flips in their minds which is amuch more involved task than to recall types of a given distribution Their assess-ments then might be wrong for other reasons See Bodoh-Creed Benjamin andRabin (2013) for a detailed discussion

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consist of naturally defined groups with known distributions overa given space of types and a corresponding set of beliefs about thedistribution of each group over that space of types This wouldallow us to test for exaggeration of true differences betweengroups and to ask whether this exaggeration is well predictedby overweighting representative types To identify a causal rolefor representativeness or context dependence we would need ex-ogenous variation in either the comparison group ndashG or in thedistributions over the type spaces This is unavailable in existingdata sets Accordingly we take a two-pronged approach First wecreate a controlled laboratory environment that allows us toinduce the exogenous variation in representative types that weneed to test causality then we reanalyze existing field evidence tocheck for consistency with our predictions

In testing our model we focus on the two main implicationsof representativeness-based stereotypes

Context dependence the stereotype of a target group de-pends on the characteristics of the reference group it iscompared to

Kernel of truth stereotypes depend on group character-istics andmdashin most (precisely characterized) settingsmdashare slanted toward representative types

We test the first property with a lab experiment (SectionIVA) We then turn to survey data on beliefs about US politicalgroups (Section IVB) for an empirical analysis that explores thesecond property The survey data are more tightly linked to ourinterest in social stereotypes The laboratory experiment allowsus to directly test the role of representativeness in generatingcontext dependent beliefs Online Appendixes F and G provideall details and additional results for the experiments and fieldevidence

IVA Lab Evidence on Representativeness and ContextDependence

The influence of the representativeness heuristic on recalland on beliefs has been extensively documented in the lab(Kahneman and Tversky 1972 1973) Our goal is to considerhow representativeness as formalized in equation (2) gives riseto context-dependent beliefs To our knowledge the possibility

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that representativeness may generate context dependence hasnot been tested before

To assess this prediction we perform a controlled laboratoryexperiment that allows us to isolate representativeness frommany confounding factorsmdashhistorical sociological or other-wisemdashthat may affect stereotype formation in the real worldWe construct our own groups of ordinary objects creating atarget group G and a comparison group ndashG We hold thetarget group G fixed and explore how participant impressions ofit change as we change the comparison group ndashG and thusrepresentativeness

We conducted several experiments in the laboratory and onAmazon Mechanical Turk Each involves a basic three-stepdesign First participants are shown the target group and a ran-domly assigned comparison group for 15 seconds In this timedifferences between groups can be noticed but the groupsrsquo precisecompositions cannot be memorized The second step consists of afew filler questions which briefly draw the participantsrsquo cognitivebandwidth away from their observation Finally participants areasked to assess the groups they saw Participants are incentiv-ized to provide accurate answers

We randomly assign participants to either the Control or theRepresentativeness condition In the Control condition G and ndashGhave nearly identical distributions so that all types are similarlyrepresentative for each group In the Representativeness condi-tion ndashG is changed in such a way that a certain type becomes veryrepresentative for G Context dependence implies that the assess-ment of G should now overweight this representative type eventhough the distribution of G itself has not changed

We ran six experiments of this form with design changesfocused on reducing participant confusion and removing con-founds We describe the final and most refined version of theseexperiments here In an attempt to provide a overview of the re-sults while remaining concise we provide the results from pooledspecifications that use all data collected In Online Appendix Fwe offer additional details and report all experiments conductedWe also give instructions and materials for each experiment thefull data set is available by request

Consider first the experiment illustrated in Figure II Agroup of 25 cartoon girls is presented next to a group of 25 cartoonboys in T-shirts of different colors blue green or purple In theControl condition (Figure II Panel a) the groups have identical

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color distributions (13 purple 12 green) so no color is represen-tative of either group The Representativeness condition (Panel b)compares the same group of girls with a different group of boysfor whom green shirts are replaced with blue shirts Now onlygirls wear green and only boys wear blue These colors althoughstill not the most frequent for either group are now most repre-sentative For each group girls and boys participants are asked anumber of questions concerning the frequency of T-shirts of dif-ferent colors worn by that group

Applying our model in the control condition the type space isT frac14 fgreen purpleg and the groups are G = girls and ndashG = boysGiven that the color distributions are identical across groups both

types are equally representativegreengirls

greenboysfrac14 1 frac14

purplegirls

purpleboys As a result

assessment of G should be correct on average stcontrolgreengirls frac14 greengirls

and stcontrolpurplegirls frac14 purplegirls for any weighing function (the same is

true about assessments of ndashG)In the treatment condition the distribution of shirt colors re-

mains the same for girls For boys green shirts are changed intoblue Thus the type space changes to T frac14 fgreen purple bluegand the representative color for girls becomes greengreengirls

greenboysfrac14 1 gt 1 frac14

purplegirls

purpleboys while that for boys becomes blue As

a result in the treatment condition subjects should inflate the

frequency of green shirts relative to the truth sttreatmentgreengirls

gt greengirls (the same should happen to assessments of blueshirts for boys) We also expect the assessed frequency of greenshirts to go up relative to the control condition namely

sttreatmentgreengirls gt stcontrol

greengirls Critically the only factor that varies

across treatments is the representativeness of the 12-colorshirt Thus if we see differences across conditions the causalrole of representativeness-based recall in shaping group judg-ments is clear24

24 We vary which colors are used in which roles across participants Someparticipants saw this particular color distribution while others see for examplegreen as the modal color and purple as the diagnostic color for boys in theRepresentativeness condition and blue as the diagnostic color for girls in theRepresentativeness condition We vary the colors across the roles to avoid con-founding the characteristics of any particular color with its diagnosticity

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FIG

UR

EII

T-S

hir

tsE

xp

erim

ent

Fig

ure

sap

pea

red

inco

lor

top

art

icip

an

tsin

the

exp

erim

ent

For

clari

ty

we

have

ad

ded

ale

tter

toea

chT

-sh

irt

toid

enti

fyth

eco

lor

for

the

read

er

lsquolsquoGrsquorsquo

ind

icate

sgre

en

lsquolsquoPrsquorsquo

ind

icate

sp

urp

le

lsquolsquoBrsquorsquo

ind

icate

sblu

eT

hes

ele

tter

sd

idn

otap

pea

rto

part

icip

an

tsan

dare

for

read

erre

fere

nce

only

P

lease

see

onli

ne

ver

sion

ofp

ubli

shed

art

icle

for

colo

rfi

gu

reex

act

lyas

itap

pea

red

top

art

icip

an

ts

STEREOTYPES 1779

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We collected data from 301 participants using this T-shirtsdesign25 Since the number of green and purple shirts is verysimilar we first ask each participant the simplest question ofwhich shirt color is modal Next we ask participants to assessthe share of green and purple shirts

Consistent with the role of representativeness participantsassigned to the Representativeness condition are 105 percentagepoints more likely to recall the less frequent color (green for girlsor blue for boys) as the modal color when it is representative of agroup (35 of participants guess the less frequent color is modalin the Control condition this proportion increases to 46 in theRepresentativeness condition p = 01 estimated from a probitregression reported in Online Appendix F)

We now turn to subjectsrsquo estimates of how many T-shirts ofeach color they saw in each group In both conditions the truedifference in counts is 1 (13 purple shirts 12 green or blue shirts)In the Control condition participants on average believe they saw054 more purple shirts than green or blue shirts In theRepresentativeness condition participants believe they saw072 fewer purple shirts than green or blue shirts (the acrosstreatment difference is significant with p = 01 from OLS regres-sion reported in Online Appendix F)

In total we collected data for six experiments of this generalstructure gathering evidence from more than 1000 participantsAs we describe in Online Appendix F although there is substan-tial variation across experiments when we pool all of the data wefind significant aggregate treatment effects in line with a role ofrepresentativeness in judgment We employ four different unor-dered types designs similar to the T-shirts experiment using sixsamples (four online and two in the laboratory) with 741 partic-ipants We find effects in the predicted direction for five of the sixsamples Using a probit regression that pools the data for theseunordered type experiments we find that participants are 93 per-centage points more likely to guess that the less frequent type ismodal when it is representative than when it is not (p = 002) Wealso run a family of ordered types experiments (two designs fivesamples 402 participants) Unlike the simpler T-shirts style

25 Throughout our analysis we exclude any participant who participated in aprevious version of the experiment and any participant who self-identified as color-blind In Online Appendix F we show that our results are unchanged if we includethese additional observations

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design the theoretical predictions for the ordered types designsare more sensitive to the specific assumptions one makes aboutthe weighting function of the DM26 We find effects in the pre-dicted direction for three of the five samples As we discuss inmore detail in Online Appendix F the ordered types resultsvary by platform with consistently stronger results on AmazonMechanical Turk than in the laboratory samples Pooling all or-dered types experiments participants are 93 percentage pointsmore likely to guess that the group of interest has a greater av-erage than the comparison group when the right tail is represen-tative (p = 062) Given our simple experimental setting withgroups of mundane objects we interpret our resultsmdasha signifi-cant and reasonably sized impact on average beliefsmdashas an im-portant proof of concept the presence of representative typesbiases ex post assessment

IVB Empirical Evidence on Political Stereotypes

We examine two data sets on political preferences and be-liefs about political preferences in the United States We inves-tigate the roles of representativeness and context dependence byseparately testing for hypotheses that allow us to assess the lead-ing theories of stereotypes

First we test whether beliefs are correct or depart systemat-ically from the truth The statistical discrimination approachbuilds on the assumption that people hold rational expectationsof group traits Comparing beliefs to the truth allows us to assessthe validity of this assumption in our data

Second we test if beliefs depart from the truth by exagger-ating (mean) differences among groups per the kernel of truthhypothesis This is an implicit test of context dependence be-cause it implies that beliefs about the target groups are shapednot only by that grouprsquos characteristics but also by those of thereference group27

Third we test if distortions in beliefs can be accounted for bythe overweighting of highly representative types (defined astypes that are relatively more frequent in the target relative to

26 This is due in part to our choice to not study MLRP distributions We moti-vate and discuss this design decision in Online Appendix F

27 Of course unlike in the laboratory experiment in this setting we cannot testfor context dependence by exogenously varying the reference group

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the reference group) The second and third tests address the keypredictions of our model

1 The Data We have two data sets on political preferences andbeliefs about political preferences The first data set from GrahamNosek and Haidt (GNH 2012) contains data from the MoralFoundations Questionnaire Respondents (1174 self-identified lib-erals and 500 self-identified conservatives) answer questions abouttheir position on a subset of 45 issues 20 moral relevance state-ments (eg lsquolsquowhen you decide whether something is right orwrong to what extent are the following considerations relevantto your thinkingrsquorsquo) and 25 moral judgments (eg lsquolsquoindicate theextent to which you would agree or disagreersquorsquo) For each issue arandomly determined subset of participants states their own posi-tion another subset states their belief on the position of a lsquolsquotypicalliberalrsquorsquo and a third subset states their belief on the position of alsquolsquotypical conservativersquorsquo The data thus include the distribution overpositions for both liberal and conservatives as well as the averagebelieved typical position of liberals and of conservatives on the 45issues Each position is elicited on 1ndash6 scale

The second data set comes from the American NationalElection Survey (ANES) and contains data from more than20000 respondents between 1964 and 201228 The surveycovers political issues of the day such as the optimal amount ofgovernment spending and service provision (1984ndash2000) or theplace of women in society (1972ndash1998) We focus on the 10 issuesthat ask participants to respond on a 1ndash7 scale (rather than justindicate binary agreement or disagreement) all 10 issues areasked in multiple years Participants are asked to provide theirown position on the scale and their believed position of theDemocratic and Republican parties (lsquolsquoWhere would you placethe Democratic [Republican] party on this scalersquorsquo) The data in-clude for each issue-year observation the distribution of partic-ipant positions for self-identified liberals and self-identifiedconservatives as well as the distribution of believed typical posi-tions of the Democratic and Republican parties

28 These data are publicly available at httpwwwelectionstudiesorgstudy-pagesanes_timeseries_cdfanes_timeseries_cdfhtm

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2 Empirical Strategy Our analysis focuses on beliefs abouttwo groups Conservatives and Liberals The types are the possi-ble positions for each issue (1 2 6 7) For the GNH data weinterpret beliefs about the lsquolsquotypicalrsquorsquo element of a group to coincidewith the believed average position in that group Similarly forthe ANES data we use the believed party positions as a proxy forbelieved mean of each group29 We then take as a benchmark thehypothesis that individuals hold accurate beliefs about eachgroup and in particular that believed mean position shouldequal true mean position at least on average across subjectsThe accurate beliefs hypothesis underlies the most common eco-nomic model of stereotyping statistical discrimination

To assess our representativeness-based model we perform aregression exercise To test our model in a linear regressionframework we rely on linear approximations of the weightingfunction Our model then yields two regression specifications

PROPOSITION 4 Let G 2 fconservative liberal g and assume

ht h tG

tG

be a differentiable and strictly increasing weight-

ing function as in Definition 2 The following hold as a first-order approximation around identical distributions G

Gfrac14 1

(i) Kernel of truth regression There exists a constant gt 0such that

EstethtjGTHORN frac14 EethtjGTHORNeth1thorn THORN EethtjGTHORNeth5THORN

(ii) Representativeness regression Denote H frac14 fT 2 Tg

the right tail of types and RconsH frac14

PHtconsPHtlib

as the average

representativeness of right tail types for conservatives

29 This assumption is consistent with the authorsrsquo interpretation of the GNHdata (GNH 2012) and with previous studies using ANES (eg Westfall et al 2015)Furthermore to the extent that this assumption holds equally well for most issueswithin a data set our focus on cross-issue differences should allow us to test thepredictions of our model even with an imperfect proxy for beliefs of mean positionsFinally the data provide some insight into whether subjects are reporting (per-ceived) modal or mean types As we show the modal type is a poor prediction ofstated beliefs while a distorted mean slanted toward representative types is anaccurate prediction of stated beliefs

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Under the further approximation where tcons

tlibampRcons

H for

t 2 H

EstethtjconsTHORN frac14 EethtjconsTHORN thorn consethR

consH 1THORNeth6THORN

EstethtjlibTHORN frac14 EethtjlibTHORN libethR

consH 1THORNeth7THORN

where lcons and llib are positive constants

The first regression allows us to test for the kernel of truthhypothesis and the second set of regressions allows us to test forthe role of representativeness

Equation (5) says that respondents in our model inflate theaverage position of a group say the conservatives if and only ifthe group has a higher average position than the other groupnamely the liberals Formally EstethtjconsTHORN gt EethtjconsTHORN if and onlyif EethtjconsTHORN gt EethtjlibTHORN Because in our measurement scale highertypes mean lsquolsquomore conservativersquorsquo we expect (i) believed conserva-tive average to be higher than the truth and (ii) the extent ofoverstatement to decrease in the average liberal position EethtjlibTHORNConversely we expect the average liberal position to be lowerthan the truth the more so the higher the average conservativeposition EethtjconsTHORN

As previously discussed the basis of these predictions is con-text dependence information about the distribution of ndashG is rel-evant for the beliefs about G This context dependence isinconsistent with rational expectations in which only thegrouprsquos own means should affect beliefs We test the hypothesisthat the true mean EethtjGTHORN is a significant predictor of the believedmean E

stethtjGTHORN with a positive sign and the other grouprsquos truemean EethtjGTHORN is a predictor of the believed mean with a negativesign

Equations (6) and (7) say that repondentsrsquo assessment bias isshaped by representativeness When the right tail is more repre-sentative for conservatives (Rcons

H 1 positive and large) partici-pants should inflate the average conservative position more(higher E

stethtjconsTHORN EethtjconsTHORN) and deflate the average liberal po-sition more (lower E

stethtjlibTHORN EethtjlibTHORN) We test the hypothesisthat the inflation in conservative positions is positively associatedwith the representativeness of the right tail for the conservativesand the inflation in liberal positions is negatively associated with

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it Once again the representativeness of the right tail is com-puted using the true distribution of positions

In equations (6) and (7) in many cases the representative tailis also the most likely one As a consequence these tests cannotdistinguish a representativeness-based from a likelihood-basedmodel of distorted beliefs We perform two additional testsFirst we run versions of equations (6) and (7) in which we controlfor the likelihood of tails (see Table A4 in Online Appendix G)Second we compute numerically the predictions of a representa-tiveness-based model of stereotypes and a likelihood-based modelof stereotypes We then assess which of these two is better able tomatch the data on beliefs

3 Empirical Results To begin we illustrate the structure ofthe data and the nature of our predictions with two simple exam-ples from the GNH data set focusing on beliefs about conserva-tives In example 1 participants are asked about their agreementwith the statement lsquolsquoIt can never be right to kill a human beingrsquorsquoIn example 2 participants are asked about the moral relevance oflsquolsquowhether or not someone cared for someone weak or vulnerablersquorsquoAs can be seen in Figure III in example 1 the modal position(strongly disagree (1)) and most representative positions(strongly disagree (1)) coincide for conservatives In contrast inexample 2 in Figure III the most representative types (slightlyrelevant (3) not at all relevant (1)) are not most likely for theconservative group Following Proposition 1 we predict that be-liefs will be distorted in the direction of the most representativetypes Thus we expect more exaggeration in example 2 than inexample 1 since in example 2 the most representative types (inthe left tail) are far from the modal type whereas in example 1they coincide This is what we find the conservative position isexaggerated by only 009 positions in Example 1 (true mean 299believed mean 290) but by 106 positions in Example 2 (truemean 421 believed mean 315)

In the full data sets we treat each (issue year) pair as anobservation and we cluster standard errors at the issue level Forthe GNH data we have 45 observations 45 issues measured inthe same year For the ANES data we have 66 observations 10issues measured in multiple years To begin we simply docu-ment systematic exaggeration in both data sets This is a primaryfocus of the original analysis in GNH (2012) and also in Westfall

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FIGURE III

Two Examples

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et al (2015)rsquos analysis of the ANES data30 Figure IV shows thatthe believed difference between typical conservative and typicalliberal positions is larger than the true difference in mean posi-tions for 109 of the 111 observations The data for both GNH(squares) and ANES (triangles) lie above the 45-degree line(dashed)31 Average exaggeration is 062 positions on the scale(066 in the GNH data 059 in the ANES data)32

The systematic and significant exaggeration of mean differ-ences suggests that the benchmark model of accurate beliefs ismissing something important Indeed this exaggeration reflectsthe fact that believed means are typically more extreme than truemeans First note that the kernel of truth regression (equation(5)) generates exaggeration of mean differences just as docu-mented in Figure IV

EstethtjGTHORN E

stethtjGTHORN frac14 eth1thorn 2THORN frac12EethtjGTHORN EethtjGTHORN

To bring this prediction to the data we regress the believedmean position for each group EBethtjGTHORN on the true mean of thegroup EethtjGTHORN and the true mean of the comparison groupEethtjGTHORN across issues We do this for each group (liberals con-servatives) in each data set separately We also present pooledspecifications that combine the data sets to make a prediction fora given group (liberals conservatives) In these pooled specifica-tions we include a dummy variable indicating whether theobservation came from the ANES data set For all specificationswe cluster observations at the issue level33 The results from re-gression are shown in Table I In every specification we find thatEethtjGTHORN is a significant predictor of EBethtjGTHORN with the predicted pos-itive sign Crucially for five of the six specifications the mean of

30 Chambers and Melnyk (2006) also find evidence of exaggeration of truedifferences in beliefs about political positions

31 For convenience we recode all issues so that the high end of the scale (67)represents the stereotypically more conservative position

32 A natural question to ask is how beliefs vary across liberals and conserva-tives That is do beliefs about a group G depend on membership in G versus ndashG Ourmodel does not speak to this issue However in Online Appendix G we show thatthe results we document below hold for both beliefs held by conservatives and be-liefs held by liberals see Tables A9 A10 and A11

33 In general the results presented below for the ANES data are not largelyimpacted by the decision to cluster at the issue level Similar results are obtained ifthe data are not clustered

STEREOTYPES 1787

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the comparison group EethtjGTHORN is also a significant predictor ofE

BethtjGTHORN with the predicted negative signAlthough these results provide strong evidence of context

dependence and are consistent with our model they do not pindown a role for representativeness of types Our next test relatesthe magnitude of representativeness of tail types to the magni-tude of belief distortions

To this end we implement the regressions in equations (6)and (7) Following Proposition 4 we compute the average repre-

sentativeness of tail types for conservatives RconsH frac14

PtT2tconsPtT2tlib

We

again test the hypothesis that RconsH is a significant predictor of Est

ethtjconsTHORN with a positive sign and a predictor of EstethtjlibTHORN with a

negative sign Table II shows that conditional on true mean RconsH

predicts believed mean for each group G as expected The firstthree specifications display the results for predicting beliefs heldabout conservatives In both data sets the average representa-tiveness of tail types for conservatives is a significant positivepredictor of beliefs held about conservatives The final three spe-cifications display the results for predicting beliefs held about

FIGURE IV

Exaggeration of Differences

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liberals We find that the average representativeness of tail typesfor conservatives is a negative predictor of beliefs held about lib-erals This effect is significant in the GNH data and marginallysignificant in the ANES data

We present several additional results in Online Appendix GTo further examine the role of representativeness in driving be-liefs we first show the results of Table II carry through when we

TABLE II

AVERAGE REPRESENTATIVENESS OF TAIL POSITIONS PREDICTS BELIEFS

OLS Predicting Believed Mean of Group G for Each Issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position

of group G for issue

078 024 051 072 018 041

(006) (008) (009) (005) (005) (010)

Avg rep of tail types for

conservatives RconsH

019 055 025 014 012 024

(007) (022) (008) (006) (007) (005)

Constant 101 260 184 093 271 201

(026) (045) (029) (022) (025) (032)

R2 082 048 060 091 031 070

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

TABLE I

INFORMATION ABOUT ndashG PREDICTS BELIEFS ABOUT G

OLS predicting believed mean of group G for each issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position of

conservatives for issue

102 098 096 021 019 025

(0097) (0133) (0076) (0060) (0116) (0060)

True mean position of

liberals for issue

035 086 058 0987 039 073

(0106) (0134) (0131) (0066) (0106) (0135)

Constant 151 335 235 069 258 156

(0195) (0269) (0279) (0122) (0249) (0270)

R2 083 053 066 092 032 068

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

STEREOTYPES 1789

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control for the average likelihood on the tail positions (see Table A4in Online Appendix G) Most tellingly we use the model to predictbeliefs across issues and compare those to the data For simplicitywe use the rank-based truncation specification to predict mean be-liefs when stereotypes include the d most representative types ford frac14 1 T We compare these predictions to those of a model inwhich beliefs are obtained by restricting the distribution to the dmost likely types Our benchmark for both models is predicting thebelieved mean from the entire distribution where d = T We showthat the predictions of the rank-based truncation model with d = 4or 5 compare favorably to both a likelihood-based truncation model(with any d) and the accurate beliefs benchmark Interestingly thisresult suggests that stereotypical beliefs are well approximated byneglecting the least representative types (as opposed to focusingonly on the most representative types) and so represent a moderatethough systematic departure from the standard benchmarkFinally we show that the results we document above hold forboth beliefs held by conservatives and beliefs held by liberals (seeTables A9 A10 and A11 in Online Appendix G)

V Conclusion

We present a model of stereotypical thinking in which DMsmaking predictions about a group overweight the grouprsquos mostdistinctive types These overweighted types are not the mostlikely ones given the DMrsquos data but the most representativeones in the sense of being the most diagnostic of the group rela-tive to other groups Representativeness implies that what ismost distinctive of a group depends on what group it is comparedwith We present experimental evidence that confirms this con-text dependence in recall-based assessments of groups Finallywe evaluated the predictions of the model using political data fromexisting large-scale surveys We find context dependence to be akey feature of beliefs Given the richness of the political data wecan go a step further and identify a role for representativeness inparticular As the representativeness of tail types increases beliefsof a group are distorted in the direction of that tail

Our approach provides a parsimonious and psychologicallyfounded account of how DMs generate simplified representationsof reality from social groups to stock returns and offers a unifiedaccount of disparate pieces of evidence relating to this type of

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uncertainty The model captures the central fact that stereotypeshighlight the greatest difference between groups thus explainingwhy some stereotypes are very accurate while others lack valid-ity Still stereotypes often have a kernel of truth when they arebased on systematicmdasheven if smallmdashdifferences between groupsThis logic allows us to describe a number of heuristics and psy-chological biases many of which arise in the context of predictionproblems Generically our model generates overreaction to diag-nostic information

Our model is based on representativeness and does not cap-ture all the features of stereotypical thinking However it cap-tures perhaps the central feature when we think of a group wefocus on what is most distinctive about it and neglect or under-weight the rest

Saeuroıd Business School University of Oxford

Ohio State University and Harvard Business School

Universita Bocconi and Innocenzo Gasparini Institute

for Economic Research

Harvard University

Supplementary Material

An Online Appendix for this article can be found at QJEonline (qjeoxfordjournalorg)

References

Adorno Theodor Else Frenkel-Brunswik Daniel Levinson and Nevitt SanfordThe Authoritarian Personality (New York Harper amp Row 1950)

Arrow Kenneth lsquolsquoThe Theory of Discriminationrsquorsquo in Discrimination in LaborMarkets Orley Ashenfelter and Albert Rees eds (Princeton NJPrinceton University Press 1973)

Ashton Michael and Victoria Esses lsquolsquoStereotype Accuracy Estimating theAcademic Performance of Ethnic Groupsrsquorsquo Personality and SocialPsychology Bulletin 25 (1999) 225ndash236

Barberis Nicholas Andrei Shleifer and Robert Vishny lsquolsquoA Model of InvestorSentimentrsquorsquo Journal of Financial Economics 49 (1998) 307ndash343

Bayer Sylvia lsquolsquoThe Accuracy of Academic Gender Stereotypesrsquorsquo Sex Roles 40(1999) 787ndash813

Benjamin Dan James Choi and Joshua Strickland lsquolsquoSocial Identity andPreferencesrsquorsquo American Economic Review 100 (2010) 1913ndash1928

Benjamin Dan Matthew Rabin and Collin Raymond lsquolsquoA Model of Non-Belief inthe Law of Large Numbersrsquorsquo Journal of the European Economic Association15 (2015) 515ndash544

Bertrand Marianne lsquolsquoNew Perspectives on Genderrsquorsquo Handbook of LaborEconomics 4 (2011) 1543ndash1590

Bodoh-Creed Aaron Dan Benjamin and Matthew Rabin lsquolsquoThe Dynamics of Base-Rate Neglectrsquorsquo mimeo Haas Business School 2013

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Bohnet Iris Alexandra van Geen and Max Bazerman lsquolsquoWhen PerformanceTrumps Gender Bias Joint versus Separate Evaluationrsquorsquo ManagementScience 5 (2016) 1225ndash1234

Bordalo Pedro Nicola Gennaioli and Andrei Shleifer lsquolsquoSalience Theory of Choiceunder Riskrsquorsquo Quarterly Journal of Economics 127 (2012) 1243ndash1285

mdashmdashmdash lsquolsquoSalience and Consumer Choicersquorsquo Journal of Political Economy 121(2013) 803ndash843

Briton Nancy and Judith Hall lsquolsquoBeliefs about Female and Male NonverbalCommunicationrsquorsquo Sex Roles 32 (1995) 79ndash90

Buser Thomas Muriel Niederle and Hessel Oosterbeek lsquolsquoGenderCompetitiveness and Career Choicesrsquorsquo Quarterly Journal of Economics 129(2014) 1409ndash1447

Carrell Scott Marianne Page and James West lsquolsquoSex and Science How ProfessorGender Perpetuates the Gender Gaprsquorsquo Quarterly Journal of Economics 125(2010) 1101ndash1144

Chambers John and Darya Melnyk lsquolsquoWhy Do I Hate Thee ConflictMisperceptions and Intergroup Mistrustrsquorsquo Personality and SocialPsychology Bulletin 32 (2006) 1295ndash1311

Chan Wayne Robert R McCrae Filip De Fruyt Lee Jussim CorinnaE Lockenhoff Marleen De Bolle Paul T Costa Jr Angelina R SutinAnu Realo Juri Allik Katsuharu Nakazato Yoshiko ShimonakaMartina Hrebıckova Sylvie Graf Michelle Yik Marina Brunner-SciarraNora Leibovich De Figueora Vanina Schmidt Chang-kyo Ahn Hyun-nie Ahn Maria E Aguilar-Vafaie Jerzy Siuta Barbara SzmigielskaThomas R Cain Janet T Crawford Khairul Anwar Mastor Jean-Pierre Rolland Florence Nansubuga Daniel R MiramontezVeronica Benet-Martınez Jerome Rossier Denis Bratko Iris MarusicJamin Halberstadt Mami Yamaguchi Goran Knezevic Thomas A MartinMirona Gheorghiu Peter B Smith Claudio Barbaranelli Lei WangJane Shakespeare-Finch Margarida P Lima Waldemar KlinkoszAndrzej Sekowski Lidia Alcalay Franco Simonetti Tatyana V AvdeyevaV S Pramila and Antonio Terracciano lsquolsquoStereotypes of Age Differences inPersonality Traits Universal and Accuratersquorsquo Journal of Personality andSocial Psychology 103 (2012) 1050ndash1066

Chen Yan Sherry Xin Liu Tracy Xiao and Margaret Shih lsquolsquoWhich Hat to WearImpact of Natural Identities on Coordination and Cooperationrsquorsquo Games andEconomic Behavior 84 (2014) 58ndash86

Coffman Katherine lsquolsquoEvidence on Self-Stereotyping and the Contribution ofIdeasrsquorsquo Quarterly Journal of Economics 129 (2014) 1625ndash1660

Cunningham Tom lsquolsquoComparisons and Choicersquorsquo mimeo Stockholm University2013

Diekman Amanda Alice Eagly and Patrick Kulesa lsquolsquoAccuracy and Bias in theStereotypes about the Social and Political Attitudes of Women and MenrsquorsquoJournal of Experimental Social Psychology 38 (2002) 268ndash282

Eccles Jacquelynne S Janis E Jacobs and Rena D Harold lsquolsquoGender RoleStereotypes Expectancy Effects and Parentsrsquo Socialization of GenderDifferencesrsquorsquo Journal of Social Issues 46 (1990) 183ndash201

Fryer Roland and Matthew Jackson lsquolsquoA Categorical Model of Cognition andBiased Decision-Makingrsquorsquo BE Journal of Theoretical Economics 8 (2008)1ndash42

Fryer Roland and Steven Levitt lsquolsquoAn Empirical Analysis of the Gender Gap inMathematicsrsquorsquo American Economic Journal Applied Economics 2 (2010)210ndash240

Gennaioli Nicola and Andrei Shleifer lsquolsquoWhat Comes to Mindrsquorsquo Quarterly Journalof Economics 125 (2010) 1399ndash1433

Gennaioli Nicola Andrei Shleifer and Robert Vishny lsquolsquoNeglected RisksFinancial Innovation and Financial Fragilityrsquorsquo Journal of FinancialEconomics 104 (2012) 452ndash468

Gilens Martin lsquolsquoRace and Poverty in America Public Misperceptions and theAmerican News Mediarsquorsquo Public Opinion Quarterly 60 (1996) 515ndash541

Glaeser Edward lsquolsquoThe Political Economy of Hatredrsquorsquo Quarterly Journal ofEconomics 120 (2005) 45ndash86

QUARTERLY JOURNAL OF ECONOMICS1792

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ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

Glover Dyland Amanda Pallais and William Pariente lsquolsquoDiscrimination as a Self-Fulfilling Prophecy Evidence from French Grocery Storesrsquorsquo mimeo HarvardUniversity 2015

Goldin Claudia Lawrence Katz and Ilyana Kuziemko lsquolsquoThe Homecoming ofAmerican College Women The Reversal of the College Gender GaprsquorsquoJournal of Economic Perspectives 20 (2006) 133ndash156

Graham Jesse Brian Nosek and Jonathan Haidt lsquolsquoThe Moral Stereotypes ofLiberals and Conservatives Exaggeration of Differences across thePolitical Spectrumrsquorsquo PLoS One 7 (2012) 1ndash13

Grether David lsquolsquoBayes Rule as a Descriptive Model The RepresentativenessHeuristicrsquorsquo Quarterly Journal of Economics 95 (1980) 537ndash557

Griffin Dale and Amos Tversky lsquolsquoThe Weighing of Evidence and theDeterminants of Confidencersquorsquo Cognitive Psychology 24 (1992) 411ndash435

Guiso Luigi Ferdinando Monte Paola Sapienza and Luigi Zingales lsquolsquoCultureGender and Mathrsquorsquo Science 320 (2008) 1164ndash1165

Hilton James and William Von Hippel lsquolsquoStereotypesrsquorsquo Annual Review ofPsychology 47 (1996) 237ndash271

Hyde Janet Sara Lindberg Marcia Linn Amy Ellis and Caroline WilliamslsquolsquoGender Similarities Characterize Math Performancersquorsquo Science 321 (2008)494ndash495

Judd Charles and Bernardette Park lsquolsquoDefinition and Assessment of Accuracy inSocial Stereotypesrsquorsquo Psychological Review 100 (1993) 109ndash128

Jussim Lee Jarret Crawford Stephanie Anglin John Chambers Sean Stevensand Florette Cohen lsquolsquoStereotype Accuracy One of the Largest and MostReplicable Effects in All of Social Psychologyrsquorsquo in The Handbook ofPrejudice Stereotyping and Discrimination Todd Nelson ed (MahwahNJ Lawrence Erlbaum 2015)

Kahneman Daniel and Amos Tversky lsquolsquoSubjective Probability A Judgment ofRepresentativenessrsquorsquo Cognitive Psychology 3 (1972) 430ndash454

mdashmdashmdash lsquolsquoOn the Psychology of Predictionrsquorsquo Psychological Review 80 (1973) 237ndash251

Kaplowitz Stan Bradley Fisher and Clifford Broman lsquolsquoHow Accurate ArePerceptions of Social Statistics about Blacks and Whitesrsquorsquo Public OpinionQuarterly 67 (2003) 237ndash243

Kersten Daniel Pascal Mamassian and Alan Yuille lsquolsquoObject Perception asBayesian Inferencersquorsquo Annual Review of Psychology 55 (2004) 271ndash304

Klein Richard Kate A Ratliff Michelangelo Vianello Reginald B Adams JrStepan Bahnik Michael J Bernstein Konrad Bocian Mark J BrandtBeach Brooks Claudia Chloe Brumbaugh Zeynep CemalcilarJesse Chandler Winnee Cheong William E Davis Thierry DevosMatthew Eisner Natalia Frankowska David Furrow Elisa Maria GallianiFred Hasselman Joshua A Hicks James F Hovermale S Jane HuntJeffrey R Huntsinger Hans IJzerman Melissa-Sue John Jennifer A Joy-Gaba Heather Barry Kappes Lacy E Krueger Jaime Kurtz CarmelA Levitan Robyn Mallett Wendy L Morris Anthony J Nelson JasonA Nier Grant Packard Ronaldo Pilati Abraham M RutchickKathleen Schmidt Jeanine L Skorinko Robert Smith Troy G SteinerJustin Storbeck Lyn M Van Swol Donna Thompson Anna van rsquot VeerLeigh Ann Vaughn Marek Vranka Aaron Wichman Julie A Woodzickaand Brian A Nosek lsquolsquoInvestigating Variation in Replicability A ManyLabs Replication Projectrsquorsquo Social Psychology 45 (2014) 142ndash152

Lundberg Shelly and Richard Startz lsquolsquoPrivate Discrimination and SocialIntervention in Competitive Labor Marketsrsquorsquo American Economic Review73 (1983) 340ndash347

Madon Stephanie Max Guyll Kathy Aboufadel Eulices Montiel Alison SmithPolly Palumbo and Lee Jussim lsquolsquoEthnic and National Stereotypes ThePrinceton Trilogy Revisited and Revisedrsquorsquo Personality and SocialPsychological Bulletin 27 (2001) 996ndash1010

Martin Carol lsquolsquoA Ratio Measure of Sex Stereotypingrsquorsquo Journal of Personality andSocial Psychology 52 (1987) 489ndash499

STEREOTYPES 1793

at Harvard L

ibrary on October 28 2016

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ownloaded from

McCauley Clark Krishna Thangavelu and Paul Rozin lsquolsquoSex Stereotyping ofOccupations in Relation to Television Representations and Census FactsrsquorsquoBasic and Applied Social Psychology 9 (1988) 197ndash212

Mullainathan Sendhil lsquolsquoThinking through Categoriesrsquorsquo mimeo HarvardUniversity 2002

Ortoleva Pietro and Erik Snowberg lsquolsquoOverconfidence in Political BehaviorrsquorsquoAmerican Economic Review 105 (2015) 504ndash535

Phelps Edmund lsquolsquoThe Statistical Theory of Racism and Sexismrsquorsquo AmericanEconomic Review 62 (1972) 659ndash661

Pope Devin and Justin Sydnor lsquolsquoGeographic Variation in the Gender Differencesin Test Scoresrsquorsquo Journal of Economic Perspectives 24 (2010) 95ndash108

Rabin Matthew lsquolsquoInference by Believers in the Law of Small NumbersrsquorsquoQuarterly Journal of Economics 117 (2002) 775ndash816

Rabin Matthew and Joel Schrag lsquolsquoFirst Impressions Matter A Model ofConfirmatory Biasrsquorsquo Quarterly Journal of Economics 114 (1999) 37ndash82

Rabin Matthew and Dimitri Vayanos lsquolsquoThe Gamblerrsquos and Hot-Hand FallaciesTheory and Applicationsrsquorsquo Review of Economic Studies 77 (2010) 730ndash778

Reuben Ernesto Paola Sapienza and Luigi Zingales lsquolsquoHow Stereotypes ImpairWomenrsquos Careers in Sciencersquorsquo Proceedings of the National Academy ofSciences 111 (2014) 4403ndash4408

Rosch Eleanor lsquolsquoNatural Categoriesrsquorsquo Cognitive Psychology 4 (1973) 328ndash350Ryan Carey S lsquolsquoAccuracy of Black and White College Studentsrsquo In-Group and

Out-Group Stereotypesrsquorsquo Personality and Social Psychology Bulletin 22(1996) 1114ndash1127

Schneider David The Psychology of Stereotyping (New York Guilford Press2004)

Schneider David Albert Hastorf and Phoebe Ellsworth Person Perception(Reading MA Addison-Wesley 1979)

Shih Margaret Todd Pittinsky and Nalini Ambady lsquolsquoStereotype SusceptibilityIdentity Salience and Shifts in Quantitative Performancersquorsquo PsychologicalScience 10 (1999) 80ndash83

Shih Margaret Todd Pittinsky and Amy Trahan lsquolsquoDomain-Specific Effects ofStereotypes on Performancersquorsquo Self and Identity 5 (2006) 1ndash14

Steele Claude Whistling Vivaldi How Stereotypes Affect Us and What We CanDo (New York Norton 2010)

Tenenbaum Joshua and Thomas Griffiths lsquolsquoThe Rational Basis ofRepresentativenessrsquorsquo 23rd Annual Conference of the Cognitive ScienceSociety (2001) 1036ndash1041

Tversky Amos and Daniel Kahneman lsquolsquoExtensional versus Intuitive ReasoningThe Conjunction Fallacy in Probability Judgmentrsquorsquo Psychological Review 90(1983) 293ndash315

Weinberger Catherin lsquolsquoIs the Science and Engineering Workforce Drawn fromthe Far Upper Tail of the Math Ability Distributionrsquorsquo mimeo UCSB 2005

Westfall Jacob Leaf Van Boven John Chambers and Charles Judd lsquolsquoPerceivingPolitical Polarization in the United States Party Identity Strength andAttitude Extremity Exacerbate the Perceived Partisan DividersquorsquoPsychological Science 10 (2015) 145ndash158

Wolsko Christopher Bernadette Park Charles Judd and Bernd WittenbrinklsquolsquoFraming Interethnic Ideology Effects of Multicultural and Color-BlindPerspectives on Judgments of Groups and Individualsrsquorsquo Journal ofPersonality and Social Psychology 78 (2000) 635ndash654

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Page 10: I. Introduction · uneducated at the beginning of the 20th century, and as high achievers at the beginning of the 21st (Madon et al. 2001). Social science has produced three broad

DEFINITION 2 The DM attaches to each type t 2 T in group G adistorted probability

sttG frac14 tG

htethRethtGGTHORNTHORNPs2T sGhsethRethtGGTHORNTHORN

eth3THORN

where ht RTthornRthorn is a weighting function such that

(i) The weight ht is a symmetric function of the representa-

tiveness of types s 6frac14 t Formally ht frac14 h tG

tG

sG

sG

s2Tn tf g

where h Rthorn RT1thorn Rthorn is a function that is invariant to

a permutation of the last T ndash 1 arguments(ii) Weighing of a type increases in own representativeness

and decreases in the representativeness of other typesFormally the function hethTHORN is weakly increasing in itsfirst argument and weakly decreasing in the other T 1arguments

We call the distribution ethsttGTHORNt2T the stereotype for G If a type

t is objectively more likely namely tG is higher then the ste-reotype attaches higher probability to it By property i distor-tions are due exclusively to the fact that a type is more or lessrepresentative than the others In particular if all types areequally representative the DM equally weighs all of them ath(1) and holds rational expectations about G If instead the rep-resentativeness of different types differs property ii implies thatthe stereotype ceteris paribus overweights the probability of morerepresentative types

Most of the results we explore in this article hold for a gen-eral weighing function htethTHORN Specific functional forms captureadded assumptions about the psychology of representativeness-based recall and are useful in applications We outline a few spe-cifications and their properties

Rank-based stereotypes the ranking of the representa-tiveness of different types shapes distortions Denote byrethtTHORN 2 f1 Tg the representativeness ranking of type tWhen r(t) = 1 type t is the most representative one (po-tentially with ties) We can specify two ways in which atypersquos representativeness ranking distorts its probability

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(i) Rank-based truncation the DM only recalls the typesthat have representativeness ranking of at most dnamely ft 2 TjrethtTHORN dg Zero probability is attachedto the remaining types10 Denote by IethrethtTHORN dTHORN an in-dicator function taking the value 1 if the representa-tiveness ranking of t is at most d Then theweighting function is ht frac14 IethrethtTHORN dTHORN so that

sttG frac14 tG

IethrethtTHORN dTHORNPs2T sGIethrethsTHORN dTHORN

which is the true conditional probability within re-called types This assumption is used in Gennaioliand Shleifer (2010)11

(ii) Rank-based discounting the DM discounts by a con-stant factor 2 frac1201 the odds of type t relative to itsimmediate predecessors in the representativenessranking Lower implies stronger discounting ofless representative types Formally the weightingfunction is ht frac14

rethtTHORN so that

sttG frac14 tG

rethtTHORNPs2T sG

rethsTHORN

Representativness-based discounting all else equal theweight attached by the DM to type t increases continuouslywith its representativeness One convenient formulation is

ht frac14tG

tG

so that

10 These neglected types are not viewed as impossible they are just assignedzero probability in the DMrsquos current thinking This formulation allows us to modelsurprise and reactions to unforeseen contingencies which have proved useful in-gredients in modeling probabilistic judgments (GS 2010) as well as neglect of risk infinancial crises (Gennaioli Shleifer and Vishny 2012)

11 Specifically in GS (2010) the assessed probability that a certain hypothesisG is true is equal to

Pr ethGTHORN frac14

Pt tGIethrethtTHORN dTHORNP

t tGIethrethtTHORN dTHORN thornP

t t=GIethrethtTHORN dTHORN

which increases in the ratio between the total probability mass recalled for Gand that recalled for G frac14 nG

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sttG frac14 tG

tG

tG

P

s2T sGsG

sG

where 0 captures the extent to which representative-ness distorts beliefs This formulation is particularly con-venient when dealing with continuous distributions ofthe exponential or power classes

These functional forms all embody the main idea of our modelthat the stereotype overweights the probability of more represen-tative types Rank-based truncation captures a central manifes-tation of limited memory forgetting unrepresentative typesSmoother discounting (based on ranking or on representative-ness) may be more appropriate when the type space is smalland smooth discounting can be more tractable in certain settings

Section III characterizes the general properties of stereotypesIn particular it shows their ability to account for social psycholo-gistsrsquo kernel of truth hypothesis under the general weighting func-tion of Definition 2 To bring the model to the data in Section IVBwe derive linear approximations of stereotypical beliefs by assum-ing that the weighting function is differentiable with respect to atypersquos representativeness This assumption excludes rank-basedweighting but allows for many possibilities

IIB Discussion of Assumptions

Before moving to the formal analysis we discuss some prop-erties and limitations of our approach Representativeness-basedrecall the idea that individuals recall distinctive group types canbe viewed as an instance of what Kahneman and Tversky calllsquolsquoattribute substitutionrsquorsquo When dealing with the difficult questionlsquolsquowhat is the distribution of hair color among the Irishrsquorsquo peopleintuitively answer to the simpler question lsquolsquowhich hair color dis-tinguishes the Irish peoplersquorsquo Critically as discussed byKahneman and Tversky attribute substitution does not occurbecause people misunderstand the original question or mechan-ically confuse the assessment of PrethtjGTHORN with that of PrethGjtTHORNRather it occurs because the distinctive or representative typesimmediately come to mind and individuals anchor their overallprobability judgment to them As a consequence subjects do notonly make mistakes in judging the probability that a Floridian is

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over age 65 They also give too high an answer to the questionlsquolsquowhat is the average age of a Floridianrsquorsquo12

One interesting question is whether the process of stereotyp-ing we describe is optimal in some sense Focusing mental repre-sentations on a few types can be justified by the costs of thinkingor retrieval This approach however is not enough to explainwhy individuals should focus on representative rather thanlikely types We do not formally analyze the optimality of repre-sentativeness here but we mention some relevant considerationsfrom cognitive psychology Kahneman and Tversky (1979) stressthe similarity between many perceptual and cognitive operationsFor instance the highlight of contrastmdasha key principle of visualperceptionmdashis invoked to justify the prospect theory assumptionthat the carriers of utility are changes relative to a referencepoint The same logic applies to our model in which stereotypesprecisely highlight the contrast between groups

In visual perception assessing properties such as brightnesscolor size or distance to an object by comparing them to otherproximate objects has been shown to be optimal in the presence ofmultiplicative background noise (Kersten Mamassian andYuille 2004 Cunningham 2013) Our formulation of representa-tiveness is related to the same idea in the sense that individualsestimating properties of one group stress differences from an-other group In a noisy world in which attention is limited thisprocess may optimally allow for swift reactions to changes ingroup characteristics even if errors are sometimes made13

12 Indeed in many cases mere confusion of PrethtjGTHORNwith PrethGjtTHORNwould not yieldthe phenomenon of stereotyping In the Irish hair color example the probability ofbeing Irish conditional on having red hair is

PrethIrishjredTHORN frac14PrethredjIrishTHORNPrethIrishTHORN

PrethredjIrishTHORNPrethIrishTHORN thorn PrethredjNonIrishTHORNPrethNonIrishTHORN

This probability is clearly very small given that the Irish population is a tinyfraction of the world population Confusion of PrethtjGTHORN with PrethGjtTHORN in this casewould lead to an understatement of the probability of the red-haired Irish

13 To give a simple example suppose thatmdashas in the case of Proposition 3mdashthevariance in the environment increases in the sense that extreme tail events becomemore likely Then a likelihood-based stereotype would detect no change whereas arepresentativeness-based stereotype would focus on the heightened probability ofthe tails In particular an asymmetric increase in tail probabilities that shifts themean would be detected by a representativeness-based stereotype even if the dis-tributionrsquos mode does not change

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Exploring this idea formally is an interesting avenue for futurework

Consider some limitations of our model First representa-tiveness is not the only heuristic that shapes recall Decisionmakers may for instance find it easier to recall types that aresufficiently likely Another potentially important mechanism isavailability understood by Kahneman and Tversky (1972) as thelsquolsquoeasersquorsquo with which information comes to mind (because of actualfrequency or repetition) In Online Appendix E we present a trun-cation-based recall mechanism in which distortions are driven bya combination of representativeness and likelihood of types(which is equivalent to relaxing property i in Definition 2) Thismodel can offer a useful starting point to capture availability aswell even though a full model of availability is beyond the scopeof this article Even in this more general setting the influence ofrepresentativeness on recall is the driving force of stereotypesthat in line with the social psychology perspective are basedon underlying differences among groups As we show in SectionIV this feature is critical in accounting for the evidence

The second set of model-related issues concerns how to spe-cify the elements of Definition 1 in applications group G the typespace T and the reference group ndashG Take the specification of thegroup G and of the type space T Often the problem itself pro-vides a natural specification of these features This is the case inthe empirically important class of lsquolsquoclosedrsquorsquo questions such asthose used in surveys which provide respondents with a set ofalternatives as in the data we use in Section IV More generallythe problem solved by the DMmdashsuch as evaluating the resume ofa job applicant coming from a certain ethnic groupmdashprimes agroup a dimension of interest and a set of types (eg the appli-cantrsquos qualification or skill levels) When types have a naturalorder such as income age or education the granularity of T isalso naturally given by the problem (income age and years ofschooling brackets) When the set of types is not specified by theproblem DMs spontaneously generate one14 It would be useful tohave a model of which dimensions and types come to mind par-ticularly for more open-ended problems Psychologists have

14 For example suppose a person is asked to guess the typical occupation of ademocratic voter in an lsquolsquoopen-endedrsquorsquo format (without being provided a set of alter-natives) Here the level of granularity at which types are defined is not obvious (egteacher versus a university teacher vs a professor of comparative literature)

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sought to construct a theory of natural types and dimensions(Rosch 1973) We do not make a contribution to this problembut we note that in many problems of interest in economics thedimension as well as the set of types is naturally givenFurthermore in our model details of the type space can be impor-tant under rank-based truncation but they matter less undersmooth discounting

Consider finally the role of the comparison group ndashG Thisgroup captures the context in which a stereotype is formed andagain is often implied by the problem when G = Floridians ndashG =rest of US population when G = African Americans ndashG = whiteAmericans A distinctive prediction of our model confirmed byour experiments in Section IVA is that the stereotype for agiven group G depends on the comparison group ndashG15 WhenndashG is not pinned down by the problem itself to derive testablepredictions from representativeness we set G frac14 nG where

is the natural population over which the unconditional distribu-tion of types is measured

III Properties of Stereotypes

We now study stereotypical beliefs and their accuracy Toillustrate the role of representativeness we first ask to whatextent the most representative type is a good fit for the groupnamely whether it is modal Next we assess the accuracy of theentire stereotypical distribution To do so we focus on a cardinaltypes and compare the stereotypersquos mean and variance to the trueones

15 Some empirical papers have taken a similar approach exogenously varyingthe natural comparison group through priming Benjamin Choi and Strickland(2010) show that priming racial or ethnic identity can affect the risk preferences ofparticipants Chen et al (2014) find that Asian students cooperate less with out-group members when primed with their ethnic identity rather than their universityidentity Shih Pittinsky and Ambady (1999) show that Asian American womenstereotype themselves as better or worse in math with corresponding impact onperformance when their ethnicity or gender respectively is primed ShihPittinsky and Trahan (2006) replicate this effect using a verbal task documentingthat Asian American women performed better when their gender rather than theirethnicity was primed Although the generalizability and replicability of priminghas been doubted (Klein et al 2014) this body of evidence is consistent with contextdependence

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IIIA Likely versus Unlikely Exemplars

The most representative type for a group is the one thatagents most easily recall and associate with the group itself forinstance a red-haired Irishman or a 65+-year-old FloridianSocial psychologists call this type the exemplar of the groupAccordingly we define

DEFINITION 3 A type t is an exemplar for G given comparisongroup ndashG when

t 2 arg maxt

tG

tG

Under any specification of the weighting function ht inDefinition 2 overweighting (weakly) increases as we movetoward more representative types so the exemplar is also thetype whose probability is overweighted the most16 By analyzingthe exemplar then we can gauge whether representativenessinduces the DM to overweight a likely type (as happens in stan-dard models of categorical thinking) or an unlikely type Whenoverweighting occurs in unlikely and extreme types the biases ofstereotypes can be particularly severe17

Equation (2) yields the following characterization

PROPOSITION 1 Suppose the conditional distributions G and G

are not identical Consider two extreme cases

(i) If for all t t0

2 T we have that tG gt t0 G if and only iftG gt t0 G then the modal type is not an exemplar forat least one group

(ii) If for all t t0

2 T we have that tG gt t0 G if and only iftG lt t0 G then for each group the modal type is theexemplar

16 Consider the function hethTHORN from Definition 2 When applied to more repre-sentative types the first argument of the function increases while one of the otherT ndash 1 arguments decreases As a result the weighting factor ht (and thus overweigh-ing

sttG

tG) increases as well

17 In the rank-based truncation model the frequency of the exemplar providesa measure of stereotype accuracy By accuracy we mean the extent to which thestereotype minimizes the distance

Pt eth

sttG tGTHORN

2 When d = 1 and only one type isrecalled (there are no ties) accuracy is maximized if the exemplar is the most likelytype and minimized if the exemplar is the least likely type

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Case i says that when groups have similar distributions inthe sense of having the same likelihood ranking the most repre-sentative type is unlikely for at least one group potentially bothRepresentativeness draws the DMrsquos attention to group differ-ences neglecting the fact that the groups are similar and havethe same mode This mechanism generates inaccurate stereo-types and is illustrated by the Florida example This resultholds under any measure of representativeness that differenti-ates the two groups (eg the difference tG tG)

Case ii says that the most representative type tends to belikely for both groups when the distributions are very differentIn this case groups differ the most around their modes so repre-sentativeness and likelihood coincide Thinking of Swedes aslsquolsquoblondrsquorsquo and Europeans as lsquolsquodark hairedrsquorsquo is accurate precisely be-cause these are majority traits of the Swedish and European pop-ulations respectively In these cases stereotyping yields fairlyreliable models Of course there is still some inaccuracy Evenin the case of likely exemplars judgment errors can be signifi-cant For instance voters in some US states are perceived aslsquolsquobluersquorsquo or lsquolsquoredrsquorsquo because a majority of the population votesDemocrat or Republican In reality even in lsquolsquobluersquorsquo states farfrom everyone votes Democrat In the 2012 presidential electionvote shares of either candidate in most states ranged from 40 to6018

When DMs strongly overweight representative types themost severe biases occur when those types are unlikely and ex-treme This is true both under rank based truncations and undersmooth discounting functions (see Section IIIB) Ethnic stereo-types based on crime or terrorism exhibit this error they neglectthe fact that by far the most common types in all groups arehonest and peaceful

IIIB Stereotypical Moments

We now characterize how the first two moments of a distri-bution are distorted by the process of stereotyping To do so wemust restrict our analysis to cardinal ordered types The follow-ing results hold for any weighting function htethTHORN satisfyingDefinition 2 We consider two canonical cases that prove usefulin illustrating the predictions of the model

18 Presidential Election Results NBCNewscom see httpelectionsnbcnewscomnspolitics2012allpresident (accessed 5 September 2016)

STEREOTYPES 1769

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In the first case groups G and ndashG are such that the likelihoodratio tG

tGis monotonic in t The monotone likelihood ratio prop-

erty (MLRP) holds to a first approximation in many empiricalsettings and is also assumed in many economic models such asstandard agency models19 If tG

tGis monotonically increasing (de-

creasing) in t then group G is associated with higher (lower)values of t relative to the comparison group ndashG Formally

PROPOSITION 2 Suppose that MLRP holds and assume wlogthat the likelihood ratio tG

tGis strictly increasing in t Then

for any weighting function htethTHORN that is not constant in therelevant range

EstethtjGTHORN gt EethtjGTHORN gt EethtjGTHORN gt E

stethtjGTHORN

Under MLRP the most representative part of the distribu-tion for G is the right tail if tG

tGincreases in t or the left tail if tG

tG

decreases in t The representative tail is then overweighted whilethe nonrepresentative tail is underweighted As a consequencethe assessed mean E

stethtjGTHORN is too extreme in the direction of therepresentative tail

Critically in line with the social cognition perspective the ste-reotype contains a kernel of truth the DM overestimates the meanof G if this group has a higher mean than the comparison groupnamely EethtjGTHORN gt EethtjGTHORN and conversely if EethtjGTHORN lt EethtjGTHORN TheDM exaggerates this true difference because he inflates the asso-ciation of G with its most representative types20 For instancewhen judging an asset manager who performs well we tend to

19 Examples include the binomial and the Poisson families of distributionswith different parameters The characterization of distributions satisfying MLRPis easier in the case of continuous distributions (see Online Appendix D) two dis-tributions f(x) f ethx THORN that differ only in their mean satisfy MLRP if and only if thedistribution f(x) is log-concave Examples include the exponential and normal dis-tributions To the extent that discrete distributions sufficiently approximate thesedistributions (as the Poisson distribution PoisethTHORN approximates the normal distri-bution Neth THORN for large l) they will also satisfy MLRP

20 Depending on the distribution and the weighing function the DMrsquos assess-ment of the variance VarethtjGTHORNmay also be dampened relative to the truth This isoften true under the truncation weighing function In this case stereotyping effec-tively leads to a form of overconfidence in which the DM holds extreme views andoverestimates the precision of his assessment That extreme views and overconfi-dence (in the sense of over precision) go together has been documented in the settingof political ideology among others (Ortoleva and Snowberg 2015)

QUARTERLY JOURNAL OF ECONOMICS1770

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overemphasize skill relative to luck because higher skill levels arerelatively more associated with higher performance This occurseven if for both skilled and unskilled managers high performanceis mostly due to luck

In the second case for which we characterize the stereotypi-cal distributions groups G and ndashG have the same mean EethtjGTHORNfrac14 EethtjGTHORN frac14 EethtTHORN but differ in their variance We abstract fromskewness and higher moments by considering distributionsethtGTHORNt2T and ethtGTHORNt2T that share the same support and are sym-metric around the medianmean EethtTHORN

PROPOSITION 3 Suppose that in G more extreme types are rela-tively more frequent than in ndashG Formally the likelihoodratio tG

tGis U-shaped in t around EethtTHORN Then for any weight-

ing function htethTHORN that is not constant in the relevant rangestereotypical beliefs satisfy

VarstethtjGTHORN gt VarethtjGTHORN gt VarethtjGTHORN gt VarstethtjGTHORN

EstethtjGTHORN frac14 E

stethtjGTHORN frac14 EethtTHORN

When group G has a higher relative prevalence of extremetypes its representative types are located at both extremes of thedistribution The DMrsquos beliefs about G are then formed by over-weighting both tails while underweighting the unrepresentativemiddle The overweighting of Grsquos tails causes the assessment ofits variance VarstethtjGTHORN to be too high For example the skill dis-tribution of immigrants to the United States may be perceived ashaving very fat tails or even bimodal with immigrants beingperceived as either unskilled or very skilled relative to the resi-dent population The mean of the group in contrast is assessedcorrectly because the stereotypical distribution remains symmet-ric around EethtTHORN As before the stereotype contains a kernel oftruth It induces the agent to exaggerate the true differences be-tween groups namely the higher variance of G relative to itscounterpart

We present a number of extensions of the model in the OnlineAppendix We first consider multidimensional type spaces andshow that stereotypes center around the dimension wheregroups differ the most in line with the kernel of truth logic(Online Appendix C) Multidimensional stereotypes imply thatthe dimension we think about is influenced by context For

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example the Irish are stereotyped as red-haired when comparedwith the European population However when compared withthe Scots a more plausible stereotype for the Irish is lsquolsquoCatholicrsquorsquobecause religion is the dimension along which Irish and Scotsdiffer the most

In Online Appendix D we extend the model to continuoustype spaces Many settings of interest in economics can be use-fully described by continuous probability distributions and weshow our model is particularly tractable in this case In OnlineAppendix E we relax Definition 2 and allow weighting of types toalso be influenced by their likelihood We show that the basicinsight that stereotypes contain a kernel of truth carries throughto these cases as well

To summarize the psychology of representativeness yieldsstereotypes that are consistent with the social cognition approachin which individuals assess groups by recalling and focusing ondistinctive group traits When there are systematic differencesbetween groups stereotypes get the direction right but exagger-ate differences

IIIC Some Examples

A growing body of field and experimental evidence points to awidespread belief that women are worse than men at mathemat-ics (Eccles Jacobs and Harold 1990 Guiso et al 2008 CarrellPage and West 2010) This belief persists despite the fact that fordecades women have been gaining ground in average schoolgrades including mathematics and have recently surpassedmen in overall school performance (Goldin Katz and Kuziemko2006 Hyde et al 2008) This belief shared by men and women(Reuben Sapienza and Zingales 2014) may help account for thegender gap in the choices of high school tracks college degreesand careers with women disproportionately choosing humanitiesand health-related areas (Weinberger 2005 Buser Niederle andOosterbeek 2014) and forgoing significant wage premiums toquantitative skills (Bertrand 2011)

Gender stereotypes in mathematics particularly beliefs thatexaggerate the extent of average differences are consistent withthe predictions of our model The fact that men are overrepre-sented at the very highest performance levels leads a stereotyp-ical thinker to exaggerate the magnitude of mean differencesFigure I shows the score distributions from the mathematics

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section of 2013rsquos Scholastic Aptitude Test (SAT) for men andwomen21 The distributions are very similar with averagescores slightly higher for men (531 versus 499 out of 800)However scores for men have a heavier right tail with mentwice as likely to have a perfect SAT math score than women22

In light of such data the stereotypical male performance in math-ematics is high while the stereotypical female performance ispoor Predictions based on such stereotypes are inaccurate exag-gerating true differences Consistent with this prediction exper-imental evidence shows that both genders underestimatewomenrsquos ability in simple math tasks even controlling for pastperformance (Reuben Sapienza and Zingales 2014) Coffman(2014) shows a similar pattern extends to confidence about ownability in other male-typed domains with women reporting sig-nificantly less confidence in gender-incongruent than gender-congruent tasks Our model suggests that these patterns mightcome from stereotypes based on gender differences in the righttail of the distribution While differences in the right tail of thedistribution are unlikely to be relevant for most decisions stereo-typical thinking driven by these differences has the potential toimpact economically important decisions whether through self-stereotyping (ie choice of careers or majors as in BuserNiederle and Oosterbeek 2014) or through discrimination (iehiring decisions as in Bohnet van Geen and Bazerman 2016)

The logic of exaggerated yet directionally correct stereotypesalso sheds light on the well-documented phenomenon of base rateneglect (Kahneman and Tversky 1973) Indeed Proposition 2implies that the DM overreacts to information that assigns

21 Standardized test performance measures not only innate ability but alsoeffort and investment by third parties (Hyde et al 2008) The mapping of test per-formance into inferences about innate ability is an issue not addressed by ourmodel

22 For 2013 SAT Mathematics scores see httpmediacollegeboardcomdigitalServicespdfresearchSAT-Percentile-Ranks-By-Gender-Ethnicity-2013pdf Results are similar for the National Assessment of Educational Progress(NAEP) which are more representative of the overall population For 2012NAEP scores for 17-year-olds in mathematics see httpnationsreportcardgovltt_2012age17maspx See Hyde et al (2008) Fryer and Levitt (2010) and Popeand Sydnor (2010) for in-depth empirical analyses of the gender gap inmathematics

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people to groups precisely because such information generatesextreme stereotypes Consider the classic example in which amedical test for a particular disease with a 5 prevalence has a90 rate of true positives and a 5 rate of false positives The testassigns each person to one of two groups + (positive test) or ndash(negative test) The DM estimates the frequency of the sick type(s) and the healthy type (h) in each group The test is informativea positive result increases the relative likelihood of sickness anda negative result increases the relative likelihood of health forany prior Formally

PreththornjsTHORN

PreththornjhTHORNgt 1 gt

PrethjsTHORN

PrethjhTHORNeth4THORN

This condition has clear implications the representative personwho tests positive is sick while the representative person whotests negative is healthy Following Proposition 2 the DMreacts to the test by moving his priors too far in the right di-rection generating extreme stereotypes He greatly boosts hisassessment that a positively tested person is sick but also thata negatively tested person is healthy Because most people arehealthy the DMrsquos assessment about the group that tested neg-ative is fairly accurate but is severely biased for the group that

FIGURE I

SAT Mathematics Scores by Gender (2013)

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tested positive This analysis formalizes Tversky andKahnemanrsquos (1983) verbal account of base rate neglect23

The same mechanism may underlie several other instanceswhere DMs overweight diagnostic information When assessingan employeersquos skill level an employer attributes high perfor-mance to high skill because high performance is the distinctivemark of a talented employee Because he neglects the possibilitythat some talented employees perform poorly and that somenontalented ones perform well (perhaps due to stochasticity inthe environment) the employer has too much faith in skill andneglects the role of luck in accounting for the output Similarlywhen assessing the performance of firms in a hot sector of theeconomy (eg G = internet) an investor recalls highly successfulfirms in that sector (t = return of Google Amazon etc) He ne-glects the possibility of firms being unsuccessful because lack ofsuccess is statistically nondiagnostic and psychologically nonrep-resentative of a growing sectormdasheven if it is likely This causesexcessive optimism (in that the expectation of growth is unrea-sonably high) and overconfidence (in that the variability in earn-ings growth considered possible is truncated) True the hot sectormay have better growth opportunities on average but represen-tativeness exaggerates this feature and induces the investor toneglect a significant risk of failure

IV Evidence on Representativeness and Stereotypes

Testing our model requires evaluating the beliefs individualshold about a target group against the true distribution of thattarget group over an attribute space An ideal data set would

23 Our account is distinct from a mechanical underweighting of base rates inBayes rule as in Grether (1980) and Bodoh-Creed Benjamin and Rabin (2013) Inthose models upon receiving the test results the DM can update his beliefs in thewrong direction he can be less confident that a person is healthy after a negativetest than under his prior which cannot happen in our model Although this predic-tion of our model seems consistent with introspection we are not aware of experi-mental evidence on this point Griffin and Tversky (1992) present evidenceconsistent with pure neglect of base rates but in a significantly different tasknamely inferring the bias of a coin from a history of coin flips Such experimentsare hard to compare with the predictions of our model because subjects are asked togenerate distributions of different numbers of coin flips in their minds which is amuch more involved task than to recall types of a given distribution Their assess-ments then might be wrong for other reasons See Bodoh-Creed Benjamin andRabin (2013) for a detailed discussion

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consist of naturally defined groups with known distributions overa given space of types and a corresponding set of beliefs about thedistribution of each group over that space of types This wouldallow us to test for exaggeration of true differences betweengroups and to ask whether this exaggeration is well predictedby overweighting representative types To identify a causal rolefor representativeness or context dependence we would need ex-ogenous variation in either the comparison group ndashG or in thedistributions over the type spaces This is unavailable in existingdata sets Accordingly we take a two-pronged approach First wecreate a controlled laboratory environment that allows us toinduce the exogenous variation in representative types that weneed to test causality then we reanalyze existing field evidence tocheck for consistency with our predictions

In testing our model we focus on the two main implicationsof representativeness-based stereotypes

Context dependence the stereotype of a target group de-pends on the characteristics of the reference group it iscompared to

Kernel of truth stereotypes depend on group character-istics andmdashin most (precisely characterized) settingsmdashare slanted toward representative types

We test the first property with a lab experiment (SectionIVA) We then turn to survey data on beliefs about US politicalgroups (Section IVB) for an empirical analysis that explores thesecond property The survey data are more tightly linked to ourinterest in social stereotypes The laboratory experiment allowsus to directly test the role of representativeness in generatingcontext dependent beliefs Online Appendixes F and G provideall details and additional results for the experiments and fieldevidence

IVA Lab Evidence on Representativeness and ContextDependence

The influence of the representativeness heuristic on recalland on beliefs has been extensively documented in the lab(Kahneman and Tversky 1972 1973) Our goal is to considerhow representativeness as formalized in equation (2) gives riseto context-dependent beliefs To our knowledge the possibility

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that representativeness may generate context dependence hasnot been tested before

To assess this prediction we perform a controlled laboratoryexperiment that allows us to isolate representativeness frommany confounding factorsmdashhistorical sociological or other-wisemdashthat may affect stereotype formation in the real worldWe construct our own groups of ordinary objects creating atarget group G and a comparison group ndashG We hold thetarget group G fixed and explore how participant impressions ofit change as we change the comparison group ndashG and thusrepresentativeness

We conducted several experiments in the laboratory and onAmazon Mechanical Turk Each involves a basic three-stepdesign First participants are shown the target group and a ran-domly assigned comparison group for 15 seconds In this timedifferences between groups can be noticed but the groupsrsquo precisecompositions cannot be memorized The second step consists of afew filler questions which briefly draw the participantsrsquo cognitivebandwidth away from their observation Finally participants areasked to assess the groups they saw Participants are incentiv-ized to provide accurate answers

We randomly assign participants to either the Control or theRepresentativeness condition In the Control condition G and ndashGhave nearly identical distributions so that all types are similarlyrepresentative for each group In the Representativeness condi-tion ndashG is changed in such a way that a certain type becomes veryrepresentative for G Context dependence implies that the assess-ment of G should now overweight this representative type eventhough the distribution of G itself has not changed

We ran six experiments of this form with design changesfocused on reducing participant confusion and removing con-founds We describe the final and most refined version of theseexperiments here In an attempt to provide a overview of the re-sults while remaining concise we provide the results from pooledspecifications that use all data collected In Online Appendix Fwe offer additional details and report all experiments conductedWe also give instructions and materials for each experiment thefull data set is available by request

Consider first the experiment illustrated in Figure II Agroup of 25 cartoon girls is presented next to a group of 25 cartoonboys in T-shirts of different colors blue green or purple In theControl condition (Figure II Panel a) the groups have identical

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color distributions (13 purple 12 green) so no color is represen-tative of either group The Representativeness condition (Panel b)compares the same group of girls with a different group of boysfor whom green shirts are replaced with blue shirts Now onlygirls wear green and only boys wear blue These colors althoughstill not the most frequent for either group are now most repre-sentative For each group girls and boys participants are asked anumber of questions concerning the frequency of T-shirts of dif-ferent colors worn by that group

Applying our model in the control condition the type space isT frac14 fgreen purpleg and the groups are G = girls and ndashG = boysGiven that the color distributions are identical across groups both

types are equally representativegreengirls

greenboysfrac14 1 frac14

purplegirls

purpleboys As a result

assessment of G should be correct on average stcontrolgreengirls frac14 greengirls

and stcontrolpurplegirls frac14 purplegirls for any weighing function (the same is

true about assessments of ndashG)In the treatment condition the distribution of shirt colors re-

mains the same for girls For boys green shirts are changed intoblue Thus the type space changes to T frac14 fgreen purple bluegand the representative color for girls becomes greengreengirls

greenboysfrac14 1 gt 1 frac14

purplegirls

purpleboys while that for boys becomes blue As

a result in the treatment condition subjects should inflate the

frequency of green shirts relative to the truth sttreatmentgreengirls

gt greengirls (the same should happen to assessments of blueshirts for boys) We also expect the assessed frequency of greenshirts to go up relative to the control condition namely

sttreatmentgreengirls gt stcontrol

greengirls Critically the only factor that varies

across treatments is the representativeness of the 12-colorshirt Thus if we see differences across conditions the causalrole of representativeness-based recall in shaping group judg-ments is clear24

24 We vary which colors are used in which roles across participants Someparticipants saw this particular color distribution while others see for examplegreen as the modal color and purple as the diagnostic color for boys in theRepresentativeness condition and blue as the diagnostic color for girls in theRepresentativeness condition We vary the colors across the roles to avoid con-founding the characteristics of any particular color with its diagnosticity

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FIG

UR

EII

T-S

hir

tsE

xp

erim

ent

Fig

ure

sap

pea

red

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lor

top

art

icip

an

tsin

the

exp

erim

ent

For

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ty

we

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ded

ale

tter

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irt

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enti

fyth

eco

lor

for

the

read

er

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ind

icate

sgre

en

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ind

icate

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urp

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ind

icate

sblu

eT

hes

ele

tter

sd

idn

otap

pea

rto

part

icip

an

tsan

dare

for

read

erre

fere

nce

only

P

lease

see

onli

ne

ver

sion

ofp

ubli

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icle

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colo

rfi

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reex

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lyas

itap

pea

red

top

art

icip

an

ts

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We collected data from 301 participants using this T-shirtsdesign25 Since the number of green and purple shirts is verysimilar we first ask each participant the simplest question ofwhich shirt color is modal Next we ask participants to assessthe share of green and purple shirts

Consistent with the role of representativeness participantsassigned to the Representativeness condition are 105 percentagepoints more likely to recall the less frequent color (green for girlsor blue for boys) as the modal color when it is representative of agroup (35 of participants guess the less frequent color is modalin the Control condition this proportion increases to 46 in theRepresentativeness condition p = 01 estimated from a probitregression reported in Online Appendix F)

We now turn to subjectsrsquo estimates of how many T-shirts ofeach color they saw in each group In both conditions the truedifference in counts is 1 (13 purple shirts 12 green or blue shirts)In the Control condition participants on average believe they saw054 more purple shirts than green or blue shirts In theRepresentativeness condition participants believe they saw072 fewer purple shirts than green or blue shirts (the acrosstreatment difference is significant with p = 01 from OLS regres-sion reported in Online Appendix F)

In total we collected data for six experiments of this generalstructure gathering evidence from more than 1000 participantsAs we describe in Online Appendix F although there is substan-tial variation across experiments when we pool all of the data wefind significant aggregate treatment effects in line with a role ofrepresentativeness in judgment We employ four different unor-dered types designs similar to the T-shirts experiment using sixsamples (four online and two in the laboratory) with 741 partic-ipants We find effects in the predicted direction for five of the sixsamples Using a probit regression that pools the data for theseunordered type experiments we find that participants are 93 per-centage points more likely to guess that the less frequent type ismodal when it is representative than when it is not (p = 002) Wealso run a family of ordered types experiments (two designs fivesamples 402 participants) Unlike the simpler T-shirts style

25 Throughout our analysis we exclude any participant who participated in aprevious version of the experiment and any participant who self-identified as color-blind In Online Appendix F we show that our results are unchanged if we includethese additional observations

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design the theoretical predictions for the ordered types designsare more sensitive to the specific assumptions one makes aboutthe weighting function of the DM26 We find effects in the pre-dicted direction for three of the five samples As we discuss inmore detail in Online Appendix F the ordered types resultsvary by platform with consistently stronger results on AmazonMechanical Turk than in the laboratory samples Pooling all or-dered types experiments participants are 93 percentage pointsmore likely to guess that the group of interest has a greater av-erage than the comparison group when the right tail is represen-tative (p = 062) Given our simple experimental setting withgroups of mundane objects we interpret our resultsmdasha signifi-cant and reasonably sized impact on average beliefsmdashas an im-portant proof of concept the presence of representative typesbiases ex post assessment

IVB Empirical Evidence on Political Stereotypes

We examine two data sets on political preferences and be-liefs about political preferences in the United States We inves-tigate the roles of representativeness and context dependence byseparately testing for hypotheses that allow us to assess the lead-ing theories of stereotypes

First we test whether beliefs are correct or depart systemat-ically from the truth The statistical discrimination approachbuilds on the assumption that people hold rational expectationsof group traits Comparing beliefs to the truth allows us to assessthe validity of this assumption in our data

Second we test if beliefs depart from the truth by exagger-ating (mean) differences among groups per the kernel of truthhypothesis This is an implicit test of context dependence be-cause it implies that beliefs about the target groups are shapednot only by that grouprsquos characteristics but also by those of thereference group27

Third we test if distortions in beliefs can be accounted for bythe overweighting of highly representative types (defined astypes that are relatively more frequent in the target relative to

26 This is due in part to our choice to not study MLRP distributions We moti-vate and discuss this design decision in Online Appendix F

27 Of course unlike in the laboratory experiment in this setting we cannot testfor context dependence by exogenously varying the reference group

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the reference group) The second and third tests address the keypredictions of our model

1 The Data We have two data sets on political preferences andbeliefs about political preferences The first data set from GrahamNosek and Haidt (GNH 2012) contains data from the MoralFoundations Questionnaire Respondents (1174 self-identified lib-erals and 500 self-identified conservatives) answer questions abouttheir position on a subset of 45 issues 20 moral relevance state-ments (eg lsquolsquowhen you decide whether something is right orwrong to what extent are the following considerations relevantto your thinkingrsquorsquo) and 25 moral judgments (eg lsquolsquoindicate theextent to which you would agree or disagreersquorsquo) For each issue arandomly determined subset of participants states their own posi-tion another subset states their belief on the position of a lsquolsquotypicalliberalrsquorsquo and a third subset states their belief on the position of alsquolsquotypical conservativersquorsquo The data thus include the distribution overpositions for both liberal and conservatives as well as the averagebelieved typical position of liberals and of conservatives on the 45issues Each position is elicited on 1ndash6 scale

The second data set comes from the American NationalElection Survey (ANES) and contains data from more than20000 respondents between 1964 and 201228 The surveycovers political issues of the day such as the optimal amount ofgovernment spending and service provision (1984ndash2000) or theplace of women in society (1972ndash1998) We focus on the 10 issuesthat ask participants to respond on a 1ndash7 scale (rather than justindicate binary agreement or disagreement) all 10 issues areasked in multiple years Participants are asked to provide theirown position on the scale and their believed position of theDemocratic and Republican parties (lsquolsquoWhere would you placethe Democratic [Republican] party on this scalersquorsquo) The data in-clude for each issue-year observation the distribution of partic-ipant positions for self-identified liberals and self-identifiedconservatives as well as the distribution of believed typical posi-tions of the Democratic and Republican parties

28 These data are publicly available at httpwwwelectionstudiesorgstudy-pagesanes_timeseries_cdfanes_timeseries_cdfhtm

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2 Empirical Strategy Our analysis focuses on beliefs abouttwo groups Conservatives and Liberals The types are the possi-ble positions for each issue (1 2 6 7) For the GNH data weinterpret beliefs about the lsquolsquotypicalrsquorsquo element of a group to coincidewith the believed average position in that group Similarly forthe ANES data we use the believed party positions as a proxy forbelieved mean of each group29 We then take as a benchmark thehypothesis that individuals hold accurate beliefs about eachgroup and in particular that believed mean position shouldequal true mean position at least on average across subjectsThe accurate beliefs hypothesis underlies the most common eco-nomic model of stereotyping statistical discrimination

To assess our representativeness-based model we perform aregression exercise To test our model in a linear regressionframework we rely on linear approximations of the weightingfunction Our model then yields two regression specifications

PROPOSITION 4 Let G 2 fconservative liberal g and assume

ht h tG

tG

be a differentiable and strictly increasing weight-

ing function as in Definition 2 The following hold as a first-order approximation around identical distributions G

Gfrac14 1

(i) Kernel of truth regression There exists a constant gt 0such that

EstethtjGTHORN frac14 EethtjGTHORNeth1thorn THORN EethtjGTHORNeth5THORN

(ii) Representativeness regression Denote H frac14 fT 2 Tg

the right tail of types and RconsH frac14

PHtconsPHtlib

as the average

representativeness of right tail types for conservatives

29 This assumption is consistent with the authorsrsquo interpretation of the GNHdata (GNH 2012) and with previous studies using ANES (eg Westfall et al 2015)Furthermore to the extent that this assumption holds equally well for most issueswithin a data set our focus on cross-issue differences should allow us to test thepredictions of our model even with an imperfect proxy for beliefs of mean positionsFinally the data provide some insight into whether subjects are reporting (per-ceived) modal or mean types As we show the modal type is a poor prediction ofstated beliefs while a distorted mean slanted toward representative types is anaccurate prediction of stated beliefs

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Under the further approximation where tcons

tlibampRcons

H for

t 2 H

EstethtjconsTHORN frac14 EethtjconsTHORN thorn consethR

consH 1THORNeth6THORN

EstethtjlibTHORN frac14 EethtjlibTHORN libethR

consH 1THORNeth7THORN

where lcons and llib are positive constants

The first regression allows us to test for the kernel of truthhypothesis and the second set of regressions allows us to test forthe role of representativeness

Equation (5) says that respondents in our model inflate theaverage position of a group say the conservatives if and only ifthe group has a higher average position than the other groupnamely the liberals Formally EstethtjconsTHORN gt EethtjconsTHORN if and onlyif EethtjconsTHORN gt EethtjlibTHORN Because in our measurement scale highertypes mean lsquolsquomore conservativersquorsquo we expect (i) believed conserva-tive average to be higher than the truth and (ii) the extent ofoverstatement to decrease in the average liberal position EethtjlibTHORNConversely we expect the average liberal position to be lowerthan the truth the more so the higher the average conservativeposition EethtjconsTHORN

As previously discussed the basis of these predictions is con-text dependence information about the distribution of ndashG is rel-evant for the beliefs about G This context dependence isinconsistent with rational expectations in which only thegrouprsquos own means should affect beliefs We test the hypothesisthat the true mean EethtjGTHORN is a significant predictor of the believedmean E

stethtjGTHORN with a positive sign and the other grouprsquos truemean EethtjGTHORN is a predictor of the believed mean with a negativesign

Equations (6) and (7) say that repondentsrsquo assessment bias isshaped by representativeness When the right tail is more repre-sentative for conservatives (Rcons

H 1 positive and large) partici-pants should inflate the average conservative position more(higher E

stethtjconsTHORN EethtjconsTHORN) and deflate the average liberal po-sition more (lower E

stethtjlibTHORN EethtjlibTHORN) We test the hypothesisthat the inflation in conservative positions is positively associatedwith the representativeness of the right tail for the conservativesand the inflation in liberal positions is negatively associated with

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it Once again the representativeness of the right tail is com-puted using the true distribution of positions

In equations (6) and (7) in many cases the representative tailis also the most likely one As a consequence these tests cannotdistinguish a representativeness-based from a likelihood-basedmodel of distorted beliefs We perform two additional testsFirst we run versions of equations (6) and (7) in which we controlfor the likelihood of tails (see Table A4 in Online Appendix G)Second we compute numerically the predictions of a representa-tiveness-based model of stereotypes and a likelihood-based modelof stereotypes We then assess which of these two is better able tomatch the data on beliefs

3 Empirical Results To begin we illustrate the structure ofthe data and the nature of our predictions with two simple exam-ples from the GNH data set focusing on beliefs about conserva-tives In example 1 participants are asked about their agreementwith the statement lsquolsquoIt can never be right to kill a human beingrsquorsquoIn example 2 participants are asked about the moral relevance oflsquolsquowhether or not someone cared for someone weak or vulnerablersquorsquoAs can be seen in Figure III in example 1 the modal position(strongly disagree (1)) and most representative positions(strongly disagree (1)) coincide for conservatives In contrast inexample 2 in Figure III the most representative types (slightlyrelevant (3) not at all relevant (1)) are not most likely for theconservative group Following Proposition 1 we predict that be-liefs will be distorted in the direction of the most representativetypes Thus we expect more exaggeration in example 2 than inexample 1 since in example 2 the most representative types (inthe left tail) are far from the modal type whereas in example 1they coincide This is what we find the conservative position isexaggerated by only 009 positions in Example 1 (true mean 299believed mean 290) but by 106 positions in Example 2 (truemean 421 believed mean 315)

In the full data sets we treat each (issue year) pair as anobservation and we cluster standard errors at the issue level Forthe GNH data we have 45 observations 45 issues measured inthe same year For the ANES data we have 66 observations 10issues measured in multiple years To begin we simply docu-ment systematic exaggeration in both data sets This is a primaryfocus of the original analysis in GNH (2012) and also in Westfall

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FIGURE III

Two Examples

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et al (2015)rsquos analysis of the ANES data30 Figure IV shows thatthe believed difference between typical conservative and typicalliberal positions is larger than the true difference in mean posi-tions for 109 of the 111 observations The data for both GNH(squares) and ANES (triangles) lie above the 45-degree line(dashed)31 Average exaggeration is 062 positions on the scale(066 in the GNH data 059 in the ANES data)32

The systematic and significant exaggeration of mean differ-ences suggests that the benchmark model of accurate beliefs ismissing something important Indeed this exaggeration reflectsthe fact that believed means are typically more extreme than truemeans First note that the kernel of truth regression (equation(5)) generates exaggeration of mean differences just as docu-mented in Figure IV

EstethtjGTHORN E

stethtjGTHORN frac14 eth1thorn 2THORN frac12EethtjGTHORN EethtjGTHORN

To bring this prediction to the data we regress the believedmean position for each group EBethtjGTHORN on the true mean of thegroup EethtjGTHORN and the true mean of the comparison groupEethtjGTHORN across issues We do this for each group (liberals con-servatives) in each data set separately We also present pooledspecifications that combine the data sets to make a prediction fora given group (liberals conservatives) In these pooled specifica-tions we include a dummy variable indicating whether theobservation came from the ANES data set For all specificationswe cluster observations at the issue level33 The results from re-gression are shown in Table I In every specification we find thatEethtjGTHORN is a significant predictor of EBethtjGTHORN with the predicted pos-itive sign Crucially for five of the six specifications the mean of

30 Chambers and Melnyk (2006) also find evidence of exaggeration of truedifferences in beliefs about political positions

31 For convenience we recode all issues so that the high end of the scale (67)represents the stereotypically more conservative position

32 A natural question to ask is how beliefs vary across liberals and conserva-tives That is do beliefs about a group G depend on membership in G versus ndashG Ourmodel does not speak to this issue However in Online Appendix G we show thatthe results we document below hold for both beliefs held by conservatives and be-liefs held by liberals see Tables A9 A10 and A11

33 In general the results presented below for the ANES data are not largelyimpacted by the decision to cluster at the issue level Similar results are obtained ifthe data are not clustered

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the comparison group EethtjGTHORN is also a significant predictor ofE

BethtjGTHORN with the predicted negative signAlthough these results provide strong evidence of context

dependence and are consistent with our model they do not pindown a role for representativeness of types Our next test relatesthe magnitude of representativeness of tail types to the magni-tude of belief distortions

To this end we implement the regressions in equations (6)and (7) Following Proposition 4 we compute the average repre-

sentativeness of tail types for conservatives RconsH frac14

PtT2tconsPtT2tlib

We

again test the hypothesis that RconsH is a significant predictor of Est

ethtjconsTHORN with a positive sign and a predictor of EstethtjlibTHORN with a

negative sign Table II shows that conditional on true mean RconsH

predicts believed mean for each group G as expected The firstthree specifications display the results for predicting beliefs heldabout conservatives In both data sets the average representa-tiveness of tail types for conservatives is a significant positivepredictor of beliefs held about conservatives The final three spe-cifications display the results for predicting beliefs held about

FIGURE IV

Exaggeration of Differences

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liberals We find that the average representativeness of tail typesfor conservatives is a negative predictor of beliefs held about lib-erals This effect is significant in the GNH data and marginallysignificant in the ANES data

We present several additional results in Online Appendix GTo further examine the role of representativeness in driving be-liefs we first show the results of Table II carry through when we

TABLE II

AVERAGE REPRESENTATIVENESS OF TAIL POSITIONS PREDICTS BELIEFS

OLS Predicting Believed Mean of Group G for Each Issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position

of group G for issue

078 024 051 072 018 041

(006) (008) (009) (005) (005) (010)

Avg rep of tail types for

conservatives RconsH

019 055 025 014 012 024

(007) (022) (008) (006) (007) (005)

Constant 101 260 184 093 271 201

(026) (045) (029) (022) (025) (032)

R2 082 048 060 091 031 070

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

TABLE I

INFORMATION ABOUT ndashG PREDICTS BELIEFS ABOUT G

OLS predicting believed mean of group G for each issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position of

conservatives for issue

102 098 096 021 019 025

(0097) (0133) (0076) (0060) (0116) (0060)

True mean position of

liberals for issue

035 086 058 0987 039 073

(0106) (0134) (0131) (0066) (0106) (0135)

Constant 151 335 235 069 258 156

(0195) (0269) (0279) (0122) (0249) (0270)

R2 083 053 066 092 032 068

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

STEREOTYPES 1789

at Harvard L

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control for the average likelihood on the tail positions (see Table A4in Online Appendix G) Most tellingly we use the model to predictbeliefs across issues and compare those to the data For simplicitywe use the rank-based truncation specification to predict mean be-liefs when stereotypes include the d most representative types ford frac14 1 T We compare these predictions to those of a model inwhich beliefs are obtained by restricting the distribution to the dmost likely types Our benchmark for both models is predicting thebelieved mean from the entire distribution where d = T We showthat the predictions of the rank-based truncation model with d = 4or 5 compare favorably to both a likelihood-based truncation model(with any d) and the accurate beliefs benchmark Interestingly thisresult suggests that stereotypical beliefs are well approximated byneglecting the least representative types (as opposed to focusingonly on the most representative types) and so represent a moderatethough systematic departure from the standard benchmarkFinally we show that the results we document above hold forboth beliefs held by conservatives and beliefs held by liberals (seeTables A9 A10 and A11 in Online Appendix G)

V Conclusion

We present a model of stereotypical thinking in which DMsmaking predictions about a group overweight the grouprsquos mostdistinctive types These overweighted types are not the mostlikely ones given the DMrsquos data but the most representativeones in the sense of being the most diagnostic of the group rela-tive to other groups Representativeness implies that what ismost distinctive of a group depends on what group it is comparedwith We present experimental evidence that confirms this con-text dependence in recall-based assessments of groups Finallywe evaluated the predictions of the model using political data fromexisting large-scale surveys We find context dependence to be akey feature of beliefs Given the richness of the political data wecan go a step further and identify a role for representativeness inparticular As the representativeness of tail types increases beliefsof a group are distorted in the direction of that tail

Our approach provides a parsimonious and psychologicallyfounded account of how DMs generate simplified representationsof reality from social groups to stock returns and offers a unifiedaccount of disparate pieces of evidence relating to this type of

QUARTERLY JOURNAL OF ECONOMICS1790

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uncertainty The model captures the central fact that stereotypeshighlight the greatest difference between groups thus explainingwhy some stereotypes are very accurate while others lack valid-ity Still stereotypes often have a kernel of truth when they arebased on systematicmdasheven if smallmdashdifferences between groupsThis logic allows us to describe a number of heuristics and psy-chological biases many of which arise in the context of predictionproblems Generically our model generates overreaction to diag-nostic information

Our model is based on representativeness and does not cap-ture all the features of stereotypical thinking However it cap-tures perhaps the central feature when we think of a group wefocus on what is most distinctive about it and neglect or under-weight the rest

Saeuroıd Business School University of Oxford

Ohio State University and Harvard Business School

Universita Bocconi and Innocenzo Gasparini Institute

for Economic Research

Harvard University

Supplementary Material

An Online Appendix for this article can be found at QJEonline (qjeoxfordjournalorg)

References

Adorno Theodor Else Frenkel-Brunswik Daniel Levinson and Nevitt SanfordThe Authoritarian Personality (New York Harper amp Row 1950)

Arrow Kenneth lsquolsquoThe Theory of Discriminationrsquorsquo in Discrimination in LaborMarkets Orley Ashenfelter and Albert Rees eds (Princeton NJPrinceton University Press 1973)

Ashton Michael and Victoria Esses lsquolsquoStereotype Accuracy Estimating theAcademic Performance of Ethnic Groupsrsquorsquo Personality and SocialPsychology Bulletin 25 (1999) 225ndash236

Barberis Nicholas Andrei Shleifer and Robert Vishny lsquolsquoA Model of InvestorSentimentrsquorsquo Journal of Financial Economics 49 (1998) 307ndash343

Bayer Sylvia lsquolsquoThe Accuracy of Academic Gender Stereotypesrsquorsquo Sex Roles 40(1999) 787ndash813

Benjamin Dan James Choi and Joshua Strickland lsquolsquoSocial Identity andPreferencesrsquorsquo American Economic Review 100 (2010) 1913ndash1928

Benjamin Dan Matthew Rabin and Collin Raymond lsquolsquoA Model of Non-Belief inthe Law of Large Numbersrsquorsquo Journal of the European Economic Association15 (2015) 515ndash544

Bertrand Marianne lsquolsquoNew Perspectives on Genderrsquorsquo Handbook of LaborEconomics 4 (2011) 1543ndash1590

Bodoh-Creed Aaron Dan Benjamin and Matthew Rabin lsquolsquoThe Dynamics of Base-Rate Neglectrsquorsquo mimeo Haas Business School 2013

STEREOTYPES 1791

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

Bohnet Iris Alexandra van Geen and Max Bazerman lsquolsquoWhen PerformanceTrumps Gender Bias Joint versus Separate Evaluationrsquorsquo ManagementScience 5 (2016) 1225ndash1234

Bordalo Pedro Nicola Gennaioli and Andrei Shleifer lsquolsquoSalience Theory of Choiceunder Riskrsquorsquo Quarterly Journal of Economics 127 (2012) 1243ndash1285

mdashmdashmdash lsquolsquoSalience and Consumer Choicersquorsquo Journal of Political Economy 121(2013) 803ndash843

Briton Nancy and Judith Hall lsquolsquoBeliefs about Female and Male NonverbalCommunicationrsquorsquo Sex Roles 32 (1995) 79ndash90

Buser Thomas Muriel Niederle and Hessel Oosterbeek lsquolsquoGenderCompetitiveness and Career Choicesrsquorsquo Quarterly Journal of Economics 129(2014) 1409ndash1447

Carrell Scott Marianne Page and James West lsquolsquoSex and Science How ProfessorGender Perpetuates the Gender Gaprsquorsquo Quarterly Journal of Economics 125(2010) 1101ndash1144

Chambers John and Darya Melnyk lsquolsquoWhy Do I Hate Thee ConflictMisperceptions and Intergroup Mistrustrsquorsquo Personality and SocialPsychology Bulletin 32 (2006) 1295ndash1311

Chan Wayne Robert R McCrae Filip De Fruyt Lee Jussim CorinnaE Lockenhoff Marleen De Bolle Paul T Costa Jr Angelina R SutinAnu Realo Juri Allik Katsuharu Nakazato Yoshiko ShimonakaMartina Hrebıckova Sylvie Graf Michelle Yik Marina Brunner-SciarraNora Leibovich De Figueora Vanina Schmidt Chang-kyo Ahn Hyun-nie Ahn Maria E Aguilar-Vafaie Jerzy Siuta Barbara SzmigielskaThomas R Cain Janet T Crawford Khairul Anwar Mastor Jean-Pierre Rolland Florence Nansubuga Daniel R MiramontezVeronica Benet-Martınez Jerome Rossier Denis Bratko Iris MarusicJamin Halberstadt Mami Yamaguchi Goran Knezevic Thomas A MartinMirona Gheorghiu Peter B Smith Claudio Barbaranelli Lei WangJane Shakespeare-Finch Margarida P Lima Waldemar KlinkoszAndrzej Sekowski Lidia Alcalay Franco Simonetti Tatyana V AvdeyevaV S Pramila and Antonio Terracciano lsquolsquoStereotypes of Age Differences inPersonality Traits Universal and Accuratersquorsquo Journal of Personality andSocial Psychology 103 (2012) 1050ndash1066

Chen Yan Sherry Xin Liu Tracy Xiao and Margaret Shih lsquolsquoWhich Hat to WearImpact of Natural Identities on Coordination and Cooperationrsquorsquo Games andEconomic Behavior 84 (2014) 58ndash86

Coffman Katherine lsquolsquoEvidence on Self-Stereotyping and the Contribution ofIdeasrsquorsquo Quarterly Journal of Economics 129 (2014) 1625ndash1660

Cunningham Tom lsquolsquoComparisons and Choicersquorsquo mimeo Stockholm University2013

Diekman Amanda Alice Eagly and Patrick Kulesa lsquolsquoAccuracy and Bias in theStereotypes about the Social and Political Attitudes of Women and MenrsquorsquoJournal of Experimental Social Psychology 38 (2002) 268ndash282

Eccles Jacquelynne S Janis E Jacobs and Rena D Harold lsquolsquoGender RoleStereotypes Expectancy Effects and Parentsrsquo Socialization of GenderDifferencesrsquorsquo Journal of Social Issues 46 (1990) 183ndash201

Fryer Roland and Matthew Jackson lsquolsquoA Categorical Model of Cognition andBiased Decision-Makingrsquorsquo BE Journal of Theoretical Economics 8 (2008)1ndash42

Fryer Roland and Steven Levitt lsquolsquoAn Empirical Analysis of the Gender Gap inMathematicsrsquorsquo American Economic Journal Applied Economics 2 (2010)210ndash240

Gennaioli Nicola and Andrei Shleifer lsquolsquoWhat Comes to Mindrsquorsquo Quarterly Journalof Economics 125 (2010) 1399ndash1433

Gennaioli Nicola Andrei Shleifer and Robert Vishny lsquolsquoNeglected RisksFinancial Innovation and Financial Fragilityrsquorsquo Journal of FinancialEconomics 104 (2012) 452ndash468

Gilens Martin lsquolsquoRace and Poverty in America Public Misperceptions and theAmerican News Mediarsquorsquo Public Opinion Quarterly 60 (1996) 515ndash541

Glaeser Edward lsquolsquoThe Political Economy of Hatredrsquorsquo Quarterly Journal ofEconomics 120 (2005) 45ndash86

QUARTERLY JOURNAL OF ECONOMICS1792

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

Glover Dyland Amanda Pallais and William Pariente lsquolsquoDiscrimination as a Self-Fulfilling Prophecy Evidence from French Grocery Storesrsquorsquo mimeo HarvardUniversity 2015

Goldin Claudia Lawrence Katz and Ilyana Kuziemko lsquolsquoThe Homecoming ofAmerican College Women The Reversal of the College Gender GaprsquorsquoJournal of Economic Perspectives 20 (2006) 133ndash156

Graham Jesse Brian Nosek and Jonathan Haidt lsquolsquoThe Moral Stereotypes ofLiberals and Conservatives Exaggeration of Differences across thePolitical Spectrumrsquorsquo PLoS One 7 (2012) 1ndash13

Grether David lsquolsquoBayes Rule as a Descriptive Model The RepresentativenessHeuristicrsquorsquo Quarterly Journal of Economics 95 (1980) 537ndash557

Griffin Dale and Amos Tversky lsquolsquoThe Weighing of Evidence and theDeterminants of Confidencersquorsquo Cognitive Psychology 24 (1992) 411ndash435

Guiso Luigi Ferdinando Monte Paola Sapienza and Luigi Zingales lsquolsquoCultureGender and Mathrsquorsquo Science 320 (2008) 1164ndash1165

Hilton James and William Von Hippel lsquolsquoStereotypesrsquorsquo Annual Review ofPsychology 47 (1996) 237ndash271

Hyde Janet Sara Lindberg Marcia Linn Amy Ellis and Caroline WilliamslsquolsquoGender Similarities Characterize Math Performancersquorsquo Science 321 (2008)494ndash495

Judd Charles and Bernardette Park lsquolsquoDefinition and Assessment of Accuracy inSocial Stereotypesrsquorsquo Psychological Review 100 (1993) 109ndash128

Jussim Lee Jarret Crawford Stephanie Anglin John Chambers Sean Stevensand Florette Cohen lsquolsquoStereotype Accuracy One of the Largest and MostReplicable Effects in All of Social Psychologyrsquorsquo in The Handbook ofPrejudice Stereotyping and Discrimination Todd Nelson ed (MahwahNJ Lawrence Erlbaum 2015)

Kahneman Daniel and Amos Tversky lsquolsquoSubjective Probability A Judgment ofRepresentativenessrsquorsquo Cognitive Psychology 3 (1972) 430ndash454

mdashmdashmdash lsquolsquoOn the Psychology of Predictionrsquorsquo Psychological Review 80 (1973) 237ndash251

Kaplowitz Stan Bradley Fisher and Clifford Broman lsquolsquoHow Accurate ArePerceptions of Social Statistics about Blacks and Whitesrsquorsquo Public OpinionQuarterly 67 (2003) 237ndash243

Kersten Daniel Pascal Mamassian and Alan Yuille lsquolsquoObject Perception asBayesian Inferencersquorsquo Annual Review of Psychology 55 (2004) 271ndash304

Klein Richard Kate A Ratliff Michelangelo Vianello Reginald B Adams JrStepan Bahnik Michael J Bernstein Konrad Bocian Mark J BrandtBeach Brooks Claudia Chloe Brumbaugh Zeynep CemalcilarJesse Chandler Winnee Cheong William E Davis Thierry DevosMatthew Eisner Natalia Frankowska David Furrow Elisa Maria GallianiFred Hasselman Joshua A Hicks James F Hovermale S Jane HuntJeffrey R Huntsinger Hans IJzerman Melissa-Sue John Jennifer A Joy-Gaba Heather Barry Kappes Lacy E Krueger Jaime Kurtz CarmelA Levitan Robyn Mallett Wendy L Morris Anthony J Nelson JasonA Nier Grant Packard Ronaldo Pilati Abraham M RutchickKathleen Schmidt Jeanine L Skorinko Robert Smith Troy G SteinerJustin Storbeck Lyn M Van Swol Donna Thompson Anna van rsquot VeerLeigh Ann Vaughn Marek Vranka Aaron Wichman Julie A Woodzickaand Brian A Nosek lsquolsquoInvestigating Variation in Replicability A ManyLabs Replication Projectrsquorsquo Social Psychology 45 (2014) 142ndash152

Lundberg Shelly and Richard Startz lsquolsquoPrivate Discrimination and SocialIntervention in Competitive Labor Marketsrsquorsquo American Economic Review73 (1983) 340ndash347

Madon Stephanie Max Guyll Kathy Aboufadel Eulices Montiel Alison SmithPolly Palumbo and Lee Jussim lsquolsquoEthnic and National Stereotypes ThePrinceton Trilogy Revisited and Revisedrsquorsquo Personality and SocialPsychological Bulletin 27 (2001) 996ndash1010

Martin Carol lsquolsquoA Ratio Measure of Sex Stereotypingrsquorsquo Journal of Personality andSocial Psychology 52 (1987) 489ndash499

STEREOTYPES 1793

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

McCauley Clark Krishna Thangavelu and Paul Rozin lsquolsquoSex Stereotyping ofOccupations in Relation to Television Representations and Census FactsrsquorsquoBasic and Applied Social Psychology 9 (1988) 197ndash212

Mullainathan Sendhil lsquolsquoThinking through Categoriesrsquorsquo mimeo HarvardUniversity 2002

Ortoleva Pietro and Erik Snowberg lsquolsquoOverconfidence in Political BehaviorrsquorsquoAmerican Economic Review 105 (2015) 504ndash535

Phelps Edmund lsquolsquoThe Statistical Theory of Racism and Sexismrsquorsquo AmericanEconomic Review 62 (1972) 659ndash661

Pope Devin and Justin Sydnor lsquolsquoGeographic Variation in the Gender Differencesin Test Scoresrsquorsquo Journal of Economic Perspectives 24 (2010) 95ndash108

Rabin Matthew lsquolsquoInference by Believers in the Law of Small NumbersrsquorsquoQuarterly Journal of Economics 117 (2002) 775ndash816

Rabin Matthew and Joel Schrag lsquolsquoFirst Impressions Matter A Model ofConfirmatory Biasrsquorsquo Quarterly Journal of Economics 114 (1999) 37ndash82

Rabin Matthew and Dimitri Vayanos lsquolsquoThe Gamblerrsquos and Hot-Hand FallaciesTheory and Applicationsrsquorsquo Review of Economic Studies 77 (2010) 730ndash778

Reuben Ernesto Paola Sapienza and Luigi Zingales lsquolsquoHow Stereotypes ImpairWomenrsquos Careers in Sciencersquorsquo Proceedings of the National Academy ofSciences 111 (2014) 4403ndash4408

Rosch Eleanor lsquolsquoNatural Categoriesrsquorsquo Cognitive Psychology 4 (1973) 328ndash350Ryan Carey S lsquolsquoAccuracy of Black and White College Studentsrsquo In-Group and

Out-Group Stereotypesrsquorsquo Personality and Social Psychology Bulletin 22(1996) 1114ndash1127

Schneider David The Psychology of Stereotyping (New York Guilford Press2004)

Schneider David Albert Hastorf and Phoebe Ellsworth Person Perception(Reading MA Addison-Wesley 1979)

Shih Margaret Todd Pittinsky and Nalini Ambady lsquolsquoStereotype SusceptibilityIdentity Salience and Shifts in Quantitative Performancersquorsquo PsychologicalScience 10 (1999) 80ndash83

Shih Margaret Todd Pittinsky and Amy Trahan lsquolsquoDomain-Specific Effects ofStereotypes on Performancersquorsquo Self and Identity 5 (2006) 1ndash14

Steele Claude Whistling Vivaldi How Stereotypes Affect Us and What We CanDo (New York Norton 2010)

Tenenbaum Joshua and Thomas Griffiths lsquolsquoThe Rational Basis ofRepresentativenessrsquorsquo 23rd Annual Conference of the Cognitive ScienceSociety (2001) 1036ndash1041

Tversky Amos and Daniel Kahneman lsquolsquoExtensional versus Intuitive ReasoningThe Conjunction Fallacy in Probability Judgmentrsquorsquo Psychological Review 90(1983) 293ndash315

Weinberger Catherin lsquolsquoIs the Science and Engineering Workforce Drawn fromthe Far Upper Tail of the Math Ability Distributionrsquorsquo mimeo UCSB 2005

Westfall Jacob Leaf Van Boven John Chambers and Charles Judd lsquolsquoPerceivingPolitical Polarization in the United States Party Identity Strength andAttitude Extremity Exacerbate the Perceived Partisan DividersquorsquoPsychological Science 10 (2015) 145ndash158

Wolsko Christopher Bernadette Park Charles Judd and Bernd WittenbrinklsquolsquoFraming Interethnic Ideology Effects of Multicultural and Color-BlindPerspectives on Judgments of Groups and Individualsrsquorsquo Journal ofPersonality and Social Psychology 78 (2000) 635ndash654

QUARTERLY JOURNAL OF ECONOMICS1794

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

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Page 11: I. Introduction · uneducated at the beginning of the 20th century, and as high achievers at the beginning of the 21st (Madon et al. 2001). Social science has produced three broad

(i) Rank-based truncation the DM only recalls the typesthat have representativeness ranking of at most dnamely ft 2 TjrethtTHORN dg Zero probability is attachedto the remaining types10 Denote by IethrethtTHORN dTHORN an in-dicator function taking the value 1 if the representa-tiveness ranking of t is at most d Then theweighting function is ht frac14 IethrethtTHORN dTHORN so that

sttG frac14 tG

IethrethtTHORN dTHORNPs2T sGIethrethsTHORN dTHORN

which is the true conditional probability within re-called types This assumption is used in Gennaioliand Shleifer (2010)11

(ii) Rank-based discounting the DM discounts by a con-stant factor 2 frac1201 the odds of type t relative to itsimmediate predecessors in the representativenessranking Lower implies stronger discounting ofless representative types Formally the weightingfunction is ht frac14

rethtTHORN so that

sttG frac14 tG

rethtTHORNPs2T sG

rethsTHORN

Representativness-based discounting all else equal theweight attached by the DM to type t increases continuouslywith its representativeness One convenient formulation is

ht frac14tG

tG

so that

10 These neglected types are not viewed as impossible they are just assignedzero probability in the DMrsquos current thinking This formulation allows us to modelsurprise and reactions to unforeseen contingencies which have proved useful in-gredients in modeling probabilistic judgments (GS 2010) as well as neglect of risk infinancial crises (Gennaioli Shleifer and Vishny 2012)

11 Specifically in GS (2010) the assessed probability that a certain hypothesisG is true is equal to

Pr ethGTHORN frac14

Pt tGIethrethtTHORN dTHORNP

t tGIethrethtTHORN dTHORN thornP

t t=GIethrethtTHORN dTHORN

which increases in the ratio between the total probability mass recalled for Gand that recalled for G frac14 nG

STEREOTYPES 1763

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sttG frac14 tG

tG

tG

P

s2T sGsG

sG

where 0 captures the extent to which representative-ness distorts beliefs This formulation is particularly con-venient when dealing with continuous distributions ofthe exponential or power classes

These functional forms all embody the main idea of our modelthat the stereotype overweights the probability of more represen-tative types Rank-based truncation captures a central manifes-tation of limited memory forgetting unrepresentative typesSmoother discounting (based on ranking or on representative-ness) may be more appropriate when the type space is smalland smooth discounting can be more tractable in certain settings

Section III characterizes the general properties of stereotypesIn particular it shows their ability to account for social psycholo-gistsrsquo kernel of truth hypothesis under the general weighting func-tion of Definition 2 To bring the model to the data in Section IVBwe derive linear approximations of stereotypical beliefs by assum-ing that the weighting function is differentiable with respect to atypersquos representativeness This assumption excludes rank-basedweighting but allows for many possibilities

IIB Discussion of Assumptions

Before moving to the formal analysis we discuss some prop-erties and limitations of our approach Representativeness-basedrecall the idea that individuals recall distinctive group types canbe viewed as an instance of what Kahneman and Tversky calllsquolsquoattribute substitutionrsquorsquo When dealing with the difficult questionlsquolsquowhat is the distribution of hair color among the Irishrsquorsquo peopleintuitively answer to the simpler question lsquolsquowhich hair color dis-tinguishes the Irish peoplersquorsquo Critically as discussed byKahneman and Tversky attribute substitution does not occurbecause people misunderstand the original question or mechan-ically confuse the assessment of PrethtjGTHORN with that of PrethGjtTHORNRather it occurs because the distinctive or representative typesimmediately come to mind and individuals anchor their overallprobability judgment to them As a consequence subjects do notonly make mistakes in judging the probability that a Floridian is

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over age 65 They also give too high an answer to the questionlsquolsquowhat is the average age of a Floridianrsquorsquo12

One interesting question is whether the process of stereotyp-ing we describe is optimal in some sense Focusing mental repre-sentations on a few types can be justified by the costs of thinkingor retrieval This approach however is not enough to explainwhy individuals should focus on representative rather thanlikely types We do not formally analyze the optimality of repre-sentativeness here but we mention some relevant considerationsfrom cognitive psychology Kahneman and Tversky (1979) stressthe similarity between many perceptual and cognitive operationsFor instance the highlight of contrastmdasha key principle of visualperceptionmdashis invoked to justify the prospect theory assumptionthat the carriers of utility are changes relative to a referencepoint The same logic applies to our model in which stereotypesprecisely highlight the contrast between groups

In visual perception assessing properties such as brightnesscolor size or distance to an object by comparing them to otherproximate objects has been shown to be optimal in the presence ofmultiplicative background noise (Kersten Mamassian andYuille 2004 Cunningham 2013) Our formulation of representa-tiveness is related to the same idea in the sense that individualsestimating properties of one group stress differences from an-other group In a noisy world in which attention is limited thisprocess may optimally allow for swift reactions to changes ingroup characteristics even if errors are sometimes made13

12 Indeed in many cases mere confusion of PrethtjGTHORNwith PrethGjtTHORNwould not yieldthe phenomenon of stereotyping In the Irish hair color example the probability ofbeing Irish conditional on having red hair is

PrethIrishjredTHORN frac14PrethredjIrishTHORNPrethIrishTHORN

PrethredjIrishTHORNPrethIrishTHORN thorn PrethredjNonIrishTHORNPrethNonIrishTHORN

This probability is clearly very small given that the Irish population is a tinyfraction of the world population Confusion of PrethtjGTHORN with PrethGjtTHORN in this casewould lead to an understatement of the probability of the red-haired Irish

13 To give a simple example suppose thatmdashas in the case of Proposition 3mdashthevariance in the environment increases in the sense that extreme tail events becomemore likely Then a likelihood-based stereotype would detect no change whereas arepresentativeness-based stereotype would focus on the heightened probability ofthe tails In particular an asymmetric increase in tail probabilities that shifts themean would be detected by a representativeness-based stereotype even if the dis-tributionrsquos mode does not change

STEREOTYPES 1765

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Exploring this idea formally is an interesting avenue for futurework

Consider some limitations of our model First representa-tiveness is not the only heuristic that shapes recall Decisionmakers may for instance find it easier to recall types that aresufficiently likely Another potentially important mechanism isavailability understood by Kahneman and Tversky (1972) as thelsquolsquoeasersquorsquo with which information comes to mind (because of actualfrequency or repetition) In Online Appendix E we present a trun-cation-based recall mechanism in which distortions are driven bya combination of representativeness and likelihood of types(which is equivalent to relaxing property i in Definition 2) Thismodel can offer a useful starting point to capture availability aswell even though a full model of availability is beyond the scopeof this article Even in this more general setting the influence ofrepresentativeness on recall is the driving force of stereotypesthat in line with the social psychology perspective are basedon underlying differences among groups As we show in SectionIV this feature is critical in accounting for the evidence

The second set of model-related issues concerns how to spe-cify the elements of Definition 1 in applications group G the typespace T and the reference group ndashG Take the specification of thegroup G and of the type space T Often the problem itself pro-vides a natural specification of these features This is the case inthe empirically important class of lsquolsquoclosedrsquorsquo questions such asthose used in surveys which provide respondents with a set ofalternatives as in the data we use in Section IV More generallythe problem solved by the DMmdashsuch as evaluating the resume ofa job applicant coming from a certain ethnic groupmdashprimes agroup a dimension of interest and a set of types (eg the appli-cantrsquos qualification or skill levels) When types have a naturalorder such as income age or education the granularity of T isalso naturally given by the problem (income age and years ofschooling brackets) When the set of types is not specified by theproblem DMs spontaneously generate one14 It would be useful tohave a model of which dimensions and types come to mind par-ticularly for more open-ended problems Psychologists have

14 For example suppose a person is asked to guess the typical occupation of ademocratic voter in an lsquolsquoopen-endedrsquorsquo format (without being provided a set of alter-natives) Here the level of granularity at which types are defined is not obvious (egteacher versus a university teacher vs a professor of comparative literature)

QUARTERLY JOURNAL OF ECONOMICS1766

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sought to construct a theory of natural types and dimensions(Rosch 1973) We do not make a contribution to this problembut we note that in many problems of interest in economics thedimension as well as the set of types is naturally givenFurthermore in our model details of the type space can be impor-tant under rank-based truncation but they matter less undersmooth discounting

Consider finally the role of the comparison group ndashG Thisgroup captures the context in which a stereotype is formed andagain is often implied by the problem when G = Floridians ndashG =rest of US population when G = African Americans ndashG = whiteAmericans A distinctive prediction of our model confirmed byour experiments in Section IVA is that the stereotype for agiven group G depends on the comparison group ndashG15 WhenndashG is not pinned down by the problem itself to derive testablepredictions from representativeness we set G frac14 nG where

is the natural population over which the unconditional distribu-tion of types is measured

III Properties of Stereotypes

We now study stereotypical beliefs and their accuracy Toillustrate the role of representativeness we first ask to whatextent the most representative type is a good fit for the groupnamely whether it is modal Next we assess the accuracy of theentire stereotypical distribution To do so we focus on a cardinaltypes and compare the stereotypersquos mean and variance to the trueones

15 Some empirical papers have taken a similar approach exogenously varyingthe natural comparison group through priming Benjamin Choi and Strickland(2010) show that priming racial or ethnic identity can affect the risk preferences ofparticipants Chen et al (2014) find that Asian students cooperate less with out-group members when primed with their ethnic identity rather than their universityidentity Shih Pittinsky and Ambady (1999) show that Asian American womenstereotype themselves as better or worse in math with corresponding impact onperformance when their ethnicity or gender respectively is primed ShihPittinsky and Trahan (2006) replicate this effect using a verbal task documentingthat Asian American women performed better when their gender rather than theirethnicity was primed Although the generalizability and replicability of priminghas been doubted (Klein et al 2014) this body of evidence is consistent with contextdependence

STEREOTYPES 1767

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IIIA Likely versus Unlikely Exemplars

The most representative type for a group is the one thatagents most easily recall and associate with the group itself forinstance a red-haired Irishman or a 65+-year-old FloridianSocial psychologists call this type the exemplar of the groupAccordingly we define

DEFINITION 3 A type t is an exemplar for G given comparisongroup ndashG when

t 2 arg maxt

tG

tG

Under any specification of the weighting function ht inDefinition 2 overweighting (weakly) increases as we movetoward more representative types so the exemplar is also thetype whose probability is overweighted the most16 By analyzingthe exemplar then we can gauge whether representativenessinduces the DM to overweight a likely type (as happens in stan-dard models of categorical thinking) or an unlikely type Whenoverweighting occurs in unlikely and extreme types the biases ofstereotypes can be particularly severe17

Equation (2) yields the following characterization

PROPOSITION 1 Suppose the conditional distributions G and G

are not identical Consider two extreme cases

(i) If for all t t0

2 T we have that tG gt t0 G if and only iftG gt t0 G then the modal type is not an exemplar forat least one group

(ii) If for all t t0

2 T we have that tG gt t0 G if and only iftG lt t0 G then for each group the modal type is theexemplar

16 Consider the function hethTHORN from Definition 2 When applied to more repre-sentative types the first argument of the function increases while one of the otherT ndash 1 arguments decreases As a result the weighting factor ht (and thus overweigh-ing

sttG

tG) increases as well

17 In the rank-based truncation model the frequency of the exemplar providesa measure of stereotype accuracy By accuracy we mean the extent to which thestereotype minimizes the distance

Pt eth

sttG tGTHORN

2 When d = 1 and only one type isrecalled (there are no ties) accuracy is maximized if the exemplar is the most likelytype and minimized if the exemplar is the least likely type

QUARTERLY JOURNAL OF ECONOMICS1768

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Case i says that when groups have similar distributions inthe sense of having the same likelihood ranking the most repre-sentative type is unlikely for at least one group potentially bothRepresentativeness draws the DMrsquos attention to group differ-ences neglecting the fact that the groups are similar and havethe same mode This mechanism generates inaccurate stereo-types and is illustrated by the Florida example This resultholds under any measure of representativeness that differenti-ates the two groups (eg the difference tG tG)

Case ii says that the most representative type tends to belikely for both groups when the distributions are very differentIn this case groups differ the most around their modes so repre-sentativeness and likelihood coincide Thinking of Swedes aslsquolsquoblondrsquorsquo and Europeans as lsquolsquodark hairedrsquorsquo is accurate precisely be-cause these are majority traits of the Swedish and European pop-ulations respectively In these cases stereotyping yields fairlyreliable models Of course there is still some inaccuracy Evenin the case of likely exemplars judgment errors can be signifi-cant For instance voters in some US states are perceived aslsquolsquobluersquorsquo or lsquolsquoredrsquorsquo because a majority of the population votesDemocrat or Republican In reality even in lsquolsquobluersquorsquo states farfrom everyone votes Democrat In the 2012 presidential electionvote shares of either candidate in most states ranged from 40 to6018

When DMs strongly overweight representative types themost severe biases occur when those types are unlikely and ex-treme This is true both under rank based truncations and undersmooth discounting functions (see Section IIIB) Ethnic stereo-types based on crime or terrorism exhibit this error they neglectthe fact that by far the most common types in all groups arehonest and peaceful

IIIB Stereotypical Moments

We now characterize how the first two moments of a distri-bution are distorted by the process of stereotyping To do so wemust restrict our analysis to cardinal ordered types The follow-ing results hold for any weighting function htethTHORN satisfyingDefinition 2 We consider two canonical cases that prove usefulin illustrating the predictions of the model

18 Presidential Election Results NBCNewscom see httpelectionsnbcnewscomnspolitics2012allpresident (accessed 5 September 2016)

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In the first case groups G and ndashG are such that the likelihoodratio tG

tGis monotonic in t The monotone likelihood ratio prop-

erty (MLRP) holds to a first approximation in many empiricalsettings and is also assumed in many economic models such asstandard agency models19 If tG

tGis monotonically increasing (de-

creasing) in t then group G is associated with higher (lower)values of t relative to the comparison group ndashG Formally

PROPOSITION 2 Suppose that MLRP holds and assume wlogthat the likelihood ratio tG

tGis strictly increasing in t Then

for any weighting function htethTHORN that is not constant in therelevant range

EstethtjGTHORN gt EethtjGTHORN gt EethtjGTHORN gt E

stethtjGTHORN

Under MLRP the most representative part of the distribu-tion for G is the right tail if tG

tGincreases in t or the left tail if tG

tG

decreases in t The representative tail is then overweighted whilethe nonrepresentative tail is underweighted As a consequencethe assessed mean E

stethtjGTHORN is too extreme in the direction of therepresentative tail

Critically in line with the social cognition perspective the ste-reotype contains a kernel of truth the DM overestimates the meanof G if this group has a higher mean than the comparison groupnamely EethtjGTHORN gt EethtjGTHORN and conversely if EethtjGTHORN lt EethtjGTHORN TheDM exaggerates this true difference because he inflates the asso-ciation of G with its most representative types20 For instancewhen judging an asset manager who performs well we tend to

19 Examples include the binomial and the Poisson families of distributionswith different parameters The characterization of distributions satisfying MLRPis easier in the case of continuous distributions (see Online Appendix D) two dis-tributions f(x) f ethx THORN that differ only in their mean satisfy MLRP if and only if thedistribution f(x) is log-concave Examples include the exponential and normal dis-tributions To the extent that discrete distributions sufficiently approximate thesedistributions (as the Poisson distribution PoisethTHORN approximates the normal distri-bution Neth THORN for large l) they will also satisfy MLRP

20 Depending on the distribution and the weighing function the DMrsquos assess-ment of the variance VarethtjGTHORNmay also be dampened relative to the truth This isoften true under the truncation weighing function In this case stereotyping effec-tively leads to a form of overconfidence in which the DM holds extreme views andoverestimates the precision of his assessment That extreme views and overconfi-dence (in the sense of over precision) go together has been documented in the settingof political ideology among others (Ortoleva and Snowberg 2015)

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overemphasize skill relative to luck because higher skill levels arerelatively more associated with higher performance This occurseven if for both skilled and unskilled managers high performanceis mostly due to luck

In the second case for which we characterize the stereotypi-cal distributions groups G and ndashG have the same mean EethtjGTHORNfrac14 EethtjGTHORN frac14 EethtTHORN but differ in their variance We abstract fromskewness and higher moments by considering distributionsethtGTHORNt2T and ethtGTHORNt2T that share the same support and are sym-metric around the medianmean EethtTHORN

PROPOSITION 3 Suppose that in G more extreme types are rela-tively more frequent than in ndashG Formally the likelihoodratio tG

tGis U-shaped in t around EethtTHORN Then for any weight-

ing function htethTHORN that is not constant in the relevant rangestereotypical beliefs satisfy

VarstethtjGTHORN gt VarethtjGTHORN gt VarethtjGTHORN gt VarstethtjGTHORN

EstethtjGTHORN frac14 E

stethtjGTHORN frac14 EethtTHORN

When group G has a higher relative prevalence of extremetypes its representative types are located at both extremes of thedistribution The DMrsquos beliefs about G are then formed by over-weighting both tails while underweighting the unrepresentativemiddle The overweighting of Grsquos tails causes the assessment ofits variance VarstethtjGTHORN to be too high For example the skill dis-tribution of immigrants to the United States may be perceived ashaving very fat tails or even bimodal with immigrants beingperceived as either unskilled or very skilled relative to the resi-dent population The mean of the group in contrast is assessedcorrectly because the stereotypical distribution remains symmet-ric around EethtTHORN As before the stereotype contains a kernel oftruth It induces the agent to exaggerate the true differences be-tween groups namely the higher variance of G relative to itscounterpart

We present a number of extensions of the model in the OnlineAppendix We first consider multidimensional type spaces andshow that stereotypes center around the dimension wheregroups differ the most in line with the kernel of truth logic(Online Appendix C) Multidimensional stereotypes imply thatthe dimension we think about is influenced by context For

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example the Irish are stereotyped as red-haired when comparedwith the European population However when compared withthe Scots a more plausible stereotype for the Irish is lsquolsquoCatholicrsquorsquobecause religion is the dimension along which Irish and Scotsdiffer the most

In Online Appendix D we extend the model to continuoustype spaces Many settings of interest in economics can be use-fully described by continuous probability distributions and weshow our model is particularly tractable in this case In OnlineAppendix E we relax Definition 2 and allow weighting of types toalso be influenced by their likelihood We show that the basicinsight that stereotypes contain a kernel of truth carries throughto these cases as well

To summarize the psychology of representativeness yieldsstereotypes that are consistent with the social cognition approachin which individuals assess groups by recalling and focusing ondistinctive group traits When there are systematic differencesbetween groups stereotypes get the direction right but exagger-ate differences

IIIC Some Examples

A growing body of field and experimental evidence points to awidespread belief that women are worse than men at mathemat-ics (Eccles Jacobs and Harold 1990 Guiso et al 2008 CarrellPage and West 2010) This belief persists despite the fact that fordecades women have been gaining ground in average schoolgrades including mathematics and have recently surpassedmen in overall school performance (Goldin Katz and Kuziemko2006 Hyde et al 2008) This belief shared by men and women(Reuben Sapienza and Zingales 2014) may help account for thegender gap in the choices of high school tracks college degreesand careers with women disproportionately choosing humanitiesand health-related areas (Weinberger 2005 Buser Niederle andOosterbeek 2014) and forgoing significant wage premiums toquantitative skills (Bertrand 2011)

Gender stereotypes in mathematics particularly beliefs thatexaggerate the extent of average differences are consistent withthe predictions of our model The fact that men are overrepre-sented at the very highest performance levels leads a stereotyp-ical thinker to exaggerate the magnitude of mean differencesFigure I shows the score distributions from the mathematics

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section of 2013rsquos Scholastic Aptitude Test (SAT) for men andwomen21 The distributions are very similar with averagescores slightly higher for men (531 versus 499 out of 800)However scores for men have a heavier right tail with mentwice as likely to have a perfect SAT math score than women22

In light of such data the stereotypical male performance in math-ematics is high while the stereotypical female performance ispoor Predictions based on such stereotypes are inaccurate exag-gerating true differences Consistent with this prediction exper-imental evidence shows that both genders underestimatewomenrsquos ability in simple math tasks even controlling for pastperformance (Reuben Sapienza and Zingales 2014) Coffman(2014) shows a similar pattern extends to confidence about ownability in other male-typed domains with women reporting sig-nificantly less confidence in gender-incongruent than gender-congruent tasks Our model suggests that these patterns mightcome from stereotypes based on gender differences in the righttail of the distribution While differences in the right tail of thedistribution are unlikely to be relevant for most decisions stereo-typical thinking driven by these differences has the potential toimpact economically important decisions whether through self-stereotyping (ie choice of careers or majors as in BuserNiederle and Oosterbeek 2014) or through discrimination (iehiring decisions as in Bohnet van Geen and Bazerman 2016)

The logic of exaggerated yet directionally correct stereotypesalso sheds light on the well-documented phenomenon of base rateneglect (Kahneman and Tversky 1973) Indeed Proposition 2implies that the DM overreacts to information that assigns

21 Standardized test performance measures not only innate ability but alsoeffort and investment by third parties (Hyde et al 2008) The mapping of test per-formance into inferences about innate ability is an issue not addressed by ourmodel

22 For 2013 SAT Mathematics scores see httpmediacollegeboardcomdigitalServicespdfresearchSAT-Percentile-Ranks-By-Gender-Ethnicity-2013pdf Results are similar for the National Assessment of Educational Progress(NAEP) which are more representative of the overall population For 2012NAEP scores for 17-year-olds in mathematics see httpnationsreportcardgovltt_2012age17maspx See Hyde et al (2008) Fryer and Levitt (2010) and Popeand Sydnor (2010) for in-depth empirical analyses of the gender gap inmathematics

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people to groups precisely because such information generatesextreme stereotypes Consider the classic example in which amedical test for a particular disease with a 5 prevalence has a90 rate of true positives and a 5 rate of false positives The testassigns each person to one of two groups + (positive test) or ndash(negative test) The DM estimates the frequency of the sick type(s) and the healthy type (h) in each group The test is informativea positive result increases the relative likelihood of sickness anda negative result increases the relative likelihood of health forany prior Formally

PreththornjsTHORN

PreththornjhTHORNgt 1 gt

PrethjsTHORN

PrethjhTHORNeth4THORN

This condition has clear implications the representative personwho tests positive is sick while the representative person whotests negative is healthy Following Proposition 2 the DMreacts to the test by moving his priors too far in the right di-rection generating extreme stereotypes He greatly boosts hisassessment that a positively tested person is sick but also thata negatively tested person is healthy Because most people arehealthy the DMrsquos assessment about the group that tested neg-ative is fairly accurate but is severely biased for the group that

FIGURE I

SAT Mathematics Scores by Gender (2013)

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tested positive This analysis formalizes Tversky andKahnemanrsquos (1983) verbal account of base rate neglect23

The same mechanism may underlie several other instanceswhere DMs overweight diagnostic information When assessingan employeersquos skill level an employer attributes high perfor-mance to high skill because high performance is the distinctivemark of a talented employee Because he neglects the possibilitythat some talented employees perform poorly and that somenontalented ones perform well (perhaps due to stochasticity inthe environment) the employer has too much faith in skill andneglects the role of luck in accounting for the output Similarlywhen assessing the performance of firms in a hot sector of theeconomy (eg G = internet) an investor recalls highly successfulfirms in that sector (t = return of Google Amazon etc) He ne-glects the possibility of firms being unsuccessful because lack ofsuccess is statistically nondiagnostic and psychologically nonrep-resentative of a growing sectormdasheven if it is likely This causesexcessive optimism (in that the expectation of growth is unrea-sonably high) and overconfidence (in that the variability in earn-ings growth considered possible is truncated) True the hot sectormay have better growth opportunities on average but represen-tativeness exaggerates this feature and induces the investor toneglect a significant risk of failure

IV Evidence on Representativeness and Stereotypes

Testing our model requires evaluating the beliefs individualshold about a target group against the true distribution of thattarget group over an attribute space An ideal data set would

23 Our account is distinct from a mechanical underweighting of base rates inBayes rule as in Grether (1980) and Bodoh-Creed Benjamin and Rabin (2013) Inthose models upon receiving the test results the DM can update his beliefs in thewrong direction he can be less confident that a person is healthy after a negativetest than under his prior which cannot happen in our model Although this predic-tion of our model seems consistent with introspection we are not aware of experi-mental evidence on this point Griffin and Tversky (1992) present evidenceconsistent with pure neglect of base rates but in a significantly different tasknamely inferring the bias of a coin from a history of coin flips Such experimentsare hard to compare with the predictions of our model because subjects are asked togenerate distributions of different numbers of coin flips in their minds which is amuch more involved task than to recall types of a given distribution Their assess-ments then might be wrong for other reasons See Bodoh-Creed Benjamin andRabin (2013) for a detailed discussion

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consist of naturally defined groups with known distributions overa given space of types and a corresponding set of beliefs about thedistribution of each group over that space of types This wouldallow us to test for exaggeration of true differences betweengroups and to ask whether this exaggeration is well predictedby overweighting representative types To identify a causal rolefor representativeness or context dependence we would need ex-ogenous variation in either the comparison group ndashG or in thedistributions over the type spaces This is unavailable in existingdata sets Accordingly we take a two-pronged approach First wecreate a controlled laboratory environment that allows us toinduce the exogenous variation in representative types that weneed to test causality then we reanalyze existing field evidence tocheck for consistency with our predictions

In testing our model we focus on the two main implicationsof representativeness-based stereotypes

Context dependence the stereotype of a target group de-pends on the characteristics of the reference group it iscompared to

Kernel of truth stereotypes depend on group character-istics andmdashin most (precisely characterized) settingsmdashare slanted toward representative types

We test the first property with a lab experiment (SectionIVA) We then turn to survey data on beliefs about US politicalgroups (Section IVB) for an empirical analysis that explores thesecond property The survey data are more tightly linked to ourinterest in social stereotypes The laboratory experiment allowsus to directly test the role of representativeness in generatingcontext dependent beliefs Online Appendixes F and G provideall details and additional results for the experiments and fieldevidence

IVA Lab Evidence on Representativeness and ContextDependence

The influence of the representativeness heuristic on recalland on beliefs has been extensively documented in the lab(Kahneman and Tversky 1972 1973) Our goal is to considerhow representativeness as formalized in equation (2) gives riseto context-dependent beliefs To our knowledge the possibility

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that representativeness may generate context dependence hasnot been tested before

To assess this prediction we perform a controlled laboratoryexperiment that allows us to isolate representativeness frommany confounding factorsmdashhistorical sociological or other-wisemdashthat may affect stereotype formation in the real worldWe construct our own groups of ordinary objects creating atarget group G and a comparison group ndashG We hold thetarget group G fixed and explore how participant impressions ofit change as we change the comparison group ndashG and thusrepresentativeness

We conducted several experiments in the laboratory and onAmazon Mechanical Turk Each involves a basic three-stepdesign First participants are shown the target group and a ran-domly assigned comparison group for 15 seconds In this timedifferences between groups can be noticed but the groupsrsquo precisecompositions cannot be memorized The second step consists of afew filler questions which briefly draw the participantsrsquo cognitivebandwidth away from their observation Finally participants areasked to assess the groups they saw Participants are incentiv-ized to provide accurate answers

We randomly assign participants to either the Control or theRepresentativeness condition In the Control condition G and ndashGhave nearly identical distributions so that all types are similarlyrepresentative for each group In the Representativeness condi-tion ndashG is changed in such a way that a certain type becomes veryrepresentative for G Context dependence implies that the assess-ment of G should now overweight this representative type eventhough the distribution of G itself has not changed

We ran six experiments of this form with design changesfocused on reducing participant confusion and removing con-founds We describe the final and most refined version of theseexperiments here In an attempt to provide a overview of the re-sults while remaining concise we provide the results from pooledspecifications that use all data collected In Online Appendix Fwe offer additional details and report all experiments conductedWe also give instructions and materials for each experiment thefull data set is available by request

Consider first the experiment illustrated in Figure II Agroup of 25 cartoon girls is presented next to a group of 25 cartoonboys in T-shirts of different colors blue green or purple In theControl condition (Figure II Panel a) the groups have identical

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color distributions (13 purple 12 green) so no color is represen-tative of either group The Representativeness condition (Panel b)compares the same group of girls with a different group of boysfor whom green shirts are replaced with blue shirts Now onlygirls wear green and only boys wear blue These colors althoughstill not the most frequent for either group are now most repre-sentative For each group girls and boys participants are asked anumber of questions concerning the frequency of T-shirts of dif-ferent colors worn by that group

Applying our model in the control condition the type space isT frac14 fgreen purpleg and the groups are G = girls and ndashG = boysGiven that the color distributions are identical across groups both

types are equally representativegreengirls

greenboysfrac14 1 frac14

purplegirls

purpleboys As a result

assessment of G should be correct on average stcontrolgreengirls frac14 greengirls

and stcontrolpurplegirls frac14 purplegirls for any weighing function (the same is

true about assessments of ndashG)In the treatment condition the distribution of shirt colors re-

mains the same for girls For boys green shirts are changed intoblue Thus the type space changes to T frac14 fgreen purple bluegand the representative color for girls becomes greengreengirls

greenboysfrac14 1 gt 1 frac14

purplegirls

purpleboys while that for boys becomes blue As

a result in the treatment condition subjects should inflate the

frequency of green shirts relative to the truth sttreatmentgreengirls

gt greengirls (the same should happen to assessments of blueshirts for boys) We also expect the assessed frequency of greenshirts to go up relative to the control condition namely

sttreatmentgreengirls gt stcontrol

greengirls Critically the only factor that varies

across treatments is the representativeness of the 12-colorshirt Thus if we see differences across conditions the causalrole of representativeness-based recall in shaping group judg-ments is clear24

24 We vary which colors are used in which roles across participants Someparticipants saw this particular color distribution while others see for examplegreen as the modal color and purple as the diagnostic color for boys in theRepresentativeness condition and blue as the diagnostic color for girls in theRepresentativeness condition We vary the colors across the roles to avoid con-founding the characteristics of any particular color with its diagnosticity

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FIG

UR

EII

T-S

hir

tsE

xp

erim

ent

Fig

ure

sap

pea

red

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lor

top

art

icip

an

tsin

the

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ent

For

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ty

we

have

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ded

ale

tter

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-sh

irt

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enti

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lor

for

the

read

er

lsquolsquoGrsquorsquo

ind

icate

sgre

en

lsquolsquoPrsquorsquo

ind

icate

sp

urp

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ind

icate

sblu

eT

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ele

tter

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rto

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icip

an

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dare

for

read

erre

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nce

only

P

lease

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onli

ne

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sion

ofp

ubli

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icle

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We collected data from 301 participants using this T-shirtsdesign25 Since the number of green and purple shirts is verysimilar we first ask each participant the simplest question ofwhich shirt color is modal Next we ask participants to assessthe share of green and purple shirts

Consistent with the role of representativeness participantsassigned to the Representativeness condition are 105 percentagepoints more likely to recall the less frequent color (green for girlsor blue for boys) as the modal color when it is representative of agroup (35 of participants guess the less frequent color is modalin the Control condition this proportion increases to 46 in theRepresentativeness condition p = 01 estimated from a probitregression reported in Online Appendix F)

We now turn to subjectsrsquo estimates of how many T-shirts ofeach color they saw in each group In both conditions the truedifference in counts is 1 (13 purple shirts 12 green or blue shirts)In the Control condition participants on average believe they saw054 more purple shirts than green or blue shirts In theRepresentativeness condition participants believe they saw072 fewer purple shirts than green or blue shirts (the acrosstreatment difference is significant with p = 01 from OLS regres-sion reported in Online Appendix F)

In total we collected data for six experiments of this generalstructure gathering evidence from more than 1000 participantsAs we describe in Online Appendix F although there is substan-tial variation across experiments when we pool all of the data wefind significant aggregate treatment effects in line with a role ofrepresentativeness in judgment We employ four different unor-dered types designs similar to the T-shirts experiment using sixsamples (four online and two in the laboratory) with 741 partic-ipants We find effects in the predicted direction for five of the sixsamples Using a probit regression that pools the data for theseunordered type experiments we find that participants are 93 per-centage points more likely to guess that the less frequent type ismodal when it is representative than when it is not (p = 002) Wealso run a family of ordered types experiments (two designs fivesamples 402 participants) Unlike the simpler T-shirts style

25 Throughout our analysis we exclude any participant who participated in aprevious version of the experiment and any participant who self-identified as color-blind In Online Appendix F we show that our results are unchanged if we includethese additional observations

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design the theoretical predictions for the ordered types designsare more sensitive to the specific assumptions one makes aboutthe weighting function of the DM26 We find effects in the pre-dicted direction for three of the five samples As we discuss inmore detail in Online Appendix F the ordered types resultsvary by platform with consistently stronger results on AmazonMechanical Turk than in the laboratory samples Pooling all or-dered types experiments participants are 93 percentage pointsmore likely to guess that the group of interest has a greater av-erage than the comparison group when the right tail is represen-tative (p = 062) Given our simple experimental setting withgroups of mundane objects we interpret our resultsmdasha signifi-cant and reasonably sized impact on average beliefsmdashas an im-portant proof of concept the presence of representative typesbiases ex post assessment

IVB Empirical Evidence on Political Stereotypes

We examine two data sets on political preferences and be-liefs about political preferences in the United States We inves-tigate the roles of representativeness and context dependence byseparately testing for hypotheses that allow us to assess the lead-ing theories of stereotypes

First we test whether beliefs are correct or depart systemat-ically from the truth The statistical discrimination approachbuilds on the assumption that people hold rational expectationsof group traits Comparing beliefs to the truth allows us to assessthe validity of this assumption in our data

Second we test if beliefs depart from the truth by exagger-ating (mean) differences among groups per the kernel of truthhypothesis This is an implicit test of context dependence be-cause it implies that beliefs about the target groups are shapednot only by that grouprsquos characteristics but also by those of thereference group27

Third we test if distortions in beliefs can be accounted for bythe overweighting of highly representative types (defined astypes that are relatively more frequent in the target relative to

26 This is due in part to our choice to not study MLRP distributions We moti-vate and discuss this design decision in Online Appendix F

27 Of course unlike in the laboratory experiment in this setting we cannot testfor context dependence by exogenously varying the reference group

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the reference group) The second and third tests address the keypredictions of our model

1 The Data We have two data sets on political preferences andbeliefs about political preferences The first data set from GrahamNosek and Haidt (GNH 2012) contains data from the MoralFoundations Questionnaire Respondents (1174 self-identified lib-erals and 500 self-identified conservatives) answer questions abouttheir position on a subset of 45 issues 20 moral relevance state-ments (eg lsquolsquowhen you decide whether something is right orwrong to what extent are the following considerations relevantto your thinkingrsquorsquo) and 25 moral judgments (eg lsquolsquoindicate theextent to which you would agree or disagreersquorsquo) For each issue arandomly determined subset of participants states their own posi-tion another subset states their belief on the position of a lsquolsquotypicalliberalrsquorsquo and a third subset states their belief on the position of alsquolsquotypical conservativersquorsquo The data thus include the distribution overpositions for both liberal and conservatives as well as the averagebelieved typical position of liberals and of conservatives on the 45issues Each position is elicited on 1ndash6 scale

The second data set comes from the American NationalElection Survey (ANES) and contains data from more than20000 respondents between 1964 and 201228 The surveycovers political issues of the day such as the optimal amount ofgovernment spending and service provision (1984ndash2000) or theplace of women in society (1972ndash1998) We focus on the 10 issuesthat ask participants to respond on a 1ndash7 scale (rather than justindicate binary agreement or disagreement) all 10 issues areasked in multiple years Participants are asked to provide theirown position on the scale and their believed position of theDemocratic and Republican parties (lsquolsquoWhere would you placethe Democratic [Republican] party on this scalersquorsquo) The data in-clude for each issue-year observation the distribution of partic-ipant positions for self-identified liberals and self-identifiedconservatives as well as the distribution of believed typical posi-tions of the Democratic and Republican parties

28 These data are publicly available at httpwwwelectionstudiesorgstudy-pagesanes_timeseries_cdfanes_timeseries_cdfhtm

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2 Empirical Strategy Our analysis focuses on beliefs abouttwo groups Conservatives and Liberals The types are the possi-ble positions for each issue (1 2 6 7) For the GNH data weinterpret beliefs about the lsquolsquotypicalrsquorsquo element of a group to coincidewith the believed average position in that group Similarly forthe ANES data we use the believed party positions as a proxy forbelieved mean of each group29 We then take as a benchmark thehypothesis that individuals hold accurate beliefs about eachgroup and in particular that believed mean position shouldequal true mean position at least on average across subjectsThe accurate beliefs hypothesis underlies the most common eco-nomic model of stereotyping statistical discrimination

To assess our representativeness-based model we perform aregression exercise To test our model in a linear regressionframework we rely on linear approximations of the weightingfunction Our model then yields two regression specifications

PROPOSITION 4 Let G 2 fconservative liberal g and assume

ht h tG

tG

be a differentiable and strictly increasing weight-

ing function as in Definition 2 The following hold as a first-order approximation around identical distributions G

Gfrac14 1

(i) Kernel of truth regression There exists a constant gt 0such that

EstethtjGTHORN frac14 EethtjGTHORNeth1thorn THORN EethtjGTHORNeth5THORN

(ii) Representativeness regression Denote H frac14 fT 2 Tg

the right tail of types and RconsH frac14

PHtconsPHtlib

as the average

representativeness of right tail types for conservatives

29 This assumption is consistent with the authorsrsquo interpretation of the GNHdata (GNH 2012) and with previous studies using ANES (eg Westfall et al 2015)Furthermore to the extent that this assumption holds equally well for most issueswithin a data set our focus on cross-issue differences should allow us to test thepredictions of our model even with an imperfect proxy for beliefs of mean positionsFinally the data provide some insight into whether subjects are reporting (per-ceived) modal or mean types As we show the modal type is a poor prediction ofstated beliefs while a distorted mean slanted toward representative types is anaccurate prediction of stated beliefs

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Under the further approximation where tcons

tlibampRcons

H for

t 2 H

EstethtjconsTHORN frac14 EethtjconsTHORN thorn consethR

consH 1THORNeth6THORN

EstethtjlibTHORN frac14 EethtjlibTHORN libethR

consH 1THORNeth7THORN

where lcons and llib are positive constants

The first regression allows us to test for the kernel of truthhypothesis and the second set of regressions allows us to test forthe role of representativeness

Equation (5) says that respondents in our model inflate theaverage position of a group say the conservatives if and only ifthe group has a higher average position than the other groupnamely the liberals Formally EstethtjconsTHORN gt EethtjconsTHORN if and onlyif EethtjconsTHORN gt EethtjlibTHORN Because in our measurement scale highertypes mean lsquolsquomore conservativersquorsquo we expect (i) believed conserva-tive average to be higher than the truth and (ii) the extent ofoverstatement to decrease in the average liberal position EethtjlibTHORNConversely we expect the average liberal position to be lowerthan the truth the more so the higher the average conservativeposition EethtjconsTHORN

As previously discussed the basis of these predictions is con-text dependence information about the distribution of ndashG is rel-evant for the beliefs about G This context dependence isinconsistent with rational expectations in which only thegrouprsquos own means should affect beliefs We test the hypothesisthat the true mean EethtjGTHORN is a significant predictor of the believedmean E

stethtjGTHORN with a positive sign and the other grouprsquos truemean EethtjGTHORN is a predictor of the believed mean with a negativesign

Equations (6) and (7) say that repondentsrsquo assessment bias isshaped by representativeness When the right tail is more repre-sentative for conservatives (Rcons

H 1 positive and large) partici-pants should inflate the average conservative position more(higher E

stethtjconsTHORN EethtjconsTHORN) and deflate the average liberal po-sition more (lower E

stethtjlibTHORN EethtjlibTHORN) We test the hypothesisthat the inflation in conservative positions is positively associatedwith the representativeness of the right tail for the conservativesand the inflation in liberal positions is negatively associated with

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it Once again the representativeness of the right tail is com-puted using the true distribution of positions

In equations (6) and (7) in many cases the representative tailis also the most likely one As a consequence these tests cannotdistinguish a representativeness-based from a likelihood-basedmodel of distorted beliefs We perform two additional testsFirst we run versions of equations (6) and (7) in which we controlfor the likelihood of tails (see Table A4 in Online Appendix G)Second we compute numerically the predictions of a representa-tiveness-based model of stereotypes and a likelihood-based modelof stereotypes We then assess which of these two is better able tomatch the data on beliefs

3 Empirical Results To begin we illustrate the structure ofthe data and the nature of our predictions with two simple exam-ples from the GNH data set focusing on beliefs about conserva-tives In example 1 participants are asked about their agreementwith the statement lsquolsquoIt can never be right to kill a human beingrsquorsquoIn example 2 participants are asked about the moral relevance oflsquolsquowhether or not someone cared for someone weak or vulnerablersquorsquoAs can be seen in Figure III in example 1 the modal position(strongly disagree (1)) and most representative positions(strongly disagree (1)) coincide for conservatives In contrast inexample 2 in Figure III the most representative types (slightlyrelevant (3) not at all relevant (1)) are not most likely for theconservative group Following Proposition 1 we predict that be-liefs will be distorted in the direction of the most representativetypes Thus we expect more exaggeration in example 2 than inexample 1 since in example 2 the most representative types (inthe left tail) are far from the modal type whereas in example 1they coincide This is what we find the conservative position isexaggerated by only 009 positions in Example 1 (true mean 299believed mean 290) but by 106 positions in Example 2 (truemean 421 believed mean 315)

In the full data sets we treat each (issue year) pair as anobservation and we cluster standard errors at the issue level Forthe GNH data we have 45 observations 45 issues measured inthe same year For the ANES data we have 66 observations 10issues measured in multiple years To begin we simply docu-ment systematic exaggeration in both data sets This is a primaryfocus of the original analysis in GNH (2012) and also in Westfall

STEREOTYPES 1785

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FIGURE III

Two Examples

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et al (2015)rsquos analysis of the ANES data30 Figure IV shows thatthe believed difference between typical conservative and typicalliberal positions is larger than the true difference in mean posi-tions for 109 of the 111 observations The data for both GNH(squares) and ANES (triangles) lie above the 45-degree line(dashed)31 Average exaggeration is 062 positions on the scale(066 in the GNH data 059 in the ANES data)32

The systematic and significant exaggeration of mean differ-ences suggests that the benchmark model of accurate beliefs ismissing something important Indeed this exaggeration reflectsthe fact that believed means are typically more extreme than truemeans First note that the kernel of truth regression (equation(5)) generates exaggeration of mean differences just as docu-mented in Figure IV

EstethtjGTHORN E

stethtjGTHORN frac14 eth1thorn 2THORN frac12EethtjGTHORN EethtjGTHORN

To bring this prediction to the data we regress the believedmean position for each group EBethtjGTHORN on the true mean of thegroup EethtjGTHORN and the true mean of the comparison groupEethtjGTHORN across issues We do this for each group (liberals con-servatives) in each data set separately We also present pooledspecifications that combine the data sets to make a prediction fora given group (liberals conservatives) In these pooled specifica-tions we include a dummy variable indicating whether theobservation came from the ANES data set For all specificationswe cluster observations at the issue level33 The results from re-gression are shown in Table I In every specification we find thatEethtjGTHORN is a significant predictor of EBethtjGTHORN with the predicted pos-itive sign Crucially for five of the six specifications the mean of

30 Chambers and Melnyk (2006) also find evidence of exaggeration of truedifferences in beliefs about political positions

31 For convenience we recode all issues so that the high end of the scale (67)represents the stereotypically more conservative position

32 A natural question to ask is how beliefs vary across liberals and conserva-tives That is do beliefs about a group G depend on membership in G versus ndashG Ourmodel does not speak to this issue However in Online Appendix G we show thatthe results we document below hold for both beliefs held by conservatives and be-liefs held by liberals see Tables A9 A10 and A11

33 In general the results presented below for the ANES data are not largelyimpacted by the decision to cluster at the issue level Similar results are obtained ifthe data are not clustered

STEREOTYPES 1787

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the comparison group EethtjGTHORN is also a significant predictor ofE

BethtjGTHORN with the predicted negative signAlthough these results provide strong evidence of context

dependence and are consistent with our model they do not pindown a role for representativeness of types Our next test relatesthe magnitude of representativeness of tail types to the magni-tude of belief distortions

To this end we implement the regressions in equations (6)and (7) Following Proposition 4 we compute the average repre-

sentativeness of tail types for conservatives RconsH frac14

PtT2tconsPtT2tlib

We

again test the hypothesis that RconsH is a significant predictor of Est

ethtjconsTHORN with a positive sign and a predictor of EstethtjlibTHORN with a

negative sign Table II shows that conditional on true mean RconsH

predicts believed mean for each group G as expected The firstthree specifications display the results for predicting beliefs heldabout conservatives In both data sets the average representa-tiveness of tail types for conservatives is a significant positivepredictor of beliefs held about conservatives The final three spe-cifications display the results for predicting beliefs held about

FIGURE IV

Exaggeration of Differences

QUARTERLY JOURNAL OF ECONOMICS1788

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liberals We find that the average representativeness of tail typesfor conservatives is a negative predictor of beliefs held about lib-erals This effect is significant in the GNH data and marginallysignificant in the ANES data

We present several additional results in Online Appendix GTo further examine the role of representativeness in driving be-liefs we first show the results of Table II carry through when we

TABLE II

AVERAGE REPRESENTATIVENESS OF TAIL POSITIONS PREDICTS BELIEFS

OLS Predicting Believed Mean of Group G for Each Issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position

of group G for issue

078 024 051 072 018 041

(006) (008) (009) (005) (005) (010)

Avg rep of tail types for

conservatives RconsH

019 055 025 014 012 024

(007) (022) (008) (006) (007) (005)

Constant 101 260 184 093 271 201

(026) (045) (029) (022) (025) (032)

R2 082 048 060 091 031 070

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

TABLE I

INFORMATION ABOUT ndashG PREDICTS BELIEFS ABOUT G

OLS predicting believed mean of group G for each issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position of

conservatives for issue

102 098 096 021 019 025

(0097) (0133) (0076) (0060) (0116) (0060)

True mean position of

liberals for issue

035 086 058 0987 039 073

(0106) (0134) (0131) (0066) (0106) (0135)

Constant 151 335 235 069 258 156

(0195) (0269) (0279) (0122) (0249) (0270)

R2 083 053 066 092 032 068

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

STEREOTYPES 1789

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control for the average likelihood on the tail positions (see Table A4in Online Appendix G) Most tellingly we use the model to predictbeliefs across issues and compare those to the data For simplicitywe use the rank-based truncation specification to predict mean be-liefs when stereotypes include the d most representative types ford frac14 1 T We compare these predictions to those of a model inwhich beliefs are obtained by restricting the distribution to the dmost likely types Our benchmark for both models is predicting thebelieved mean from the entire distribution where d = T We showthat the predictions of the rank-based truncation model with d = 4or 5 compare favorably to both a likelihood-based truncation model(with any d) and the accurate beliefs benchmark Interestingly thisresult suggests that stereotypical beliefs are well approximated byneglecting the least representative types (as opposed to focusingonly on the most representative types) and so represent a moderatethough systematic departure from the standard benchmarkFinally we show that the results we document above hold forboth beliefs held by conservatives and beliefs held by liberals (seeTables A9 A10 and A11 in Online Appendix G)

V Conclusion

We present a model of stereotypical thinking in which DMsmaking predictions about a group overweight the grouprsquos mostdistinctive types These overweighted types are not the mostlikely ones given the DMrsquos data but the most representativeones in the sense of being the most diagnostic of the group rela-tive to other groups Representativeness implies that what ismost distinctive of a group depends on what group it is comparedwith We present experimental evidence that confirms this con-text dependence in recall-based assessments of groups Finallywe evaluated the predictions of the model using political data fromexisting large-scale surveys We find context dependence to be akey feature of beliefs Given the richness of the political data wecan go a step further and identify a role for representativeness inparticular As the representativeness of tail types increases beliefsof a group are distorted in the direction of that tail

Our approach provides a parsimonious and psychologicallyfounded account of how DMs generate simplified representationsof reality from social groups to stock returns and offers a unifiedaccount of disparate pieces of evidence relating to this type of

QUARTERLY JOURNAL OF ECONOMICS1790

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uncertainty The model captures the central fact that stereotypeshighlight the greatest difference between groups thus explainingwhy some stereotypes are very accurate while others lack valid-ity Still stereotypes often have a kernel of truth when they arebased on systematicmdasheven if smallmdashdifferences between groupsThis logic allows us to describe a number of heuristics and psy-chological biases many of which arise in the context of predictionproblems Generically our model generates overreaction to diag-nostic information

Our model is based on representativeness and does not cap-ture all the features of stereotypical thinking However it cap-tures perhaps the central feature when we think of a group wefocus on what is most distinctive about it and neglect or under-weight the rest

Saeuroıd Business School University of Oxford

Ohio State University and Harvard Business School

Universita Bocconi and Innocenzo Gasparini Institute

for Economic Research

Harvard University

Supplementary Material

An Online Appendix for this article can be found at QJEonline (qjeoxfordjournalorg)

References

Adorno Theodor Else Frenkel-Brunswik Daniel Levinson and Nevitt SanfordThe Authoritarian Personality (New York Harper amp Row 1950)

Arrow Kenneth lsquolsquoThe Theory of Discriminationrsquorsquo in Discrimination in LaborMarkets Orley Ashenfelter and Albert Rees eds (Princeton NJPrinceton University Press 1973)

Ashton Michael and Victoria Esses lsquolsquoStereotype Accuracy Estimating theAcademic Performance of Ethnic Groupsrsquorsquo Personality and SocialPsychology Bulletin 25 (1999) 225ndash236

Barberis Nicholas Andrei Shleifer and Robert Vishny lsquolsquoA Model of InvestorSentimentrsquorsquo Journal of Financial Economics 49 (1998) 307ndash343

Bayer Sylvia lsquolsquoThe Accuracy of Academic Gender Stereotypesrsquorsquo Sex Roles 40(1999) 787ndash813

Benjamin Dan James Choi and Joshua Strickland lsquolsquoSocial Identity andPreferencesrsquorsquo American Economic Review 100 (2010) 1913ndash1928

Benjamin Dan Matthew Rabin and Collin Raymond lsquolsquoA Model of Non-Belief inthe Law of Large Numbersrsquorsquo Journal of the European Economic Association15 (2015) 515ndash544

Bertrand Marianne lsquolsquoNew Perspectives on Genderrsquorsquo Handbook of LaborEconomics 4 (2011) 1543ndash1590

Bodoh-Creed Aaron Dan Benjamin and Matthew Rabin lsquolsquoThe Dynamics of Base-Rate Neglectrsquorsquo mimeo Haas Business School 2013

STEREOTYPES 1791

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

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Bohnet Iris Alexandra van Geen and Max Bazerman lsquolsquoWhen PerformanceTrumps Gender Bias Joint versus Separate Evaluationrsquorsquo ManagementScience 5 (2016) 1225ndash1234

Bordalo Pedro Nicola Gennaioli and Andrei Shleifer lsquolsquoSalience Theory of Choiceunder Riskrsquorsquo Quarterly Journal of Economics 127 (2012) 1243ndash1285

mdashmdashmdash lsquolsquoSalience and Consumer Choicersquorsquo Journal of Political Economy 121(2013) 803ndash843

Briton Nancy and Judith Hall lsquolsquoBeliefs about Female and Male NonverbalCommunicationrsquorsquo Sex Roles 32 (1995) 79ndash90

Buser Thomas Muriel Niederle and Hessel Oosterbeek lsquolsquoGenderCompetitiveness and Career Choicesrsquorsquo Quarterly Journal of Economics 129(2014) 1409ndash1447

Carrell Scott Marianne Page and James West lsquolsquoSex and Science How ProfessorGender Perpetuates the Gender Gaprsquorsquo Quarterly Journal of Economics 125(2010) 1101ndash1144

Chambers John and Darya Melnyk lsquolsquoWhy Do I Hate Thee ConflictMisperceptions and Intergroup Mistrustrsquorsquo Personality and SocialPsychology Bulletin 32 (2006) 1295ndash1311

Chan Wayne Robert R McCrae Filip De Fruyt Lee Jussim CorinnaE Lockenhoff Marleen De Bolle Paul T Costa Jr Angelina R SutinAnu Realo Juri Allik Katsuharu Nakazato Yoshiko ShimonakaMartina Hrebıckova Sylvie Graf Michelle Yik Marina Brunner-SciarraNora Leibovich De Figueora Vanina Schmidt Chang-kyo Ahn Hyun-nie Ahn Maria E Aguilar-Vafaie Jerzy Siuta Barbara SzmigielskaThomas R Cain Janet T Crawford Khairul Anwar Mastor Jean-Pierre Rolland Florence Nansubuga Daniel R MiramontezVeronica Benet-Martınez Jerome Rossier Denis Bratko Iris MarusicJamin Halberstadt Mami Yamaguchi Goran Knezevic Thomas A MartinMirona Gheorghiu Peter B Smith Claudio Barbaranelli Lei WangJane Shakespeare-Finch Margarida P Lima Waldemar KlinkoszAndrzej Sekowski Lidia Alcalay Franco Simonetti Tatyana V AvdeyevaV S Pramila and Antonio Terracciano lsquolsquoStereotypes of Age Differences inPersonality Traits Universal and Accuratersquorsquo Journal of Personality andSocial Psychology 103 (2012) 1050ndash1066

Chen Yan Sherry Xin Liu Tracy Xiao and Margaret Shih lsquolsquoWhich Hat to WearImpact of Natural Identities on Coordination and Cooperationrsquorsquo Games andEconomic Behavior 84 (2014) 58ndash86

Coffman Katherine lsquolsquoEvidence on Self-Stereotyping and the Contribution ofIdeasrsquorsquo Quarterly Journal of Economics 129 (2014) 1625ndash1660

Cunningham Tom lsquolsquoComparisons and Choicersquorsquo mimeo Stockholm University2013

Diekman Amanda Alice Eagly and Patrick Kulesa lsquolsquoAccuracy and Bias in theStereotypes about the Social and Political Attitudes of Women and MenrsquorsquoJournal of Experimental Social Psychology 38 (2002) 268ndash282

Eccles Jacquelynne S Janis E Jacobs and Rena D Harold lsquolsquoGender RoleStereotypes Expectancy Effects and Parentsrsquo Socialization of GenderDifferencesrsquorsquo Journal of Social Issues 46 (1990) 183ndash201

Fryer Roland and Matthew Jackson lsquolsquoA Categorical Model of Cognition andBiased Decision-Makingrsquorsquo BE Journal of Theoretical Economics 8 (2008)1ndash42

Fryer Roland and Steven Levitt lsquolsquoAn Empirical Analysis of the Gender Gap inMathematicsrsquorsquo American Economic Journal Applied Economics 2 (2010)210ndash240

Gennaioli Nicola and Andrei Shleifer lsquolsquoWhat Comes to Mindrsquorsquo Quarterly Journalof Economics 125 (2010) 1399ndash1433

Gennaioli Nicola Andrei Shleifer and Robert Vishny lsquolsquoNeglected RisksFinancial Innovation and Financial Fragilityrsquorsquo Journal of FinancialEconomics 104 (2012) 452ndash468

Gilens Martin lsquolsquoRace and Poverty in America Public Misperceptions and theAmerican News Mediarsquorsquo Public Opinion Quarterly 60 (1996) 515ndash541

Glaeser Edward lsquolsquoThe Political Economy of Hatredrsquorsquo Quarterly Journal ofEconomics 120 (2005) 45ndash86

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Glover Dyland Amanda Pallais and William Pariente lsquolsquoDiscrimination as a Self-Fulfilling Prophecy Evidence from French Grocery Storesrsquorsquo mimeo HarvardUniversity 2015

Goldin Claudia Lawrence Katz and Ilyana Kuziemko lsquolsquoThe Homecoming ofAmerican College Women The Reversal of the College Gender GaprsquorsquoJournal of Economic Perspectives 20 (2006) 133ndash156

Graham Jesse Brian Nosek and Jonathan Haidt lsquolsquoThe Moral Stereotypes ofLiberals and Conservatives Exaggeration of Differences across thePolitical Spectrumrsquorsquo PLoS One 7 (2012) 1ndash13

Grether David lsquolsquoBayes Rule as a Descriptive Model The RepresentativenessHeuristicrsquorsquo Quarterly Journal of Economics 95 (1980) 537ndash557

Griffin Dale and Amos Tversky lsquolsquoThe Weighing of Evidence and theDeterminants of Confidencersquorsquo Cognitive Psychology 24 (1992) 411ndash435

Guiso Luigi Ferdinando Monte Paola Sapienza and Luigi Zingales lsquolsquoCultureGender and Mathrsquorsquo Science 320 (2008) 1164ndash1165

Hilton James and William Von Hippel lsquolsquoStereotypesrsquorsquo Annual Review ofPsychology 47 (1996) 237ndash271

Hyde Janet Sara Lindberg Marcia Linn Amy Ellis and Caroline WilliamslsquolsquoGender Similarities Characterize Math Performancersquorsquo Science 321 (2008)494ndash495

Judd Charles and Bernardette Park lsquolsquoDefinition and Assessment of Accuracy inSocial Stereotypesrsquorsquo Psychological Review 100 (1993) 109ndash128

Jussim Lee Jarret Crawford Stephanie Anglin John Chambers Sean Stevensand Florette Cohen lsquolsquoStereotype Accuracy One of the Largest and MostReplicable Effects in All of Social Psychologyrsquorsquo in The Handbook ofPrejudice Stereotyping and Discrimination Todd Nelson ed (MahwahNJ Lawrence Erlbaum 2015)

Kahneman Daniel and Amos Tversky lsquolsquoSubjective Probability A Judgment ofRepresentativenessrsquorsquo Cognitive Psychology 3 (1972) 430ndash454

mdashmdashmdash lsquolsquoOn the Psychology of Predictionrsquorsquo Psychological Review 80 (1973) 237ndash251

Kaplowitz Stan Bradley Fisher and Clifford Broman lsquolsquoHow Accurate ArePerceptions of Social Statistics about Blacks and Whitesrsquorsquo Public OpinionQuarterly 67 (2003) 237ndash243

Kersten Daniel Pascal Mamassian and Alan Yuille lsquolsquoObject Perception asBayesian Inferencersquorsquo Annual Review of Psychology 55 (2004) 271ndash304

Klein Richard Kate A Ratliff Michelangelo Vianello Reginald B Adams JrStepan Bahnik Michael J Bernstein Konrad Bocian Mark J BrandtBeach Brooks Claudia Chloe Brumbaugh Zeynep CemalcilarJesse Chandler Winnee Cheong William E Davis Thierry DevosMatthew Eisner Natalia Frankowska David Furrow Elisa Maria GallianiFred Hasselman Joshua A Hicks James F Hovermale S Jane HuntJeffrey R Huntsinger Hans IJzerman Melissa-Sue John Jennifer A Joy-Gaba Heather Barry Kappes Lacy E Krueger Jaime Kurtz CarmelA Levitan Robyn Mallett Wendy L Morris Anthony J Nelson JasonA Nier Grant Packard Ronaldo Pilati Abraham M RutchickKathleen Schmidt Jeanine L Skorinko Robert Smith Troy G SteinerJustin Storbeck Lyn M Van Swol Donna Thompson Anna van rsquot VeerLeigh Ann Vaughn Marek Vranka Aaron Wichman Julie A Woodzickaand Brian A Nosek lsquolsquoInvestigating Variation in Replicability A ManyLabs Replication Projectrsquorsquo Social Psychology 45 (2014) 142ndash152

Lundberg Shelly and Richard Startz lsquolsquoPrivate Discrimination and SocialIntervention in Competitive Labor Marketsrsquorsquo American Economic Review73 (1983) 340ndash347

Madon Stephanie Max Guyll Kathy Aboufadel Eulices Montiel Alison SmithPolly Palumbo and Lee Jussim lsquolsquoEthnic and National Stereotypes ThePrinceton Trilogy Revisited and Revisedrsquorsquo Personality and SocialPsychological Bulletin 27 (2001) 996ndash1010

Martin Carol lsquolsquoA Ratio Measure of Sex Stereotypingrsquorsquo Journal of Personality andSocial Psychology 52 (1987) 489ndash499

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httpqjeoxfordjournalsorgD

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McCauley Clark Krishna Thangavelu and Paul Rozin lsquolsquoSex Stereotyping ofOccupations in Relation to Television Representations and Census FactsrsquorsquoBasic and Applied Social Psychology 9 (1988) 197ndash212

Mullainathan Sendhil lsquolsquoThinking through Categoriesrsquorsquo mimeo HarvardUniversity 2002

Ortoleva Pietro and Erik Snowberg lsquolsquoOverconfidence in Political BehaviorrsquorsquoAmerican Economic Review 105 (2015) 504ndash535

Phelps Edmund lsquolsquoThe Statistical Theory of Racism and Sexismrsquorsquo AmericanEconomic Review 62 (1972) 659ndash661

Pope Devin and Justin Sydnor lsquolsquoGeographic Variation in the Gender Differencesin Test Scoresrsquorsquo Journal of Economic Perspectives 24 (2010) 95ndash108

Rabin Matthew lsquolsquoInference by Believers in the Law of Small NumbersrsquorsquoQuarterly Journal of Economics 117 (2002) 775ndash816

Rabin Matthew and Joel Schrag lsquolsquoFirst Impressions Matter A Model ofConfirmatory Biasrsquorsquo Quarterly Journal of Economics 114 (1999) 37ndash82

Rabin Matthew and Dimitri Vayanos lsquolsquoThe Gamblerrsquos and Hot-Hand FallaciesTheory and Applicationsrsquorsquo Review of Economic Studies 77 (2010) 730ndash778

Reuben Ernesto Paola Sapienza and Luigi Zingales lsquolsquoHow Stereotypes ImpairWomenrsquos Careers in Sciencersquorsquo Proceedings of the National Academy ofSciences 111 (2014) 4403ndash4408

Rosch Eleanor lsquolsquoNatural Categoriesrsquorsquo Cognitive Psychology 4 (1973) 328ndash350Ryan Carey S lsquolsquoAccuracy of Black and White College Studentsrsquo In-Group and

Out-Group Stereotypesrsquorsquo Personality and Social Psychology Bulletin 22(1996) 1114ndash1127

Schneider David The Psychology of Stereotyping (New York Guilford Press2004)

Schneider David Albert Hastorf and Phoebe Ellsworth Person Perception(Reading MA Addison-Wesley 1979)

Shih Margaret Todd Pittinsky and Nalini Ambady lsquolsquoStereotype SusceptibilityIdentity Salience and Shifts in Quantitative Performancersquorsquo PsychologicalScience 10 (1999) 80ndash83

Shih Margaret Todd Pittinsky and Amy Trahan lsquolsquoDomain-Specific Effects ofStereotypes on Performancersquorsquo Self and Identity 5 (2006) 1ndash14

Steele Claude Whistling Vivaldi How Stereotypes Affect Us and What We CanDo (New York Norton 2010)

Tenenbaum Joshua and Thomas Griffiths lsquolsquoThe Rational Basis ofRepresentativenessrsquorsquo 23rd Annual Conference of the Cognitive ScienceSociety (2001) 1036ndash1041

Tversky Amos and Daniel Kahneman lsquolsquoExtensional versus Intuitive ReasoningThe Conjunction Fallacy in Probability Judgmentrsquorsquo Psychological Review 90(1983) 293ndash315

Weinberger Catherin lsquolsquoIs the Science and Engineering Workforce Drawn fromthe Far Upper Tail of the Math Ability Distributionrsquorsquo mimeo UCSB 2005

Westfall Jacob Leaf Van Boven John Chambers and Charles Judd lsquolsquoPerceivingPolitical Polarization in the United States Party Identity Strength andAttitude Extremity Exacerbate the Perceived Partisan DividersquorsquoPsychological Science 10 (2015) 145ndash158

Wolsko Christopher Bernadette Park Charles Judd and Bernd WittenbrinklsquolsquoFraming Interethnic Ideology Effects of Multicultural and Color-BlindPerspectives on Judgments of Groups and Individualsrsquorsquo Journal ofPersonality and Social Psychology 78 (2000) 635ndash654

QUARTERLY JOURNAL OF ECONOMICS1794

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httpqjeoxfordjournalsorgD

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Page 12: I. Introduction · uneducated at the beginning of the 20th century, and as high achievers at the beginning of the 21st (Madon et al. 2001). Social science has produced three broad

sttG frac14 tG

tG

tG

P

s2T sGsG

sG

where 0 captures the extent to which representative-ness distorts beliefs This formulation is particularly con-venient when dealing with continuous distributions ofthe exponential or power classes

These functional forms all embody the main idea of our modelthat the stereotype overweights the probability of more represen-tative types Rank-based truncation captures a central manifes-tation of limited memory forgetting unrepresentative typesSmoother discounting (based on ranking or on representative-ness) may be more appropriate when the type space is smalland smooth discounting can be more tractable in certain settings

Section III characterizes the general properties of stereotypesIn particular it shows their ability to account for social psycholo-gistsrsquo kernel of truth hypothesis under the general weighting func-tion of Definition 2 To bring the model to the data in Section IVBwe derive linear approximations of stereotypical beliefs by assum-ing that the weighting function is differentiable with respect to atypersquos representativeness This assumption excludes rank-basedweighting but allows for many possibilities

IIB Discussion of Assumptions

Before moving to the formal analysis we discuss some prop-erties and limitations of our approach Representativeness-basedrecall the idea that individuals recall distinctive group types canbe viewed as an instance of what Kahneman and Tversky calllsquolsquoattribute substitutionrsquorsquo When dealing with the difficult questionlsquolsquowhat is the distribution of hair color among the Irishrsquorsquo peopleintuitively answer to the simpler question lsquolsquowhich hair color dis-tinguishes the Irish peoplersquorsquo Critically as discussed byKahneman and Tversky attribute substitution does not occurbecause people misunderstand the original question or mechan-ically confuse the assessment of PrethtjGTHORN with that of PrethGjtTHORNRather it occurs because the distinctive or representative typesimmediately come to mind and individuals anchor their overallprobability judgment to them As a consequence subjects do notonly make mistakes in judging the probability that a Floridian is

QUARTERLY JOURNAL OF ECONOMICS1764

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over age 65 They also give too high an answer to the questionlsquolsquowhat is the average age of a Floridianrsquorsquo12

One interesting question is whether the process of stereotyp-ing we describe is optimal in some sense Focusing mental repre-sentations on a few types can be justified by the costs of thinkingor retrieval This approach however is not enough to explainwhy individuals should focus on representative rather thanlikely types We do not formally analyze the optimality of repre-sentativeness here but we mention some relevant considerationsfrom cognitive psychology Kahneman and Tversky (1979) stressthe similarity between many perceptual and cognitive operationsFor instance the highlight of contrastmdasha key principle of visualperceptionmdashis invoked to justify the prospect theory assumptionthat the carriers of utility are changes relative to a referencepoint The same logic applies to our model in which stereotypesprecisely highlight the contrast between groups

In visual perception assessing properties such as brightnesscolor size or distance to an object by comparing them to otherproximate objects has been shown to be optimal in the presence ofmultiplicative background noise (Kersten Mamassian andYuille 2004 Cunningham 2013) Our formulation of representa-tiveness is related to the same idea in the sense that individualsestimating properties of one group stress differences from an-other group In a noisy world in which attention is limited thisprocess may optimally allow for swift reactions to changes ingroup characteristics even if errors are sometimes made13

12 Indeed in many cases mere confusion of PrethtjGTHORNwith PrethGjtTHORNwould not yieldthe phenomenon of stereotyping In the Irish hair color example the probability ofbeing Irish conditional on having red hair is

PrethIrishjredTHORN frac14PrethredjIrishTHORNPrethIrishTHORN

PrethredjIrishTHORNPrethIrishTHORN thorn PrethredjNonIrishTHORNPrethNonIrishTHORN

This probability is clearly very small given that the Irish population is a tinyfraction of the world population Confusion of PrethtjGTHORN with PrethGjtTHORN in this casewould lead to an understatement of the probability of the red-haired Irish

13 To give a simple example suppose thatmdashas in the case of Proposition 3mdashthevariance in the environment increases in the sense that extreme tail events becomemore likely Then a likelihood-based stereotype would detect no change whereas arepresentativeness-based stereotype would focus on the heightened probability ofthe tails In particular an asymmetric increase in tail probabilities that shifts themean would be detected by a representativeness-based stereotype even if the dis-tributionrsquos mode does not change

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Exploring this idea formally is an interesting avenue for futurework

Consider some limitations of our model First representa-tiveness is not the only heuristic that shapes recall Decisionmakers may for instance find it easier to recall types that aresufficiently likely Another potentially important mechanism isavailability understood by Kahneman and Tversky (1972) as thelsquolsquoeasersquorsquo with which information comes to mind (because of actualfrequency or repetition) In Online Appendix E we present a trun-cation-based recall mechanism in which distortions are driven bya combination of representativeness and likelihood of types(which is equivalent to relaxing property i in Definition 2) Thismodel can offer a useful starting point to capture availability aswell even though a full model of availability is beyond the scopeof this article Even in this more general setting the influence ofrepresentativeness on recall is the driving force of stereotypesthat in line with the social psychology perspective are basedon underlying differences among groups As we show in SectionIV this feature is critical in accounting for the evidence

The second set of model-related issues concerns how to spe-cify the elements of Definition 1 in applications group G the typespace T and the reference group ndashG Take the specification of thegroup G and of the type space T Often the problem itself pro-vides a natural specification of these features This is the case inthe empirically important class of lsquolsquoclosedrsquorsquo questions such asthose used in surveys which provide respondents with a set ofalternatives as in the data we use in Section IV More generallythe problem solved by the DMmdashsuch as evaluating the resume ofa job applicant coming from a certain ethnic groupmdashprimes agroup a dimension of interest and a set of types (eg the appli-cantrsquos qualification or skill levels) When types have a naturalorder such as income age or education the granularity of T isalso naturally given by the problem (income age and years ofschooling brackets) When the set of types is not specified by theproblem DMs spontaneously generate one14 It would be useful tohave a model of which dimensions and types come to mind par-ticularly for more open-ended problems Psychologists have

14 For example suppose a person is asked to guess the typical occupation of ademocratic voter in an lsquolsquoopen-endedrsquorsquo format (without being provided a set of alter-natives) Here the level of granularity at which types are defined is not obvious (egteacher versus a university teacher vs a professor of comparative literature)

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sought to construct a theory of natural types and dimensions(Rosch 1973) We do not make a contribution to this problembut we note that in many problems of interest in economics thedimension as well as the set of types is naturally givenFurthermore in our model details of the type space can be impor-tant under rank-based truncation but they matter less undersmooth discounting

Consider finally the role of the comparison group ndashG Thisgroup captures the context in which a stereotype is formed andagain is often implied by the problem when G = Floridians ndashG =rest of US population when G = African Americans ndashG = whiteAmericans A distinctive prediction of our model confirmed byour experiments in Section IVA is that the stereotype for agiven group G depends on the comparison group ndashG15 WhenndashG is not pinned down by the problem itself to derive testablepredictions from representativeness we set G frac14 nG where

is the natural population over which the unconditional distribu-tion of types is measured

III Properties of Stereotypes

We now study stereotypical beliefs and their accuracy Toillustrate the role of representativeness we first ask to whatextent the most representative type is a good fit for the groupnamely whether it is modal Next we assess the accuracy of theentire stereotypical distribution To do so we focus on a cardinaltypes and compare the stereotypersquos mean and variance to the trueones

15 Some empirical papers have taken a similar approach exogenously varyingthe natural comparison group through priming Benjamin Choi and Strickland(2010) show that priming racial or ethnic identity can affect the risk preferences ofparticipants Chen et al (2014) find that Asian students cooperate less with out-group members when primed with their ethnic identity rather than their universityidentity Shih Pittinsky and Ambady (1999) show that Asian American womenstereotype themselves as better or worse in math with corresponding impact onperformance when their ethnicity or gender respectively is primed ShihPittinsky and Trahan (2006) replicate this effect using a verbal task documentingthat Asian American women performed better when their gender rather than theirethnicity was primed Although the generalizability and replicability of priminghas been doubted (Klein et al 2014) this body of evidence is consistent with contextdependence

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IIIA Likely versus Unlikely Exemplars

The most representative type for a group is the one thatagents most easily recall and associate with the group itself forinstance a red-haired Irishman or a 65+-year-old FloridianSocial psychologists call this type the exemplar of the groupAccordingly we define

DEFINITION 3 A type t is an exemplar for G given comparisongroup ndashG when

t 2 arg maxt

tG

tG

Under any specification of the weighting function ht inDefinition 2 overweighting (weakly) increases as we movetoward more representative types so the exemplar is also thetype whose probability is overweighted the most16 By analyzingthe exemplar then we can gauge whether representativenessinduces the DM to overweight a likely type (as happens in stan-dard models of categorical thinking) or an unlikely type Whenoverweighting occurs in unlikely and extreme types the biases ofstereotypes can be particularly severe17

Equation (2) yields the following characterization

PROPOSITION 1 Suppose the conditional distributions G and G

are not identical Consider two extreme cases

(i) If for all t t0

2 T we have that tG gt t0 G if and only iftG gt t0 G then the modal type is not an exemplar forat least one group

(ii) If for all t t0

2 T we have that tG gt t0 G if and only iftG lt t0 G then for each group the modal type is theexemplar

16 Consider the function hethTHORN from Definition 2 When applied to more repre-sentative types the first argument of the function increases while one of the otherT ndash 1 arguments decreases As a result the weighting factor ht (and thus overweigh-ing

sttG

tG) increases as well

17 In the rank-based truncation model the frequency of the exemplar providesa measure of stereotype accuracy By accuracy we mean the extent to which thestereotype minimizes the distance

Pt eth

sttG tGTHORN

2 When d = 1 and only one type isrecalled (there are no ties) accuracy is maximized if the exemplar is the most likelytype and minimized if the exemplar is the least likely type

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Case i says that when groups have similar distributions inthe sense of having the same likelihood ranking the most repre-sentative type is unlikely for at least one group potentially bothRepresentativeness draws the DMrsquos attention to group differ-ences neglecting the fact that the groups are similar and havethe same mode This mechanism generates inaccurate stereo-types and is illustrated by the Florida example This resultholds under any measure of representativeness that differenti-ates the two groups (eg the difference tG tG)

Case ii says that the most representative type tends to belikely for both groups when the distributions are very differentIn this case groups differ the most around their modes so repre-sentativeness and likelihood coincide Thinking of Swedes aslsquolsquoblondrsquorsquo and Europeans as lsquolsquodark hairedrsquorsquo is accurate precisely be-cause these are majority traits of the Swedish and European pop-ulations respectively In these cases stereotyping yields fairlyreliable models Of course there is still some inaccuracy Evenin the case of likely exemplars judgment errors can be signifi-cant For instance voters in some US states are perceived aslsquolsquobluersquorsquo or lsquolsquoredrsquorsquo because a majority of the population votesDemocrat or Republican In reality even in lsquolsquobluersquorsquo states farfrom everyone votes Democrat In the 2012 presidential electionvote shares of either candidate in most states ranged from 40 to6018

When DMs strongly overweight representative types themost severe biases occur when those types are unlikely and ex-treme This is true both under rank based truncations and undersmooth discounting functions (see Section IIIB) Ethnic stereo-types based on crime or terrorism exhibit this error they neglectthe fact that by far the most common types in all groups arehonest and peaceful

IIIB Stereotypical Moments

We now characterize how the first two moments of a distri-bution are distorted by the process of stereotyping To do so wemust restrict our analysis to cardinal ordered types The follow-ing results hold for any weighting function htethTHORN satisfyingDefinition 2 We consider two canonical cases that prove usefulin illustrating the predictions of the model

18 Presidential Election Results NBCNewscom see httpelectionsnbcnewscomnspolitics2012allpresident (accessed 5 September 2016)

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In the first case groups G and ndashG are such that the likelihoodratio tG

tGis monotonic in t The monotone likelihood ratio prop-

erty (MLRP) holds to a first approximation in many empiricalsettings and is also assumed in many economic models such asstandard agency models19 If tG

tGis monotonically increasing (de-

creasing) in t then group G is associated with higher (lower)values of t relative to the comparison group ndashG Formally

PROPOSITION 2 Suppose that MLRP holds and assume wlogthat the likelihood ratio tG

tGis strictly increasing in t Then

for any weighting function htethTHORN that is not constant in therelevant range

EstethtjGTHORN gt EethtjGTHORN gt EethtjGTHORN gt E

stethtjGTHORN

Under MLRP the most representative part of the distribu-tion for G is the right tail if tG

tGincreases in t or the left tail if tG

tG

decreases in t The representative tail is then overweighted whilethe nonrepresentative tail is underweighted As a consequencethe assessed mean E

stethtjGTHORN is too extreme in the direction of therepresentative tail

Critically in line with the social cognition perspective the ste-reotype contains a kernel of truth the DM overestimates the meanof G if this group has a higher mean than the comparison groupnamely EethtjGTHORN gt EethtjGTHORN and conversely if EethtjGTHORN lt EethtjGTHORN TheDM exaggerates this true difference because he inflates the asso-ciation of G with its most representative types20 For instancewhen judging an asset manager who performs well we tend to

19 Examples include the binomial and the Poisson families of distributionswith different parameters The characterization of distributions satisfying MLRPis easier in the case of continuous distributions (see Online Appendix D) two dis-tributions f(x) f ethx THORN that differ only in their mean satisfy MLRP if and only if thedistribution f(x) is log-concave Examples include the exponential and normal dis-tributions To the extent that discrete distributions sufficiently approximate thesedistributions (as the Poisson distribution PoisethTHORN approximates the normal distri-bution Neth THORN for large l) they will also satisfy MLRP

20 Depending on the distribution and the weighing function the DMrsquos assess-ment of the variance VarethtjGTHORNmay also be dampened relative to the truth This isoften true under the truncation weighing function In this case stereotyping effec-tively leads to a form of overconfidence in which the DM holds extreme views andoverestimates the precision of his assessment That extreme views and overconfi-dence (in the sense of over precision) go together has been documented in the settingof political ideology among others (Ortoleva and Snowberg 2015)

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overemphasize skill relative to luck because higher skill levels arerelatively more associated with higher performance This occurseven if for both skilled and unskilled managers high performanceis mostly due to luck

In the second case for which we characterize the stereotypi-cal distributions groups G and ndashG have the same mean EethtjGTHORNfrac14 EethtjGTHORN frac14 EethtTHORN but differ in their variance We abstract fromskewness and higher moments by considering distributionsethtGTHORNt2T and ethtGTHORNt2T that share the same support and are sym-metric around the medianmean EethtTHORN

PROPOSITION 3 Suppose that in G more extreme types are rela-tively more frequent than in ndashG Formally the likelihoodratio tG

tGis U-shaped in t around EethtTHORN Then for any weight-

ing function htethTHORN that is not constant in the relevant rangestereotypical beliefs satisfy

VarstethtjGTHORN gt VarethtjGTHORN gt VarethtjGTHORN gt VarstethtjGTHORN

EstethtjGTHORN frac14 E

stethtjGTHORN frac14 EethtTHORN

When group G has a higher relative prevalence of extremetypes its representative types are located at both extremes of thedistribution The DMrsquos beliefs about G are then formed by over-weighting both tails while underweighting the unrepresentativemiddle The overweighting of Grsquos tails causes the assessment ofits variance VarstethtjGTHORN to be too high For example the skill dis-tribution of immigrants to the United States may be perceived ashaving very fat tails or even bimodal with immigrants beingperceived as either unskilled or very skilled relative to the resi-dent population The mean of the group in contrast is assessedcorrectly because the stereotypical distribution remains symmet-ric around EethtTHORN As before the stereotype contains a kernel oftruth It induces the agent to exaggerate the true differences be-tween groups namely the higher variance of G relative to itscounterpart

We present a number of extensions of the model in the OnlineAppendix We first consider multidimensional type spaces andshow that stereotypes center around the dimension wheregroups differ the most in line with the kernel of truth logic(Online Appendix C) Multidimensional stereotypes imply thatthe dimension we think about is influenced by context For

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example the Irish are stereotyped as red-haired when comparedwith the European population However when compared withthe Scots a more plausible stereotype for the Irish is lsquolsquoCatholicrsquorsquobecause religion is the dimension along which Irish and Scotsdiffer the most

In Online Appendix D we extend the model to continuoustype spaces Many settings of interest in economics can be use-fully described by continuous probability distributions and weshow our model is particularly tractable in this case In OnlineAppendix E we relax Definition 2 and allow weighting of types toalso be influenced by their likelihood We show that the basicinsight that stereotypes contain a kernel of truth carries throughto these cases as well

To summarize the psychology of representativeness yieldsstereotypes that are consistent with the social cognition approachin which individuals assess groups by recalling and focusing ondistinctive group traits When there are systematic differencesbetween groups stereotypes get the direction right but exagger-ate differences

IIIC Some Examples

A growing body of field and experimental evidence points to awidespread belief that women are worse than men at mathemat-ics (Eccles Jacobs and Harold 1990 Guiso et al 2008 CarrellPage and West 2010) This belief persists despite the fact that fordecades women have been gaining ground in average schoolgrades including mathematics and have recently surpassedmen in overall school performance (Goldin Katz and Kuziemko2006 Hyde et al 2008) This belief shared by men and women(Reuben Sapienza and Zingales 2014) may help account for thegender gap in the choices of high school tracks college degreesand careers with women disproportionately choosing humanitiesand health-related areas (Weinberger 2005 Buser Niederle andOosterbeek 2014) and forgoing significant wage premiums toquantitative skills (Bertrand 2011)

Gender stereotypes in mathematics particularly beliefs thatexaggerate the extent of average differences are consistent withthe predictions of our model The fact that men are overrepre-sented at the very highest performance levels leads a stereotyp-ical thinker to exaggerate the magnitude of mean differencesFigure I shows the score distributions from the mathematics

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section of 2013rsquos Scholastic Aptitude Test (SAT) for men andwomen21 The distributions are very similar with averagescores slightly higher for men (531 versus 499 out of 800)However scores for men have a heavier right tail with mentwice as likely to have a perfect SAT math score than women22

In light of such data the stereotypical male performance in math-ematics is high while the stereotypical female performance ispoor Predictions based on such stereotypes are inaccurate exag-gerating true differences Consistent with this prediction exper-imental evidence shows that both genders underestimatewomenrsquos ability in simple math tasks even controlling for pastperformance (Reuben Sapienza and Zingales 2014) Coffman(2014) shows a similar pattern extends to confidence about ownability in other male-typed domains with women reporting sig-nificantly less confidence in gender-incongruent than gender-congruent tasks Our model suggests that these patterns mightcome from stereotypes based on gender differences in the righttail of the distribution While differences in the right tail of thedistribution are unlikely to be relevant for most decisions stereo-typical thinking driven by these differences has the potential toimpact economically important decisions whether through self-stereotyping (ie choice of careers or majors as in BuserNiederle and Oosterbeek 2014) or through discrimination (iehiring decisions as in Bohnet van Geen and Bazerman 2016)

The logic of exaggerated yet directionally correct stereotypesalso sheds light on the well-documented phenomenon of base rateneglect (Kahneman and Tversky 1973) Indeed Proposition 2implies that the DM overreacts to information that assigns

21 Standardized test performance measures not only innate ability but alsoeffort and investment by third parties (Hyde et al 2008) The mapping of test per-formance into inferences about innate ability is an issue not addressed by ourmodel

22 For 2013 SAT Mathematics scores see httpmediacollegeboardcomdigitalServicespdfresearchSAT-Percentile-Ranks-By-Gender-Ethnicity-2013pdf Results are similar for the National Assessment of Educational Progress(NAEP) which are more representative of the overall population For 2012NAEP scores for 17-year-olds in mathematics see httpnationsreportcardgovltt_2012age17maspx See Hyde et al (2008) Fryer and Levitt (2010) and Popeand Sydnor (2010) for in-depth empirical analyses of the gender gap inmathematics

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people to groups precisely because such information generatesextreme stereotypes Consider the classic example in which amedical test for a particular disease with a 5 prevalence has a90 rate of true positives and a 5 rate of false positives The testassigns each person to one of two groups + (positive test) or ndash(negative test) The DM estimates the frequency of the sick type(s) and the healthy type (h) in each group The test is informativea positive result increases the relative likelihood of sickness anda negative result increases the relative likelihood of health forany prior Formally

PreththornjsTHORN

PreththornjhTHORNgt 1 gt

PrethjsTHORN

PrethjhTHORNeth4THORN

This condition has clear implications the representative personwho tests positive is sick while the representative person whotests negative is healthy Following Proposition 2 the DMreacts to the test by moving his priors too far in the right di-rection generating extreme stereotypes He greatly boosts hisassessment that a positively tested person is sick but also thata negatively tested person is healthy Because most people arehealthy the DMrsquos assessment about the group that tested neg-ative is fairly accurate but is severely biased for the group that

FIGURE I

SAT Mathematics Scores by Gender (2013)

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tested positive This analysis formalizes Tversky andKahnemanrsquos (1983) verbal account of base rate neglect23

The same mechanism may underlie several other instanceswhere DMs overweight diagnostic information When assessingan employeersquos skill level an employer attributes high perfor-mance to high skill because high performance is the distinctivemark of a talented employee Because he neglects the possibilitythat some talented employees perform poorly and that somenontalented ones perform well (perhaps due to stochasticity inthe environment) the employer has too much faith in skill andneglects the role of luck in accounting for the output Similarlywhen assessing the performance of firms in a hot sector of theeconomy (eg G = internet) an investor recalls highly successfulfirms in that sector (t = return of Google Amazon etc) He ne-glects the possibility of firms being unsuccessful because lack ofsuccess is statistically nondiagnostic and psychologically nonrep-resentative of a growing sectormdasheven if it is likely This causesexcessive optimism (in that the expectation of growth is unrea-sonably high) and overconfidence (in that the variability in earn-ings growth considered possible is truncated) True the hot sectormay have better growth opportunities on average but represen-tativeness exaggerates this feature and induces the investor toneglect a significant risk of failure

IV Evidence on Representativeness and Stereotypes

Testing our model requires evaluating the beliefs individualshold about a target group against the true distribution of thattarget group over an attribute space An ideal data set would

23 Our account is distinct from a mechanical underweighting of base rates inBayes rule as in Grether (1980) and Bodoh-Creed Benjamin and Rabin (2013) Inthose models upon receiving the test results the DM can update his beliefs in thewrong direction he can be less confident that a person is healthy after a negativetest than under his prior which cannot happen in our model Although this predic-tion of our model seems consistent with introspection we are not aware of experi-mental evidence on this point Griffin and Tversky (1992) present evidenceconsistent with pure neglect of base rates but in a significantly different tasknamely inferring the bias of a coin from a history of coin flips Such experimentsare hard to compare with the predictions of our model because subjects are asked togenerate distributions of different numbers of coin flips in their minds which is amuch more involved task than to recall types of a given distribution Their assess-ments then might be wrong for other reasons See Bodoh-Creed Benjamin andRabin (2013) for a detailed discussion

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consist of naturally defined groups with known distributions overa given space of types and a corresponding set of beliefs about thedistribution of each group over that space of types This wouldallow us to test for exaggeration of true differences betweengroups and to ask whether this exaggeration is well predictedby overweighting representative types To identify a causal rolefor representativeness or context dependence we would need ex-ogenous variation in either the comparison group ndashG or in thedistributions over the type spaces This is unavailable in existingdata sets Accordingly we take a two-pronged approach First wecreate a controlled laboratory environment that allows us toinduce the exogenous variation in representative types that weneed to test causality then we reanalyze existing field evidence tocheck for consistency with our predictions

In testing our model we focus on the two main implicationsof representativeness-based stereotypes

Context dependence the stereotype of a target group de-pends on the characteristics of the reference group it iscompared to

Kernel of truth stereotypes depend on group character-istics andmdashin most (precisely characterized) settingsmdashare slanted toward representative types

We test the first property with a lab experiment (SectionIVA) We then turn to survey data on beliefs about US politicalgroups (Section IVB) for an empirical analysis that explores thesecond property The survey data are more tightly linked to ourinterest in social stereotypes The laboratory experiment allowsus to directly test the role of representativeness in generatingcontext dependent beliefs Online Appendixes F and G provideall details and additional results for the experiments and fieldevidence

IVA Lab Evidence on Representativeness and ContextDependence

The influence of the representativeness heuristic on recalland on beliefs has been extensively documented in the lab(Kahneman and Tversky 1972 1973) Our goal is to considerhow representativeness as formalized in equation (2) gives riseto context-dependent beliefs To our knowledge the possibility

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that representativeness may generate context dependence hasnot been tested before

To assess this prediction we perform a controlled laboratoryexperiment that allows us to isolate representativeness frommany confounding factorsmdashhistorical sociological or other-wisemdashthat may affect stereotype formation in the real worldWe construct our own groups of ordinary objects creating atarget group G and a comparison group ndashG We hold thetarget group G fixed and explore how participant impressions ofit change as we change the comparison group ndashG and thusrepresentativeness

We conducted several experiments in the laboratory and onAmazon Mechanical Turk Each involves a basic three-stepdesign First participants are shown the target group and a ran-domly assigned comparison group for 15 seconds In this timedifferences between groups can be noticed but the groupsrsquo precisecompositions cannot be memorized The second step consists of afew filler questions which briefly draw the participantsrsquo cognitivebandwidth away from their observation Finally participants areasked to assess the groups they saw Participants are incentiv-ized to provide accurate answers

We randomly assign participants to either the Control or theRepresentativeness condition In the Control condition G and ndashGhave nearly identical distributions so that all types are similarlyrepresentative for each group In the Representativeness condi-tion ndashG is changed in such a way that a certain type becomes veryrepresentative for G Context dependence implies that the assess-ment of G should now overweight this representative type eventhough the distribution of G itself has not changed

We ran six experiments of this form with design changesfocused on reducing participant confusion and removing con-founds We describe the final and most refined version of theseexperiments here In an attempt to provide a overview of the re-sults while remaining concise we provide the results from pooledspecifications that use all data collected In Online Appendix Fwe offer additional details and report all experiments conductedWe also give instructions and materials for each experiment thefull data set is available by request

Consider first the experiment illustrated in Figure II Agroup of 25 cartoon girls is presented next to a group of 25 cartoonboys in T-shirts of different colors blue green or purple In theControl condition (Figure II Panel a) the groups have identical

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color distributions (13 purple 12 green) so no color is represen-tative of either group The Representativeness condition (Panel b)compares the same group of girls with a different group of boysfor whom green shirts are replaced with blue shirts Now onlygirls wear green and only boys wear blue These colors althoughstill not the most frequent for either group are now most repre-sentative For each group girls and boys participants are asked anumber of questions concerning the frequency of T-shirts of dif-ferent colors worn by that group

Applying our model in the control condition the type space isT frac14 fgreen purpleg and the groups are G = girls and ndashG = boysGiven that the color distributions are identical across groups both

types are equally representativegreengirls

greenboysfrac14 1 frac14

purplegirls

purpleboys As a result

assessment of G should be correct on average stcontrolgreengirls frac14 greengirls

and stcontrolpurplegirls frac14 purplegirls for any weighing function (the same is

true about assessments of ndashG)In the treatment condition the distribution of shirt colors re-

mains the same for girls For boys green shirts are changed intoblue Thus the type space changes to T frac14 fgreen purple bluegand the representative color for girls becomes greengreengirls

greenboysfrac14 1 gt 1 frac14

purplegirls

purpleboys while that for boys becomes blue As

a result in the treatment condition subjects should inflate the

frequency of green shirts relative to the truth sttreatmentgreengirls

gt greengirls (the same should happen to assessments of blueshirts for boys) We also expect the assessed frequency of greenshirts to go up relative to the control condition namely

sttreatmentgreengirls gt stcontrol

greengirls Critically the only factor that varies

across treatments is the representativeness of the 12-colorshirt Thus if we see differences across conditions the causalrole of representativeness-based recall in shaping group judg-ments is clear24

24 We vary which colors are used in which roles across participants Someparticipants saw this particular color distribution while others see for examplegreen as the modal color and purple as the diagnostic color for boys in theRepresentativeness condition and blue as the diagnostic color for girls in theRepresentativeness condition We vary the colors across the roles to avoid con-founding the characteristics of any particular color with its diagnosticity

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FIG

UR

EII

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We collected data from 301 participants using this T-shirtsdesign25 Since the number of green and purple shirts is verysimilar we first ask each participant the simplest question ofwhich shirt color is modal Next we ask participants to assessthe share of green and purple shirts

Consistent with the role of representativeness participantsassigned to the Representativeness condition are 105 percentagepoints more likely to recall the less frequent color (green for girlsor blue for boys) as the modal color when it is representative of agroup (35 of participants guess the less frequent color is modalin the Control condition this proportion increases to 46 in theRepresentativeness condition p = 01 estimated from a probitregression reported in Online Appendix F)

We now turn to subjectsrsquo estimates of how many T-shirts ofeach color they saw in each group In both conditions the truedifference in counts is 1 (13 purple shirts 12 green or blue shirts)In the Control condition participants on average believe they saw054 more purple shirts than green or blue shirts In theRepresentativeness condition participants believe they saw072 fewer purple shirts than green or blue shirts (the acrosstreatment difference is significant with p = 01 from OLS regres-sion reported in Online Appendix F)

In total we collected data for six experiments of this generalstructure gathering evidence from more than 1000 participantsAs we describe in Online Appendix F although there is substan-tial variation across experiments when we pool all of the data wefind significant aggregate treatment effects in line with a role ofrepresentativeness in judgment We employ four different unor-dered types designs similar to the T-shirts experiment using sixsamples (four online and two in the laboratory) with 741 partic-ipants We find effects in the predicted direction for five of the sixsamples Using a probit regression that pools the data for theseunordered type experiments we find that participants are 93 per-centage points more likely to guess that the less frequent type ismodal when it is representative than when it is not (p = 002) Wealso run a family of ordered types experiments (two designs fivesamples 402 participants) Unlike the simpler T-shirts style

25 Throughout our analysis we exclude any participant who participated in aprevious version of the experiment and any participant who self-identified as color-blind In Online Appendix F we show that our results are unchanged if we includethese additional observations

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design the theoretical predictions for the ordered types designsare more sensitive to the specific assumptions one makes aboutthe weighting function of the DM26 We find effects in the pre-dicted direction for three of the five samples As we discuss inmore detail in Online Appendix F the ordered types resultsvary by platform with consistently stronger results on AmazonMechanical Turk than in the laboratory samples Pooling all or-dered types experiments participants are 93 percentage pointsmore likely to guess that the group of interest has a greater av-erage than the comparison group when the right tail is represen-tative (p = 062) Given our simple experimental setting withgroups of mundane objects we interpret our resultsmdasha signifi-cant and reasonably sized impact on average beliefsmdashas an im-portant proof of concept the presence of representative typesbiases ex post assessment

IVB Empirical Evidence on Political Stereotypes

We examine two data sets on political preferences and be-liefs about political preferences in the United States We inves-tigate the roles of representativeness and context dependence byseparately testing for hypotheses that allow us to assess the lead-ing theories of stereotypes

First we test whether beliefs are correct or depart systemat-ically from the truth The statistical discrimination approachbuilds on the assumption that people hold rational expectationsof group traits Comparing beliefs to the truth allows us to assessthe validity of this assumption in our data

Second we test if beliefs depart from the truth by exagger-ating (mean) differences among groups per the kernel of truthhypothesis This is an implicit test of context dependence be-cause it implies that beliefs about the target groups are shapednot only by that grouprsquos characteristics but also by those of thereference group27

Third we test if distortions in beliefs can be accounted for bythe overweighting of highly representative types (defined astypes that are relatively more frequent in the target relative to

26 This is due in part to our choice to not study MLRP distributions We moti-vate and discuss this design decision in Online Appendix F

27 Of course unlike in the laboratory experiment in this setting we cannot testfor context dependence by exogenously varying the reference group

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the reference group) The second and third tests address the keypredictions of our model

1 The Data We have two data sets on political preferences andbeliefs about political preferences The first data set from GrahamNosek and Haidt (GNH 2012) contains data from the MoralFoundations Questionnaire Respondents (1174 self-identified lib-erals and 500 self-identified conservatives) answer questions abouttheir position on a subset of 45 issues 20 moral relevance state-ments (eg lsquolsquowhen you decide whether something is right orwrong to what extent are the following considerations relevantto your thinkingrsquorsquo) and 25 moral judgments (eg lsquolsquoindicate theextent to which you would agree or disagreersquorsquo) For each issue arandomly determined subset of participants states their own posi-tion another subset states their belief on the position of a lsquolsquotypicalliberalrsquorsquo and a third subset states their belief on the position of alsquolsquotypical conservativersquorsquo The data thus include the distribution overpositions for both liberal and conservatives as well as the averagebelieved typical position of liberals and of conservatives on the 45issues Each position is elicited on 1ndash6 scale

The second data set comes from the American NationalElection Survey (ANES) and contains data from more than20000 respondents between 1964 and 201228 The surveycovers political issues of the day such as the optimal amount ofgovernment spending and service provision (1984ndash2000) or theplace of women in society (1972ndash1998) We focus on the 10 issuesthat ask participants to respond on a 1ndash7 scale (rather than justindicate binary agreement or disagreement) all 10 issues areasked in multiple years Participants are asked to provide theirown position on the scale and their believed position of theDemocratic and Republican parties (lsquolsquoWhere would you placethe Democratic [Republican] party on this scalersquorsquo) The data in-clude for each issue-year observation the distribution of partic-ipant positions for self-identified liberals and self-identifiedconservatives as well as the distribution of believed typical posi-tions of the Democratic and Republican parties

28 These data are publicly available at httpwwwelectionstudiesorgstudy-pagesanes_timeseries_cdfanes_timeseries_cdfhtm

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2 Empirical Strategy Our analysis focuses on beliefs abouttwo groups Conservatives and Liberals The types are the possi-ble positions for each issue (1 2 6 7) For the GNH data weinterpret beliefs about the lsquolsquotypicalrsquorsquo element of a group to coincidewith the believed average position in that group Similarly forthe ANES data we use the believed party positions as a proxy forbelieved mean of each group29 We then take as a benchmark thehypothesis that individuals hold accurate beliefs about eachgroup and in particular that believed mean position shouldequal true mean position at least on average across subjectsThe accurate beliefs hypothesis underlies the most common eco-nomic model of stereotyping statistical discrimination

To assess our representativeness-based model we perform aregression exercise To test our model in a linear regressionframework we rely on linear approximations of the weightingfunction Our model then yields two regression specifications

PROPOSITION 4 Let G 2 fconservative liberal g and assume

ht h tG

tG

be a differentiable and strictly increasing weight-

ing function as in Definition 2 The following hold as a first-order approximation around identical distributions G

Gfrac14 1

(i) Kernel of truth regression There exists a constant gt 0such that

EstethtjGTHORN frac14 EethtjGTHORNeth1thorn THORN EethtjGTHORNeth5THORN

(ii) Representativeness regression Denote H frac14 fT 2 Tg

the right tail of types and RconsH frac14

PHtconsPHtlib

as the average

representativeness of right tail types for conservatives

29 This assumption is consistent with the authorsrsquo interpretation of the GNHdata (GNH 2012) and with previous studies using ANES (eg Westfall et al 2015)Furthermore to the extent that this assumption holds equally well for most issueswithin a data set our focus on cross-issue differences should allow us to test thepredictions of our model even with an imperfect proxy for beliefs of mean positionsFinally the data provide some insight into whether subjects are reporting (per-ceived) modal or mean types As we show the modal type is a poor prediction ofstated beliefs while a distorted mean slanted toward representative types is anaccurate prediction of stated beliefs

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Under the further approximation where tcons

tlibampRcons

H for

t 2 H

EstethtjconsTHORN frac14 EethtjconsTHORN thorn consethR

consH 1THORNeth6THORN

EstethtjlibTHORN frac14 EethtjlibTHORN libethR

consH 1THORNeth7THORN

where lcons and llib are positive constants

The first regression allows us to test for the kernel of truthhypothesis and the second set of regressions allows us to test forthe role of representativeness

Equation (5) says that respondents in our model inflate theaverage position of a group say the conservatives if and only ifthe group has a higher average position than the other groupnamely the liberals Formally EstethtjconsTHORN gt EethtjconsTHORN if and onlyif EethtjconsTHORN gt EethtjlibTHORN Because in our measurement scale highertypes mean lsquolsquomore conservativersquorsquo we expect (i) believed conserva-tive average to be higher than the truth and (ii) the extent ofoverstatement to decrease in the average liberal position EethtjlibTHORNConversely we expect the average liberal position to be lowerthan the truth the more so the higher the average conservativeposition EethtjconsTHORN

As previously discussed the basis of these predictions is con-text dependence information about the distribution of ndashG is rel-evant for the beliefs about G This context dependence isinconsistent with rational expectations in which only thegrouprsquos own means should affect beliefs We test the hypothesisthat the true mean EethtjGTHORN is a significant predictor of the believedmean E

stethtjGTHORN with a positive sign and the other grouprsquos truemean EethtjGTHORN is a predictor of the believed mean with a negativesign

Equations (6) and (7) say that repondentsrsquo assessment bias isshaped by representativeness When the right tail is more repre-sentative for conservatives (Rcons

H 1 positive and large) partici-pants should inflate the average conservative position more(higher E

stethtjconsTHORN EethtjconsTHORN) and deflate the average liberal po-sition more (lower E

stethtjlibTHORN EethtjlibTHORN) We test the hypothesisthat the inflation in conservative positions is positively associatedwith the representativeness of the right tail for the conservativesand the inflation in liberal positions is negatively associated with

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it Once again the representativeness of the right tail is com-puted using the true distribution of positions

In equations (6) and (7) in many cases the representative tailis also the most likely one As a consequence these tests cannotdistinguish a representativeness-based from a likelihood-basedmodel of distorted beliefs We perform two additional testsFirst we run versions of equations (6) and (7) in which we controlfor the likelihood of tails (see Table A4 in Online Appendix G)Second we compute numerically the predictions of a representa-tiveness-based model of stereotypes and a likelihood-based modelof stereotypes We then assess which of these two is better able tomatch the data on beliefs

3 Empirical Results To begin we illustrate the structure ofthe data and the nature of our predictions with two simple exam-ples from the GNH data set focusing on beliefs about conserva-tives In example 1 participants are asked about their agreementwith the statement lsquolsquoIt can never be right to kill a human beingrsquorsquoIn example 2 participants are asked about the moral relevance oflsquolsquowhether or not someone cared for someone weak or vulnerablersquorsquoAs can be seen in Figure III in example 1 the modal position(strongly disagree (1)) and most representative positions(strongly disagree (1)) coincide for conservatives In contrast inexample 2 in Figure III the most representative types (slightlyrelevant (3) not at all relevant (1)) are not most likely for theconservative group Following Proposition 1 we predict that be-liefs will be distorted in the direction of the most representativetypes Thus we expect more exaggeration in example 2 than inexample 1 since in example 2 the most representative types (inthe left tail) are far from the modal type whereas in example 1they coincide This is what we find the conservative position isexaggerated by only 009 positions in Example 1 (true mean 299believed mean 290) but by 106 positions in Example 2 (truemean 421 believed mean 315)

In the full data sets we treat each (issue year) pair as anobservation and we cluster standard errors at the issue level Forthe GNH data we have 45 observations 45 issues measured inthe same year For the ANES data we have 66 observations 10issues measured in multiple years To begin we simply docu-ment systematic exaggeration in both data sets This is a primaryfocus of the original analysis in GNH (2012) and also in Westfall

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FIGURE III

Two Examples

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et al (2015)rsquos analysis of the ANES data30 Figure IV shows thatthe believed difference between typical conservative and typicalliberal positions is larger than the true difference in mean posi-tions for 109 of the 111 observations The data for both GNH(squares) and ANES (triangles) lie above the 45-degree line(dashed)31 Average exaggeration is 062 positions on the scale(066 in the GNH data 059 in the ANES data)32

The systematic and significant exaggeration of mean differ-ences suggests that the benchmark model of accurate beliefs ismissing something important Indeed this exaggeration reflectsthe fact that believed means are typically more extreme than truemeans First note that the kernel of truth regression (equation(5)) generates exaggeration of mean differences just as docu-mented in Figure IV

EstethtjGTHORN E

stethtjGTHORN frac14 eth1thorn 2THORN frac12EethtjGTHORN EethtjGTHORN

To bring this prediction to the data we regress the believedmean position for each group EBethtjGTHORN on the true mean of thegroup EethtjGTHORN and the true mean of the comparison groupEethtjGTHORN across issues We do this for each group (liberals con-servatives) in each data set separately We also present pooledspecifications that combine the data sets to make a prediction fora given group (liberals conservatives) In these pooled specifica-tions we include a dummy variable indicating whether theobservation came from the ANES data set For all specificationswe cluster observations at the issue level33 The results from re-gression are shown in Table I In every specification we find thatEethtjGTHORN is a significant predictor of EBethtjGTHORN with the predicted pos-itive sign Crucially for five of the six specifications the mean of

30 Chambers and Melnyk (2006) also find evidence of exaggeration of truedifferences in beliefs about political positions

31 For convenience we recode all issues so that the high end of the scale (67)represents the stereotypically more conservative position

32 A natural question to ask is how beliefs vary across liberals and conserva-tives That is do beliefs about a group G depend on membership in G versus ndashG Ourmodel does not speak to this issue However in Online Appendix G we show thatthe results we document below hold for both beliefs held by conservatives and be-liefs held by liberals see Tables A9 A10 and A11

33 In general the results presented below for the ANES data are not largelyimpacted by the decision to cluster at the issue level Similar results are obtained ifthe data are not clustered

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the comparison group EethtjGTHORN is also a significant predictor ofE

BethtjGTHORN with the predicted negative signAlthough these results provide strong evidence of context

dependence and are consistent with our model they do not pindown a role for representativeness of types Our next test relatesthe magnitude of representativeness of tail types to the magni-tude of belief distortions

To this end we implement the regressions in equations (6)and (7) Following Proposition 4 we compute the average repre-

sentativeness of tail types for conservatives RconsH frac14

PtT2tconsPtT2tlib

We

again test the hypothesis that RconsH is a significant predictor of Est

ethtjconsTHORN with a positive sign and a predictor of EstethtjlibTHORN with a

negative sign Table II shows that conditional on true mean RconsH

predicts believed mean for each group G as expected The firstthree specifications display the results for predicting beliefs heldabout conservatives In both data sets the average representa-tiveness of tail types for conservatives is a significant positivepredictor of beliefs held about conservatives The final three spe-cifications display the results for predicting beliefs held about

FIGURE IV

Exaggeration of Differences

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liberals We find that the average representativeness of tail typesfor conservatives is a negative predictor of beliefs held about lib-erals This effect is significant in the GNH data and marginallysignificant in the ANES data

We present several additional results in Online Appendix GTo further examine the role of representativeness in driving be-liefs we first show the results of Table II carry through when we

TABLE II

AVERAGE REPRESENTATIVENESS OF TAIL POSITIONS PREDICTS BELIEFS

OLS Predicting Believed Mean of Group G for Each Issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position

of group G for issue

078 024 051 072 018 041

(006) (008) (009) (005) (005) (010)

Avg rep of tail types for

conservatives RconsH

019 055 025 014 012 024

(007) (022) (008) (006) (007) (005)

Constant 101 260 184 093 271 201

(026) (045) (029) (022) (025) (032)

R2 082 048 060 091 031 070

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

TABLE I

INFORMATION ABOUT ndashG PREDICTS BELIEFS ABOUT G

OLS predicting believed mean of group G for each issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position of

conservatives for issue

102 098 096 021 019 025

(0097) (0133) (0076) (0060) (0116) (0060)

True mean position of

liberals for issue

035 086 058 0987 039 073

(0106) (0134) (0131) (0066) (0106) (0135)

Constant 151 335 235 069 258 156

(0195) (0269) (0279) (0122) (0249) (0270)

R2 083 053 066 092 032 068

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

STEREOTYPES 1789

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control for the average likelihood on the tail positions (see Table A4in Online Appendix G) Most tellingly we use the model to predictbeliefs across issues and compare those to the data For simplicitywe use the rank-based truncation specification to predict mean be-liefs when stereotypes include the d most representative types ford frac14 1 T We compare these predictions to those of a model inwhich beliefs are obtained by restricting the distribution to the dmost likely types Our benchmark for both models is predicting thebelieved mean from the entire distribution where d = T We showthat the predictions of the rank-based truncation model with d = 4or 5 compare favorably to both a likelihood-based truncation model(with any d) and the accurate beliefs benchmark Interestingly thisresult suggests that stereotypical beliefs are well approximated byneglecting the least representative types (as opposed to focusingonly on the most representative types) and so represent a moderatethough systematic departure from the standard benchmarkFinally we show that the results we document above hold forboth beliefs held by conservatives and beliefs held by liberals (seeTables A9 A10 and A11 in Online Appendix G)

V Conclusion

We present a model of stereotypical thinking in which DMsmaking predictions about a group overweight the grouprsquos mostdistinctive types These overweighted types are not the mostlikely ones given the DMrsquos data but the most representativeones in the sense of being the most diagnostic of the group rela-tive to other groups Representativeness implies that what ismost distinctive of a group depends on what group it is comparedwith We present experimental evidence that confirms this con-text dependence in recall-based assessments of groups Finallywe evaluated the predictions of the model using political data fromexisting large-scale surveys We find context dependence to be akey feature of beliefs Given the richness of the political data wecan go a step further and identify a role for representativeness inparticular As the representativeness of tail types increases beliefsof a group are distorted in the direction of that tail

Our approach provides a parsimonious and psychologicallyfounded account of how DMs generate simplified representationsof reality from social groups to stock returns and offers a unifiedaccount of disparate pieces of evidence relating to this type of

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uncertainty The model captures the central fact that stereotypeshighlight the greatest difference between groups thus explainingwhy some stereotypes are very accurate while others lack valid-ity Still stereotypes often have a kernel of truth when they arebased on systematicmdasheven if smallmdashdifferences between groupsThis logic allows us to describe a number of heuristics and psy-chological biases many of which arise in the context of predictionproblems Generically our model generates overreaction to diag-nostic information

Our model is based on representativeness and does not cap-ture all the features of stereotypical thinking However it cap-tures perhaps the central feature when we think of a group wefocus on what is most distinctive about it and neglect or under-weight the rest

Saeuroıd Business School University of Oxford

Ohio State University and Harvard Business School

Universita Bocconi and Innocenzo Gasparini Institute

for Economic Research

Harvard University

Supplementary Material

An Online Appendix for this article can be found at QJEonline (qjeoxfordjournalorg)

References

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Arrow Kenneth lsquolsquoThe Theory of Discriminationrsquorsquo in Discrimination in LaborMarkets Orley Ashenfelter and Albert Rees eds (Princeton NJPrinceton University Press 1973)

Ashton Michael and Victoria Esses lsquolsquoStereotype Accuracy Estimating theAcademic Performance of Ethnic Groupsrsquorsquo Personality and SocialPsychology Bulletin 25 (1999) 225ndash236

Barberis Nicholas Andrei Shleifer and Robert Vishny lsquolsquoA Model of InvestorSentimentrsquorsquo Journal of Financial Economics 49 (1998) 307ndash343

Bayer Sylvia lsquolsquoThe Accuracy of Academic Gender Stereotypesrsquorsquo Sex Roles 40(1999) 787ndash813

Benjamin Dan James Choi and Joshua Strickland lsquolsquoSocial Identity andPreferencesrsquorsquo American Economic Review 100 (2010) 1913ndash1928

Benjamin Dan Matthew Rabin and Collin Raymond lsquolsquoA Model of Non-Belief inthe Law of Large Numbersrsquorsquo Journal of the European Economic Association15 (2015) 515ndash544

Bertrand Marianne lsquolsquoNew Perspectives on Genderrsquorsquo Handbook of LaborEconomics 4 (2011) 1543ndash1590

Bodoh-Creed Aaron Dan Benjamin and Matthew Rabin lsquolsquoThe Dynamics of Base-Rate Neglectrsquorsquo mimeo Haas Business School 2013

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Bohnet Iris Alexandra van Geen and Max Bazerman lsquolsquoWhen PerformanceTrumps Gender Bias Joint versus Separate Evaluationrsquorsquo ManagementScience 5 (2016) 1225ndash1234

Bordalo Pedro Nicola Gennaioli and Andrei Shleifer lsquolsquoSalience Theory of Choiceunder Riskrsquorsquo Quarterly Journal of Economics 127 (2012) 1243ndash1285

mdashmdashmdash lsquolsquoSalience and Consumer Choicersquorsquo Journal of Political Economy 121(2013) 803ndash843

Briton Nancy and Judith Hall lsquolsquoBeliefs about Female and Male NonverbalCommunicationrsquorsquo Sex Roles 32 (1995) 79ndash90

Buser Thomas Muriel Niederle and Hessel Oosterbeek lsquolsquoGenderCompetitiveness and Career Choicesrsquorsquo Quarterly Journal of Economics 129(2014) 1409ndash1447

Carrell Scott Marianne Page and James West lsquolsquoSex and Science How ProfessorGender Perpetuates the Gender Gaprsquorsquo Quarterly Journal of Economics 125(2010) 1101ndash1144

Chambers John and Darya Melnyk lsquolsquoWhy Do I Hate Thee ConflictMisperceptions and Intergroup Mistrustrsquorsquo Personality and SocialPsychology Bulletin 32 (2006) 1295ndash1311

Chan Wayne Robert R McCrae Filip De Fruyt Lee Jussim CorinnaE Lockenhoff Marleen De Bolle Paul T Costa Jr Angelina R SutinAnu Realo Juri Allik Katsuharu Nakazato Yoshiko ShimonakaMartina Hrebıckova Sylvie Graf Michelle Yik Marina Brunner-SciarraNora Leibovich De Figueora Vanina Schmidt Chang-kyo Ahn Hyun-nie Ahn Maria E Aguilar-Vafaie Jerzy Siuta Barbara SzmigielskaThomas R Cain Janet T Crawford Khairul Anwar Mastor Jean-Pierre Rolland Florence Nansubuga Daniel R MiramontezVeronica Benet-Martınez Jerome Rossier Denis Bratko Iris MarusicJamin Halberstadt Mami Yamaguchi Goran Knezevic Thomas A MartinMirona Gheorghiu Peter B Smith Claudio Barbaranelli Lei WangJane Shakespeare-Finch Margarida P Lima Waldemar KlinkoszAndrzej Sekowski Lidia Alcalay Franco Simonetti Tatyana V AvdeyevaV S Pramila and Antonio Terracciano lsquolsquoStereotypes of Age Differences inPersonality Traits Universal and Accuratersquorsquo Journal of Personality andSocial Psychology 103 (2012) 1050ndash1066

Chen Yan Sherry Xin Liu Tracy Xiao and Margaret Shih lsquolsquoWhich Hat to WearImpact of Natural Identities on Coordination and Cooperationrsquorsquo Games andEconomic Behavior 84 (2014) 58ndash86

Coffman Katherine lsquolsquoEvidence on Self-Stereotyping and the Contribution ofIdeasrsquorsquo Quarterly Journal of Economics 129 (2014) 1625ndash1660

Cunningham Tom lsquolsquoComparisons and Choicersquorsquo mimeo Stockholm University2013

Diekman Amanda Alice Eagly and Patrick Kulesa lsquolsquoAccuracy and Bias in theStereotypes about the Social and Political Attitudes of Women and MenrsquorsquoJournal of Experimental Social Psychology 38 (2002) 268ndash282

Eccles Jacquelynne S Janis E Jacobs and Rena D Harold lsquolsquoGender RoleStereotypes Expectancy Effects and Parentsrsquo Socialization of GenderDifferencesrsquorsquo Journal of Social Issues 46 (1990) 183ndash201

Fryer Roland and Matthew Jackson lsquolsquoA Categorical Model of Cognition andBiased Decision-Makingrsquorsquo BE Journal of Theoretical Economics 8 (2008)1ndash42

Fryer Roland and Steven Levitt lsquolsquoAn Empirical Analysis of the Gender Gap inMathematicsrsquorsquo American Economic Journal Applied Economics 2 (2010)210ndash240

Gennaioli Nicola and Andrei Shleifer lsquolsquoWhat Comes to Mindrsquorsquo Quarterly Journalof Economics 125 (2010) 1399ndash1433

Gennaioli Nicola Andrei Shleifer and Robert Vishny lsquolsquoNeglected RisksFinancial Innovation and Financial Fragilityrsquorsquo Journal of FinancialEconomics 104 (2012) 452ndash468

Gilens Martin lsquolsquoRace and Poverty in America Public Misperceptions and theAmerican News Mediarsquorsquo Public Opinion Quarterly 60 (1996) 515ndash541

Glaeser Edward lsquolsquoThe Political Economy of Hatredrsquorsquo Quarterly Journal ofEconomics 120 (2005) 45ndash86

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Glover Dyland Amanda Pallais and William Pariente lsquolsquoDiscrimination as a Self-Fulfilling Prophecy Evidence from French Grocery Storesrsquorsquo mimeo HarvardUniversity 2015

Goldin Claudia Lawrence Katz and Ilyana Kuziemko lsquolsquoThe Homecoming ofAmerican College Women The Reversal of the College Gender GaprsquorsquoJournal of Economic Perspectives 20 (2006) 133ndash156

Graham Jesse Brian Nosek and Jonathan Haidt lsquolsquoThe Moral Stereotypes ofLiberals and Conservatives Exaggeration of Differences across thePolitical Spectrumrsquorsquo PLoS One 7 (2012) 1ndash13

Grether David lsquolsquoBayes Rule as a Descriptive Model The RepresentativenessHeuristicrsquorsquo Quarterly Journal of Economics 95 (1980) 537ndash557

Griffin Dale and Amos Tversky lsquolsquoThe Weighing of Evidence and theDeterminants of Confidencersquorsquo Cognitive Psychology 24 (1992) 411ndash435

Guiso Luigi Ferdinando Monte Paola Sapienza and Luigi Zingales lsquolsquoCultureGender and Mathrsquorsquo Science 320 (2008) 1164ndash1165

Hilton James and William Von Hippel lsquolsquoStereotypesrsquorsquo Annual Review ofPsychology 47 (1996) 237ndash271

Hyde Janet Sara Lindberg Marcia Linn Amy Ellis and Caroline WilliamslsquolsquoGender Similarities Characterize Math Performancersquorsquo Science 321 (2008)494ndash495

Judd Charles and Bernardette Park lsquolsquoDefinition and Assessment of Accuracy inSocial Stereotypesrsquorsquo Psychological Review 100 (1993) 109ndash128

Jussim Lee Jarret Crawford Stephanie Anglin John Chambers Sean Stevensand Florette Cohen lsquolsquoStereotype Accuracy One of the Largest and MostReplicable Effects in All of Social Psychologyrsquorsquo in The Handbook ofPrejudice Stereotyping and Discrimination Todd Nelson ed (MahwahNJ Lawrence Erlbaum 2015)

Kahneman Daniel and Amos Tversky lsquolsquoSubjective Probability A Judgment ofRepresentativenessrsquorsquo Cognitive Psychology 3 (1972) 430ndash454

mdashmdashmdash lsquolsquoOn the Psychology of Predictionrsquorsquo Psychological Review 80 (1973) 237ndash251

Kaplowitz Stan Bradley Fisher and Clifford Broman lsquolsquoHow Accurate ArePerceptions of Social Statistics about Blacks and Whitesrsquorsquo Public OpinionQuarterly 67 (2003) 237ndash243

Kersten Daniel Pascal Mamassian and Alan Yuille lsquolsquoObject Perception asBayesian Inferencersquorsquo Annual Review of Psychology 55 (2004) 271ndash304

Klein Richard Kate A Ratliff Michelangelo Vianello Reginald B Adams JrStepan Bahnik Michael J Bernstein Konrad Bocian Mark J BrandtBeach Brooks Claudia Chloe Brumbaugh Zeynep CemalcilarJesse Chandler Winnee Cheong William E Davis Thierry DevosMatthew Eisner Natalia Frankowska David Furrow Elisa Maria GallianiFred Hasselman Joshua A Hicks James F Hovermale S Jane HuntJeffrey R Huntsinger Hans IJzerman Melissa-Sue John Jennifer A Joy-Gaba Heather Barry Kappes Lacy E Krueger Jaime Kurtz CarmelA Levitan Robyn Mallett Wendy L Morris Anthony J Nelson JasonA Nier Grant Packard Ronaldo Pilati Abraham M RutchickKathleen Schmidt Jeanine L Skorinko Robert Smith Troy G SteinerJustin Storbeck Lyn M Van Swol Donna Thompson Anna van rsquot VeerLeigh Ann Vaughn Marek Vranka Aaron Wichman Julie A Woodzickaand Brian A Nosek lsquolsquoInvestigating Variation in Replicability A ManyLabs Replication Projectrsquorsquo Social Psychology 45 (2014) 142ndash152

Lundberg Shelly and Richard Startz lsquolsquoPrivate Discrimination and SocialIntervention in Competitive Labor Marketsrsquorsquo American Economic Review73 (1983) 340ndash347

Madon Stephanie Max Guyll Kathy Aboufadel Eulices Montiel Alison SmithPolly Palumbo and Lee Jussim lsquolsquoEthnic and National Stereotypes ThePrinceton Trilogy Revisited and Revisedrsquorsquo Personality and SocialPsychological Bulletin 27 (2001) 996ndash1010

Martin Carol lsquolsquoA Ratio Measure of Sex Stereotypingrsquorsquo Journal of Personality andSocial Psychology 52 (1987) 489ndash499

STEREOTYPES 1793

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ibrary on October 28 2016

httpqjeoxfordjournalsorgD

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McCauley Clark Krishna Thangavelu and Paul Rozin lsquolsquoSex Stereotyping ofOccupations in Relation to Television Representations and Census FactsrsquorsquoBasic and Applied Social Psychology 9 (1988) 197ndash212

Mullainathan Sendhil lsquolsquoThinking through Categoriesrsquorsquo mimeo HarvardUniversity 2002

Ortoleva Pietro and Erik Snowberg lsquolsquoOverconfidence in Political BehaviorrsquorsquoAmerican Economic Review 105 (2015) 504ndash535

Phelps Edmund lsquolsquoThe Statistical Theory of Racism and Sexismrsquorsquo AmericanEconomic Review 62 (1972) 659ndash661

Pope Devin and Justin Sydnor lsquolsquoGeographic Variation in the Gender Differencesin Test Scoresrsquorsquo Journal of Economic Perspectives 24 (2010) 95ndash108

Rabin Matthew lsquolsquoInference by Believers in the Law of Small NumbersrsquorsquoQuarterly Journal of Economics 117 (2002) 775ndash816

Rabin Matthew and Joel Schrag lsquolsquoFirst Impressions Matter A Model ofConfirmatory Biasrsquorsquo Quarterly Journal of Economics 114 (1999) 37ndash82

Rabin Matthew and Dimitri Vayanos lsquolsquoThe Gamblerrsquos and Hot-Hand FallaciesTheory and Applicationsrsquorsquo Review of Economic Studies 77 (2010) 730ndash778

Reuben Ernesto Paola Sapienza and Luigi Zingales lsquolsquoHow Stereotypes ImpairWomenrsquos Careers in Sciencersquorsquo Proceedings of the National Academy ofSciences 111 (2014) 4403ndash4408

Rosch Eleanor lsquolsquoNatural Categoriesrsquorsquo Cognitive Psychology 4 (1973) 328ndash350Ryan Carey S lsquolsquoAccuracy of Black and White College Studentsrsquo In-Group and

Out-Group Stereotypesrsquorsquo Personality and Social Psychology Bulletin 22(1996) 1114ndash1127

Schneider David The Psychology of Stereotyping (New York Guilford Press2004)

Schneider David Albert Hastorf and Phoebe Ellsworth Person Perception(Reading MA Addison-Wesley 1979)

Shih Margaret Todd Pittinsky and Nalini Ambady lsquolsquoStereotype SusceptibilityIdentity Salience and Shifts in Quantitative Performancersquorsquo PsychologicalScience 10 (1999) 80ndash83

Shih Margaret Todd Pittinsky and Amy Trahan lsquolsquoDomain-Specific Effects ofStereotypes on Performancersquorsquo Self and Identity 5 (2006) 1ndash14

Steele Claude Whistling Vivaldi How Stereotypes Affect Us and What We CanDo (New York Norton 2010)

Tenenbaum Joshua and Thomas Griffiths lsquolsquoThe Rational Basis ofRepresentativenessrsquorsquo 23rd Annual Conference of the Cognitive ScienceSociety (2001) 1036ndash1041

Tversky Amos and Daniel Kahneman lsquolsquoExtensional versus Intuitive ReasoningThe Conjunction Fallacy in Probability Judgmentrsquorsquo Psychological Review 90(1983) 293ndash315

Weinberger Catherin lsquolsquoIs the Science and Engineering Workforce Drawn fromthe Far Upper Tail of the Math Ability Distributionrsquorsquo mimeo UCSB 2005

Westfall Jacob Leaf Van Boven John Chambers and Charles Judd lsquolsquoPerceivingPolitical Polarization in the United States Party Identity Strength andAttitude Extremity Exacerbate the Perceived Partisan DividersquorsquoPsychological Science 10 (2015) 145ndash158

Wolsko Christopher Bernadette Park Charles Judd and Bernd WittenbrinklsquolsquoFraming Interethnic Ideology Effects of Multicultural and Color-BlindPerspectives on Judgments of Groups and Individualsrsquorsquo Journal ofPersonality and Social Psychology 78 (2000) 635ndash654

QUARTERLY JOURNAL OF ECONOMICS1794

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Page 13: I. Introduction · uneducated at the beginning of the 20th century, and as high achievers at the beginning of the 21st (Madon et al. 2001). Social science has produced three broad

over age 65 They also give too high an answer to the questionlsquolsquowhat is the average age of a Floridianrsquorsquo12

One interesting question is whether the process of stereotyp-ing we describe is optimal in some sense Focusing mental repre-sentations on a few types can be justified by the costs of thinkingor retrieval This approach however is not enough to explainwhy individuals should focus on representative rather thanlikely types We do not formally analyze the optimality of repre-sentativeness here but we mention some relevant considerationsfrom cognitive psychology Kahneman and Tversky (1979) stressthe similarity between many perceptual and cognitive operationsFor instance the highlight of contrastmdasha key principle of visualperceptionmdashis invoked to justify the prospect theory assumptionthat the carriers of utility are changes relative to a referencepoint The same logic applies to our model in which stereotypesprecisely highlight the contrast between groups

In visual perception assessing properties such as brightnesscolor size or distance to an object by comparing them to otherproximate objects has been shown to be optimal in the presence ofmultiplicative background noise (Kersten Mamassian andYuille 2004 Cunningham 2013) Our formulation of representa-tiveness is related to the same idea in the sense that individualsestimating properties of one group stress differences from an-other group In a noisy world in which attention is limited thisprocess may optimally allow for swift reactions to changes ingroup characteristics even if errors are sometimes made13

12 Indeed in many cases mere confusion of PrethtjGTHORNwith PrethGjtTHORNwould not yieldthe phenomenon of stereotyping In the Irish hair color example the probability ofbeing Irish conditional on having red hair is

PrethIrishjredTHORN frac14PrethredjIrishTHORNPrethIrishTHORN

PrethredjIrishTHORNPrethIrishTHORN thorn PrethredjNonIrishTHORNPrethNonIrishTHORN

This probability is clearly very small given that the Irish population is a tinyfraction of the world population Confusion of PrethtjGTHORN with PrethGjtTHORN in this casewould lead to an understatement of the probability of the red-haired Irish

13 To give a simple example suppose thatmdashas in the case of Proposition 3mdashthevariance in the environment increases in the sense that extreme tail events becomemore likely Then a likelihood-based stereotype would detect no change whereas arepresentativeness-based stereotype would focus on the heightened probability ofthe tails In particular an asymmetric increase in tail probabilities that shifts themean would be detected by a representativeness-based stereotype even if the dis-tributionrsquos mode does not change

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Exploring this idea formally is an interesting avenue for futurework

Consider some limitations of our model First representa-tiveness is not the only heuristic that shapes recall Decisionmakers may for instance find it easier to recall types that aresufficiently likely Another potentially important mechanism isavailability understood by Kahneman and Tversky (1972) as thelsquolsquoeasersquorsquo with which information comes to mind (because of actualfrequency or repetition) In Online Appendix E we present a trun-cation-based recall mechanism in which distortions are driven bya combination of representativeness and likelihood of types(which is equivalent to relaxing property i in Definition 2) Thismodel can offer a useful starting point to capture availability aswell even though a full model of availability is beyond the scopeof this article Even in this more general setting the influence ofrepresentativeness on recall is the driving force of stereotypesthat in line with the social psychology perspective are basedon underlying differences among groups As we show in SectionIV this feature is critical in accounting for the evidence

The second set of model-related issues concerns how to spe-cify the elements of Definition 1 in applications group G the typespace T and the reference group ndashG Take the specification of thegroup G and of the type space T Often the problem itself pro-vides a natural specification of these features This is the case inthe empirically important class of lsquolsquoclosedrsquorsquo questions such asthose used in surveys which provide respondents with a set ofalternatives as in the data we use in Section IV More generallythe problem solved by the DMmdashsuch as evaluating the resume ofa job applicant coming from a certain ethnic groupmdashprimes agroup a dimension of interest and a set of types (eg the appli-cantrsquos qualification or skill levels) When types have a naturalorder such as income age or education the granularity of T isalso naturally given by the problem (income age and years ofschooling brackets) When the set of types is not specified by theproblem DMs spontaneously generate one14 It would be useful tohave a model of which dimensions and types come to mind par-ticularly for more open-ended problems Psychologists have

14 For example suppose a person is asked to guess the typical occupation of ademocratic voter in an lsquolsquoopen-endedrsquorsquo format (without being provided a set of alter-natives) Here the level of granularity at which types are defined is not obvious (egteacher versus a university teacher vs a professor of comparative literature)

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sought to construct a theory of natural types and dimensions(Rosch 1973) We do not make a contribution to this problembut we note that in many problems of interest in economics thedimension as well as the set of types is naturally givenFurthermore in our model details of the type space can be impor-tant under rank-based truncation but they matter less undersmooth discounting

Consider finally the role of the comparison group ndashG Thisgroup captures the context in which a stereotype is formed andagain is often implied by the problem when G = Floridians ndashG =rest of US population when G = African Americans ndashG = whiteAmericans A distinctive prediction of our model confirmed byour experiments in Section IVA is that the stereotype for agiven group G depends on the comparison group ndashG15 WhenndashG is not pinned down by the problem itself to derive testablepredictions from representativeness we set G frac14 nG where

is the natural population over which the unconditional distribu-tion of types is measured

III Properties of Stereotypes

We now study stereotypical beliefs and their accuracy Toillustrate the role of representativeness we first ask to whatextent the most representative type is a good fit for the groupnamely whether it is modal Next we assess the accuracy of theentire stereotypical distribution To do so we focus on a cardinaltypes and compare the stereotypersquos mean and variance to the trueones

15 Some empirical papers have taken a similar approach exogenously varyingthe natural comparison group through priming Benjamin Choi and Strickland(2010) show that priming racial or ethnic identity can affect the risk preferences ofparticipants Chen et al (2014) find that Asian students cooperate less with out-group members when primed with their ethnic identity rather than their universityidentity Shih Pittinsky and Ambady (1999) show that Asian American womenstereotype themselves as better or worse in math with corresponding impact onperformance when their ethnicity or gender respectively is primed ShihPittinsky and Trahan (2006) replicate this effect using a verbal task documentingthat Asian American women performed better when their gender rather than theirethnicity was primed Although the generalizability and replicability of priminghas been doubted (Klein et al 2014) this body of evidence is consistent with contextdependence

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IIIA Likely versus Unlikely Exemplars

The most representative type for a group is the one thatagents most easily recall and associate with the group itself forinstance a red-haired Irishman or a 65+-year-old FloridianSocial psychologists call this type the exemplar of the groupAccordingly we define

DEFINITION 3 A type t is an exemplar for G given comparisongroup ndashG when

t 2 arg maxt

tG

tG

Under any specification of the weighting function ht inDefinition 2 overweighting (weakly) increases as we movetoward more representative types so the exemplar is also thetype whose probability is overweighted the most16 By analyzingthe exemplar then we can gauge whether representativenessinduces the DM to overweight a likely type (as happens in stan-dard models of categorical thinking) or an unlikely type Whenoverweighting occurs in unlikely and extreme types the biases ofstereotypes can be particularly severe17

Equation (2) yields the following characterization

PROPOSITION 1 Suppose the conditional distributions G and G

are not identical Consider two extreme cases

(i) If for all t t0

2 T we have that tG gt t0 G if and only iftG gt t0 G then the modal type is not an exemplar forat least one group

(ii) If for all t t0

2 T we have that tG gt t0 G if and only iftG lt t0 G then for each group the modal type is theexemplar

16 Consider the function hethTHORN from Definition 2 When applied to more repre-sentative types the first argument of the function increases while one of the otherT ndash 1 arguments decreases As a result the weighting factor ht (and thus overweigh-ing

sttG

tG) increases as well

17 In the rank-based truncation model the frequency of the exemplar providesa measure of stereotype accuracy By accuracy we mean the extent to which thestereotype minimizes the distance

Pt eth

sttG tGTHORN

2 When d = 1 and only one type isrecalled (there are no ties) accuracy is maximized if the exemplar is the most likelytype and minimized if the exemplar is the least likely type

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Case i says that when groups have similar distributions inthe sense of having the same likelihood ranking the most repre-sentative type is unlikely for at least one group potentially bothRepresentativeness draws the DMrsquos attention to group differ-ences neglecting the fact that the groups are similar and havethe same mode This mechanism generates inaccurate stereo-types and is illustrated by the Florida example This resultholds under any measure of representativeness that differenti-ates the two groups (eg the difference tG tG)

Case ii says that the most representative type tends to belikely for both groups when the distributions are very differentIn this case groups differ the most around their modes so repre-sentativeness and likelihood coincide Thinking of Swedes aslsquolsquoblondrsquorsquo and Europeans as lsquolsquodark hairedrsquorsquo is accurate precisely be-cause these are majority traits of the Swedish and European pop-ulations respectively In these cases stereotyping yields fairlyreliable models Of course there is still some inaccuracy Evenin the case of likely exemplars judgment errors can be signifi-cant For instance voters in some US states are perceived aslsquolsquobluersquorsquo or lsquolsquoredrsquorsquo because a majority of the population votesDemocrat or Republican In reality even in lsquolsquobluersquorsquo states farfrom everyone votes Democrat In the 2012 presidential electionvote shares of either candidate in most states ranged from 40 to6018

When DMs strongly overweight representative types themost severe biases occur when those types are unlikely and ex-treme This is true both under rank based truncations and undersmooth discounting functions (see Section IIIB) Ethnic stereo-types based on crime or terrorism exhibit this error they neglectthe fact that by far the most common types in all groups arehonest and peaceful

IIIB Stereotypical Moments

We now characterize how the first two moments of a distri-bution are distorted by the process of stereotyping To do so wemust restrict our analysis to cardinal ordered types The follow-ing results hold for any weighting function htethTHORN satisfyingDefinition 2 We consider two canonical cases that prove usefulin illustrating the predictions of the model

18 Presidential Election Results NBCNewscom see httpelectionsnbcnewscomnspolitics2012allpresident (accessed 5 September 2016)

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In the first case groups G and ndashG are such that the likelihoodratio tG

tGis monotonic in t The monotone likelihood ratio prop-

erty (MLRP) holds to a first approximation in many empiricalsettings and is also assumed in many economic models such asstandard agency models19 If tG

tGis monotonically increasing (de-

creasing) in t then group G is associated with higher (lower)values of t relative to the comparison group ndashG Formally

PROPOSITION 2 Suppose that MLRP holds and assume wlogthat the likelihood ratio tG

tGis strictly increasing in t Then

for any weighting function htethTHORN that is not constant in therelevant range

EstethtjGTHORN gt EethtjGTHORN gt EethtjGTHORN gt E

stethtjGTHORN

Under MLRP the most representative part of the distribu-tion for G is the right tail if tG

tGincreases in t or the left tail if tG

tG

decreases in t The representative tail is then overweighted whilethe nonrepresentative tail is underweighted As a consequencethe assessed mean E

stethtjGTHORN is too extreme in the direction of therepresentative tail

Critically in line with the social cognition perspective the ste-reotype contains a kernel of truth the DM overestimates the meanof G if this group has a higher mean than the comparison groupnamely EethtjGTHORN gt EethtjGTHORN and conversely if EethtjGTHORN lt EethtjGTHORN TheDM exaggerates this true difference because he inflates the asso-ciation of G with its most representative types20 For instancewhen judging an asset manager who performs well we tend to

19 Examples include the binomial and the Poisson families of distributionswith different parameters The characterization of distributions satisfying MLRPis easier in the case of continuous distributions (see Online Appendix D) two dis-tributions f(x) f ethx THORN that differ only in their mean satisfy MLRP if and only if thedistribution f(x) is log-concave Examples include the exponential and normal dis-tributions To the extent that discrete distributions sufficiently approximate thesedistributions (as the Poisson distribution PoisethTHORN approximates the normal distri-bution Neth THORN for large l) they will also satisfy MLRP

20 Depending on the distribution and the weighing function the DMrsquos assess-ment of the variance VarethtjGTHORNmay also be dampened relative to the truth This isoften true under the truncation weighing function In this case stereotyping effec-tively leads to a form of overconfidence in which the DM holds extreme views andoverestimates the precision of his assessment That extreme views and overconfi-dence (in the sense of over precision) go together has been documented in the settingof political ideology among others (Ortoleva and Snowberg 2015)

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overemphasize skill relative to luck because higher skill levels arerelatively more associated with higher performance This occurseven if for both skilled and unskilled managers high performanceis mostly due to luck

In the second case for which we characterize the stereotypi-cal distributions groups G and ndashG have the same mean EethtjGTHORNfrac14 EethtjGTHORN frac14 EethtTHORN but differ in their variance We abstract fromskewness and higher moments by considering distributionsethtGTHORNt2T and ethtGTHORNt2T that share the same support and are sym-metric around the medianmean EethtTHORN

PROPOSITION 3 Suppose that in G more extreme types are rela-tively more frequent than in ndashG Formally the likelihoodratio tG

tGis U-shaped in t around EethtTHORN Then for any weight-

ing function htethTHORN that is not constant in the relevant rangestereotypical beliefs satisfy

VarstethtjGTHORN gt VarethtjGTHORN gt VarethtjGTHORN gt VarstethtjGTHORN

EstethtjGTHORN frac14 E

stethtjGTHORN frac14 EethtTHORN

When group G has a higher relative prevalence of extremetypes its representative types are located at both extremes of thedistribution The DMrsquos beliefs about G are then formed by over-weighting both tails while underweighting the unrepresentativemiddle The overweighting of Grsquos tails causes the assessment ofits variance VarstethtjGTHORN to be too high For example the skill dis-tribution of immigrants to the United States may be perceived ashaving very fat tails or even bimodal with immigrants beingperceived as either unskilled or very skilled relative to the resi-dent population The mean of the group in contrast is assessedcorrectly because the stereotypical distribution remains symmet-ric around EethtTHORN As before the stereotype contains a kernel oftruth It induces the agent to exaggerate the true differences be-tween groups namely the higher variance of G relative to itscounterpart

We present a number of extensions of the model in the OnlineAppendix We first consider multidimensional type spaces andshow that stereotypes center around the dimension wheregroups differ the most in line with the kernel of truth logic(Online Appendix C) Multidimensional stereotypes imply thatthe dimension we think about is influenced by context For

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example the Irish are stereotyped as red-haired when comparedwith the European population However when compared withthe Scots a more plausible stereotype for the Irish is lsquolsquoCatholicrsquorsquobecause religion is the dimension along which Irish and Scotsdiffer the most

In Online Appendix D we extend the model to continuoustype spaces Many settings of interest in economics can be use-fully described by continuous probability distributions and weshow our model is particularly tractable in this case In OnlineAppendix E we relax Definition 2 and allow weighting of types toalso be influenced by their likelihood We show that the basicinsight that stereotypes contain a kernel of truth carries throughto these cases as well

To summarize the psychology of representativeness yieldsstereotypes that are consistent with the social cognition approachin which individuals assess groups by recalling and focusing ondistinctive group traits When there are systematic differencesbetween groups stereotypes get the direction right but exagger-ate differences

IIIC Some Examples

A growing body of field and experimental evidence points to awidespread belief that women are worse than men at mathemat-ics (Eccles Jacobs and Harold 1990 Guiso et al 2008 CarrellPage and West 2010) This belief persists despite the fact that fordecades women have been gaining ground in average schoolgrades including mathematics and have recently surpassedmen in overall school performance (Goldin Katz and Kuziemko2006 Hyde et al 2008) This belief shared by men and women(Reuben Sapienza and Zingales 2014) may help account for thegender gap in the choices of high school tracks college degreesand careers with women disproportionately choosing humanitiesand health-related areas (Weinberger 2005 Buser Niederle andOosterbeek 2014) and forgoing significant wage premiums toquantitative skills (Bertrand 2011)

Gender stereotypes in mathematics particularly beliefs thatexaggerate the extent of average differences are consistent withthe predictions of our model The fact that men are overrepre-sented at the very highest performance levels leads a stereotyp-ical thinker to exaggerate the magnitude of mean differencesFigure I shows the score distributions from the mathematics

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section of 2013rsquos Scholastic Aptitude Test (SAT) for men andwomen21 The distributions are very similar with averagescores slightly higher for men (531 versus 499 out of 800)However scores for men have a heavier right tail with mentwice as likely to have a perfect SAT math score than women22

In light of such data the stereotypical male performance in math-ematics is high while the stereotypical female performance ispoor Predictions based on such stereotypes are inaccurate exag-gerating true differences Consistent with this prediction exper-imental evidence shows that both genders underestimatewomenrsquos ability in simple math tasks even controlling for pastperformance (Reuben Sapienza and Zingales 2014) Coffman(2014) shows a similar pattern extends to confidence about ownability in other male-typed domains with women reporting sig-nificantly less confidence in gender-incongruent than gender-congruent tasks Our model suggests that these patterns mightcome from stereotypes based on gender differences in the righttail of the distribution While differences in the right tail of thedistribution are unlikely to be relevant for most decisions stereo-typical thinking driven by these differences has the potential toimpact economically important decisions whether through self-stereotyping (ie choice of careers or majors as in BuserNiederle and Oosterbeek 2014) or through discrimination (iehiring decisions as in Bohnet van Geen and Bazerman 2016)

The logic of exaggerated yet directionally correct stereotypesalso sheds light on the well-documented phenomenon of base rateneglect (Kahneman and Tversky 1973) Indeed Proposition 2implies that the DM overreacts to information that assigns

21 Standardized test performance measures not only innate ability but alsoeffort and investment by third parties (Hyde et al 2008) The mapping of test per-formance into inferences about innate ability is an issue not addressed by ourmodel

22 For 2013 SAT Mathematics scores see httpmediacollegeboardcomdigitalServicespdfresearchSAT-Percentile-Ranks-By-Gender-Ethnicity-2013pdf Results are similar for the National Assessment of Educational Progress(NAEP) which are more representative of the overall population For 2012NAEP scores for 17-year-olds in mathematics see httpnationsreportcardgovltt_2012age17maspx See Hyde et al (2008) Fryer and Levitt (2010) and Popeand Sydnor (2010) for in-depth empirical analyses of the gender gap inmathematics

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people to groups precisely because such information generatesextreme stereotypes Consider the classic example in which amedical test for a particular disease with a 5 prevalence has a90 rate of true positives and a 5 rate of false positives The testassigns each person to one of two groups + (positive test) or ndash(negative test) The DM estimates the frequency of the sick type(s) and the healthy type (h) in each group The test is informativea positive result increases the relative likelihood of sickness anda negative result increases the relative likelihood of health forany prior Formally

PreththornjsTHORN

PreththornjhTHORNgt 1 gt

PrethjsTHORN

PrethjhTHORNeth4THORN

This condition has clear implications the representative personwho tests positive is sick while the representative person whotests negative is healthy Following Proposition 2 the DMreacts to the test by moving his priors too far in the right di-rection generating extreme stereotypes He greatly boosts hisassessment that a positively tested person is sick but also thata negatively tested person is healthy Because most people arehealthy the DMrsquos assessment about the group that tested neg-ative is fairly accurate but is severely biased for the group that

FIGURE I

SAT Mathematics Scores by Gender (2013)

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tested positive This analysis formalizes Tversky andKahnemanrsquos (1983) verbal account of base rate neglect23

The same mechanism may underlie several other instanceswhere DMs overweight diagnostic information When assessingan employeersquos skill level an employer attributes high perfor-mance to high skill because high performance is the distinctivemark of a talented employee Because he neglects the possibilitythat some talented employees perform poorly and that somenontalented ones perform well (perhaps due to stochasticity inthe environment) the employer has too much faith in skill andneglects the role of luck in accounting for the output Similarlywhen assessing the performance of firms in a hot sector of theeconomy (eg G = internet) an investor recalls highly successfulfirms in that sector (t = return of Google Amazon etc) He ne-glects the possibility of firms being unsuccessful because lack ofsuccess is statistically nondiagnostic and psychologically nonrep-resentative of a growing sectormdasheven if it is likely This causesexcessive optimism (in that the expectation of growth is unrea-sonably high) and overconfidence (in that the variability in earn-ings growth considered possible is truncated) True the hot sectormay have better growth opportunities on average but represen-tativeness exaggerates this feature and induces the investor toneglect a significant risk of failure

IV Evidence on Representativeness and Stereotypes

Testing our model requires evaluating the beliefs individualshold about a target group against the true distribution of thattarget group over an attribute space An ideal data set would

23 Our account is distinct from a mechanical underweighting of base rates inBayes rule as in Grether (1980) and Bodoh-Creed Benjamin and Rabin (2013) Inthose models upon receiving the test results the DM can update his beliefs in thewrong direction he can be less confident that a person is healthy after a negativetest than under his prior which cannot happen in our model Although this predic-tion of our model seems consistent with introspection we are not aware of experi-mental evidence on this point Griffin and Tversky (1992) present evidenceconsistent with pure neglect of base rates but in a significantly different tasknamely inferring the bias of a coin from a history of coin flips Such experimentsare hard to compare with the predictions of our model because subjects are asked togenerate distributions of different numbers of coin flips in their minds which is amuch more involved task than to recall types of a given distribution Their assess-ments then might be wrong for other reasons See Bodoh-Creed Benjamin andRabin (2013) for a detailed discussion

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consist of naturally defined groups with known distributions overa given space of types and a corresponding set of beliefs about thedistribution of each group over that space of types This wouldallow us to test for exaggeration of true differences betweengroups and to ask whether this exaggeration is well predictedby overweighting representative types To identify a causal rolefor representativeness or context dependence we would need ex-ogenous variation in either the comparison group ndashG or in thedistributions over the type spaces This is unavailable in existingdata sets Accordingly we take a two-pronged approach First wecreate a controlled laboratory environment that allows us toinduce the exogenous variation in representative types that weneed to test causality then we reanalyze existing field evidence tocheck for consistency with our predictions

In testing our model we focus on the two main implicationsof representativeness-based stereotypes

Context dependence the stereotype of a target group de-pends on the characteristics of the reference group it iscompared to

Kernel of truth stereotypes depend on group character-istics andmdashin most (precisely characterized) settingsmdashare slanted toward representative types

We test the first property with a lab experiment (SectionIVA) We then turn to survey data on beliefs about US politicalgroups (Section IVB) for an empirical analysis that explores thesecond property The survey data are more tightly linked to ourinterest in social stereotypes The laboratory experiment allowsus to directly test the role of representativeness in generatingcontext dependent beliefs Online Appendixes F and G provideall details and additional results for the experiments and fieldevidence

IVA Lab Evidence on Representativeness and ContextDependence

The influence of the representativeness heuristic on recalland on beliefs has been extensively documented in the lab(Kahneman and Tversky 1972 1973) Our goal is to considerhow representativeness as formalized in equation (2) gives riseto context-dependent beliefs To our knowledge the possibility

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that representativeness may generate context dependence hasnot been tested before

To assess this prediction we perform a controlled laboratoryexperiment that allows us to isolate representativeness frommany confounding factorsmdashhistorical sociological or other-wisemdashthat may affect stereotype formation in the real worldWe construct our own groups of ordinary objects creating atarget group G and a comparison group ndashG We hold thetarget group G fixed and explore how participant impressions ofit change as we change the comparison group ndashG and thusrepresentativeness

We conducted several experiments in the laboratory and onAmazon Mechanical Turk Each involves a basic three-stepdesign First participants are shown the target group and a ran-domly assigned comparison group for 15 seconds In this timedifferences between groups can be noticed but the groupsrsquo precisecompositions cannot be memorized The second step consists of afew filler questions which briefly draw the participantsrsquo cognitivebandwidth away from their observation Finally participants areasked to assess the groups they saw Participants are incentiv-ized to provide accurate answers

We randomly assign participants to either the Control or theRepresentativeness condition In the Control condition G and ndashGhave nearly identical distributions so that all types are similarlyrepresentative for each group In the Representativeness condi-tion ndashG is changed in such a way that a certain type becomes veryrepresentative for G Context dependence implies that the assess-ment of G should now overweight this representative type eventhough the distribution of G itself has not changed

We ran six experiments of this form with design changesfocused on reducing participant confusion and removing con-founds We describe the final and most refined version of theseexperiments here In an attempt to provide a overview of the re-sults while remaining concise we provide the results from pooledspecifications that use all data collected In Online Appendix Fwe offer additional details and report all experiments conductedWe also give instructions and materials for each experiment thefull data set is available by request

Consider first the experiment illustrated in Figure II Agroup of 25 cartoon girls is presented next to a group of 25 cartoonboys in T-shirts of different colors blue green or purple In theControl condition (Figure II Panel a) the groups have identical

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color distributions (13 purple 12 green) so no color is represen-tative of either group The Representativeness condition (Panel b)compares the same group of girls with a different group of boysfor whom green shirts are replaced with blue shirts Now onlygirls wear green and only boys wear blue These colors althoughstill not the most frequent for either group are now most repre-sentative For each group girls and boys participants are asked anumber of questions concerning the frequency of T-shirts of dif-ferent colors worn by that group

Applying our model in the control condition the type space isT frac14 fgreen purpleg and the groups are G = girls and ndashG = boysGiven that the color distributions are identical across groups both

types are equally representativegreengirls

greenboysfrac14 1 frac14

purplegirls

purpleboys As a result

assessment of G should be correct on average stcontrolgreengirls frac14 greengirls

and stcontrolpurplegirls frac14 purplegirls for any weighing function (the same is

true about assessments of ndashG)In the treatment condition the distribution of shirt colors re-

mains the same for girls For boys green shirts are changed intoblue Thus the type space changes to T frac14 fgreen purple bluegand the representative color for girls becomes greengreengirls

greenboysfrac14 1 gt 1 frac14

purplegirls

purpleboys while that for boys becomes blue As

a result in the treatment condition subjects should inflate the

frequency of green shirts relative to the truth sttreatmentgreengirls

gt greengirls (the same should happen to assessments of blueshirts for boys) We also expect the assessed frequency of greenshirts to go up relative to the control condition namely

sttreatmentgreengirls gt stcontrol

greengirls Critically the only factor that varies

across treatments is the representativeness of the 12-colorshirt Thus if we see differences across conditions the causalrole of representativeness-based recall in shaping group judg-ments is clear24

24 We vary which colors are used in which roles across participants Someparticipants saw this particular color distribution while others see for examplegreen as the modal color and purple as the diagnostic color for boys in theRepresentativeness condition and blue as the diagnostic color for girls in theRepresentativeness condition We vary the colors across the roles to avoid con-founding the characteristics of any particular color with its diagnosticity

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FIG

UR

EII

T-S

hir

tsE

xp

erim

ent

Fig

ure

sap

pea

red

inco

lor

top

art

icip

an

tsin

the

exp

erim

ent

For

clari

ty

we

have

ad

ded

ale

tter

toea

chT

-sh

irt

toid

enti

fyth

eco

lor

for

the

read

er

lsquolsquoGrsquorsquo

ind

icate

sgre

en

lsquolsquoPrsquorsquo

ind

icate

sp

urp

le

lsquolsquoBrsquorsquo

ind

icate

sblu

eT

hes

ele

tter

sd

idn

otap

pea

rto

part

icip

an

tsan

dare

for

read

erre

fere

nce

only

P

lease

see

onli

ne

ver

sion

ofp

ubli

shed

art

icle

for

colo

rfi

gu

reex

act

lyas

itap

pea

red

top

art

icip

an

ts

STEREOTYPES 1779

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We collected data from 301 participants using this T-shirtsdesign25 Since the number of green and purple shirts is verysimilar we first ask each participant the simplest question ofwhich shirt color is modal Next we ask participants to assessthe share of green and purple shirts

Consistent with the role of representativeness participantsassigned to the Representativeness condition are 105 percentagepoints more likely to recall the less frequent color (green for girlsor blue for boys) as the modal color when it is representative of agroup (35 of participants guess the less frequent color is modalin the Control condition this proportion increases to 46 in theRepresentativeness condition p = 01 estimated from a probitregression reported in Online Appendix F)

We now turn to subjectsrsquo estimates of how many T-shirts ofeach color they saw in each group In both conditions the truedifference in counts is 1 (13 purple shirts 12 green or blue shirts)In the Control condition participants on average believe they saw054 more purple shirts than green or blue shirts In theRepresentativeness condition participants believe they saw072 fewer purple shirts than green or blue shirts (the acrosstreatment difference is significant with p = 01 from OLS regres-sion reported in Online Appendix F)

In total we collected data for six experiments of this generalstructure gathering evidence from more than 1000 participantsAs we describe in Online Appendix F although there is substan-tial variation across experiments when we pool all of the data wefind significant aggregate treatment effects in line with a role ofrepresentativeness in judgment We employ four different unor-dered types designs similar to the T-shirts experiment using sixsamples (four online and two in the laboratory) with 741 partic-ipants We find effects in the predicted direction for five of the sixsamples Using a probit regression that pools the data for theseunordered type experiments we find that participants are 93 per-centage points more likely to guess that the less frequent type ismodal when it is representative than when it is not (p = 002) Wealso run a family of ordered types experiments (two designs fivesamples 402 participants) Unlike the simpler T-shirts style

25 Throughout our analysis we exclude any participant who participated in aprevious version of the experiment and any participant who self-identified as color-blind In Online Appendix F we show that our results are unchanged if we includethese additional observations

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design the theoretical predictions for the ordered types designsare more sensitive to the specific assumptions one makes aboutthe weighting function of the DM26 We find effects in the pre-dicted direction for three of the five samples As we discuss inmore detail in Online Appendix F the ordered types resultsvary by platform with consistently stronger results on AmazonMechanical Turk than in the laboratory samples Pooling all or-dered types experiments participants are 93 percentage pointsmore likely to guess that the group of interest has a greater av-erage than the comparison group when the right tail is represen-tative (p = 062) Given our simple experimental setting withgroups of mundane objects we interpret our resultsmdasha signifi-cant and reasonably sized impact on average beliefsmdashas an im-portant proof of concept the presence of representative typesbiases ex post assessment

IVB Empirical Evidence on Political Stereotypes

We examine two data sets on political preferences and be-liefs about political preferences in the United States We inves-tigate the roles of representativeness and context dependence byseparately testing for hypotheses that allow us to assess the lead-ing theories of stereotypes

First we test whether beliefs are correct or depart systemat-ically from the truth The statistical discrimination approachbuilds on the assumption that people hold rational expectationsof group traits Comparing beliefs to the truth allows us to assessthe validity of this assumption in our data

Second we test if beliefs depart from the truth by exagger-ating (mean) differences among groups per the kernel of truthhypothesis This is an implicit test of context dependence be-cause it implies that beliefs about the target groups are shapednot only by that grouprsquos characteristics but also by those of thereference group27

Third we test if distortions in beliefs can be accounted for bythe overweighting of highly representative types (defined astypes that are relatively more frequent in the target relative to

26 This is due in part to our choice to not study MLRP distributions We moti-vate and discuss this design decision in Online Appendix F

27 Of course unlike in the laboratory experiment in this setting we cannot testfor context dependence by exogenously varying the reference group

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the reference group) The second and third tests address the keypredictions of our model

1 The Data We have two data sets on political preferences andbeliefs about political preferences The first data set from GrahamNosek and Haidt (GNH 2012) contains data from the MoralFoundations Questionnaire Respondents (1174 self-identified lib-erals and 500 self-identified conservatives) answer questions abouttheir position on a subset of 45 issues 20 moral relevance state-ments (eg lsquolsquowhen you decide whether something is right orwrong to what extent are the following considerations relevantto your thinkingrsquorsquo) and 25 moral judgments (eg lsquolsquoindicate theextent to which you would agree or disagreersquorsquo) For each issue arandomly determined subset of participants states their own posi-tion another subset states their belief on the position of a lsquolsquotypicalliberalrsquorsquo and a third subset states their belief on the position of alsquolsquotypical conservativersquorsquo The data thus include the distribution overpositions for both liberal and conservatives as well as the averagebelieved typical position of liberals and of conservatives on the 45issues Each position is elicited on 1ndash6 scale

The second data set comes from the American NationalElection Survey (ANES) and contains data from more than20000 respondents between 1964 and 201228 The surveycovers political issues of the day such as the optimal amount ofgovernment spending and service provision (1984ndash2000) or theplace of women in society (1972ndash1998) We focus on the 10 issuesthat ask participants to respond on a 1ndash7 scale (rather than justindicate binary agreement or disagreement) all 10 issues areasked in multiple years Participants are asked to provide theirown position on the scale and their believed position of theDemocratic and Republican parties (lsquolsquoWhere would you placethe Democratic [Republican] party on this scalersquorsquo) The data in-clude for each issue-year observation the distribution of partic-ipant positions for self-identified liberals and self-identifiedconservatives as well as the distribution of believed typical posi-tions of the Democratic and Republican parties

28 These data are publicly available at httpwwwelectionstudiesorgstudy-pagesanes_timeseries_cdfanes_timeseries_cdfhtm

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2 Empirical Strategy Our analysis focuses on beliefs abouttwo groups Conservatives and Liberals The types are the possi-ble positions for each issue (1 2 6 7) For the GNH data weinterpret beliefs about the lsquolsquotypicalrsquorsquo element of a group to coincidewith the believed average position in that group Similarly forthe ANES data we use the believed party positions as a proxy forbelieved mean of each group29 We then take as a benchmark thehypothesis that individuals hold accurate beliefs about eachgroup and in particular that believed mean position shouldequal true mean position at least on average across subjectsThe accurate beliefs hypothesis underlies the most common eco-nomic model of stereotyping statistical discrimination

To assess our representativeness-based model we perform aregression exercise To test our model in a linear regressionframework we rely on linear approximations of the weightingfunction Our model then yields two regression specifications

PROPOSITION 4 Let G 2 fconservative liberal g and assume

ht h tG

tG

be a differentiable and strictly increasing weight-

ing function as in Definition 2 The following hold as a first-order approximation around identical distributions G

Gfrac14 1

(i) Kernel of truth regression There exists a constant gt 0such that

EstethtjGTHORN frac14 EethtjGTHORNeth1thorn THORN EethtjGTHORNeth5THORN

(ii) Representativeness regression Denote H frac14 fT 2 Tg

the right tail of types and RconsH frac14

PHtconsPHtlib

as the average

representativeness of right tail types for conservatives

29 This assumption is consistent with the authorsrsquo interpretation of the GNHdata (GNH 2012) and with previous studies using ANES (eg Westfall et al 2015)Furthermore to the extent that this assumption holds equally well for most issueswithin a data set our focus on cross-issue differences should allow us to test thepredictions of our model even with an imperfect proxy for beliefs of mean positionsFinally the data provide some insight into whether subjects are reporting (per-ceived) modal or mean types As we show the modal type is a poor prediction ofstated beliefs while a distorted mean slanted toward representative types is anaccurate prediction of stated beliefs

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Under the further approximation where tcons

tlibampRcons

H for

t 2 H

EstethtjconsTHORN frac14 EethtjconsTHORN thorn consethR

consH 1THORNeth6THORN

EstethtjlibTHORN frac14 EethtjlibTHORN libethR

consH 1THORNeth7THORN

where lcons and llib are positive constants

The first regression allows us to test for the kernel of truthhypothesis and the second set of regressions allows us to test forthe role of representativeness

Equation (5) says that respondents in our model inflate theaverage position of a group say the conservatives if and only ifthe group has a higher average position than the other groupnamely the liberals Formally EstethtjconsTHORN gt EethtjconsTHORN if and onlyif EethtjconsTHORN gt EethtjlibTHORN Because in our measurement scale highertypes mean lsquolsquomore conservativersquorsquo we expect (i) believed conserva-tive average to be higher than the truth and (ii) the extent ofoverstatement to decrease in the average liberal position EethtjlibTHORNConversely we expect the average liberal position to be lowerthan the truth the more so the higher the average conservativeposition EethtjconsTHORN

As previously discussed the basis of these predictions is con-text dependence information about the distribution of ndashG is rel-evant for the beliefs about G This context dependence isinconsistent with rational expectations in which only thegrouprsquos own means should affect beliefs We test the hypothesisthat the true mean EethtjGTHORN is a significant predictor of the believedmean E

stethtjGTHORN with a positive sign and the other grouprsquos truemean EethtjGTHORN is a predictor of the believed mean with a negativesign

Equations (6) and (7) say that repondentsrsquo assessment bias isshaped by representativeness When the right tail is more repre-sentative for conservatives (Rcons

H 1 positive and large) partici-pants should inflate the average conservative position more(higher E

stethtjconsTHORN EethtjconsTHORN) and deflate the average liberal po-sition more (lower E

stethtjlibTHORN EethtjlibTHORN) We test the hypothesisthat the inflation in conservative positions is positively associatedwith the representativeness of the right tail for the conservativesand the inflation in liberal positions is negatively associated with

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it Once again the representativeness of the right tail is com-puted using the true distribution of positions

In equations (6) and (7) in many cases the representative tailis also the most likely one As a consequence these tests cannotdistinguish a representativeness-based from a likelihood-basedmodel of distorted beliefs We perform two additional testsFirst we run versions of equations (6) and (7) in which we controlfor the likelihood of tails (see Table A4 in Online Appendix G)Second we compute numerically the predictions of a representa-tiveness-based model of stereotypes and a likelihood-based modelof stereotypes We then assess which of these two is better able tomatch the data on beliefs

3 Empirical Results To begin we illustrate the structure ofthe data and the nature of our predictions with two simple exam-ples from the GNH data set focusing on beliefs about conserva-tives In example 1 participants are asked about their agreementwith the statement lsquolsquoIt can never be right to kill a human beingrsquorsquoIn example 2 participants are asked about the moral relevance oflsquolsquowhether or not someone cared for someone weak or vulnerablersquorsquoAs can be seen in Figure III in example 1 the modal position(strongly disagree (1)) and most representative positions(strongly disagree (1)) coincide for conservatives In contrast inexample 2 in Figure III the most representative types (slightlyrelevant (3) not at all relevant (1)) are not most likely for theconservative group Following Proposition 1 we predict that be-liefs will be distorted in the direction of the most representativetypes Thus we expect more exaggeration in example 2 than inexample 1 since in example 2 the most representative types (inthe left tail) are far from the modal type whereas in example 1they coincide This is what we find the conservative position isexaggerated by only 009 positions in Example 1 (true mean 299believed mean 290) but by 106 positions in Example 2 (truemean 421 believed mean 315)

In the full data sets we treat each (issue year) pair as anobservation and we cluster standard errors at the issue level Forthe GNH data we have 45 observations 45 issues measured inthe same year For the ANES data we have 66 observations 10issues measured in multiple years To begin we simply docu-ment systematic exaggeration in both data sets This is a primaryfocus of the original analysis in GNH (2012) and also in Westfall

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FIGURE III

Two Examples

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et al (2015)rsquos analysis of the ANES data30 Figure IV shows thatthe believed difference between typical conservative and typicalliberal positions is larger than the true difference in mean posi-tions for 109 of the 111 observations The data for both GNH(squares) and ANES (triangles) lie above the 45-degree line(dashed)31 Average exaggeration is 062 positions on the scale(066 in the GNH data 059 in the ANES data)32

The systematic and significant exaggeration of mean differ-ences suggests that the benchmark model of accurate beliefs ismissing something important Indeed this exaggeration reflectsthe fact that believed means are typically more extreme than truemeans First note that the kernel of truth regression (equation(5)) generates exaggeration of mean differences just as docu-mented in Figure IV

EstethtjGTHORN E

stethtjGTHORN frac14 eth1thorn 2THORN frac12EethtjGTHORN EethtjGTHORN

To bring this prediction to the data we regress the believedmean position for each group EBethtjGTHORN on the true mean of thegroup EethtjGTHORN and the true mean of the comparison groupEethtjGTHORN across issues We do this for each group (liberals con-servatives) in each data set separately We also present pooledspecifications that combine the data sets to make a prediction fora given group (liberals conservatives) In these pooled specifica-tions we include a dummy variable indicating whether theobservation came from the ANES data set For all specificationswe cluster observations at the issue level33 The results from re-gression are shown in Table I In every specification we find thatEethtjGTHORN is a significant predictor of EBethtjGTHORN with the predicted pos-itive sign Crucially for five of the six specifications the mean of

30 Chambers and Melnyk (2006) also find evidence of exaggeration of truedifferences in beliefs about political positions

31 For convenience we recode all issues so that the high end of the scale (67)represents the stereotypically more conservative position

32 A natural question to ask is how beliefs vary across liberals and conserva-tives That is do beliefs about a group G depend on membership in G versus ndashG Ourmodel does not speak to this issue However in Online Appendix G we show thatthe results we document below hold for both beliefs held by conservatives and be-liefs held by liberals see Tables A9 A10 and A11

33 In general the results presented below for the ANES data are not largelyimpacted by the decision to cluster at the issue level Similar results are obtained ifthe data are not clustered

STEREOTYPES 1787

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the comparison group EethtjGTHORN is also a significant predictor ofE

BethtjGTHORN with the predicted negative signAlthough these results provide strong evidence of context

dependence and are consistent with our model they do not pindown a role for representativeness of types Our next test relatesthe magnitude of representativeness of tail types to the magni-tude of belief distortions

To this end we implement the regressions in equations (6)and (7) Following Proposition 4 we compute the average repre-

sentativeness of tail types for conservatives RconsH frac14

PtT2tconsPtT2tlib

We

again test the hypothesis that RconsH is a significant predictor of Est

ethtjconsTHORN with a positive sign and a predictor of EstethtjlibTHORN with a

negative sign Table II shows that conditional on true mean RconsH

predicts believed mean for each group G as expected The firstthree specifications display the results for predicting beliefs heldabout conservatives In both data sets the average representa-tiveness of tail types for conservatives is a significant positivepredictor of beliefs held about conservatives The final three spe-cifications display the results for predicting beliefs held about

FIGURE IV

Exaggeration of Differences

QUARTERLY JOURNAL OF ECONOMICS1788

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liberals We find that the average representativeness of tail typesfor conservatives is a negative predictor of beliefs held about lib-erals This effect is significant in the GNH data and marginallysignificant in the ANES data

We present several additional results in Online Appendix GTo further examine the role of representativeness in driving be-liefs we first show the results of Table II carry through when we

TABLE II

AVERAGE REPRESENTATIVENESS OF TAIL POSITIONS PREDICTS BELIEFS

OLS Predicting Believed Mean of Group G for Each Issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position

of group G for issue

078 024 051 072 018 041

(006) (008) (009) (005) (005) (010)

Avg rep of tail types for

conservatives RconsH

019 055 025 014 012 024

(007) (022) (008) (006) (007) (005)

Constant 101 260 184 093 271 201

(026) (045) (029) (022) (025) (032)

R2 082 048 060 091 031 070

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

TABLE I

INFORMATION ABOUT ndashG PREDICTS BELIEFS ABOUT G

OLS predicting believed mean of group G for each issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position of

conservatives for issue

102 098 096 021 019 025

(0097) (0133) (0076) (0060) (0116) (0060)

True mean position of

liberals for issue

035 086 058 0987 039 073

(0106) (0134) (0131) (0066) (0106) (0135)

Constant 151 335 235 069 258 156

(0195) (0269) (0279) (0122) (0249) (0270)

R2 083 053 066 092 032 068

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

STEREOTYPES 1789

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control for the average likelihood on the tail positions (see Table A4in Online Appendix G) Most tellingly we use the model to predictbeliefs across issues and compare those to the data For simplicitywe use the rank-based truncation specification to predict mean be-liefs when stereotypes include the d most representative types ford frac14 1 T We compare these predictions to those of a model inwhich beliefs are obtained by restricting the distribution to the dmost likely types Our benchmark for both models is predicting thebelieved mean from the entire distribution where d = T We showthat the predictions of the rank-based truncation model with d = 4or 5 compare favorably to both a likelihood-based truncation model(with any d) and the accurate beliefs benchmark Interestingly thisresult suggests that stereotypical beliefs are well approximated byneglecting the least representative types (as opposed to focusingonly on the most representative types) and so represent a moderatethough systematic departure from the standard benchmarkFinally we show that the results we document above hold forboth beliefs held by conservatives and beliefs held by liberals (seeTables A9 A10 and A11 in Online Appendix G)

V Conclusion

We present a model of stereotypical thinking in which DMsmaking predictions about a group overweight the grouprsquos mostdistinctive types These overweighted types are not the mostlikely ones given the DMrsquos data but the most representativeones in the sense of being the most diagnostic of the group rela-tive to other groups Representativeness implies that what ismost distinctive of a group depends on what group it is comparedwith We present experimental evidence that confirms this con-text dependence in recall-based assessments of groups Finallywe evaluated the predictions of the model using political data fromexisting large-scale surveys We find context dependence to be akey feature of beliefs Given the richness of the political data wecan go a step further and identify a role for representativeness inparticular As the representativeness of tail types increases beliefsof a group are distorted in the direction of that tail

Our approach provides a parsimonious and psychologicallyfounded account of how DMs generate simplified representationsof reality from social groups to stock returns and offers a unifiedaccount of disparate pieces of evidence relating to this type of

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uncertainty The model captures the central fact that stereotypeshighlight the greatest difference between groups thus explainingwhy some stereotypes are very accurate while others lack valid-ity Still stereotypes often have a kernel of truth when they arebased on systematicmdasheven if smallmdashdifferences between groupsThis logic allows us to describe a number of heuristics and psy-chological biases many of which arise in the context of predictionproblems Generically our model generates overreaction to diag-nostic information

Our model is based on representativeness and does not cap-ture all the features of stereotypical thinking However it cap-tures perhaps the central feature when we think of a group wefocus on what is most distinctive about it and neglect or under-weight the rest

Saeuroıd Business School University of Oxford

Ohio State University and Harvard Business School

Universita Bocconi and Innocenzo Gasparini Institute

for Economic Research

Harvard University

Supplementary Material

An Online Appendix for this article can be found at QJEonline (qjeoxfordjournalorg)

References

Adorno Theodor Else Frenkel-Brunswik Daniel Levinson and Nevitt SanfordThe Authoritarian Personality (New York Harper amp Row 1950)

Arrow Kenneth lsquolsquoThe Theory of Discriminationrsquorsquo in Discrimination in LaborMarkets Orley Ashenfelter and Albert Rees eds (Princeton NJPrinceton University Press 1973)

Ashton Michael and Victoria Esses lsquolsquoStereotype Accuracy Estimating theAcademic Performance of Ethnic Groupsrsquorsquo Personality and SocialPsychology Bulletin 25 (1999) 225ndash236

Barberis Nicholas Andrei Shleifer and Robert Vishny lsquolsquoA Model of InvestorSentimentrsquorsquo Journal of Financial Economics 49 (1998) 307ndash343

Bayer Sylvia lsquolsquoThe Accuracy of Academic Gender Stereotypesrsquorsquo Sex Roles 40(1999) 787ndash813

Benjamin Dan James Choi and Joshua Strickland lsquolsquoSocial Identity andPreferencesrsquorsquo American Economic Review 100 (2010) 1913ndash1928

Benjamin Dan Matthew Rabin and Collin Raymond lsquolsquoA Model of Non-Belief inthe Law of Large Numbersrsquorsquo Journal of the European Economic Association15 (2015) 515ndash544

Bertrand Marianne lsquolsquoNew Perspectives on Genderrsquorsquo Handbook of LaborEconomics 4 (2011) 1543ndash1590

Bodoh-Creed Aaron Dan Benjamin and Matthew Rabin lsquolsquoThe Dynamics of Base-Rate Neglectrsquorsquo mimeo Haas Business School 2013

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ibrary on October 28 2016

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Bohnet Iris Alexandra van Geen and Max Bazerman lsquolsquoWhen PerformanceTrumps Gender Bias Joint versus Separate Evaluationrsquorsquo ManagementScience 5 (2016) 1225ndash1234

Bordalo Pedro Nicola Gennaioli and Andrei Shleifer lsquolsquoSalience Theory of Choiceunder Riskrsquorsquo Quarterly Journal of Economics 127 (2012) 1243ndash1285

mdashmdashmdash lsquolsquoSalience and Consumer Choicersquorsquo Journal of Political Economy 121(2013) 803ndash843

Briton Nancy and Judith Hall lsquolsquoBeliefs about Female and Male NonverbalCommunicationrsquorsquo Sex Roles 32 (1995) 79ndash90

Buser Thomas Muriel Niederle and Hessel Oosterbeek lsquolsquoGenderCompetitiveness and Career Choicesrsquorsquo Quarterly Journal of Economics 129(2014) 1409ndash1447

Carrell Scott Marianne Page and James West lsquolsquoSex and Science How ProfessorGender Perpetuates the Gender Gaprsquorsquo Quarterly Journal of Economics 125(2010) 1101ndash1144

Chambers John and Darya Melnyk lsquolsquoWhy Do I Hate Thee ConflictMisperceptions and Intergroup Mistrustrsquorsquo Personality and SocialPsychology Bulletin 32 (2006) 1295ndash1311

Chan Wayne Robert R McCrae Filip De Fruyt Lee Jussim CorinnaE Lockenhoff Marleen De Bolle Paul T Costa Jr Angelina R SutinAnu Realo Juri Allik Katsuharu Nakazato Yoshiko ShimonakaMartina Hrebıckova Sylvie Graf Michelle Yik Marina Brunner-SciarraNora Leibovich De Figueora Vanina Schmidt Chang-kyo Ahn Hyun-nie Ahn Maria E Aguilar-Vafaie Jerzy Siuta Barbara SzmigielskaThomas R Cain Janet T Crawford Khairul Anwar Mastor Jean-Pierre Rolland Florence Nansubuga Daniel R MiramontezVeronica Benet-Martınez Jerome Rossier Denis Bratko Iris MarusicJamin Halberstadt Mami Yamaguchi Goran Knezevic Thomas A MartinMirona Gheorghiu Peter B Smith Claudio Barbaranelli Lei WangJane Shakespeare-Finch Margarida P Lima Waldemar KlinkoszAndrzej Sekowski Lidia Alcalay Franco Simonetti Tatyana V AvdeyevaV S Pramila and Antonio Terracciano lsquolsquoStereotypes of Age Differences inPersonality Traits Universal and Accuratersquorsquo Journal of Personality andSocial Psychology 103 (2012) 1050ndash1066

Chen Yan Sherry Xin Liu Tracy Xiao and Margaret Shih lsquolsquoWhich Hat to WearImpact of Natural Identities on Coordination and Cooperationrsquorsquo Games andEconomic Behavior 84 (2014) 58ndash86

Coffman Katherine lsquolsquoEvidence on Self-Stereotyping and the Contribution ofIdeasrsquorsquo Quarterly Journal of Economics 129 (2014) 1625ndash1660

Cunningham Tom lsquolsquoComparisons and Choicersquorsquo mimeo Stockholm University2013

Diekman Amanda Alice Eagly and Patrick Kulesa lsquolsquoAccuracy and Bias in theStereotypes about the Social and Political Attitudes of Women and MenrsquorsquoJournal of Experimental Social Psychology 38 (2002) 268ndash282

Eccles Jacquelynne S Janis E Jacobs and Rena D Harold lsquolsquoGender RoleStereotypes Expectancy Effects and Parentsrsquo Socialization of GenderDifferencesrsquorsquo Journal of Social Issues 46 (1990) 183ndash201

Fryer Roland and Matthew Jackson lsquolsquoA Categorical Model of Cognition andBiased Decision-Makingrsquorsquo BE Journal of Theoretical Economics 8 (2008)1ndash42

Fryer Roland and Steven Levitt lsquolsquoAn Empirical Analysis of the Gender Gap inMathematicsrsquorsquo American Economic Journal Applied Economics 2 (2010)210ndash240

Gennaioli Nicola and Andrei Shleifer lsquolsquoWhat Comes to Mindrsquorsquo Quarterly Journalof Economics 125 (2010) 1399ndash1433

Gennaioli Nicola Andrei Shleifer and Robert Vishny lsquolsquoNeglected RisksFinancial Innovation and Financial Fragilityrsquorsquo Journal of FinancialEconomics 104 (2012) 452ndash468

Gilens Martin lsquolsquoRace and Poverty in America Public Misperceptions and theAmerican News Mediarsquorsquo Public Opinion Quarterly 60 (1996) 515ndash541

Glaeser Edward lsquolsquoThe Political Economy of Hatredrsquorsquo Quarterly Journal ofEconomics 120 (2005) 45ndash86

QUARTERLY JOURNAL OF ECONOMICS1792

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

Glover Dyland Amanda Pallais and William Pariente lsquolsquoDiscrimination as a Self-Fulfilling Prophecy Evidence from French Grocery Storesrsquorsquo mimeo HarvardUniversity 2015

Goldin Claudia Lawrence Katz and Ilyana Kuziemko lsquolsquoThe Homecoming ofAmerican College Women The Reversal of the College Gender GaprsquorsquoJournal of Economic Perspectives 20 (2006) 133ndash156

Graham Jesse Brian Nosek and Jonathan Haidt lsquolsquoThe Moral Stereotypes ofLiberals and Conservatives Exaggeration of Differences across thePolitical Spectrumrsquorsquo PLoS One 7 (2012) 1ndash13

Grether David lsquolsquoBayes Rule as a Descriptive Model The RepresentativenessHeuristicrsquorsquo Quarterly Journal of Economics 95 (1980) 537ndash557

Griffin Dale and Amos Tversky lsquolsquoThe Weighing of Evidence and theDeterminants of Confidencersquorsquo Cognitive Psychology 24 (1992) 411ndash435

Guiso Luigi Ferdinando Monte Paola Sapienza and Luigi Zingales lsquolsquoCultureGender and Mathrsquorsquo Science 320 (2008) 1164ndash1165

Hilton James and William Von Hippel lsquolsquoStereotypesrsquorsquo Annual Review ofPsychology 47 (1996) 237ndash271

Hyde Janet Sara Lindberg Marcia Linn Amy Ellis and Caroline WilliamslsquolsquoGender Similarities Characterize Math Performancersquorsquo Science 321 (2008)494ndash495

Judd Charles and Bernardette Park lsquolsquoDefinition and Assessment of Accuracy inSocial Stereotypesrsquorsquo Psychological Review 100 (1993) 109ndash128

Jussim Lee Jarret Crawford Stephanie Anglin John Chambers Sean Stevensand Florette Cohen lsquolsquoStereotype Accuracy One of the Largest and MostReplicable Effects in All of Social Psychologyrsquorsquo in The Handbook ofPrejudice Stereotyping and Discrimination Todd Nelson ed (MahwahNJ Lawrence Erlbaum 2015)

Kahneman Daniel and Amos Tversky lsquolsquoSubjective Probability A Judgment ofRepresentativenessrsquorsquo Cognitive Psychology 3 (1972) 430ndash454

mdashmdashmdash lsquolsquoOn the Psychology of Predictionrsquorsquo Psychological Review 80 (1973) 237ndash251

Kaplowitz Stan Bradley Fisher and Clifford Broman lsquolsquoHow Accurate ArePerceptions of Social Statistics about Blacks and Whitesrsquorsquo Public OpinionQuarterly 67 (2003) 237ndash243

Kersten Daniel Pascal Mamassian and Alan Yuille lsquolsquoObject Perception asBayesian Inferencersquorsquo Annual Review of Psychology 55 (2004) 271ndash304

Klein Richard Kate A Ratliff Michelangelo Vianello Reginald B Adams JrStepan Bahnik Michael J Bernstein Konrad Bocian Mark J BrandtBeach Brooks Claudia Chloe Brumbaugh Zeynep CemalcilarJesse Chandler Winnee Cheong William E Davis Thierry DevosMatthew Eisner Natalia Frankowska David Furrow Elisa Maria GallianiFred Hasselman Joshua A Hicks James F Hovermale S Jane HuntJeffrey R Huntsinger Hans IJzerman Melissa-Sue John Jennifer A Joy-Gaba Heather Barry Kappes Lacy E Krueger Jaime Kurtz CarmelA Levitan Robyn Mallett Wendy L Morris Anthony J Nelson JasonA Nier Grant Packard Ronaldo Pilati Abraham M RutchickKathleen Schmidt Jeanine L Skorinko Robert Smith Troy G SteinerJustin Storbeck Lyn M Van Swol Donna Thompson Anna van rsquot VeerLeigh Ann Vaughn Marek Vranka Aaron Wichman Julie A Woodzickaand Brian A Nosek lsquolsquoInvestigating Variation in Replicability A ManyLabs Replication Projectrsquorsquo Social Psychology 45 (2014) 142ndash152

Lundberg Shelly and Richard Startz lsquolsquoPrivate Discrimination and SocialIntervention in Competitive Labor Marketsrsquorsquo American Economic Review73 (1983) 340ndash347

Madon Stephanie Max Guyll Kathy Aboufadel Eulices Montiel Alison SmithPolly Palumbo and Lee Jussim lsquolsquoEthnic and National Stereotypes ThePrinceton Trilogy Revisited and Revisedrsquorsquo Personality and SocialPsychological Bulletin 27 (2001) 996ndash1010

Martin Carol lsquolsquoA Ratio Measure of Sex Stereotypingrsquorsquo Journal of Personality andSocial Psychology 52 (1987) 489ndash499

STEREOTYPES 1793

at Harvard L

ibrary on October 28 2016

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McCauley Clark Krishna Thangavelu and Paul Rozin lsquolsquoSex Stereotyping ofOccupations in Relation to Television Representations and Census FactsrsquorsquoBasic and Applied Social Psychology 9 (1988) 197ndash212

Mullainathan Sendhil lsquolsquoThinking through Categoriesrsquorsquo mimeo HarvardUniversity 2002

Ortoleva Pietro and Erik Snowberg lsquolsquoOverconfidence in Political BehaviorrsquorsquoAmerican Economic Review 105 (2015) 504ndash535

Phelps Edmund lsquolsquoThe Statistical Theory of Racism and Sexismrsquorsquo AmericanEconomic Review 62 (1972) 659ndash661

Pope Devin and Justin Sydnor lsquolsquoGeographic Variation in the Gender Differencesin Test Scoresrsquorsquo Journal of Economic Perspectives 24 (2010) 95ndash108

Rabin Matthew lsquolsquoInference by Believers in the Law of Small NumbersrsquorsquoQuarterly Journal of Economics 117 (2002) 775ndash816

Rabin Matthew and Joel Schrag lsquolsquoFirst Impressions Matter A Model ofConfirmatory Biasrsquorsquo Quarterly Journal of Economics 114 (1999) 37ndash82

Rabin Matthew and Dimitri Vayanos lsquolsquoThe Gamblerrsquos and Hot-Hand FallaciesTheory and Applicationsrsquorsquo Review of Economic Studies 77 (2010) 730ndash778

Reuben Ernesto Paola Sapienza and Luigi Zingales lsquolsquoHow Stereotypes ImpairWomenrsquos Careers in Sciencersquorsquo Proceedings of the National Academy ofSciences 111 (2014) 4403ndash4408

Rosch Eleanor lsquolsquoNatural Categoriesrsquorsquo Cognitive Psychology 4 (1973) 328ndash350Ryan Carey S lsquolsquoAccuracy of Black and White College Studentsrsquo In-Group and

Out-Group Stereotypesrsquorsquo Personality and Social Psychology Bulletin 22(1996) 1114ndash1127

Schneider David The Psychology of Stereotyping (New York Guilford Press2004)

Schneider David Albert Hastorf and Phoebe Ellsworth Person Perception(Reading MA Addison-Wesley 1979)

Shih Margaret Todd Pittinsky and Nalini Ambady lsquolsquoStereotype SusceptibilityIdentity Salience and Shifts in Quantitative Performancersquorsquo PsychologicalScience 10 (1999) 80ndash83

Shih Margaret Todd Pittinsky and Amy Trahan lsquolsquoDomain-Specific Effects ofStereotypes on Performancersquorsquo Self and Identity 5 (2006) 1ndash14

Steele Claude Whistling Vivaldi How Stereotypes Affect Us and What We CanDo (New York Norton 2010)

Tenenbaum Joshua and Thomas Griffiths lsquolsquoThe Rational Basis ofRepresentativenessrsquorsquo 23rd Annual Conference of the Cognitive ScienceSociety (2001) 1036ndash1041

Tversky Amos and Daniel Kahneman lsquolsquoExtensional versus Intuitive ReasoningThe Conjunction Fallacy in Probability Judgmentrsquorsquo Psychological Review 90(1983) 293ndash315

Weinberger Catherin lsquolsquoIs the Science and Engineering Workforce Drawn fromthe Far Upper Tail of the Math Ability Distributionrsquorsquo mimeo UCSB 2005

Westfall Jacob Leaf Van Boven John Chambers and Charles Judd lsquolsquoPerceivingPolitical Polarization in the United States Party Identity Strength andAttitude Extremity Exacerbate the Perceived Partisan DividersquorsquoPsychological Science 10 (2015) 145ndash158

Wolsko Christopher Bernadette Park Charles Judd and Bernd WittenbrinklsquolsquoFraming Interethnic Ideology Effects of Multicultural and Color-BlindPerspectives on Judgments of Groups and Individualsrsquorsquo Journal ofPersonality and Social Psychology 78 (2000) 635ndash654

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Page 14: I. Introduction · uneducated at the beginning of the 20th century, and as high achievers at the beginning of the 21st (Madon et al. 2001). Social science has produced three broad

Exploring this idea formally is an interesting avenue for futurework

Consider some limitations of our model First representa-tiveness is not the only heuristic that shapes recall Decisionmakers may for instance find it easier to recall types that aresufficiently likely Another potentially important mechanism isavailability understood by Kahneman and Tversky (1972) as thelsquolsquoeasersquorsquo with which information comes to mind (because of actualfrequency or repetition) In Online Appendix E we present a trun-cation-based recall mechanism in which distortions are driven bya combination of representativeness and likelihood of types(which is equivalent to relaxing property i in Definition 2) Thismodel can offer a useful starting point to capture availability aswell even though a full model of availability is beyond the scopeof this article Even in this more general setting the influence ofrepresentativeness on recall is the driving force of stereotypesthat in line with the social psychology perspective are basedon underlying differences among groups As we show in SectionIV this feature is critical in accounting for the evidence

The second set of model-related issues concerns how to spe-cify the elements of Definition 1 in applications group G the typespace T and the reference group ndashG Take the specification of thegroup G and of the type space T Often the problem itself pro-vides a natural specification of these features This is the case inthe empirically important class of lsquolsquoclosedrsquorsquo questions such asthose used in surveys which provide respondents with a set ofalternatives as in the data we use in Section IV More generallythe problem solved by the DMmdashsuch as evaluating the resume ofa job applicant coming from a certain ethnic groupmdashprimes agroup a dimension of interest and a set of types (eg the appli-cantrsquos qualification or skill levels) When types have a naturalorder such as income age or education the granularity of T isalso naturally given by the problem (income age and years ofschooling brackets) When the set of types is not specified by theproblem DMs spontaneously generate one14 It would be useful tohave a model of which dimensions and types come to mind par-ticularly for more open-ended problems Psychologists have

14 For example suppose a person is asked to guess the typical occupation of ademocratic voter in an lsquolsquoopen-endedrsquorsquo format (without being provided a set of alter-natives) Here the level of granularity at which types are defined is not obvious (egteacher versus a university teacher vs a professor of comparative literature)

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sought to construct a theory of natural types and dimensions(Rosch 1973) We do not make a contribution to this problembut we note that in many problems of interest in economics thedimension as well as the set of types is naturally givenFurthermore in our model details of the type space can be impor-tant under rank-based truncation but they matter less undersmooth discounting

Consider finally the role of the comparison group ndashG Thisgroup captures the context in which a stereotype is formed andagain is often implied by the problem when G = Floridians ndashG =rest of US population when G = African Americans ndashG = whiteAmericans A distinctive prediction of our model confirmed byour experiments in Section IVA is that the stereotype for agiven group G depends on the comparison group ndashG15 WhenndashG is not pinned down by the problem itself to derive testablepredictions from representativeness we set G frac14 nG where

is the natural population over which the unconditional distribu-tion of types is measured

III Properties of Stereotypes

We now study stereotypical beliefs and their accuracy Toillustrate the role of representativeness we first ask to whatextent the most representative type is a good fit for the groupnamely whether it is modal Next we assess the accuracy of theentire stereotypical distribution To do so we focus on a cardinaltypes and compare the stereotypersquos mean and variance to the trueones

15 Some empirical papers have taken a similar approach exogenously varyingthe natural comparison group through priming Benjamin Choi and Strickland(2010) show that priming racial or ethnic identity can affect the risk preferences ofparticipants Chen et al (2014) find that Asian students cooperate less with out-group members when primed with their ethnic identity rather than their universityidentity Shih Pittinsky and Ambady (1999) show that Asian American womenstereotype themselves as better or worse in math with corresponding impact onperformance when their ethnicity or gender respectively is primed ShihPittinsky and Trahan (2006) replicate this effect using a verbal task documentingthat Asian American women performed better when their gender rather than theirethnicity was primed Although the generalizability and replicability of priminghas been doubted (Klein et al 2014) this body of evidence is consistent with contextdependence

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IIIA Likely versus Unlikely Exemplars

The most representative type for a group is the one thatagents most easily recall and associate with the group itself forinstance a red-haired Irishman or a 65+-year-old FloridianSocial psychologists call this type the exemplar of the groupAccordingly we define

DEFINITION 3 A type t is an exemplar for G given comparisongroup ndashG when

t 2 arg maxt

tG

tG

Under any specification of the weighting function ht inDefinition 2 overweighting (weakly) increases as we movetoward more representative types so the exemplar is also thetype whose probability is overweighted the most16 By analyzingthe exemplar then we can gauge whether representativenessinduces the DM to overweight a likely type (as happens in stan-dard models of categorical thinking) or an unlikely type Whenoverweighting occurs in unlikely and extreme types the biases ofstereotypes can be particularly severe17

Equation (2) yields the following characterization

PROPOSITION 1 Suppose the conditional distributions G and G

are not identical Consider two extreme cases

(i) If for all t t0

2 T we have that tG gt t0 G if and only iftG gt t0 G then the modal type is not an exemplar forat least one group

(ii) If for all t t0

2 T we have that tG gt t0 G if and only iftG lt t0 G then for each group the modal type is theexemplar

16 Consider the function hethTHORN from Definition 2 When applied to more repre-sentative types the first argument of the function increases while one of the otherT ndash 1 arguments decreases As a result the weighting factor ht (and thus overweigh-ing

sttG

tG) increases as well

17 In the rank-based truncation model the frequency of the exemplar providesa measure of stereotype accuracy By accuracy we mean the extent to which thestereotype minimizes the distance

Pt eth

sttG tGTHORN

2 When d = 1 and only one type isrecalled (there are no ties) accuracy is maximized if the exemplar is the most likelytype and minimized if the exemplar is the least likely type

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Case i says that when groups have similar distributions inthe sense of having the same likelihood ranking the most repre-sentative type is unlikely for at least one group potentially bothRepresentativeness draws the DMrsquos attention to group differ-ences neglecting the fact that the groups are similar and havethe same mode This mechanism generates inaccurate stereo-types and is illustrated by the Florida example This resultholds under any measure of representativeness that differenti-ates the two groups (eg the difference tG tG)

Case ii says that the most representative type tends to belikely for both groups when the distributions are very differentIn this case groups differ the most around their modes so repre-sentativeness and likelihood coincide Thinking of Swedes aslsquolsquoblondrsquorsquo and Europeans as lsquolsquodark hairedrsquorsquo is accurate precisely be-cause these are majority traits of the Swedish and European pop-ulations respectively In these cases stereotyping yields fairlyreliable models Of course there is still some inaccuracy Evenin the case of likely exemplars judgment errors can be signifi-cant For instance voters in some US states are perceived aslsquolsquobluersquorsquo or lsquolsquoredrsquorsquo because a majority of the population votesDemocrat or Republican In reality even in lsquolsquobluersquorsquo states farfrom everyone votes Democrat In the 2012 presidential electionvote shares of either candidate in most states ranged from 40 to6018

When DMs strongly overweight representative types themost severe biases occur when those types are unlikely and ex-treme This is true both under rank based truncations and undersmooth discounting functions (see Section IIIB) Ethnic stereo-types based on crime or terrorism exhibit this error they neglectthe fact that by far the most common types in all groups arehonest and peaceful

IIIB Stereotypical Moments

We now characterize how the first two moments of a distri-bution are distorted by the process of stereotyping To do so wemust restrict our analysis to cardinal ordered types The follow-ing results hold for any weighting function htethTHORN satisfyingDefinition 2 We consider two canonical cases that prove usefulin illustrating the predictions of the model

18 Presidential Election Results NBCNewscom see httpelectionsnbcnewscomnspolitics2012allpresident (accessed 5 September 2016)

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In the first case groups G and ndashG are such that the likelihoodratio tG

tGis monotonic in t The monotone likelihood ratio prop-

erty (MLRP) holds to a first approximation in many empiricalsettings and is also assumed in many economic models such asstandard agency models19 If tG

tGis monotonically increasing (de-

creasing) in t then group G is associated with higher (lower)values of t relative to the comparison group ndashG Formally

PROPOSITION 2 Suppose that MLRP holds and assume wlogthat the likelihood ratio tG

tGis strictly increasing in t Then

for any weighting function htethTHORN that is not constant in therelevant range

EstethtjGTHORN gt EethtjGTHORN gt EethtjGTHORN gt E

stethtjGTHORN

Under MLRP the most representative part of the distribu-tion for G is the right tail if tG

tGincreases in t or the left tail if tG

tG

decreases in t The representative tail is then overweighted whilethe nonrepresentative tail is underweighted As a consequencethe assessed mean E

stethtjGTHORN is too extreme in the direction of therepresentative tail

Critically in line with the social cognition perspective the ste-reotype contains a kernel of truth the DM overestimates the meanof G if this group has a higher mean than the comparison groupnamely EethtjGTHORN gt EethtjGTHORN and conversely if EethtjGTHORN lt EethtjGTHORN TheDM exaggerates this true difference because he inflates the asso-ciation of G with its most representative types20 For instancewhen judging an asset manager who performs well we tend to

19 Examples include the binomial and the Poisson families of distributionswith different parameters The characterization of distributions satisfying MLRPis easier in the case of continuous distributions (see Online Appendix D) two dis-tributions f(x) f ethx THORN that differ only in their mean satisfy MLRP if and only if thedistribution f(x) is log-concave Examples include the exponential and normal dis-tributions To the extent that discrete distributions sufficiently approximate thesedistributions (as the Poisson distribution PoisethTHORN approximates the normal distri-bution Neth THORN for large l) they will also satisfy MLRP

20 Depending on the distribution and the weighing function the DMrsquos assess-ment of the variance VarethtjGTHORNmay also be dampened relative to the truth This isoften true under the truncation weighing function In this case stereotyping effec-tively leads to a form of overconfidence in which the DM holds extreme views andoverestimates the precision of his assessment That extreme views and overconfi-dence (in the sense of over precision) go together has been documented in the settingof political ideology among others (Ortoleva and Snowberg 2015)

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overemphasize skill relative to luck because higher skill levels arerelatively more associated with higher performance This occurseven if for both skilled and unskilled managers high performanceis mostly due to luck

In the second case for which we characterize the stereotypi-cal distributions groups G and ndashG have the same mean EethtjGTHORNfrac14 EethtjGTHORN frac14 EethtTHORN but differ in their variance We abstract fromskewness and higher moments by considering distributionsethtGTHORNt2T and ethtGTHORNt2T that share the same support and are sym-metric around the medianmean EethtTHORN

PROPOSITION 3 Suppose that in G more extreme types are rela-tively more frequent than in ndashG Formally the likelihoodratio tG

tGis U-shaped in t around EethtTHORN Then for any weight-

ing function htethTHORN that is not constant in the relevant rangestereotypical beliefs satisfy

VarstethtjGTHORN gt VarethtjGTHORN gt VarethtjGTHORN gt VarstethtjGTHORN

EstethtjGTHORN frac14 E

stethtjGTHORN frac14 EethtTHORN

When group G has a higher relative prevalence of extremetypes its representative types are located at both extremes of thedistribution The DMrsquos beliefs about G are then formed by over-weighting both tails while underweighting the unrepresentativemiddle The overweighting of Grsquos tails causes the assessment ofits variance VarstethtjGTHORN to be too high For example the skill dis-tribution of immigrants to the United States may be perceived ashaving very fat tails or even bimodal with immigrants beingperceived as either unskilled or very skilled relative to the resi-dent population The mean of the group in contrast is assessedcorrectly because the stereotypical distribution remains symmet-ric around EethtTHORN As before the stereotype contains a kernel oftruth It induces the agent to exaggerate the true differences be-tween groups namely the higher variance of G relative to itscounterpart

We present a number of extensions of the model in the OnlineAppendix We first consider multidimensional type spaces andshow that stereotypes center around the dimension wheregroups differ the most in line with the kernel of truth logic(Online Appendix C) Multidimensional stereotypes imply thatthe dimension we think about is influenced by context For

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example the Irish are stereotyped as red-haired when comparedwith the European population However when compared withthe Scots a more plausible stereotype for the Irish is lsquolsquoCatholicrsquorsquobecause religion is the dimension along which Irish and Scotsdiffer the most

In Online Appendix D we extend the model to continuoustype spaces Many settings of interest in economics can be use-fully described by continuous probability distributions and weshow our model is particularly tractable in this case In OnlineAppendix E we relax Definition 2 and allow weighting of types toalso be influenced by their likelihood We show that the basicinsight that stereotypes contain a kernel of truth carries throughto these cases as well

To summarize the psychology of representativeness yieldsstereotypes that are consistent with the social cognition approachin which individuals assess groups by recalling and focusing ondistinctive group traits When there are systematic differencesbetween groups stereotypes get the direction right but exagger-ate differences

IIIC Some Examples

A growing body of field and experimental evidence points to awidespread belief that women are worse than men at mathemat-ics (Eccles Jacobs and Harold 1990 Guiso et al 2008 CarrellPage and West 2010) This belief persists despite the fact that fordecades women have been gaining ground in average schoolgrades including mathematics and have recently surpassedmen in overall school performance (Goldin Katz and Kuziemko2006 Hyde et al 2008) This belief shared by men and women(Reuben Sapienza and Zingales 2014) may help account for thegender gap in the choices of high school tracks college degreesand careers with women disproportionately choosing humanitiesand health-related areas (Weinberger 2005 Buser Niederle andOosterbeek 2014) and forgoing significant wage premiums toquantitative skills (Bertrand 2011)

Gender stereotypes in mathematics particularly beliefs thatexaggerate the extent of average differences are consistent withthe predictions of our model The fact that men are overrepre-sented at the very highest performance levels leads a stereotyp-ical thinker to exaggerate the magnitude of mean differencesFigure I shows the score distributions from the mathematics

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section of 2013rsquos Scholastic Aptitude Test (SAT) for men andwomen21 The distributions are very similar with averagescores slightly higher for men (531 versus 499 out of 800)However scores for men have a heavier right tail with mentwice as likely to have a perfect SAT math score than women22

In light of such data the stereotypical male performance in math-ematics is high while the stereotypical female performance ispoor Predictions based on such stereotypes are inaccurate exag-gerating true differences Consistent with this prediction exper-imental evidence shows that both genders underestimatewomenrsquos ability in simple math tasks even controlling for pastperformance (Reuben Sapienza and Zingales 2014) Coffman(2014) shows a similar pattern extends to confidence about ownability in other male-typed domains with women reporting sig-nificantly less confidence in gender-incongruent than gender-congruent tasks Our model suggests that these patterns mightcome from stereotypes based on gender differences in the righttail of the distribution While differences in the right tail of thedistribution are unlikely to be relevant for most decisions stereo-typical thinking driven by these differences has the potential toimpact economically important decisions whether through self-stereotyping (ie choice of careers or majors as in BuserNiederle and Oosterbeek 2014) or through discrimination (iehiring decisions as in Bohnet van Geen and Bazerman 2016)

The logic of exaggerated yet directionally correct stereotypesalso sheds light on the well-documented phenomenon of base rateneglect (Kahneman and Tversky 1973) Indeed Proposition 2implies that the DM overreacts to information that assigns

21 Standardized test performance measures not only innate ability but alsoeffort and investment by third parties (Hyde et al 2008) The mapping of test per-formance into inferences about innate ability is an issue not addressed by ourmodel

22 For 2013 SAT Mathematics scores see httpmediacollegeboardcomdigitalServicespdfresearchSAT-Percentile-Ranks-By-Gender-Ethnicity-2013pdf Results are similar for the National Assessment of Educational Progress(NAEP) which are more representative of the overall population For 2012NAEP scores for 17-year-olds in mathematics see httpnationsreportcardgovltt_2012age17maspx See Hyde et al (2008) Fryer and Levitt (2010) and Popeand Sydnor (2010) for in-depth empirical analyses of the gender gap inmathematics

STEREOTYPES 1773

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people to groups precisely because such information generatesextreme stereotypes Consider the classic example in which amedical test for a particular disease with a 5 prevalence has a90 rate of true positives and a 5 rate of false positives The testassigns each person to one of two groups + (positive test) or ndash(negative test) The DM estimates the frequency of the sick type(s) and the healthy type (h) in each group The test is informativea positive result increases the relative likelihood of sickness anda negative result increases the relative likelihood of health forany prior Formally

PreththornjsTHORN

PreththornjhTHORNgt 1 gt

PrethjsTHORN

PrethjhTHORNeth4THORN

This condition has clear implications the representative personwho tests positive is sick while the representative person whotests negative is healthy Following Proposition 2 the DMreacts to the test by moving his priors too far in the right di-rection generating extreme stereotypes He greatly boosts hisassessment that a positively tested person is sick but also thata negatively tested person is healthy Because most people arehealthy the DMrsquos assessment about the group that tested neg-ative is fairly accurate but is severely biased for the group that

FIGURE I

SAT Mathematics Scores by Gender (2013)

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tested positive This analysis formalizes Tversky andKahnemanrsquos (1983) verbal account of base rate neglect23

The same mechanism may underlie several other instanceswhere DMs overweight diagnostic information When assessingan employeersquos skill level an employer attributes high perfor-mance to high skill because high performance is the distinctivemark of a talented employee Because he neglects the possibilitythat some talented employees perform poorly and that somenontalented ones perform well (perhaps due to stochasticity inthe environment) the employer has too much faith in skill andneglects the role of luck in accounting for the output Similarlywhen assessing the performance of firms in a hot sector of theeconomy (eg G = internet) an investor recalls highly successfulfirms in that sector (t = return of Google Amazon etc) He ne-glects the possibility of firms being unsuccessful because lack ofsuccess is statistically nondiagnostic and psychologically nonrep-resentative of a growing sectormdasheven if it is likely This causesexcessive optimism (in that the expectation of growth is unrea-sonably high) and overconfidence (in that the variability in earn-ings growth considered possible is truncated) True the hot sectormay have better growth opportunities on average but represen-tativeness exaggerates this feature and induces the investor toneglect a significant risk of failure

IV Evidence on Representativeness and Stereotypes

Testing our model requires evaluating the beliefs individualshold about a target group against the true distribution of thattarget group over an attribute space An ideal data set would

23 Our account is distinct from a mechanical underweighting of base rates inBayes rule as in Grether (1980) and Bodoh-Creed Benjamin and Rabin (2013) Inthose models upon receiving the test results the DM can update his beliefs in thewrong direction he can be less confident that a person is healthy after a negativetest than under his prior which cannot happen in our model Although this predic-tion of our model seems consistent with introspection we are not aware of experi-mental evidence on this point Griffin and Tversky (1992) present evidenceconsistent with pure neglect of base rates but in a significantly different tasknamely inferring the bias of a coin from a history of coin flips Such experimentsare hard to compare with the predictions of our model because subjects are asked togenerate distributions of different numbers of coin flips in their minds which is amuch more involved task than to recall types of a given distribution Their assess-ments then might be wrong for other reasons See Bodoh-Creed Benjamin andRabin (2013) for a detailed discussion

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consist of naturally defined groups with known distributions overa given space of types and a corresponding set of beliefs about thedistribution of each group over that space of types This wouldallow us to test for exaggeration of true differences betweengroups and to ask whether this exaggeration is well predictedby overweighting representative types To identify a causal rolefor representativeness or context dependence we would need ex-ogenous variation in either the comparison group ndashG or in thedistributions over the type spaces This is unavailable in existingdata sets Accordingly we take a two-pronged approach First wecreate a controlled laboratory environment that allows us toinduce the exogenous variation in representative types that weneed to test causality then we reanalyze existing field evidence tocheck for consistency with our predictions

In testing our model we focus on the two main implicationsof representativeness-based stereotypes

Context dependence the stereotype of a target group de-pends on the characteristics of the reference group it iscompared to

Kernel of truth stereotypes depend on group character-istics andmdashin most (precisely characterized) settingsmdashare slanted toward representative types

We test the first property with a lab experiment (SectionIVA) We then turn to survey data on beliefs about US politicalgroups (Section IVB) for an empirical analysis that explores thesecond property The survey data are more tightly linked to ourinterest in social stereotypes The laboratory experiment allowsus to directly test the role of representativeness in generatingcontext dependent beliefs Online Appendixes F and G provideall details and additional results for the experiments and fieldevidence

IVA Lab Evidence on Representativeness and ContextDependence

The influence of the representativeness heuristic on recalland on beliefs has been extensively documented in the lab(Kahneman and Tversky 1972 1973) Our goal is to considerhow representativeness as formalized in equation (2) gives riseto context-dependent beliefs To our knowledge the possibility

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that representativeness may generate context dependence hasnot been tested before

To assess this prediction we perform a controlled laboratoryexperiment that allows us to isolate representativeness frommany confounding factorsmdashhistorical sociological or other-wisemdashthat may affect stereotype formation in the real worldWe construct our own groups of ordinary objects creating atarget group G and a comparison group ndashG We hold thetarget group G fixed and explore how participant impressions ofit change as we change the comparison group ndashG and thusrepresentativeness

We conducted several experiments in the laboratory and onAmazon Mechanical Turk Each involves a basic three-stepdesign First participants are shown the target group and a ran-domly assigned comparison group for 15 seconds In this timedifferences between groups can be noticed but the groupsrsquo precisecompositions cannot be memorized The second step consists of afew filler questions which briefly draw the participantsrsquo cognitivebandwidth away from their observation Finally participants areasked to assess the groups they saw Participants are incentiv-ized to provide accurate answers

We randomly assign participants to either the Control or theRepresentativeness condition In the Control condition G and ndashGhave nearly identical distributions so that all types are similarlyrepresentative for each group In the Representativeness condi-tion ndashG is changed in such a way that a certain type becomes veryrepresentative for G Context dependence implies that the assess-ment of G should now overweight this representative type eventhough the distribution of G itself has not changed

We ran six experiments of this form with design changesfocused on reducing participant confusion and removing con-founds We describe the final and most refined version of theseexperiments here In an attempt to provide a overview of the re-sults while remaining concise we provide the results from pooledspecifications that use all data collected In Online Appendix Fwe offer additional details and report all experiments conductedWe also give instructions and materials for each experiment thefull data set is available by request

Consider first the experiment illustrated in Figure II Agroup of 25 cartoon girls is presented next to a group of 25 cartoonboys in T-shirts of different colors blue green or purple In theControl condition (Figure II Panel a) the groups have identical

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color distributions (13 purple 12 green) so no color is represen-tative of either group The Representativeness condition (Panel b)compares the same group of girls with a different group of boysfor whom green shirts are replaced with blue shirts Now onlygirls wear green and only boys wear blue These colors althoughstill not the most frequent for either group are now most repre-sentative For each group girls and boys participants are asked anumber of questions concerning the frequency of T-shirts of dif-ferent colors worn by that group

Applying our model in the control condition the type space isT frac14 fgreen purpleg and the groups are G = girls and ndashG = boysGiven that the color distributions are identical across groups both

types are equally representativegreengirls

greenboysfrac14 1 frac14

purplegirls

purpleboys As a result

assessment of G should be correct on average stcontrolgreengirls frac14 greengirls

and stcontrolpurplegirls frac14 purplegirls for any weighing function (the same is

true about assessments of ndashG)In the treatment condition the distribution of shirt colors re-

mains the same for girls For boys green shirts are changed intoblue Thus the type space changes to T frac14 fgreen purple bluegand the representative color for girls becomes greengreengirls

greenboysfrac14 1 gt 1 frac14

purplegirls

purpleboys while that for boys becomes blue As

a result in the treatment condition subjects should inflate the

frequency of green shirts relative to the truth sttreatmentgreengirls

gt greengirls (the same should happen to assessments of blueshirts for boys) We also expect the assessed frequency of greenshirts to go up relative to the control condition namely

sttreatmentgreengirls gt stcontrol

greengirls Critically the only factor that varies

across treatments is the representativeness of the 12-colorshirt Thus if we see differences across conditions the causalrole of representativeness-based recall in shaping group judg-ments is clear24

24 We vary which colors are used in which roles across participants Someparticipants saw this particular color distribution while others see for examplegreen as the modal color and purple as the diagnostic color for boys in theRepresentativeness condition and blue as the diagnostic color for girls in theRepresentativeness condition We vary the colors across the roles to avoid con-founding the characteristics of any particular color with its diagnosticity

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FIG

UR

EII

T-S

hir

tsE

xp

erim

ent

Fig

ure

sap

pea

red

inco

lor

top

art

icip

an

tsin

the

exp

erim

ent

For

clari

ty

we

have

ad

ded

ale

tter

toea

chT

-sh

irt

toid

enti

fyth

eco

lor

for

the

read

er

lsquolsquoGrsquorsquo

ind

icate

sgre

en

lsquolsquoPrsquorsquo

ind

icate

sp

urp

le

lsquolsquoBrsquorsquo

ind

icate

sblu

eT

hes

ele

tter

sd

idn

otap

pea

rto

part

icip

an

tsan

dare

for

read

erre

fere

nce

only

P

lease

see

onli

ne

ver

sion

ofp

ubli

shed

art

icle

for

colo

rfi

gu

reex

act

lyas

itap

pea

red

top

art

icip

an

ts

STEREOTYPES 1779

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We collected data from 301 participants using this T-shirtsdesign25 Since the number of green and purple shirts is verysimilar we first ask each participant the simplest question ofwhich shirt color is modal Next we ask participants to assessthe share of green and purple shirts

Consistent with the role of representativeness participantsassigned to the Representativeness condition are 105 percentagepoints more likely to recall the less frequent color (green for girlsor blue for boys) as the modal color when it is representative of agroup (35 of participants guess the less frequent color is modalin the Control condition this proportion increases to 46 in theRepresentativeness condition p = 01 estimated from a probitregression reported in Online Appendix F)

We now turn to subjectsrsquo estimates of how many T-shirts ofeach color they saw in each group In both conditions the truedifference in counts is 1 (13 purple shirts 12 green or blue shirts)In the Control condition participants on average believe they saw054 more purple shirts than green or blue shirts In theRepresentativeness condition participants believe they saw072 fewer purple shirts than green or blue shirts (the acrosstreatment difference is significant with p = 01 from OLS regres-sion reported in Online Appendix F)

In total we collected data for six experiments of this generalstructure gathering evidence from more than 1000 participantsAs we describe in Online Appendix F although there is substan-tial variation across experiments when we pool all of the data wefind significant aggregate treatment effects in line with a role ofrepresentativeness in judgment We employ four different unor-dered types designs similar to the T-shirts experiment using sixsamples (four online and two in the laboratory) with 741 partic-ipants We find effects in the predicted direction for five of the sixsamples Using a probit regression that pools the data for theseunordered type experiments we find that participants are 93 per-centage points more likely to guess that the less frequent type ismodal when it is representative than when it is not (p = 002) Wealso run a family of ordered types experiments (two designs fivesamples 402 participants) Unlike the simpler T-shirts style

25 Throughout our analysis we exclude any participant who participated in aprevious version of the experiment and any participant who self-identified as color-blind In Online Appendix F we show that our results are unchanged if we includethese additional observations

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design the theoretical predictions for the ordered types designsare more sensitive to the specific assumptions one makes aboutthe weighting function of the DM26 We find effects in the pre-dicted direction for three of the five samples As we discuss inmore detail in Online Appendix F the ordered types resultsvary by platform with consistently stronger results on AmazonMechanical Turk than in the laboratory samples Pooling all or-dered types experiments participants are 93 percentage pointsmore likely to guess that the group of interest has a greater av-erage than the comparison group when the right tail is represen-tative (p = 062) Given our simple experimental setting withgroups of mundane objects we interpret our resultsmdasha signifi-cant and reasonably sized impact on average beliefsmdashas an im-portant proof of concept the presence of representative typesbiases ex post assessment

IVB Empirical Evidence on Political Stereotypes

We examine two data sets on political preferences and be-liefs about political preferences in the United States We inves-tigate the roles of representativeness and context dependence byseparately testing for hypotheses that allow us to assess the lead-ing theories of stereotypes

First we test whether beliefs are correct or depart systemat-ically from the truth The statistical discrimination approachbuilds on the assumption that people hold rational expectationsof group traits Comparing beliefs to the truth allows us to assessthe validity of this assumption in our data

Second we test if beliefs depart from the truth by exagger-ating (mean) differences among groups per the kernel of truthhypothesis This is an implicit test of context dependence be-cause it implies that beliefs about the target groups are shapednot only by that grouprsquos characteristics but also by those of thereference group27

Third we test if distortions in beliefs can be accounted for bythe overweighting of highly representative types (defined astypes that are relatively more frequent in the target relative to

26 This is due in part to our choice to not study MLRP distributions We moti-vate and discuss this design decision in Online Appendix F

27 Of course unlike in the laboratory experiment in this setting we cannot testfor context dependence by exogenously varying the reference group

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the reference group) The second and third tests address the keypredictions of our model

1 The Data We have two data sets on political preferences andbeliefs about political preferences The first data set from GrahamNosek and Haidt (GNH 2012) contains data from the MoralFoundations Questionnaire Respondents (1174 self-identified lib-erals and 500 self-identified conservatives) answer questions abouttheir position on a subset of 45 issues 20 moral relevance state-ments (eg lsquolsquowhen you decide whether something is right orwrong to what extent are the following considerations relevantto your thinkingrsquorsquo) and 25 moral judgments (eg lsquolsquoindicate theextent to which you would agree or disagreersquorsquo) For each issue arandomly determined subset of participants states their own posi-tion another subset states their belief on the position of a lsquolsquotypicalliberalrsquorsquo and a third subset states their belief on the position of alsquolsquotypical conservativersquorsquo The data thus include the distribution overpositions for both liberal and conservatives as well as the averagebelieved typical position of liberals and of conservatives on the 45issues Each position is elicited on 1ndash6 scale

The second data set comes from the American NationalElection Survey (ANES) and contains data from more than20000 respondents between 1964 and 201228 The surveycovers political issues of the day such as the optimal amount ofgovernment spending and service provision (1984ndash2000) or theplace of women in society (1972ndash1998) We focus on the 10 issuesthat ask participants to respond on a 1ndash7 scale (rather than justindicate binary agreement or disagreement) all 10 issues areasked in multiple years Participants are asked to provide theirown position on the scale and their believed position of theDemocratic and Republican parties (lsquolsquoWhere would you placethe Democratic [Republican] party on this scalersquorsquo) The data in-clude for each issue-year observation the distribution of partic-ipant positions for self-identified liberals and self-identifiedconservatives as well as the distribution of believed typical posi-tions of the Democratic and Republican parties

28 These data are publicly available at httpwwwelectionstudiesorgstudy-pagesanes_timeseries_cdfanes_timeseries_cdfhtm

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2 Empirical Strategy Our analysis focuses on beliefs abouttwo groups Conservatives and Liberals The types are the possi-ble positions for each issue (1 2 6 7) For the GNH data weinterpret beliefs about the lsquolsquotypicalrsquorsquo element of a group to coincidewith the believed average position in that group Similarly forthe ANES data we use the believed party positions as a proxy forbelieved mean of each group29 We then take as a benchmark thehypothesis that individuals hold accurate beliefs about eachgroup and in particular that believed mean position shouldequal true mean position at least on average across subjectsThe accurate beliefs hypothesis underlies the most common eco-nomic model of stereotyping statistical discrimination

To assess our representativeness-based model we perform aregression exercise To test our model in a linear regressionframework we rely on linear approximations of the weightingfunction Our model then yields two regression specifications

PROPOSITION 4 Let G 2 fconservative liberal g and assume

ht h tG

tG

be a differentiable and strictly increasing weight-

ing function as in Definition 2 The following hold as a first-order approximation around identical distributions G

Gfrac14 1

(i) Kernel of truth regression There exists a constant gt 0such that

EstethtjGTHORN frac14 EethtjGTHORNeth1thorn THORN EethtjGTHORNeth5THORN

(ii) Representativeness regression Denote H frac14 fT 2 Tg

the right tail of types and RconsH frac14

PHtconsPHtlib

as the average

representativeness of right tail types for conservatives

29 This assumption is consistent with the authorsrsquo interpretation of the GNHdata (GNH 2012) and with previous studies using ANES (eg Westfall et al 2015)Furthermore to the extent that this assumption holds equally well for most issueswithin a data set our focus on cross-issue differences should allow us to test thepredictions of our model even with an imperfect proxy for beliefs of mean positionsFinally the data provide some insight into whether subjects are reporting (per-ceived) modal or mean types As we show the modal type is a poor prediction ofstated beliefs while a distorted mean slanted toward representative types is anaccurate prediction of stated beliefs

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Under the further approximation where tcons

tlibampRcons

H for

t 2 H

EstethtjconsTHORN frac14 EethtjconsTHORN thorn consethR

consH 1THORNeth6THORN

EstethtjlibTHORN frac14 EethtjlibTHORN libethR

consH 1THORNeth7THORN

where lcons and llib are positive constants

The first regression allows us to test for the kernel of truthhypothesis and the second set of regressions allows us to test forthe role of representativeness

Equation (5) says that respondents in our model inflate theaverage position of a group say the conservatives if and only ifthe group has a higher average position than the other groupnamely the liberals Formally EstethtjconsTHORN gt EethtjconsTHORN if and onlyif EethtjconsTHORN gt EethtjlibTHORN Because in our measurement scale highertypes mean lsquolsquomore conservativersquorsquo we expect (i) believed conserva-tive average to be higher than the truth and (ii) the extent ofoverstatement to decrease in the average liberal position EethtjlibTHORNConversely we expect the average liberal position to be lowerthan the truth the more so the higher the average conservativeposition EethtjconsTHORN

As previously discussed the basis of these predictions is con-text dependence information about the distribution of ndashG is rel-evant for the beliefs about G This context dependence isinconsistent with rational expectations in which only thegrouprsquos own means should affect beliefs We test the hypothesisthat the true mean EethtjGTHORN is a significant predictor of the believedmean E

stethtjGTHORN with a positive sign and the other grouprsquos truemean EethtjGTHORN is a predictor of the believed mean with a negativesign

Equations (6) and (7) say that repondentsrsquo assessment bias isshaped by representativeness When the right tail is more repre-sentative for conservatives (Rcons

H 1 positive and large) partici-pants should inflate the average conservative position more(higher E

stethtjconsTHORN EethtjconsTHORN) and deflate the average liberal po-sition more (lower E

stethtjlibTHORN EethtjlibTHORN) We test the hypothesisthat the inflation in conservative positions is positively associatedwith the representativeness of the right tail for the conservativesand the inflation in liberal positions is negatively associated with

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it Once again the representativeness of the right tail is com-puted using the true distribution of positions

In equations (6) and (7) in many cases the representative tailis also the most likely one As a consequence these tests cannotdistinguish a representativeness-based from a likelihood-basedmodel of distorted beliefs We perform two additional testsFirst we run versions of equations (6) and (7) in which we controlfor the likelihood of tails (see Table A4 in Online Appendix G)Second we compute numerically the predictions of a representa-tiveness-based model of stereotypes and a likelihood-based modelof stereotypes We then assess which of these two is better able tomatch the data on beliefs

3 Empirical Results To begin we illustrate the structure ofthe data and the nature of our predictions with two simple exam-ples from the GNH data set focusing on beliefs about conserva-tives In example 1 participants are asked about their agreementwith the statement lsquolsquoIt can never be right to kill a human beingrsquorsquoIn example 2 participants are asked about the moral relevance oflsquolsquowhether or not someone cared for someone weak or vulnerablersquorsquoAs can be seen in Figure III in example 1 the modal position(strongly disagree (1)) and most representative positions(strongly disagree (1)) coincide for conservatives In contrast inexample 2 in Figure III the most representative types (slightlyrelevant (3) not at all relevant (1)) are not most likely for theconservative group Following Proposition 1 we predict that be-liefs will be distorted in the direction of the most representativetypes Thus we expect more exaggeration in example 2 than inexample 1 since in example 2 the most representative types (inthe left tail) are far from the modal type whereas in example 1they coincide This is what we find the conservative position isexaggerated by only 009 positions in Example 1 (true mean 299believed mean 290) but by 106 positions in Example 2 (truemean 421 believed mean 315)

In the full data sets we treat each (issue year) pair as anobservation and we cluster standard errors at the issue level Forthe GNH data we have 45 observations 45 issues measured inthe same year For the ANES data we have 66 observations 10issues measured in multiple years To begin we simply docu-ment systematic exaggeration in both data sets This is a primaryfocus of the original analysis in GNH (2012) and also in Westfall

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FIGURE III

Two Examples

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et al (2015)rsquos analysis of the ANES data30 Figure IV shows thatthe believed difference between typical conservative and typicalliberal positions is larger than the true difference in mean posi-tions for 109 of the 111 observations The data for both GNH(squares) and ANES (triangles) lie above the 45-degree line(dashed)31 Average exaggeration is 062 positions on the scale(066 in the GNH data 059 in the ANES data)32

The systematic and significant exaggeration of mean differ-ences suggests that the benchmark model of accurate beliefs ismissing something important Indeed this exaggeration reflectsthe fact that believed means are typically more extreme than truemeans First note that the kernel of truth regression (equation(5)) generates exaggeration of mean differences just as docu-mented in Figure IV

EstethtjGTHORN E

stethtjGTHORN frac14 eth1thorn 2THORN frac12EethtjGTHORN EethtjGTHORN

To bring this prediction to the data we regress the believedmean position for each group EBethtjGTHORN on the true mean of thegroup EethtjGTHORN and the true mean of the comparison groupEethtjGTHORN across issues We do this for each group (liberals con-servatives) in each data set separately We also present pooledspecifications that combine the data sets to make a prediction fora given group (liberals conservatives) In these pooled specifica-tions we include a dummy variable indicating whether theobservation came from the ANES data set For all specificationswe cluster observations at the issue level33 The results from re-gression are shown in Table I In every specification we find thatEethtjGTHORN is a significant predictor of EBethtjGTHORN with the predicted pos-itive sign Crucially for five of the six specifications the mean of

30 Chambers and Melnyk (2006) also find evidence of exaggeration of truedifferences in beliefs about political positions

31 For convenience we recode all issues so that the high end of the scale (67)represents the stereotypically more conservative position

32 A natural question to ask is how beliefs vary across liberals and conserva-tives That is do beliefs about a group G depend on membership in G versus ndashG Ourmodel does not speak to this issue However in Online Appendix G we show thatthe results we document below hold for both beliefs held by conservatives and be-liefs held by liberals see Tables A9 A10 and A11

33 In general the results presented below for the ANES data are not largelyimpacted by the decision to cluster at the issue level Similar results are obtained ifthe data are not clustered

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the comparison group EethtjGTHORN is also a significant predictor ofE

BethtjGTHORN with the predicted negative signAlthough these results provide strong evidence of context

dependence and are consistent with our model they do not pindown a role for representativeness of types Our next test relatesthe magnitude of representativeness of tail types to the magni-tude of belief distortions

To this end we implement the regressions in equations (6)and (7) Following Proposition 4 we compute the average repre-

sentativeness of tail types for conservatives RconsH frac14

PtT2tconsPtT2tlib

We

again test the hypothesis that RconsH is a significant predictor of Est

ethtjconsTHORN with a positive sign and a predictor of EstethtjlibTHORN with a

negative sign Table II shows that conditional on true mean RconsH

predicts believed mean for each group G as expected The firstthree specifications display the results for predicting beliefs heldabout conservatives In both data sets the average representa-tiveness of tail types for conservatives is a significant positivepredictor of beliefs held about conservatives The final three spe-cifications display the results for predicting beliefs held about

FIGURE IV

Exaggeration of Differences

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liberals We find that the average representativeness of tail typesfor conservatives is a negative predictor of beliefs held about lib-erals This effect is significant in the GNH data and marginallysignificant in the ANES data

We present several additional results in Online Appendix GTo further examine the role of representativeness in driving be-liefs we first show the results of Table II carry through when we

TABLE II

AVERAGE REPRESENTATIVENESS OF TAIL POSITIONS PREDICTS BELIEFS

OLS Predicting Believed Mean of Group G for Each Issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position

of group G for issue

078 024 051 072 018 041

(006) (008) (009) (005) (005) (010)

Avg rep of tail types for

conservatives RconsH

019 055 025 014 012 024

(007) (022) (008) (006) (007) (005)

Constant 101 260 184 093 271 201

(026) (045) (029) (022) (025) (032)

R2 082 048 060 091 031 070

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

TABLE I

INFORMATION ABOUT ndashG PREDICTS BELIEFS ABOUT G

OLS predicting believed mean of group G for each issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position of

conservatives for issue

102 098 096 021 019 025

(0097) (0133) (0076) (0060) (0116) (0060)

True mean position of

liberals for issue

035 086 058 0987 039 073

(0106) (0134) (0131) (0066) (0106) (0135)

Constant 151 335 235 069 258 156

(0195) (0269) (0279) (0122) (0249) (0270)

R2 083 053 066 092 032 068

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

STEREOTYPES 1789

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control for the average likelihood on the tail positions (see Table A4in Online Appendix G) Most tellingly we use the model to predictbeliefs across issues and compare those to the data For simplicitywe use the rank-based truncation specification to predict mean be-liefs when stereotypes include the d most representative types ford frac14 1 T We compare these predictions to those of a model inwhich beliefs are obtained by restricting the distribution to the dmost likely types Our benchmark for both models is predicting thebelieved mean from the entire distribution where d = T We showthat the predictions of the rank-based truncation model with d = 4or 5 compare favorably to both a likelihood-based truncation model(with any d) and the accurate beliefs benchmark Interestingly thisresult suggests that stereotypical beliefs are well approximated byneglecting the least representative types (as opposed to focusingonly on the most representative types) and so represent a moderatethough systematic departure from the standard benchmarkFinally we show that the results we document above hold forboth beliefs held by conservatives and beliefs held by liberals (seeTables A9 A10 and A11 in Online Appendix G)

V Conclusion

We present a model of stereotypical thinking in which DMsmaking predictions about a group overweight the grouprsquos mostdistinctive types These overweighted types are not the mostlikely ones given the DMrsquos data but the most representativeones in the sense of being the most diagnostic of the group rela-tive to other groups Representativeness implies that what ismost distinctive of a group depends on what group it is comparedwith We present experimental evidence that confirms this con-text dependence in recall-based assessments of groups Finallywe evaluated the predictions of the model using political data fromexisting large-scale surveys We find context dependence to be akey feature of beliefs Given the richness of the political data wecan go a step further and identify a role for representativeness inparticular As the representativeness of tail types increases beliefsof a group are distorted in the direction of that tail

Our approach provides a parsimonious and psychologicallyfounded account of how DMs generate simplified representationsof reality from social groups to stock returns and offers a unifiedaccount of disparate pieces of evidence relating to this type of

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uncertainty The model captures the central fact that stereotypeshighlight the greatest difference between groups thus explainingwhy some stereotypes are very accurate while others lack valid-ity Still stereotypes often have a kernel of truth when they arebased on systematicmdasheven if smallmdashdifferences between groupsThis logic allows us to describe a number of heuristics and psy-chological biases many of which arise in the context of predictionproblems Generically our model generates overreaction to diag-nostic information

Our model is based on representativeness and does not cap-ture all the features of stereotypical thinking However it cap-tures perhaps the central feature when we think of a group wefocus on what is most distinctive about it and neglect or under-weight the rest

Saeuroıd Business School University of Oxford

Ohio State University and Harvard Business School

Universita Bocconi and Innocenzo Gasparini Institute

for Economic Research

Harvard University

Supplementary Material

An Online Appendix for this article can be found at QJEonline (qjeoxfordjournalorg)

References

Adorno Theodor Else Frenkel-Brunswik Daniel Levinson and Nevitt SanfordThe Authoritarian Personality (New York Harper amp Row 1950)

Arrow Kenneth lsquolsquoThe Theory of Discriminationrsquorsquo in Discrimination in LaborMarkets Orley Ashenfelter and Albert Rees eds (Princeton NJPrinceton University Press 1973)

Ashton Michael and Victoria Esses lsquolsquoStereotype Accuracy Estimating theAcademic Performance of Ethnic Groupsrsquorsquo Personality and SocialPsychology Bulletin 25 (1999) 225ndash236

Barberis Nicholas Andrei Shleifer and Robert Vishny lsquolsquoA Model of InvestorSentimentrsquorsquo Journal of Financial Economics 49 (1998) 307ndash343

Bayer Sylvia lsquolsquoThe Accuracy of Academic Gender Stereotypesrsquorsquo Sex Roles 40(1999) 787ndash813

Benjamin Dan James Choi and Joshua Strickland lsquolsquoSocial Identity andPreferencesrsquorsquo American Economic Review 100 (2010) 1913ndash1928

Benjamin Dan Matthew Rabin and Collin Raymond lsquolsquoA Model of Non-Belief inthe Law of Large Numbersrsquorsquo Journal of the European Economic Association15 (2015) 515ndash544

Bertrand Marianne lsquolsquoNew Perspectives on Genderrsquorsquo Handbook of LaborEconomics 4 (2011) 1543ndash1590

Bodoh-Creed Aaron Dan Benjamin and Matthew Rabin lsquolsquoThe Dynamics of Base-Rate Neglectrsquorsquo mimeo Haas Business School 2013

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Bohnet Iris Alexandra van Geen and Max Bazerman lsquolsquoWhen PerformanceTrumps Gender Bias Joint versus Separate Evaluationrsquorsquo ManagementScience 5 (2016) 1225ndash1234

Bordalo Pedro Nicola Gennaioli and Andrei Shleifer lsquolsquoSalience Theory of Choiceunder Riskrsquorsquo Quarterly Journal of Economics 127 (2012) 1243ndash1285

mdashmdashmdash lsquolsquoSalience and Consumer Choicersquorsquo Journal of Political Economy 121(2013) 803ndash843

Briton Nancy and Judith Hall lsquolsquoBeliefs about Female and Male NonverbalCommunicationrsquorsquo Sex Roles 32 (1995) 79ndash90

Buser Thomas Muriel Niederle and Hessel Oosterbeek lsquolsquoGenderCompetitiveness and Career Choicesrsquorsquo Quarterly Journal of Economics 129(2014) 1409ndash1447

Carrell Scott Marianne Page and James West lsquolsquoSex and Science How ProfessorGender Perpetuates the Gender Gaprsquorsquo Quarterly Journal of Economics 125(2010) 1101ndash1144

Chambers John and Darya Melnyk lsquolsquoWhy Do I Hate Thee ConflictMisperceptions and Intergroup Mistrustrsquorsquo Personality and SocialPsychology Bulletin 32 (2006) 1295ndash1311

Chan Wayne Robert R McCrae Filip De Fruyt Lee Jussim CorinnaE Lockenhoff Marleen De Bolle Paul T Costa Jr Angelina R SutinAnu Realo Juri Allik Katsuharu Nakazato Yoshiko ShimonakaMartina Hrebıckova Sylvie Graf Michelle Yik Marina Brunner-SciarraNora Leibovich De Figueora Vanina Schmidt Chang-kyo Ahn Hyun-nie Ahn Maria E Aguilar-Vafaie Jerzy Siuta Barbara SzmigielskaThomas R Cain Janet T Crawford Khairul Anwar Mastor Jean-Pierre Rolland Florence Nansubuga Daniel R MiramontezVeronica Benet-Martınez Jerome Rossier Denis Bratko Iris MarusicJamin Halberstadt Mami Yamaguchi Goran Knezevic Thomas A MartinMirona Gheorghiu Peter B Smith Claudio Barbaranelli Lei WangJane Shakespeare-Finch Margarida P Lima Waldemar KlinkoszAndrzej Sekowski Lidia Alcalay Franco Simonetti Tatyana V AvdeyevaV S Pramila and Antonio Terracciano lsquolsquoStereotypes of Age Differences inPersonality Traits Universal and Accuratersquorsquo Journal of Personality andSocial Psychology 103 (2012) 1050ndash1066

Chen Yan Sherry Xin Liu Tracy Xiao and Margaret Shih lsquolsquoWhich Hat to WearImpact of Natural Identities on Coordination and Cooperationrsquorsquo Games andEconomic Behavior 84 (2014) 58ndash86

Coffman Katherine lsquolsquoEvidence on Self-Stereotyping and the Contribution ofIdeasrsquorsquo Quarterly Journal of Economics 129 (2014) 1625ndash1660

Cunningham Tom lsquolsquoComparisons and Choicersquorsquo mimeo Stockholm University2013

Diekman Amanda Alice Eagly and Patrick Kulesa lsquolsquoAccuracy and Bias in theStereotypes about the Social and Political Attitudes of Women and MenrsquorsquoJournal of Experimental Social Psychology 38 (2002) 268ndash282

Eccles Jacquelynne S Janis E Jacobs and Rena D Harold lsquolsquoGender RoleStereotypes Expectancy Effects and Parentsrsquo Socialization of GenderDifferencesrsquorsquo Journal of Social Issues 46 (1990) 183ndash201

Fryer Roland and Matthew Jackson lsquolsquoA Categorical Model of Cognition andBiased Decision-Makingrsquorsquo BE Journal of Theoretical Economics 8 (2008)1ndash42

Fryer Roland and Steven Levitt lsquolsquoAn Empirical Analysis of the Gender Gap inMathematicsrsquorsquo American Economic Journal Applied Economics 2 (2010)210ndash240

Gennaioli Nicola and Andrei Shleifer lsquolsquoWhat Comes to Mindrsquorsquo Quarterly Journalof Economics 125 (2010) 1399ndash1433

Gennaioli Nicola Andrei Shleifer and Robert Vishny lsquolsquoNeglected RisksFinancial Innovation and Financial Fragilityrsquorsquo Journal of FinancialEconomics 104 (2012) 452ndash468

Gilens Martin lsquolsquoRace and Poverty in America Public Misperceptions and theAmerican News Mediarsquorsquo Public Opinion Quarterly 60 (1996) 515ndash541

Glaeser Edward lsquolsquoThe Political Economy of Hatredrsquorsquo Quarterly Journal ofEconomics 120 (2005) 45ndash86

QUARTERLY JOURNAL OF ECONOMICS1792

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ibrary on October 28 2016

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ownloaded from

Glover Dyland Amanda Pallais and William Pariente lsquolsquoDiscrimination as a Self-Fulfilling Prophecy Evidence from French Grocery Storesrsquorsquo mimeo HarvardUniversity 2015

Goldin Claudia Lawrence Katz and Ilyana Kuziemko lsquolsquoThe Homecoming ofAmerican College Women The Reversal of the College Gender GaprsquorsquoJournal of Economic Perspectives 20 (2006) 133ndash156

Graham Jesse Brian Nosek and Jonathan Haidt lsquolsquoThe Moral Stereotypes ofLiberals and Conservatives Exaggeration of Differences across thePolitical Spectrumrsquorsquo PLoS One 7 (2012) 1ndash13

Grether David lsquolsquoBayes Rule as a Descriptive Model The RepresentativenessHeuristicrsquorsquo Quarterly Journal of Economics 95 (1980) 537ndash557

Griffin Dale and Amos Tversky lsquolsquoThe Weighing of Evidence and theDeterminants of Confidencersquorsquo Cognitive Psychology 24 (1992) 411ndash435

Guiso Luigi Ferdinando Monte Paola Sapienza and Luigi Zingales lsquolsquoCultureGender and Mathrsquorsquo Science 320 (2008) 1164ndash1165

Hilton James and William Von Hippel lsquolsquoStereotypesrsquorsquo Annual Review ofPsychology 47 (1996) 237ndash271

Hyde Janet Sara Lindberg Marcia Linn Amy Ellis and Caroline WilliamslsquolsquoGender Similarities Characterize Math Performancersquorsquo Science 321 (2008)494ndash495

Judd Charles and Bernardette Park lsquolsquoDefinition and Assessment of Accuracy inSocial Stereotypesrsquorsquo Psychological Review 100 (1993) 109ndash128

Jussim Lee Jarret Crawford Stephanie Anglin John Chambers Sean Stevensand Florette Cohen lsquolsquoStereotype Accuracy One of the Largest and MostReplicable Effects in All of Social Psychologyrsquorsquo in The Handbook ofPrejudice Stereotyping and Discrimination Todd Nelson ed (MahwahNJ Lawrence Erlbaum 2015)

Kahneman Daniel and Amos Tversky lsquolsquoSubjective Probability A Judgment ofRepresentativenessrsquorsquo Cognitive Psychology 3 (1972) 430ndash454

mdashmdashmdash lsquolsquoOn the Psychology of Predictionrsquorsquo Psychological Review 80 (1973) 237ndash251

Kaplowitz Stan Bradley Fisher and Clifford Broman lsquolsquoHow Accurate ArePerceptions of Social Statistics about Blacks and Whitesrsquorsquo Public OpinionQuarterly 67 (2003) 237ndash243

Kersten Daniel Pascal Mamassian and Alan Yuille lsquolsquoObject Perception asBayesian Inferencersquorsquo Annual Review of Psychology 55 (2004) 271ndash304

Klein Richard Kate A Ratliff Michelangelo Vianello Reginald B Adams JrStepan Bahnik Michael J Bernstein Konrad Bocian Mark J BrandtBeach Brooks Claudia Chloe Brumbaugh Zeynep CemalcilarJesse Chandler Winnee Cheong William E Davis Thierry DevosMatthew Eisner Natalia Frankowska David Furrow Elisa Maria GallianiFred Hasselman Joshua A Hicks James F Hovermale S Jane HuntJeffrey R Huntsinger Hans IJzerman Melissa-Sue John Jennifer A Joy-Gaba Heather Barry Kappes Lacy E Krueger Jaime Kurtz CarmelA Levitan Robyn Mallett Wendy L Morris Anthony J Nelson JasonA Nier Grant Packard Ronaldo Pilati Abraham M RutchickKathleen Schmidt Jeanine L Skorinko Robert Smith Troy G SteinerJustin Storbeck Lyn M Van Swol Donna Thompson Anna van rsquot VeerLeigh Ann Vaughn Marek Vranka Aaron Wichman Julie A Woodzickaand Brian A Nosek lsquolsquoInvestigating Variation in Replicability A ManyLabs Replication Projectrsquorsquo Social Psychology 45 (2014) 142ndash152

Lundberg Shelly and Richard Startz lsquolsquoPrivate Discrimination and SocialIntervention in Competitive Labor Marketsrsquorsquo American Economic Review73 (1983) 340ndash347

Madon Stephanie Max Guyll Kathy Aboufadel Eulices Montiel Alison SmithPolly Palumbo and Lee Jussim lsquolsquoEthnic and National Stereotypes ThePrinceton Trilogy Revisited and Revisedrsquorsquo Personality and SocialPsychological Bulletin 27 (2001) 996ndash1010

Martin Carol lsquolsquoA Ratio Measure of Sex Stereotypingrsquorsquo Journal of Personality andSocial Psychology 52 (1987) 489ndash499

STEREOTYPES 1793

at Harvard L

ibrary on October 28 2016

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McCauley Clark Krishna Thangavelu and Paul Rozin lsquolsquoSex Stereotyping ofOccupations in Relation to Television Representations and Census FactsrsquorsquoBasic and Applied Social Psychology 9 (1988) 197ndash212

Mullainathan Sendhil lsquolsquoThinking through Categoriesrsquorsquo mimeo HarvardUniversity 2002

Ortoleva Pietro and Erik Snowberg lsquolsquoOverconfidence in Political BehaviorrsquorsquoAmerican Economic Review 105 (2015) 504ndash535

Phelps Edmund lsquolsquoThe Statistical Theory of Racism and Sexismrsquorsquo AmericanEconomic Review 62 (1972) 659ndash661

Pope Devin and Justin Sydnor lsquolsquoGeographic Variation in the Gender Differencesin Test Scoresrsquorsquo Journal of Economic Perspectives 24 (2010) 95ndash108

Rabin Matthew lsquolsquoInference by Believers in the Law of Small NumbersrsquorsquoQuarterly Journal of Economics 117 (2002) 775ndash816

Rabin Matthew and Joel Schrag lsquolsquoFirst Impressions Matter A Model ofConfirmatory Biasrsquorsquo Quarterly Journal of Economics 114 (1999) 37ndash82

Rabin Matthew and Dimitri Vayanos lsquolsquoThe Gamblerrsquos and Hot-Hand FallaciesTheory and Applicationsrsquorsquo Review of Economic Studies 77 (2010) 730ndash778

Reuben Ernesto Paola Sapienza and Luigi Zingales lsquolsquoHow Stereotypes ImpairWomenrsquos Careers in Sciencersquorsquo Proceedings of the National Academy ofSciences 111 (2014) 4403ndash4408

Rosch Eleanor lsquolsquoNatural Categoriesrsquorsquo Cognitive Psychology 4 (1973) 328ndash350Ryan Carey S lsquolsquoAccuracy of Black and White College Studentsrsquo In-Group and

Out-Group Stereotypesrsquorsquo Personality and Social Psychology Bulletin 22(1996) 1114ndash1127

Schneider David The Psychology of Stereotyping (New York Guilford Press2004)

Schneider David Albert Hastorf and Phoebe Ellsworth Person Perception(Reading MA Addison-Wesley 1979)

Shih Margaret Todd Pittinsky and Nalini Ambady lsquolsquoStereotype SusceptibilityIdentity Salience and Shifts in Quantitative Performancersquorsquo PsychologicalScience 10 (1999) 80ndash83

Shih Margaret Todd Pittinsky and Amy Trahan lsquolsquoDomain-Specific Effects ofStereotypes on Performancersquorsquo Self and Identity 5 (2006) 1ndash14

Steele Claude Whistling Vivaldi How Stereotypes Affect Us and What We CanDo (New York Norton 2010)

Tenenbaum Joshua and Thomas Griffiths lsquolsquoThe Rational Basis ofRepresentativenessrsquorsquo 23rd Annual Conference of the Cognitive ScienceSociety (2001) 1036ndash1041

Tversky Amos and Daniel Kahneman lsquolsquoExtensional versus Intuitive ReasoningThe Conjunction Fallacy in Probability Judgmentrsquorsquo Psychological Review 90(1983) 293ndash315

Weinberger Catherin lsquolsquoIs the Science and Engineering Workforce Drawn fromthe Far Upper Tail of the Math Ability Distributionrsquorsquo mimeo UCSB 2005

Westfall Jacob Leaf Van Boven John Chambers and Charles Judd lsquolsquoPerceivingPolitical Polarization in the United States Party Identity Strength andAttitude Extremity Exacerbate the Perceived Partisan DividersquorsquoPsychological Science 10 (2015) 145ndash158

Wolsko Christopher Bernadette Park Charles Judd and Bernd WittenbrinklsquolsquoFraming Interethnic Ideology Effects of Multicultural and Color-BlindPerspectives on Judgments of Groups and Individualsrsquorsquo Journal ofPersonality and Social Psychology 78 (2000) 635ndash654

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Page 15: I. Introduction · uneducated at the beginning of the 20th century, and as high achievers at the beginning of the 21st (Madon et al. 2001). Social science has produced three broad

sought to construct a theory of natural types and dimensions(Rosch 1973) We do not make a contribution to this problembut we note that in many problems of interest in economics thedimension as well as the set of types is naturally givenFurthermore in our model details of the type space can be impor-tant under rank-based truncation but they matter less undersmooth discounting

Consider finally the role of the comparison group ndashG Thisgroup captures the context in which a stereotype is formed andagain is often implied by the problem when G = Floridians ndashG =rest of US population when G = African Americans ndashG = whiteAmericans A distinctive prediction of our model confirmed byour experiments in Section IVA is that the stereotype for agiven group G depends on the comparison group ndashG15 WhenndashG is not pinned down by the problem itself to derive testablepredictions from representativeness we set G frac14 nG where

is the natural population over which the unconditional distribu-tion of types is measured

III Properties of Stereotypes

We now study stereotypical beliefs and their accuracy Toillustrate the role of representativeness we first ask to whatextent the most representative type is a good fit for the groupnamely whether it is modal Next we assess the accuracy of theentire stereotypical distribution To do so we focus on a cardinaltypes and compare the stereotypersquos mean and variance to the trueones

15 Some empirical papers have taken a similar approach exogenously varyingthe natural comparison group through priming Benjamin Choi and Strickland(2010) show that priming racial or ethnic identity can affect the risk preferences ofparticipants Chen et al (2014) find that Asian students cooperate less with out-group members when primed with their ethnic identity rather than their universityidentity Shih Pittinsky and Ambady (1999) show that Asian American womenstereotype themselves as better or worse in math with corresponding impact onperformance when their ethnicity or gender respectively is primed ShihPittinsky and Trahan (2006) replicate this effect using a verbal task documentingthat Asian American women performed better when their gender rather than theirethnicity was primed Although the generalizability and replicability of priminghas been doubted (Klein et al 2014) this body of evidence is consistent with contextdependence

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IIIA Likely versus Unlikely Exemplars

The most representative type for a group is the one thatagents most easily recall and associate with the group itself forinstance a red-haired Irishman or a 65+-year-old FloridianSocial psychologists call this type the exemplar of the groupAccordingly we define

DEFINITION 3 A type t is an exemplar for G given comparisongroup ndashG when

t 2 arg maxt

tG

tG

Under any specification of the weighting function ht inDefinition 2 overweighting (weakly) increases as we movetoward more representative types so the exemplar is also thetype whose probability is overweighted the most16 By analyzingthe exemplar then we can gauge whether representativenessinduces the DM to overweight a likely type (as happens in stan-dard models of categorical thinking) or an unlikely type Whenoverweighting occurs in unlikely and extreme types the biases ofstereotypes can be particularly severe17

Equation (2) yields the following characterization

PROPOSITION 1 Suppose the conditional distributions G and G

are not identical Consider two extreme cases

(i) If for all t t0

2 T we have that tG gt t0 G if and only iftG gt t0 G then the modal type is not an exemplar forat least one group

(ii) If for all t t0

2 T we have that tG gt t0 G if and only iftG lt t0 G then for each group the modal type is theexemplar

16 Consider the function hethTHORN from Definition 2 When applied to more repre-sentative types the first argument of the function increases while one of the otherT ndash 1 arguments decreases As a result the weighting factor ht (and thus overweigh-ing

sttG

tG) increases as well

17 In the rank-based truncation model the frequency of the exemplar providesa measure of stereotype accuracy By accuracy we mean the extent to which thestereotype minimizes the distance

Pt eth

sttG tGTHORN

2 When d = 1 and only one type isrecalled (there are no ties) accuracy is maximized if the exemplar is the most likelytype and minimized if the exemplar is the least likely type

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Case i says that when groups have similar distributions inthe sense of having the same likelihood ranking the most repre-sentative type is unlikely for at least one group potentially bothRepresentativeness draws the DMrsquos attention to group differ-ences neglecting the fact that the groups are similar and havethe same mode This mechanism generates inaccurate stereo-types and is illustrated by the Florida example This resultholds under any measure of representativeness that differenti-ates the two groups (eg the difference tG tG)

Case ii says that the most representative type tends to belikely for both groups when the distributions are very differentIn this case groups differ the most around their modes so repre-sentativeness and likelihood coincide Thinking of Swedes aslsquolsquoblondrsquorsquo and Europeans as lsquolsquodark hairedrsquorsquo is accurate precisely be-cause these are majority traits of the Swedish and European pop-ulations respectively In these cases stereotyping yields fairlyreliable models Of course there is still some inaccuracy Evenin the case of likely exemplars judgment errors can be signifi-cant For instance voters in some US states are perceived aslsquolsquobluersquorsquo or lsquolsquoredrsquorsquo because a majority of the population votesDemocrat or Republican In reality even in lsquolsquobluersquorsquo states farfrom everyone votes Democrat In the 2012 presidential electionvote shares of either candidate in most states ranged from 40 to6018

When DMs strongly overweight representative types themost severe biases occur when those types are unlikely and ex-treme This is true both under rank based truncations and undersmooth discounting functions (see Section IIIB) Ethnic stereo-types based on crime or terrorism exhibit this error they neglectthe fact that by far the most common types in all groups arehonest and peaceful

IIIB Stereotypical Moments

We now characterize how the first two moments of a distri-bution are distorted by the process of stereotyping To do so wemust restrict our analysis to cardinal ordered types The follow-ing results hold for any weighting function htethTHORN satisfyingDefinition 2 We consider two canonical cases that prove usefulin illustrating the predictions of the model

18 Presidential Election Results NBCNewscom see httpelectionsnbcnewscomnspolitics2012allpresident (accessed 5 September 2016)

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In the first case groups G and ndashG are such that the likelihoodratio tG

tGis monotonic in t The monotone likelihood ratio prop-

erty (MLRP) holds to a first approximation in many empiricalsettings and is also assumed in many economic models such asstandard agency models19 If tG

tGis monotonically increasing (de-

creasing) in t then group G is associated with higher (lower)values of t relative to the comparison group ndashG Formally

PROPOSITION 2 Suppose that MLRP holds and assume wlogthat the likelihood ratio tG

tGis strictly increasing in t Then

for any weighting function htethTHORN that is not constant in therelevant range

EstethtjGTHORN gt EethtjGTHORN gt EethtjGTHORN gt E

stethtjGTHORN

Under MLRP the most representative part of the distribu-tion for G is the right tail if tG

tGincreases in t or the left tail if tG

tG

decreases in t The representative tail is then overweighted whilethe nonrepresentative tail is underweighted As a consequencethe assessed mean E

stethtjGTHORN is too extreme in the direction of therepresentative tail

Critically in line with the social cognition perspective the ste-reotype contains a kernel of truth the DM overestimates the meanof G if this group has a higher mean than the comparison groupnamely EethtjGTHORN gt EethtjGTHORN and conversely if EethtjGTHORN lt EethtjGTHORN TheDM exaggerates this true difference because he inflates the asso-ciation of G with its most representative types20 For instancewhen judging an asset manager who performs well we tend to

19 Examples include the binomial and the Poisson families of distributionswith different parameters The characterization of distributions satisfying MLRPis easier in the case of continuous distributions (see Online Appendix D) two dis-tributions f(x) f ethx THORN that differ only in their mean satisfy MLRP if and only if thedistribution f(x) is log-concave Examples include the exponential and normal dis-tributions To the extent that discrete distributions sufficiently approximate thesedistributions (as the Poisson distribution PoisethTHORN approximates the normal distri-bution Neth THORN for large l) they will also satisfy MLRP

20 Depending on the distribution and the weighing function the DMrsquos assess-ment of the variance VarethtjGTHORNmay also be dampened relative to the truth This isoften true under the truncation weighing function In this case stereotyping effec-tively leads to a form of overconfidence in which the DM holds extreme views andoverestimates the precision of his assessment That extreme views and overconfi-dence (in the sense of over precision) go together has been documented in the settingof political ideology among others (Ortoleva and Snowberg 2015)

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overemphasize skill relative to luck because higher skill levels arerelatively more associated with higher performance This occurseven if for both skilled and unskilled managers high performanceis mostly due to luck

In the second case for which we characterize the stereotypi-cal distributions groups G and ndashG have the same mean EethtjGTHORNfrac14 EethtjGTHORN frac14 EethtTHORN but differ in their variance We abstract fromskewness and higher moments by considering distributionsethtGTHORNt2T and ethtGTHORNt2T that share the same support and are sym-metric around the medianmean EethtTHORN

PROPOSITION 3 Suppose that in G more extreme types are rela-tively more frequent than in ndashG Formally the likelihoodratio tG

tGis U-shaped in t around EethtTHORN Then for any weight-

ing function htethTHORN that is not constant in the relevant rangestereotypical beliefs satisfy

VarstethtjGTHORN gt VarethtjGTHORN gt VarethtjGTHORN gt VarstethtjGTHORN

EstethtjGTHORN frac14 E

stethtjGTHORN frac14 EethtTHORN

When group G has a higher relative prevalence of extremetypes its representative types are located at both extremes of thedistribution The DMrsquos beliefs about G are then formed by over-weighting both tails while underweighting the unrepresentativemiddle The overweighting of Grsquos tails causes the assessment ofits variance VarstethtjGTHORN to be too high For example the skill dis-tribution of immigrants to the United States may be perceived ashaving very fat tails or even bimodal with immigrants beingperceived as either unskilled or very skilled relative to the resi-dent population The mean of the group in contrast is assessedcorrectly because the stereotypical distribution remains symmet-ric around EethtTHORN As before the stereotype contains a kernel oftruth It induces the agent to exaggerate the true differences be-tween groups namely the higher variance of G relative to itscounterpart

We present a number of extensions of the model in the OnlineAppendix We first consider multidimensional type spaces andshow that stereotypes center around the dimension wheregroups differ the most in line with the kernel of truth logic(Online Appendix C) Multidimensional stereotypes imply thatthe dimension we think about is influenced by context For

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example the Irish are stereotyped as red-haired when comparedwith the European population However when compared withthe Scots a more plausible stereotype for the Irish is lsquolsquoCatholicrsquorsquobecause religion is the dimension along which Irish and Scotsdiffer the most

In Online Appendix D we extend the model to continuoustype spaces Many settings of interest in economics can be use-fully described by continuous probability distributions and weshow our model is particularly tractable in this case In OnlineAppendix E we relax Definition 2 and allow weighting of types toalso be influenced by their likelihood We show that the basicinsight that stereotypes contain a kernel of truth carries throughto these cases as well

To summarize the psychology of representativeness yieldsstereotypes that are consistent with the social cognition approachin which individuals assess groups by recalling and focusing ondistinctive group traits When there are systematic differencesbetween groups stereotypes get the direction right but exagger-ate differences

IIIC Some Examples

A growing body of field and experimental evidence points to awidespread belief that women are worse than men at mathemat-ics (Eccles Jacobs and Harold 1990 Guiso et al 2008 CarrellPage and West 2010) This belief persists despite the fact that fordecades women have been gaining ground in average schoolgrades including mathematics and have recently surpassedmen in overall school performance (Goldin Katz and Kuziemko2006 Hyde et al 2008) This belief shared by men and women(Reuben Sapienza and Zingales 2014) may help account for thegender gap in the choices of high school tracks college degreesand careers with women disproportionately choosing humanitiesand health-related areas (Weinberger 2005 Buser Niederle andOosterbeek 2014) and forgoing significant wage premiums toquantitative skills (Bertrand 2011)

Gender stereotypes in mathematics particularly beliefs thatexaggerate the extent of average differences are consistent withthe predictions of our model The fact that men are overrepre-sented at the very highest performance levels leads a stereotyp-ical thinker to exaggerate the magnitude of mean differencesFigure I shows the score distributions from the mathematics

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section of 2013rsquos Scholastic Aptitude Test (SAT) for men andwomen21 The distributions are very similar with averagescores slightly higher for men (531 versus 499 out of 800)However scores for men have a heavier right tail with mentwice as likely to have a perfect SAT math score than women22

In light of such data the stereotypical male performance in math-ematics is high while the stereotypical female performance ispoor Predictions based on such stereotypes are inaccurate exag-gerating true differences Consistent with this prediction exper-imental evidence shows that both genders underestimatewomenrsquos ability in simple math tasks even controlling for pastperformance (Reuben Sapienza and Zingales 2014) Coffman(2014) shows a similar pattern extends to confidence about ownability in other male-typed domains with women reporting sig-nificantly less confidence in gender-incongruent than gender-congruent tasks Our model suggests that these patterns mightcome from stereotypes based on gender differences in the righttail of the distribution While differences in the right tail of thedistribution are unlikely to be relevant for most decisions stereo-typical thinking driven by these differences has the potential toimpact economically important decisions whether through self-stereotyping (ie choice of careers or majors as in BuserNiederle and Oosterbeek 2014) or through discrimination (iehiring decisions as in Bohnet van Geen and Bazerman 2016)

The logic of exaggerated yet directionally correct stereotypesalso sheds light on the well-documented phenomenon of base rateneglect (Kahneman and Tversky 1973) Indeed Proposition 2implies that the DM overreacts to information that assigns

21 Standardized test performance measures not only innate ability but alsoeffort and investment by third parties (Hyde et al 2008) The mapping of test per-formance into inferences about innate ability is an issue not addressed by ourmodel

22 For 2013 SAT Mathematics scores see httpmediacollegeboardcomdigitalServicespdfresearchSAT-Percentile-Ranks-By-Gender-Ethnicity-2013pdf Results are similar for the National Assessment of Educational Progress(NAEP) which are more representative of the overall population For 2012NAEP scores for 17-year-olds in mathematics see httpnationsreportcardgovltt_2012age17maspx See Hyde et al (2008) Fryer and Levitt (2010) and Popeand Sydnor (2010) for in-depth empirical analyses of the gender gap inmathematics

STEREOTYPES 1773

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people to groups precisely because such information generatesextreme stereotypes Consider the classic example in which amedical test for a particular disease with a 5 prevalence has a90 rate of true positives and a 5 rate of false positives The testassigns each person to one of two groups + (positive test) or ndash(negative test) The DM estimates the frequency of the sick type(s) and the healthy type (h) in each group The test is informativea positive result increases the relative likelihood of sickness anda negative result increases the relative likelihood of health forany prior Formally

PreththornjsTHORN

PreththornjhTHORNgt 1 gt

PrethjsTHORN

PrethjhTHORNeth4THORN

This condition has clear implications the representative personwho tests positive is sick while the representative person whotests negative is healthy Following Proposition 2 the DMreacts to the test by moving his priors too far in the right di-rection generating extreme stereotypes He greatly boosts hisassessment that a positively tested person is sick but also thata negatively tested person is healthy Because most people arehealthy the DMrsquos assessment about the group that tested neg-ative is fairly accurate but is severely biased for the group that

FIGURE I

SAT Mathematics Scores by Gender (2013)

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tested positive This analysis formalizes Tversky andKahnemanrsquos (1983) verbal account of base rate neglect23

The same mechanism may underlie several other instanceswhere DMs overweight diagnostic information When assessingan employeersquos skill level an employer attributes high perfor-mance to high skill because high performance is the distinctivemark of a talented employee Because he neglects the possibilitythat some talented employees perform poorly and that somenontalented ones perform well (perhaps due to stochasticity inthe environment) the employer has too much faith in skill andneglects the role of luck in accounting for the output Similarlywhen assessing the performance of firms in a hot sector of theeconomy (eg G = internet) an investor recalls highly successfulfirms in that sector (t = return of Google Amazon etc) He ne-glects the possibility of firms being unsuccessful because lack ofsuccess is statistically nondiagnostic and psychologically nonrep-resentative of a growing sectormdasheven if it is likely This causesexcessive optimism (in that the expectation of growth is unrea-sonably high) and overconfidence (in that the variability in earn-ings growth considered possible is truncated) True the hot sectormay have better growth opportunities on average but represen-tativeness exaggerates this feature and induces the investor toneglect a significant risk of failure

IV Evidence on Representativeness and Stereotypes

Testing our model requires evaluating the beliefs individualshold about a target group against the true distribution of thattarget group over an attribute space An ideal data set would

23 Our account is distinct from a mechanical underweighting of base rates inBayes rule as in Grether (1980) and Bodoh-Creed Benjamin and Rabin (2013) Inthose models upon receiving the test results the DM can update his beliefs in thewrong direction he can be less confident that a person is healthy after a negativetest than under his prior which cannot happen in our model Although this predic-tion of our model seems consistent with introspection we are not aware of experi-mental evidence on this point Griffin and Tversky (1992) present evidenceconsistent with pure neglect of base rates but in a significantly different tasknamely inferring the bias of a coin from a history of coin flips Such experimentsare hard to compare with the predictions of our model because subjects are asked togenerate distributions of different numbers of coin flips in their minds which is amuch more involved task than to recall types of a given distribution Their assess-ments then might be wrong for other reasons See Bodoh-Creed Benjamin andRabin (2013) for a detailed discussion

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consist of naturally defined groups with known distributions overa given space of types and a corresponding set of beliefs about thedistribution of each group over that space of types This wouldallow us to test for exaggeration of true differences betweengroups and to ask whether this exaggeration is well predictedby overweighting representative types To identify a causal rolefor representativeness or context dependence we would need ex-ogenous variation in either the comparison group ndashG or in thedistributions over the type spaces This is unavailable in existingdata sets Accordingly we take a two-pronged approach First wecreate a controlled laboratory environment that allows us toinduce the exogenous variation in representative types that weneed to test causality then we reanalyze existing field evidence tocheck for consistency with our predictions

In testing our model we focus on the two main implicationsof representativeness-based stereotypes

Context dependence the stereotype of a target group de-pends on the characteristics of the reference group it iscompared to

Kernel of truth stereotypes depend on group character-istics andmdashin most (precisely characterized) settingsmdashare slanted toward representative types

We test the first property with a lab experiment (SectionIVA) We then turn to survey data on beliefs about US politicalgroups (Section IVB) for an empirical analysis that explores thesecond property The survey data are more tightly linked to ourinterest in social stereotypes The laboratory experiment allowsus to directly test the role of representativeness in generatingcontext dependent beliefs Online Appendixes F and G provideall details and additional results for the experiments and fieldevidence

IVA Lab Evidence on Representativeness and ContextDependence

The influence of the representativeness heuristic on recalland on beliefs has been extensively documented in the lab(Kahneman and Tversky 1972 1973) Our goal is to considerhow representativeness as formalized in equation (2) gives riseto context-dependent beliefs To our knowledge the possibility

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that representativeness may generate context dependence hasnot been tested before

To assess this prediction we perform a controlled laboratoryexperiment that allows us to isolate representativeness frommany confounding factorsmdashhistorical sociological or other-wisemdashthat may affect stereotype formation in the real worldWe construct our own groups of ordinary objects creating atarget group G and a comparison group ndashG We hold thetarget group G fixed and explore how participant impressions ofit change as we change the comparison group ndashG and thusrepresentativeness

We conducted several experiments in the laboratory and onAmazon Mechanical Turk Each involves a basic three-stepdesign First participants are shown the target group and a ran-domly assigned comparison group for 15 seconds In this timedifferences between groups can be noticed but the groupsrsquo precisecompositions cannot be memorized The second step consists of afew filler questions which briefly draw the participantsrsquo cognitivebandwidth away from their observation Finally participants areasked to assess the groups they saw Participants are incentiv-ized to provide accurate answers

We randomly assign participants to either the Control or theRepresentativeness condition In the Control condition G and ndashGhave nearly identical distributions so that all types are similarlyrepresentative for each group In the Representativeness condi-tion ndashG is changed in such a way that a certain type becomes veryrepresentative for G Context dependence implies that the assess-ment of G should now overweight this representative type eventhough the distribution of G itself has not changed

We ran six experiments of this form with design changesfocused on reducing participant confusion and removing con-founds We describe the final and most refined version of theseexperiments here In an attempt to provide a overview of the re-sults while remaining concise we provide the results from pooledspecifications that use all data collected In Online Appendix Fwe offer additional details and report all experiments conductedWe also give instructions and materials for each experiment thefull data set is available by request

Consider first the experiment illustrated in Figure II Agroup of 25 cartoon girls is presented next to a group of 25 cartoonboys in T-shirts of different colors blue green or purple In theControl condition (Figure II Panel a) the groups have identical

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color distributions (13 purple 12 green) so no color is represen-tative of either group The Representativeness condition (Panel b)compares the same group of girls with a different group of boysfor whom green shirts are replaced with blue shirts Now onlygirls wear green and only boys wear blue These colors althoughstill not the most frequent for either group are now most repre-sentative For each group girls and boys participants are asked anumber of questions concerning the frequency of T-shirts of dif-ferent colors worn by that group

Applying our model in the control condition the type space isT frac14 fgreen purpleg and the groups are G = girls and ndashG = boysGiven that the color distributions are identical across groups both

types are equally representativegreengirls

greenboysfrac14 1 frac14

purplegirls

purpleboys As a result

assessment of G should be correct on average stcontrolgreengirls frac14 greengirls

and stcontrolpurplegirls frac14 purplegirls for any weighing function (the same is

true about assessments of ndashG)In the treatment condition the distribution of shirt colors re-

mains the same for girls For boys green shirts are changed intoblue Thus the type space changes to T frac14 fgreen purple bluegand the representative color for girls becomes greengreengirls

greenboysfrac14 1 gt 1 frac14

purplegirls

purpleboys while that for boys becomes blue As

a result in the treatment condition subjects should inflate the

frequency of green shirts relative to the truth sttreatmentgreengirls

gt greengirls (the same should happen to assessments of blueshirts for boys) We also expect the assessed frequency of greenshirts to go up relative to the control condition namely

sttreatmentgreengirls gt stcontrol

greengirls Critically the only factor that varies

across treatments is the representativeness of the 12-colorshirt Thus if we see differences across conditions the causalrole of representativeness-based recall in shaping group judg-ments is clear24

24 We vary which colors are used in which roles across participants Someparticipants saw this particular color distribution while others see for examplegreen as the modal color and purple as the diagnostic color for boys in theRepresentativeness condition and blue as the diagnostic color for girls in theRepresentativeness condition We vary the colors across the roles to avoid con-founding the characteristics of any particular color with its diagnosticity

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FIG

UR

EII

T-S

hir

tsE

xp

erim

ent

Fig

ure

sap

pea

red

inco

lor

top

art

icip

an

tsin

the

exp

erim

ent

For

clari

ty

we

have

ad

ded

ale

tter

toea

chT

-sh

irt

toid

enti

fyth

eco

lor

for

the

read

er

lsquolsquoGrsquorsquo

ind

icate

sgre

en

lsquolsquoPrsquorsquo

ind

icate

sp

urp

le

lsquolsquoBrsquorsquo

ind

icate

sblu

eT

hes

ele

tter

sd

idn

otap

pea

rto

part

icip

an

tsan

dare

for

read

erre

fere

nce

only

P

lease

see

onli

ne

ver

sion

ofp

ubli

shed

art

icle

for

colo

rfi

gu

reex

act

lyas

itap

pea

red

top

art

icip

an

ts

STEREOTYPES 1779

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We collected data from 301 participants using this T-shirtsdesign25 Since the number of green and purple shirts is verysimilar we first ask each participant the simplest question ofwhich shirt color is modal Next we ask participants to assessthe share of green and purple shirts

Consistent with the role of representativeness participantsassigned to the Representativeness condition are 105 percentagepoints more likely to recall the less frequent color (green for girlsor blue for boys) as the modal color when it is representative of agroup (35 of participants guess the less frequent color is modalin the Control condition this proportion increases to 46 in theRepresentativeness condition p = 01 estimated from a probitregression reported in Online Appendix F)

We now turn to subjectsrsquo estimates of how many T-shirts ofeach color they saw in each group In both conditions the truedifference in counts is 1 (13 purple shirts 12 green or blue shirts)In the Control condition participants on average believe they saw054 more purple shirts than green or blue shirts In theRepresentativeness condition participants believe they saw072 fewer purple shirts than green or blue shirts (the acrosstreatment difference is significant with p = 01 from OLS regres-sion reported in Online Appendix F)

In total we collected data for six experiments of this generalstructure gathering evidence from more than 1000 participantsAs we describe in Online Appendix F although there is substan-tial variation across experiments when we pool all of the data wefind significant aggregate treatment effects in line with a role ofrepresentativeness in judgment We employ four different unor-dered types designs similar to the T-shirts experiment using sixsamples (four online and two in the laboratory) with 741 partic-ipants We find effects in the predicted direction for five of the sixsamples Using a probit regression that pools the data for theseunordered type experiments we find that participants are 93 per-centage points more likely to guess that the less frequent type ismodal when it is representative than when it is not (p = 002) Wealso run a family of ordered types experiments (two designs fivesamples 402 participants) Unlike the simpler T-shirts style

25 Throughout our analysis we exclude any participant who participated in aprevious version of the experiment and any participant who self-identified as color-blind In Online Appendix F we show that our results are unchanged if we includethese additional observations

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design the theoretical predictions for the ordered types designsare more sensitive to the specific assumptions one makes aboutthe weighting function of the DM26 We find effects in the pre-dicted direction for three of the five samples As we discuss inmore detail in Online Appendix F the ordered types resultsvary by platform with consistently stronger results on AmazonMechanical Turk than in the laboratory samples Pooling all or-dered types experiments participants are 93 percentage pointsmore likely to guess that the group of interest has a greater av-erage than the comparison group when the right tail is represen-tative (p = 062) Given our simple experimental setting withgroups of mundane objects we interpret our resultsmdasha signifi-cant and reasonably sized impact on average beliefsmdashas an im-portant proof of concept the presence of representative typesbiases ex post assessment

IVB Empirical Evidence on Political Stereotypes

We examine two data sets on political preferences and be-liefs about political preferences in the United States We inves-tigate the roles of representativeness and context dependence byseparately testing for hypotheses that allow us to assess the lead-ing theories of stereotypes

First we test whether beliefs are correct or depart systemat-ically from the truth The statistical discrimination approachbuilds on the assumption that people hold rational expectationsof group traits Comparing beliefs to the truth allows us to assessthe validity of this assumption in our data

Second we test if beliefs depart from the truth by exagger-ating (mean) differences among groups per the kernel of truthhypothesis This is an implicit test of context dependence be-cause it implies that beliefs about the target groups are shapednot only by that grouprsquos characteristics but also by those of thereference group27

Third we test if distortions in beliefs can be accounted for bythe overweighting of highly representative types (defined astypes that are relatively more frequent in the target relative to

26 This is due in part to our choice to not study MLRP distributions We moti-vate and discuss this design decision in Online Appendix F

27 Of course unlike in the laboratory experiment in this setting we cannot testfor context dependence by exogenously varying the reference group

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the reference group) The second and third tests address the keypredictions of our model

1 The Data We have two data sets on political preferences andbeliefs about political preferences The first data set from GrahamNosek and Haidt (GNH 2012) contains data from the MoralFoundations Questionnaire Respondents (1174 self-identified lib-erals and 500 self-identified conservatives) answer questions abouttheir position on a subset of 45 issues 20 moral relevance state-ments (eg lsquolsquowhen you decide whether something is right orwrong to what extent are the following considerations relevantto your thinkingrsquorsquo) and 25 moral judgments (eg lsquolsquoindicate theextent to which you would agree or disagreersquorsquo) For each issue arandomly determined subset of participants states their own posi-tion another subset states their belief on the position of a lsquolsquotypicalliberalrsquorsquo and a third subset states their belief on the position of alsquolsquotypical conservativersquorsquo The data thus include the distribution overpositions for both liberal and conservatives as well as the averagebelieved typical position of liberals and of conservatives on the 45issues Each position is elicited on 1ndash6 scale

The second data set comes from the American NationalElection Survey (ANES) and contains data from more than20000 respondents between 1964 and 201228 The surveycovers political issues of the day such as the optimal amount ofgovernment spending and service provision (1984ndash2000) or theplace of women in society (1972ndash1998) We focus on the 10 issuesthat ask participants to respond on a 1ndash7 scale (rather than justindicate binary agreement or disagreement) all 10 issues areasked in multiple years Participants are asked to provide theirown position on the scale and their believed position of theDemocratic and Republican parties (lsquolsquoWhere would you placethe Democratic [Republican] party on this scalersquorsquo) The data in-clude for each issue-year observation the distribution of partic-ipant positions for self-identified liberals and self-identifiedconservatives as well as the distribution of believed typical posi-tions of the Democratic and Republican parties

28 These data are publicly available at httpwwwelectionstudiesorgstudy-pagesanes_timeseries_cdfanes_timeseries_cdfhtm

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2 Empirical Strategy Our analysis focuses on beliefs abouttwo groups Conservatives and Liberals The types are the possi-ble positions for each issue (1 2 6 7) For the GNH data weinterpret beliefs about the lsquolsquotypicalrsquorsquo element of a group to coincidewith the believed average position in that group Similarly forthe ANES data we use the believed party positions as a proxy forbelieved mean of each group29 We then take as a benchmark thehypothesis that individuals hold accurate beliefs about eachgroup and in particular that believed mean position shouldequal true mean position at least on average across subjectsThe accurate beliefs hypothesis underlies the most common eco-nomic model of stereotyping statistical discrimination

To assess our representativeness-based model we perform aregression exercise To test our model in a linear regressionframework we rely on linear approximations of the weightingfunction Our model then yields two regression specifications

PROPOSITION 4 Let G 2 fconservative liberal g and assume

ht h tG

tG

be a differentiable and strictly increasing weight-

ing function as in Definition 2 The following hold as a first-order approximation around identical distributions G

Gfrac14 1

(i) Kernel of truth regression There exists a constant gt 0such that

EstethtjGTHORN frac14 EethtjGTHORNeth1thorn THORN EethtjGTHORNeth5THORN

(ii) Representativeness regression Denote H frac14 fT 2 Tg

the right tail of types and RconsH frac14

PHtconsPHtlib

as the average

representativeness of right tail types for conservatives

29 This assumption is consistent with the authorsrsquo interpretation of the GNHdata (GNH 2012) and with previous studies using ANES (eg Westfall et al 2015)Furthermore to the extent that this assumption holds equally well for most issueswithin a data set our focus on cross-issue differences should allow us to test thepredictions of our model even with an imperfect proxy for beliefs of mean positionsFinally the data provide some insight into whether subjects are reporting (per-ceived) modal or mean types As we show the modal type is a poor prediction ofstated beliefs while a distorted mean slanted toward representative types is anaccurate prediction of stated beliefs

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Under the further approximation where tcons

tlibampRcons

H for

t 2 H

EstethtjconsTHORN frac14 EethtjconsTHORN thorn consethR

consH 1THORNeth6THORN

EstethtjlibTHORN frac14 EethtjlibTHORN libethR

consH 1THORNeth7THORN

where lcons and llib are positive constants

The first regression allows us to test for the kernel of truthhypothesis and the second set of regressions allows us to test forthe role of representativeness

Equation (5) says that respondents in our model inflate theaverage position of a group say the conservatives if and only ifthe group has a higher average position than the other groupnamely the liberals Formally EstethtjconsTHORN gt EethtjconsTHORN if and onlyif EethtjconsTHORN gt EethtjlibTHORN Because in our measurement scale highertypes mean lsquolsquomore conservativersquorsquo we expect (i) believed conserva-tive average to be higher than the truth and (ii) the extent ofoverstatement to decrease in the average liberal position EethtjlibTHORNConversely we expect the average liberal position to be lowerthan the truth the more so the higher the average conservativeposition EethtjconsTHORN

As previously discussed the basis of these predictions is con-text dependence information about the distribution of ndashG is rel-evant for the beliefs about G This context dependence isinconsistent with rational expectations in which only thegrouprsquos own means should affect beliefs We test the hypothesisthat the true mean EethtjGTHORN is a significant predictor of the believedmean E

stethtjGTHORN with a positive sign and the other grouprsquos truemean EethtjGTHORN is a predictor of the believed mean with a negativesign

Equations (6) and (7) say that repondentsrsquo assessment bias isshaped by representativeness When the right tail is more repre-sentative for conservatives (Rcons

H 1 positive and large) partici-pants should inflate the average conservative position more(higher E

stethtjconsTHORN EethtjconsTHORN) and deflate the average liberal po-sition more (lower E

stethtjlibTHORN EethtjlibTHORN) We test the hypothesisthat the inflation in conservative positions is positively associatedwith the representativeness of the right tail for the conservativesand the inflation in liberal positions is negatively associated with

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it Once again the representativeness of the right tail is com-puted using the true distribution of positions

In equations (6) and (7) in many cases the representative tailis also the most likely one As a consequence these tests cannotdistinguish a representativeness-based from a likelihood-basedmodel of distorted beliefs We perform two additional testsFirst we run versions of equations (6) and (7) in which we controlfor the likelihood of tails (see Table A4 in Online Appendix G)Second we compute numerically the predictions of a representa-tiveness-based model of stereotypes and a likelihood-based modelof stereotypes We then assess which of these two is better able tomatch the data on beliefs

3 Empirical Results To begin we illustrate the structure ofthe data and the nature of our predictions with two simple exam-ples from the GNH data set focusing on beliefs about conserva-tives In example 1 participants are asked about their agreementwith the statement lsquolsquoIt can never be right to kill a human beingrsquorsquoIn example 2 participants are asked about the moral relevance oflsquolsquowhether or not someone cared for someone weak or vulnerablersquorsquoAs can be seen in Figure III in example 1 the modal position(strongly disagree (1)) and most representative positions(strongly disagree (1)) coincide for conservatives In contrast inexample 2 in Figure III the most representative types (slightlyrelevant (3) not at all relevant (1)) are not most likely for theconservative group Following Proposition 1 we predict that be-liefs will be distorted in the direction of the most representativetypes Thus we expect more exaggeration in example 2 than inexample 1 since in example 2 the most representative types (inthe left tail) are far from the modal type whereas in example 1they coincide This is what we find the conservative position isexaggerated by only 009 positions in Example 1 (true mean 299believed mean 290) but by 106 positions in Example 2 (truemean 421 believed mean 315)

In the full data sets we treat each (issue year) pair as anobservation and we cluster standard errors at the issue level Forthe GNH data we have 45 observations 45 issues measured inthe same year For the ANES data we have 66 observations 10issues measured in multiple years To begin we simply docu-ment systematic exaggeration in both data sets This is a primaryfocus of the original analysis in GNH (2012) and also in Westfall

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FIGURE III

Two Examples

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et al (2015)rsquos analysis of the ANES data30 Figure IV shows thatthe believed difference between typical conservative and typicalliberal positions is larger than the true difference in mean posi-tions for 109 of the 111 observations The data for both GNH(squares) and ANES (triangles) lie above the 45-degree line(dashed)31 Average exaggeration is 062 positions on the scale(066 in the GNH data 059 in the ANES data)32

The systematic and significant exaggeration of mean differ-ences suggests that the benchmark model of accurate beliefs ismissing something important Indeed this exaggeration reflectsthe fact that believed means are typically more extreme than truemeans First note that the kernel of truth regression (equation(5)) generates exaggeration of mean differences just as docu-mented in Figure IV

EstethtjGTHORN E

stethtjGTHORN frac14 eth1thorn 2THORN frac12EethtjGTHORN EethtjGTHORN

To bring this prediction to the data we regress the believedmean position for each group EBethtjGTHORN on the true mean of thegroup EethtjGTHORN and the true mean of the comparison groupEethtjGTHORN across issues We do this for each group (liberals con-servatives) in each data set separately We also present pooledspecifications that combine the data sets to make a prediction fora given group (liberals conservatives) In these pooled specifica-tions we include a dummy variable indicating whether theobservation came from the ANES data set For all specificationswe cluster observations at the issue level33 The results from re-gression are shown in Table I In every specification we find thatEethtjGTHORN is a significant predictor of EBethtjGTHORN with the predicted pos-itive sign Crucially for five of the six specifications the mean of

30 Chambers and Melnyk (2006) also find evidence of exaggeration of truedifferences in beliefs about political positions

31 For convenience we recode all issues so that the high end of the scale (67)represents the stereotypically more conservative position

32 A natural question to ask is how beliefs vary across liberals and conserva-tives That is do beliefs about a group G depend on membership in G versus ndashG Ourmodel does not speak to this issue However in Online Appendix G we show thatthe results we document below hold for both beliefs held by conservatives and be-liefs held by liberals see Tables A9 A10 and A11

33 In general the results presented below for the ANES data are not largelyimpacted by the decision to cluster at the issue level Similar results are obtained ifthe data are not clustered

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the comparison group EethtjGTHORN is also a significant predictor ofE

BethtjGTHORN with the predicted negative signAlthough these results provide strong evidence of context

dependence and are consistent with our model they do not pindown a role for representativeness of types Our next test relatesthe magnitude of representativeness of tail types to the magni-tude of belief distortions

To this end we implement the regressions in equations (6)and (7) Following Proposition 4 we compute the average repre-

sentativeness of tail types for conservatives RconsH frac14

PtT2tconsPtT2tlib

We

again test the hypothesis that RconsH is a significant predictor of Est

ethtjconsTHORN with a positive sign and a predictor of EstethtjlibTHORN with a

negative sign Table II shows that conditional on true mean RconsH

predicts believed mean for each group G as expected The firstthree specifications display the results for predicting beliefs heldabout conservatives In both data sets the average representa-tiveness of tail types for conservatives is a significant positivepredictor of beliefs held about conservatives The final three spe-cifications display the results for predicting beliefs held about

FIGURE IV

Exaggeration of Differences

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liberals We find that the average representativeness of tail typesfor conservatives is a negative predictor of beliefs held about lib-erals This effect is significant in the GNH data and marginallysignificant in the ANES data

We present several additional results in Online Appendix GTo further examine the role of representativeness in driving be-liefs we first show the results of Table II carry through when we

TABLE II

AVERAGE REPRESENTATIVENESS OF TAIL POSITIONS PREDICTS BELIEFS

OLS Predicting Believed Mean of Group G for Each Issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position

of group G for issue

078 024 051 072 018 041

(006) (008) (009) (005) (005) (010)

Avg rep of tail types for

conservatives RconsH

019 055 025 014 012 024

(007) (022) (008) (006) (007) (005)

Constant 101 260 184 093 271 201

(026) (045) (029) (022) (025) (032)

R2 082 048 060 091 031 070

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

TABLE I

INFORMATION ABOUT ndashG PREDICTS BELIEFS ABOUT G

OLS predicting believed mean of group G for each issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position of

conservatives for issue

102 098 096 021 019 025

(0097) (0133) (0076) (0060) (0116) (0060)

True mean position of

liberals for issue

035 086 058 0987 039 073

(0106) (0134) (0131) (0066) (0106) (0135)

Constant 151 335 235 069 258 156

(0195) (0269) (0279) (0122) (0249) (0270)

R2 083 053 066 092 032 068

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

STEREOTYPES 1789

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control for the average likelihood on the tail positions (see Table A4in Online Appendix G) Most tellingly we use the model to predictbeliefs across issues and compare those to the data For simplicitywe use the rank-based truncation specification to predict mean be-liefs when stereotypes include the d most representative types ford frac14 1 T We compare these predictions to those of a model inwhich beliefs are obtained by restricting the distribution to the dmost likely types Our benchmark for both models is predicting thebelieved mean from the entire distribution where d = T We showthat the predictions of the rank-based truncation model with d = 4or 5 compare favorably to both a likelihood-based truncation model(with any d) and the accurate beliefs benchmark Interestingly thisresult suggests that stereotypical beliefs are well approximated byneglecting the least representative types (as opposed to focusingonly on the most representative types) and so represent a moderatethough systematic departure from the standard benchmarkFinally we show that the results we document above hold forboth beliefs held by conservatives and beliefs held by liberals (seeTables A9 A10 and A11 in Online Appendix G)

V Conclusion

We present a model of stereotypical thinking in which DMsmaking predictions about a group overweight the grouprsquos mostdistinctive types These overweighted types are not the mostlikely ones given the DMrsquos data but the most representativeones in the sense of being the most diagnostic of the group rela-tive to other groups Representativeness implies that what ismost distinctive of a group depends on what group it is comparedwith We present experimental evidence that confirms this con-text dependence in recall-based assessments of groups Finallywe evaluated the predictions of the model using political data fromexisting large-scale surveys We find context dependence to be akey feature of beliefs Given the richness of the political data wecan go a step further and identify a role for representativeness inparticular As the representativeness of tail types increases beliefsof a group are distorted in the direction of that tail

Our approach provides a parsimonious and psychologicallyfounded account of how DMs generate simplified representationsof reality from social groups to stock returns and offers a unifiedaccount of disparate pieces of evidence relating to this type of

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uncertainty The model captures the central fact that stereotypeshighlight the greatest difference between groups thus explainingwhy some stereotypes are very accurate while others lack valid-ity Still stereotypes often have a kernel of truth when they arebased on systematicmdasheven if smallmdashdifferences between groupsThis logic allows us to describe a number of heuristics and psy-chological biases many of which arise in the context of predictionproblems Generically our model generates overreaction to diag-nostic information

Our model is based on representativeness and does not cap-ture all the features of stereotypical thinking However it cap-tures perhaps the central feature when we think of a group wefocus on what is most distinctive about it and neglect or under-weight the rest

Saeuroıd Business School University of Oxford

Ohio State University and Harvard Business School

Universita Bocconi and Innocenzo Gasparini Institute

for Economic Research

Harvard University

Supplementary Material

An Online Appendix for this article can be found at QJEonline (qjeoxfordjournalorg)

References

Adorno Theodor Else Frenkel-Brunswik Daniel Levinson and Nevitt SanfordThe Authoritarian Personality (New York Harper amp Row 1950)

Arrow Kenneth lsquolsquoThe Theory of Discriminationrsquorsquo in Discrimination in LaborMarkets Orley Ashenfelter and Albert Rees eds (Princeton NJPrinceton University Press 1973)

Ashton Michael and Victoria Esses lsquolsquoStereotype Accuracy Estimating theAcademic Performance of Ethnic Groupsrsquorsquo Personality and SocialPsychology Bulletin 25 (1999) 225ndash236

Barberis Nicholas Andrei Shleifer and Robert Vishny lsquolsquoA Model of InvestorSentimentrsquorsquo Journal of Financial Economics 49 (1998) 307ndash343

Bayer Sylvia lsquolsquoThe Accuracy of Academic Gender Stereotypesrsquorsquo Sex Roles 40(1999) 787ndash813

Benjamin Dan James Choi and Joshua Strickland lsquolsquoSocial Identity andPreferencesrsquorsquo American Economic Review 100 (2010) 1913ndash1928

Benjamin Dan Matthew Rabin and Collin Raymond lsquolsquoA Model of Non-Belief inthe Law of Large Numbersrsquorsquo Journal of the European Economic Association15 (2015) 515ndash544

Bertrand Marianne lsquolsquoNew Perspectives on Genderrsquorsquo Handbook of LaborEconomics 4 (2011) 1543ndash1590

Bodoh-Creed Aaron Dan Benjamin and Matthew Rabin lsquolsquoThe Dynamics of Base-Rate Neglectrsquorsquo mimeo Haas Business School 2013

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Bohnet Iris Alexandra van Geen and Max Bazerman lsquolsquoWhen PerformanceTrumps Gender Bias Joint versus Separate Evaluationrsquorsquo ManagementScience 5 (2016) 1225ndash1234

Bordalo Pedro Nicola Gennaioli and Andrei Shleifer lsquolsquoSalience Theory of Choiceunder Riskrsquorsquo Quarterly Journal of Economics 127 (2012) 1243ndash1285

mdashmdashmdash lsquolsquoSalience and Consumer Choicersquorsquo Journal of Political Economy 121(2013) 803ndash843

Briton Nancy and Judith Hall lsquolsquoBeliefs about Female and Male NonverbalCommunicationrsquorsquo Sex Roles 32 (1995) 79ndash90

Buser Thomas Muriel Niederle and Hessel Oosterbeek lsquolsquoGenderCompetitiveness and Career Choicesrsquorsquo Quarterly Journal of Economics 129(2014) 1409ndash1447

Carrell Scott Marianne Page and James West lsquolsquoSex and Science How ProfessorGender Perpetuates the Gender Gaprsquorsquo Quarterly Journal of Economics 125(2010) 1101ndash1144

Chambers John and Darya Melnyk lsquolsquoWhy Do I Hate Thee ConflictMisperceptions and Intergroup Mistrustrsquorsquo Personality and SocialPsychology Bulletin 32 (2006) 1295ndash1311

Chan Wayne Robert R McCrae Filip De Fruyt Lee Jussim CorinnaE Lockenhoff Marleen De Bolle Paul T Costa Jr Angelina R SutinAnu Realo Juri Allik Katsuharu Nakazato Yoshiko ShimonakaMartina Hrebıckova Sylvie Graf Michelle Yik Marina Brunner-SciarraNora Leibovich De Figueora Vanina Schmidt Chang-kyo Ahn Hyun-nie Ahn Maria E Aguilar-Vafaie Jerzy Siuta Barbara SzmigielskaThomas R Cain Janet T Crawford Khairul Anwar Mastor Jean-Pierre Rolland Florence Nansubuga Daniel R MiramontezVeronica Benet-Martınez Jerome Rossier Denis Bratko Iris MarusicJamin Halberstadt Mami Yamaguchi Goran Knezevic Thomas A MartinMirona Gheorghiu Peter B Smith Claudio Barbaranelli Lei WangJane Shakespeare-Finch Margarida P Lima Waldemar KlinkoszAndrzej Sekowski Lidia Alcalay Franco Simonetti Tatyana V AvdeyevaV S Pramila and Antonio Terracciano lsquolsquoStereotypes of Age Differences inPersonality Traits Universal and Accuratersquorsquo Journal of Personality andSocial Psychology 103 (2012) 1050ndash1066

Chen Yan Sherry Xin Liu Tracy Xiao and Margaret Shih lsquolsquoWhich Hat to WearImpact of Natural Identities on Coordination and Cooperationrsquorsquo Games andEconomic Behavior 84 (2014) 58ndash86

Coffman Katherine lsquolsquoEvidence on Self-Stereotyping and the Contribution ofIdeasrsquorsquo Quarterly Journal of Economics 129 (2014) 1625ndash1660

Cunningham Tom lsquolsquoComparisons and Choicersquorsquo mimeo Stockholm University2013

Diekman Amanda Alice Eagly and Patrick Kulesa lsquolsquoAccuracy and Bias in theStereotypes about the Social and Political Attitudes of Women and MenrsquorsquoJournal of Experimental Social Psychology 38 (2002) 268ndash282

Eccles Jacquelynne S Janis E Jacobs and Rena D Harold lsquolsquoGender RoleStereotypes Expectancy Effects and Parentsrsquo Socialization of GenderDifferencesrsquorsquo Journal of Social Issues 46 (1990) 183ndash201

Fryer Roland and Matthew Jackson lsquolsquoA Categorical Model of Cognition andBiased Decision-Makingrsquorsquo BE Journal of Theoretical Economics 8 (2008)1ndash42

Fryer Roland and Steven Levitt lsquolsquoAn Empirical Analysis of the Gender Gap inMathematicsrsquorsquo American Economic Journal Applied Economics 2 (2010)210ndash240

Gennaioli Nicola and Andrei Shleifer lsquolsquoWhat Comes to Mindrsquorsquo Quarterly Journalof Economics 125 (2010) 1399ndash1433

Gennaioli Nicola Andrei Shleifer and Robert Vishny lsquolsquoNeglected RisksFinancial Innovation and Financial Fragilityrsquorsquo Journal of FinancialEconomics 104 (2012) 452ndash468

Gilens Martin lsquolsquoRace and Poverty in America Public Misperceptions and theAmerican News Mediarsquorsquo Public Opinion Quarterly 60 (1996) 515ndash541

Glaeser Edward lsquolsquoThe Political Economy of Hatredrsquorsquo Quarterly Journal ofEconomics 120 (2005) 45ndash86

QUARTERLY JOURNAL OF ECONOMICS1792

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

Glover Dyland Amanda Pallais and William Pariente lsquolsquoDiscrimination as a Self-Fulfilling Prophecy Evidence from French Grocery Storesrsquorsquo mimeo HarvardUniversity 2015

Goldin Claudia Lawrence Katz and Ilyana Kuziemko lsquolsquoThe Homecoming ofAmerican College Women The Reversal of the College Gender GaprsquorsquoJournal of Economic Perspectives 20 (2006) 133ndash156

Graham Jesse Brian Nosek and Jonathan Haidt lsquolsquoThe Moral Stereotypes ofLiberals and Conservatives Exaggeration of Differences across thePolitical Spectrumrsquorsquo PLoS One 7 (2012) 1ndash13

Grether David lsquolsquoBayes Rule as a Descriptive Model The RepresentativenessHeuristicrsquorsquo Quarterly Journal of Economics 95 (1980) 537ndash557

Griffin Dale and Amos Tversky lsquolsquoThe Weighing of Evidence and theDeterminants of Confidencersquorsquo Cognitive Psychology 24 (1992) 411ndash435

Guiso Luigi Ferdinando Monte Paola Sapienza and Luigi Zingales lsquolsquoCultureGender and Mathrsquorsquo Science 320 (2008) 1164ndash1165

Hilton James and William Von Hippel lsquolsquoStereotypesrsquorsquo Annual Review ofPsychology 47 (1996) 237ndash271

Hyde Janet Sara Lindberg Marcia Linn Amy Ellis and Caroline WilliamslsquolsquoGender Similarities Characterize Math Performancersquorsquo Science 321 (2008)494ndash495

Judd Charles and Bernardette Park lsquolsquoDefinition and Assessment of Accuracy inSocial Stereotypesrsquorsquo Psychological Review 100 (1993) 109ndash128

Jussim Lee Jarret Crawford Stephanie Anglin John Chambers Sean Stevensand Florette Cohen lsquolsquoStereotype Accuracy One of the Largest and MostReplicable Effects in All of Social Psychologyrsquorsquo in The Handbook ofPrejudice Stereotyping and Discrimination Todd Nelson ed (MahwahNJ Lawrence Erlbaum 2015)

Kahneman Daniel and Amos Tversky lsquolsquoSubjective Probability A Judgment ofRepresentativenessrsquorsquo Cognitive Psychology 3 (1972) 430ndash454

mdashmdashmdash lsquolsquoOn the Psychology of Predictionrsquorsquo Psychological Review 80 (1973) 237ndash251

Kaplowitz Stan Bradley Fisher and Clifford Broman lsquolsquoHow Accurate ArePerceptions of Social Statistics about Blacks and Whitesrsquorsquo Public OpinionQuarterly 67 (2003) 237ndash243

Kersten Daniel Pascal Mamassian and Alan Yuille lsquolsquoObject Perception asBayesian Inferencersquorsquo Annual Review of Psychology 55 (2004) 271ndash304

Klein Richard Kate A Ratliff Michelangelo Vianello Reginald B Adams JrStepan Bahnik Michael J Bernstein Konrad Bocian Mark J BrandtBeach Brooks Claudia Chloe Brumbaugh Zeynep CemalcilarJesse Chandler Winnee Cheong William E Davis Thierry DevosMatthew Eisner Natalia Frankowska David Furrow Elisa Maria GallianiFred Hasselman Joshua A Hicks James F Hovermale S Jane HuntJeffrey R Huntsinger Hans IJzerman Melissa-Sue John Jennifer A Joy-Gaba Heather Barry Kappes Lacy E Krueger Jaime Kurtz CarmelA Levitan Robyn Mallett Wendy L Morris Anthony J Nelson JasonA Nier Grant Packard Ronaldo Pilati Abraham M RutchickKathleen Schmidt Jeanine L Skorinko Robert Smith Troy G SteinerJustin Storbeck Lyn M Van Swol Donna Thompson Anna van rsquot VeerLeigh Ann Vaughn Marek Vranka Aaron Wichman Julie A Woodzickaand Brian A Nosek lsquolsquoInvestigating Variation in Replicability A ManyLabs Replication Projectrsquorsquo Social Psychology 45 (2014) 142ndash152

Lundberg Shelly and Richard Startz lsquolsquoPrivate Discrimination and SocialIntervention in Competitive Labor Marketsrsquorsquo American Economic Review73 (1983) 340ndash347

Madon Stephanie Max Guyll Kathy Aboufadel Eulices Montiel Alison SmithPolly Palumbo and Lee Jussim lsquolsquoEthnic and National Stereotypes ThePrinceton Trilogy Revisited and Revisedrsquorsquo Personality and SocialPsychological Bulletin 27 (2001) 996ndash1010

Martin Carol lsquolsquoA Ratio Measure of Sex Stereotypingrsquorsquo Journal of Personality andSocial Psychology 52 (1987) 489ndash499

STEREOTYPES 1793

at Harvard L

ibrary on October 28 2016

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ownloaded from

McCauley Clark Krishna Thangavelu and Paul Rozin lsquolsquoSex Stereotyping ofOccupations in Relation to Television Representations and Census FactsrsquorsquoBasic and Applied Social Psychology 9 (1988) 197ndash212

Mullainathan Sendhil lsquolsquoThinking through Categoriesrsquorsquo mimeo HarvardUniversity 2002

Ortoleva Pietro and Erik Snowberg lsquolsquoOverconfidence in Political BehaviorrsquorsquoAmerican Economic Review 105 (2015) 504ndash535

Phelps Edmund lsquolsquoThe Statistical Theory of Racism and Sexismrsquorsquo AmericanEconomic Review 62 (1972) 659ndash661

Pope Devin and Justin Sydnor lsquolsquoGeographic Variation in the Gender Differencesin Test Scoresrsquorsquo Journal of Economic Perspectives 24 (2010) 95ndash108

Rabin Matthew lsquolsquoInference by Believers in the Law of Small NumbersrsquorsquoQuarterly Journal of Economics 117 (2002) 775ndash816

Rabin Matthew and Joel Schrag lsquolsquoFirst Impressions Matter A Model ofConfirmatory Biasrsquorsquo Quarterly Journal of Economics 114 (1999) 37ndash82

Rabin Matthew and Dimitri Vayanos lsquolsquoThe Gamblerrsquos and Hot-Hand FallaciesTheory and Applicationsrsquorsquo Review of Economic Studies 77 (2010) 730ndash778

Reuben Ernesto Paola Sapienza and Luigi Zingales lsquolsquoHow Stereotypes ImpairWomenrsquos Careers in Sciencersquorsquo Proceedings of the National Academy ofSciences 111 (2014) 4403ndash4408

Rosch Eleanor lsquolsquoNatural Categoriesrsquorsquo Cognitive Psychology 4 (1973) 328ndash350Ryan Carey S lsquolsquoAccuracy of Black and White College Studentsrsquo In-Group and

Out-Group Stereotypesrsquorsquo Personality and Social Psychology Bulletin 22(1996) 1114ndash1127

Schneider David The Psychology of Stereotyping (New York Guilford Press2004)

Schneider David Albert Hastorf and Phoebe Ellsworth Person Perception(Reading MA Addison-Wesley 1979)

Shih Margaret Todd Pittinsky and Nalini Ambady lsquolsquoStereotype SusceptibilityIdentity Salience and Shifts in Quantitative Performancersquorsquo PsychologicalScience 10 (1999) 80ndash83

Shih Margaret Todd Pittinsky and Amy Trahan lsquolsquoDomain-Specific Effects ofStereotypes on Performancersquorsquo Self and Identity 5 (2006) 1ndash14

Steele Claude Whistling Vivaldi How Stereotypes Affect Us and What We CanDo (New York Norton 2010)

Tenenbaum Joshua and Thomas Griffiths lsquolsquoThe Rational Basis ofRepresentativenessrsquorsquo 23rd Annual Conference of the Cognitive ScienceSociety (2001) 1036ndash1041

Tversky Amos and Daniel Kahneman lsquolsquoExtensional versus Intuitive ReasoningThe Conjunction Fallacy in Probability Judgmentrsquorsquo Psychological Review 90(1983) 293ndash315

Weinberger Catherin lsquolsquoIs the Science and Engineering Workforce Drawn fromthe Far Upper Tail of the Math Ability Distributionrsquorsquo mimeo UCSB 2005

Westfall Jacob Leaf Van Boven John Chambers and Charles Judd lsquolsquoPerceivingPolitical Polarization in the United States Party Identity Strength andAttitude Extremity Exacerbate the Perceived Partisan DividersquorsquoPsychological Science 10 (2015) 145ndash158

Wolsko Christopher Bernadette Park Charles Judd and Bernd WittenbrinklsquolsquoFraming Interethnic Ideology Effects of Multicultural and Color-BlindPerspectives on Judgments of Groups and Individualsrsquorsquo Journal ofPersonality and Social Psychology 78 (2000) 635ndash654

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Page 16: I. Introduction · uneducated at the beginning of the 20th century, and as high achievers at the beginning of the 21st (Madon et al. 2001). Social science has produced three broad

IIIA Likely versus Unlikely Exemplars

The most representative type for a group is the one thatagents most easily recall and associate with the group itself forinstance a red-haired Irishman or a 65+-year-old FloridianSocial psychologists call this type the exemplar of the groupAccordingly we define

DEFINITION 3 A type t is an exemplar for G given comparisongroup ndashG when

t 2 arg maxt

tG

tG

Under any specification of the weighting function ht inDefinition 2 overweighting (weakly) increases as we movetoward more representative types so the exemplar is also thetype whose probability is overweighted the most16 By analyzingthe exemplar then we can gauge whether representativenessinduces the DM to overweight a likely type (as happens in stan-dard models of categorical thinking) or an unlikely type Whenoverweighting occurs in unlikely and extreme types the biases ofstereotypes can be particularly severe17

Equation (2) yields the following characterization

PROPOSITION 1 Suppose the conditional distributions G and G

are not identical Consider two extreme cases

(i) If for all t t0

2 T we have that tG gt t0 G if and only iftG gt t0 G then the modal type is not an exemplar forat least one group

(ii) If for all t t0

2 T we have that tG gt t0 G if and only iftG lt t0 G then for each group the modal type is theexemplar

16 Consider the function hethTHORN from Definition 2 When applied to more repre-sentative types the first argument of the function increases while one of the otherT ndash 1 arguments decreases As a result the weighting factor ht (and thus overweigh-ing

sttG

tG) increases as well

17 In the rank-based truncation model the frequency of the exemplar providesa measure of stereotype accuracy By accuracy we mean the extent to which thestereotype minimizes the distance

Pt eth

sttG tGTHORN

2 When d = 1 and only one type isrecalled (there are no ties) accuracy is maximized if the exemplar is the most likelytype and minimized if the exemplar is the least likely type

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Case i says that when groups have similar distributions inthe sense of having the same likelihood ranking the most repre-sentative type is unlikely for at least one group potentially bothRepresentativeness draws the DMrsquos attention to group differ-ences neglecting the fact that the groups are similar and havethe same mode This mechanism generates inaccurate stereo-types and is illustrated by the Florida example This resultholds under any measure of representativeness that differenti-ates the two groups (eg the difference tG tG)

Case ii says that the most representative type tends to belikely for both groups when the distributions are very differentIn this case groups differ the most around their modes so repre-sentativeness and likelihood coincide Thinking of Swedes aslsquolsquoblondrsquorsquo and Europeans as lsquolsquodark hairedrsquorsquo is accurate precisely be-cause these are majority traits of the Swedish and European pop-ulations respectively In these cases stereotyping yields fairlyreliable models Of course there is still some inaccuracy Evenin the case of likely exemplars judgment errors can be signifi-cant For instance voters in some US states are perceived aslsquolsquobluersquorsquo or lsquolsquoredrsquorsquo because a majority of the population votesDemocrat or Republican In reality even in lsquolsquobluersquorsquo states farfrom everyone votes Democrat In the 2012 presidential electionvote shares of either candidate in most states ranged from 40 to6018

When DMs strongly overweight representative types themost severe biases occur when those types are unlikely and ex-treme This is true both under rank based truncations and undersmooth discounting functions (see Section IIIB) Ethnic stereo-types based on crime or terrorism exhibit this error they neglectthe fact that by far the most common types in all groups arehonest and peaceful

IIIB Stereotypical Moments

We now characterize how the first two moments of a distri-bution are distorted by the process of stereotyping To do so wemust restrict our analysis to cardinal ordered types The follow-ing results hold for any weighting function htethTHORN satisfyingDefinition 2 We consider two canonical cases that prove usefulin illustrating the predictions of the model

18 Presidential Election Results NBCNewscom see httpelectionsnbcnewscomnspolitics2012allpresident (accessed 5 September 2016)

STEREOTYPES 1769

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In the first case groups G and ndashG are such that the likelihoodratio tG

tGis monotonic in t The monotone likelihood ratio prop-

erty (MLRP) holds to a first approximation in many empiricalsettings and is also assumed in many economic models such asstandard agency models19 If tG

tGis monotonically increasing (de-

creasing) in t then group G is associated with higher (lower)values of t relative to the comparison group ndashG Formally

PROPOSITION 2 Suppose that MLRP holds and assume wlogthat the likelihood ratio tG

tGis strictly increasing in t Then

for any weighting function htethTHORN that is not constant in therelevant range

EstethtjGTHORN gt EethtjGTHORN gt EethtjGTHORN gt E

stethtjGTHORN

Under MLRP the most representative part of the distribu-tion for G is the right tail if tG

tGincreases in t or the left tail if tG

tG

decreases in t The representative tail is then overweighted whilethe nonrepresentative tail is underweighted As a consequencethe assessed mean E

stethtjGTHORN is too extreme in the direction of therepresentative tail

Critically in line with the social cognition perspective the ste-reotype contains a kernel of truth the DM overestimates the meanof G if this group has a higher mean than the comparison groupnamely EethtjGTHORN gt EethtjGTHORN and conversely if EethtjGTHORN lt EethtjGTHORN TheDM exaggerates this true difference because he inflates the asso-ciation of G with its most representative types20 For instancewhen judging an asset manager who performs well we tend to

19 Examples include the binomial and the Poisson families of distributionswith different parameters The characterization of distributions satisfying MLRPis easier in the case of continuous distributions (see Online Appendix D) two dis-tributions f(x) f ethx THORN that differ only in their mean satisfy MLRP if and only if thedistribution f(x) is log-concave Examples include the exponential and normal dis-tributions To the extent that discrete distributions sufficiently approximate thesedistributions (as the Poisson distribution PoisethTHORN approximates the normal distri-bution Neth THORN for large l) they will also satisfy MLRP

20 Depending on the distribution and the weighing function the DMrsquos assess-ment of the variance VarethtjGTHORNmay also be dampened relative to the truth This isoften true under the truncation weighing function In this case stereotyping effec-tively leads to a form of overconfidence in which the DM holds extreme views andoverestimates the precision of his assessment That extreme views and overconfi-dence (in the sense of over precision) go together has been documented in the settingof political ideology among others (Ortoleva and Snowberg 2015)

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overemphasize skill relative to luck because higher skill levels arerelatively more associated with higher performance This occurseven if for both skilled and unskilled managers high performanceis mostly due to luck

In the second case for which we characterize the stereotypi-cal distributions groups G and ndashG have the same mean EethtjGTHORNfrac14 EethtjGTHORN frac14 EethtTHORN but differ in their variance We abstract fromskewness and higher moments by considering distributionsethtGTHORNt2T and ethtGTHORNt2T that share the same support and are sym-metric around the medianmean EethtTHORN

PROPOSITION 3 Suppose that in G more extreme types are rela-tively more frequent than in ndashG Formally the likelihoodratio tG

tGis U-shaped in t around EethtTHORN Then for any weight-

ing function htethTHORN that is not constant in the relevant rangestereotypical beliefs satisfy

VarstethtjGTHORN gt VarethtjGTHORN gt VarethtjGTHORN gt VarstethtjGTHORN

EstethtjGTHORN frac14 E

stethtjGTHORN frac14 EethtTHORN

When group G has a higher relative prevalence of extremetypes its representative types are located at both extremes of thedistribution The DMrsquos beliefs about G are then formed by over-weighting both tails while underweighting the unrepresentativemiddle The overweighting of Grsquos tails causes the assessment ofits variance VarstethtjGTHORN to be too high For example the skill dis-tribution of immigrants to the United States may be perceived ashaving very fat tails or even bimodal with immigrants beingperceived as either unskilled or very skilled relative to the resi-dent population The mean of the group in contrast is assessedcorrectly because the stereotypical distribution remains symmet-ric around EethtTHORN As before the stereotype contains a kernel oftruth It induces the agent to exaggerate the true differences be-tween groups namely the higher variance of G relative to itscounterpart

We present a number of extensions of the model in the OnlineAppendix We first consider multidimensional type spaces andshow that stereotypes center around the dimension wheregroups differ the most in line with the kernel of truth logic(Online Appendix C) Multidimensional stereotypes imply thatthe dimension we think about is influenced by context For

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example the Irish are stereotyped as red-haired when comparedwith the European population However when compared withthe Scots a more plausible stereotype for the Irish is lsquolsquoCatholicrsquorsquobecause religion is the dimension along which Irish and Scotsdiffer the most

In Online Appendix D we extend the model to continuoustype spaces Many settings of interest in economics can be use-fully described by continuous probability distributions and weshow our model is particularly tractable in this case In OnlineAppendix E we relax Definition 2 and allow weighting of types toalso be influenced by their likelihood We show that the basicinsight that stereotypes contain a kernel of truth carries throughto these cases as well

To summarize the psychology of representativeness yieldsstereotypes that are consistent with the social cognition approachin which individuals assess groups by recalling and focusing ondistinctive group traits When there are systematic differencesbetween groups stereotypes get the direction right but exagger-ate differences

IIIC Some Examples

A growing body of field and experimental evidence points to awidespread belief that women are worse than men at mathemat-ics (Eccles Jacobs and Harold 1990 Guiso et al 2008 CarrellPage and West 2010) This belief persists despite the fact that fordecades women have been gaining ground in average schoolgrades including mathematics and have recently surpassedmen in overall school performance (Goldin Katz and Kuziemko2006 Hyde et al 2008) This belief shared by men and women(Reuben Sapienza and Zingales 2014) may help account for thegender gap in the choices of high school tracks college degreesand careers with women disproportionately choosing humanitiesand health-related areas (Weinberger 2005 Buser Niederle andOosterbeek 2014) and forgoing significant wage premiums toquantitative skills (Bertrand 2011)

Gender stereotypes in mathematics particularly beliefs thatexaggerate the extent of average differences are consistent withthe predictions of our model The fact that men are overrepre-sented at the very highest performance levels leads a stereotyp-ical thinker to exaggerate the magnitude of mean differencesFigure I shows the score distributions from the mathematics

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section of 2013rsquos Scholastic Aptitude Test (SAT) for men andwomen21 The distributions are very similar with averagescores slightly higher for men (531 versus 499 out of 800)However scores for men have a heavier right tail with mentwice as likely to have a perfect SAT math score than women22

In light of such data the stereotypical male performance in math-ematics is high while the stereotypical female performance ispoor Predictions based on such stereotypes are inaccurate exag-gerating true differences Consistent with this prediction exper-imental evidence shows that both genders underestimatewomenrsquos ability in simple math tasks even controlling for pastperformance (Reuben Sapienza and Zingales 2014) Coffman(2014) shows a similar pattern extends to confidence about ownability in other male-typed domains with women reporting sig-nificantly less confidence in gender-incongruent than gender-congruent tasks Our model suggests that these patterns mightcome from stereotypes based on gender differences in the righttail of the distribution While differences in the right tail of thedistribution are unlikely to be relevant for most decisions stereo-typical thinking driven by these differences has the potential toimpact economically important decisions whether through self-stereotyping (ie choice of careers or majors as in BuserNiederle and Oosterbeek 2014) or through discrimination (iehiring decisions as in Bohnet van Geen and Bazerman 2016)

The logic of exaggerated yet directionally correct stereotypesalso sheds light on the well-documented phenomenon of base rateneglect (Kahneman and Tversky 1973) Indeed Proposition 2implies that the DM overreacts to information that assigns

21 Standardized test performance measures not only innate ability but alsoeffort and investment by third parties (Hyde et al 2008) The mapping of test per-formance into inferences about innate ability is an issue not addressed by ourmodel

22 For 2013 SAT Mathematics scores see httpmediacollegeboardcomdigitalServicespdfresearchSAT-Percentile-Ranks-By-Gender-Ethnicity-2013pdf Results are similar for the National Assessment of Educational Progress(NAEP) which are more representative of the overall population For 2012NAEP scores for 17-year-olds in mathematics see httpnationsreportcardgovltt_2012age17maspx See Hyde et al (2008) Fryer and Levitt (2010) and Popeand Sydnor (2010) for in-depth empirical analyses of the gender gap inmathematics

STEREOTYPES 1773

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people to groups precisely because such information generatesextreme stereotypes Consider the classic example in which amedical test for a particular disease with a 5 prevalence has a90 rate of true positives and a 5 rate of false positives The testassigns each person to one of two groups + (positive test) or ndash(negative test) The DM estimates the frequency of the sick type(s) and the healthy type (h) in each group The test is informativea positive result increases the relative likelihood of sickness anda negative result increases the relative likelihood of health forany prior Formally

PreththornjsTHORN

PreththornjhTHORNgt 1 gt

PrethjsTHORN

PrethjhTHORNeth4THORN

This condition has clear implications the representative personwho tests positive is sick while the representative person whotests negative is healthy Following Proposition 2 the DMreacts to the test by moving his priors too far in the right di-rection generating extreme stereotypes He greatly boosts hisassessment that a positively tested person is sick but also thata negatively tested person is healthy Because most people arehealthy the DMrsquos assessment about the group that tested neg-ative is fairly accurate but is severely biased for the group that

FIGURE I

SAT Mathematics Scores by Gender (2013)

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tested positive This analysis formalizes Tversky andKahnemanrsquos (1983) verbal account of base rate neglect23

The same mechanism may underlie several other instanceswhere DMs overweight diagnostic information When assessingan employeersquos skill level an employer attributes high perfor-mance to high skill because high performance is the distinctivemark of a talented employee Because he neglects the possibilitythat some talented employees perform poorly and that somenontalented ones perform well (perhaps due to stochasticity inthe environment) the employer has too much faith in skill andneglects the role of luck in accounting for the output Similarlywhen assessing the performance of firms in a hot sector of theeconomy (eg G = internet) an investor recalls highly successfulfirms in that sector (t = return of Google Amazon etc) He ne-glects the possibility of firms being unsuccessful because lack ofsuccess is statistically nondiagnostic and psychologically nonrep-resentative of a growing sectormdasheven if it is likely This causesexcessive optimism (in that the expectation of growth is unrea-sonably high) and overconfidence (in that the variability in earn-ings growth considered possible is truncated) True the hot sectormay have better growth opportunities on average but represen-tativeness exaggerates this feature and induces the investor toneglect a significant risk of failure

IV Evidence on Representativeness and Stereotypes

Testing our model requires evaluating the beliefs individualshold about a target group against the true distribution of thattarget group over an attribute space An ideal data set would

23 Our account is distinct from a mechanical underweighting of base rates inBayes rule as in Grether (1980) and Bodoh-Creed Benjamin and Rabin (2013) Inthose models upon receiving the test results the DM can update his beliefs in thewrong direction he can be less confident that a person is healthy after a negativetest than under his prior which cannot happen in our model Although this predic-tion of our model seems consistent with introspection we are not aware of experi-mental evidence on this point Griffin and Tversky (1992) present evidenceconsistent with pure neglect of base rates but in a significantly different tasknamely inferring the bias of a coin from a history of coin flips Such experimentsare hard to compare with the predictions of our model because subjects are asked togenerate distributions of different numbers of coin flips in their minds which is amuch more involved task than to recall types of a given distribution Their assess-ments then might be wrong for other reasons See Bodoh-Creed Benjamin andRabin (2013) for a detailed discussion

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consist of naturally defined groups with known distributions overa given space of types and a corresponding set of beliefs about thedistribution of each group over that space of types This wouldallow us to test for exaggeration of true differences betweengroups and to ask whether this exaggeration is well predictedby overweighting representative types To identify a causal rolefor representativeness or context dependence we would need ex-ogenous variation in either the comparison group ndashG or in thedistributions over the type spaces This is unavailable in existingdata sets Accordingly we take a two-pronged approach First wecreate a controlled laboratory environment that allows us toinduce the exogenous variation in representative types that weneed to test causality then we reanalyze existing field evidence tocheck for consistency with our predictions

In testing our model we focus on the two main implicationsof representativeness-based stereotypes

Context dependence the stereotype of a target group de-pends on the characteristics of the reference group it iscompared to

Kernel of truth stereotypes depend on group character-istics andmdashin most (precisely characterized) settingsmdashare slanted toward representative types

We test the first property with a lab experiment (SectionIVA) We then turn to survey data on beliefs about US politicalgroups (Section IVB) for an empirical analysis that explores thesecond property The survey data are more tightly linked to ourinterest in social stereotypes The laboratory experiment allowsus to directly test the role of representativeness in generatingcontext dependent beliefs Online Appendixes F and G provideall details and additional results for the experiments and fieldevidence

IVA Lab Evidence on Representativeness and ContextDependence

The influence of the representativeness heuristic on recalland on beliefs has been extensively documented in the lab(Kahneman and Tversky 1972 1973) Our goal is to considerhow representativeness as formalized in equation (2) gives riseto context-dependent beliefs To our knowledge the possibility

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that representativeness may generate context dependence hasnot been tested before

To assess this prediction we perform a controlled laboratoryexperiment that allows us to isolate representativeness frommany confounding factorsmdashhistorical sociological or other-wisemdashthat may affect stereotype formation in the real worldWe construct our own groups of ordinary objects creating atarget group G and a comparison group ndashG We hold thetarget group G fixed and explore how participant impressions ofit change as we change the comparison group ndashG and thusrepresentativeness

We conducted several experiments in the laboratory and onAmazon Mechanical Turk Each involves a basic three-stepdesign First participants are shown the target group and a ran-domly assigned comparison group for 15 seconds In this timedifferences between groups can be noticed but the groupsrsquo precisecompositions cannot be memorized The second step consists of afew filler questions which briefly draw the participantsrsquo cognitivebandwidth away from their observation Finally participants areasked to assess the groups they saw Participants are incentiv-ized to provide accurate answers

We randomly assign participants to either the Control or theRepresentativeness condition In the Control condition G and ndashGhave nearly identical distributions so that all types are similarlyrepresentative for each group In the Representativeness condi-tion ndashG is changed in such a way that a certain type becomes veryrepresentative for G Context dependence implies that the assess-ment of G should now overweight this representative type eventhough the distribution of G itself has not changed

We ran six experiments of this form with design changesfocused on reducing participant confusion and removing con-founds We describe the final and most refined version of theseexperiments here In an attempt to provide a overview of the re-sults while remaining concise we provide the results from pooledspecifications that use all data collected In Online Appendix Fwe offer additional details and report all experiments conductedWe also give instructions and materials for each experiment thefull data set is available by request

Consider first the experiment illustrated in Figure II Agroup of 25 cartoon girls is presented next to a group of 25 cartoonboys in T-shirts of different colors blue green or purple In theControl condition (Figure II Panel a) the groups have identical

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color distributions (13 purple 12 green) so no color is represen-tative of either group The Representativeness condition (Panel b)compares the same group of girls with a different group of boysfor whom green shirts are replaced with blue shirts Now onlygirls wear green and only boys wear blue These colors althoughstill not the most frequent for either group are now most repre-sentative For each group girls and boys participants are asked anumber of questions concerning the frequency of T-shirts of dif-ferent colors worn by that group

Applying our model in the control condition the type space isT frac14 fgreen purpleg and the groups are G = girls and ndashG = boysGiven that the color distributions are identical across groups both

types are equally representativegreengirls

greenboysfrac14 1 frac14

purplegirls

purpleboys As a result

assessment of G should be correct on average stcontrolgreengirls frac14 greengirls

and stcontrolpurplegirls frac14 purplegirls for any weighing function (the same is

true about assessments of ndashG)In the treatment condition the distribution of shirt colors re-

mains the same for girls For boys green shirts are changed intoblue Thus the type space changes to T frac14 fgreen purple bluegand the representative color for girls becomes greengreengirls

greenboysfrac14 1 gt 1 frac14

purplegirls

purpleboys while that for boys becomes blue As

a result in the treatment condition subjects should inflate the

frequency of green shirts relative to the truth sttreatmentgreengirls

gt greengirls (the same should happen to assessments of blueshirts for boys) We also expect the assessed frequency of greenshirts to go up relative to the control condition namely

sttreatmentgreengirls gt stcontrol

greengirls Critically the only factor that varies

across treatments is the representativeness of the 12-colorshirt Thus if we see differences across conditions the causalrole of representativeness-based recall in shaping group judg-ments is clear24

24 We vary which colors are used in which roles across participants Someparticipants saw this particular color distribution while others see for examplegreen as the modal color and purple as the diagnostic color for boys in theRepresentativeness condition and blue as the diagnostic color for girls in theRepresentativeness condition We vary the colors across the roles to avoid con-founding the characteristics of any particular color with its diagnosticity

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FIG

UR

EII

T-S

hir

tsE

xp

erim

ent

Fig

ure

sap

pea

red

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lor

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ent

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ty

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icate

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icate

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tter

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idn

otap

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part

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P

lease

see

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sion

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icle

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STEREOTYPES 1779

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We collected data from 301 participants using this T-shirtsdesign25 Since the number of green and purple shirts is verysimilar we first ask each participant the simplest question ofwhich shirt color is modal Next we ask participants to assessthe share of green and purple shirts

Consistent with the role of representativeness participantsassigned to the Representativeness condition are 105 percentagepoints more likely to recall the less frequent color (green for girlsor blue for boys) as the modal color when it is representative of agroup (35 of participants guess the less frequent color is modalin the Control condition this proportion increases to 46 in theRepresentativeness condition p = 01 estimated from a probitregression reported in Online Appendix F)

We now turn to subjectsrsquo estimates of how many T-shirts ofeach color they saw in each group In both conditions the truedifference in counts is 1 (13 purple shirts 12 green or blue shirts)In the Control condition participants on average believe they saw054 more purple shirts than green or blue shirts In theRepresentativeness condition participants believe they saw072 fewer purple shirts than green or blue shirts (the acrosstreatment difference is significant with p = 01 from OLS regres-sion reported in Online Appendix F)

In total we collected data for six experiments of this generalstructure gathering evidence from more than 1000 participantsAs we describe in Online Appendix F although there is substan-tial variation across experiments when we pool all of the data wefind significant aggregate treatment effects in line with a role ofrepresentativeness in judgment We employ four different unor-dered types designs similar to the T-shirts experiment using sixsamples (four online and two in the laboratory) with 741 partic-ipants We find effects in the predicted direction for five of the sixsamples Using a probit regression that pools the data for theseunordered type experiments we find that participants are 93 per-centage points more likely to guess that the less frequent type ismodal when it is representative than when it is not (p = 002) Wealso run a family of ordered types experiments (two designs fivesamples 402 participants) Unlike the simpler T-shirts style

25 Throughout our analysis we exclude any participant who participated in aprevious version of the experiment and any participant who self-identified as color-blind In Online Appendix F we show that our results are unchanged if we includethese additional observations

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design the theoretical predictions for the ordered types designsare more sensitive to the specific assumptions one makes aboutthe weighting function of the DM26 We find effects in the pre-dicted direction for three of the five samples As we discuss inmore detail in Online Appendix F the ordered types resultsvary by platform with consistently stronger results on AmazonMechanical Turk than in the laboratory samples Pooling all or-dered types experiments participants are 93 percentage pointsmore likely to guess that the group of interest has a greater av-erage than the comparison group when the right tail is represen-tative (p = 062) Given our simple experimental setting withgroups of mundane objects we interpret our resultsmdasha signifi-cant and reasonably sized impact on average beliefsmdashas an im-portant proof of concept the presence of representative typesbiases ex post assessment

IVB Empirical Evidence on Political Stereotypes

We examine two data sets on political preferences and be-liefs about political preferences in the United States We inves-tigate the roles of representativeness and context dependence byseparately testing for hypotheses that allow us to assess the lead-ing theories of stereotypes

First we test whether beliefs are correct or depart systemat-ically from the truth The statistical discrimination approachbuilds on the assumption that people hold rational expectationsof group traits Comparing beliefs to the truth allows us to assessthe validity of this assumption in our data

Second we test if beliefs depart from the truth by exagger-ating (mean) differences among groups per the kernel of truthhypothesis This is an implicit test of context dependence be-cause it implies that beliefs about the target groups are shapednot only by that grouprsquos characteristics but also by those of thereference group27

Third we test if distortions in beliefs can be accounted for bythe overweighting of highly representative types (defined astypes that are relatively more frequent in the target relative to

26 This is due in part to our choice to not study MLRP distributions We moti-vate and discuss this design decision in Online Appendix F

27 Of course unlike in the laboratory experiment in this setting we cannot testfor context dependence by exogenously varying the reference group

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the reference group) The second and third tests address the keypredictions of our model

1 The Data We have two data sets on political preferences andbeliefs about political preferences The first data set from GrahamNosek and Haidt (GNH 2012) contains data from the MoralFoundations Questionnaire Respondents (1174 self-identified lib-erals and 500 self-identified conservatives) answer questions abouttheir position on a subset of 45 issues 20 moral relevance state-ments (eg lsquolsquowhen you decide whether something is right orwrong to what extent are the following considerations relevantto your thinkingrsquorsquo) and 25 moral judgments (eg lsquolsquoindicate theextent to which you would agree or disagreersquorsquo) For each issue arandomly determined subset of participants states their own posi-tion another subset states their belief on the position of a lsquolsquotypicalliberalrsquorsquo and a third subset states their belief on the position of alsquolsquotypical conservativersquorsquo The data thus include the distribution overpositions for both liberal and conservatives as well as the averagebelieved typical position of liberals and of conservatives on the 45issues Each position is elicited on 1ndash6 scale

The second data set comes from the American NationalElection Survey (ANES) and contains data from more than20000 respondents between 1964 and 201228 The surveycovers political issues of the day such as the optimal amount ofgovernment spending and service provision (1984ndash2000) or theplace of women in society (1972ndash1998) We focus on the 10 issuesthat ask participants to respond on a 1ndash7 scale (rather than justindicate binary agreement or disagreement) all 10 issues areasked in multiple years Participants are asked to provide theirown position on the scale and their believed position of theDemocratic and Republican parties (lsquolsquoWhere would you placethe Democratic [Republican] party on this scalersquorsquo) The data in-clude for each issue-year observation the distribution of partic-ipant positions for self-identified liberals and self-identifiedconservatives as well as the distribution of believed typical posi-tions of the Democratic and Republican parties

28 These data are publicly available at httpwwwelectionstudiesorgstudy-pagesanes_timeseries_cdfanes_timeseries_cdfhtm

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2 Empirical Strategy Our analysis focuses on beliefs abouttwo groups Conservatives and Liberals The types are the possi-ble positions for each issue (1 2 6 7) For the GNH data weinterpret beliefs about the lsquolsquotypicalrsquorsquo element of a group to coincidewith the believed average position in that group Similarly forthe ANES data we use the believed party positions as a proxy forbelieved mean of each group29 We then take as a benchmark thehypothesis that individuals hold accurate beliefs about eachgroup and in particular that believed mean position shouldequal true mean position at least on average across subjectsThe accurate beliefs hypothesis underlies the most common eco-nomic model of stereotyping statistical discrimination

To assess our representativeness-based model we perform aregression exercise To test our model in a linear regressionframework we rely on linear approximations of the weightingfunction Our model then yields two regression specifications

PROPOSITION 4 Let G 2 fconservative liberal g and assume

ht h tG

tG

be a differentiable and strictly increasing weight-

ing function as in Definition 2 The following hold as a first-order approximation around identical distributions G

Gfrac14 1

(i) Kernel of truth regression There exists a constant gt 0such that

EstethtjGTHORN frac14 EethtjGTHORNeth1thorn THORN EethtjGTHORNeth5THORN

(ii) Representativeness regression Denote H frac14 fT 2 Tg

the right tail of types and RconsH frac14

PHtconsPHtlib

as the average

representativeness of right tail types for conservatives

29 This assumption is consistent with the authorsrsquo interpretation of the GNHdata (GNH 2012) and with previous studies using ANES (eg Westfall et al 2015)Furthermore to the extent that this assumption holds equally well for most issueswithin a data set our focus on cross-issue differences should allow us to test thepredictions of our model even with an imperfect proxy for beliefs of mean positionsFinally the data provide some insight into whether subjects are reporting (per-ceived) modal or mean types As we show the modal type is a poor prediction ofstated beliefs while a distorted mean slanted toward representative types is anaccurate prediction of stated beliefs

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Under the further approximation where tcons

tlibampRcons

H for

t 2 H

EstethtjconsTHORN frac14 EethtjconsTHORN thorn consethR

consH 1THORNeth6THORN

EstethtjlibTHORN frac14 EethtjlibTHORN libethR

consH 1THORNeth7THORN

where lcons and llib are positive constants

The first regression allows us to test for the kernel of truthhypothesis and the second set of regressions allows us to test forthe role of representativeness

Equation (5) says that respondents in our model inflate theaverage position of a group say the conservatives if and only ifthe group has a higher average position than the other groupnamely the liberals Formally EstethtjconsTHORN gt EethtjconsTHORN if and onlyif EethtjconsTHORN gt EethtjlibTHORN Because in our measurement scale highertypes mean lsquolsquomore conservativersquorsquo we expect (i) believed conserva-tive average to be higher than the truth and (ii) the extent ofoverstatement to decrease in the average liberal position EethtjlibTHORNConversely we expect the average liberal position to be lowerthan the truth the more so the higher the average conservativeposition EethtjconsTHORN

As previously discussed the basis of these predictions is con-text dependence information about the distribution of ndashG is rel-evant for the beliefs about G This context dependence isinconsistent with rational expectations in which only thegrouprsquos own means should affect beliefs We test the hypothesisthat the true mean EethtjGTHORN is a significant predictor of the believedmean E

stethtjGTHORN with a positive sign and the other grouprsquos truemean EethtjGTHORN is a predictor of the believed mean with a negativesign

Equations (6) and (7) say that repondentsrsquo assessment bias isshaped by representativeness When the right tail is more repre-sentative for conservatives (Rcons

H 1 positive and large) partici-pants should inflate the average conservative position more(higher E

stethtjconsTHORN EethtjconsTHORN) and deflate the average liberal po-sition more (lower E

stethtjlibTHORN EethtjlibTHORN) We test the hypothesisthat the inflation in conservative positions is positively associatedwith the representativeness of the right tail for the conservativesand the inflation in liberal positions is negatively associated with

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it Once again the representativeness of the right tail is com-puted using the true distribution of positions

In equations (6) and (7) in many cases the representative tailis also the most likely one As a consequence these tests cannotdistinguish a representativeness-based from a likelihood-basedmodel of distorted beliefs We perform two additional testsFirst we run versions of equations (6) and (7) in which we controlfor the likelihood of tails (see Table A4 in Online Appendix G)Second we compute numerically the predictions of a representa-tiveness-based model of stereotypes and a likelihood-based modelof stereotypes We then assess which of these two is better able tomatch the data on beliefs

3 Empirical Results To begin we illustrate the structure ofthe data and the nature of our predictions with two simple exam-ples from the GNH data set focusing on beliefs about conserva-tives In example 1 participants are asked about their agreementwith the statement lsquolsquoIt can never be right to kill a human beingrsquorsquoIn example 2 participants are asked about the moral relevance oflsquolsquowhether or not someone cared for someone weak or vulnerablersquorsquoAs can be seen in Figure III in example 1 the modal position(strongly disagree (1)) and most representative positions(strongly disagree (1)) coincide for conservatives In contrast inexample 2 in Figure III the most representative types (slightlyrelevant (3) not at all relevant (1)) are not most likely for theconservative group Following Proposition 1 we predict that be-liefs will be distorted in the direction of the most representativetypes Thus we expect more exaggeration in example 2 than inexample 1 since in example 2 the most representative types (inthe left tail) are far from the modal type whereas in example 1they coincide This is what we find the conservative position isexaggerated by only 009 positions in Example 1 (true mean 299believed mean 290) but by 106 positions in Example 2 (truemean 421 believed mean 315)

In the full data sets we treat each (issue year) pair as anobservation and we cluster standard errors at the issue level Forthe GNH data we have 45 observations 45 issues measured inthe same year For the ANES data we have 66 observations 10issues measured in multiple years To begin we simply docu-ment systematic exaggeration in both data sets This is a primaryfocus of the original analysis in GNH (2012) and also in Westfall

STEREOTYPES 1785

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FIGURE III

Two Examples

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et al (2015)rsquos analysis of the ANES data30 Figure IV shows thatthe believed difference between typical conservative and typicalliberal positions is larger than the true difference in mean posi-tions for 109 of the 111 observations The data for both GNH(squares) and ANES (triangles) lie above the 45-degree line(dashed)31 Average exaggeration is 062 positions on the scale(066 in the GNH data 059 in the ANES data)32

The systematic and significant exaggeration of mean differ-ences suggests that the benchmark model of accurate beliefs ismissing something important Indeed this exaggeration reflectsthe fact that believed means are typically more extreme than truemeans First note that the kernel of truth regression (equation(5)) generates exaggeration of mean differences just as docu-mented in Figure IV

EstethtjGTHORN E

stethtjGTHORN frac14 eth1thorn 2THORN frac12EethtjGTHORN EethtjGTHORN

To bring this prediction to the data we regress the believedmean position for each group EBethtjGTHORN on the true mean of thegroup EethtjGTHORN and the true mean of the comparison groupEethtjGTHORN across issues We do this for each group (liberals con-servatives) in each data set separately We also present pooledspecifications that combine the data sets to make a prediction fora given group (liberals conservatives) In these pooled specifica-tions we include a dummy variable indicating whether theobservation came from the ANES data set For all specificationswe cluster observations at the issue level33 The results from re-gression are shown in Table I In every specification we find thatEethtjGTHORN is a significant predictor of EBethtjGTHORN with the predicted pos-itive sign Crucially for five of the six specifications the mean of

30 Chambers and Melnyk (2006) also find evidence of exaggeration of truedifferences in beliefs about political positions

31 For convenience we recode all issues so that the high end of the scale (67)represents the stereotypically more conservative position

32 A natural question to ask is how beliefs vary across liberals and conserva-tives That is do beliefs about a group G depend on membership in G versus ndashG Ourmodel does not speak to this issue However in Online Appendix G we show thatthe results we document below hold for both beliefs held by conservatives and be-liefs held by liberals see Tables A9 A10 and A11

33 In general the results presented below for the ANES data are not largelyimpacted by the decision to cluster at the issue level Similar results are obtained ifthe data are not clustered

STEREOTYPES 1787

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the comparison group EethtjGTHORN is also a significant predictor ofE

BethtjGTHORN with the predicted negative signAlthough these results provide strong evidence of context

dependence and are consistent with our model they do not pindown a role for representativeness of types Our next test relatesthe magnitude of representativeness of tail types to the magni-tude of belief distortions

To this end we implement the regressions in equations (6)and (7) Following Proposition 4 we compute the average repre-

sentativeness of tail types for conservatives RconsH frac14

PtT2tconsPtT2tlib

We

again test the hypothesis that RconsH is a significant predictor of Est

ethtjconsTHORN with a positive sign and a predictor of EstethtjlibTHORN with a

negative sign Table II shows that conditional on true mean RconsH

predicts believed mean for each group G as expected The firstthree specifications display the results for predicting beliefs heldabout conservatives In both data sets the average representa-tiveness of tail types for conservatives is a significant positivepredictor of beliefs held about conservatives The final three spe-cifications display the results for predicting beliefs held about

FIGURE IV

Exaggeration of Differences

QUARTERLY JOURNAL OF ECONOMICS1788

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liberals We find that the average representativeness of tail typesfor conservatives is a negative predictor of beliefs held about lib-erals This effect is significant in the GNH data and marginallysignificant in the ANES data

We present several additional results in Online Appendix GTo further examine the role of representativeness in driving be-liefs we first show the results of Table II carry through when we

TABLE II

AVERAGE REPRESENTATIVENESS OF TAIL POSITIONS PREDICTS BELIEFS

OLS Predicting Believed Mean of Group G for Each Issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position

of group G for issue

078 024 051 072 018 041

(006) (008) (009) (005) (005) (010)

Avg rep of tail types for

conservatives RconsH

019 055 025 014 012 024

(007) (022) (008) (006) (007) (005)

Constant 101 260 184 093 271 201

(026) (045) (029) (022) (025) (032)

R2 082 048 060 091 031 070

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

TABLE I

INFORMATION ABOUT ndashG PREDICTS BELIEFS ABOUT G

OLS predicting believed mean of group G for each issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position of

conservatives for issue

102 098 096 021 019 025

(0097) (0133) (0076) (0060) (0116) (0060)

True mean position of

liberals for issue

035 086 058 0987 039 073

(0106) (0134) (0131) (0066) (0106) (0135)

Constant 151 335 235 069 258 156

(0195) (0269) (0279) (0122) (0249) (0270)

R2 083 053 066 092 032 068

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

STEREOTYPES 1789

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control for the average likelihood on the tail positions (see Table A4in Online Appendix G) Most tellingly we use the model to predictbeliefs across issues and compare those to the data For simplicitywe use the rank-based truncation specification to predict mean be-liefs when stereotypes include the d most representative types ford frac14 1 T We compare these predictions to those of a model inwhich beliefs are obtained by restricting the distribution to the dmost likely types Our benchmark for both models is predicting thebelieved mean from the entire distribution where d = T We showthat the predictions of the rank-based truncation model with d = 4or 5 compare favorably to both a likelihood-based truncation model(with any d) and the accurate beliefs benchmark Interestingly thisresult suggests that stereotypical beliefs are well approximated byneglecting the least representative types (as opposed to focusingonly on the most representative types) and so represent a moderatethough systematic departure from the standard benchmarkFinally we show that the results we document above hold forboth beliefs held by conservatives and beliefs held by liberals (seeTables A9 A10 and A11 in Online Appendix G)

V Conclusion

We present a model of stereotypical thinking in which DMsmaking predictions about a group overweight the grouprsquos mostdistinctive types These overweighted types are not the mostlikely ones given the DMrsquos data but the most representativeones in the sense of being the most diagnostic of the group rela-tive to other groups Representativeness implies that what ismost distinctive of a group depends on what group it is comparedwith We present experimental evidence that confirms this con-text dependence in recall-based assessments of groups Finallywe evaluated the predictions of the model using political data fromexisting large-scale surveys We find context dependence to be akey feature of beliefs Given the richness of the political data wecan go a step further and identify a role for representativeness inparticular As the representativeness of tail types increases beliefsof a group are distorted in the direction of that tail

Our approach provides a parsimonious and psychologicallyfounded account of how DMs generate simplified representationsof reality from social groups to stock returns and offers a unifiedaccount of disparate pieces of evidence relating to this type of

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uncertainty The model captures the central fact that stereotypeshighlight the greatest difference between groups thus explainingwhy some stereotypes are very accurate while others lack valid-ity Still stereotypes often have a kernel of truth when they arebased on systematicmdasheven if smallmdashdifferences between groupsThis logic allows us to describe a number of heuristics and psy-chological biases many of which arise in the context of predictionproblems Generically our model generates overreaction to diag-nostic information

Our model is based on representativeness and does not cap-ture all the features of stereotypical thinking However it cap-tures perhaps the central feature when we think of a group wefocus on what is most distinctive about it and neglect or under-weight the rest

Saeuroıd Business School University of Oxford

Ohio State University and Harvard Business School

Universita Bocconi and Innocenzo Gasparini Institute

for Economic Research

Harvard University

Supplementary Material

An Online Appendix for this article can be found at QJEonline (qjeoxfordjournalorg)

References

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Arrow Kenneth lsquolsquoThe Theory of Discriminationrsquorsquo in Discrimination in LaborMarkets Orley Ashenfelter and Albert Rees eds (Princeton NJPrinceton University Press 1973)

Ashton Michael and Victoria Esses lsquolsquoStereotype Accuracy Estimating theAcademic Performance of Ethnic Groupsrsquorsquo Personality and SocialPsychology Bulletin 25 (1999) 225ndash236

Barberis Nicholas Andrei Shleifer and Robert Vishny lsquolsquoA Model of InvestorSentimentrsquorsquo Journal of Financial Economics 49 (1998) 307ndash343

Bayer Sylvia lsquolsquoThe Accuracy of Academic Gender Stereotypesrsquorsquo Sex Roles 40(1999) 787ndash813

Benjamin Dan James Choi and Joshua Strickland lsquolsquoSocial Identity andPreferencesrsquorsquo American Economic Review 100 (2010) 1913ndash1928

Benjamin Dan Matthew Rabin and Collin Raymond lsquolsquoA Model of Non-Belief inthe Law of Large Numbersrsquorsquo Journal of the European Economic Association15 (2015) 515ndash544

Bertrand Marianne lsquolsquoNew Perspectives on Genderrsquorsquo Handbook of LaborEconomics 4 (2011) 1543ndash1590

Bodoh-Creed Aaron Dan Benjamin and Matthew Rabin lsquolsquoThe Dynamics of Base-Rate Neglectrsquorsquo mimeo Haas Business School 2013

STEREOTYPES 1791

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Bohnet Iris Alexandra van Geen and Max Bazerman lsquolsquoWhen PerformanceTrumps Gender Bias Joint versus Separate Evaluationrsquorsquo ManagementScience 5 (2016) 1225ndash1234

Bordalo Pedro Nicola Gennaioli and Andrei Shleifer lsquolsquoSalience Theory of Choiceunder Riskrsquorsquo Quarterly Journal of Economics 127 (2012) 1243ndash1285

mdashmdashmdash lsquolsquoSalience and Consumer Choicersquorsquo Journal of Political Economy 121(2013) 803ndash843

Briton Nancy and Judith Hall lsquolsquoBeliefs about Female and Male NonverbalCommunicationrsquorsquo Sex Roles 32 (1995) 79ndash90

Buser Thomas Muriel Niederle and Hessel Oosterbeek lsquolsquoGenderCompetitiveness and Career Choicesrsquorsquo Quarterly Journal of Economics 129(2014) 1409ndash1447

Carrell Scott Marianne Page and James West lsquolsquoSex and Science How ProfessorGender Perpetuates the Gender Gaprsquorsquo Quarterly Journal of Economics 125(2010) 1101ndash1144

Chambers John and Darya Melnyk lsquolsquoWhy Do I Hate Thee ConflictMisperceptions and Intergroup Mistrustrsquorsquo Personality and SocialPsychology Bulletin 32 (2006) 1295ndash1311

Chan Wayne Robert R McCrae Filip De Fruyt Lee Jussim CorinnaE Lockenhoff Marleen De Bolle Paul T Costa Jr Angelina R SutinAnu Realo Juri Allik Katsuharu Nakazato Yoshiko ShimonakaMartina Hrebıckova Sylvie Graf Michelle Yik Marina Brunner-SciarraNora Leibovich De Figueora Vanina Schmidt Chang-kyo Ahn Hyun-nie Ahn Maria E Aguilar-Vafaie Jerzy Siuta Barbara SzmigielskaThomas R Cain Janet T Crawford Khairul Anwar Mastor Jean-Pierre Rolland Florence Nansubuga Daniel R MiramontezVeronica Benet-Martınez Jerome Rossier Denis Bratko Iris MarusicJamin Halberstadt Mami Yamaguchi Goran Knezevic Thomas A MartinMirona Gheorghiu Peter B Smith Claudio Barbaranelli Lei WangJane Shakespeare-Finch Margarida P Lima Waldemar KlinkoszAndrzej Sekowski Lidia Alcalay Franco Simonetti Tatyana V AvdeyevaV S Pramila and Antonio Terracciano lsquolsquoStereotypes of Age Differences inPersonality Traits Universal and Accuratersquorsquo Journal of Personality andSocial Psychology 103 (2012) 1050ndash1066

Chen Yan Sherry Xin Liu Tracy Xiao and Margaret Shih lsquolsquoWhich Hat to WearImpact of Natural Identities on Coordination and Cooperationrsquorsquo Games andEconomic Behavior 84 (2014) 58ndash86

Coffman Katherine lsquolsquoEvidence on Self-Stereotyping and the Contribution ofIdeasrsquorsquo Quarterly Journal of Economics 129 (2014) 1625ndash1660

Cunningham Tom lsquolsquoComparisons and Choicersquorsquo mimeo Stockholm University2013

Diekman Amanda Alice Eagly and Patrick Kulesa lsquolsquoAccuracy and Bias in theStereotypes about the Social and Political Attitudes of Women and MenrsquorsquoJournal of Experimental Social Psychology 38 (2002) 268ndash282

Eccles Jacquelynne S Janis E Jacobs and Rena D Harold lsquolsquoGender RoleStereotypes Expectancy Effects and Parentsrsquo Socialization of GenderDifferencesrsquorsquo Journal of Social Issues 46 (1990) 183ndash201

Fryer Roland and Matthew Jackson lsquolsquoA Categorical Model of Cognition andBiased Decision-Makingrsquorsquo BE Journal of Theoretical Economics 8 (2008)1ndash42

Fryer Roland and Steven Levitt lsquolsquoAn Empirical Analysis of the Gender Gap inMathematicsrsquorsquo American Economic Journal Applied Economics 2 (2010)210ndash240

Gennaioli Nicola and Andrei Shleifer lsquolsquoWhat Comes to Mindrsquorsquo Quarterly Journalof Economics 125 (2010) 1399ndash1433

Gennaioli Nicola Andrei Shleifer and Robert Vishny lsquolsquoNeglected RisksFinancial Innovation and Financial Fragilityrsquorsquo Journal of FinancialEconomics 104 (2012) 452ndash468

Gilens Martin lsquolsquoRace and Poverty in America Public Misperceptions and theAmerican News Mediarsquorsquo Public Opinion Quarterly 60 (1996) 515ndash541

Glaeser Edward lsquolsquoThe Political Economy of Hatredrsquorsquo Quarterly Journal ofEconomics 120 (2005) 45ndash86

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Glover Dyland Amanda Pallais and William Pariente lsquolsquoDiscrimination as a Self-Fulfilling Prophecy Evidence from French Grocery Storesrsquorsquo mimeo HarvardUniversity 2015

Goldin Claudia Lawrence Katz and Ilyana Kuziemko lsquolsquoThe Homecoming ofAmerican College Women The Reversal of the College Gender GaprsquorsquoJournal of Economic Perspectives 20 (2006) 133ndash156

Graham Jesse Brian Nosek and Jonathan Haidt lsquolsquoThe Moral Stereotypes ofLiberals and Conservatives Exaggeration of Differences across thePolitical Spectrumrsquorsquo PLoS One 7 (2012) 1ndash13

Grether David lsquolsquoBayes Rule as a Descriptive Model The RepresentativenessHeuristicrsquorsquo Quarterly Journal of Economics 95 (1980) 537ndash557

Griffin Dale and Amos Tversky lsquolsquoThe Weighing of Evidence and theDeterminants of Confidencersquorsquo Cognitive Psychology 24 (1992) 411ndash435

Guiso Luigi Ferdinando Monte Paola Sapienza and Luigi Zingales lsquolsquoCultureGender and Mathrsquorsquo Science 320 (2008) 1164ndash1165

Hilton James and William Von Hippel lsquolsquoStereotypesrsquorsquo Annual Review ofPsychology 47 (1996) 237ndash271

Hyde Janet Sara Lindberg Marcia Linn Amy Ellis and Caroline WilliamslsquolsquoGender Similarities Characterize Math Performancersquorsquo Science 321 (2008)494ndash495

Judd Charles and Bernardette Park lsquolsquoDefinition and Assessment of Accuracy inSocial Stereotypesrsquorsquo Psychological Review 100 (1993) 109ndash128

Jussim Lee Jarret Crawford Stephanie Anglin John Chambers Sean Stevensand Florette Cohen lsquolsquoStereotype Accuracy One of the Largest and MostReplicable Effects in All of Social Psychologyrsquorsquo in The Handbook ofPrejudice Stereotyping and Discrimination Todd Nelson ed (MahwahNJ Lawrence Erlbaum 2015)

Kahneman Daniel and Amos Tversky lsquolsquoSubjective Probability A Judgment ofRepresentativenessrsquorsquo Cognitive Psychology 3 (1972) 430ndash454

mdashmdashmdash lsquolsquoOn the Psychology of Predictionrsquorsquo Psychological Review 80 (1973) 237ndash251

Kaplowitz Stan Bradley Fisher and Clifford Broman lsquolsquoHow Accurate ArePerceptions of Social Statistics about Blacks and Whitesrsquorsquo Public OpinionQuarterly 67 (2003) 237ndash243

Kersten Daniel Pascal Mamassian and Alan Yuille lsquolsquoObject Perception asBayesian Inferencersquorsquo Annual Review of Psychology 55 (2004) 271ndash304

Klein Richard Kate A Ratliff Michelangelo Vianello Reginald B Adams JrStepan Bahnik Michael J Bernstein Konrad Bocian Mark J BrandtBeach Brooks Claudia Chloe Brumbaugh Zeynep CemalcilarJesse Chandler Winnee Cheong William E Davis Thierry DevosMatthew Eisner Natalia Frankowska David Furrow Elisa Maria GallianiFred Hasselman Joshua A Hicks James F Hovermale S Jane HuntJeffrey R Huntsinger Hans IJzerman Melissa-Sue John Jennifer A Joy-Gaba Heather Barry Kappes Lacy E Krueger Jaime Kurtz CarmelA Levitan Robyn Mallett Wendy L Morris Anthony J Nelson JasonA Nier Grant Packard Ronaldo Pilati Abraham M RutchickKathleen Schmidt Jeanine L Skorinko Robert Smith Troy G SteinerJustin Storbeck Lyn M Van Swol Donna Thompson Anna van rsquot VeerLeigh Ann Vaughn Marek Vranka Aaron Wichman Julie A Woodzickaand Brian A Nosek lsquolsquoInvestigating Variation in Replicability A ManyLabs Replication Projectrsquorsquo Social Psychology 45 (2014) 142ndash152

Lundberg Shelly and Richard Startz lsquolsquoPrivate Discrimination and SocialIntervention in Competitive Labor Marketsrsquorsquo American Economic Review73 (1983) 340ndash347

Madon Stephanie Max Guyll Kathy Aboufadel Eulices Montiel Alison SmithPolly Palumbo and Lee Jussim lsquolsquoEthnic and National Stereotypes ThePrinceton Trilogy Revisited and Revisedrsquorsquo Personality and SocialPsychological Bulletin 27 (2001) 996ndash1010

Martin Carol lsquolsquoA Ratio Measure of Sex Stereotypingrsquorsquo Journal of Personality andSocial Psychology 52 (1987) 489ndash499

STEREOTYPES 1793

at Harvard L

ibrary on October 28 2016

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McCauley Clark Krishna Thangavelu and Paul Rozin lsquolsquoSex Stereotyping ofOccupations in Relation to Television Representations and Census FactsrsquorsquoBasic and Applied Social Psychology 9 (1988) 197ndash212

Mullainathan Sendhil lsquolsquoThinking through Categoriesrsquorsquo mimeo HarvardUniversity 2002

Ortoleva Pietro and Erik Snowberg lsquolsquoOverconfidence in Political BehaviorrsquorsquoAmerican Economic Review 105 (2015) 504ndash535

Phelps Edmund lsquolsquoThe Statistical Theory of Racism and Sexismrsquorsquo AmericanEconomic Review 62 (1972) 659ndash661

Pope Devin and Justin Sydnor lsquolsquoGeographic Variation in the Gender Differencesin Test Scoresrsquorsquo Journal of Economic Perspectives 24 (2010) 95ndash108

Rabin Matthew lsquolsquoInference by Believers in the Law of Small NumbersrsquorsquoQuarterly Journal of Economics 117 (2002) 775ndash816

Rabin Matthew and Joel Schrag lsquolsquoFirst Impressions Matter A Model ofConfirmatory Biasrsquorsquo Quarterly Journal of Economics 114 (1999) 37ndash82

Rabin Matthew and Dimitri Vayanos lsquolsquoThe Gamblerrsquos and Hot-Hand FallaciesTheory and Applicationsrsquorsquo Review of Economic Studies 77 (2010) 730ndash778

Reuben Ernesto Paola Sapienza and Luigi Zingales lsquolsquoHow Stereotypes ImpairWomenrsquos Careers in Sciencersquorsquo Proceedings of the National Academy ofSciences 111 (2014) 4403ndash4408

Rosch Eleanor lsquolsquoNatural Categoriesrsquorsquo Cognitive Psychology 4 (1973) 328ndash350Ryan Carey S lsquolsquoAccuracy of Black and White College Studentsrsquo In-Group and

Out-Group Stereotypesrsquorsquo Personality and Social Psychology Bulletin 22(1996) 1114ndash1127

Schneider David The Psychology of Stereotyping (New York Guilford Press2004)

Schneider David Albert Hastorf and Phoebe Ellsworth Person Perception(Reading MA Addison-Wesley 1979)

Shih Margaret Todd Pittinsky and Nalini Ambady lsquolsquoStereotype SusceptibilityIdentity Salience and Shifts in Quantitative Performancersquorsquo PsychologicalScience 10 (1999) 80ndash83

Shih Margaret Todd Pittinsky and Amy Trahan lsquolsquoDomain-Specific Effects ofStereotypes on Performancersquorsquo Self and Identity 5 (2006) 1ndash14

Steele Claude Whistling Vivaldi How Stereotypes Affect Us and What We CanDo (New York Norton 2010)

Tenenbaum Joshua and Thomas Griffiths lsquolsquoThe Rational Basis ofRepresentativenessrsquorsquo 23rd Annual Conference of the Cognitive ScienceSociety (2001) 1036ndash1041

Tversky Amos and Daniel Kahneman lsquolsquoExtensional versus Intuitive ReasoningThe Conjunction Fallacy in Probability Judgmentrsquorsquo Psychological Review 90(1983) 293ndash315

Weinberger Catherin lsquolsquoIs the Science and Engineering Workforce Drawn fromthe Far Upper Tail of the Math Ability Distributionrsquorsquo mimeo UCSB 2005

Westfall Jacob Leaf Van Boven John Chambers and Charles Judd lsquolsquoPerceivingPolitical Polarization in the United States Party Identity Strength andAttitude Extremity Exacerbate the Perceived Partisan DividersquorsquoPsychological Science 10 (2015) 145ndash158

Wolsko Christopher Bernadette Park Charles Judd and Bernd WittenbrinklsquolsquoFraming Interethnic Ideology Effects of Multicultural and Color-BlindPerspectives on Judgments of Groups and Individualsrsquorsquo Journal ofPersonality and Social Psychology 78 (2000) 635ndash654

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Page 17: I. Introduction · uneducated at the beginning of the 20th century, and as high achievers at the beginning of the 21st (Madon et al. 2001). Social science has produced three broad

Case i says that when groups have similar distributions inthe sense of having the same likelihood ranking the most repre-sentative type is unlikely for at least one group potentially bothRepresentativeness draws the DMrsquos attention to group differ-ences neglecting the fact that the groups are similar and havethe same mode This mechanism generates inaccurate stereo-types and is illustrated by the Florida example This resultholds under any measure of representativeness that differenti-ates the two groups (eg the difference tG tG)

Case ii says that the most representative type tends to belikely for both groups when the distributions are very differentIn this case groups differ the most around their modes so repre-sentativeness and likelihood coincide Thinking of Swedes aslsquolsquoblondrsquorsquo and Europeans as lsquolsquodark hairedrsquorsquo is accurate precisely be-cause these are majority traits of the Swedish and European pop-ulations respectively In these cases stereotyping yields fairlyreliable models Of course there is still some inaccuracy Evenin the case of likely exemplars judgment errors can be signifi-cant For instance voters in some US states are perceived aslsquolsquobluersquorsquo or lsquolsquoredrsquorsquo because a majority of the population votesDemocrat or Republican In reality even in lsquolsquobluersquorsquo states farfrom everyone votes Democrat In the 2012 presidential electionvote shares of either candidate in most states ranged from 40 to6018

When DMs strongly overweight representative types themost severe biases occur when those types are unlikely and ex-treme This is true both under rank based truncations and undersmooth discounting functions (see Section IIIB) Ethnic stereo-types based on crime or terrorism exhibit this error they neglectthe fact that by far the most common types in all groups arehonest and peaceful

IIIB Stereotypical Moments

We now characterize how the first two moments of a distri-bution are distorted by the process of stereotyping To do so wemust restrict our analysis to cardinal ordered types The follow-ing results hold for any weighting function htethTHORN satisfyingDefinition 2 We consider two canonical cases that prove usefulin illustrating the predictions of the model

18 Presidential Election Results NBCNewscom see httpelectionsnbcnewscomnspolitics2012allpresident (accessed 5 September 2016)

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In the first case groups G and ndashG are such that the likelihoodratio tG

tGis monotonic in t The monotone likelihood ratio prop-

erty (MLRP) holds to a first approximation in many empiricalsettings and is also assumed in many economic models such asstandard agency models19 If tG

tGis monotonically increasing (de-

creasing) in t then group G is associated with higher (lower)values of t relative to the comparison group ndashG Formally

PROPOSITION 2 Suppose that MLRP holds and assume wlogthat the likelihood ratio tG

tGis strictly increasing in t Then

for any weighting function htethTHORN that is not constant in therelevant range

EstethtjGTHORN gt EethtjGTHORN gt EethtjGTHORN gt E

stethtjGTHORN

Under MLRP the most representative part of the distribu-tion for G is the right tail if tG

tGincreases in t or the left tail if tG

tG

decreases in t The representative tail is then overweighted whilethe nonrepresentative tail is underweighted As a consequencethe assessed mean E

stethtjGTHORN is too extreme in the direction of therepresentative tail

Critically in line with the social cognition perspective the ste-reotype contains a kernel of truth the DM overestimates the meanof G if this group has a higher mean than the comparison groupnamely EethtjGTHORN gt EethtjGTHORN and conversely if EethtjGTHORN lt EethtjGTHORN TheDM exaggerates this true difference because he inflates the asso-ciation of G with its most representative types20 For instancewhen judging an asset manager who performs well we tend to

19 Examples include the binomial and the Poisson families of distributionswith different parameters The characterization of distributions satisfying MLRPis easier in the case of continuous distributions (see Online Appendix D) two dis-tributions f(x) f ethx THORN that differ only in their mean satisfy MLRP if and only if thedistribution f(x) is log-concave Examples include the exponential and normal dis-tributions To the extent that discrete distributions sufficiently approximate thesedistributions (as the Poisson distribution PoisethTHORN approximates the normal distri-bution Neth THORN for large l) they will also satisfy MLRP

20 Depending on the distribution and the weighing function the DMrsquos assess-ment of the variance VarethtjGTHORNmay also be dampened relative to the truth This isoften true under the truncation weighing function In this case stereotyping effec-tively leads to a form of overconfidence in which the DM holds extreme views andoverestimates the precision of his assessment That extreme views and overconfi-dence (in the sense of over precision) go together has been documented in the settingof political ideology among others (Ortoleva and Snowberg 2015)

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overemphasize skill relative to luck because higher skill levels arerelatively more associated with higher performance This occurseven if for both skilled and unskilled managers high performanceis mostly due to luck

In the second case for which we characterize the stereotypi-cal distributions groups G and ndashG have the same mean EethtjGTHORNfrac14 EethtjGTHORN frac14 EethtTHORN but differ in their variance We abstract fromskewness and higher moments by considering distributionsethtGTHORNt2T and ethtGTHORNt2T that share the same support and are sym-metric around the medianmean EethtTHORN

PROPOSITION 3 Suppose that in G more extreme types are rela-tively more frequent than in ndashG Formally the likelihoodratio tG

tGis U-shaped in t around EethtTHORN Then for any weight-

ing function htethTHORN that is not constant in the relevant rangestereotypical beliefs satisfy

VarstethtjGTHORN gt VarethtjGTHORN gt VarethtjGTHORN gt VarstethtjGTHORN

EstethtjGTHORN frac14 E

stethtjGTHORN frac14 EethtTHORN

When group G has a higher relative prevalence of extremetypes its representative types are located at both extremes of thedistribution The DMrsquos beliefs about G are then formed by over-weighting both tails while underweighting the unrepresentativemiddle The overweighting of Grsquos tails causes the assessment ofits variance VarstethtjGTHORN to be too high For example the skill dis-tribution of immigrants to the United States may be perceived ashaving very fat tails or even bimodal with immigrants beingperceived as either unskilled or very skilled relative to the resi-dent population The mean of the group in contrast is assessedcorrectly because the stereotypical distribution remains symmet-ric around EethtTHORN As before the stereotype contains a kernel oftruth It induces the agent to exaggerate the true differences be-tween groups namely the higher variance of G relative to itscounterpart

We present a number of extensions of the model in the OnlineAppendix We first consider multidimensional type spaces andshow that stereotypes center around the dimension wheregroups differ the most in line with the kernel of truth logic(Online Appendix C) Multidimensional stereotypes imply thatthe dimension we think about is influenced by context For

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example the Irish are stereotyped as red-haired when comparedwith the European population However when compared withthe Scots a more plausible stereotype for the Irish is lsquolsquoCatholicrsquorsquobecause religion is the dimension along which Irish and Scotsdiffer the most

In Online Appendix D we extend the model to continuoustype spaces Many settings of interest in economics can be use-fully described by continuous probability distributions and weshow our model is particularly tractable in this case In OnlineAppendix E we relax Definition 2 and allow weighting of types toalso be influenced by their likelihood We show that the basicinsight that stereotypes contain a kernel of truth carries throughto these cases as well

To summarize the psychology of representativeness yieldsstereotypes that are consistent with the social cognition approachin which individuals assess groups by recalling and focusing ondistinctive group traits When there are systematic differencesbetween groups stereotypes get the direction right but exagger-ate differences

IIIC Some Examples

A growing body of field and experimental evidence points to awidespread belief that women are worse than men at mathemat-ics (Eccles Jacobs and Harold 1990 Guiso et al 2008 CarrellPage and West 2010) This belief persists despite the fact that fordecades women have been gaining ground in average schoolgrades including mathematics and have recently surpassedmen in overall school performance (Goldin Katz and Kuziemko2006 Hyde et al 2008) This belief shared by men and women(Reuben Sapienza and Zingales 2014) may help account for thegender gap in the choices of high school tracks college degreesand careers with women disproportionately choosing humanitiesand health-related areas (Weinberger 2005 Buser Niederle andOosterbeek 2014) and forgoing significant wage premiums toquantitative skills (Bertrand 2011)

Gender stereotypes in mathematics particularly beliefs thatexaggerate the extent of average differences are consistent withthe predictions of our model The fact that men are overrepre-sented at the very highest performance levels leads a stereotyp-ical thinker to exaggerate the magnitude of mean differencesFigure I shows the score distributions from the mathematics

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section of 2013rsquos Scholastic Aptitude Test (SAT) for men andwomen21 The distributions are very similar with averagescores slightly higher for men (531 versus 499 out of 800)However scores for men have a heavier right tail with mentwice as likely to have a perfect SAT math score than women22

In light of such data the stereotypical male performance in math-ematics is high while the stereotypical female performance ispoor Predictions based on such stereotypes are inaccurate exag-gerating true differences Consistent with this prediction exper-imental evidence shows that both genders underestimatewomenrsquos ability in simple math tasks even controlling for pastperformance (Reuben Sapienza and Zingales 2014) Coffman(2014) shows a similar pattern extends to confidence about ownability in other male-typed domains with women reporting sig-nificantly less confidence in gender-incongruent than gender-congruent tasks Our model suggests that these patterns mightcome from stereotypes based on gender differences in the righttail of the distribution While differences in the right tail of thedistribution are unlikely to be relevant for most decisions stereo-typical thinking driven by these differences has the potential toimpact economically important decisions whether through self-stereotyping (ie choice of careers or majors as in BuserNiederle and Oosterbeek 2014) or through discrimination (iehiring decisions as in Bohnet van Geen and Bazerman 2016)

The logic of exaggerated yet directionally correct stereotypesalso sheds light on the well-documented phenomenon of base rateneglect (Kahneman and Tversky 1973) Indeed Proposition 2implies that the DM overreacts to information that assigns

21 Standardized test performance measures not only innate ability but alsoeffort and investment by third parties (Hyde et al 2008) The mapping of test per-formance into inferences about innate ability is an issue not addressed by ourmodel

22 For 2013 SAT Mathematics scores see httpmediacollegeboardcomdigitalServicespdfresearchSAT-Percentile-Ranks-By-Gender-Ethnicity-2013pdf Results are similar for the National Assessment of Educational Progress(NAEP) which are more representative of the overall population For 2012NAEP scores for 17-year-olds in mathematics see httpnationsreportcardgovltt_2012age17maspx See Hyde et al (2008) Fryer and Levitt (2010) and Popeand Sydnor (2010) for in-depth empirical analyses of the gender gap inmathematics

STEREOTYPES 1773

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people to groups precisely because such information generatesextreme stereotypes Consider the classic example in which amedical test for a particular disease with a 5 prevalence has a90 rate of true positives and a 5 rate of false positives The testassigns each person to one of two groups + (positive test) or ndash(negative test) The DM estimates the frequency of the sick type(s) and the healthy type (h) in each group The test is informativea positive result increases the relative likelihood of sickness anda negative result increases the relative likelihood of health forany prior Formally

PreththornjsTHORN

PreththornjhTHORNgt 1 gt

PrethjsTHORN

PrethjhTHORNeth4THORN

This condition has clear implications the representative personwho tests positive is sick while the representative person whotests negative is healthy Following Proposition 2 the DMreacts to the test by moving his priors too far in the right di-rection generating extreme stereotypes He greatly boosts hisassessment that a positively tested person is sick but also thata negatively tested person is healthy Because most people arehealthy the DMrsquos assessment about the group that tested neg-ative is fairly accurate but is severely biased for the group that

FIGURE I

SAT Mathematics Scores by Gender (2013)

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tested positive This analysis formalizes Tversky andKahnemanrsquos (1983) verbal account of base rate neglect23

The same mechanism may underlie several other instanceswhere DMs overweight diagnostic information When assessingan employeersquos skill level an employer attributes high perfor-mance to high skill because high performance is the distinctivemark of a talented employee Because he neglects the possibilitythat some talented employees perform poorly and that somenontalented ones perform well (perhaps due to stochasticity inthe environment) the employer has too much faith in skill andneglects the role of luck in accounting for the output Similarlywhen assessing the performance of firms in a hot sector of theeconomy (eg G = internet) an investor recalls highly successfulfirms in that sector (t = return of Google Amazon etc) He ne-glects the possibility of firms being unsuccessful because lack ofsuccess is statistically nondiagnostic and psychologically nonrep-resentative of a growing sectormdasheven if it is likely This causesexcessive optimism (in that the expectation of growth is unrea-sonably high) and overconfidence (in that the variability in earn-ings growth considered possible is truncated) True the hot sectormay have better growth opportunities on average but represen-tativeness exaggerates this feature and induces the investor toneglect a significant risk of failure

IV Evidence on Representativeness and Stereotypes

Testing our model requires evaluating the beliefs individualshold about a target group against the true distribution of thattarget group over an attribute space An ideal data set would

23 Our account is distinct from a mechanical underweighting of base rates inBayes rule as in Grether (1980) and Bodoh-Creed Benjamin and Rabin (2013) Inthose models upon receiving the test results the DM can update his beliefs in thewrong direction he can be less confident that a person is healthy after a negativetest than under his prior which cannot happen in our model Although this predic-tion of our model seems consistent with introspection we are not aware of experi-mental evidence on this point Griffin and Tversky (1992) present evidenceconsistent with pure neglect of base rates but in a significantly different tasknamely inferring the bias of a coin from a history of coin flips Such experimentsare hard to compare with the predictions of our model because subjects are asked togenerate distributions of different numbers of coin flips in their minds which is amuch more involved task than to recall types of a given distribution Their assess-ments then might be wrong for other reasons See Bodoh-Creed Benjamin andRabin (2013) for a detailed discussion

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consist of naturally defined groups with known distributions overa given space of types and a corresponding set of beliefs about thedistribution of each group over that space of types This wouldallow us to test for exaggeration of true differences betweengroups and to ask whether this exaggeration is well predictedby overweighting representative types To identify a causal rolefor representativeness or context dependence we would need ex-ogenous variation in either the comparison group ndashG or in thedistributions over the type spaces This is unavailable in existingdata sets Accordingly we take a two-pronged approach First wecreate a controlled laboratory environment that allows us toinduce the exogenous variation in representative types that weneed to test causality then we reanalyze existing field evidence tocheck for consistency with our predictions

In testing our model we focus on the two main implicationsof representativeness-based stereotypes

Context dependence the stereotype of a target group de-pends on the characteristics of the reference group it iscompared to

Kernel of truth stereotypes depend on group character-istics andmdashin most (precisely characterized) settingsmdashare slanted toward representative types

We test the first property with a lab experiment (SectionIVA) We then turn to survey data on beliefs about US politicalgroups (Section IVB) for an empirical analysis that explores thesecond property The survey data are more tightly linked to ourinterest in social stereotypes The laboratory experiment allowsus to directly test the role of representativeness in generatingcontext dependent beliefs Online Appendixes F and G provideall details and additional results for the experiments and fieldevidence

IVA Lab Evidence on Representativeness and ContextDependence

The influence of the representativeness heuristic on recalland on beliefs has been extensively documented in the lab(Kahneman and Tversky 1972 1973) Our goal is to considerhow representativeness as formalized in equation (2) gives riseto context-dependent beliefs To our knowledge the possibility

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that representativeness may generate context dependence hasnot been tested before

To assess this prediction we perform a controlled laboratoryexperiment that allows us to isolate representativeness frommany confounding factorsmdashhistorical sociological or other-wisemdashthat may affect stereotype formation in the real worldWe construct our own groups of ordinary objects creating atarget group G and a comparison group ndashG We hold thetarget group G fixed and explore how participant impressions ofit change as we change the comparison group ndashG and thusrepresentativeness

We conducted several experiments in the laboratory and onAmazon Mechanical Turk Each involves a basic three-stepdesign First participants are shown the target group and a ran-domly assigned comparison group for 15 seconds In this timedifferences between groups can be noticed but the groupsrsquo precisecompositions cannot be memorized The second step consists of afew filler questions which briefly draw the participantsrsquo cognitivebandwidth away from their observation Finally participants areasked to assess the groups they saw Participants are incentiv-ized to provide accurate answers

We randomly assign participants to either the Control or theRepresentativeness condition In the Control condition G and ndashGhave nearly identical distributions so that all types are similarlyrepresentative for each group In the Representativeness condi-tion ndashG is changed in such a way that a certain type becomes veryrepresentative for G Context dependence implies that the assess-ment of G should now overweight this representative type eventhough the distribution of G itself has not changed

We ran six experiments of this form with design changesfocused on reducing participant confusion and removing con-founds We describe the final and most refined version of theseexperiments here In an attempt to provide a overview of the re-sults while remaining concise we provide the results from pooledspecifications that use all data collected In Online Appendix Fwe offer additional details and report all experiments conductedWe also give instructions and materials for each experiment thefull data set is available by request

Consider first the experiment illustrated in Figure II Agroup of 25 cartoon girls is presented next to a group of 25 cartoonboys in T-shirts of different colors blue green or purple In theControl condition (Figure II Panel a) the groups have identical

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color distributions (13 purple 12 green) so no color is represen-tative of either group The Representativeness condition (Panel b)compares the same group of girls with a different group of boysfor whom green shirts are replaced with blue shirts Now onlygirls wear green and only boys wear blue These colors althoughstill not the most frequent for either group are now most repre-sentative For each group girls and boys participants are asked anumber of questions concerning the frequency of T-shirts of dif-ferent colors worn by that group

Applying our model in the control condition the type space isT frac14 fgreen purpleg and the groups are G = girls and ndashG = boysGiven that the color distributions are identical across groups both

types are equally representativegreengirls

greenboysfrac14 1 frac14

purplegirls

purpleboys As a result

assessment of G should be correct on average stcontrolgreengirls frac14 greengirls

and stcontrolpurplegirls frac14 purplegirls for any weighing function (the same is

true about assessments of ndashG)In the treatment condition the distribution of shirt colors re-

mains the same for girls For boys green shirts are changed intoblue Thus the type space changes to T frac14 fgreen purple bluegand the representative color for girls becomes greengreengirls

greenboysfrac14 1 gt 1 frac14

purplegirls

purpleboys while that for boys becomes blue As

a result in the treatment condition subjects should inflate the

frequency of green shirts relative to the truth sttreatmentgreengirls

gt greengirls (the same should happen to assessments of blueshirts for boys) We also expect the assessed frequency of greenshirts to go up relative to the control condition namely

sttreatmentgreengirls gt stcontrol

greengirls Critically the only factor that varies

across treatments is the representativeness of the 12-colorshirt Thus if we see differences across conditions the causalrole of representativeness-based recall in shaping group judg-ments is clear24

24 We vary which colors are used in which roles across participants Someparticipants saw this particular color distribution while others see for examplegreen as the modal color and purple as the diagnostic color for boys in theRepresentativeness condition and blue as the diagnostic color for girls in theRepresentativeness condition We vary the colors across the roles to avoid con-founding the characteristics of any particular color with its diagnosticity

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FIG

UR

EII

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ure

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ty

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tter

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irt

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er

lsquolsquoGrsquorsquo

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sgre

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lsquolsquoPrsquorsquo

ind

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sblu

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onli

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STEREOTYPES 1779

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We collected data from 301 participants using this T-shirtsdesign25 Since the number of green and purple shirts is verysimilar we first ask each participant the simplest question ofwhich shirt color is modal Next we ask participants to assessthe share of green and purple shirts

Consistent with the role of representativeness participantsassigned to the Representativeness condition are 105 percentagepoints more likely to recall the less frequent color (green for girlsor blue for boys) as the modal color when it is representative of agroup (35 of participants guess the less frequent color is modalin the Control condition this proportion increases to 46 in theRepresentativeness condition p = 01 estimated from a probitregression reported in Online Appendix F)

We now turn to subjectsrsquo estimates of how many T-shirts ofeach color they saw in each group In both conditions the truedifference in counts is 1 (13 purple shirts 12 green or blue shirts)In the Control condition participants on average believe they saw054 more purple shirts than green or blue shirts In theRepresentativeness condition participants believe they saw072 fewer purple shirts than green or blue shirts (the acrosstreatment difference is significant with p = 01 from OLS regres-sion reported in Online Appendix F)

In total we collected data for six experiments of this generalstructure gathering evidence from more than 1000 participantsAs we describe in Online Appendix F although there is substan-tial variation across experiments when we pool all of the data wefind significant aggregate treatment effects in line with a role ofrepresentativeness in judgment We employ four different unor-dered types designs similar to the T-shirts experiment using sixsamples (four online and two in the laboratory) with 741 partic-ipants We find effects in the predicted direction for five of the sixsamples Using a probit regression that pools the data for theseunordered type experiments we find that participants are 93 per-centage points more likely to guess that the less frequent type ismodal when it is representative than when it is not (p = 002) Wealso run a family of ordered types experiments (two designs fivesamples 402 participants) Unlike the simpler T-shirts style

25 Throughout our analysis we exclude any participant who participated in aprevious version of the experiment and any participant who self-identified as color-blind In Online Appendix F we show that our results are unchanged if we includethese additional observations

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design the theoretical predictions for the ordered types designsare more sensitive to the specific assumptions one makes aboutthe weighting function of the DM26 We find effects in the pre-dicted direction for three of the five samples As we discuss inmore detail in Online Appendix F the ordered types resultsvary by platform with consistently stronger results on AmazonMechanical Turk than in the laboratory samples Pooling all or-dered types experiments participants are 93 percentage pointsmore likely to guess that the group of interest has a greater av-erage than the comparison group when the right tail is represen-tative (p = 062) Given our simple experimental setting withgroups of mundane objects we interpret our resultsmdasha signifi-cant and reasonably sized impact on average beliefsmdashas an im-portant proof of concept the presence of representative typesbiases ex post assessment

IVB Empirical Evidence on Political Stereotypes

We examine two data sets on political preferences and be-liefs about political preferences in the United States We inves-tigate the roles of representativeness and context dependence byseparately testing for hypotheses that allow us to assess the lead-ing theories of stereotypes

First we test whether beliefs are correct or depart systemat-ically from the truth The statistical discrimination approachbuilds on the assumption that people hold rational expectationsof group traits Comparing beliefs to the truth allows us to assessthe validity of this assumption in our data

Second we test if beliefs depart from the truth by exagger-ating (mean) differences among groups per the kernel of truthhypothesis This is an implicit test of context dependence be-cause it implies that beliefs about the target groups are shapednot only by that grouprsquos characteristics but also by those of thereference group27

Third we test if distortions in beliefs can be accounted for bythe overweighting of highly representative types (defined astypes that are relatively more frequent in the target relative to

26 This is due in part to our choice to not study MLRP distributions We moti-vate and discuss this design decision in Online Appendix F

27 Of course unlike in the laboratory experiment in this setting we cannot testfor context dependence by exogenously varying the reference group

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the reference group) The second and third tests address the keypredictions of our model

1 The Data We have two data sets on political preferences andbeliefs about political preferences The first data set from GrahamNosek and Haidt (GNH 2012) contains data from the MoralFoundations Questionnaire Respondents (1174 self-identified lib-erals and 500 self-identified conservatives) answer questions abouttheir position on a subset of 45 issues 20 moral relevance state-ments (eg lsquolsquowhen you decide whether something is right orwrong to what extent are the following considerations relevantto your thinkingrsquorsquo) and 25 moral judgments (eg lsquolsquoindicate theextent to which you would agree or disagreersquorsquo) For each issue arandomly determined subset of participants states their own posi-tion another subset states their belief on the position of a lsquolsquotypicalliberalrsquorsquo and a third subset states their belief on the position of alsquolsquotypical conservativersquorsquo The data thus include the distribution overpositions for both liberal and conservatives as well as the averagebelieved typical position of liberals and of conservatives on the 45issues Each position is elicited on 1ndash6 scale

The second data set comes from the American NationalElection Survey (ANES) and contains data from more than20000 respondents between 1964 and 201228 The surveycovers political issues of the day such as the optimal amount ofgovernment spending and service provision (1984ndash2000) or theplace of women in society (1972ndash1998) We focus on the 10 issuesthat ask participants to respond on a 1ndash7 scale (rather than justindicate binary agreement or disagreement) all 10 issues areasked in multiple years Participants are asked to provide theirown position on the scale and their believed position of theDemocratic and Republican parties (lsquolsquoWhere would you placethe Democratic [Republican] party on this scalersquorsquo) The data in-clude for each issue-year observation the distribution of partic-ipant positions for self-identified liberals and self-identifiedconservatives as well as the distribution of believed typical posi-tions of the Democratic and Republican parties

28 These data are publicly available at httpwwwelectionstudiesorgstudy-pagesanes_timeseries_cdfanes_timeseries_cdfhtm

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2 Empirical Strategy Our analysis focuses on beliefs abouttwo groups Conservatives and Liberals The types are the possi-ble positions for each issue (1 2 6 7) For the GNH data weinterpret beliefs about the lsquolsquotypicalrsquorsquo element of a group to coincidewith the believed average position in that group Similarly forthe ANES data we use the believed party positions as a proxy forbelieved mean of each group29 We then take as a benchmark thehypothesis that individuals hold accurate beliefs about eachgroup and in particular that believed mean position shouldequal true mean position at least on average across subjectsThe accurate beliefs hypothesis underlies the most common eco-nomic model of stereotyping statistical discrimination

To assess our representativeness-based model we perform aregression exercise To test our model in a linear regressionframework we rely on linear approximations of the weightingfunction Our model then yields two regression specifications

PROPOSITION 4 Let G 2 fconservative liberal g and assume

ht h tG

tG

be a differentiable and strictly increasing weight-

ing function as in Definition 2 The following hold as a first-order approximation around identical distributions G

Gfrac14 1

(i) Kernel of truth regression There exists a constant gt 0such that

EstethtjGTHORN frac14 EethtjGTHORNeth1thorn THORN EethtjGTHORNeth5THORN

(ii) Representativeness regression Denote H frac14 fT 2 Tg

the right tail of types and RconsH frac14

PHtconsPHtlib

as the average

representativeness of right tail types for conservatives

29 This assumption is consistent with the authorsrsquo interpretation of the GNHdata (GNH 2012) and with previous studies using ANES (eg Westfall et al 2015)Furthermore to the extent that this assumption holds equally well for most issueswithin a data set our focus on cross-issue differences should allow us to test thepredictions of our model even with an imperfect proxy for beliefs of mean positionsFinally the data provide some insight into whether subjects are reporting (per-ceived) modal or mean types As we show the modal type is a poor prediction ofstated beliefs while a distorted mean slanted toward representative types is anaccurate prediction of stated beliefs

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Under the further approximation where tcons

tlibampRcons

H for

t 2 H

EstethtjconsTHORN frac14 EethtjconsTHORN thorn consethR

consH 1THORNeth6THORN

EstethtjlibTHORN frac14 EethtjlibTHORN libethR

consH 1THORNeth7THORN

where lcons and llib are positive constants

The first regression allows us to test for the kernel of truthhypothesis and the second set of regressions allows us to test forthe role of representativeness

Equation (5) says that respondents in our model inflate theaverage position of a group say the conservatives if and only ifthe group has a higher average position than the other groupnamely the liberals Formally EstethtjconsTHORN gt EethtjconsTHORN if and onlyif EethtjconsTHORN gt EethtjlibTHORN Because in our measurement scale highertypes mean lsquolsquomore conservativersquorsquo we expect (i) believed conserva-tive average to be higher than the truth and (ii) the extent ofoverstatement to decrease in the average liberal position EethtjlibTHORNConversely we expect the average liberal position to be lowerthan the truth the more so the higher the average conservativeposition EethtjconsTHORN

As previously discussed the basis of these predictions is con-text dependence information about the distribution of ndashG is rel-evant for the beliefs about G This context dependence isinconsistent with rational expectations in which only thegrouprsquos own means should affect beliefs We test the hypothesisthat the true mean EethtjGTHORN is a significant predictor of the believedmean E

stethtjGTHORN with a positive sign and the other grouprsquos truemean EethtjGTHORN is a predictor of the believed mean with a negativesign

Equations (6) and (7) say that repondentsrsquo assessment bias isshaped by representativeness When the right tail is more repre-sentative for conservatives (Rcons

H 1 positive and large) partici-pants should inflate the average conservative position more(higher E

stethtjconsTHORN EethtjconsTHORN) and deflate the average liberal po-sition more (lower E

stethtjlibTHORN EethtjlibTHORN) We test the hypothesisthat the inflation in conservative positions is positively associatedwith the representativeness of the right tail for the conservativesand the inflation in liberal positions is negatively associated with

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it Once again the representativeness of the right tail is com-puted using the true distribution of positions

In equations (6) and (7) in many cases the representative tailis also the most likely one As a consequence these tests cannotdistinguish a representativeness-based from a likelihood-basedmodel of distorted beliefs We perform two additional testsFirst we run versions of equations (6) and (7) in which we controlfor the likelihood of tails (see Table A4 in Online Appendix G)Second we compute numerically the predictions of a representa-tiveness-based model of stereotypes and a likelihood-based modelof stereotypes We then assess which of these two is better able tomatch the data on beliefs

3 Empirical Results To begin we illustrate the structure ofthe data and the nature of our predictions with two simple exam-ples from the GNH data set focusing on beliefs about conserva-tives In example 1 participants are asked about their agreementwith the statement lsquolsquoIt can never be right to kill a human beingrsquorsquoIn example 2 participants are asked about the moral relevance oflsquolsquowhether or not someone cared for someone weak or vulnerablersquorsquoAs can be seen in Figure III in example 1 the modal position(strongly disagree (1)) and most representative positions(strongly disagree (1)) coincide for conservatives In contrast inexample 2 in Figure III the most representative types (slightlyrelevant (3) not at all relevant (1)) are not most likely for theconservative group Following Proposition 1 we predict that be-liefs will be distorted in the direction of the most representativetypes Thus we expect more exaggeration in example 2 than inexample 1 since in example 2 the most representative types (inthe left tail) are far from the modal type whereas in example 1they coincide This is what we find the conservative position isexaggerated by only 009 positions in Example 1 (true mean 299believed mean 290) but by 106 positions in Example 2 (truemean 421 believed mean 315)

In the full data sets we treat each (issue year) pair as anobservation and we cluster standard errors at the issue level Forthe GNH data we have 45 observations 45 issues measured inthe same year For the ANES data we have 66 observations 10issues measured in multiple years To begin we simply docu-ment systematic exaggeration in both data sets This is a primaryfocus of the original analysis in GNH (2012) and also in Westfall

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FIGURE III

Two Examples

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et al (2015)rsquos analysis of the ANES data30 Figure IV shows thatthe believed difference between typical conservative and typicalliberal positions is larger than the true difference in mean posi-tions for 109 of the 111 observations The data for both GNH(squares) and ANES (triangles) lie above the 45-degree line(dashed)31 Average exaggeration is 062 positions on the scale(066 in the GNH data 059 in the ANES data)32

The systematic and significant exaggeration of mean differ-ences suggests that the benchmark model of accurate beliefs ismissing something important Indeed this exaggeration reflectsthe fact that believed means are typically more extreme than truemeans First note that the kernel of truth regression (equation(5)) generates exaggeration of mean differences just as docu-mented in Figure IV

EstethtjGTHORN E

stethtjGTHORN frac14 eth1thorn 2THORN frac12EethtjGTHORN EethtjGTHORN

To bring this prediction to the data we regress the believedmean position for each group EBethtjGTHORN on the true mean of thegroup EethtjGTHORN and the true mean of the comparison groupEethtjGTHORN across issues We do this for each group (liberals con-servatives) in each data set separately We also present pooledspecifications that combine the data sets to make a prediction fora given group (liberals conservatives) In these pooled specifica-tions we include a dummy variable indicating whether theobservation came from the ANES data set For all specificationswe cluster observations at the issue level33 The results from re-gression are shown in Table I In every specification we find thatEethtjGTHORN is a significant predictor of EBethtjGTHORN with the predicted pos-itive sign Crucially for five of the six specifications the mean of

30 Chambers and Melnyk (2006) also find evidence of exaggeration of truedifferences in beliefs about political positions

31 For convenience we recode all issues so that the high end of the scale (67)represents the stereotypically more conservative position

32 A natural question to ask is how beliefs vary across liberals and conserva-tives That is do beliefs about a group G depend on membership in G versus ndashG Ourmodel does not speak to this issue However in Online Appendix G we show thatthe results we document below hold for both beliefs held by conservatives and be-liefs held by liberals see Tables A9 A10 and A11

33 In general the results presented below for the ANES data are not largelyimpacted by the decision to cluster at the issue level Similar results are obtained ifthe data are not clustered

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the comparison group EethtjGTHORN is also a significant predictor ofE

BethtjGTHORN with the predicted negative signAlthough these results provide strong evidence of context

dependence and are consistent with our model they do not pindown a role for representativeness of types Our next test relatesthe magnitude of representativeness of tail types to the magni-tude of belief distortions

To this end we implement the regressions in equations (6)and (7) Following Proposition 4 we compute the average repre-

sentativeness of tail types for conservatives RconsH frac14

PtT2tconsPtT2tlib

We

again test the hypothesis that RconsH is a significant predictor of Est

ethtjconsTHORN with a positive sign and a predictor of EstethtjlibTHORN with a

negative sign Table II shows that conditional on true mean RconsH

predicts believed mean for each group G as expected The firstthree specifications display the results for predicting beliefs heldabout conservatives In both data sets the average representa-tiveness of tail types for conservatives is a significant positivepredictor of beliefs held about conservatives The final three spe-cifications display the results for predicting beliefs held about

FIGURE IV

Exaggeration of Differences

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liberals We find that the average representativeness of tail typesfor conservatives is a negative predictor of beliefs held about lib-erals This effect is significant in the GNH data and marginallysignificant in the ANES data

We present several additional results in Online Appendix GTo further examine the role of representativeness in driving be-liefs we first show the results of Table II carry through when we

TABLE II

AVERAGE REPRESENTATIVENESS OF TAIL POSITIONS PREDICTS BELIEFS

OLS Predicting Believed Mean of Group G for Each Issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position

of group G for issue

078 024 051 072 018 041

(006) (008) (009) (005) (005) (010)

Avg rep of tail types for

conservatives RconsH

019 055 025 014 012 024

(007) (022) (008) (006) (007) (005)

Constant 101 260 184 093 271 201

(026) (045) (029) (022) (025) (032)

R2 082 048 060 091 031 070

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

TABLE I

INFORMATION ABOUT ndashG PREDICTS BELIEFS ABOUT G

OLS predicting believed mean of group G for each issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position of

conservatives for issue

102 098 096 021 019 025

(0097) (0133) (0076) (0060) (0116) (0060)

True mean position of

liberals for issue

035 086 058 0987 039 073

(0106) (0134) (0131) (0066) (0106) (0135)

Constant 151 335 235 069 258 156

(0195) (0269) (0279) (0122) (0249) (0270)

R2 083 053 066 092 032 068

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

STEREOTYPES 1789

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control for the average likelihood on the tail positions (see Table A4in Online Appendix G) Most tellingly we use the model to predictbeliefs across issues and compare those to the data For simplicitywe use the rank-based truncation specification to predict mean be-liefs when stereotypes include the d most representative types ford frac14 1 T We compare these predictions to those of a model inwhich beliefs are obtained by restricting the distribution to the dmost likely types Our benchmark for both models is predicting thebelieved mean from the entire distribution where d = T We showthat the predictions of the rank-based truncation model with d = 4or 5 compare favorably to both a likelihood-based truncation model(with any d) and the accurate beliefs benchmark Interestingly thisresult suggests that stereotypical beliefs are well approximated byneglecting the least representative types (as opposed to focusingonly on the most representative types) and so represent a moderatethough systematic departure from the standard benchmarkFinally we show that the results we document above hold forboth beliefs held by conservatives and beliefs held by liberals (seeTables A9 A10 and A11 in Online Appendix G)

V Conclusion

We present a model of stereotypical thinking in which DMsmaking predictions about a group overweight the grouprsquos mostdistinctive types These overweighted types are not the mostlikely ones given the DMrsquos data but the most representativeones in the sense of being the most diagnostic of the group rela-tive to other groups Representativeness implies that what ismost distinctive of a group depends on what group it is comparedwith We present experimental evidence that confirms this con-text dependence in recall-based assessments of groups Finallywe evaluated the predictions of the model using political data fromexisting large-scale surveys We find context dependence to be akey feature of beliefs Given the richness of the political data wecan go a step further and identify a role for representativeness inparticular As the representativeness of tail types increases beliefsof a group are distorted in the direction of that tail

Our approach provides a parsimonious and psychologicallyfounded account of how DMs generate simplified representationsof reality from social groups to stock returns and offers a unifiedaccount of disparate pieces of evidence relating to this type of

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uncertainty The model captures the central fact that stereotypeshighlight the greatest difference between groups thus explainingwhy some stereotypes are very accurate while others lack valid-ity Still stereotypes often have a kernel of truth when they arebased on systematicmdasheven if smallmdashdifferences between groupsThis logic allows us to describe a number of heuristics and psy-chological biases many of which arise in the context of predictionproblems Generically our model generates overreaction to diag-nostic information

Our model is based on representativeness and does not cap-ture all the features of stereotypical thinking However it cap-tures perhaps the central feature when we think of a group wefocus on what is most distinctive about it and neglect or under-weight the rest

Saeuroıd Business School University of Oxford

Ohio State University and Harvard Business School

Universita Bocconi and Innocenzo Gasparini Institute

for Economic Research

Harvard University

Supplementary Material

An Online Appendix for this article can be found at QJEonline (qjeoxfordjournalorg)

References

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Arrow Kenneth lsquolsquoThe Theory of Discriminationrsquorsquo in Discrimination in LaborMarkets Orley Ashenfelter and Albert Rees eds (Princeton NJPrinceton University Press 1973)

Ashton Michael and Victoria Esses lsquolsquoStereotype Accuracy Estimating theAcademic Performance of Ethnic Groupsrsquorsquo Personality and SocialPsychology Bulletin 25 (1999) 225ndash236

Barberis Nicholas Andrei Shleifer and Robert Vishny lsquolsquoA Model of InvestorSentimentrsquorsquo Journal of Financial Economics 49 (1998) 307ndash343

Bayer Sylvia lsquolsquoThe Accuracy of Academic Gender Stereotypesrsquorsquo Sex Roles 40(1999) 787ndash813

Benjamin Dan James Choi and Joshua Strickland lsquolsquoSocial Identity andPreferencesrsquorsquo American Economic Review 100 (2010) 1913ndash1928

Benjamin Dan Matthew Rabin and Collin Raymond lsquolsquoA Model of Non-Belief inthe Law of Large Numbersrsquorsquo Journal of the European Economic Association15 (2015) 515ndash544

Bertrand Marianne lsquolsquoNew Perspectives on Genderrsquorsquo Handbook of LaborEconomics 4 (2011) 1543ndash1590

Bodoh-Creed Aaron Dan Benjamin and Matthew Rabin lsquolsquoThe Dynamics of Base-Rate Neglectrsquorsquo mimeo Haas Business School 2013

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Bohnet Iris Alexandra van Geen and Max Bazerman lsquolsquoWhen PerformanceTrumps Gender Bias Joint versus Separate Evaluationrsquorsquo ManagementScience 5 (2016) 1225ndash1234

Bordalo Pedro Nicola Gennaioli and Andrei Shleifer lsquolsquoSalience Theory of Choiceunder Riskrsquorsquo Quarterly Journal of Economics 127 (2012) 1243ndash1285

mdashmdashmdash lsquolsquoSalience and Consumer Choicersquorsquo Journal of Political Economy 121(2013) 803ndash843

Briton Nancy and Judith Hall lsquolsquoBeliefs about Female and Male NonverbalCommunicationrsquorsquo Sex Roles 32 (1995) 79ndash90

Buser Thomas Muriel Niederle and Hessel Oosterbeek lsquolsquoGenderCompetitiveness and Career Choicesrsquorsquo Quarterly Journal of Economics 129(2014) 1409ndash1447

Carrell Scott Marianne Page and James West lsquolsquoSex and Science How ProfessorGender Perpetuates the Gender Gaprsquorsquo Quarterly Journal of Economics 125(2010) 1101ndash1144

Chambers John and Darya Melnyk lsquolsquoWhy Do I Hate Thee ConflictMisperceptions and Intergroup Mistrustrsquorsquo Personality and SocialPsychology Bulletin 32 (2006) 1295ndash1311

Chan Wayne Robert R McCrae Filip De Fruyt Lee Jussim CorinnaE Lockenhoff Marleen De Bolle Paul T Costa Jr Angelina R SutinAnu Realo Juri Allik Katsuharu Nakazato Yoshiko ShimonakaMartina Hrebıckova Sylvie Graf Michelle Yik Marina Brunner-SciarraNora Leibovich De Figueora Vanina Schmidt Chang-kyo Ahn Hyun-nie Ahn Maria E Aguilar-Vafaie Jerzy Siuta Barbara SzmigielskaThomas R Cain Janet T Crawford Khairul Anwar Mastor Jean-Pierre Rolland Florence Nansubuga Daniel R MiramontezVeronica Benet-Martınez Jerome Rossier Denis Bratko Iris MarusicJamin Halberstadt Mami Yamaguchi Goran Knezevic Thomas A MartinMirona Gheorghiu Peter B Smith Claudio Barbaranelli Lei WangJane Shakespeare-Finch Margarida P Lima Waldemar KlinkoszAndrzej Sekowski Lidia Alcalay Franco Simonetti Tatyana V AvdeyevaV S Pramila and Antonio Terracciano lsquolsquoStereotypes of Age Differences inPersonality Traits Universal and Accuratersquorsquo Journal of Personality andSocial Psychology 103 (2012) 1050ndash1066

Chen Yan Sherry Xin Liu Tracy Xiao and Margaret Shih lsquolsquoWhich Hat to WearImpact of Natural Identities on Coordination and Cooperationrsquorsquo Games andEconomic Behavior 84 (2014) 58ndash86

Coffman Katherine lsquolsquoEvidence on Self-Stereotyping and the Contribution ofIdeasrsquorsquo Quarterly Journal of Economics 129 (2014) 1625ndash1660

Cunningham Tom lsquolsquoComparisons and Choicersquorsquo mimeo Stockholm University2013

Diekman Amanda Alice Eagly and Patrick Kulesa lsquolsquoAccuracy and Bias in theStereotypes about the Social and Political Attitudes of Women and MenrsquorsquoJournal of Experimental Social Psychology 38 (2002) 268ndash282

Eccles Jacquelynne S Janis E Jacobs and Rena D Harold lsquolsquoGender RoleStereotypes Expectancy Effects and Parentsrsquo Socialization of GenderDifferencesrsquorsquo Journal of Social Issues 46 (1990) 183ndash201

Fryer Roland and Matthew Jackson lsquolsquoA Categorical Model of Cognition andBiased Decision-Makingrsquorsquo BE Journal of Theoretical Economics 8 (2008)1ndash42

Fryer Roland and Steven Levitt lsquolsquoAn Empirical Analysis of the Gender Gap inMathematicsrsquorsquo American Economic Journal Applied Economics 2 (2010)210ndash240

Gennaioli Nicola and Andrei Shleifer lsquolsquoWhat Comes to Mindrsquorsquo Quarterly Journalof Economics 125 (2010) 1399ndash1433

Gennaioli Nicola Andrei Shleifer and Robert Vishny lsquolsquoNeglected RisksFinancial Innovation and Financial Fragilityrsquorsquo Journal of FinancialEconomics 104 (2012) 452ndash468

Gilens Martin lsquolsquoRace and Poverty in America Public Misperceptions and theAmerican News Mediarsquorsquo Public Opinion Quarterly 60 (1996) 515ndash541

Glaeser Edward lsquolsquoThe Political Economy of Hatredrsquorsquo Quarterly Journal ofEconomics 120 (2005) 45ndash86

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Glover Dyland Amanda Pallais and William Pariente lsquolsquoDiscrimination as a Self-Fulfilling Prophecy Evidence from French Grocery Storesrsquorsquo mimeo HarvardUniversity 2015

Goldin Claudia Lawrence Katz and Ilyana Kuziemko lsquolsquoThe Homecoming ofAmerican College Women The Reversal of the College Gender GaprsquorsquoJournal of Economic Perspectives 20 (2006) 133ndash156

Graham Jesse Brian Nosek and Jonathan Haidt lsquolsquoThe Moral Stereotypes ofLiberals and Conservatives Exaggeration of Differences across thePolitical Spectrumrsquorsquo PLoS One 7 (2012) 1ndash13

Grether David lsquolsquoBayes Rule as a Descriptive Model The RepresentativenessHeuristicrsquorsquo Quarterly Journal of Economics 95 (1980) 537ndash557

Griffin Dale and Amos Tversky lsquolsquoThe Weighing of Evidence and theDeterminants of Confidencersquorsquo Cognitive Psychology 24 (1992) 411ndash435

Guiso Luigi Ferdinando Monte Paola Sapienza and Luigi Zingales lsquolsquoCultureGender and Mathrsquorsquo Science 320 (2008) 1164ndash1165

Hilton James and William Von Hippel lsquolsquoStereotypesrsquorsquo Annual Review ofPsychology 47 (1996) 237ndash271

Hyde Janet Sara Lindberg Marcia Linn Amy Ellis and Caroline WilliamslsquolsquoGender Similarities Characterize Math Performancersquorsquo Science 321 (2008)494ndash495

Judd Charles and Bernardette Park lsquolsquoDefinition and Assessment of Accuracy inSocial Stereotypesrsquorsquo Psychological Review 100 (1993) 109ndash128

Jussim Lee Jarret Crawford Stephanie Anglin John Chambers Sean Stevensand Florette Cohen lsquolsquoStereotype Accuracy One of the Largest and MostReplicable Effects in All of Social Psychologyrsquorsquo in The Handbook ofPrejudice Stereotyping and Discrimination Todd Nelson ed (MahwahNJ Lawrence Erlbaum 2015)

Kahneman Daniel and Amos Tversky lsquolsquoSubjective Probability A Judgment ofRepresentativenessrsquorsquo Cognitive Psychology 3 (1972) 430ndash454

mdashmdashmdash lsquolsquoOn the Psychology of Predictionrsquorsquo Psychological Review 80 (1973) 237ndash251

Kaplowitz Stan Bradley Fisher and Clifford Broman lsquolsquoHow Accurate ArePerceptions of Social Statistics about Blacks and Whitesrsquorsquo Public OpinionQuarterly 67 (2003) 237ndash243

Kersten Daniel Pascal Mamassian and Alan Yuille lsquolsquoObject Perception asBayesian Inferencersquorsquo Annual Review of Psychology 55 (2004) 271ndash304

Klein Richard Kate A Ratliff Michelangelo Vianello Reginald B Adams JrStepan Bahnik Michael J Bernstein Konrad Bocian Mark J BrandtBeach Brooks Claudia Chloe Brumbaugh Zeynep CemalcilarJesse Chandler Winnee Cheong William E Davis Thierry DevosMatthew Eisner Natalia Frankowska David Furrow Elisa Maria GallianiFred Hasselman Joshua A Hicks James F Hovermale S Jane HuntJeffrey R Huntsinger Hans IJzerman Melissa-Sue John Jennifer A Joy-Gaba Heather Barry Kappes Lacy E Krueger Jaime Kurtz CarmelA Levitan Robyn Mallett Wendy L Morris Anthony J Nelson JasonA Nier Grant Packard Ronaldo Pilati Abraham M RutchickKathleen Schmidt Jeanine L Skorinko Robert Smith Troy G SteinerJustin Storbeck Lyn M Van Swol Donna Thompson Anna van rsquot VeerLeigh Ann Vaughn Marek Vranka Aaron Wichman Julie A Woodzickaand Brian A Nosek lsquolsquoInvestigating Variation in Replicability A ManyLabs Replication Projectrsquorsquo Social Psychology 45 (2014) 142ndash152

Lundberg Shelly and Richard Startz lsquolsquoPrivate Discrimination and SocialIntervention in Competitive Labor Marketsrsquorsquo American Economic Review73 (1983) 340ndash347

Madon Stephanie Max Guyll Kathy Aboufadel Eulices Montiel Alison SmithPolly Palumbo and Lee Jussim lsquolsquoEthnic and National Stereotypes ThePrinceton Trilogy Revisited and Revisedrsquorsquo Personality and SocialPsychological Bulletin 27 (2001) 996ndash1010

Martin Carol lsquolsquoA Ratio Measure of Sex Stereotypingrsquorsquo Journal of Personality andSocial Psychology 52 (1987) 489ndash499

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McCauley Clark Krishna Thangavelu and Paul Rozin lsquolsquoSex Stereotyping ofOccupations in Relation to Television Representations and Census FactsrsquorsquoBasic and Applied Social Psychology 9 (1988) 197ndash212

Mullainathan Sendhil lsquolsquoThinking through Categoriesrsquorsquo mimeo HarvardUniversity 2002

Ortoleva Pietro and Erik Snowberg lsquolsquoOverconfidence in Political BehaviorrsquorsquoAmerican Economic Review 105 (2015) 504ndash535

Phelps Edmund lsquolsquoThe Statistical Theory of Racism and Sexismrsquorsquo AmericanEconomic Review 62 (1972) 659ndash661

Pope Devin and Justin Sydnor lsquolsquoGeographic Variation in the Gender Differencesin Test Scoresrsquorsquo Journal of Economic Perspectives 24 (2010) 95ndash108

Rabin Matthew lsquolsquoInference by Believers in the Law of Small NumbersrsquorsquoQuarterly Journal of Economics 117 (2002) 775ndash816

Rabin Matthew and Joel Schrag lsquolsquoFirst Impressions Matter A Model ofConfirmatory Biasrsquorsquo Quarterly Journal of Economics 114 (1999) 37ndash82

Rabin Matthew and Dimitri Vayanos lsquolsquoThe Gamblerrsquos and Hot-Hand FallaciesTheory and Applicationsrsquorsquo Review of Economic Studies 77 (2010) 730ndash778

Reuben Ernesto Paola Sapienza and Luigi Zingales lsquolsquoHow Stereotypes ImpairWomenrsquos Careers in Sciencersquorsquo Proceedings of the National Academy ofSciences 111 (2014) 4403ndash4408

Rosch Eleanor lsquolsquoNatural Categoriesrsquorsquo Cognitive Psychology 4 (1973) 328ndash350Ryan Carey S lsquolsquoAccuracy of Black and White College Studentsrsquo In-Group and

Out-Group Stereotypesrsquorsquo Personality and Social Psychology Bulletin 22(1996) 1114ndash1127

Schneider David The Psychology of Stereotyping (New York Guilford Press2004)

Schneider David Albert Hastorf and Phoebe Ellsworth Person Perception(Reading MA Addison-Wesley 1979)

Shih Margaret Todd Pittinsky and Nalini Ambady lsquolsquoStereotype SusceptibilityIdentity Salience and Shifts in Quantitative Performancersquorsquo PsychologicalScience 10 (1999) 80ndash83

Shih Margaret Todd Pittinsky and Amy Trahan lsquolsquoDomain-Specific Effects ofStereotypes on Performancersquorsquo Self and Identity 5 (2006) 1ndash14

Steele Claude Whistling Vivaldi How Stereotypes Affect Us and What We CanDo (New York Norton 2010)

Tenenbaum Joshua and Thomas Griffiths lsquolsquoThe Rational Basis ofRepresentativenessrsquorsquo 23rd Annual Conference of the Cognitive ScienceSociety (2001) 1036ndash1041

Tversky Amos and Daniel Kahneman lsquolsquoExtensional versus Intuitive ReasoningThe Conjunction Fallacy in Probability Judgmentrsquorsquo Psychological Review 90(1983) 293ndash315

Weinberger Catherin lsquolsquoIs the Science and Engineering Workforce Drawn fromthe Far Upper Tail of the Math Ability Distributionrsquorsquo mimeo UCSB 2005

Westfall Jacob Leaf Van Boven John Chambers and Charles Judd lsquolsquoPerceivingPolitical Polarization in the United States Party Identity Strength andAttitude Extremity Exacerbate the Perceived Partisan DividersquorsquoPsychological Science 10 (2015) 145ndash158

Wolsko Christopher Bernadette Park Charles Judd and Bernd WittenbrinklsquolsquoFraming Interethnic Ideology Effects of Multicultural and Color-BlindPerspectives on Judgments of Groups and Individualsrsquorsquo Journal ofPersonality and Social Psychology 78 (2000) 635ndash654

QUARTERLY JOURNAL OF ECONOMICS1794

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Page 18: I. Introduction · uneducated at the beginning of the 20th century, and as high achievers at the beginning of the 21st (Madon et al. 2001). Social science has produced three broad

In the first case groups G and ndashG are such that the likelihoodratio tG

tGis monotonic in t The monotone likelihood ratio prop-

erty (MLRP) holds to a first approximation in many empiricalsettings and is also assumed in many economic models such asstandard agency models19 If tG

tGis monotonically increasing (de-

creasing) in t then group G is associated with higher (lower)values of t relative to the comparison group ndashG Formally

PROPOSITION 2 Suppose that MLRP holds and assume wlogthat the likelihood ratio tG

tGis strictly increasing in t Then

for any weighting function htethTHORN that is not constant in therelevant range

EstethtjGTHORN gt EethtjGTHORN gt EethtjGTHORN gt E

stethtjGTHORN

Under MLRP the most representative part of the distribu-tion for G is the right tail if tG

tGincreases in t or the left tail if tG

tG

decreases in t The representative tail is then overweighted whilethe nonrepresentative tail is underweighted As a consequencethe assessed mean E

stethtjGTHORN is too extreme in the direction of therepresentative tail

Critically in line with the social cognition perspective the ste-reotype contains a kernel of truth the DM overestimates the meanof G if this group has a higher mean than the comparison groupnamely EethtjGTHORN gt EethtjGTHORN and conversely if EethtjGTHORN lt EethtjGTHORN TheDM exaggerates this true difference because he inflates the asso-ciation of G with its most representative types20 For instancewhen judging an asset manager who performs well we tend to

19 Examples include the binomial and the Poisson families of distributionswith different parameters The characterization of distributions satisfying MLRPis easier in the case of continuous distributions (see Online Appendix D) two dis-tributions f(x) f ethx THORN that differ only in their mean satisfy MLRP if and only if thedistribution f(x) is log-concave Examples include the exponential and normal dis-tributions To the extent that discrete distributions sufficiently approximate thesedistributions (as the Poisson distribution PoisethTHORN approximates the normal distri-bution Neth THORN for large l) they will also satisfy MLRP

20 Depending on the distribution and the weighing function the DMrsquos assess-ment of the variance VarethtjGTHORNmay also be dampened relative to the truth This isoften true under the truncation weighing function In this case stereotyping effec-tively leads to a form of overconfidence in which the DM holds extreme views andoverestimates the precision of his assessment That extreme views and overconfi-dence (in the sense of over precision) go together has been documented in the settingof political ideology among others (Ortoleva and Snowberg 2015)

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overemphasize skill relative to luck because higher skill levels arerelatively more associated with higher performance This occurseven if for both skilled and unskilled managers high performanceis mostly due to luck

In the second case for which we characterize the stereotypi-cal distributions groups G and ndashG have the same mean EethtjGTHORNfrac14 EethtjGTHORN frac14 EethtTHORN but differ in their variance We abstract fromskewness and higher moments by considering distributionsethtGTHORNt2T and ethtGTHORNt2T that share the same support and are sym-metric around the medianmean EethtTHORN

PROPOSITION 3 Suppose that in G more extreme types are rela-tively more frequent than in ndashG Formally the likelihoodratio tG

tGis U-shaped in t around EethtTHORN Then for any weight-

ing function htethTHORN that is not constant in the relevant rangestereotypical beliefs satisfy

VarstethtjGTHORN gt VarethtjGTHORN gt VarethtjGTHORN gt VarstethtjGTHORN

EstethtjGTHORN frac14 E

stethtjGTHORN frac14 EethtTHORN

When group G has a higher relative prevalence of extremetypes its representative types are located at both extremes of thedistribution The DMrsquos beliefs about G are then formed by over-weighting both tails while underweighting the unrepresentativemiddle The overweighting of Grsquos tails causes the assessment ofits variance VarstethtjGTHORN to be too high For example the skill dis-tribution of immigrants to the United States may be perceived ashaving very fat tails or even bimodal with immigrants beingperceived as either unskilled or very skilled relative to the resi-dent population The mean of the group in contrast is assessedcorrectly because the stereotypical distribution remains symmet-ric around EethtTHORN As before the stereotype contains a kernel oftruth It induces the agent to exaggerate the true differences be-tween groups namely the higher variance of G relative to itscounterpart

We present a number of extensions of the model in the OnlineAppendix We first consider multidimensional type spaces andshow that stereotypes center around the dimension wheregroups differ the most in line with the kernel of truth logic(Online Appendix C) Multidimensional stereotypes imply thatthe dimension we think about is influenced by context For

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example the Irish are stereotyped as red-haired when comparedwith the European population However when compared withthe Scots a more plausible stereotype for the Irish is lsquolsquoCatholicrsquorsquobecause religion is the dimension along which Irish and Scotsdiffer the most

In Online Appendix D we extend the model to continuoustype spaces Many settings of interest in economics can be use-fully described by continuous probability distributions and weshow our model is particularly tractable in this case In OnlineAppendix E we relax Definition 2 and allow weighting of types toalso be influenced by their likelihood We show that the basicinsight that stereotypes contain a kernel of truth carries throughto these cases as well

To summarize the psychology of representativeness yieldsstereotypes that are consistent with the social cognition approachin which individuals assess groups by recalling and focusing ondistinctive group traits When there are systematic differencesbetween groups stereotypes get the direction right but exagger-ate differences

IIIC Some Examples

A growing body of field and experimental evidence points to awidespread belief that women are worse than men at mathemat-ics (Eccles Jacobs and Harold 1990 Guiso et al 2008 CarrellPage and West 2010) This belief persists despite the fact that fordecades women have been gaining ground in average schoolgrades including mathematics and have recently surpassedmen in overall school performance (Goldin Katz and Kuziemko2006 Hyde et al 2008) This belief shared by men and women(Reuben Sapienza and Zingales 2014) may help account for thegender gap in the choices of high school tracks college degreesand careers with women disproportionately choosing humanitiesand health-related areas (Weinberger 2005 Buser Niederle andOosterbeek 2014) and forgoing significant wage premiums toquantitative skills (Bertrand 2011)

Gender stereotypes in mathematics particularly beliefs thatexaggerate the extent of average differences are consistent withthe predictions of our model The fact that men are overrepre-sented at the very highest performance levels leads a stereotyp-ical thinker to exaggerate the magnitude of mean differencesFigure I shows the score distributions from the mathematics

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section of 2013rsquos Scholastic Aptitude Test (SAT) for men andwomen21 The distributions are very similar with averagescores slightly higher for men (531 versus 499 out of 800)However scores for men have a heavier right tail with mentwice as likely to have a perfect SAT math score than women22

In light of such data the stereotypical male performance in math-ematics is high while the stereotypical female performance ispoor Predictions based on such stereotypes are inaccurate exag-gerating true differences Consistent with this prediction exper-imental evidence shows that both genders underestimatewomenrsquos ability in simple math tasks even controlling for pastperformance (Reuben Sapienza and Zingales 2014) Coffman(2014) shows a similar pattern extends to confidence about ownability in other male-typed domains with women reporting sig-nificantly less confidence in gender-incongruent than gender-congruent tasks Our model suggests that these patterns mightcome from stereotypes based on gender differences in the righttail of the distribution While differences in the right tail of thedistribution are unlikely to be relevant for most decisions stereo-typical thinking driven by these differences has the potential toimpact economically important decisions whether through self-stereotyping (ie choice of careers or majors as in BuserNiederle and Oosterbeek 2014) or through discrimination (iehiring decisions as in Bohnet van Geen and Bazerman 2016)

The logic of exaggerated yet directionally correct stereotypesalso sheds light on the well-documented phenomenon of base rateneglect (Kahneman and Tversky 1973) Indeed Proposition 2implies that the DM overreacts to information that assigns

21 Standardized test performance measures not only innate ability but alsoeffort and investment by third parties (Hyde et al 2008) The mapping of test per-formance into inferences about innate ability is an issue not addressed by ourmodel

22 For 2013 SAT Mathematics scores see httpmediacollegeboardcomdigitalServicespdfresearchSAT-Percentile-Ranks-By-Gender-Ethnicity-2013pdf Results are similar for the National Assessment of Educational Progress(NAEP) which are more representative of the overall population For 2012NAEP scores for 17-year-olds in mathematics see httpnationsreportcardgovltt_2012age17maspx See Hyde et al (2008) Fryer and Levitt (2010) and Popeand Sydnor (2010) for in-depth empirical analyses of the gender gap inmathematics

STEREOTYPES 1773

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people to groups precisely because such information generatesextreme stereotypes Consider the classic example in which amedical test for a particular disease with a 5 prevalence has a90 rate of true positives and a 5 rate of false positives The testassigns each person to one of two groups + (positive test) or ndash(negative test) The DM estimates the frequency of the sick type(s) and the healthy type (h) in each group The test is informativea positive result increases the relative likelihood of sickness anda negative result increases the relative likelihood of health forany prior Formally

PreththornjsTHORN

PreththornjhTHORNgt 1 gt

PrethjsTHORN

PrethjhTHORNeth4THORN

This condition has clear implications the representative personwho tests positive is sick while the representative person whotests negative is healthy Following Proposition 2 the DMreacts to the test by moving his priors too far in the right di-rection generating extreme stereotypes He greatly boosts hisassessment that a positively tested person is sick but also thata negatively tested person is healthy Because most people arehealthy the DMrsquos assessment about the group that tested neg-ative is fairly accurate but is severely biased for the group that

FIGURE I

SAT Mathematics Scores by Gender (2013)

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tested positive This analysis formalizes Tversky andKahnemanrsquos (1983) verbal account of base rate neglect23

The same mechanism may underlie several other instanceswhere DMs overweight diagnostic information When assessingan employeersquos skill level an employer attributes high perfor-mance to high skill because high performance is the distinctivemark of a talented employee Because he neglects the possibilitythat some talented employees perform poorly and that somenontalented ones perform well (perhaps due to stochasticity inthe environment) the employer has too much faith in skill andneglects the role of luck in accounting for the output Similarlywhen assessing the performance of firms in a hot sector of theeconomy (eg G = internet) an investor recalls highly successfulfirms in that sector (t = return of Google Amazon etc) He ne-glects the possibility of firms being unsuccessful because lack ofsuccess is statistically nondiagnostic and psychologically nonrep-resentative of a growing sectormdasheven if it is likely This causesexcessive optimism (in that the expectation of growth is unrea-sonably high) and overconfidence (in that the variability in earn-ings growth considered possible is truncated) True the hot sectormay have better growth opportunities on average but represen-tativeness exaggerates this feature and induces the investor toneglect a significant risk of failure

IV Evidence on Representativeness and Stereotypes

Testing our model requires evaluating the beliefs individualshold about a target group against the true distribution of thattarget group over an attribute space An ideal data set would

23 Our account is distinct from a mechanical underweighting of base rates inBayes rule as in Grether (1980) and Bodoh-Creed Benjamin and Rabin (2013) Inthose models upon receiving the test results the DM can update his beliefs in thewrong direction he can be less confident that a person is healthy after a negativetest than under his prior which cannot happen in our model Although this predic-tion of our model seems consistent with introspection we are not aware of experi-mental evidence on this point Griffin and Tversky (1992) present evidenceconsistent with pure neglect of base rates but in a significantly different tasknamely inferring the bias of a coin from a history of coin flips Such experimentsare hard to compare with the predictions of our model because subjects are asked togenerate distributions of different numbers of coin flips in their minds which is amuch more involved task than to recall types of a given distribution Their assess-ments then might be wrong for other reasons See Bodoh-Creed Benjamin andRabin (2013) for a detailed discussion

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consist of naturally defined groups with known distributions overa given space of types and a corresponding set of beliefs about thedistribution of each group over that space of types This wouldallow us to test for exaggeration of true differences betweengroups and to ask whether this exaggeration is well predictedby overweighting representative types To identify a causal rolefor representativeness or context dependence we would need ex-ogenous variation in either the comparison group ndashG or in thedistributions over the type spaces This is unavailable in existingdata sets Accordingly we take a two-pronged approach First wecreate a controlled laboratory environment that allows us toinduce the exogenous variation in representative types that weneed to test causality then we reanalyze existing field evidence tocheck for consistency with our predictions

In testing our model we focus on the two main implicationsof representativeness-based stereotypes

Context dependence the stereotype of a target group de-pends on the characteristics of the reference group it iscompared to

Kernel of truth stereotypes depend on group character-istics andmdashin most (precisely characterized) settingsmdashare slanted toward representative types

We test the first property with a lab experiment (SectionIVA) We then turn to survey data on beliefs about US politicalgroups (Section IVB) for an empirical analysis that explores thesecond property The survey data are more tightly linked to ourinterest in social stereotypes The laboratory experiment allowsus to directly test the role of representativeness in generatingcontext dependent beliefs Online Appendixes F and G provideall details and additional results for the experiments and fieldevidence

IVA Lab Evidence on Representativeness and ContextDependence

The influence of the representativeness heuristic on recalland on beliefs has been extensively documented in the lab(Kahneman and Tversky 1972 1973) Our goal is to considerhow representativeness as formalized in equation (2) gives riseto context-dependent beliefs To our knowledge the possibility

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that representativeness may generate context dependence hasnot been tested before

To assess this prediction we perform a controlled laboratoryexperiment that allows us to isolate representativeness frommany confounding factorsmdashhistorical sociological or other-wisemdashthat may affect stereotype formation in the real worldWe construct our own groups of ordinary objects creating atarget group G and a comparison group ndashG We hold thetarget group G fixed and explore how participant impressions ofit change as we change the comparison group ndashG and thusrepresentativeness

We conducted several experiments in the laboratory and onAmazon Mechanical Turk Each involves a basic three-stepdesign First participants are shown the target group and a ran-domly assigned comparison group for 15 seconds In this timedifferences between groups can be noticed but the groupsrsquo precisecompositions cannot be memorized The second step consists of afew filler questions which briefly draw the participantsrsquo cognitivebandwidth away from their observation Finally participants areasked to assess the groups they saw Participants are incentiv-ized to provide accurate answers

We randomly assign participants to either the Control or theRepresentativeness condition In the Control condition G and ndashGhave nearly identical distributions so that all types are similarlyrepresentative for each group In the Representativeness condi-tion ndashG is changed in such a way that a certain type becomes veryrepresentative for G Context dependence implies that the assess-ment of G should now overweight this representative type eventhough the distribution of G itself has not changed

We ran six experiments of this form with design changesfocused on reducing participant confusion and removing con-founds We describe the final and most refined version of theseexperiments here In an attempt to provide a overview of the re-sults while remaining concise we provide the results from pooledspecifications that use all data collected In Online Appendix Fwe offer additional details and report all experiments conductedWe also give instructions and materials for each experiment thefull data set is available by request

Consider first the experiment illustrated in Figure II Agroup of 25 cartoon girls is presented next to a group of 25 cartoonboys in T-shirts of different colors blue green or purple In theControl condition (Figure II Panel a) the groups have identical

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color distributions (13 purple 12 green) so no color is represen-tative of either group The Representativeness condition (Panel b)compares the same group of girls with a different group of boysfor whom green shirts are replaced with blue shirts Now onlygirls wear green and only boys wear blue These colors althoughstill not the most frequent for either group are now most repre-sentative For each group girls and boys participants are asked anumber of questions concerning the frequency of T-shirts of dif-ferent colors worn by that group

Applying our model in the control condition the type space isT frac14 fgreen purpleg and the groups are G = girls and ndashG = boysGiven that the color distributions are identical across groups both

types are equally representativegreengirls

greenboysfrac14 1 frac14

purplegirls

purpleboys As a result

assessment of G should be correct on average stcontrolgreengirls frac14 greengirls

and stcontrolpurplegirls frac14 purplegirls for any weighing function (the same is

true about assessments of ndashG)In the treatment condition the distribution of shirt colors re-

mains the same for girls For boys green shirts are changed intoblue Thus the type space changes to T frac14 fgreen purple bluegand the representative color for girls becomes greengreengirls

greenboysfrac14 1 gt 1 frac14

purplegirls

purpleboys while that for boys becomes blue As

a result in the treatment condition subjects should inflate the

frequency of green shirts relative to the truth sttreatmentgreengirls

gt greengirls (the same should happen to assessments of blueshirts for boys) We also expect the assessed frequency of greenshirts to go up relative to the control condition namely

sttreatmentgreengirls gt stcontrol

greengirls Critically the only factor that varies

across treatments is the representativeness of the 12-colorshirt Thus if we see differences across conditions the causalrole of representativeness-based recall in shaping group judg-ments is clear24

24 We vary which colors are used in which roles across participants Someparticipants saw this particular color distribution while others see for examplegreen as the modal color and purple as the diagnostic color for boys in theRepresentativeness condition and blue as the diagnostic color for girls in theRepresentativeness condition We vary the colors across the roles to avoid con-founding the characteristics of any particular color with its diagnosticity

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FIG

UR

EII

T-S

hir

tsE

xp

erim

ent

Fig

ure

sap

pea

red

inco

lor

top

art

icip

an

tsin

the

exp

erim

ent

For

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ty

we

have

ad

ded

ale

tter

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chT

-sh

irt

toid

enti

fyth

eco

lor

for

the

read

er

lsquolsquoGrsquorsquo

ind

icate

sgre

en

lsquolsquoPrsquorsquo

ind

icate

sp

urp

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lsquolsquoBrsquorsquo

ind

icate

sblu

eT

hes

ele

tter

sd

idn

otap

pea

rto

part

icip

an

tsan

dare

for

read

erre

fere

nce

only

P

lease

see

onli

ne

ver

sion

ofp

ubli

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art

icle

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rfi

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reex

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pea

red

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STEREOTYPES 1779

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We collected data from 301 participants using this T-shirtsdesign25 Since the number of green and purple shirts is verysimilar we first ask each participant the simplest question ofwhich shirt color is modal Next we ask participants to assessthe share of green and purple shirts

Consistent with the role of representativeness participantsassigned to the Representativeness condition are 105 percentagepoints more likely to recall the less frequent color (green for girlsor blue for boys) as the modal color when it is representative of agroup (35 of participants guess the less frequent color is modalin the Control condition this proportion increases to 46 in theRepresentativeness condition p = 01 estimated from a probitregression reported in Online Appendix F)

We now turn to subjectsrsquo estimates of how many T-shirts ofeach color they saw in each group In both conditions the truedifference in counts is 1 (13 purple shirts 12 green or blue shirts)In the Control condition participants on average believe they saw054 more purple shirts than green or blue shirts In theRepresentativeness condition participants believe they saw072 fewer purple shirts than green or blue shirts (the acrosstreatment difference is significant with p = 01 from OLS regres-sion reported in Online Appendix F)

In total we collected data for six experiments of this generalstructure gathering evidence from more than 1000 participantsAs we describe in Online Appendix F although there is substan-tial variation across experiments when we pool all of the data wefind significant aggregate treatment effects in line with a role ofrepresentativeness in judgment We employ four different unor-dered types designs similar to the T-shirts experiment using sixsamples (four online and two in the laboratory) with 741 partic-ipants We find effects in the predicted direction for five of the sixsamples Using a probit regression that pools the data for theseunordered type experiments we find that participants are 93 per-centage points more likely to guess that the less frequent type ismodal when it is representative than when it is not (p = 002) Wealso run a family of ordered types experiments (two designs fivesamples 402 participants) Unlike the simpler T-shirts style

25 Throughout our analysis we exclude any participant who participated in aprevious version of the experiment and any participant who self-identified as color-blind In Online Appendix F we show that our results are unchanged if we includethese additional observations

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design the theoretical predictions for the ordered types designsare more sensitive to the specific assumptions one makes aboutthe weighting function of the DM26 We find effects in the pre-dicted direction for three of the five samples As we discuss inmore detail in Online Appendix F the ordered types resultsvary by platform with consistently stronger results on AmazonMechanical Turk than in the laboratory samples Pooling all or-dered types experiments participants are 93 percentage pointsmore likely to guess that the group of interest has a greater av-erage than the comparison group when the right tail is represen-tative (p = 062) Given our simple experimental setting withgroups of mundane objects we interpret our resultsmdasha signifi-cant and reasonably sized impact on average beliefsmdashas an im-portant proof of concept the presence of representative typesbiases ex post assessment

IVB Empirical Evidence on Political Stereotypes

We examine two data sets on political preferences and be-liefs about political preferences in the United States We inves-tigate the roles of representativeness and context dependence byseparately testing for hypotheses that allow us to assess the lead-ing theories of stereotypes

First we test whether beliefs are correct or depart systemat-ically from the truth The statistical discrimination approachbuilds on the assumption that people hold rational expectationsof group traits Comparing beliefs to the truth allows us to assessthe validity of this assumption in our data

Second we test if beliefs depart from the truth by exagger-ating (mean) differences among groups per the kernel of truthhypothesis This is an implicit test of context dependence be-cause it implies that beliefs about the target groups are shapednot only by that grouprsquos characteristics but also by those of thereference group27

Third we test if distortions in beliefs can be accounted for bythe overweighting of highly representative types (defined astypes that are relatively more frequent in the target relative to

26 This is due in part to our choice to not study MLRP distributions We moti-vate and discuss this design decision in Online Appendix F

27 Of course unlike in the laboratory experiment in this setting we cannot testfor context dependence by exogenously varying the reference group

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the reference group) The second and third tests address the keypredictions of our model

1 The Data We have two data sets on political preferences andbeliefs about political preferences The first data set from GrahamNosek and Haidt (GNH 2012) contains data from the MoralFoundations Questionnaire Respondents (1174 self-identified lib-erals and 500 self-identified conservatives) answer questions abouttheir position on a subset of 45 issues 20 moral relevance state-ments (eg lsquolsquowhen you decide whether something is right orwrong to what extent are the following considerations relevantto your thinkingrsquorsquo) and 25 moral judgments (eg lsquolsquoindicate theextent to which you would agree or disagreersquorsquo) For each issue arandomly determined subset of participants states their own posi-tion another subset states their belief on the position of a lsquolsquotypicalliberalrsquorsquo and a third subset states their belief on the position of alsquolsquotypical conservativersquorsquo The data thus include the distribution overpositions for both liberal and conservatives as well as the averagebelieved typical position of liberals and of conservatives on the 45issues Each position is elicited on 1ndash6 scale

The second data set comes from the American NationalElection Survey (ANES) and contains data from more than20000 respondents between 1964 and 201228 The surveycovers political issues of the day such as the optimal amount ofgovernment spending and service provision (1984ndash2000) or theplace of women in society (1972ndash1998) We focus on the 10 issuesthat ask participants to respond on a 1ndash7 scale (rather than justindicate binary agreement or disagreement) all 10 issues areasked in multiple years Participants are asked to provide theirown position on the scale and their believed position of theDemocratic and Republican parties (lsquolsquoWhere would you placethe Democratic [Republican] party on this scalersquorsquo) The data in-clude for each issue-year observation the distribution of partic-ipant positions for self-identified liberals and self-identifiedconservatives as well as the distribution of believed typical posi-tions of the Democratic and Republican parties

28 These data are publicly available at httpwwwelectionstudiesorgstudy-pagesanes_timeseries_cdfanes_timeseries_cdfhtm

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2 Empirical Strategy Our analysis focuses on beliefs abouttwo groups Conservatives and Liberals The types are the possi-ble positions for each issue (1 2 6 7) For the GNH data weinterpret beliefs about the lsquolsquotypicalrsquorsquo element of a group to coincidewith the believed average position in that group Similarly forthe ANES data we use the believed party positions as a proxy forbelieved mean of each group29 We then take as a benchmark thehypothesis that individuals hold accurate beliefs about eachgroup and in particular that believed mean position shouldequal true mean position at least on average across subjectsThe accurate beliefs hypothesis underlies the most common eco-nomic model of stereotyping statistical discrimination

To assess our representativeness-based model we perform aregression exercise To test our model in a linear regressionframework we rely on linear approximations of the weightingfunction Our model then yields two regression specifications

PROPOSITION 4 Let G 2 fconservative liberal g and assume

ht h tG

tG

be a differentiable and strictly increasing weight-

ing function as in Definition 2 The following hold as a first-order approximation around identical distributions G

Gfrac14 1

(i) Kernel of truth regression There exists a constant gt 0such that

EstethtjGTHORN frac14 EethtjGTHORNeth1thorn THORN EethtjGTHORNeth5THORN

(ii) Representativeness regression Denote H frac14 fT 2 Tg

the right tail of types and RconsH frac14

PHtconsPHtlib

as the average

representativeness of right tail types for conservatives

29 This assumption is consistent with the authorsrsquo interpretation of the GNHdata (GNH 2012) and with previous studies using ANES (eg Westfall et al 2015)Furthermore to the extent that this assumption holds equally well for most issueswithin a data set our focus on cross-issue differences should allow us to test thepredictions of our model even with an imperfect proxy for beliefs of mean positionsFinally the data provide some insight into whether subjects are reporting (per-ceived) modal or mean types As we show the modal type is a poor prediction ofstated beliefs while a distorted mean slanted toward representative types is anaccurate prediction of stated beliefs

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Under the further approximation where tcons

tlibampRcons

H for

t 2 H

EstethtjconsTHORN frac14 EethtjconsTHORN thorn consethR

consH 1THORNeth6THORN

EstethtjlibTHORN frac14 EethtjlibTHORN libethR

consH 1THORNeth7THORN

where lcons and llib are positive constants

The first regression allows us to test for the kernel of truthhypothesis and the second set of regressions allows us to test forthe role of representativeness

Equation (5) says that respondents in our model inflate theaverage position of a group say the conservatives if and only ifthe group has a higher average position than the other groupnamely the liberals Formally EstethtjconsTHORN gt EethtjconsTHORN if and onlyif EethtjconsTHORN gt EethtjlibTHORN Because in our measurement scale highertypes mean lsquolsquomore conservativersquorsquo we expect (i) believed conserva-tive average to be higher than the truth and (ii) the extent ofoverstatement to decrease in the average liberal position EethtjlibTHORNConversely we expect the average liberal position to be lowerthan the truth the more so the higher the average conservativeposition EethtjconsTHORN

As previously discussed the basis of these predictions is con-text dependence information about the distribution of ndashG is rel-evant for the beliefs about G This context dependence isinconsistent with rational expectations in which only thegrouprsquos own means should affect beliefs We test the hypothesisthat the true mean EethtjGTHORN is a significant predictor of the believedmean E

stethtjGTHORN with a positive sign and the other grouprsquos truemean EethtjGTHORN is a predictor of the believed mean with a negativesign

Equations (6) and (7) say that repondentsrsquo assessment bias isshaped by representativeness When the right tail is more repre-sentative for conservatives (Rcons

H 1 positive and large) partici-pants should inflate the average conservative position more(higher E

stethtjconsTHORN EethtjconsTHORN) and deflate the average liberal po-sition more (lower E

stethtjlibTHORN EethtjlibTHORN) We test the hypothesisthat the inflation in conservative positions is positively associatedwith the representativeness of the right tail for the conservativesand the inflation in liberal positions is negatively associated with

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it Once again the representativeness of the right tail is com-puted using the true distribution of positions

In equations (6) and (7) in many cases the representative tailis also the most likely one As a consequence these tests cannotdistinguish a representativeness-based from a likelihood-basedmodel of distorted beliefs We perform two additional testsFirst we run versions of equations (6) and (7) in which we controlfor the likelihood of tails (see Table A4 in Online Appendix G)Second we compute numerically the predictions of a representa-tiveness-based model of stereotypes and a likelihood-based modelof stereotypes We then assess which of these two is better able tomatch the data on beliefs

3 Empirical Results To begin we illustrate the structure ofthe data and the nature of our predictions with two simple exam-ples from the GNH data set focusing on beliefs about conserva-tives In example 1 participants are asked about their agreementwith the statement lsquolsquoIt can never be right to kill a human beingrsquorsquoIn example 2 participants are asked about the moral relevance oflsquolsquowhether or not someone cared for someone weak or vulnerablersquorsquoAs can be seen in Figure III in example 1 the modal position(strongly disagree (1)) and most representative positions(strongly disagree (1)) coincide for conservatives In contrast inexample 2 in Figure III the most representative types (slightlyrelevant (3) not at all relevant (1)) are not most likely for theconservative group Following Proposition 1 we predict that be-liefs will be distorted in the direction of the most representativetypes Thus we expect more exaggeration in example 2 than inexample 1 since in example 2 the most representative types (inthe left tail) are far from the modal type whereas in example 1they coincide This is what we find the conservative position isexaggerated by only 009 positions in Example 1 (true mean 299believed mean 290) but by 106 positions in Example 2 (truemean 421 believed mean 315)

In the full data sets we treat each (issue year) pair as anobservation and we cluster standard errors at the issue level Forthe GNH data we have 45 observations 45 issues measured inthe same year For the ANES data we have 66 observations 10issues measured in multiple years To begin we simply docu-ment systematic exaggeration in both data sets This is a primaryfocus of the original analysis in GNH (2012) and also in Westfall

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FIGURE III

Two Examples

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et al (2015)rsquos analysis of the ANES data30 Figure IV shows thatthe believed difference between typical conservative and typicalliberal positions is larger than the true difference in mean posi-tions for 109 of the 111 observations The data for both GNH(squares) and ANES (triangles) lie above the 45-degree line(dashed)31 Average exaggeration is 062 positions on the scale(066 in the GNH data 059 in the ANES data)32

The systematic and significant exaggeration of mean differ-ences suggests that the benchmark model of accurate beliefs ismissing something important Indeed this exaggeration reflectsthe fact that believed means are typically more extreme than truemeans First note that the kernel of truth regression (equation(5)) generates exaggeration of mean differences just as docu-mented in Figure IV

EstethtjGTHORN E

stethtjGTHORN frac14 eth1thorn 2THORN frac12EethtjGTHORN EethtjGTHORN

To bring this prediction to the data we regress the believedmean position for each group EBethtjGTHORN on the true mean of thegroup EethtjGTHORN and the true mean of the comparison groupEethtjGTHORN across issues We do this for each group (liberals con-servatives) in each data set separately We also present pooledspecifications that combine the data sets to make a prediction fora given group (liberals conservatives) In these pooled specifica-tions we include a dummy variable indicating whether theobservation came from the ANES data set For all specificationswe cluster observations at the issue level33 The results from re-gression are shown in Table I In every specification we find thatEethtjGTHORN is a significant predictor of EBethtjGTHORN with the predicted pos-itive sign Crucially for five of the six specifications the mean of

30 Chambers and Melnyk (2006) also find evidence of exaggeration of truedifferences in beliefs about political positions

31 For convenience we recode all issues so that the high end of the scale (67)represents the stereotypically more conservative position

32 A natural question to ask is how beliefs vary across liberals and conserva-tives That is do beliefs about a group G depend on membership in G versus ndashG Ourmodel does not speak to this issue However in Online Appendix G we show thatthe results we document below hold for both beliefs held by conservatives and be-liefs held by liberals see Tables A9 A10 and A11

33 In general the results presented below for the ANES data are not largelyimpacted by the decision to cluster at the issue level Similar results are obtained ifthe data are not clustered

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the comparison group EethtjGTHORN is also a significant predictor ofE

BethtjGTHORN with the predicted negative signAlthough these results provide strong evidence of context

dependence and are consistent with our model they do not pindown a role for representativeness of types Our next test relatesthe magnitude of representativeness of tail types to the magni-tude of belief distortions

To this end we implement the regressions in equations (6)and (7) Following Proposition 4 we compute the average repre-

sentativeness of tail types for conservatives RconsH frac14

PtT2tconsPtT2tlib

We

again test the hypothesis that RconsH is a significant predictor of Est

ethtjconsTHORN with a positive sign and a predictor of EstethtjlibTHORN with a

negative sign Table II shows that conditional on true mean RconsH

predicts believed mean for each group G as expected The firstthree specifications display the results for predicting beliefs heldabout conservatives In both data sets the average representa-tiveness of tail types for conservatives is a significant positivepredictor of beliefs held about conservatives The final three spe-cifications display the results for predicting beliefs held about

FIGURE IV

Exaggeration of Differences

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liberals We find that the average representativeness of tail typesfor conservatives is a negative predictor of beliefs held about lib-erals This effect is significant in the GNH data and marginallysignificant in the ANES data

We present several additional results in Online Appendix GTo further examine the role of representativeness in driving be-liefs we first show the results of Table II carry through when we

TABLE II

AVERAGE REPRESENTATIVENESS OF TAIL POSITIONS PREDICTS BELIEFS

OLS Predicting Believed Mean of Group G for Each Issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position

of group G for issue

078 024 051 072 018 041

(006) (008) (009) (005) (005) (010)

Avg rep of tail types for

conservatives RconsH

019 055 025 014 012 024

(007) (022) (008) (006) (007) (005)

Constant 101 260 184 093 271 201

(026) (045) (029) (022) (025) (032)

R2 082 048 060 091 031 070

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

TABLE I

INFORMATION ABOUT ndashG PREDICTS BELIEFS ABOUT G

OLS predicting believed mean of group G for each issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position of

conservatives for issue

102 098 096 021 019 025

(0097) (0133) (0076) (0060) (0116) (0060)

True mean position of

liberals for issue

035 086 058 0987 039 073

(0106) (0134) (0131) (0066) (0106) (0135)

Constant 151 335 235 069 258 156

(0195) (0269) (0279) (0122) (0249) (0270)

R2 083 053 066 092 032 068

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

STEREOTYPES 1789

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control for the average likelihood on the tail positions (see Table A4in Online Appendix G) Most tellingly we use the model to predictbeliefs across issues and compare those to the data For simplicitywe use the rank-based truncation specification to predict mean be-liefs when stereotypes include the d most representative types ford frac14 1 T We compare these predictions to those of a model inwhich beliefs are obtained by restricting the distribution to the dmost likely types Our benchmark for both models is predicting thebelieved mean from the entire distribution where d = T We showthat the predictions of the rank-based truncation model with d = 4or 5 compare favorably to both a likelihood-based truncation model(with any d) and the accurate beliefs benchmark Interestingly thisresult suggests that stereotypical beliefs are well approximated byneglecting the least representative types (as opposed to focusingonly on the most representative types) and so represent a moderatethough systematic departure from the standard benchmarkFinally we show that the results we document above hold forboth beliefs held by conservatives and beliefs held by liberals (seeTables A9 A10 and A11 in Online Appendix G)

V Conclusion

We present a model of stereotypical thinking in which DMsmaking predictions about a group overweight the grouprsquos mostdistinctive types These overweighted types are not the mostlikely ones given the DMrsquos data but the most representativeones in the sense of being the most diagnostic of the group rela-tive to other groups Representativeness implies that what ismost distinctive of a group depends on what group it is comparedwith We present experimental evidence that confirms this con-text dependence in recall-based assessments of groups Finallywe evaluated the predictions of the model using political data fromexisting large-scale surveys We find context dependence to be akey feature of beliefs Given the richness of the political data wecan go a step further and identify a role for representativeness inparticular As the representativeness of tail types increases beliefsof a group are distorted in the direction of that tail

Our approach provides a parsimonious and psychologicallyfounded account of how DMs generate simplified representationsof reality from social groups to stock returns and offers a unifiedaccount of disparate pieces of evidence relating to this type of

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uncertainty The model captures the central fact that stereotypeshighlight the greatest difference between groups thus explainingwhy some stereotypes are very accurate while others lack valid-ity Still stereotypes often have a kernel of truth when they arebased on systematicmdasheven if smallmdashdifferences between groupsThis logic allows us to describe a number of heuristics and psy-chological biases many of which arise in the context of predictionproblems Generically our model generates overreaction to diag-nostic information

Our model is based on representativeness and does not cap-ture all the features of stereotypical thinking However it cap-tures perhaps the central feature when we think of a group wefocus on what is most distinctive about it and neglect or under-weight the rest

Saeuroıd Business School University of Oxford

Ohio State University and Harvard Business School

Universita Bocconi and Innocenzo Gasparini Institute

for Economic Research

Harvard University

Supplementary Material

An Online Appendix for this article can be found at QJEonline (qjeoxfordjournalorg)

References

Adorno Theodor Else Frenkel-Brunswik Daniel Levinson and Nevitt SanfordThe Authoritarian Personality (New York Harper amp Row 1950)

Arrow Kenneth lsquolsquoThe Theory of Discriminationrsquorsquo in Discrimination in LaborMarkets Orley Ashenfelter and Albert Rees eds (Princeton NJPrinceton University Press 1973)

Ashton Michael and Victoria Esses lsquolsquoStereotype Accuracy Estimating theAcademic Performance of Ethnic Groupsrsquorsquo Personality and SocialPsychology Bulletin 25 (1999) 225ndash236

Barberis Nicholas Andrei Shleifer and Robert Vishny lsquolsquoA Model of InvestorSentimentrsquorsquo Journal of Financial Economics 49 (1998) 307ndash343

Bayer Sylvia lsquolsquoThe Accuracy of Academic Gender Stereotypesrsquorsquo Sex Roles 40(1999) 787ndash813

Benjamin Dan James Choi and Joshua Strickland lsquolsquoSocial Identity andPreferencesrsquorsquo American Economic Review 100 (2010) 1913ndash1928

Benjamin Dan Matthew Rabin and Collin Raymond lsquolsquoA Model of Non-Belief inthe Law of Large Numbersrsquorsquo Journal of the European Economic Association15 (2015) 515ndash544

Bertrand Marianne lsquolsquoNew Perspectives on Genderrsquorsquo Handbook of LaborEconomics 4 (2011) 1543ndash1590

Bodoh-Creed Aaron Dan Benjamin and Matthew Rabin lsquolsquoThe Dynamics of Base-Rate Neglectrsquorsquo mimeo Haas Business School 2013

STEREOTYPES 1791

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

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Bohnet Iris Alexandra van Geen and Max Bazerman lsquolsquoWhen PerformanceTrumps Gender Bias Joint versus Separate Evaluationrsquorsquo ManagementScience 5 (2016) 1225ndash1234

Bordalo Pedro Nicola Gennaioli and Andrei Shleifer lsquolsquoSalience Theory of Choiceunder Riskrsquorsquo Quarterly Journal of Economics 127 (2012) 1243ndash1285

mdashmdashmdash lsquolsquoSalience and Consumer Choicersquorsquo Journal of Political Economy 121(2013) 803ndash843

Briton Nancy and Judith Hall lsquolsquoBeliefs about Female and Male NonverbalCommunicationrsquorsquo Sex Roles 32 (1995) 79ndash90

Buser Thomas Muriel Niederle and Hessel Oosterbeek lsquolsquoGenderCompetitiveness and Career Choicesrsquorsquo Quarterly Journal of Economics 129(2014) 1409ndash1447

Carrell Scott Marianne Page and James West lsquolsquoSex and Science How ProfessorGender Perpetuates the Gender Gaprsquorsquo Quarterly Journal of Economics 125(2010) 1101ndash1144

Chambers John and Darya Melnyk lsquolsquoWhy Do I Hate Thee ConflictMisperceptions and Intergroup Mistrustrsquorsquo Personality and SocialPsychology Bulletin 32 (2006) 1295ndash1311

Chan Wayne Robert R McCrae Filip De Fruyt Lee Jussim CorinnaE Lockenhoff Marleen De Bolle Paul T Costa Jr Angelina R SutinAnu Realo Juri Allik Katsuharu Nakazato Yoshiko ShimonakaMartina Hrebıckova Sylvie Graf Michelle Yik Marina Brunner-SciarraNora Leibovich De Figueora Vanina Schmidt Chang-kyo Ahn Hyun-nie Ahn Maria E Aguilar-Vafaie Jerzy Siuta Barbara SzmigielskaThomas R Cain Janet T Crawford Khairul Anwar Mastor Jean-Pierre Rolland Florence Nansubuga Daniel R MiramontezVeronica Benet-Martınez Jerome Rossier Denis Bratko Iris MarusicJamin Halberstadt Mami Yamaguchi Goran Knezevic Thomas A MartinMirona Gheorghiu Peter B Smith Claudio Barbaranelli Lei WangJane Shakespeare-Finch Margarida P Lima Waldemar KlinkoszAndrzej Sekowski Lidia Alcalay Franco Simonetti Tatyana V AvdeyevaV S Pramila and Antonio Terracciano lsquolsquoStereotypes of Age Differences inPersonality Traits Universal and Accuratersquorsquo Journal of Personality andSocial Psychology 103 (2012) 1050ndash1066

Chen Yan Sherry Xin Liu Tracy Xiao and Margaret Shih lsquolsquoWhich Hat to WearImpact of Natural Identities on Coordination and Cooperationrsquorsquo Games andEconomic Behavior 84 (2014) 58ndash86

Coffman Katherine lsquolsquoEvidence on Self-Stereotyping and the Contribution ofIdeasrsquorsquo Quarterly Journal of Economics 129 (2014) 1625ndash1660

Cunningham Tom lsquolsquoComparisons and Choicersquorsquo mimeo Stockholm University2013

Diekman Amanda Alice Eagly and Patrick Kulesa lsquolsquoAccuracy and Bias in theStereotypes about the Social and Political Attitudes of Women and MenrsquorsquoJournal of Experimental Social Psychology 38 (2002) 268ndash282

Eccles Jacquelynne S Janis E Jacobs and Rena D Harold lsquolsquoGender RoleStereotypes Expectancy Effects and Parentsrsquo Socialization of GenderDifferencesrsquorsquo Journal of Social Issues 46 (1990) 183ndash201

Fryer Roland and Matthew Jackson lsquolsquoA Categorical Model of Cognition andBiased Decision-Makingrsquorsquo BE Journal of Theoretical Economics 8 (2008)1ndash42

Fryer Roland and Steven Levitt lsquolsquoAn Empirical Analysis of the Gender Gap inMathematicsrsquorsquo American Economic Journal Applied Economics 2 (2010)210ndash240

Gennaioli Nicola and Andrei Shleifer lsquolsquoWhat Comes to Mindrsquorsquo Quarterly Journalof Economics 125 (2010) 1399ndash1433

Gennaioli Nicola Andrei Shleifer and Robert Vishny lsquolsquoNeglected RisksFinancial Innovation and Financial Fragilityrsquorsquo Journal of FinancialEconomics 104 (2012) 452ndash468

Gilens Martin lsquolsquoRace and Poverty in America Public Misperceptions and theAmerican News Mediarsquorsquo Public Opinion Quarterly 60 (1996) 515ndash541

Glaeser Edward lsquolsquoThe Political Economy of Hatredrsquorsquo Quarterly Journal ofEconomics 120 (2005) 45ndash86

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Glover Dyland Amanda Pallais and William Pariente lsquolsquoDiscrimination as a Self-Fulfilling Prophecy Evidence from French Grocery Storesrsquorsquo mimeo HarvardUniversity 2015

Goldin Claudia Lawrence Katz and Ilyana Kuziemko lsquolsquoThe Homecoming ofAmerican College Women The Reversal of the College Gender GaprsquorsquoJournal of Economic Perspectives 20 (2006) 133ndash156

Graham Jesse Brian Nosek and Jonathan Haidt lsquolsquoThe Moral Stereotypes ofLiberals and Conservatives Exaggeration of Differences across thePolitical Spectrumrsquorsquo PLoS One 7 (2012) 1ndash13

Grether David lsquolsquoBayes Rule as a Descriptive Model The RepresentativenessHeuristicrsquorsquo Quarterly Journal of Economics 95 (1980) 537ndash557

Griffin Dale and Amos Tversky lsquolsquoThe Weighing of Evidence and theDeterminants of Confidencersquorsquo Cognitive Psychology 24 (1992) 411ndash435

Guiso Luigi Ferdinando Monte Paola Sapienza and Luigi Zingales lsquolsquoCultureGender and Mathrsquorsquo Science 320 (2008) 1164ndash1165

Hilton James and William Von Hippel lsquolsquoStereotypesrsquorsquo Annual Review ofPsychology 47 (1996) 237ndash271

Hyde Janet Sara Lindberg Marcia Linn Amy Ellis and Caroline WilliamslsquolsquoGender Similarities Characterize Math Performancersquorsquo Science 321 (2008)494ndash495

Judd Charles and Bernardette Park lsquolsquoDefinition and Assessment of Accuracy inSocial Stereotypesrsquorsquo Psychological Review 100 (1993) 109ndash128

Jussim Lee Jarret Crawford Stephanie Anglin John Chambers Sean Stevensand Florette Cohen lsquolsquoStereotype Accuracy One of the Largest and MostReplicable Effects in All of Social Psychologyrsquorsquo in The Handbook ofPrejudice Stereotyping and Discrimination Todd Nelson ed (MahwahNJ Lawrence Erlbaum 2015)

Kahneman Daniel and Amos Tversky lsquolsquoSubjective Probability A Judgment ofRepresentativenessrsquorsquo Cognitive Psychology 3 (1972) 430ndash454

mdashmdashmdash lsquolsquoOn the Psychology of Predictionrsquorsquo Psychological Review 80 (1973) 237ndash251

Kaplowitz Stan Bradley Fisher and Clifford Broman lsquolsquoHow Accurate ArePerceptions of Social Statistics about Blacks and Whitesrsquorsquo Public OpinionQuarterly 67 (2003) 237ndash243

Kersten Daniel Pascal Mamassian and Alan Yuille lsquolsquoObject Perception asBayesian Inferencersquorsquo Annual Review of Psychology 55 (2004) 271ndash304

Klein Richard Kate A Ratliff Michelangelo Vianello Reginald B Adams JrStepan Bahnik Michael J Bernstein Konrad Bocian Mark J BrandtBeach Brooks Claudia Chloe Brumbaugh Zeynep CemalcilarJesse Chandler Winnee Cheong William E Davis Thierry DevosMatthew Eisner Natalia Frankowska David Furrow Elisa Maria GallianiFred Hasselman Joshua A Hicks James F Hovermale S Jane HuntJeffrey R Huntsinger Hans IJzerman Melissa-Sue John Jennifer A Joy-Gaba Heather Barry Kappes Lacy E Krueger Jaime Kurtz CarmelA Levitan Robyn Mallett Wendy L Morris Anthony J Nelson JasonA Nier Grant Packard Ronaldo Pilati Abraham M RutchickKathleen Schmidt Jeanine L Skorinko Robert Smith Troy G SteinerJustin Storbeck Lyn M Van Swol Donna Thompson Anna van rsquot VeerLeigh Ann Vaughn Marek Vranka Aaron Wichman Julie A Woodzickaand Brian A Nosek lsquolsquoInvestigating Variation in Replicability A ManyLabs Replication Projectrsquorsquo Social Psychology 45 (2014) 142ndash152

Lundberg Shelly and Richard Startz lsquolsquoPrivate Discrimination and SocialIntervention in Competitive Labor Marketsrsquorsquo American Economic Review73 (1983) 340ndash347

Madon Stephanie Max Guyll Kathy Aboufadel Eulices Montiel Alison SmithPolly Palumbo and Lee Jussim lsquolsquoEthnic and National Stereotypes ThePrinceton Trilogy Revisited and Revisedrsquorsquo Personality and SocialPsychological Bulletin 27 (2001) 996ndash1010

Martin Carol lsquolsquoA Ratio Measure of Sex Stereotypingrsquorsquo Journal of Personality andSocial Psychology 52 (1987) 489ndash499

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httpqjeoxfordjournalsorgD

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McCauley Clark Krishna Thangavelu and Paul Rozin lsquolsquoSex Stereotyping ofOccupations in Relation to Television Representations and Census FactsrsquorsquoBasic and Applied Social Psychology 9 (1988) 197ndash212

Mullainathan Sendhil lsquolsquoThinking through Categoriesrsquorsquo mimeo HarvardUniversity 2002

Ortoleva Pietro and Erik Snowberg lsquolsquoOverconfidence in Political BehaviorrsquorsquoAmerican Economic Review 105 (2015) 504ndash535

Phelps Edmund lsquolsquoThe Statistical Theory of Racism and Sexismrsquorsquo AmericanEconomic Review 62 (1972) 659ndash661

Pope Devin and Justin Sydnor lsquolsquoGeographic Variation in the Gender Differencesin Test Scoresrsquorsquo Journal of Economic Perspectives 24 (2010) 95ndash108

Rabin Matthew lsquolsquoInference by Believers in the Law of Small NumbersrsquorsquoQuarterly Journal of Economics 117 (2002) 775ndash816

Rabin Matthew and Joel Schrag lsquolsquoFirst Impressions Matter A Model ofConfirmatory Biasrsquorsquo Quarterly Journal of Economics 114 (1999) 37ndash82

Rabin Matthew and Dimitri Vayanos lsquolsquoThe Gamblerrsquos and Hot-Hand FallaciesTheory and Applicationsrsquorsquo Review of Economic Studies 77 (2010) 730ndash778

Reuben Ernesto Paola Sapienza and Luigi Zingales lsquolsquoHow Stereotypes ImpairWomenrsquos Careers in Sciencersquorsquo Proceedings of the National Academy ofSciences 111 (2014) 4403ndash4408

Rosch Eleanor lsquolsquoNatural Categoriesrsquorsquo Cognitive Psychology 4 (1973) 328ndash350Ryan Carey S lsquolsquoAccuracy of Black and White College Studentsrsquo In-Group and

Out-Group Stereotypesrsquorsquo Personality and Social Psychology Bulletin 22(1996) 1114ndash1127

Schneider David The Psychology of Stereotyping (New York Guilford Press2004)

Schneider David Albert Hastorf and Phoebe Ellsworth Person Perception(Reading MA Addison-Wesley 1979)

Shih Margaret Todd Pittinsky and Nalini Ambady lsquolsquoStereotype SusceptibilityIdentity Salience and Shifts in Quantitative Performancersquorsquo PsychologicalScience 10 (1999) 80ndash83

Shih Margaret Todd Pittinsky and Amy Trahan lsquolsquoDomain-Specific Effects ofStereotypes on Performancersquorsquo Self and Identity 5 (2006) 1ndash14

Steele Claude Whistling Vivaldi How Stereotypes Affect Us and What We CanDo (New York Norton 2010)

Tenenbaum Joshua and Thomas Griffiths lsquolsquoThe Rational Basis ofRepresentativenessrsquorsquo 23rd Annual Conference of the Cognitive ScienceSociety (2001) 1036ndash1041

Tversky Amos and Daniel Kahneman lsquolsquoExtensional versus Intuitive ReasoningThe Conjunction Fallacy in Probability Judgmentrsquorsquo Psychological Review 90(1983) 293ndash315

Weinberger Catherin lsquolsquoIs the Science and Engineering Workforce Drawn fromthe Far Upper Tail of the Math Ability Distributionrsquorsquo mimeo UCSB 2005

Westfall Jacob Leaf Van Boven John Chambers and Charles Judd lsquolsquoPerceivingPolitical Polarization in the United States Party Identity Strength andAttitude Extremity Exacerbate the Perceived Partisan DividersquorsquoPsychological Science 10 (2015) 145ndash158

Wolsko Christopher Bernadette Park Charles Judd and Bernd WittenbrinklsquolsquoFraming Interethnic Ideology Effects of Multicultural and Color-BlindPerspectives on Judgments of Groups and Individualsrsquorsquo Journal ofPersonality and Social Psychology 78 (2000) 635ndash654

QUARTERLY JOURNAL OF ECONOMICS1794

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httpqjeoxfordjournalsorgD

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Page 19: I. Introduction · uneducated at the beginning of the 20th century, and as high achievers at the beginning of the 21st (Madon et al. 2001). Social science has produced three broad

overemphasize skill relative to luck because higher skill levels arerelatively more associated with higher performance This occurseven if for both skilled and unskilled managers high performanceis mostly due to luck

In the second case for which we characterize the stereotypi-cal distributions groups G and ndashG have the same mean EethtjGTHORNfrac14 EethtjGTHORN frac14 EethtTHORN but differ in their variance We abstract fromskewness and higher moments by considering distributionsethtGTHORNt2T and ethtGTHORNt2T that share the same support and are sym-metric around the medianmean EethtTHORN

PROPOSITION 3 Suppose that in G more extreme types are rela-tively more frequent than in ndashG Formally the likelihoodratio tG

tGis U-shaped in t around EethtTHORN Then for any weight-

ing function htethTHORN that is not constant in the relevant rangestereotypical beliefs satisfy

VarstethtjGTHORN gt VarethtjGTHORN gt VarethtjGTHORN gt VarstethtjGTHORN

EstethtjGTHORN frac14 E

stethtjGTHORN frac14 EethtTHORN

When group G has a higher relative prevalence of extremetypes its representative types are located at both extremes of thedistribution The DMrsquos beliefs about G are then formed by over-weighting both tails while underweighting the unrepresentativemiddle The overweighting of Grsquos tails causes the assessment ofits variance VarstethtjGTHORN to be too high For example the skill dis-tribution of immigrants to the United States may be perceived ashaving very fat tails or even bimodal with immigrants beingperceived as either unskilled or very skilled relative to the resi-dent population The mean of the group in contrast is assessedcorrectly because the stereotypical distribution remains symmet-ric around EethtTHORN As before the stereotype contains a kernel oftruth It induces the agent to exaggerate the true differences be-tween groups namely the higher variance of G relative to itscounterpart

We present a number of extensions of the model in the OnlineAppendix We first consider multidimensional type spaces andshow that stereotypes center around the dimension wheregroups differ the most in line with the kernel of truth logic(Online Appendix C) Multidimensional stereotypes imply thatthe dimension we think about is influenced by context For

STEREOTYPES 1771

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example the Irish are stereotyped as red-haired when comparedwith the European population However when compared withthe Scots a more plausible stereotype for the Irish is lsquolsquoCatholicrsquorsquobecause religion is the dimension along which Irish and Scotsdiffer the most

In Online Appendix D we extend the model to continuoustype spaces Many settings of interest in economics can be use-fully described by continuous probability distributions and weshow our model is particularly tractable in this case In OnlineAppendix E we relax Definition 2 and allow weighting of types toalso be influenced by their likelihood We show that the basicinsight that stereotypes contain a kernel of truth carries throughto these cases as well

To summarize the psychology of representativeness yieldsstereotypes that are consistent with the social cognition approachin which individuals assess groups by recalling and focusing ondistinctive group traits When there are systematic differencesbetween groups stereotypes get the direction right but exagger-ate differences

IIIC Some Examples

A growing body of field and experimental evidence points to awidespread belief that women are worse than men at mathemat-ics (Eccles Jacobs and Harold 1990 Guiso et al 2008 CarrellPage and West 2010) This belief persists despite the fact that fordecades women have been gaining ground in average schoolgrades including mathematics and have recently surpassedmen in overall school performance (Goldin Katz and Kuziemko2006 Hyde et al 2008) This belief shared by men and women(Reuben Sapienza and Zingales 2014) may help account for thegender gap in the choices of high school tracks college degreesand careers with women disproportionately choosing humanitiesand health-related areas (Weinberger 2005 Buser Niederle andOosterbeek 2014) and forgoing significant wage premiums toquantitative skills (Bertrand 2011)

Gender stereotypes in mathematics particularly beliefs thatexaggerate the extent of average differences are consistent withthe predictions of our model The fact that men are overrepre-sented at the very highest performance levels leads a stereotyp-ical thinker to exaggerate the magnitude of mean differencesFigure I shows the score distributions from the mathematics

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section of 2013rsquos Scholastic Aptitude Test (SAT) for men andwomen21 The distributions are very similar with averagescores slightly higher for men (531 versus 499 out of 800)However scores for men have a heavier right tail with mentwice as likely to have a perfect SAT math score than women22

In light of such data the stereotypical male performance in math-ematics is high while the stereotypical female performance ispoor Predictions based on such stereotypes are inaccurate exag-gerating true differences Consistent with this prediction exper-imental evidence shows that both genders underestimatewomenrsquos ability in simple math tasks even controlling for pastperformance (Reuben Sapienza and Zingales 2014) Coffman(2014) shows a similar pattern extends to confidence about ownability in other male-typed domains with women reporting sig-nificantly less confidence in gender-incongruent than gender-congruent tasks Our model suggests that these patterns mightcome from stereotypes based on gender differences in the righttail of the distribution While differences in the right tail of thedistribution are unlikely to be relevant for most decisions stereo-typical thinking driven by these differences has the potential toimpact economically important decisions whether through self-stereotyping (ie choice of careers or majors as in BuserNiederle and Oosterbeek 2014) or through discrimination (iehiring decisions as in Bohnet van Geen and Bazerman 2016)

The logic of exaggerated yet directionally correct stereotypesalso sheds light on the well-documented phenomenon of base rateneglect (Kahneman and Tversky 1973) Indeed Proposition 2implies that the DM overreacts to information that assigns

21 Standardized test performance measures not only innate ability but alsoeffort and investment by third parties (Hyde et al 2008) The mapping of test per-formance into inferences about innate ability is an issue not addressed by ourmodel

22 For 2013 SAT Mathematics scores see httpmediacollegeboardcomdigitalServicespdfresearchSAT-Percentile-Ranks-By-Gender-Ethnicity-2013pdf Results are similar for the National Assessment of Educational Progress(NAEP) which are more representative of the overall population For 2012NAEP scores for 17-year-olds in mathematics see httpnationsreportcardgovltt_2012age17maspx See Hyde et al (2008) Fryer and Levitt (2010) and Popeand Sydnor (2010) for in-depth empirical analyses of the gender gap inmathematics

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people to groups precisely because such information generatesextreme stereotypes Consider the classic example in which amedical test for a particular disease with a 5 prevalence has a90 rate of true positives and a 5 rate of false positives The testassigns each person to one of two groups + (positive test) or ndash(negative test) The DM estimates the frequency of the sick type(s) and the healthy type (h) in each group The test is informativea positive result increases the relative likelihood of sickness anda negative result increases the relative likelihood of health forany prior Formally

PreththornjsTHORN

PreththornjhTHORNgt 1 gt

PrethjsTHORN

PrethjhTHORNeth4THORN

This condition has clear implications the representative personwho tests positive is sick while the representative person whotests negative is healthy Following Proposition 2 the DMreacts to the test by moving his priors too far in the right di-rection generating extreme stereotypes He greatly boosts hisassessment that a positively tested person is sick but also thata negatively tested person is healthy Because most people arehealthy the DMrsquos assessment about the group that tested neg-ative is fairly accurate but is severely biased for the group that

FIGURE I

SAT Mathematics Scores by Gender (2013)

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tested positive This analysis formalizes Tversky andKahnemanrsquos (1983) verbal account of base rate neglect23

The same mechanism may underlie several other instanceswhere DMs overweight diagnostic information When assessingan employeersquos skill level an employer attributes high perfor-mance to high skill because high performance is the distinctivemark of a talented employee Because he neglects the possibilitythat some talented employees perform poorly and that somenontalented ones perform well (perhaps due to stochasticity inthe environment) the employer has too much faith in skill andneglects the role of luck in accounting for the output Similarlywhen assessing the performance of firms in a hot sector of theeconomy (eg G = internet) an investor recalls highly successfulfirms in that sector (t = return of Google Amazon etc) He ne-glects the possibility of firms being unsuccessful because lack ofsuccess is statistically nondiagnostic and psychologically nonrep-resentative of a growing sectormdasheven if it is likely This causesexcessive optimism (in that the expectation of growth is unrea-sonably high) and overconfidence (in that the variability in earn-ings growth considered possible is truncated) True the hot sectormay have better growth opportunities on average but represen-tativeness exaggerates this feature and induces the investor toneglect a significant risk of failure

IV Evidence on Representativeness and Stereotypes

Testing our model requires evaluating the beliefs individualshold about a target group against the true distribution of thattarget group over an attribute space An ideal data set would

23 Our account is distinct from a mechanical underweighting of base rates inBayes rule as in Grether (1980) and Bodoh-Creed Benjamin and Rabin (2013) Inthose models upon receiving the test results the DM can update his beliefs in thewrong direction he can be less confident that a person is healthy after a negativetest than under his prior which cannot happen in our model Although this predic-tion of our model seems consistent with introspection we are not aware of experi-mental evidence on this point Griffin and Tversky (1992) present evidenceconsistent with pure neglect of base rates but in a significantly different tasknamely inferring the bias of a coin from a history of coin flips Such experimentsare hard to compare with the predictions of our model because subjects are asked togenerate distributions of different numbers of coin flips in their minds which is amuch more involved task than to recall types of a given distribution Their assess-ments then might be wrong for other reasons See Bodoh-Creed Benjamin andRabin (2013) for a detailed discussion

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consist of naturally defined groups with known distributions overa given space of types and a corresponding set of beliefs about thedistribution of each group over that space of types This wouldallow us to test for exaggeration of true differences betweengroups and to ask whether this exaggeration is well predictedby overweighting representative types To identify a causal rolefor representativeness or context dependence we would need ex-ogenous variation in either the comparison group ndashG or in thedistributions over the type spaces This is unavailable in existingdata sets Accordingly we take a two-pronged approach First wecreate a controlled laboratory environment that allows us toinduce the exogenous variation in representative types that weneed to test causality then we reanalyze existing field evidence tocheck for consistency with our predictions

In testing our model we focus on the two main implicationsof representativeness-based stereotypes

Context dependence the stereotype of a target group de-pends on the characteristics of the reference group it iscompared to

Kernel of truth stereotypes depend on group character-istics andmdashin most (precisely characterized) settingsmdashare slanted toward representative types

We test the first property with a lab experiment (SectionIVA) We then turn to survey data on beliefs about US politicalgroups (Section IVB) for an empirical analysis that explores thesecond property The survey data are more tightly linked to ourinterest in social stereotypes The laboratory experiment allowsus to directly test the role of representativeness in generatingcontext dependent beliefs Online Appendixes F and G provideall details and additional results for the experiments and fieldevidence

IVA Lab Evidence on Representativeness and ContextDependence

The influence of the representativeness heuristic on recalland on beliefs has been extensively documented in the lab(Kahneman and Tversky 1972 1973) Our goal is to considerhow representativeness as formalized in equation (2) gives riseto context-dependent beliefs To our knowledge the possibility

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that representativeness may generate context dependence hasnot been tested before

To assess this prediction we perform a controlled laboratoryexperiment that allows us to isolate representativeness frommany confounding factorsmdashhistorical sociological or other-wisemdashthat may affect stereotype formation in the real worldWe construct our own groups of ordinary objects creating atarget group G and a comparison group ndashG We hold thetarget group G fixed and explore how participant impressions ofit change as we change the comparison group ndashG and thusrepresentativeness

We conducted several experiments in the laboratory and onAmazon Mechanical Turk Each involves a basic three-stepdesign First participants are shown the target group and a ran-domly assigned comparison group for 15 seconds In this timedifferences between groups can be noticed but the groupsrsquo precisecompositions cannot be memorized The second step consists of afew filler questions which briefly draw the participantsrsquo cognitivebandwidth away from their observation Finally participants areasked to assess the groups they saw Participants are incentiv-ized to provide accurate answers

We randomly assign participants to either the Control or theRepresentativeness condition In the Control condition G and ndashGhave nearly identical distributions so that all types are similarlyrepresentative for each group In the Representativeness condi-tion ndashG is changed in such a way that a certain type becomes veryrepresentative for G Context dependence implies that the assess-ment of G should now overweight this representative type eventhough the distribution of G itself has not changed

We ran six experiments of this form with design changesfocused on reducing participant confusion and removing con-founds We describe the final and most refined version of theseexperiments here In an attempt to provide a overview of the re-sults while remaining concise we provide the results from pooledspecifications that use all data collected In Online Appendix Fwe offer additional details and report all experiments conductedWe also give instructions and materials for each experiment thefull data set is available by request

Consider first the experiment illustrated in Figure II Agroup of 25 cartoon girls is presented next to a group of 25 cartoonboys in T-shirts of different colors blue green or purple In theControl condition (Figure II Panel a) the groups have identical

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color distributions (13 purple 12 green) so no color is represen-tative of either group The Representativeness condition (Panel b)compares the same group of girls with a different group of boysfor whom green shirts are replaced with blue shirts Now onlygirls wear green and only boys wear blue These colors althoughstill not the most frequent for either group are now most repre-sentative For each group girls and boys participants are asked anumber of questions concerning the frequency of T-shirts of dif-ferent colors worn by that group

Applying our model in the control condition the type space isT frac14 fgreen purpleg and the groups are G = girls and ndashG = boysGiven that the color distributions are identical across groups both

types are equally representativegreengirls

greenboysfrac14 1 frac14

purplegirls

purpleboys As a result

assessment of G should be correct on average stcontrolgreengirls frac14 greengirls

and stcontrolpurplegirls frac14 purplegirls for any weighing function (the same is

true about assessments of ndashG)In the treatment condition the distribution of shirt colors re-

mains the same for girls For boys green shirts are changed intoblue Thus the type space changes to T frac14 fgreen purple bluegand the representative color for girls becomes greengreengirls

greenboysfrac14 1 gt 1 frac14

purplegirls

purpleboys while that for boys becomes blue As

a result in the treatment condition subjects should inflate the

frequency of green shirts relative to the truth sttreatmentgreengirls

gt greengirls (the same should happen to assessments of blueshirts for boys) We also expect the assessed frequency of greenshirts to go up relative to the control condition namely

sttreatmentgreengirls gt stcontrol

greengirls Critically the only factor that varies

across treatments is the representativeness of the 12-colorshirt Thus if we see differences across conditions the causalrole of representativeness-based recall in shaping group judg-ments is clear24

24 We vary which colors are used in which roles across participants Someparticipants saw this particular color distribution while others see for examplegreen as the modal color and purple as the diagnostic color for boys in theRepresentativeness condition and blue as the diagnostic color for girls in theRepresentativeness condition We vary the colors across the roles to avoid con-founding the characteristics of any particular color with its diagnosticity

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FIG

UR

EII

T-S

hir

tsE

xp

erim

ent

Fig

ure

sap

pea

red

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lor

top

art

icip

an

tsin

the

exp

erim

ent

For

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ty

we

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ded

ale

tter

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irt

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enti

fyth

eco

lor

for

the

read

er

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ind

icate

sgre

en

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ind

icate

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urp

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ind

icate

sblu

eT

hes

ele

tter

sd

idn

otap

pea

rto

part

icip

an

tsan

dare

for

read

erre

fere

nce

only

P

lease

see

onli

ne

ver

sion

ofp

ubli

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icle

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colo

rfi

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reex

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lyas

itap

pea

red

top

art

icip

an

ts

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We collected data from 301 participants using this T-shirtsdesign25 Since the number of green and purple shirts is verysimilar we first ask each participant the simplest question ofwhich shirt color is modal Next we ask participants to assessthe share of green and purple shirts

Consistent with the role of representativeness participantsassigned to the Representativeness condition are 105 percentagepoints more likely to recall the less frequent color (green for girlsor blue for boys) as the modal color when it is representative of agroup (35 of participants guess the less frequent color is modalin the Control condition this proportion increases to 46 in theRepresentativeness condition p = 01 estimated from a probitregression reported in Online Appendix F)

We now turn to subjectsrsquo estimates of how many T-shirts ofeach color they saw in each group In both conditions the truedifference in counts is 1 (13 purple shirts 12 green or blue shirts)In the Control condition participants on average believe they saw054 more purple shirts than green or blue shirts In theRepresentativeness condition participants believe they saw072 fewer purple shirts than green or blue shirts (the acrosstreatment difference is significant with p = 01 from OLS regres-sion reported in Online Appendix F)

In total we collected data for six experiments of this generalstructure gathering evidence from more than 1000 participantsAs we describe in Online Appendix F although there is substan-tial variation across experiments when we pool all of the data wefind significant aggregate treatment effects in line with a role ofrepresentativeness in judgment We employ four different unor-dered types designs similar to the T-shirts experiment using sixsamples (four online and two in the laboratory) with 741 partic-ipants We find effects in the predicted direction for five of the sixsamples Using a probit regression that pools the data for theseunordered type experiments we find that participants are 93 per-centage points more likely to guess that the less frequent type ismodal when it is representative than when it is not (p = 002) Wealso run a family of ordered types experiments (two designs fivesamples 402 participants) Unlike the simpler T-shirts style

25 Throughout our analysis we exclude any participant who participated in aprevious version of the experiment and any participant who self-identified as color-blind In Online Appendix F we show that our results are unchanged if we includethese additional observations

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design the theoretical predictions for the ordered types designsare more sensitive to the specific assumptions one makes aboutthe weighting function of the DM26 We find effects in the pre-dicted direction for three of the five samples As we discuss inmore detail in Online Appendix F the ordered types resultsvary by platform with consistently stronger results on AmazonMechanical Turk than in the laboratory samples Pooling all or-dered types experiments participants are 93 percentage pointsmore likely to guess that the group of interest has a greater av-erage than the comparison group when the right tail is represen-tative (p = 062) Given our simple experimental setting withgroups of mundane objects we interpret our resultsmdasha signifi-cant and reasonably sized impact on average beliefsmdashas an im-portant proof of concept the presence of representative typesbiases ex post assessment

IVB Empirical Evidence on Political Stereotypes

We examine two data sets on political preferences and be-liefs about political preferences in the United States We inves-tigate the roles of representativeness and context dependence byseparately testing for hypotheses that allow us to assess the lead-ing theories of stereotypes

First we test whether beliefs are correct or depart systemat-ically from the truth The statistical discrimination approachbuilds on the assumption that people hold rational expectationsof group traits Comparing beliefs to the truth allows us to assessthe validity of this assumption in our data

Second we test if beliefs depart from the truth by exagger-ating (mean) differences among groups per the kernel of truthhypothesis This is an implicit test of context dependence be-cause it implies that beliefs about the target groups are shapednot only by that grouprsquos characteristics but also by those of thereference group27

Third we test if distortions in beliefs can be accounted for bythe overweighting of highly representative types (defined astypes that are relatively more frequent in the target relative to

26 This is due in part to our choice to not study MLRP distributions We moti-vate and discuss this design decision in Online Appendix F

27 Of course unlike in the laboratory experiment in this setting we cannot testfor context dependence by exogenously varying the reference group

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the reference group) The second and third tests address the keypredictions of our model

1 The Data We have two data sets on political preferences andbeliefs about political preferences The first data set from GrahamNosek and Haidt (GNH 2012) contains data from the MoralFoundations Questionnaire Respondents (1174 self-identified lib-erals and 500 self-identified conservatives) answer questions abouttheir position on a subset of 45 issues 20 moral relevance state-ments (eg lsquolsquowhen you decide whether something is right orwrong to what extent are the following considerations relevantto your thinkingrsquorsquo) and 25 moral judgments (eg lsquolsquoindicate theextent to which you would agree or disagreersquorsquo) For each issue arandomly determined subset of participants states their own posi-tion another subset states their belief on the position of a lsquolsquotypicalliberalrsquorsquo and a third subset states their belief on the position of alsquolsquotypical conservativersquorsquo The data thus include the distribution overpositions for both liberal and conservatives as well as the averagebelieved typical position of liberals and of conservatives on the 45issues Each position is elicited on 1ndash6 scale

The second data set comes from the American NationalElection Survey (ANES) and contains data from more than20000 respondents between 1964 and 201228 The surveycovers political issues of the day such as the optimal amount ofgovernment spending and service provision (1984ndash2000) or theplace of women in society (1972ndash1998) We focus on the 10 issuesthat ask participants to respond on a 1ndash7 scale (rather than justindicate binary agreement or disagreement) all 10 issues areasked in multiple years Participants are asked to provide theirown position on the scale and their believed position of theDemocratic and Republican parties (lsquolsquoWhere would you placethe Democratic [Republican] party on this scalersquorsquo) The data in-clude for each issue-year observation the distribution of partic-ipant positions for self-identified liberals and self-identifiedconservatives as well as the distribution of believed typical posi-tions of the Democratic and Republican parties

28 These data are publicly available at httpwwwelectionstudiesorgstudy-pagesanes_timeseries_cdfanes_timeseries_cdfhtm

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2 Empirical Strategy Our analysis focuses on beliefs abouttwo groups Conservatives and Liberals The types are the possi-ble positions for each issue (1 2 6 7) For the GNH data weinterpret beliefs about the lsquolsquotypicalrsquorsquo element of a group to coincidewith the believed average position in that group Similarly forthe ANES data we use the believed party positions as a proxy forbelieved mean of each group29 We then take as a benchmark thehypothesis that individuals hold accurate beliefs about eachgroup and in particular that believed mean position shouldequal true mean position at least on average across subjectsThe accurate beliefs hypothesis underlies the most common eco-nomic model of stereotyping statistical discrimination

To assess our representativeness-based model we perform aregression exercise To test our model in a linear regressionframework we rely on linear approximations of the weightingfunction Our model then yields two regression specifications

PROPOSITION 4 Let G 2 fconservative liberal g and assume

ht h tG

tG

be a differentiable and strictly increasing weight-

ing function as in Definition 2 The following hold as a first-order approximation around identical distributions G

Gfrac14 1

(i) Kernel of truth regression There exists a constant gt 0such that

EstethtjGTHORN frac14 EethtjGTHORNeth1thorn THORN EethtjGTHORNeth5THORN

(ii) Representativeness regression Denote H frac14 fT 2 Tg

the right tail of types and RconsH frac14

PHtconsPHtlib

as the average

representativeness of right tail types for conservatives

29 This assumption is consistent with the authorsrsquo interpretation of the GNHdata (GNH 2012) and with previous studies using ANES (eg Westfall et al 2015)Furthermore to the extent that this assumption holds equally well for most issueswithin a data set our focus on cross-issue differences should allow us to test thepredictions of our model even with an imperfect proxy for beliefs of mean positionsFinally the data provide some insight into whether subjects are reporting (per-ceived) modal or mean types As we show the modal type is a poor prediction ofstated beliefs while a distorted mean slanted toward representative types is anaccurate prediction of stated beliefs

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Under the further approximation where tcons

tlibampRcons

H for

t 2 H

EstethtjconsTHORN frac14 EethtjconsTHORN thorn consethR

consH 1THORNeth6THORN

EstethtjlibTHORN frac14 EethtjlibTHORN libethR

consH 1THORNeth7THORN

where lcons and llib are positive constants

The first regression allows us to test for the kernel of truthhypothesis and the second set of regressions allows us to test forthe role of representativeness

Equation (5) says that respondents in our model inflate theaverage position of a group say the conservatives if and only ifthe group has a higher average position than the other groupnamely the liberals Formally EstethtjconsTHORN gt EethtjconsTHORN if and onlyif EethtjconsTHORN gt EethtjlibTHORN Because in our measurement scale highertypes mean lsquolsquomore conservativersquorsquo we expect (i) believed conserva-tive average to be higher than the truth and (ii) the extent ofoverstatement to decrease in the average liberal position EethtjlibTHORNConversely we expect the average liberal position to be lowerthan the truth the more so the higher the average conservativeposition EethtjconsTHORN

As previously discussed the basis of these predictions is con-text dependence information about the distribution of ndashG is rel-evant for the beliefs about G This context dependence isinconsistent with rational expectations in which only thegrouprsquos own means should affect beliefs We test the hypothesisthat the true mean EethtjGTHORN is a significant predictor of the believedmean E

stethtjGTHORN with a positive sign and the other grouprsquos truemean EethtjGTHORN is a predictor of the believed mean with a negativesign

Equations (6) and (7) say that repondentsrsquo assessment bias isshaped by representativeness When the right tail is more repre-sentative for conservatives (Rcons

H 1 positive and large) partici-pants should inflate the average conservative position more(higher E

stethtjconsTHORN EethtjconsTHORN) and deflate the average liberal po-sition more (lower E

stethtjlibTHORN EethtjlibTHORN) We test the hypothesisthat the inflation in conservative positions is positively associatedwith the representativeness of the right tail for the conservativesand the inflation in liberal positions is negatively associated with

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it Once again the representativeness of the right tail is com-puted using the true distribution of positions

In equations (6) and (7) in many cases the representative tailis also the most likely one As a consequence these tests cannotdistinguish a representativeness-based from a likelihood-basedmodel of distorted beliefs We perform two additional testsFirst we run versions of equations (6) and (7) in which we controlfor the likelihood of tails (see Table A4 in Online Appendix G)Second we compute numerically the predictions of a representa-tiveness-based model of stereotypes and a likelihood-based modelof stereotypes We then assess which of these two is better able tomatch the data on beliefs

3 Empirical Results To begin we illustrate the structure ofthe data and the nature of our predictions with two simple exam-ples from the GNH data set focusing on beliefs about conserva-tives In example 1 participants are asked about their agreementwith the statement lsquolsquoIt can never be right to kill a human beingrsquorsquoIn example 2 participants are asked about the moral relevance oflsquolsquowhether or not someone cared for someone weak or vulnerablersquorsquoAs can be seen in Figure III in example 1 the modal position(strongly disagree (1)) and most representative positions(strongly disagree (1)) coincide for conservatives In contrast inexample 2 in Figure III the most representative types (slightlyrelevant (3) not at all relevant (1)) are not most likely for theconservative group Following Proposition 1 we predict that be-liefs will be distorted in the direction of the most representativetypes Thus we expect more exaggeration in example 2 than inexample 1 since in example 2 the most representative types (inthe left tail) are far from the modal type whereas in example 1they coincide This is what we find the conservative position isexaggerated by only 009 positions in Example 1 (true mean 299believed mean 290) but by 106 positions in Example 2 (truemean 421 believed mean 315)

In the full data sets we treat each (issue year) pair as anobservation and we cluster standard errors at the issue level Forthe GNH data we have 45 observations 45 issues measured inthe same year For the ANES data we have 66 observations 10issues measured in multiple years To begin we simply docu-ment systematic exaggeration in both data sets This is a primaryfocus of the original analysis in GNH (2012) and also in Westfall

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FIGURE III

Two Examples

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et al (2015)rsquos analysis of the ANES data30 Figure IV shows thatthe believed difference between typical conservative and typicalliberal positions is larger than the true difference in mean posi-tions for 109 of the 111 observations The data for both GNH(squares) and ANES (triangles) lie above the 45-degree line(dashed)31 Average exaggeration is 062 positions on the scale(066 in the GNH data 059 in the ANES data)32

The systematic and significant exaggeration of mean differ-ences suggests that the benchmark model of accurate beliefs ismissing something important Indeed this exaggeration reflectsthe fact that believed means are typically more extreme than truemeans First note that the kernel of truth regression (equation(5)) generates exaggeration of mean differences just as docu-mented in Figure IV

EstethtjGTHORN E

stethtjGTHORN frac14 eth1thorn 2THORN frac12EethtjGTHORN EethtjGTHORN

To bring this prediction to the data we regress the believedmean position for each group EBethtjGTHORN on the true mean of thegroup EethtjGTHORN and the true mean of the comparison groupEethtjGTHORN across issues We do this for each group (liberals con-servatives) in each data set separately We also present pooledspecifications that combine the data sets to make a prediction fora given group (liberals conservatives) In these pooled specifica-tions we include a dummy variable indicating whether theobservation came from the ANES data set For all specificationswe cluster observations at the issue level33 The results from re-gression are shown in Table I In every specification we find thatEethtjGTHORN is a significant predictor of EBethtjGTHORN with the predicted pos-itive sign Crucially for five of the six specifications the mean of

30 Chambers and Melnyk (2006) also find evidence of exaggeration of truedifferences in beliefs about political positions

31 For convenience we recode all issues so that the high end of the scale (67)represents the stereotypically more conservative position

32 A natural question to ask is how beliefs vary across liberals and conserva-tives That is do beliefs about a group G depend on membership in G versus ndashG Ourmodel does not speak to this issue However in Online Appendix G we show thatthe results we document below hold for both beliefs held by conservatives and be-liefs held by liberals see Tables A9 A10 and A11

33 In general the results presented below for the ANES data are not largelyimpacted by the decision to cluster at the issue level Similar results are obtained ifthe data are not clustered

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the comparison group EethtjGTHORN is also a significant predictor ofE

BethtjGTHORN with the predicted negative signAlthough these results provide strong evidence of context

dependence and are consistent with our model they do not pindown a role for representativeness of types Our next test relatesthe magnitude of representativeness of tail types to the magni-tude of belief distortions

To this end we implement the regressions in equations (6)and (7) Following Proposition 4 we compute the average repre-

sentativeness of tail types for conservatives RconsH frac14

PtT2tconsPtT2tlib

We

again test the hypothesis that RconsH is a significant predictor of Est

ethtjconsTHORN with a positive sign and a predictor of EstethtjlibTHORN with a

negative sign Table II shows that conditional on true mean RconsH

predicts believed mean for each group G as expected The firstthree specifications display the results for predicting beliefs heldabout conservatives In both data sets the average representa-tiveness of tail types for conservatives is a significant positivepredictor of beliefs held about conservatives The final three spe-cifications display the results for predicting beliefs held about

FIGURE IV

Exaggeration of Differences

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liberals We find that the average representativeness of tail typesfor conservatives is a negative predictor of beliefs held about lib-erals This effect is significant in the GNH data and marginallysignificant in the ANES data

We present several additional results in Online Appendix GTo further examine the role of representativeness in driving be-liefs we first show the results of Table II carry through when we

TABLE II

AVERAGE REPRESENTATIVENESS OF TAIL POSITIONS PREDICTS BELIEFS

OLS Predicting Believed Mean of Group G for Each Issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position

of group G for issue

078 024 051 072 018 041

(006) (008) (009) (005) (005) (010)

Avg rep of tail types for

conservatives RconsH

019 055 025 014 012 024

(007) (022) (008) (006) (007) (005)

Constant 101 260 184 093 271 201

(026) (045) (029) (022) (025) (032)

R2 082 048 060 091 031 070

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

TABLE I

INFORMATION ABOUT ndashG PREDICTS BELIEFS ABOUT G

OLS predicting believed mean of group G for each issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position of

conservatives for issue

102 098 096 021 019 025

(0097) (0133) (0076) (0060) (0116) (0060)

True mean position of

liberals for issue

035 086 058 0987 039 073

(0106) (0134) (0131) (0066) (0106) (0135)

Constant 151 335 235 069 258 156

(0195) (0269) (0279) (0122) (0249) (0270)

R2 083 053 066 092 032 068

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

STEREOTYPES 1789

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control for the average likelihood on the tail positions (see Table A4in Online Appendix G) Most tellingly we use the model to predictbeliefs across issues and compare those to the data For simplicitywe use the rank-based truncation specification to predict mean be-liefs when stereotypes include the d most representative types ford frac14 1 T We compare these predictions to those of a model inwhich beliefs are obtained by restricting the distribution to the dmost likely types Our benchmark for both models is predicting thebelieved mean from the entire distribution where d = T We showthat the predictions of the rank-based truncation model with d = 4or 5 compare favorably to both a likelihood-based truncation model(with any d) and the accurate beliefs benchmark Interestingly thisresult suggests that stereotypical beliefs are well approximated byneglecting the least representative types (as opposed to focusingonly on the most representative types) and so represent a moderatethough systematic departure from the standard benchmarkFinally we show that the results we document above hold forboth beliefs held by conservatives and beliefs held by liberals (seeTables A9 A10 and A11 in Online Appendix G)

V Conclusion

We present a model of stereotypical thinking in which DMsmaking predictions about a group overweight the grouprsquos mostdistinctive types These overweighted types are not the mostlikely ones given the DMrsquos data but the most representativeones in the sense of being the most diagnostic of the group rela-tive to other groups Representativeness implies that what ismost distinctive of a group depends on what group it is comparedwith We present experimental evidence that confirms this con-text dependence in recall-based assessments of groups Finallywe evaluated the predictions of the model using political data fromexisting large-scale surveys We find context dependence to be akey feature of beliefs Given the richness of the political data wecan go a step further and identify a role for representativeness inparticular As the representativeness of tail types increases beliefsof a group are distorted in the direction of that tail

Our approach provides a parsimonious and psychologicallyfounded account of how DMs generate simplified representationsof reality from social groups to stock returns and offers a unifiedaccount of disparate pieces of evidence relating to this type of

QUARTERLY JOURNAL OF ECONOMICS1790

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uncertainty The model captures the central fact that stereotypeshighlight the greatest difference between groups thus explainingwhy some stereotypes are very accurate while others lack valid-ity Still stereotypes often have a kernel of truth when they arebased on systematicmdasheven if smallmdashdifferences between groupsThis logic allows us to describe a number of heuristics and psy-chological biases many of which arise in the context of predictionproblems Generically our model generates overreaction to diag-nostic information

Our model is based on representativeness and does not cap-ture all the features of stereotypical thinking However it cap-tures perhaps the central feature when we think of a group wefocus on what is most distinctive about it and neglect or under-weight the rest

Saeuroıd Business School University of Oxford

Ohio State University and Harvard Business School

Universita Bocconi and Innocenzo Gasparini Institute

for Economic Research

Harvard University

Supplementary Material

An Online Appendix for this article can be found at QJEonline (qjeoxfordjournalorg)

References

Adorno Theodor Else Frenkel-Brunswik Daniel Levinson and Nevitt SanfordThe Authoritarian Personality (New York Harper amp Row 1950)

Arrow Kenneth lsquolsquoThe Theory of Discriminationrsquorsquo in Discrimination in LaborMarkets Orley Ashenfelter and Albert Rees eds (Princeton NJPrinceton University Press 1973)

Ashton Michael and Victoria Esses lsquolsquoStereotype Accuracy Estimating theAcademic Performance of Ethnic Groupsrsquorsquo Personality and SocialPsychology Bulletin 25 (1999) 225ndash236

Barberis Nicholas Andrei Shleifer and Robert Vishny lsquolsquoA Model of InvestorSentimentrsquorsquo Journal of Financial Economics 49 (1998) 307ndash343

Bayer Sylvia lsquolsquoThe Accuracy of Academic Gender Stereotypesrsquorsquo Sex Roles 40(1999) 787ndash813

Benjamin Dan James Choi and Joshua Strickland lsquolsquoSocial Identity andPreferencesrsquorsquo American Economic Review 100 (2010) 1913ndash1928

Benjamin Dan Matthew Rabin and Collin Raymond lsquolsquoA Model of Non-Belief inthe Law of Large Numbersrsquorsquo Journal of the European Economic Association15 (2015) 515ndash544

Bertrand Marianne lsquolsquoNew Perspectives on Genderrsquorsquo Handbook of LaborEconomics 4 (2011) 1543ndash1590

Bodoh-Creed Aaron Dan Benjamin and Matthew Rabin lsquolsquoThe Dynamics of Base-Rate Neglectrsquorsquo mimeo Haas Business School 2013

STEREOTYPES 1791

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

Bohnet Iris Alexandra van Geen and Max Bazerman lsquolsquoWhen PerformanceTrumps Gender Bias Joint versus Separate Evaluationrsquorsquo ManagementScience 5 (2016) 1225ndash1234

Bordalo Pedro Nicola Gennaioli and Andrei Shleifer lsquolsquoSalience Theory of Choiceunder Riskrsquorsquo Quarterly Journal of Economics 127 (2012) 1243ndash1285

mdashmdashmdash lsquolsquoSalience and Consumer Choicersquorsquo Journal of Political Economy 121(2013) 803ndash843

Briton Nancy and Judith Hall lsquolsquoBeliefs about Female and Male NonverbalCommunicationrsquorsquo Sex Roles 32 (1995) 79ndash90

Buser Thomas Muriel Niederle and Hessel Oosterbeek lsquolsquoGenderCompetitiveness and Career Choicesrsquorsquo Quarterly Journal of Economics 129(2014) 1409ndash1447

Carrell Scott Marianne Page and James West lsquolsquoSex and Science How ProfessorGender Perpetuates the Gender Gaprsquorsquo Quarterly Journal of Economics 125(2010) 1101ndash1144

Chambers John and Darya Melnyk lsquolsquoWhy Do I Hate Thee ConflictMisperceptions and Intergroup Mistrustrsquorsquo Personality and SocialPsychology Bulletin 32 (2006) 1295ndash1311

Chan Wayne Robert R McCrae Filip De Fruyt Lee Jussim CorinnaE Lockenhoff Marleen De Bolle Paul T Costa Jr Angelina R SutinAnu Realo Juri Allik Katsuharu Nakazato Yoshiko ShimonakaMartina Hrebıckova Sylvie Graf Michelle Yik Marina Brunner-SciarraNora Leibovich De Figueora Vanina Schmidt Chang-kyo Ahn Hyun-nie Ahn Maria E Aguilar-Vafaie Jerzy Siuta Barbara SzmigielskaThomas R Cain Janet T Crawford Khairul Anwar Mastor Jean-Pierre Rolland Florence Nansubuga Daniel R MiramontezVeronica Benet-Martınez Jerome Rossier Denis Bratko Iris MarusicJamin Halberstadt Mami Yamaguchi Goran Knezevic Thomas A MartinMirona Gheorghiu Peter B Smith Claudio Barbaranelli Lei WangJane Shakespeare-Finch Margarida P Lima Waldemar KlinkoszAndrzej Sekowski Lidia Alcalay Franco Simonetti Tatyana V AvdeyevaV S Pramila and Antonio Terracciano lsquolsquoStereotypes of Age Differences inPersonality Traits Universal and Accuratersquorsquo Journal of Personality andSocial Psychology 103 (2012) 1050ndash1066

Chen Yan Sherry Xin Liu Tracy Xiao and Margaret Shih lsquolsquoWhich Hat to WearImpact of Natural Identities on Coordination and Cooperationrsquorsquo Games andEconomic Behavior 84 (2014) 58ndash86

Coffman Katherine lsquolsquoEvidence on Self-Stereotyping and the Contribution ofIdeasrsquorsquo Quarterly Journal of Economics 129 (2014) 1625ndash1660

Cunningham Tom lsquolsquoComparisons and Choicersquorsquo mimeo Stockholm University2013

Diekman Amanda Alice Eagly and Patrick Kulesa lsquolsquoAccuracy and Bias in theStereotypes about the Social and Political Attitudes of Women and MenrsquorsquoJournal of Experimental Social Psychology 38 (2002) 268ndash282

Eccles Jacquelynne S Janis E Jacobs and Rena D Harold lsquolsquoGender RoleStereotypes Expectancy Effects and Parentsrsquo Socialization of GenderDifferencesrsquorsquo Journal of Social Issues 46 (1990) 183ndash201

Fryer Roland and Matthew Jackson lsquolsquoA Categorical Model of Cognition andBiased Decision-Makingrsquorsquo BE Journal of Theoretical Economics 8 (2008)1ndash42

Fryer Roland and Steven Levitt lsquolsquoAn Empirical Analysis of the Gender Gap inMathematicsrsquorsquo American Economic Journal Applied Economics 2 (2010)210ndash240

Gennaioli Nicola and Andrei Shleifer lsquolsquoWhat Comes to Mindrsquorsquo Quarterly Journalof Economics 125 (2010) 1399ndash1433

Gennaioli Nicola Andrei Shleifer and Robert Vishny lsquolsquoNeglected RisksFinancial Innovation and Financial Fragilityrsquorsquo Journal of FinancialEconomics 104 (2012) 452ndash468

Gilens Martin lsquolsquoRace and Poverty in America Public Misperceptions and theAmerican News Mediarsquorsquo Public Opinion Quarterly 60 (1996) 515ndash541

Glaeser Edward lsquolsquoThe Political Economy of Hatredrsquorsquo Quarterly Journal ofEconomics 120 (2005) 45ndash86

QUARTERLY JOURNAL OF ECONOMICS1792

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

Glover Dyland Amanda Pallais and William Pariente lsquolsquoDiscrimination as a Self-Fulfilling Prophecy Evidence from French Grocery Storesrsquorsquo mimeo HarvardUniversity 2015

Goldin Claudia Lawrence Katz and Ilyana Kuziemko lsquolsquoThe Homecoming ofAmerican College Women The Reversal of the College Gender GaprsquorsquoJournal of Economic Perspectives 20 (2006) 133ndash156

Graham Jesse Brian Nosek and Jonathan Haidt lsquolsquoThe Moral Stereotypes ofLiberals and Conservatives Exaggeration of Differences across thePolitical Spectrumrsquorsquo PLoS One 7 (2012) 1ndash13

Grether David lsquolsquoBayes Rule as a Descriptive Model The RepresentativenessHeuristicrsquorsquo Quarterly Journal of Economics 95 (1980) 537ndash557

Griffin Dale and Amos Tversky lsquolsquoThe Weighing of Evidence and theDeterminants of Confidencersquorsquo Cognitive Psychology 24 (1992) 411ndash435

Guiso Luigi Ferdinando Monte Paola Sapienza and Luigi Zingales lsquolsquoCultureGender and Mathrsquorsquo Science 320 (2008) 1164ndash1165

Hilton James and William Von Hippel lsquolsquoStereotypesrsquorsquo Annual Review ofPsychology 47 (1996) 237ndash271

Hyde Janet Sara Lindberg Marcia Linn Amy Ellis and Caroline WilliamslsquolsquoGender Similarities Characterize Math Performancersquorsquo Science 321 (2008)494ndash495

Judd Charles and Bernardette Park lsquolsquoDefinition and Assessment of Accuracy inSocial Stereotypesrsquorsquo Psychological Review 100 (1993) 109ndash128

Jussim Lee Jarret Crawford Stephanie Anglin John Chambers Sean Stevensand Florette Cohen lsquolsquoStereotype Accuracy One of the Largest and MostReplicable Effects in All of Social Psychologyrsquorsquo in The Handbook ofPrejudice Stereotyping and Discrimination Todd Nelson ed (MahwahNJ Lawrence Erlbaum 2015)

Kahneman Daniel and Amos Tversky lsquolsquoSubjective Probability A Judgment ofRepresentativenessrsquorsquo Cognitive Psychology 3 (1972) 430ndash454

mdashmdashmdash lsquolsquoOn the Psychology of Predictionrsquorsquo Psychological Review 80 (1973) 237ndash251

Kaplowitz Stan Bradley Fisher and Clifford Broman lsquolsquoHow Accurate ArePerceptions of Social Statistics about Blacks and Whitesrsquorsquo Public OpinionQuarterly 67 (2003) 237ndash243

Kersten Daniel Pascal Mamassian and Alan Yuille lsquolsquoObject Perception asBayesian Inferencersquorsquo Annual Review of Psychology 55 (2004) 271ndash304

Klein Richard Kate A Ratliff Michelangelo Vianello Reginald B Adams JrStepan Bahnik Michael J Bernstein Konrad Bocian Mark J BrandtBeach Brooks Claudia Chloe Brumbaugh Zeynep CemalcilarJesse Chandler Winnee Cheong William E Davis Thierry DevosMatthew Eisner Natalia Frankowska David Furrow Elisa Maria GallianiFred Hasselman Joshua A Hicks James F Hovermale S Jane HuntJeffrey R Huntsinger Hans IJzerman Melissa-Sue John Jennifer A Joy-Gaba Heather Barry Kappes Lacy E Krueger Jaime Kurtz CarmelA Levitan Robyn Mallett Wendy L Morris Anthony J Nelson JasonA Nier Grant Packard Ronaldo Pilati Abraham M RutchickKathleen Schmidt Jeanine L Skorinko Robert Smith Troy G SteinerJustin Storbeck Lyn M Van Swol Donna Thompson Anna van rsquot VeerLeigh Ann Vaughn Marek Vranka Aaron Wichman Julie A Woodzickaand Brian A Nosek lsquolsquoInvestigating Variation in Replicability A ManyLabs Replication Projectrsquorsquo Social Psychology 45 (2014) 142ndash152

Lundberg Shelly and Richard Startz lsquolsquoPrivate Discrimination and SocialIntervention in Competitive Labor Marketsrsquorsquo American Economic Review73 (1983) 340ndash347

Madon Stephanie Max Guyll Kathy Aboufadel Eulices Montiel Alison SmithPolly Palumbo and Lee Jussim lsquolsquoEthnic and National Stereotypes ThePrinceton Trilogy Revisited and Revisedrsquorsquo Personality and SocialPsychological Bulletin 27 (2001) 996ndash1010

Martin Carol lsquolsquoA Ratio Measure of Sex Stereotypingrsquorsquo Journal of Personality andSocial Psychology 52 (1987) 489ndash499

STEREOTYPES 1793

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

McCauley Clark Krishna Thangavelu and Paul Rozin lsquolsquoSex Stereotyping ofOccupations in Relation to Television Representations and Census FactsrsquorsquoBasic and Applied Social Psychology 9 (1988) 197ndash212

Mullainathan Sendhil lsquolsquoThinking through Categoriesrsquorsquo mimeo HarvardUniversity 2002

Ortoleva Pietro and Erik Snowberg lsquolsquoOverconfidence in Political BehaviorrsquorsquoAmerican Economic Review 105 (2015) 504ndash535

Phelps Edmund lsquolsquoThe Statistical Theory of Racism and Sexismrsquorsquo AmericanEconomic Review 62 (1972) 659ndash661

Pope Devin and Justin Sydnor lsquolsquoGeographic Variation in the Gender Differencesin Test Scoresrsquorsquo Journal of Economic Perspectives 24 (2010) 95ndash108

Rabin Matthew lsquolsquoInference by Believers in the Law of Small NumbersrsquorsquoQuarterly Journal of Economics 117 (2002) 775ndash816

Rabin Matthew and Joel Schrag lsquolsquoFirst Impressions Matter A Model ofConfirmatory Biasrsquorsquo Quarterly Journal of Economics 114 (1999) 37ndash82

Rabin Matthew and Dimitri Vayanos lsquolsquoThe Gamblerrsquos and Hot-Hand FallaciesTheory and Applicationsrsquorsquo Review of Economic Studies 77 (2010) 730ndash778

Reuben Ernesto Paola Sapienza and Luigi Zingales lsquolsquoHow Stereotypes ImpairWomenrsquos Careers in Sciencersquorsquo Proceedings of the National Academy ofSciences 111 (2014) 4403ndash4408

Rosch Eleanor lsquolsquoNatural Categoriesrsquorsquo Cognitive Psychology 4 (1973) 328ndash350Ryan Carey S lsquolsquoAccuracy of Black and White College Studentsrsquo In-Group and

Out-Group Stereotypesrsquorsquo Personality and Social Psychology Bulletin 22(1996) 1114ndash1127

Schneider David The Psychology of Stereotyping (New York Guilford Press2004)

Schneider David Albert Hastorf and Phoebe Ellsworth Person Perception(Reading MA Addison-Wesley 1979)

Shih Margaret Todd Pittinsky and Nalini Ambady lsquolsquoStereotype SusceptibilityIdentity Salience and Shifts in Quantitative Performancersquorsquo PsychologicalScience 10 (1999) 80ndash83

Shih Margaret Todd Pittinsky and Amy Trahan lsquolsquoDomain-Specific Effects ofStereotypes on Performancersquorsquo Self and Identity 5 (2006) 1ndash14

Steele Claude Whistling Vivaldi How Stereotypes Affect Us and What We CanDo (New York Norton 2010)

Tenenbaum Joshua and Thomas Griffiths lsquolsquoThe Rational Basis ofRepresentativenessrsquorsquo 23rd Annual Conference of the Cognitive ScienceSociety (2001) 1036ndash1041

Tversky Amos and Daniel Kahneman lsquolsquoExtensional versus Intuitive ReasoningThe Conjunction Fallacy in Probability Judgmentrsquorsquo Psychological Review 90(1983) 293ndash315

Weinberger Catherin lsquolsquoIs the Science and Engineering Workforce Drawn fromthe Far Upper Tail of the Math Ability Distributionrsquorsquo mimeo UCSB 2005

Westfall Jacob Leaf Van Boven John Chambers and Charles Judd lsquolsquoPerceivingPolitical Polarization in the United States Party Identity Strength andAttitude Extremity Exacerbate the Perceived Partisan DividersquorsquoPsychological Science 10 (2015) 145ndash158

Wolsko Christopher Bernadette Park Charles Judd and Bernd WittenbrinklsquolsquoFraming Interethnic Ideology Effects of Multicultural and Color-BlindPerspectives on Judgments of Groups and Individualsrsquorsquo Journal ofPersonality and Social Psychology 78 (2000) 635ndash654

QUARTERLY JOURNAL OF ECONOMICS1794

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httpqjeoxfordjournalsorgD

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Page 20: I. Introduction · uneducated at the beginning of the 20th century, and as high achievers at the beginning of the 21st (Madon et al. 2001). Social science has produced three broad

example the Irish are stereotyped as red-haired when comparedwith the European population However when compared withthe Scots a more plausible stereotype for the Irish is lsquolsquoCatholicrsquorsquobecause religion is the dimension along which Irish and Scotsdiffer the most

In Online Appendix D we extend the model to continuoustype spaces Many settings of interest in economics can be use-fully described by continuous probability distributions and weshow our model is particularly tractable in this case In OnlineAppendix E we relax Definition 2 and allow weighting of types toalso be influenced by their likelihood We show that the basicinsight that stereotypes contain a kernel of truth carries throughto these cases as well

To summarize the psychology of representativeness yieldsstereotypes that are consistent with the social cognition approachin which individuals assess groups by recalling and focusing ondistinctive group traits When there are systematic differencesbetween groups stereotypes get the direction right but exagger-ate differences

IIIC Some Examples

A growing body of field and experimental evidence points to awidespread belief that women are worse than men at mathemat-ics (Eccles Jacobs and Harold 1990 Guiso et al 2008 CarrellPage and West 2010) This belief persists despite the fact that fordecades women have been gaining ground in average schoolgrades including mathematics and have recently surpassedmen in overall school performance (Goldin Katz and Kuziemko2006 Hyde et al 2008) This belief shared by men and women(Reuben Sapienza and Zingales 2014) may help account for thegender gap in the choices of high school tracks college degreesand careers with women disproportionately choosing humanitiesand health-related areas (Weinberger 2005 Buser Niederle andOosterbeek 2014) and forgoing significant wage premiums toquantitative skills (Bertrand 2011)

Gender stereotypes in mathematics particularly beliefs thatexaggerate the extent of average differences are consistent withthe predictions of our model The fact that men are overrepre-sented at the very highest performance levels leads a stereotyp-ical thinker to exaggerate the magnitude of mean differencesFigure I shows the score distributions from the mathematics

QUARTERLY JOURNAL OF ECONOMICS1772

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section of 2013rsquos Scholastic Aptitude Test (SAT) for men andwomen21 The distributions are very similar with averagescores slightly higher for men (531 versus 499 out of 800)However scores for men have a heavier right tail with mentwice as likely to have a perfect SAT math score than women22

In light of such data the stereotypical male performance in math-ematics is high while the stereotypical female performance ispoor Predictions based on such stereotypes are inaccurate exag-gerating true differences Consistent with this prediction exper-imental evidence shows that both genders underestimatewomenrsquos ability in simple math tasks even controlling for pastperformance (Reuben Sapienza and Zingales 2014) Coffman(2014) shows a similar pattern extends to confidence about ownability in other male-typed domains with women reporting sig-nificantly less confidence in gender-incongruent than gender-congruent tasks Our model suggests that these patterns mightcome from stereotypes based on gender differences in the righttail of the distribution While differences in the right tail of thedistribution are unlikely to be relevant for most decisions stereo-typical thinking driven by these differences has the potential toimpact economically important decisions whether through self-stereotyping (ie choice of careers or majors as in BuserNiederle and Oosterbeek 2014) or through discrimination (iehiring decisions as in Bohnet van Geen and Bazerman 2016)

The logic of exaggerated yet directionally correct stereotypesalso sheds light on the well-documented phenomenon of base rateneglect (Kahneman and Tversky 1973) Indeed Proposition 2implies that the DM overreacts to information that assigns

21 Standardized test performance measures not only innate ability but alsoeffort and investment by third parties (Hyde et al 2008) The mapping of test per-formance into inferences about innate ability is an issue not addressed by ourmodel

22 For 2013 SAT Mathematics scores see httpmediacollegeboardcomdigitalServicespdfresearchSAT-Percentile-Ranks-By-Gender-Ethnicity-2013pdf Results are similar for the National Assessment of Educational Progress(NAEP) which are more representative of the overall population For 2012NAEP scores for 17-year-olds in mathematics see httpnationsreportcardgovltt_2012age17maspx See Hyde et al (2008) Fryer and Levitt (2010) and Popeand Sydnor (2010) for in-depth empirical analyses of the gender gap inmathematics

STEREOTYPES 1773

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people to groups precisely because such information generatesextreme stereotypes Consider the classic example in which amedical test for a particular disease with a 5 prevalence has a90 rate of true positives and a 5 rate of false positives The testassigns each person to one of two groups + (positive test) or ndash(negative test) The DM estimates the frequency of the sick type(s) and the healthy type (h) in each group The test is informativea positive result increases the relative likelihood of sickness anda negative result increases the relative likelihood of health forany prior Formally

PreththornjsTHORN

PreththornjhTHORNgt 1 gt

PrethjsTHORN

PrethjhTHORNeth4THORN

This condition has clear implications the representative personwho tests positive is sick while the representative person whotests negative is healthy Following Proposition 2 the DMreacts to the test by moving his priors too far in the right di-rection generating extreme stereotypes He greatly boosts hisassessment that a positively tested person is sick but also thata negatively tested person is healthy Because most people arehealthy the DMrsquos assessment about the group that tested neg-ative is fairly accurate but is severely biased for the group that

FIGURE I

SAT Mathematics Scores by Gender (2013)

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tested positive This analysis formalizes Tversky andKahnemanrsquos (1983) verbal account of base rate neglect23

The same mechanism may underlie several other instanceswhere DMs overweight diagnostic information When assessingan employeersquos skill level an employer attributes high perfor-mance to high skill because high performance is the distinctivemark of a talented employee Because he neglects the possibilitythat some talented employees perform poorly and that somenontalented ones perform well (perhaps due to stochasticity inthe environment) the employer has too much faith in skill andneglects the role of luck in accounting for the output Similarlywhen assessing the performance of firms in a hot sector of theeconomy (eg G = internet) an investor recalls highly successfulfirms in that sector (t = return of Google Amazon etc) He ne-glects the possibility of firms being unsuccessful because lack ofsuccess is statistically nondiagnostic and psychologically nonrep-resentative of a growing sectormdasheven if it is likely This causesexcessive optimism (in that the expectation of growth is unrea-sonably high) and overconfidence (in that the variability in earn-ings growth considered possible is truncated) True the hot sectormay have better growth opportunities on average but represen-tativeness exaggerates this feature and induces the investor toneglect a significant risk of failure

IV Evidence on Representativeness and Stereotypes

Testing our model requires evaluating the beliefs individualshold about a target group against the true distribution of thattarget group over an attribute space An ideal data set would

23 Our account is distinct from a mechanical underweighting of base rates inBayes rule as in Grether (1980) and Bodoh-Creed Benjamin and Rabin (2013) Inthose models upon receiving the test results the DM can update his beliefs in thewrong direction he can be less confident that a person is healthy after a negativetest than under his prior which cannot happen in our model Although this predic-tion of our model seems consistent with introspection we are not aware of experi-mental evidence on this point Griffin and Tversky (1992) present evidenceconsistent with pure neglect of base rates but in a significantly different tasknamely inferring the bias of a coin from a history of coin flips Such experimentsare hard to compare with the predictions of our model because subjects are asked togenerate distributions of different numbers of coin flips in their minds which is amuch more involved task than to recall types of a given distribution Their assess-ments then might be wrong for other reasons See Bodoh-Creed Benjamin andRabin (2013) for a detailed discussion

STEREOTYPES 1775

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consist of naturally defined groups with known distributions overa given space of types and a corresponding set of beliefs about thedistribution of each group over that space of types This wouldallow us to test for exaggeration of true differences betweengroups and to ask whether this exaggeration is well predictedby overweighting representative types To identify a causal rolefor representativeness or context dependence we would need ex-ogenous variation in either the comparison group ndashG or in thedistributions over the type spaces This is unavailable in existingdata sets Accordingly we take a two-pronged approach First wecreate a controlled laboratory environment that allows us toinduce the exogenous variation in representative types that weneed to test causality then we reanalyze existing field evidence tocheck for consistency with our predictions

In testing our model we focus on the two main implicationsof representativeness-based stereotypes

Context dependence the stereotype of a target group de-pends on the characteristics of the reference group it iscompared to

Kernel of truth stereotypes depend on group character-istics andmdashin most (precisely characterized) settingsmdashare slanted toward representative types

We test the first property with a lab experiment (SectionIVA) We then turn to survey data on beliefs about US politicalgroups (Section IVB) for an empirical analysis that explores thesecond property The survey data are more tightly linked to ourinterest in social stereotypes The laboratory experiment allowsus to directly test the role of representativeness in generatingcontext dependent beliefs Online Appendixes F and G provideall details and additional results for the experiments and fieldevidence

IVA Lab Evidence on Representativeness and ContextDependence

The influence of the representativeness heuristic on recalland on beliefs has been extensively documented in the lab(Kahneman and Tversky 1972 1973) Our goal is to considerhow representativeness as formalized in equation (2) gives riseto context-dependent beliefs To our knowledge the possibility

QUARTERLY JOURNAL OF ECONOMICS1776

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that representativeness may generate context dependence hasnot been tested before

To assess this prediction we perform a controlled laboratoryexperiment that allows us to isolate representativeness frommany confounding factorsmdashhistorical sociological or other-wisemdashthat may affect stereotype formation in the real worldWe construct our own groups of ordinary objects creating atarget group G and a comparison group ndashG We hold thetarget group G fixed and explore how participant impressions ofit change as we change the comparison group ndashG and thusrepresentativeness

We conducted several experiments in the laboratory and onAmazon Mechanical Turk Each involves a basic three-stepdesign First participants are shown the target group and a ran-domly assigned comparison group for 15 seconds In this timedifferences between groups can be noticed but the groupsrsquo precisecompositions cannot be memorized The second step consists of afew filler questions which briefly draw the participantsrsquo cognitivebandwidth away from their observation Finally participants areasked to assess the groups they saw Participants are incentiv-ized to provide accurate answers

We randomly assign participants to either the Control or theRepresentativeness condition In the Control condition G and ndashGhave nearly identical distributions so that all types are similarlyrepresentative for each group In the Representativeness condi-tion ndashG is changed in such a way that a certain type becomes veryrepresentative for G Context dependence implies that the assess-ment of G should now overweight this representative type eventhough the distribution of G itself has not changed

We ran six experiments of this form with design changesfocused on reducing participant confusion and removing con-founds We describe the final and most refined version of theseexperiments here In an attempt to provide a overview of the re-sults while remaining concise we provide the results from pooledspecifications that use all data collected In Online Appendix Fwe offer additional details and report all experiments conductedWe also give instructions and materials for each experiment thefull data set is available by request

Consider first the experiment illustrated in Figure II Agroup of 25 cartoon girls is presented next to a group of 25 cartoonboys in T-shirts of different colors blue green or purple In theControl condition (Figure II Panel a) the groups have identical

STEREOTYPES 1777

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color distributions (13 purple 12 green) so no color is represen-tative of either group The Representativeness condition (Panel b)compares the same group of girls with a different group of boysfor whom green shirts are replaced with blue shirts Now onlygirls wear green and only boys wear blue These colors althoughstill not the most frequent for either group are now most repre-sentative For each group girls and boys participants are asked anumber of questions concerning the frequency of T-shirts of dif-ferent colors worn by that group

Applying our model in the control condition the type space isT frac14 fgreen purpleg and the groups are G = girls and ndashG = boysGiven that the color distributions are identical across groups both

types are equally representativegreengirls

greenboysfrac14 1 frac14

purplegirls

purpleboys As a result

assessment of G should be correct on average stcontrolgreengirls frac14 greengirls

and stcontrolpurplegirls frac14 purplegirls for any weighing function (the same is

true about assessments of ndashG)In the treatment condition the distribution of shirt colors re-

mains the same for girls For boys green shirts are changed intoblue Thus the type space changes to T frac14 fgreen purple bluegand the representative color for girls becomes greengreengirls

greenboysfrac14 1 gt 1 frac14

purplegirls

purpleboys while that for boys becomes blue As

a result in the treatment condition subjects should inflate the

frequency of green shirts relative to the truth sttreatmentgreengirls

gt greengirls (the same should happen to assessments of blueshirts for boys) We also expect the assessed frequency of greenshirts to go up relative to the control condition namely

sttreatmentgreengirls gt stcontrol

greengirls Critically the only factor that varies

across treatments is the representativeness of the 12-colorshirt Thus if we see differences across conditions the causalrole of representativeness-based recall in shaping group judg-ments is clear24

24 We vary which colors are used in which roles across participants Someparticipants saw this particular color distribution while others see for examplegreen as the modal color and purple as the diagnostic color for boys in theRepresentativeness condition and blue as the diagnostic color for girls in theRepresentativeness condition We vary the colors across the roles to avoid con-founding the characteristics of any particular color with its diagnosticity

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FIG

UR

EII

T-S

hir

tsE

xp

erim

ent

Fig

ure

sap

pea

red

inco

lor

top

art

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STEREOTYPES 1779

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We collected data from 301 participants using this T-shirtsdesign25 Since the number of green and purple shirts is verysimilar we first ask each participant the simplest question ofwhich shirt color is modal Next we ask participants to assessthe share of green and purple shirts

Consistent with the role of representativeness participantsassigned to the Representativeness condition are 105 percentagepoints more likely to recall the less frequent color (green for girlsor blue for boys) as the modal color when it is representative of agroup (35 of participants guess the less frequent color is modalin the Control condition this proportion increases to 46 in theRepresentativeness condition p = 01 estimated from a probitregression reported in Online Appendix F)

We now turn to subjectsrsquo estimates of how many T-shirts ofeach color they saw in each group In both conditions the truedifference in counts is 1 (13 purple shirts 12 green or blue shirts)In the Control condition participants on average believe they saw054 more purple shirts than green or blue shirts In theRepresentativeness condition participants believe they saw072 fewer purple shirts than green or blue shirts (the acrosstreatment difference is significant with p = 01 from OLS regres-sion reported in Online Appendix F)

In total we collected data for six experiments of this generalstructure gathering evidence from more than 1000 participantsAs we describe in Online Appendix F although there is substan-tial variation across experiments when we pool all of the data wefind significant aggregate treatment effects in line with a role ofrepresentativeness in judgment We employ four different unor-dered types designs similar to the T-shirts experiment using sixsamples (four online and two in the laboratory) with 741 partic-ipants We find effects in the predicted direction for five of the sixsamples Using a probit regression that pools the data for theseunordered type experiments we find that participants are 93 per-centage points more likely to guess that the less frequent type ismodal when it is representative than when it is not (p = 002) Wealso run a family of ordered types experiments (two designs fivesamples 402 participants) Unlike the simpler T-shirts style

25 Throughout our analysis we exclude any participant who participated in aprevious version of the experiment and any participant who self-identified as color-blind In Online Appendix F we show that our results are unchanged if we includethese additional observations

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design the theoretical predictions for the ordered types designsare more sensitive to the specific assumptions one makes aboutthe weighting function of the DM26 We find effects in the pre-dicted direction for three of the five samples As we discuss inmore detail in Online Appendix F the ordered types resultsvary by platform with consistently stronger results on AmazonMechanical Turk than in the laboratory samples Pooling all or-dered types experiments participants are 93 percentage pointsmore likely to guess that the group of interest has a greater av-erage than the comparison group when the right tail is represen-tative (p = 062) Given our simple experimental setting withgroups of mundane objects we interpret our resultsmdasha signifi-cant and reasonably sized impact on average beliefsmdashas an im-portant proof of concept the presence of representative typesbiases ex post assessment

IVB Empirical Evidence on Political Stereotypes

We examine two data sets on political preferences and be-liefs about political preferences in the United States We inves-tigate the roles of representativeness and context dependence byseparately testing for hypotheses that allow us to assess the lead-ing theories of stereotypes

First we test whether beliefs are correct or depart systemat-ically from the truth The statistical discrimination approachbuilds on the assumption that people hold rational expectationsof group traits Comparing beliefs to the truth allows us to assessthe validity of this assumption in our data

Second we test if beliefs depart from the truth by exagger-ating (mean) differences among groups per the kernel of truthhypothesis This is an implicit test of context dependence be-cause it implies that beliefs about the target groups are shapednot only by that grouprsquos characteristics but also by those of thereference group27

Third we test if distortions in beliefs can be accounted for bythe overweighting of highly representative types (defined astypes that are relatively more frequent in the target relative to

26 This is due in part to our choice to not study MLRP distributions We moti-vate and discuss this design decision in Online Appendix F

27 Of course unlike in the laboratory experiment in this setting we cannot testfor context dependence by exogenously varying the reference group

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the reference group) The second and third tests address the keypredictions of our model

1 The Data We have two data sets on political preferences andbeliefs about political preferences The first data set from GrahamNosek and Haidt (GNH 2012) contains data from the MoralFoundations Questionnaire Respondents (1174 self-identified lib-erals and 500 self-identified conservatives) answer questions abouttheir position on a subset of 45 issues 20 moral relevance state-ments (eg lsquolsquowhen you decide whether something is right orwrong to what extent are the following considerations relevantto your thinkingrsquorsquo) and 25 moral judgments (eg lsquolsquoindicate theextent to which you would agree or disagreersquorsquo) For each issue arandomly determined subset of participants states their own posi-tion another subset states their belief on the position of a lsquolsquotypicalliberalrsquorsquo and a third subset states their belief on the position of alsquolsquotypical conservativersquorsquo The data thus include the distribution overpositions for both liberal and conservatives as well as the averagebelieved typical position of liberals and of conservatives on the 45issues Each position is elicited on 1ndash6 scale

The second data set comes from the American NationalElection Survey (ANES) and contains data from more than20000 respondents between 1964 and 201228 The surveycovers political issues of the day such as the optimal amount ofgovernment spending and service provision (1984ndash2000) or theplace of women in society (1972ndash1998) We focus on the 10 issuesthat ask participants to respond on a 1ndash7 scale (rather than justindicate binary agreement or disagreement) all 10 issues areasked in multiple years Participants are asked to provide theirown position on the scale and their believed position of theDemocratic and Republican parties (lsquolsquoWhere would you placethe Democratic [Republican] party on this scalersquorsquo) The data in-clude for each issue-year observation the distribution of partic-ipant positions for self-identified liberals and self-identifiedconservatives as well as the distribution of believed typical posi-tions of the Democratic and Republican parties

28 These data are publicly available at httpwwwelectionstudiesorgstudy-pagesanes_timeseries_cdfanes_timeseries_cdfhtm

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2 Empirical Strategy Our analysis focuses on beliefs abouttwo groups Conservatives and Liberals The types are the possi-ble positions for each issue (1 2 6 7) For the GNH data weinterpret beliefs about the lsquolsquotypicalrsquorsquo element of a group to coincidewith the believed average position in that group Similarly forthe ANES data we use the believed party positions as a proxy forbelieved mean of each group29 We then take as a benchmark thehypothesis that individuals hold accurate beliefs about eachgroup and in particular that believed mean position shouldequal true mean position at least on average across subjectsThe accurate beliefs hypothesis underlies the most common eco-nomic model of stereotyping statistical discrimination

To assess our representativeness-based model we perform aregression exercise To test our model in a linear regressionframework we rely on linear approximations of the weightingfunction Our model then yields two regression specifications

PROPOSITION 4 Let G 2 fconservative liberal g and assume

ht h tG

tG

be a differentiable and strictly increasing weight-

ing function as in Definition 2 The following hold as a first-order approximation around identical distributions G

Gfrac14 1

(i) Kernel of truth regression There exists a constant gt 0such that

EstethtjGTHORN frac14 EethtjGTHORNeth1thorn THORN EethtjGTHORNeth5THORN

(ii) Representativeness regression Denote H frac14 fT 2 Tg

the right tail of types and RconsH frac14

PHtconsPHtlib

as the average

representativeness of right tail types for conservatives

29 This assumption is consistent with the authorsrsquo interpretation of the GNHdata (GNH 2012) and with previous studies using ANES (eg Westfall et al 2015)Furthermore to the extent that this assumption holds equally well for most issueswithin a data set our focus on cross-issue differences should allow us to test thepredictions of our model even with an imperfect proxy for beliefs of mean positionsFinally the data provide some insight into whether subjects are reporting (per-ceived) modal or mean types As we show the modal type is a poor prediction ofstated beliefs while a distorted mean slanted toward representative types is anaccurate prediction of stated beliefs

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Under the further approximation where tcons

tlibampRcons

H for

t 2 H

EstethtjconsTHORN frac14 EethtjconsTHORN thorn consethR

consH 1THORNeth6THORN

EstethtjlibTHORN frac14 EethtjlibTHORN libethR

consH 1THORNeth7THORN

where lcons and llib are positive constants

The first regression allows us to test for the kernel of truthhypothesis and the second set of regressions allows us to test forthe role of representativeness

Equation (5) says that respondents in our model inflate theaverage position of a group say the conservatives if and only ifthe group has a higher average position than the other groupnamely the liberals Formally EstethtjconsTHORN gt EethtjconsTHORN if and onlyif EethtjconsTHORN gt EethtjlibTHORN Because in our measurement scale highertypes mean lsquolsquomore conservativersquorsquo we expect (i) believed conserva-tive average to be higher than the truth and (ii) the extent ofoverstatement to decrease in the average liberal position EethtjlibTHORNConversely we expect the average liberal position to be lowerthan the truth the more so the higher the average conservativeposition EethtjconsTHORN

As previously discussed the basis of these predictions is con-text dependence information about the distribution of ndashG is rel-evant for the beliefs about G This context dependence isinconsistent with rational expectations in which only thegrouprsquos own means should affect beliefs We test the hypothesisthat the true mean EethtjGTHORN is a significant predictor of the believedmean E

stethtjGTHORN with a positive sign and the other grouprsquos truemean EethtjGTHORN is a predictor of the believed mean with a negativesign

Equations (6) and (7) say that repondentsrsquo assessment bias isshaped by representativeness When the right tail is more repre-sentative for conservatives (Rcons

H 1 positive and large) partici-pants should inflate the average conservative position more(higher E

stethtjconsTHORN EethtjconsTHORN) and deflate the average liberal po-sition more (lower E

stethtjlibTHORN EethtjlibTHORN) We test the hypothesisthat the inflation in conservative positions is positively associatedwith the representativeness of the right tail for the conservativesand the inflation in liberal positions is negatively associated with

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it Once again the representativeness of the right tail is com-puted using the true distribution of positions

In equations (6) and (7) in many cases the representative tailis also the most likely one As a consequence these tests cannotdistinguish a representativeness-based from a likelihood-basedmodel of distorted beliefs We perform two additional testsFirst we run versions of equations (6) and (7) in which we controlfor the likelihood of tails (see Table A4 in Online Appendix G)Second we compute numerically the predictions of a representa-tiveness-based model of stereotypes and a likelihood-based modelof stereotypes We then assess which of these two is better able tomatch the data on beliefs

3 Empirical Results To begin we illustrate the structure ofthe data and the nature of our predictions with two simple exam-ples from the GNH data set focusing on beliefs about conserva-tives In example 1 participants are asked about their agreementwith the statement lsquolsquoIt can never be right to kill a human beingrsquorsquoIn example 2 participants are asked about the moral relevance oflsquolsquowhether or not someone cared for someone weak or vulnerablersquorsquoAs can be seen in Figure III in example 1 the modal position(strongly disagree (1)) and most representative positions(strongly disagree (1)) coincide for conservatives In contrast inexample 2 in Figure III the most representative types (slightlyrelevant (3) not at all relevant (1)) are not most likely for theconservative group Following Proposition 1 we predict that be-liefs will be distorted in the direction of the most representativetypes Thus we expect more exaggeration in example 2 than inexample 1 since in example 2 the most representative types (inthe left tail) are far from the modal type whereas in example 1they coincide This is what we find the conservative position isexaggerated by only 009 positions in Example 1 (true mean 299believed mean 290) but by 106 positions in Example 2 (truemean 421 believed mean 315)

In the full data sets we treat each (issue year) pair as anobservation and we cluster standard errors at the issue level Forthe GNH data we have 45 observations 45 issues measured inthe same year For the ANES data we have 66 observations 10issues measured in multiple years To begin we simply docu-ment systematic exaggeration in both data sets This is a primaryfocus of the original analysis in GNH (2012) and also in Westfall

STEREOTYPES 1785

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FIGURE III

Two Examples

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et al (2015)rsquos analysis of the ANES data30 Figure IV shows thatthe believed difference between typical conservative and typicalliberal positions is larger than the true difference in mean posi-tions for 109 of the 111 observations The data for both GNH(squares) and ANES (triangles) lie above the 45-degree line(dashed)31 Average exaggeration is 062 positions on the scale(066 in the GNH data 059 in the ANES data)32

The systematic and significant exaggeration of mean differ-ences suggests that the benchmark model of accurate beliefs ismissing something important Indeed this exaggeration reflectsthe fact that believed means are typically more extreme than truemeans First note that the kernel of truth regression (equation(5)) generates exaggeration of mean differences just as docu-mented in Figure IV

EstethtjGTHORN E

stethtjGTHORN frac14 eth1thorn 2THORN frac12EethtjGTHORN EethtjGTHORN

To bring this prediction to the data we regress the believedmean position for each group EBethtjGTHORN on the true mean of thegroup EethtjGTHORN and the true mean of the comparison groupEethtjGTHORN across issues We do this for each group (liberals con-servatives) in each data set separately We also present pooledspecifications that combine the data sets to make a prediction fora given group (liberals conservatives) In these pooled specifica-tions we include a dummy variable indicating whether theobservation came from the ANES data set For all specificationswe cluster observations at the issue level33 The results from re-gression are shown in Table I In every specification we find thatEethtjGTHORN is a significant predictor of EBethtjGTHORN with the predicted pos-itive sign Crucially for five of the six specifications the mean of

30 Chambers and Melnyk (2006) also find evidence of exaggeration of truedifferences in beliefs about political positions

31 For convenience we recode all issues so that the high end of the scale (67)represents the stereotypically more conservative position

32 A natural question to ask is how beliefs vary across liberals and conserva-tives That is do beliefs about a group G depend on membership in G versus ndashG Ourmodel does not speak to this issue However in Online Appendix G we show thatthe results we document below hold for both beliefs held by conservatives and be-liefs held by liberals see Tables A9 A10 and A11

33 In general the results presented below for the ANES data are not largelyimpacted by the decision to cluster at the issue level Similar results are obtained ifthe data are not clustered

STEREOTYPES 1787

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the comparison group EethtjGTHORN is also a significant predictor ofE

BethtjGTHORN with the predicted negative signAlthough these results provide strong evidence of context

dependence and are consistent with our model they do not pindown a role for representativeness of types Our next test relatesthe magnitude of representativeness of tail types to the magni-tude of belief distortions

To this end we implement the regressions in equations (6)and (7) Following Proposition 4 we compute the average repre-

sentativeness of tail types for conservatives RconsH frac14

PtT2tconsPtT2tlib

We

again test the hypothesis that RconsH is a significant predictor of Est

ethtjconsTHORN with a positive sign and a predictor of EstethtjlibTHORN with a

negative sign Table II shows that conditional on true mean RconsH

predicts believed mean for each group G as expected The firstthree specifications display the results for predicting beliefs heldabout conservatives In both data sets the average representa-tiveness of tail types for conservatives is a significant positivepredictor of beliefs held about conservatives The final three spe-cifications display the results for predicting beliefs held about

FIGURE IV

Exaggeration of Differences

QUARTERLY JOURNAL OF ECONOMICS1788

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liberals We find that the average representativeness of tail typesfor conservatives is a negative predictor of beliefs held about lib-erals This effect is significant in the GNH data and marginallysignificant in the ANES data

We present several additional results in Online Appendix GTo further examine the role of representativeness in driving be-liefs we first show the results of Table II carry through when we

TABLE II

AVERAGE REPRESENTATIVENESS OF TAIL POSITIONS PREDICTS BELIEFS

OLS Predicting Believed Mean of Group G for Each Issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position

of group G for issue

078 024 051 072 018 041

(006) (008) (009) (005) (005) (010)

Avg rep of tail types for

conservatives RconsH

019 055 025 014 012 024

(007) (022) (008) (006) (007) (005)

Constant 101 260 184 093 271 201

(026) (045) (029) (022) (025) (032)

R2 082 048 060 091 031 070

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

TABLE I

INFORMATION ABOUT ndashG PREDICTS BELIEFS ABOUT G

OLS predicting believed mean of group G for each issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position of

conservatives for issue

102 098 096 021 019 025

(0097) (0133) (0076) (0060) (0116) (0060)

True mean position of

liberals for issue

035 086 058 0987 039 073

(0106) (0134) (0131) (0066) (0106) (0135)

Constant 151 335 235 069 258 156

(0195) (0269) (0279) (0122) (0249) (0270)

R2 083 053 066 092 032 068

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

STEREOTYPES 1789

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control for the average likelihood on the tail positions (see Table A4in Online Appendix G) Most tellingly we use the model to predictbeliefs across issues and compare those to the data For simplicitywe use the rank-based truncation specification to predict mean be-liefs when stereotypes include the d most representative types ford frac14 1 T We compare these predictions to those of a model inwhich beliefs are obtained by restricting the distribution to the dmost likely types Our benchmark for both models is predicting thebelieved mean from the entire distribution where d = T We showthat the predictions of the rank-based truncation model with d = 4or 5 compare favorably to both a likelihood-based truncation model(with any d) and the accurate beliefs benchmark Interestingly thisresult suggests that stereotypical beliefs are well approximated byneglecting the least representative types (as opposed to focusingonly on the most representative types) and so represent a moderatethough systematic departure from the standard benchmarkFinally we show that the results we document above hold forboth beliefs held by conservatives and beliefs held by liberals (seeTables A9 A10 and A11 in Online Appendix G)

V Conclusion

We present a model of stereotypical thinking in which DMsmaking predictions about a group overweight the grouprsquos mostdistinctive types These overweighted types are not the mostlikely ones given the DMrsquos data but the most representativeones in the sense of being the most diagnostic of the group rela-tive to other groups Representativeness implies that what ismost distinctive of a group depends on what group it is comparedwith We present experimental evidence that confirms this con-text dependence in recall-based assessments of groups Finallywe evaluated the predictions of the model using political data fromexisting large-scale surveys We find context dependence to be akey feature of beliefs Given the richness of the political data wecan go a step further and identify a role for representativeness inparticular As the representativeness of tail types increases beliefsof a group are distorted in the direction of that tail

Our approach provides a parsimonious and psychologicallyfounded account of how DMs generate simplified representationsof reality from social groups to stock returns and offers a unifiedaccount of disparate pieces of evidence relating to this type of

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uncertainty The model captures the central fact that stereotypeshighlight the greatest difference between groups thus explainingwhy some stereotypes are very accurate while others lack valid-ity Still stereotypes often have a kernel of truth when they arebased on systematicmdasheven if smallmdashdifferences between groupsThis logic allows us to describe a number of heuristics and psy-chological biases many of which arise in the context of predictionproblems Generically our model generates overreaction to diag-nostic information

Our model is based on representativeness and does not cap-ture all the features of stereotypical thinking However it cap-tures perhaps the central feature when we think of a group wefocus on what is most distinctive about it and neglect or under-weight the rest

Saeuroıd Business School University of Oxford

Ohio State University and Harvard Business School

Universita Bocconi and Innocenzo Gasparini Institute

for Economic Research

Harvard University

Supplementary Material

An Online Appendix for this article can be found at QJEonline (qjeoxfordjournalorg)

References

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Arrow Kenneth lsquolsquoThe Theory of Discriminationrsquorsquo in Discrimination in LaborMarkets Orley Ashenfelter and Albert Rees eds (Princeton NJPrinceton University Press 1973)

Ashton Michael and Victoria Esses lsquolsquoStereotype Accuracy Estimating theAcademic Performance of Ethnic Groupsrsquorsquo Personality and SocialPsychology Bulletin 25 (1999) 225ndash236

Barberis Nicholas Andrei Shleifer and Robert Vishny lsquolsquoA Model of InvestorSentimentrsquorsquo Journal of Financial Economics 49 (1998) 307ndash343

Bayer Sylvia lsquolsquoThe Accuracy of Academic Gender Stereotypesrsquorsquo Sex Roles 40(1999) 787ndash813

Benjamin Dan James Choi and Joshua Strickland lsquolsquoSocial Identity andPreferencesrsquorsquo American Economic Review 100 (2010) 1913ndash1928

Benjamin Dan Matthew Rabin and Collin Raymond lsquolsquoA Model of Non-Belief inthe Law of Large Numbersrsquorsquo Journal of the European Economic Association15 (2015) 515ndash544

Bertrand Marianne lsquolsquoNew Perspectives on Genderrsquorsquo Handbook of LaborEconomics 4 (2011) 1543ndash1590

Bodoh-Creed Aaron Dan Benjamin and Matthew Rabin lsquolsquoThe Dynamics of Base-Rate Neglectrsquorsquo mimeo Haas Business School 2013

STEREOTYPES 1791

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Bohnet Iris Alexandra van Geen and Max Bazerman lsquolsquoWhen PerformanceTrumps Gender Bias Joint versus Separate Evaluationrsquorsquo ManagementScience 5 (2016) 1225ndash1234

Bordalo Pedro Nicola Gennaioli and Andrei Shleifer lsquolsquoSalience Theory of Choiceunder Riskrsquorsquo Quarterly Journal of Economics 127 (2012) 1243ndash1285

mdashmdashmdash lsquolsquoSalience and Consumer Choicersquorsquo Journal of Political Economy 121(2013) 803ndash843

Briton Nancy and Judith Hall lsquolsquoBeliefs about Female and Male NonverbalCommunicationrsquorsquo Sex Roles 32 (1995) 79ndash90

Buser Thomas Muriel Niederle and Hessel Oosterbeek lsquolsquoGenderCompetitiveness and Career Choicesrsquorsquo Quarterly Journal of Economics 129(2014) 1409ndash1447

Carrell Scott Marianne Page and James West lsquolsquoSex and Science How ProfessorGender Perpetuates the Gender Gaprsquorsquo Quarterly Journal of Economics 125(2010) 1101ndash1144

Chambers John and Darya Melnyk lsquolsquoWhy Do I Hate Thee ConflictMisperceptions and Intergroup Mistrustrsquorsquo Personality and SocialPsychology Bulletin 32 (2006) 1295ndash1311

Chan Wayne Robert R McCrae Filip De Fruyt Lee Jussim CorinnaE Lockenhoff Marleen De Bolle Paul T Costa Jr Angelina R SutinAnu Realo Juri Allik Katsuharu Nakazato Yoshiko ShimonakaMartina Hrebıckova Sylvie Graf Michelle Yik Marina Brunner-SciarraNora Leibovich De Figueora Vanina Schmidt Chang-kyo Ahn Hyun-nie Ahn Maria E Aguilar-Vafaie Jerzy Siuta Barbara SzmigielskaThomas R Cain Janet T Crawford Khairul Anwar Mastor Jean-Pierre Rolland Florence Nansubuga Daniel R MiramontezVeronica Benet-Martınez Jerome Rossier Denis Bratko Iris MarusicJamin Halberstadt Mami Yamaguchi Goran Knezevic Thomas A MartinMirona Gheorghiu Peter B Smith Claudio Barbaranelli Lei WangJane Shakespeare-Finch Margarida P Lima Waldemar KlinkoszAndrzej Sekowski Lidia Alcalay Franco Simonetti Tatyana V AvdeyevaV S Pramila and Antonio Terracciano lsquolsquoStereotypes of Age Differences inPersonality Traits Universal and Accuratersquorsquo Journal of Personality andSocial Psychology 103 (2012) 1050ndash1066

Chen Yan Sherry Xin Liu Tracy Xiao and Margaret Shih lsquolsquoWhich Hat to WearImpact of Natural Identities on Coordination and Cooperationrsquorsquo Games andEconomic Behavior 84 (2014) 58ndash86

Coffman Katherine lsquolsquoEvidence on Self-Stereotyping and the Contribution ofIdeasrsquorsquo Quarterly Journal of Economics 129 (2014) 1625ndash1660

Cunningham Tom lsquolsquoComparisons and Choicersquorsquo mimeo Stockholm University2013

Diekman Amanda Alice Eagly and Patrick Kulesa lsquolsquoAccuracy and Bias in theStereotypes about the Social and Political Attitudes of Women and MenrsquorsquoJournal of Experimental Social Psychology 38 (2002) 268ndash282

Eccles Jacquelynne S Janis E Jacobs and Rena D Harold lsquolsquoGender RoleStereotypes Expectancy Effects and Parentsrsquo Socialization of GenderDifferencesrsquorsquo Journal of Social Issues 46 (1990) 183ndash201

Fryer Roland and Matthew Jackson lsquolsquoA Categorical Model of Cognition andBiased Decision-Makingrsquorsquo BE Journal of Theoretical Economics 8 (2008)1ndash42

Fryer Roland and Steven Levitt lsquolsquoAn Empirical Analysis of the Gender Gap inMathematicsrsquorsquo American Economic Journal Applied Economics 2 (2010)210ndash240

Gennaioli Nicola and Andrei Shleifer lsquolsquoWhat Comes to Mindrsquorsquo Quarterly Journalof Economics 125 (2010) 1399ndash1433

Gennaioli Nicola Andrei Shleifer and Robert Vishny lsquolsquoNeglected RisksFinancial Innovation and Financial Fragilityrsquorsquo Journal of FinancialEconomics 104 (2012) 452ndash468

Gilens Martin lsquolsquoRace and Poverty in America Public Misperceptions and theAmerican News Mediarsquorsquo Public Opinion Quarterly 60 (1996) 515ndash541

Glaeser Edward lsquolsquoThe Political Economy of Hatredrsquorsquo Quarterly Journal ofEconomics 120 (2005) 45ndash86

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Glover Dyland Amanda Pallais and William Pariente lsquolsquoDiscrimination as a Self-Fulfilling Prophecy Evidence from French Grocery Storesrsquorsquo mimeo HarvardUniversity 2015

Goldin Claudia Lawrence Katz and Ilyana Kuziemko lsquolsquoThe Homecoming ofAmerican College Women The Reversal of the College Gender GaprsquorsquoJournal of Economic Perspectives 20 (2006) 133ndash156

Graham Jesse Brian Nosek and Jonathan Haidt lsquolsquoThe Moral Stereotypes ofLiberals and Conservatives Exaggeration of Differences across thePolitical Spectrumrsquorsquo PLoS One 7 (2012) 1ndash13

Grether David lsquolsquoBayes Rule as a Descriptive Model The RepresentativenessHeuristicrsquorsquo Quarterly Journal of Economics 95 (1980) 537ndash557

Griffin Dale and Amos Tversky lsquolsquoThe Weighing of Evidence and theDeterminants of Confidencersquorsquo Cognitive Psychology 24 (1992) 411ndash435

Guiso Luigi Ferdinando Monte Paola Sapienza and Luigi Zingales lsquolsquoCultureGender and Mathrsquorsquo Science 320 (2008) 1164ndash1165

Hilton James and William Von Hippel lsquolsquoStereotypesrsquorsquo Annual Review ofPsychology 47 (1996) 237ndash271

Hyde Janet Sara Lindberg Marcia Linn Amy Ellis and Caroline WilliamslsquolsquoGender Similarities Characterize Math Performancersquorsquo Science 321 (2008)494ndash495

Judd Charles and Bernardette Park lsquolsquoDefinition and Assessment of Accuracy inSocial Stereotypesrsquorsquo Psychological Review 100 (1993) 109ndash128

Jussim Lee Jarret Crawford Stephanie Anglin John Chambers Sean Stevensand Florette Cohen lsquolsquoStereotype Accuracy One of the Largest and MostReplicable Effects in All of Social Psychologyrsquorsquo in The Handbook ofPrejudice Stereotyping and Discrimination Todd Nelson ed (MahwahNJ Lawrence Erlbaum 2015)

Kahneman Daniel and Amos Tversky lsquolsquoSubjective Probability A Judgment ofRepresentativenessrsquorsquo Cognitive Psychology 3 (1972) 430ndash454

mdashmdashmdash lsquolsquoOn the Psychology of Predictionrsquorsquo Psychological Review 80 (1973) 237ndash251

Kaplowitz Stan Bradley Fisher and Clifford Broman lsquolsquoHow Accurate ArePerceptions of Social Statistics about Blacks and Whitesrsquorsquo Public OpinionQuarterly 67 (2003) 237ndash243

Kersten Daniel Pascal Mamassian and Alan Yuille lsquolsquoObject Perception asBayesian Inferencersquorsquo Annual Review of Psychology 55 (2004) 271ndash304

Klein Richard Kate A Ratliff Michelangelo Vianello Reginald B Adams JrStepan Bahnik Michael J Bernstein Konrad Bocian Mark J BrandtBeach Brooks Claudia Chloe Brumbaugh Zeynep CemalcilarJesse Chandler Winnee Cheong William E Davis Thierry DevosMatthew Eisner Natalia Frankowska David Furrow Elisa Maria GallianiFred Hasselman Joshua A Hicks James F Hovermale S Jane HuntJeffrey R Huntsinger Hans IJzerman Melissa-Sue John Jennifer A Joy-Gaba Heather Barry Kappes Lacy E Krueger Jaime Kurtz CarmelA Levitan Robyn Mallett Wendy L Morris Anthony J Nelson JasonA Nier Grant Packard Ronaldo Pilati Abraham M RutchickKathleen Schmidt Jeanine L Skorinko Robert Smith Troy G SteinerJustin Storbeck Lyn M Van Swol Donna Thompson Anna van rsquot VeerLeigh Ann Vaughn Marek Vranka Aaron Wichman Julie A Woodzickaand Brian A Nosek lsquolsquoInvestigating Variation in Replicability A ManyLabs Replication Projectrsquorsquo Social Psychology 45 (2014) 142ndash152

Lundberg Shelly and Richard Startz lsquolsquoPrivate Discrimination and SocialIntervention in Competitive Labor Marketsrsquorsquo American Economic Review73 (1983) 340ndash347

Madon Stephanie Max Guyll Kathy Aboufadel Eulices Montiel Alison SmithPolly Palumbo and Lee Jussim lsquolsquoEthnic and National Stereotypes ThePrinceton Trilogy Revisited and Revisedrsquorsquo Personality and SocialPsychological Bulletin 27 (2001) 996ndash1010

Martin Carol lsquolsquoA Ratio Measure of Sex Stereotypingrsquorsquo Journal of Personality andSocial Psychology 52 (1987) 489ndash499

STEREOTYPES 1793

at Harvard L

ibrary on October 28 2016

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McCauley Clark Krishna Thangavelu and Paul Rozin lsquolsquoSex Stereotyping ofOccupations in Relation to Television Representations and Census FactsrsquorsquoBasic and Applied Social Psychology 9 (1988) 197ndash212

Mullainathan Sendhil lsquolsquoThinking through Categoriesrsquorsquo mimeo HarvardUniversity 2002

Ortoleva Pietro and Erik Snowberg lsquolsquoOverconfidence in Political BehaviorrsquorsquoAmerican Economic Review 105 (2015) 504ndash535

Phelps Edmund lsquolsquoThe Statistical Theory of Racism and Sexismrsquorsquo AmericanEconomic Review 62 (1972) 659ndash661

Pope Devin and Justin Sydnor lsquolsquoGeographic Variation in the Gender Differencesin Test Scoresrsquorsquo Journal of Economic Perspectives 24 (2010) 95ndash108

Rabin Matthew lsquolsquoInference by Believers in the Law of Small NumbersrsquorsquoQuarterly Journal of Economics 117 (2002) 775ndash816

Rabin Matthew and Joel Schrag lsquolsquoFirst Impressions Matter A Model ofConfirmatory Biasrsquorsquo Quarterly Journal of Economics 114 (1999) 37ndash82

Rabin Matthew and Dimitri Vayanos lsquolsquoThe Gamblerrsquos and Hot-Hand FallaciesTheory and Applicationsrsquorsquo Review of Economic Studies 77 (2010) 730ndash778

Reuben Ernesto Paola Sapienza and Luigi Zingales lsquolsquoHow Stereotypes ImpairWomenrsquos Careers in Sciencersquorsquo Proceedings of the National Academy ofSciences 111 (2014) 4403ndash4408

Rosch Eleanor lsquolsquoNatural Categoriesrsquorsquo Cognitive Psychology 4 (1973) 328ndash350Ryan Carey S lsquolsquoAccuracy of Black and White College Studentsrsquo In-Group and

Out-Group Stereotypesrsquorsquo Personality and Social Psychology Bulletin 22(1996) 1114ndash1127

Schneider David The Psychology of Stereotyping (New York Guilford Press2004)

Schneider David Albert Hastorf and Phoebe Ellsworth Person Perception(Reading MA Addison-Wesley 1979)

Shih Margaret Todd Pittinsky and Nalini Ambady lsquolsquoStereotype SusceptibilityIdentity Salience and Shifts in Quantitative Performancersquorsquo PsychologicalScience 10 (1999) 80ndash83

Shih Margaret Todd Pittinsky and Amy Trahan lsquolsquoDomain-Specific Effects ofStereotypes on Performancersquorsquo Self and Identity 5 (2006) 1ndash14

Steele Claude Whistling Vivaldi How Stereotypes Affect Us and What We CanDo (New York Norton 2010)

Tenenbaum Joshua and Thomas Griffiths lsquolsquoThe Rational Basis ofRepresentativenessrsquorsquo 23rd Annual Conference of the Cognitive ScienceSociety (2001) 1036ndash1041

Tversky Amos and Daniel Kahneman lsquolsquoExtensional versus Intuitive ReasoningThe Conjunction Fallacy in Probability Judgmentrsquorsquo Psychological Review 90(1983) 293ndash315

Weinberger Catherin lsquolsquoIs the Science and Engineering Workforce Drawn fromthe Far Upper Tail of the Math Ability Distributionrsquorsquo mimeo UCSB 2005

Westfall Jacob Leaf Van Boven John Chambers and Charles Judd lsquolsquoPerceivingPolitical Polarization in the United States Party Identity Strength andAttitude Extremity Exacerbate the Perceived Partisan DividersquorsquoPsychological Science 10 (2015) 145ndash158

Wolsko Christopher Bernadette Park Charles Judd and Bernd WittenbrinklsquolsquoFraming Interethnic Ideology Effects of Multicultural and Color-BlindPerspectives on Judgments of Groups and Individualsrsquorsquo Journal ofPersonality and Social Psychology 78 (2000) 635ndash654

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Page 21: I. Introduction · uneducated at the beginning of the 20th century, and as high achievers at the beginning of the 21st (Madon et al. 2001). Social science has produced three broad

section of 2013rsquos Scholastic Aptitude Test (SAT) for men andwomen21 The distributions are very similar with averagescores slightly higher for men (531 versus 499 out of 800)However scores for men have a heavier right tail with mentwice as likely to have a perfect SAT math score than women22

In light of such data the stereotypical male performance in math-ematics is high while the stereotypical female performance ispoor Predictions based on such stereotypes are inaccurate exag-gerating true differences Consistent with this prediction exper-imental evidence shows that both genders underestimatewomenrsquos ability in simple math tasks even controlling for pastperformance (Reuben Sapienza and Zingales 2014) Coffman(2014) shows a similar pattern extends to confidence about ownability in other male-typed domains with women reporting sig-nificantly less confidence in gender-incongruent than gender-congruent tasks Our model suggests that these patterns mightcome from stereotypes based on gender differences in the righttail of the distribution While differences in the right tail of thedistribution are unlikely to be relevant for most decisions stereo-typical thinking driven by these differences has the potential toimpact economically important decisions whether through self-stereotyping (ie choice of careers or majors as in BuserNiederle and Oosterbeek 2014) or through discrimination (iehiring decisions as in Bohnet van Geen and Bazerman 2016)

The logic of exaggerated yet directionally correct stereotypesalso sheds light on the well-documented phenomenon of base rateneglect (Kahneman and Tversky 1973) Indeed Proposition 2implies that the DM overreacts to information that assigns

21 Standardized test performance measures not only innate ability but alsoeffort and investment by third parties (Hyde et al 2008) The mapping of test per-formance into inferences about innate ability is an issue not addressed by ourmodel

22 For 2013 SAT Mathematics scores see httpmediacollegeboardcomdigitalServicespdfresearchSAT-Percentile-Ranks-By-Gender-Ethnicity-2013pdf Results are similar for the National Assessment of Educational Progress(NAEP) which are more representative of the overall population For 2012NAEP scores for 17-year-olds in mathematics see httpnationsreportcardgovltt_2012age17maspx See Hyde et al (2008) Fryer and Levitt (2010) and Popeand Sydnor (2010) for in-depth empirical analyses of the gender gap inmathematics

STEREOTYPES 1773

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people to groups precisely because such information generatesextreme stereotypes Consider the classic example in which amedical test for a particular disease with a 5 prevalence has a90 rate of true positives and a 5 rate of false positives The testassigns each person to one of two groups + (positive test) or ndash(negative test) The DM estimates the frequency of the sick type(s) and the healthy type (h) in each group The test is informativea positive result increases the relative likelihood of sickness anda negative result increases the relative likelihood of health forany prior Formally

PreththornjsTHORN

PreththornjhTHORNgt 1 gt

PrethjsTHORN

PrethjhTHORNeth4THORN

This condition has clear implications the representative personwho tests positive is sick while the representative person whotests negative is healthy Following Proposition 2 the DMreacts to the test by moving his priors too far in the right di-rection generating extreme stereotypes He greatly boosts hisassessment that a positively tested person is sick but also thata negatively tested person is healthy Because most people arehealthy the DMrsquos assessment about the group that tested neg-ative is fairly accurate but is severely biased for the group that

FIGURE I

SAT Mathematics Scores by Gender (2013)

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tested positive This analysis formalizes Tversky andKahnemanrsquos (1983) verbal account of base rate neglect23

The same mechanism may underlie several other instanceswhere DMs overweight diagnostic information When assessingan employeersquos skill level an employer attributes high perfor-mance to high skill because high performance is the distinctivemark of a talented employee Because he neglects the possibilitythat some talented employees perform poorly and that somenontalented ones perform well (perhaps due to stochasticity inthe environment) the employer has too much faith in skill andneglects the role of luck in accounting for the output Similarlywhen assessing the performance of firms in a hot sector of theeconomy (eg G = internet) an investor recalls highly successfulfirms in that sector (t = return of Google Amazon etc) He ne-glects the possibility of firms being unsuccessful because lack ofsuccess is statistically nondiagnostic and psychologically nonrep-resentative of a growing sectormdasheven if it is likely This causesexcessive optimism (in that the expectation of growth is unrea-sonably high) and overconfidence (in that the variability in earn-ings growth considered possible is truncated) True the hot sectormay have better growth opportunities on average but represen-tativeness exaggerates this feature and induces the investor toneglect a significant risk of failure

IV Evidence on Representativeness and Stereotypes

Testing our model requires evaluating the beliefs individualshold about a target group against the true distribution of thattarget group over an attribute space An ideal data set would

23 Our account is distinct from a mechanical underweighting of base rates inBayes rule as in Grether (1980) and Bodoh-Creed Benjamin and Rabin (2013) Inthose models upon receiving the test results the DM can update his beliefs in thewrong direction he can be less confident that a person is healthy after a negativetest than under his prior which cannot happen in our model Although this predic-tion of our model seems consistent with introspection we are not aware of experi-mental evidence on this point Griffin and Tversky (1992) present evidenceconsistent with pure neglect of base rates but in a significantly different tasknamely inferring the bias of a coin from a history of coin flips Such experimentsare hard to compare with the predictions of our model because subjects are asked togenerate distributions of different numbers of coin flips in their minds which is amuch more involved task than to recall types of a given distribution Their assess-ments then might be wrong for other reasons See Bodoh-Creed Benjamin andRabin (2013) for a detailed discussion

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consist of naturally defined groups with known distributions overa given space of types and a corresponding set of beliefs about thedistribution of each group over that space of types This wouldallow us to test for exaggeration of true differences betweengroups and to ask whether this exaggeration is well predictedby overweighting representative types To identify a causal rolefor representativeness or context dependence we would need ex-ogenous variation in either the comparison group ndashG or in thedistributions over the type spaces This is unavailable in existingdata sets Accordingly we take a two-pronged approach First wecreate a controlled laboratory environment that allows us toinduce the exogenous variation in representative types that weneed to test causality then we reanalyze existing field evidence tocheck for consistency with our predictions

In testing our model we focus on the two main implicationsof representativeness-based stereotypes

Context dependence the stereotype of a target group de-pends on the characteristics of the reference group it iscompared to

Kernel of truth stereotypes depend on group character-istics andmdashin most (precisely characterized) settingsmdashare slanted toward representative types

We test the first property with a lab experiment (SectionIVA) We then turn to survey data on beliefs about US politicalgroups (Section IVB) for an empirical analysis that explores thesecond property The survey data are more tightly linked to ourinterest in social stereotypes The laboratory experiment allowsus to directly test the role of representativeness in generatingcontext dependent beliefs Online Appendixes F and G provideall details and additional results for the experiments and fieldevidence

IVA Lab Evidence on Representativeness and ContextDependence

The influence of the representativeness heuristic on recalland on beliefs has been extensively documented in the lab(Kahneman and Tversky 1972 1973) Our goal is to considerhow representativeness as formalized in equation (2) gives riseto context-dependent beliefs To our knowledge the possibility

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that representativeness may generate context dependence hasnot been tested before

To assess this prediction we perform a controlled laboratoryexperiment that allows us to isolate representativeness frommany confounding factorsmdashhistorical sociological or other-wisemdashthat may affect stereotype formation in the real worldWe construct our own groups of ordinary objects creating atarget group G and a comparison group ndashG We hold thetarget group G fixed and explore how participant impressions ofit change as we change the comparison group ndashG and thusrepresentativeness

We conducted several experiments in the laboratory and onAmazon Mechanical Turk Each involves a basic three-stepdesign First participants are shown the target group and a ran-domly assigned comparison group for 15 seconds In this timedifferences between groups can be noticed but the groupsrsquo precisecompositions cannot be memorized The second step consists of afew filler questions which briefly draw the participantsrsquo cognitivebandwidth away from their observation Finally participants areasked to assess the groups they saw Participants are incentiv-ized to provide accurate answers

We randomly assign participants to either the Control or theRepresentativeness condition In the Control condition G and ndashGhave nearly identical distributions so that all types are similarlyrepresentative for each group In the Representativeness condi-tion ndashG is changed in such a way that a certain type becomes veryrepresentative for G Context dependence implies that the assess-ment of G should now overweight this representative type eventhough the distribution of G itself has not changed

We ran six experiments of this form with design changesfocused on reducing participant confusion and removing con-founds We describe the final and most refined version of theseexperiments here In an attempt to provide a overview of the re-sults while remaining concise we provide the results from pooledspecifications that use all data collected In Online Appendix Fwe offer additional details and report all experiments conductedWe also give instructions and materials for each experiment thefull data set is available by request

Consider first the experiment illustrated in Figure II Agroup of 25 cartoon girls is presented next to a group of 25 cartoonboys in T-shirts of different colors blue green or purple In theControl condition (Figure II Panel a) the groups have identical

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color distributions (13 purple 12 green) so no color is represen-tative of either group The Representativeness condition (Panel b)compares the same group of girls with a different group of boysfor whom green shirts are replaced with blue shirts Now onlygirls wear green and only boys wear blue These colors althoughstill not the most frequent for either group are now most repre-sentative For each group girls and boys participants are asked anumber of questions concerning the frequency of T-shirts of dif-ferent colors worn by that group

Applying our model in the control condition the type space isT frac14 fgreen purpleg and the groups are G = girls and ndashG = boysGiven that the color distributions are identical across groups both

types are equally representativegreengirls

greenboysfrac14 1 frac14

purplegirls

purpleboys As a result

assessment of G should be correct on average stcontrolgreengirls frac14 greengirls

and stcontrolpurplegirls frac14 purplegirls for any weighing function (the same is

true about assessments of ndashG)In the treatment condition the distribution of shirt colors re-

mains the same for girls For boys green shirts are changed intoblue Thus the type space changes to T frac14 fgreen purple bluegand the representative color for girls becomes greengreengirls

greenboysfrac14 1 gt 1 frac14

purplegirls

purpleboys while that for boys becomes blue As

a result in the treatment condition subjects should inflate the

frequency of green shirts relative to the truth sttreatmentgreengirls

gt greengirls (the same should happen to assessments of blueshirts for boys) We also expect the assessed frequency of greenshirts to go up relative to the control condition namely

sttreatmentgreengirls gt stcontrol

greengirls Critically the only factor that varies

across treatments is the representativeness of the 12-colorshirt Thus if we see differences across conditions the causalrole of representativeness-based recall in shaping group judg-ments is clear24

24 We vary which colors are used in which roles across participants Someparticipants saw this particular color distribution while others see for examplegreen as the modal color and purple as the diagnostic color for boys in theRepresentativeness condition and blue as the diagnostic color for girls in theRepresentativeness condition We vary the colors across the roles to avoid con-founding the characteristics of any particular color with its diagnosticity

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FIG

UR

EII

T-S

hir

tsE

xp

erim

ent

Fig

ure

sap

pea

red

inco

lor

top

art

icip

an

tsin

the

exp

erim

ent

For

clari

ty

we

have

ad

ded

ale

tter

toea

chT

-sh

irt

toid

enti

fyth

eco

lor

for

the

read

er

lsquolsquoGrsquorsquo

ind

icate

sgre

en

lsquolsquoPrsquorsquo

ind

icate

sp

urp

le

lsquolsquoBrsquorsquo

ind

icate

sblu

eT

hes

ele

tter

sd

idn

otap

pea

rto

part

icip

an

tsan

dare

for

read

erre

fere

nce

only

P

lease

see

onli

ne

ver

sion

ofp

ubli

shed

art

icle

for

colo

rfi

gu

reex

act

lyas

itap

pea

red

top

art

icip

an

ts

STEREOTYPES 1779

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We collected data from 301 participants using this T-shirtsdesign25 Since the number of green and purple shirts is verysimilar we first ask each participant the simplest question ofwhich shirt color is modal Next we ask participants to assessthe share of green and purple shirts

Consistent with the role of representativeness participantsassigned to the Representativeness condition are 105 percentagepoints more likely to recall the less frequent color (green for girlsor blue for boys) as the modal color when it is representative of agroup (35 of participants guess the less frequent color is modalin the Control condition this proportion increases to 46 in theRepresentativeness condition p = 01 estimated from a probitregression reported in Online Appendix F)

We now turn to subjectsrsquo estimates of how many T-shirts ofeach color they saw in each group In both conditions the truedifference in counts is 1 (13 purple shirts 12 green or blue shirts)In the Control condition participants on average believe they saw054 more purple shirts than green or blue shirts In theRepresentativeness condition participants believe they saw072 fewer purple shirts than green or blue shirts (the acrosstreatment difference is significant with p = 01 from OLS regres-sion reported in Online Appendix F)

In total we collected data for six experiments of this generalstructure gathering evidence from more than 1000 participantsAs we describe in Online Appendix F although there is substan-tial variation across experiments when we pool all of the data wefind significant aggregate treatment effects in line with a role ofrepresentativeness in judgment We employ four different unor-dered types designs similar to the T-shirts experiment using sixsamples (four online and two in the laboratory) with 741 partic-ipants We find effects in the predicted direction for five of the sixsamples Using a probit regression that pools the data for theseunordered type experiments we find that participants are 93 per-centage points more likely to guess that the less frequent type ismodal when it is representative than when it is not (p = 002) Wealso run a family of ordered types experiments (two designs fivesamples 402 participants) Unlike the simpler T-shirts style

25 Throughout our analysis we exclude any participant who participated in aprevious version of the experiment and any participant who self-identified as color-blind In Online Appendix F we show that our results are unchanged if we includethese additional observations

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design the theoretical predictions for the ordered types designsare more sensitive to the specific assumptions one makes aboutthe weighting function of the DM26 We find effects in the pre-dicted direction for three of the five samples As we discuss inmore detail in Online Appendix F the ordered types resultsvary by platform with consistently stronger results on AmazonMechanical Turk than in the laboratory samples Pooling all or-dered types experiments participants are 93 percentage pointsmore likely to guess that the group of interest has a greater av-erage than the comparison group when the right tail is represen-tative (p = 062) Given our simple experimental setting withgroups of mundane objects we interpret our resultsmdasha signifi-cant and reasonably sized impact on average beliefsmdashas an im-portant proof of concept the presence of representative typesbiases ex post assessment

IVB Empirical Evidence on Political Stereotypes

We examine two data sets on political preferences and be-liefs about political preferences in the United States We inves-tigate the roles of representativeness and context dependence byseparately testing for hypotheses that allow us to assess the lead-ing theories of stereotypes

First we test whether beliefs are correct or depart systemat-ically from the truth The statistical discrimination approachbuilds on the assumption that people hold rational expectationsof group traits Comparing beliefs to the truth allows us to assessthe validity of this assumption in our data

Second we test if beliefs depart from the truth by exagger-ating (mean) differences among groups per the kernel of truthhypothesis This is an implicit test of context dependence be-cause it implies that beliefs about the target groups are shapednot only by that grouprsquos characteristics but also by those of thereference group27

Third we test if distortions in beliefs can be accounted for bythe overweighting of highly representative types (defined astypes that are relatively more frequent in the target relative to

26 This is due in part to our choice to not study MLRP distributions We moti-vate and discuss this design decision in Online Appendix F

27 Of course unlike in the laboratory experiment in this setting we cannot testfor context dependence by exogenously varying the reference group

STEREOTYPES 1781

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the reference group) The second and third tests address the keypredictions of our model

1 The Data We have two data sets on political preferences andbeliefs about political preferences The first data set from GrahamNosek and Haidt (GNH 2012) contains data from the MoralFoundations Questionnaire Respondents (1174 self-identified lib-erals and 500 self-identified conservatives) answer questions abouttheir position on a subset of 45 issues 20 moral relevance state-ments (eg lsquolsquowhen you decide whether something is right orwrong to what extent are the following considerations relevantto your thinkingrsquorsquo) and 25 moral judgments (eg lsquolsquoindicate theextent to which you would agree or disagreersquorsquo) For each issue arandomly determined subset of participants states their own posi-tion another subset states their belief on the position of a lsquolsquotypicalliberalrsquorsquo and a third subset states their belief on the position of alsquolsquotypical conservativersquorsquo The data thus include the distribution overpositions for both liberal and conservatives as well as the averagebelieved typical position of liberals and of conservatives on the 45issues Each position is elicited on 1ndash6 scale

The second data set comes from the American NationalElection Survey (ANES) and contains data from more than20000 respondents between 1964 and 201228 The surveycovers political issues of the day such as the optimal amount ofgovernment spending and service provision (1984ndash2000) or theplace of women in society (1972ndash1998) We focus on the 10 issuesthat ask participants to respond on a 1ndash7 scale (rather than justindicate binary agreement or disagreement) all 10 issues areasked in multiple years Participants are asked to provide theirown position on the scale and their believed position of theDemocratic and Republican parties (lsquolsquoWhere would you placethe Democratic [Republican] party on this scalersquorsquo) The data in-clude for each issue-year observation the distribution of partic-ipant positions for self-identified liberals and self-identifiedconservatives as well as the distribution of believed typical posi-tions of the Democratic and Republican parties

28 These data are publicly available at httpwwwelectionstudiesorgstudy-pagesanes_timeseries_cdfanes_timeseries_cdfhtm

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2 Empirical Strategy Our analysis focuses on beliefs abouttwo groups Conservatives and Liberals The types are the possi-ble positions for each issue (1 2 6 7) For the GNH data weinterpret beliefs about the lsquolsquotypicalrsquorsquo element of a group to coincidewith the believed average position in that group Similarly forthe ANES data we use the believed party positions as a proxy forbelieved mean of each group29 We then take as a benchmark thehypothesis that individuals hold accurate beliefs about eachgroup and in particular that believed mean position shouldequal true mean position at least on average across subjectsThe accurate beliefs hypothesis underlies the most common eco-nomic model of stereotyping statistical discrimination

To assess our representativeness-based model we perform aregression exercise To test our model in a linear regressionframework we rely on linear approximations of the weightingfunction Our model then yields two regression specifications

PROPOSITION 4 Let G 2 fconservative liberal g and assume

ht h tG

tG

be a differentiable and strictly increasing weight-

ing function as in Definition 2 The following hold as a first-order approximation around identical distributions G

Gfrac14 1

(i) Kernel of truth regression There exists a constant gt 0such that

EstethtjGTHORN frac14 EethtjGTHORNeth1thorn THORN EethtjGTHORNeth5THORN

(ii) Representativeness regression Denote H frac14 fT 2 Tg

the right tail of types and RconsH frac14

PHtconsPHtlib

as the average

representativeness of right tail types for conservatives

29 This assumption is consistent with the authorsrsquo interpretation of the GNHdata (GNH 2012) and with previous studies using ANES (eg Westfall et al 2015)Furthermore to the extent that this assumption holds equally well for most issueswithin a data set our focus on cross-issue differences should allow us to test thepredictions of our model even with an imperfect proxy for beliefs of mean positionsFinally the data provide some insight into whether subjects are reporting (per-ceived) modal or mean types As we show the modal type is a poor prediction ofstated beliefs while a distorted mean slanted toward representative types is anaccurate prediction of stated beliefs

STEREOTYPES 1783

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Under the further approximation where tcons

tlibampRcons

H for

t 2 H

EstethtjconsTHORN frac14 EethtjconsTHORN thorn consethR

consH 1THORNeth6THORN

EstethtjlibTHORN frac14 EethtjlibTHORN libethR

consH 1THORNeth7THORN

where lcons and llib are positive constants

The first regression allows us to test for the kernel of truthhypothesis and the second set of regressions allows us to test forthe role of representativeness

Equation (5) says that respondents in our model inflate theaverage position of a group say the conservatives if and only ifthe group has a higher average position than the other groupnamely the liberals Formally EstethtjconsTHORN gt EethtjconsTHORN if and onlyif EethtjconsTHORN gt EethtjlibTHORN Because in our measurement scale highertypes mean lsquolsquomore conservativersquorsquo we expect (i) believed conserva-tive average to be higher than the truth and (ii) the extent ofoverstatement to decrease in the average liberal position EethtjlibTHORNConversely we expect the average liberal position to be lowerthan the truth the more so the higher the average conservativeposition EethtjconsTHORN

As previously discussed the basis of these predictions is con-text dependence information about the distribution of ndashG is rel-evant for the beliefs about G This context dependence isinconsistent with rational expectations in which only thegrouprsquos own means should affect beliefs We test the hypothesisthat the true mean EethtjGTHORN is a significant predictor of the believedmean E

stethtjGTHORN with a positive sign and the other grouprsquos truemean EethtjGTHORN is a predictor of the believed mean with a negativesign

Equations (6) and (7) say that repondentsrsquo assessment bias isshaped by representativeness When the right tail is more repre-sentative for conservatives (Rcons

H 1 positive and large) partici-pants should inflate the average conservative position more(higher E

stethtjconsTHORN EethtjconsTHORN) and deflate the average liberal po-sition more (lower E

stethtjlibTHORN EethtjlibTHORN) We test the hypothesisthat the inflation in conservative positions is positively associatedwith the representativeness of the right tail for the conservativesand the inflation in liberal positions is negatively associated with

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it Once again the representativeness of the right tail is com-puted using the true distribution of positions

In equations (6) and (7) in many cases the representative tailis also the most likely one As a consequence these tests cannotdistinguish a representativeness-based from a likelihood-basedmodel of distorted beliefs We perform two additional testsFirst we run versions of equations (6) and (7) in which we controlfor the likelihood of tails (see Table A4 in Online Appendix G)Second we compute numerically the predictions of a representa-tiveness-based model of stereotypes and a likelihood-based modelof stereotypes We then assess which of these two is better able tomatch the data on beliefs

3 Empirical Results To begin we illustrate the structure ofthe data and the nature of our predictions with two simple exam-ples from the GNH data set focusing on beliefs about conserva-tives In example 1 participants are asked about their agreementwith the statement lsquolsquoIt can never be right to kill a human beingrsquorsquoIn example 2 participants are asked about the moral relevance oflsquolsquowhether or not someone cared for someone weak or vulnerablersquorsquoAs can be seen in Figure III in example 1 the modal position(strongly disagree (1)) and most representative positions(strongly disagree (1)) coincide for conservatives In contrast inexample 2 in Figure III the most representative types (slightlyrelevant (3) not at all relevant (1)) are not most likely for theconservative group Following Proposition 1 we predict that be-liefs will be distorted in the direction of the most representativetypes Thus we expect more exaggeration in example 2 than inexample 1 since in example 2 the most representative types (inthe left tail) are far from the modal type whereas in example 1they coincide This is what we find the conservative position isexaggerated by only 009 positions in Example 1 (true mean 299believed mean 290) but by 106 positions in Example 2 (truemean 421 believed mean 315)

In the full data sets we treat each (issue year) pair as anobservation and we cluster standard errors at the issue level Forthe GNH data we have 45 observations 45 issues measured inthe same year For the ANES data we have 66 observations 10issues measured in multiple years To begin we simply docu-ment systematic exaggeration in both data sets This is a primaryfocus of the original analysis in GNH (2012) and also in Westfall

STEREOTYPES 1785

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FIGURE III

Two Examples

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et al (2015)rsquos analysis of the ANES data30 Figure IV shows thatthe believed difference between typical conservative and typicalliberal positions is larger than the true difference in mean posi-tions for 109 of the 111 observations The data for both GNH(squares) and ANES (triangles) lie above the 45-degree line(dashed)31 Average exaggeration is 062 positions on the scale(066 in the GNH data 059 in the ANES data)32

The systematic and significant exaggeration of mean differ-ences suggests that the benchmark model of accurate beliefs ismissing something important Indeed this exaggeration reflectsthe fact that believed means are typically more extreme than truemeans First note that the kernel of truth regression (equation(5)) generates exaggeration of mean differences just as docu-mented in Figure IV

EstethtjGTHORN E

stethtjGTHORN frac14 eth1thorn 2THORN frac12EethtjGTHORN EethtjGTHORN

To bring this prediction to the data we regress the believedmean position for each group EBethtjGTHORN on the true mean of thegroup EethtjGTHORN and the true mean of the comparison groupEethtjGTHORN across issues We do this for each group (liberals con-servatives) in each data set separately We also present pooledspecifications that combine the data sets to make a prediction fora given group (liberals conservatives) In these pooled specifica-tions we include a dummy variable indicating whether theobservation came from the ANES data set For all specificationswe cluster observations at the issue level33 The results from re-gression are shown in Table I In every specification we find thatEethtjGTHORN is a significant predictor of EBethtjGTHORN with the predicted pos-itive sign Crucially for five of the six specifications the mean of

30 Chambers and Melnyk (2006) also find evidence of exaggeration of truedifferences in beliefs about political positions

31 For convenience we recode all issues so that the high end of the scale (67)represents the stereotypically more conservative position

32 A natural question to ask is how beliefs vary across liberals and conserva-tives That is do beliefs about a group G depend on membership in G versus ndashG Ourmodel does not speak to this issue However in Online Appendix G we show thatthe results we document below hold for both beliefs held by conservatives and be-liefs held by liberals see Tables A9 A10 and A11

33 In general the results presented below for the ANES data are not largelyimpacted by the decision to cluster at the issue level Similar results are obtained ifthe data are not clustered

STEREOTYPES 1787

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the comparison group EethtjGTHORN is also a significant predictor ofE

BethtjGTHORN with the predicted negative signAlthough these results provide strong evidence of context

dependence and are consistent with our model they do not pindown a role for representativeness of types Our next test relatesthe magnitude of representativeness of tail types to the magni-tude of belief distortions

To this end we implement the regressions in equations (6)and (7) Following Proposition 4 we compute the average repre-

sentativeness of tail types for conservatives RconsH frac14

PtT2tconsPtT2tlib

We

again test the hypothesis that RconsH is a significant predictor of Est

ethtjconsTHORN with a positive sign and a predictor of EstethtjlibTHORN with a

negative sign Table II shows that conditional on true mean RconsH

predicts believed mean for each group G as expected The firstthree specifications display the results for predicting beliefs heldabout conservatives In both data sets the average representa-tiveness of tail types for conservatives is a significant positivepredictor of beliefs held about conservatives The final three spe-cifications display the results for predicting beliefs held about

FIGURE IV

Exaggeration of Differences

QUARTERLY JOURNAL OF ECONOMICS1788

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liberals We find that the average representativeness of tail typesfor conservatives is a negative predictor of beliefs held about lib-erals This effect is significant in the GNH data and marginallysignificant in the ANES data

We present several additional results in Online Appendix GTo further examine the role of representativeness in driving be-liefs we first show the results of Table II carry through when we

TABLE II

AVERAGE REPRESENTATIVENESS OF TAIL POSITIONS PREDICTS BELIEFS

OLS Predicting Believed Mean of Group G for Each Issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position

of group G for issue

078 024 051 072 018 041

(006) (008) (009) (005) (005) (010)

Avg rep of tail types for

conservatives RconsH

019 055 025 014 012 024

(007) (022) (008) (006) (007) (005)

Constant 101 260 184 093 271 201

(026) (045) (029) (022) (025) (032)

R2 082 048 060 091 031 070

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

TABLE I

INFORMATION ABOUT ndashG PREDICTS BELIEFS ABOUT G

OLS predicting believed mean of group G for each issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position of

conservatives for issue

102 098 096 021 019 025

(0097) (0133) (0076) (0060) (0116) (0060)

True mean position of

liberals for issue

035 086 058 0987 039 073

(0106) (0134) (0131) (0066) (0106) (0135)

Constant 151 335 235 069 258 156

(0195) (0269) (0279) (0122) (0249) (0270)

R2 083 053 066 092 032 068

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

STEREOTYPES 1789

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control for the average likelihood on the tail positions (see Table A4in Online Appendix G) Most tellingly we use the model to predictbeliefs across issues and compare those to the data For simplicitywe use the rank-based truncation specification to predict mean be-liefs when stereotypes include the d most representative types ford frac14 1 T We compare these predictions to those of a model inwhich beliefs are obtained by restricting the distribution to the dmost likely types Our benchmark for both models is predicting thebelieved mean from the entire distribution where d = T We showthat the predictions of the rank-based truncation model with d = 4or 5 compare favorably to both a likelihood-based truncation model(with any d) and the accurate beliefs benchmark Interestingly thisresult suggests that stereotypical beliefs are well approximated byneglecting the least representative types (as opposed to focusingonly on the most representative types) and so represent a moderatethough systematic departure from the standard benchmarkFinally we show that the results we document above hold forboth beliefs held by conservatives and beliefs held by liberals (seeTables A9 A10 and A11 in Online Appendix G)

V Conclusion

We present a model of stereotypical thinking in which DMsmaking predictions about a group overweight the grouprsquos mostdistinctive types These overweighted types are not the mostlikely ones given the DMrsquos data but the most representativeones in the sense of being the most diagnostic of the group rela-tive to other groups Representativeness implies that what ismost distinctive of a group depends on what group it is comparedwith We present experimental evidence that confirms this con-text dependence in recall-based assessments of groups Finallywe evaluated the predictions of the model using political data fromexisting large-scale surveys We find context dependence to be akey feature of beliefs Given the richness of the political data wecan go a step further and identify a role for representativeness inparticular As the representativeness of tail types increases beliefsof a group are distorted in the direction of that tail

Our approach provides a parsimonious and psychologicallyfounded account of how DMs generate simplified representationsof reality from social groups to stock returns and offers a unifiedaccount of disparate pieces of evidence relating to this type of

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uncertainty The model captures the central fact that stereotypeshighlight the greatest difference between groups thus explainingwhy some stereotypes are very accurate while others lack valid-ity Still stereotypes often have a kernel of truth when they arebased on systematicmdasheven if smallmdashdifferences between groupsThis logic allows us to describe a number of heuristics and psy-chological biases many of which arise in the context of predictionproblems Generically our model generates overreaction to diag-nostic information

Our model is based on representativeness and does not cap-ture all the features of stereotypical thinking However it cap-tures perhaps the central feature when we think of a group wefocus on what is most distinctive about it and neglect or under-weight the rest

Saeuroıd Business School University of Oxford

Ohio State University and Harvard Business School

Universita Bocconi and Innocenzo Gasparini Institute

for Economic Research

Harvard University

Supplementary Material

An Online Appendix for this article can be found at QJEonline (qjeoxfordjournalorg)

References

Adorno Theodor Else Frenkel-Brunswik Daniel Levinson and Nevitt SanfordThe Authoritarian Personality (New York Harper amp Row 1950)

Arrow Kenneth lsquolsquoThe Theory of Discriminationrsquorsquo in Discrimination in LaborMarkets Orley Ashenfelter and Albert Rees eds (Princeton NJPrinceton University Press 1973)

Ashton Michael and Victoria Esses lsquolsquoStereotype Accuracy Estimating theAcademic Performance of Ethnic Groupsrsquorsquo Personality and SocialPsychology Bulletin 25 (1999) 225ndash236

Barberis Nicholas Andrei Shleifer and Robert Vishny lsquolsquoA Model of InvestorSentimentrsquorsquo Journal of Financial Economics 49 (1998) 307ndash343

Bayer Sylvia lsquolsquoThe Accuracy of Academic Gender Stereotypesrsquorsquo Sex Roles 40(1999) 787ndash813

Benjamin Dan James Choi and Joshua Strickland lsquolsquoSocial Identity andPreferencesrsquorsquo American Economic Review 100 (2010) 1913ndash1928

Benjamin Dan Matthew Rabin and Collin Raymond lsquolsquoA Model of Non-Belief inthe Law of Large Numbersrsquorsquo Journal of the European Economic Association15 (2015) 515ndash544

Bertrand Marianne lsquolsquoNew Perspectives on Genderrsquorsquo Handbook of LaborEconomics 4 (2011) 1543ndash1590

Bodoh-Creed Aaron Dan Benjamin and Matthew Rabin lsquolsquoThe Dynamics of Base-Rate Neglectrsquorsquo mimeo Haas Business School 2013

STEREOTYPES 1791

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

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Bohnet Iris Alexandra van Geen and Max Bazerman lsquolsquoWhen PerformanceTrumps Gender Bias Joint versus Separate Evaluationrsquorsquo ManagementScience 5 (2016) 1225ndash1234

Bordalo Pedro Nicola Gennaioli and Andrei Shleifer lsquolsquoSalience Theory of Choiceunder Riskrsquorsquo Quarterly Journal of Economics 127 (2012) 1243ndash1285

mdashmdashmdash lsquolsquoSalience and Consumer Choicersquorsquo Journal of Political Economy 121(2013) 803ndash843

Briton Nancy and Judith Hall lsquolsquoBeliefs about Female and Male NonverbalCommunicationrsquorsquo Sex Roles 32 (1995) 79ndash90

Buser Thomas Muriel Niederle and Hessel Oosterbeek lsquolsquoGenderCompetitiveness and Career Choicesrsquorsquo Quarterly Journal of Economics 129(2014) 1409ndash1447

Carrell Scott Marianne Page and James West lsquolsquoSex and Science How ProfessorGender Perpetuates the Gender Gaprsquorsquo Quarterly Journal of Economics 125(2010) 1101ndash1144

Chambers John and Darya Melnyk lsquolsquoWhy Do I Hate Thee ConflictMisperceptions and Intergroup Mistrustrsquorsquo Personality and SocialPsychology Bulletin 32 (2006) 1295ndash1311

Chan Wayne Robert R McCrae Filip De Fruyt Lee Jussim CorinnaE Lockenhoff Marleen De Bolle Paul T Costa Jr Angelina R SutinAnu Realo Juri Allik Katsuharu Nakazato Yoshiko ShimonakaMartina Hrebıckova Sylvie Graf Michelle Yik Marina Brunner-SciarraNora Leibovich De Figueora Vanina Schmidt Chang-kyo Ahn Hyun-nie Ahn Maria E Aguilar-Vafaie Jerzy Siuta Barbara SzmigielskaThomas R Cain Janet T Crawford Khairul Anwar Mastor Jean-Pierre Rolland Florence Nansubuga Daniel R MiramontezVeronica Benet-Martınez Jerome Rossier Denis Bratko Iris MarusicJamin Halberstadt Mami Yamaguchi Goran Knezevic Thomas A MartinMirona Gheorghiu Peter B Smith Claudio Barbaranelli Lei WangJane Shakespeare-Finch Margarida P Lima Waldemar KlinkoszAndrzej Sekowski Lidia Alcalay Franco Simonetti Tatyana V AvdeyevaV S Pramila and Antonio Terracciano lsquolsquoStereotypes of Age Differences inPersonality Traits Universal and Accuratersquorsquo Journal of Personality andSocial Psychology 103 (2012) 1050ndash1066

Chen Yan Sherry Xin Liu Tracy Xiao and Margaret Shih lsquolsquoWhich Hat to WearImpact of Natural Identities on Coordination and Cooperationrsquorsquo Games andEconomic Behavior 84 (2014) 58ndash86

Coffman Katherine lsquolsquoEvidence on Self-Stereotyping and the Contribution ofIdeasrsquorsquo Quarterly Journal of Economics 129 (2014) 1625ndash1660

Cunningham Tom lsquolsquoComparisons and Choicersquorsquo mimeo Stockholm University2013

Diekman Amanda Alice Eagly and Patrick Kulesa lsquolsquoAccuracy and Bias in theStereotypes about the Social and Political Attitudes of Women and MenrsquorsquoJournal of Experimental Social Psychology 38 (2002) 268ndash282

Eccles Jacquelynne S Janis E Jacobs and Rena D Harold lsquolsquoGender RoleStereotypes Expectancy Effects and Parentsrsquo Socialization of GenderDifferencesrsquorsquo Journal of Social Issues 46 (1990) 183ndash201

Fryer Roland and Matthew Jackson lsquolsquoA Categorical Model of Cognition andBiased Decision-Makingrsquorsquo BE Journal of Theoretical Economics 8 (2008)1ndash42

Fryer Roland and Steven Levitt lsquolsquoAn Empirical Analysis of the Gender Gap inMathematicsrsquorsquo American Economic Journal Applied Economics 2 (2010)210ndash240

Gennaioli Nicola and Andrei Shleifer lsquolsquoWhat Comes to Mindrsquorsquo Quarterly Journalof Economics 125 (2010) 1399ndash1433

Gennaioli Nicola Andrei Shleifer and Robert Vishny lsquolsquoNeglected RisksFinancial Innovation and Financial Fragilityrsquorsquo Journal of FinancialEconomics 104 (2012) 452ndash468

Gilens Martin lsquolsquoRace and Poverty in America Public Misperceptions and theAmerican News Mediarsquorsquo Public Opinion Quarterly 60 (1996) 515ndash541

Glaeser Edward lsquolsquoThe Political Economy of Hatredrsquorsquo Quarterly Journal ofEconomics 120 (2005) 45ndash86

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Glover Dyland Amanda Pallais and William Pariente lsquolsquoDiscrimination as a Self-Fulfilling Prophecy Evidence from French Grocery Storesrsquorsquo mimeo HarvardUniversity 2015

Goldin Claudia Lawrence Katz and Ilyana Kuziemko lsquolsquoThe Homecoming ofAmerican College Women The Reversal of the College Gender GaprsquorsquoJournal of Economic Perspectives 20 (2006) 133ndash156

Graham Jesse Brian Nosek and Jonathan Haidt lsquolsquoThe Moral Stereotypes ofLiberals and Conservatives Exaggeration of Differences across thePolitical Spectrumrsquorsquo PLoS One 7 (2012) 1ndash13

Grether David lsquolsquoBayes Rule as a Descriptive Model The RepresentativenessHeuristicrsquorsquo Quarterly Journal of Economics 95 (1980) 537ndash557

Griffin Dale and Amos Tversky lsquolsquoThe Weighing of Evidence and theDeterminants of Confidencersquorsquo Cognitive Psychology 24 (1992) 411ndash435

Guiso Luigi Ferdinando Monte Paola Sapienza and Luigi Zingales lsquolsquoCultureGender and Mathrsquorsquo Science 320 (2008) 1164ndash1165

Hilton James and William Von Hippel lsquolsquoStereotypesrsquorsquo Annual Review ofPsychology 47 (1996) 237ndash271

Hyde Janet Sara Lindberg Marcia Linn Amy Ellis and Caroline WilliamslsquolsquoGender Similarities Characterize Math Performancersquorsquo Science 321 (2008)494ndash495

Judd Charles and Bernardette Park lsquolsquoDefinition and Assessment of Accuracy inSocial Stereotypesrsquorsquo Psychological Review 100 (1993) 109ndash128

Jussim Lee Jarret Crawford Stephanie Anglin John Chambers Sean Stevensand Florette Cohen lsquolsquoStereotype Accuracy One of the Largest and MostReplicable Effects in All of Social Psychologyrsquorsquo in The Handbook ofPrejudice Stereotyping and Discrimination Todd Nelson ed (MahwahNJ Lawrence Erlbaum 2015)

Kahneman Daniel and Amos Tversky lsquolsquoSubjective Probability A Judgment ofRepresentativenessrsquorsquo Cognitive Psychology 3 (1972) 430ndash454

mdashmdashmdash lsquolsquoOn the Psychology of Predictionrsquorsquo Psychological Review 80 (1973) 237ndash251

Kaplowitz Stan Bradley Fisher and Clifford Broman lsquolsquoHow Accurate ArePerceptions of Social Statistics about Blacks and Whitesrsquorsquo Public OpinionQuarterly 67 (2003) 237ndash243

Kersten Daniel Pascal Mamassian and Alan Yuille lsquolsquoObject Perception asBayesian Inferencersquorsquo Annual Review of Psychology 55 (2004) 271ndash304

Klein Richard Kate A Ratliff Michelangelo Vianello Reginald B Adams JrStepan Bahnik Michael J Bernstein Konrad Bocian Mark J BrandtBeach Brooks Claudia Chloe Brumbaugh Zeynep CemalcilarJesse Chandler Winnee Cheong William E Davis Thierry DevosMatthew Eisner Natalia Frankowska David Furrow Elisa Maria GallianiFred Hasselman Joshua A Hicks James F Hovermale S Jane HuntJeffrey R Huntsinger Hans IJzerman Melissa-Sue John Jennifer A Joy-Gaba Heather Barry Kappes Lacy E Krueger Jaime Kurtz CarmelA Levitan Robyn Mallett Wendy L Morris Anthony J Nelson JasonA Nier Grant Packard Ronaldo Pilati Abraham M RutchickKathleen Schmidt Jeanine L Skorinko Robert Smith Troy G SteinerJustin Storbeck Lyn M Van Swol Donna Thompson Anna van rsquot VeerLeigh Ann Vaughn Marek Vranka Aaron Wichman Julie A Woodzickaand Brian A Nosek lsquolsquoInvestigating Variation in Replicability A ManyLabs Replication Projectrsquorsquo Social Psychology 45 (2014) 142ndash152

Lundberg Shelly and Richard Startz lsquolsquoPrivate Discrimination and SocialIntervention in Competitive Labor Marketsrsquorsquo American Economic Review73 (1983) 340ndash347

Madon Stephanie Max Guyll Kathy Aboufadel Eulices Montiel Alison SmithPolly Palumbo and Lee Jussim lsquolsquoEthnic and National Stereotypes ThePrinceton Trilogy Revisited and Revisedrsquorsquo Personality and SocialPsychological Bulletin 27 (2001) 996ndash1010

Martin Carol lsquolsquoA Ratio Measure of Sex Stereotypingrsquorsquo Journal of Personality andSocial Psychology 52 (1987) 489ndash499

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httpqjeoxfordjournalsorgD

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McCauley Clark Krishna Thangavelu and Paul Rozin lsquolsquoSex Stereotyping ofOccupations in Relation to Television Representations and Census FactsrsquorsquoBasic and Applied Social Psychology 9 (1988) 197ndash212

Mullainathan Sendhil lsquolsquoThinking through Categoriesrsquorsquo mimeo HarvardUniversity 2002

Ortoleva Pietro and Erik Snowberg lsquolsquoOverconfidence in Political BehaviorrsquorsquoAmerican Economic Review 105 (2015) 504ndash535

Phelps Edmund lsquolsquoThe Statistical Theory of Racism and Sexismrsquorsquo AmericanEconomic Review 62 (1972) 659ndash661

Pope Devin and Justin Sydnor lsquolsquoGeographic Variation in the Gender Differencesin Test Scoresrsquorsquo Journal of Economic Perspectives 24 (2010) 95ndash108

Rabin Matthew lsquolsquoInference by Believers in the Law of Small NumbersrsquorsquoQuarterly Journal of Economics 117 (2002) 775ndash816

Rabin Matthew and Joel Schrag lsquolsquoFirst Impressions Matter A Model ofConfirmatory Biasrsquorsquo Quarterly Journal of Economics 114 (1999) 37ndash82

Rabin Matthew and Dimitri Vayanos lsquolsquoThe Gamblerrsquos and Hot-Hand FallaciesTheory and Applicationsrsquorsquo Review of Economic Studies 77 (2010) 730ndash778

Reuben Ernesto Paola Sapienza and Luigi Zingales lsquolsquoHow Stereotypes ImpairWomenrsquos Careers in Sciencersquorsquo Proceedings of the National Academy ofSciences 111 (2014) 4403ndash4408

Rosch Eleanor lsquolsquoNatural Categoriesrsquorsquo Cognitive Psychology 4 (1973) 328ndash350Ryan Carey S lsquolsquoAccuracy of Black and White College Studentsrsquo In-Group and

Out-Group Stereotypesrsquorsquo Personality and Social Psychology Bulletin 22(1996) 1114ndash1127

Schneider David The Psychology of Stereotyping (New York Guilford Press2004)

Schneider David Albert Hastorf and Phoebe Ellsworth Person Perception(Reading MA Addison-Wesley 1979)

Shih Margaret Todd Pittinsky and Nalini Ambady lsquolsquoStereotype SusceptibilityIdentity Salience and Shifts in Quantitative Performancersquorsquo PsychologicalScience 10 (1999) 80ndash83

Shih Margaret Todd Pittinsky and Amy Trahan lsquolsquoDomain-Specific Effects ofStereotypes on Performancersquorsquo Self and Identity 5 (2006) 1ndash14

Steele Claude Whistling Vivaldi How Stereotypes Affect Us and What We CanDo (New York Norton 2010)

Tenenbaum Joshua and Thomas Griffiths lsquolsquoThe Rational Basis ofRepresentativenessrsquorsquo 23rd Annual Conference of the Cognitive ScienceSociety (2001) 1036ndash1041

Tversky Amos and Daniel Kahneman lsquolsquoExtensional versus Intuitive ReasoningThe Conjunction Fallacy in Probability Judgmentrsquorsquo Psychological Review 90(1983) 293ndash315

Weinberger Catherin lsquolsquoIs the Science and Engineering Workforce Drawn fromthe Far Upper Tail of the Math Ability Distributionrsquorsquo mimeo UCSB 2005

Westfall Jacob Leaf Van Boven John Chambers and Charles Judd lsquolsquoPerceivingPolitical Polarization in the United States Party Identity Strength andAttitude Extremity Exacerbate the Perceived Partisan DividersquorsquoPsychological Science 10 (2015) 145ndash158

Wolsko Christopher Bernadette Park Charles Judd and Bernd WittenbrinklsquolsquoFraming Interethnic Ideology Effects of Multicultural and Color-BlindPerspectives on Judgments of Groups and Individualsrsquorsquo Journal ofPersonality and Social Psychology 78 (2000) 635ndash654

QUARTERLY JOURNAL OF ECONOMICS1794

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ibrary on October 28 2016

httpqjeoxfordjournalsorgD

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Page 22: I. Introduction · uneducated at the beginning of the 20th century, and as high achievers at the beginning of the 21st (Madon et al. 2001). Social science has produced three broad

people to groups precisely because such information generatesextreme stereotypes Consider the classic example in which amedical test for a particular disease with a 5 prevalence has a90 rate of true positives and a 5 rate of false positives The testassigns each person to one of two groups + (positive test) or ndash(negative test) The DM estimates the frequency of the sick type(s) and the healthy type (h) in each group The test is informativea positive result increases the relative likelihood of sickness anda negative result increases the relative likelihood of health forany prior Formally

PreththornjsTHORN

PreththornjhTHORNgt 1 gt

PrethjsTHORN

PrethjhTHORNeth4THORN

This condition has clear implications the representative personwho tests positive is sick while the representative person whotests negative is healthy Following Proposition 2 the DMreacts to the test by moving his priors too far in the right di-rection generating extreme stereotypes He greatly boosts hisassessment that a positively tested person is sick but also thata negatively tested person is healthy Because most people arehealthy the DMrsquos assessment about the group that tested neg-ative is fairly accurate but is severely biased for the group that

FIGURE I

SAT Mathematics Scores by Gender (2013)

QUARTERLY JOURNAL OF ECONOMICS1774

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tested positive This analysis formalizes Tversky andKahnemanrsquos (1983) verbal account of base rate neglect23

The same mechanism may underlie several other instanceswhere DMs overweight diagnostic information When assessingan employeersquos skill level an employer attributes high perfor-mance to high skill because high performance is the distinctivemark of a talented employee Because he neglects the possibilitythat some talented employees perform poorly and that somenontalented ones perform well (perhaps due to stochasticity inthe environment) the employer has too much faith in skill andneglects the role of luck in accounting for the output Similarlywhen assessing the performance of firms in a hot sector of theeconomy (eg G = internet) an investor recalls highly successfulfirms in that sector (t = return of Google Amazon etc) He ne-glects the possibility of firms being unsuccessful because lack ofsuccess is statistically nondiagnostic and psychologically nonrep-resentative of a growing sectormdasheven if it is likely This causesexcessive optimism (in that the expectation of growth is unrea-sonably high) and overconfidence (in that the variability in earn-ings growth considered possible is truncated) True the hot sectormay have better growth opportunities on average but represen-tativeness exaggerates this feature and induces the investor toneglect a significant risk of failure

IV Evidence on Representativeness and Stereotypes

Testing our model requires evaluating the beliefs individualshold about a target group against the true distribution of thattarget group over an attribute space An ideal data set would

23 Our account is distinct from a mechanical underweighting of base rates inBayes rule as in Grether (1980) and Bodoh-Creed Benjamin and Rabin (2013) Inthose models upon receiving the test results the DM can update his beliefs in thewrong direction he can be less confident that a person is healthy after a negativetest than under his prior which cannot happen in our model Although this predic-tion of our model seems consistent with introspection we are not aware of experi-mental evidence on this point Griffin and Tversky (1992) present evidenceconsistent with pure neglect of base rates but in a significantly different tasknamely inferring the bias of a coin from a history of coin flips Such experimentsare hard to compare with the predictions of our model because subjects are asked togenerate distributions of different numbers of coin flips in their minds which is amuch more involved task than to recall types of a given distribution Their assess-ments then might be wrong for other reasons See Bodoh-Creed Benjamin andRabin (2013) for a detailed discussion

STEREOTYPES 1775

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consist of naturally defined groups with known distributions overa given space of types and a corresponding set of beliefs about thedistribution of each group over that space of types This wouldallow us to test for exaggeration of true differences betweengroups and to ask whether this exaggeration is well predictedby overweighting representative types To identify a causal rolefor representativeness or context dependence we would need ex-ogenous variation in either the comparison group ndashG or in thedistributions over the type spaces This is unavailable in existingdata sets Accordingly we take a two-pronged approach First wecreate a controlled laboratory environment that allows us toinduce the exogenous variation in representative types that weneed to test causality then we reanalyze existing field evidence tocheck for consistency with our predictions

In testing our model we focus on the two main implicationsof representativeness-based stereotypes

Context dependence the stereotype of a target group de-pends on the characteristics of the reference group it iscompared to

Kernel of truth stereotypes depend on group character-istics andmdashin most (precisely characterized) settingsmdashare slanted toward representative types

We test the first property with a lab experiment (SectionIVA) We then turn to survey data on beliefs about US politicalgroups (Section IVB) for an empirical analysis that explores thesecond property The survey data are more tightly linked to ourinterest in social stereotypes The laboratory experiment allowsus to directly test the role of representativeness in generatingcontext dependent beliefs Online Appendixes F and G provideall details and additional results for the experiments and fieldevidence

IVA Lab Evidence on Representativeness and ContextDependence

The influence of the representativeness heuristic on recalland on beliefs has been extensively documented in the lab(Kahneman and Tversky 1972 1973) Our goal is to considerhow representativeness as formalized in equation (2) gives riseto context-dependent beliefs To our knowledge the possibility

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that representativeness may generate context dependence hasnot been tested before

To assess this prediction we perform a controlled laboratoryexperiment that allows us to isolate representativeness frommany confounding factorsmdashhistorical sociological or other-wisemdashthat may affect stereotype formation in the real worldWe construct our own groups of ordinary objects creating atarget group G and a comparison group ndashG We hold thetarget group G fixed and explore how participant impressions ofit change as we change the comparison group ndashG and thusrepresentativeness

We conducted several experiments in the laboratory and onAmazon Mechanical Turk Each involves a basic three-stepdesign First participants are shown the target group and a ran-domly assigned comparison group for 15 seconds In this timedifferences between groups can be noticed but the groupsrsquo precisecompositions cannot be memorized The second step consists of afew filler questions which briefly draw the participantsrsquo cognitivebandwidth away from their observation Finally participants areasked to assess the groups they saw Participants are incentiv-ized to provide accurate answers

We randomly assign participants to either the Control or theRepresentativeness condition In the Control condition G and ndashGhave nearly identical distributions so that all types are similarlyrepresentative for each group In the Representativeness condi-tion ndashG is changed in such a way that a certain type becomes veryrepresentative for G Context dependence implies that the assess-ment of G should now overweight this representative type eventhough the distribution of G itself has not changed

We ran six experiments of this form with design changesfocused on reducing participant confusion and removing con-founds We describe the final and most refined version of theseexperiments here In an attempt to provide a overview of the re-sults while remaining concise we provide the results from pooledspecifications that use all data collected In Online Appendix Fwe offer additional details and report all experiments conductedWe also give instructions and materials for each experiment thefull data set is available by request

Consider first the experiment illustrated in Figure II Agroup of 25 cartoon girls is presented next to a group of 25 cartoonboys in T-shirts of different colors blue green or purple In theControl condition (Figure II Panel a) the groups have identical

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color distributions (13 purple 12 green) so no color is represen-tative of either group The Representativeness condition (Panel b)compares the same group of girls with a different group of boysfor whom green shirts are replaced with blue shirts Now onlygirls wear green and only boys wear blue These colors althoughstill not the most frequent for either group are now most repre-sentative For each group girls and boys participants are asked anumber of questions concerning the frequency of T-shirts of dif-ferent colors worn by that group

Applying our model in the control condition the type space isT frac14 fgreen purpleg and the groups are G = girls and ndashG = boysGiven that the color distributions are identical across groups both

types are equally representativegreengirls

greenboysfrac14 1 frac14

purplegirls

purpleboys As a result

assessment of G should be correct on average stcontrolgreengirls frac14 greengirls

and stcontrolpurplegirls frac14 purplegirls for any weighing function (the same is

true about assessments of ndashG)In the treatment condition the distribution of shirt colors re-

mains the same for girls For boys green shirts are changed intoblue Thus the type space changes to T frac14 fgreen purple bluegand the representative color for girls becomes greengreengirls

greenboysfrac14 1 gt 1 frac14

purplegirls

purpleboys while that for boys becomes blue As

a result in the treatment condition subjects should inflate the

frequency of green shirts relative to the truth sttreatmentgreengirls

gt greengirls (the same should happen to assessments of blueshirts for boys) We also expect the assessed frequency of greenshirts to go up relative to the control condition namely

sttreatmentgreengirls gt stcontrol

greengirls Critically the only factor that varies

across treatments is the representativeness of the 12-colorshirt Thus if we see differences across conditions the causalrole of representativeness-based recall in shaping group judg-ments is clear24

24 We vary which colors are used in which roles across participants Someparticipants saw this particular color distribution while others see for examplegreen as the modal color and purple as the diagnostic color for boys in theRepresentativeness condition and blue as the diagnostic color for girls in theRepresentativeness condition We vary the colors across the roles to avoid con-founding the characteristics of any particular color with its diagnosticity

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FIG

UR

EII

T-S

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tsE

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ent

Fig

ure

sap

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red

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lor

top

art

icip

an

tsin

the

exp

erim

ent

For

clari

ty

we

have

ad

ded

ale

tter

toea

chT

-sh

irt

toid

enti

fyth

eco

lor

for

the

read

er

lsquolsquoGrsquorsquo

ind

icate

sgre

en

lsquolsquoPrsquorsquo

ind

icate

sp

urp

le

lsquolsquoBrsquorsquo

ind

icate

sblu

eT

hes

ele

tter

sd

idn

otap

pea

rto

part

icip

an

tsan

dare

for

read

erre

fere

nce

only

P

lease

see

onli

ne

ver

sion

ofp

ubli

shed

art

icle

for

colo

rfi

gu

reex

act

lyas

itap

pea

red

top

art

icip

an

ts

STEREOTYPES 1779

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We collected data from 301 participants using this T-shirtsdesign25 Since the number of green and purple shirts is verysimilar we first ask each participant the simplest question ofwhich shirt color is modal Next we ask participants to assessthe share of green and purple shirts

Consistent with the role of representativeness participantsassigned to the Representativeness condition are 105 percentagepoints more likely to recall the less frequent color (green for girlsor blue for boys) as the modal color when it is representative of agroup (35 of participants guess the less frequent color is modalin the Control condition this proportion increases to 46 in theRepresentativeness condition p = 01 estimated from a probitregression reported in Online Appendix F)

We now turn to subjectsrsquo estimates of how many T-shirts ofeach color they saw in each group In both conditions the truedifference in counts is 1 (13 purple shirts 12 green or blue shirts)In the Control condition participants on average believe they saw054 more purple shirts than green or blue shirts In theRepresentativeness condition participants believe they saw072 fewer purple shirts than green or blue shirts (the acrosstreatment difference is significant with p = 01 from OLS regres-sion reported in Online Appendix F)

In total we collected data for six experiments of this generalstructure gathering evidence from more than 1000 participantsAs we describe in Online Appendix F although there is substan-tial variation across experiments when we pool all of the data wefind significant aggregate treatment effects in line with a role ofrepresentativeness in judgment We employ four different unor-dered types designs similar to the T-shirts experiment using sixsamples (four online and two in the laboratory) with 741 partic-ipants We find effects in the predicted direction for five of the sixsamples Using a probit regression that pools the data for theseunordered type experiments we find that participants are 93 per-centage points more likely to guess that the less frequent type ismodal when it is representative than when it is not (p = 002) Wealso run a family of ordered types experiments (two designs fivesamples 402 participants) Unlike the simpler T-shirts style

25 Throughout our analysis we exclude any participant who participated in aprevious version of the experiment and any participant who self-identified as color-blind In Online Appendix F we show that our results are unchanged if we includethese additional observations

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design the theoretical predictions for the ordered types designsare more sensitive to the specific assumptions one makes aboutthe weighting function of the DM26 We find effects in the pre-dicted direction for three of the five samples As we discuss inmore detail in Online Appendix F the ordered types resultsvary by platform with consistently stronger results on AmazonMechanical Turk than in the laboratory samples Pooling all or-dered types experiments participants are 93 percentage pointsmore likely to guess that the group of interest has a greater av-erage than the comparison group when the right tail is represen-tative (p = 062) Given our simple experimental setting withgroups of mundane objects we interpret our resultsmdasha signifi-cant and reasonably sized impact on average beliefsmdashas an im-portant proof of concept the presence of representative typesbiases ex post assessment

IVB Empirical Evidence on Political Stereotypes

We examine two data sets on political preferences and be-liefs about political preferences in the United States We inves-tigate the roles of representativeness and context dependence byseparately testing for hypotheses that allow us to assess the lead-ing theories of stereotypes

First we test whether beliefs are correct or depart systemat-ically from the truth The statistical discrimination approachbuilds on the assumption that people hold rational expectationsof group traits Comparing beliefs to the truth allows us to assessthe validity of this assumption in our data

Second we test if beliefs depart from the truth by exagger-ating (mean) differences among groups per the kernel of truthhypothesis This is an implicit test of context dependence be-cause it implies that beliefs about the target groups are shapednot only by that grouprsquos characteristics but also by those of thereference group27

Third we test if distortions in beliefs can be accounted for bythe overweighting of highly representative types (defined astypes that are relatively more frequent in the target relative to

26 This is due in part to our choice to not study MLRP distributions We moti-vate and discuss this design decision in Online Appendix F

27 Of course unlike in the laboratory experiment in this setting we cannot testfor context dependence by exogenously varying the reference group

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the reference group) The second and third tests address the keypredictions of our model

1 The Data We have two data sets on political preferences andbeliefs about political preferences The first data set from GrahamNosek and Haidt (GNH 2012) contains data from the MoralFoundations Questionnaire Respondents (1174 self-identified lib-erals and 500 self-identified conservatives) answer questions abouttheir position on a subset of 45 issues 20 moral relevance state-ments (eg lsquolsquowhen you decide whether something is right orwrong to what extent are the following considerations relevantto your thinkingrsquorsquo) and 25 moral judgments (eg lsquolsquoindicate theextent to which you would agree or disagreersquorsquo) For each issue arandomly determined subset of participants states their own posi-tion another subset states their belief on the position of a lsquolsquotypicalliberalrsquorsquo and a third subset states their belief on the position of alsquolsquotypical conservativersquorsquo The data thus include the distribution overpositions for both liberal and conservatives as well as the averagebelieved typical position of liberals and of conservatives on the 45issues Each position is elicited on 1ndash6 scale

The second data set comes from the American NationalElection Survey (ANES) and contains data from more than20000 respondents between 1964 and 201228 The surveycovers political issues of the day such as the optimal amount ofgovernment spending and service provision (1984ndash2000) or theplace of women in society (1972ndash1998) We focus on the 10 issuesthat ask participants to respond on a 1ndash7 scale (rather than justindicate binary agreement or disagreement) all 10 issues areasked in multiple years Participants are asked to provide theirown position on the scale and their believed position of theDemocratic and Republican parties (lsquolsquoWhere would you placethe Democratic [Republican] party on this scalersquorsquo) The data in-clude for each issue-year observation the distribution of partic-ipant positions for self-identified liberals and self-identifiedconservatives as well as the distribution of believed typical posi-tions of the Democratic and Republican parties

28 These data are publicly available at httpwwwelectionstudiesorgstudy-pagesanes_timeseries_cdfanes_timeseries_cdfhtm

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2 Empirical Strategy Our analysis focuses on beliefs abouttwo groups Conservatives and Liberals The types are the possi-ble positions for each issue (1 2 6 7) For the GNH data weinterpret beliefs about the lsquolsquotypicalrsquorsquo element of a group to coincidewith the believed average position in that group Similarly forthe ANES data we use the believed party positions as a proxy forbelieved mean of each group29 We then take as a benchmark thehypothesis that individuals hold accurate beliefs about eachgroup and in particular that believed mean position shouldequal true mean position at least on average across subjectsThe accurate beliefs hypothesis underlies the most common eco-nomic model of stereotyping statistical discrimination

To assess our representativeness-based model we perform aregression exercise To test our model in a linear regressionframework we rely on linear approximations of the weightingfunction Our model then yields two regression specifications

PROPOSITION 4 Let G 2 fconservative liberal g and assume

ht h tG

tG

be a differentiable and strictly increasing weight-

ing function as in Definition 2 The following hold as a first-order approximation around identical distributions G

Gfrac14 1

(i) Kernel of truth regression There exists a constant gt 0such that

EstethtjGTHORN frac14 EethtjGTHORNeth1thorn THORN EethtjGTHORNeth5THORN

(ii) Representativeness regression Denote H frac14 fT 2 Tg

the right tail of types and RconsH frac14

PHtconsPHtlib

as the average

representativeness of right tail types for conservatives

29 This assumption is consistent with the authorsrsquo interpretation of the GNHdata (GNH 2012) and with previous studies using ANES (eg Westfall et al 2015)Furthermore to the extent that this assumption holds equally well for most issueswithin a data set our focus on cross-issue differences should allow us to test thepredictions of our model even with an imperfect proxy for beliefs of mean positionsFinally the data provide some insight into whether subjects are reporting (per-ceived) modal or mean types As we show the modal type is a poor prediction ofstated beliefs while a distorted mean slanted toward representative types is anaccurate prediction of stated beliefs

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Under the further approximation where tcons

tlibampRcons

H for

t 2 H

EstethtjconsTHORN frac14 EethtjconsTHORN thorn consethR

consH 1THORNeth6THORN

EstethtjlibTHORN frac14 EethtjlibTHORN libethR

consH 1THORNeth7THORN

where lcons and llib are positive constants

The first regression allows us to test for the kernel of truthhypothesis and the second set of regressions allows us to test forthe role of representativeness

Equation (5) says that respondents in our model inflate theaverage position of a group say the conservatives if and only ifthe group has a higher average position than the other groupnamely the liberals Formally EstethtjconsTHORN gt EethtjconsTHORN if and onlyif EethtjconsTHORN gt EethtjlibTHORN Because in our measurement scale highertypes mean lsquolsquomore conservativersquorsquo we expect (i) believed conserva-tive average to be higher than the truth and (ii) the extent ofoverstatement to decrease in the average liberal position EethtjlibTHORNConversely we expect the average liberal position to be lowerthan the truth the more so the higher the average conservativeposition EethtjconsTHORN

As previously discussed the basis of these predictions is con-text dependence information about the distribution of ndashG is rel-evant for the beliefs about G This context dependence isinconsistent with rational expectations in which only thegrouprsquos own means should affect beliefs We test the hypothesisthat the true mean EethtjGTHORN is a significant predictor of the believedmean E

stethtjGTHORN with a positive sign and the other grouprsquos truemean EethtjGTHORN is a predictor of the believed mean with a negativesign

Equations (6) and (7) say that repondentsrsquo assessment bias isshaped by representativeness When the right tail is more repre-sentative for conservatives (Rcons

H 1 positive and large) partici-pants should inflate the average conservative position more(higher E

stethtjconsTHORN EethtjconsTHORN) and deflate the average liberal po-sition more (lower E

stethtjlibTHORN EethtjlibTHORN) We test the hypothesisthat the inflation in conservative positions is positively associatedwith the representativeness of the right tail for the conservativesand the inflation in liberal positions is negatively associated with

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it Once again the representativeness of the right tail is com-puted using the true distribution of positions

In equations (6) and (7) in many cases the representative tailis also the most likely one As a consequence these tests cannotdistinguish a representativeness-based from a likelihood-basedmodel of distorted beliefs We perform two additional testsFirst we run versions of equations (6) and (7) in which we controlfor the likelihood of tails (see Table A4 in Online Appendix G)Second we compute numerically the predictions of a representa-tiveness-based model of stereotypes and a likelihood-based modelof stereotypes We then assess which of these two is better able tomatch the data on beliefs

3 Empirical Results To begin we illustrate the structure ofthe data and the nature of our predictions with two simple exam-ples from the GNH data set focusing on beliefs about conserva-tives In example 1 participants are asked about their agreementwith the statement lsquolsquoIt can never be right to kill a human beingrsquorsquoIn example 2 participants are asked about the moral relevance oflsquolsquowhether or not someone cared for someone weak or vulnerablersquorsquoAs can be seen in Figure III in example 1 the modal position(strongly disagree (1)) and most representative positions(strongly disagree (1)) coincide for conservatives In contrast inexample 2 in Figure III the most representative types (slightlyrelevant (3) not at all relevant (1)) are not most likely for theconservative group Following Proposition 1 we predict that be-liefs will be distorted in the direction of the most representativetypes Thus we expect more exaggeration in example 2 than inexample 1 since in example 2 the most representative types (inthe left tail) are far from the modal type whereas in example 1they coincide This is what we find the conservative position isexaggerated by only 009 positions in Example 1 (true mean 299believed mean 290) but by 106 positions in Example 2 (truemean 421 believed mean 315)

In the full data sets we treat each (issue year) pair as anobservation and we cluster standard errors at the issue level Forthe GNH data we have 45 observations 45 issues measured inthe same year For the ANES data we have 66 observations 10issues measured in multiple years To begin we simply docu-ment systematic exaggeration in both data sets This is a primaryfocus of the original analysis in GNH (2012) and also in Westfall

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FIGURE III

Two Examples

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et al (2015)rsquos analysis of the ANES data30 Figure IV shows thatthe believed difference between typical conservative and typicalliberal positions is larger than the true difference in mean posi-tions for 109 of the 111 observations The data for both GNH(squares) and ANES (triangles) lie above the 45-degree line(dashed)31 Average exaggeration is 062 positions on the scale(066 in the GNH data 059 in the ANES data)32

The systematic and significant exaggeration of mean differ-ences suggests that the benchmark model of accurate beliefs ismissing something important Indeed this exaggeration reflectsthe fact that believed means are typically more extreme than truemeans First note that the kernel of truth regression (equation(5)) generates exaggeration of mean differences just as docu-mented in Figure IV

EstethtjGTHORN E

stethtjGTHORN frac14 eth1thorn 2THORN frac12EethtjGTHORN EethtjGTHORN

To bring this prediction to the data we regress the believedmean position for each group EBethtjGTHORN on the true mean of thegroup EethtjGTHORN and the true mean of the comparison groupEethtjGTHORN across issues We do this for each group (liberals con-servatives) in each data set separately We also present pooledspecifications that combine the data sets to make a prediction fora given group (liberals conservatives) In these pooled specifica-tions we include a dummy variable indicating whether theobservation came from the ANES data set For all specificationswe cluster observations at the issue level33 The results from re-gression are shown in Table I In every specification we find thatEethtjGTHORN is a significant predictor of EBethtjGTHORN with the predicted pos-itive sign Crucially for five of the six specifications the mean of

30 Chambers and Melnyk (2006) also find evidence of exaggeration of truedifferences in beliefs about political positions

31 For convenience we recode all issues so that the high end of the scale (67)represents the stereotypically more conservative position

32 A natural question to ask is how beliefs vary across liberals and conserva-tives That is do beliefs about a group G depend on membership in G versus ndashG Ourmodel does not speak to this issue However in Online Appendix G we show thatthe results we document below hold for both beliefs held by conservatives and be-liefs held by liberals see Tables A9 A10 and A11

33 In general the results presented below for the ANES data are not largelyimpacted by the decision to cluster at the issue level Similar results are obtained ifthe data are not clustered

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the comparison group EethtjGTHORN is also a significant predictor ofE

BethtjGTHORN with the predicted negative signAlthough these results provide strong evidence of context

dependence and are consistent with our model they do not pindown a role for representativeness of types Our next test relatesthe magnitude of representativeness of tail types to the magni-tude of belief distortions

To this end we implement the regressions in equations (6)and (7) Following Proposition 4 we compute the average repre-

sentativeness of tail types for conservatives RconsH frac14

PtT2tconsPtT2tlib

We

again test the hypothesis that RconsH is a significant predictor of Est

ethtjconsTHORN with a positive sign and a predictor of EstethtjlibTHORN with a

negative sign Table II shows that conditional on true mean RconsH

predicts believed mean for each group G as expected The firstthree specifications display the results for predicting beliefs heldabout conservatives In both data sets the average representa-tiveness of tail types for conservatives is a significant positivepredictor of beliefs held about conservatives The final three spe-cifications display the results for predicting beliefs held about

FIGURE IV

Exaggeration of Differences

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liberals We find that the average representativeness of tail typesfor conservatives is a negative predictor of beliefs held about lib-erals This effect is significant in the GNH data and marginallysignificant in the ANES data

We present several additional results in Online Appendix GTo further examine the role of representativeness in driving be-liefs we first show the results of Table II carry through when we

TABLE II

AVERAGE REPRESENTATIVENESS OF TAIL POSITIONS PREDICTS BELIEFS

OLS Predicting Believed Mean of Group G for Each Issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position

of group G for issue

078 024 051 072 018 041

(006) (008) (009) (005) (005) (010)

Avg rep of tail types for

conservatives RconsH

019 055 025 014 012 024

(007) (022) (008) (006) (007) (005)

Constant 101 260 184 093 271 201

(026) (045) (029) (022) (025) (032)

R2 082 048 060 091 031 070

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

TABLE I

INFORMATION ABOUT ndashG PREDICTS BELIEFS ABOUT G

OLS predicting believed mean of group G for each issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position of

conservatives for issue

102 098 096 021 019 025

(0097) (0133) (0076) (0060) (0116) (0060)

True mean position of

liberals for issue

035 086 058 0987 039 073

(0106) (0134) (0131) (0066) (0106) (0135)

Constant 151 335 235 069 258 156

(0195) (0269) (0279) (0122) (0249) (0270)

R2 083 053 066 092 032 068

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

STEREOTYPES 1789

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control for the average likelihood on the tail positions (see Table A4in Online Appendix G) Most tellingly we use the model to predictbeliefs across issues and compare those to the data For simplicitywe use the rank-based truncation specification to predict mean be-liefs when stereotypes include the d most representative types ford frac14 1 T We compare these predictions to those of a model inwhich beliefs are obtained by restricting the distribution to the dmost likely types Our benchmark for both models is predicting thebelieved mean from the entire distribution where d = T We showthat the predictions of the rank-based truncation model with d = 4or 5 compare favorably to both a likelihood-based truncation model(with any d) and the accurate beliefs benchmark Interestingly thisresult suggests that stereotypical beliefs are well approximated byneglecting the least representative types (as opposed to focusingonly on the most representative types) and so represent a moderatethough systematic departure from the standard benchmarkFinally we show that the results we document above hold forboth beliefs held by conservatives and beliefs held by liberals (seeTables A9 A10 and A11 in Online Appendix G)

V Conclusion

We present a model of stereotypical thinking in which DMsmaking predictions about a group overweight the grouprsquos mostdistinctive types These overweighted types are not the mostlikely ones given the DMrsquos data but the most representativeones in the sense of being the most diagnostic of the group rela-tive to other groups Representativeness implies that what ismost distinctive of a group depends on what group it is comparedwith We present experimental evidence that confirms this con-text dependence in recall-based assessments of groups Finallywe evaluated the predictions of the model using political data fromexisting large-scale surveys We find context dependence to be akey feature of beliefs Given the richness of the political data wecan go a step further and identify a role for representativeness inparticular As the representativeness of tail types increases beliefsof a group are distorted in the direction of that tail

Our approach provides a parsimonious and psychologicallyfounded account of how DMs generate simplified representationsof reality from social groups to stock returns and offers a unifiedaccount of disparate pieces of evidence relating to this type of

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uncertainty The model captures the central fact that stereotypeshighlight the greatest difference between groups thus explainingwhy some stereotypes are very accurate while others lack valid-ity Still stereotypes often have a kernel of truth when they arebased on systematicmdasheven if smallmdashdifferences between groupsThis logic allows us to describe a number of heuristics and psy-chological biases many of which arise in the context of predictionproblems Generically our model generates overreaction to diag-nostic information

Our model is based on representativeness and does not cap-ture all the features of stereotypical thinking However it cap-tures perhaps the central feature when we think of a group wefocus on what is most distinctive about it and neglect or under-weight the rest

Saeuroıd Business School University of Oxford

Ohio State University and Harvard Business School

Universita Bocconi and Innocenzo Gasparini Institute

for Economic Research

Harvard University

Supplementary Material

An Online Appendix for this article can be found at QJEonline (qjeoxfordjournalorg)

References

Adorno Theodor Else Frenkel-Brunswik Daniel Levinson and Nevitt SanfordThe Authoritarian Personality (New York Harper amp Row 1950)

Arrow Kenneth lsquolsquoThe Theory of Discriminationrsquorsquo in Discrimination in LaborMarkets Orley Ashenfelter and Albert Rees eds (Princeton NJPrinceton University Press 1973)

Ashton Michael and Victoria Esses lsquolsquoStereotype Accuracy Estimating theAcademic Performance of Ethnic Groupsrsquorsquo Personality and SocialPsychology Bulletin 25 (1999) 225ndash236

Barberis Nicholas Andrei Shleifer and Robert Vishny lsquolsquoA Model of InvestorSentimentrsquorsquo Journal of Financial Economics 49 (1998) 307ndash343

Bayer Sylvia lsquolsquoThe Accuracy of Academic Gender Stereotypesrsquorsquo Sex Roles 40(1999) 787ndash813

Benjamin Dan James Choi and Joshua Strickland lsquolsquoSocial Identity andPreferencesrsquorsquo American Economic Review 100 (2010) 1913ndash1928

Benjamin Dan Matthew Rabin and Collin Raymond lsquolsquoA Model of Non-Belief inthe Law of Large Numbersrsquorsquo Journal of the European Economic Association15 (2015) 515ndash544

Bertrand Marianne lsquolsquoNew Perspectives on Genderrsquorsquo Handbook of LaborEconomics 4 (2011) 1543ndash1590

Bodoh-Creed Aaron Dan Benjamin and Matthew Rabin lsquolsquoThe Dynamics of Base-Rate Neglectrsquorsquo mimeo Haas Business School 2013

STEREOTYPES 1791

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ibrary on October 28 2016

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ownloaded from

Bohnet Iris Alexandra van Geen and Max Bazerman lsquolsquoWhen PerformanceTrumps Gender Bias Joint versus Separate Evaluationrsquorsquo ManagementScience 5 (2016) 1225ndash1234

Bordalo Pedro Nicola Gennaioli and Andrei Shleifer lsquolsquoSalience Theory of Choiceunder Riskrsquorsquo Quarterly Journal of Economics 127 (2012) 1243ndash1285

mdashmdashmdash lsquolsquoSalience and Consumer Choicersquorsquo Journal of Political Economy 121(2013) 803ndash843

Briton Nancy and Judith Hall lsquolsquoBeliefs about Female and Male NonverbalCommunicationrsquorsquo Sex Roles 32 (1995) 79ndash90

Buser Thomas Muriel Niederle and Hessel Oosterbeek lsquolsquoGenderCompetitiveness and Career Choicesrsquorsquo Quarterly Journal of Economics 129(2014) 1409ndash1447

Carrell Scott Marianne Page and James West lsquolsquoSex and Science How ProfessorGender Perpetuates the Gender Gaprsquorsquo Quarterly Journal of Economics 125(2010) 1101ndash1144

Chambers John and Darya Melnyk lsquolsquoWhy Do I Hate Thee ConflictMisperceptions and Intergroup Mistrustrsquorsquo Personality and SocialPsychology Bulletin 32 (2006) 1295ndash1311

Chan Wayne Robert R McCrae Filip De Fruyt Lee Jussim CorinnaE Lockenhoff Marleen De Bolle Paul T Costa Jr Angelina R SutinAnu Realo Juri Allik Katsuharu Nakazato Yoshiko ShimonakaMartina Hrebıckova Sylvie Graf Michelle Yik Marina Brunner-SciarraNora Leibovich De Figueora Vanina Schmidt Chang-kyo Ahn Hyun-nie Ahn Maria E Aguilar-Vafaie Jerzy Siuta Barbara SzmigielskaThomas R Cain Janet T Crawford Khairul Anwar Mastor Jean-Pierre Rolland Florence Nansubuga Daniel R MiramontezVeronica Benet-Martınez Jerome Rossier Denis Bratko Iris MarusicJamin Halberstadt Mami Yamaguchi Goran Knezevic Thomas A MartinMirona Gheorghiu Peter B Smith Claudio Barbaranelli Lei WangJane Shakespeare-Finch Margarida P Lima Waldemar KlinkoszAndrzej Sekowski Lidia Alcalay Franco Simonetti Tatyana V AvdeyevaV S Pramila and Antonio Terracciano lsquolsquoStereotypes of Age Differences inPersonality Traits Universal and Accuratersquorsquo Journal of Personality andSocial Psychology 103 (2012) 1050ndash1066

Chen Yan Sherry Xin Liu Tracy Xiao and Margaret Shih lsquolsquoWhich Hat to WearImpact of Natural Identities on Coordination and Cooperationrsquorsquo Games andEconomic Behavior 84 (2014) 58ndash86

Coffman Katherine lsquolsquoEvidence on Self-Stereotyping and the Contribution ofIdeasrsquorsquo Quarterly Journal of Economics 129 (2014) 1625ndash1660

Cunningham Tom lsquolsquoComparisons and Choicersquorsquo mimeo Stockholm University2013

Diekman Amanda Alice Eagly and Patrick Kulesa lsquolsquoAccuracy and Bias in theStereotypes about the Social and Political Attitudes of Women and MenrsquorsquoJournal of Experimental Social Psychology 38 (2002) 268ndash282

Eccles Jacquelynne S Janis E Jacobs and Rena D Harold lsquolsquoGender RoleStereotypes Expectancy Effects and Parentsrsquo Socialization of GenderDifferencesrsquorsquo Journal of Social Issues 46 (1990) 183ndash201

Fryer Roland and Matthew Jackson lsquolsquoA Categorical Model of Cognition andBiased Decision-Makingrsquorsquo BE Journal of Theoretical Economics 8 (2008)1ndash42

Fryer Roland and Steven Levitt lsquolsquoAn Empirical Analysis of the Gender Gap inMathematicsrsquorsquo American Economic Journal Applied Economics 2 (2010)210ndash240

Gennaioli Nicola and Andrei Shleifer lsquolsquoWhat Comes to Mindrsquorsquo Quarterly Journalof Economics 125 (2010) 1399ndash1433

Gennaioli Nicola Andrei Shleifer and Robert Vishny lsquolsquoNeglected RisksFinancial Innovation and Financial Fragilityrsquorsquo Journal of FinancialEconomics 104 (2012) 452ndash468

Gilens Martin lsquolsquoRace and Poverty in America Public Misperceptions and theAmerican News Mediarsquorsquo Public Opinion Quarterly 60 (1996) 515ndash541

Glaeser Edward lsquolsquoThe Political Economy of Hatredrsquorsquo Quarterly Journal ofEconomics 120 (2005) 45ndash86

QUARTERLY JOURNAL OF ECONOMICS1792

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

Glover Dyland Amanda Pallais and William Pariente lsquolsquoDiscrimination as a Self-Fulfilling Prophecy Evidence from French Grocery Storesrsquorsquo mimeo HarvardUniversity 2015

Goldin Claudia Lawrence Katz and Ilyana Kuziemko lsquolsquoThe Homecoming ofAmerican College Women The Reversal of the College Gender GaprsquorsquoJournal of Economic Perspectives 20 (2006) 133ndash156

Graham Jesse Brian Nosek and Jonathan Haidt lsquolsquoThe Moral Stereotypes ofLiberals and Conservatives Exaggeration of Differences across thePolitical Spectrumrsquorsquo PLoS One 7 (2012) 1ndash13

Grether David lsquolsquoBayes Rule as a Descriptive Model The RepresentativenessHeuristicrsquorsquo Quarterly Journal of Economics 95 (1980) 537ndash557

Griffin Dale and Amos Tversky lsquolsquoThe Weighing of Evidence and theDeterminants of Confidencersquorsquo Cognitive Psychology 24 (1992) 411ndash435

Guiso Luigi Ferdinando Monte Paola Sapienza and Luigi Zingales lsquolsquoCultureGender and Mathrsquorsquo Science 320 (2008) 1164ndash1165

Hilton James and William Von Hippel lsquolsquoStereotypesrsquorsquo Annual Review ofPsychology 47 (1996) 237ndash271

Hyde Janet Sara Lindberg Marcia Linn Amy Ellis and Caroline WilliamslsquolsquoGender Similarities Characterize Math Performancersquorsquo Science 321 (2008)494ndash495

Judd Charles and Bernardette Park lsquolsquoDefinition and Assessment of Accuracy inSocial Stereotypesrsquorsquo Psychological Review 100 (1993) 109ndash128

Jussim Lee Jarret Crawford Stephanie Anglin John Chambers Sean Stevensand Florette Cohen lsquolsquoStereotype Accuracy One of the Largest and MostReplicable Effects in All of Social Psychologyrsquorsquo in The Handbook ofPrejudice Stereotyping and Discrimination Todd Nelson ed (MahwahNJ Lawrence Erlbaum 2015)

Kahneman Daniel and Amos Tversky lsquolsquoSubjective Probability A Judgment ofRepresentativenessrsquorsquo Cognitive Psychology 3 (1972) 430ndash454

mdashmdashmdash lsquolsquoOn the Psychology of Predictionrsquorsquo Psychological Review 80 (1973) 237ndash251

Kaplowitz Stan Bradley Fisher and Clifford Broman lsquolsquoHow Accurate ArePerceptions of Social Statistics about Blacks and Whitesrsquorsquo Public OpinionQuarterly 67 (2003) 237ndash243

Kersten Daniel Pascal Mamassian and Alan Yuille lsquolsquoObject Perception asBayesian Inferencersquorsquo Annual Review of Psychology 55 (2004) 271ndash304

Klein Richard Kate A Ratliff Michelangelo Vianello Reginald B Adams JrStepan Bahnik Michael J Bernstein Konrad Bocian Mark J BrandtBeach Brooks Claudia Chloe Brumbaugh Zeynep CemalcilarJesse Chandler Winnee Cheong William E Davis Thierry DevosMatthew Eisner Natalia Frankowska David Furrow Elisa Maria GallianiFred Hasselman Joshua A Hicks James F Hovermale S Jane HuntJeffrey R Huntsinger Hans IJzerman Melissa-Sue John Jennifer A Joy-Gaba Heather Barry Kappes Lacy E Krueger Jaime Kurtz CarmelA Levitan Robyn Mallett Wendy L Morris Anthony J Nelson JasonA Nier Grant Packard Ronaldo Pilati Abraham M RutchickKathleen Schmidt Jeanine L Skorinko Robert Smith Troy G SteinerJustin Storbeck Lyn M Van Swol Donna Thompson Anna van rsquot VeerLeigh Ann Vaughn Marek Vranka Aaron Wichman Julie A Woodzickaand Brian A Nosek lsquolsquoInvestigating Variation in Replicability A ManyLabs Replication Projectrsquorsquo Social Psychology 45 (2014) 142ndash152

Lundberg Shelly and Richard Startz lsquolsquoPrivate Discrimination and SocialIntervention in Competitive Labor Marketsrsquorsquo American Economic Review73 (1983) 340ndash347

Madon Stephanie Max Guyll Kathy Aboufadel Eulices Montiel Alison SmithPolly Palumbo and Lee Jussim lsquolsquoEthnic and National Stereotypes ThePrinceton Trilogy Revisited and Revisedrsquorsquo Personality and SocialPsychological Bulletin 27 (2001) 996ndash1010

Martin Carol lsquolsquoA Ratio Measure of Sex Stereotypingrsquorsquo Journal of Personality andSocial Psychology 52 (1987) 489ndash499

STEREOTYPES 1793

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

McCauley Clark Krishna Thangavelu and Paul Rozin lsquolsquoSex Stereotyping ofOccupations in Relation to Television Representations and Census FactsrsquorsquoBasic and Applied Social Psychology 9 (1988) 197ndash212

Mullainathan Sendhil lsquolsquoThinking through Categoriesrsquorsquo mimeo HarvardUniversity 2002

Ortoleva Pietro and Erik Snowberg lsquolsquoOverconfidence in Political BehaviorrsquorsquoAmerican Economic Review 105 (2015) 504ndash535

Phelps Edmund lsquolsquoThe Statistical Theory of Racism and Sexismrsquorsquo AmericanEconomic Review 62 (1972) 659ndash661

Pope Devin and Justin Sydnor lsquolsquoGeographic Variation in the Gender Differencesin Test Scoresrsquorsquo Journal of Economic Perspectives 24 (2010) 95ndash108

Rabin Matthew lsquolsquoInference by Believers in the Law of Small NumbersrsquorsquoQuarterly Journal of Economics 117 (2002) 775ndash816

Rabin Matthew and Joel Schrag lsquolsquoFirst Impressions Matter A Model ofConfirmatory Biasrsquorsquo Quarterly Journal of Economics 114 (1999) 37ndash82

Rabin Matthew and Dimitri Vayanos lsquolsquoThe Gamblerrsquos and Hot-Hand FallaciesTheory and Applicationsrsquorsquo Review of Economic Studies 77 (2010) 730ndash778

Reuben Ernesto Paola Sapienza and Luigi Zingales lsquolsquoHow Stereotypes ImpairWomenrsquos Careers in Sciencersquorsquo Proceedings of the National Academy ofSciences 111 (2014) 4403ndash4408

Rosch Eleanor lsquolsquoNatural Categoriesrsquorsquo Cognitive Psychology 4 (1973) 328ndash350Ryan Carey S lsquolsquoAccuracy of Black and White College Studentsrsquo In-Group and

Out-Group Stereotypesrsquorsquo Personality and Social Psychology Bulletin 22(1996) 1114ndash1127

Schneider David The Psychology of Stereotyping (New York Guilford Press2004)

Schneider David Albert Hastorf and Phoebe Ellsworth Person Perception(Reading MA Addison-Wesley 1979)

Shih Margaret Todd Pittinsky and Nalini Ambady lsquolsquoStereotype SusceptibilityIdentity Salience and Shifts in Quantitative Performancersquorsquo PsychologicalScience 10 (1999) 80ndash83

Shih Margaret Todd Pittinsky and Amy Trahan lsquolsquoDomain-Specific Effects ofStereotypes on Performancersquorsquo Self and Identity 5 (2006) 1ndash14

Steele Claude Whistling Vivaldi How Stereotypes Affect Us and What We CanDo (New York Norton 2010)

Tenenbaum Joshua and Thomas Griffiths lsquolsquoThe Rational Basis ofRepresentativenessrsquorsquo 23rd Annual Conference of the Cognitive ScienceSociety (2001) 1036ndash1041

Tversky Amos and Daniel Kahneman lsquolsquoExtensional versus Intuitive ReasoningThe Conjunction Fallacy in Probability Judgmentrsquorsquo Psychological Review 90(1983) 293ndash315

Weinberger Catherin lsquolsquoIs the Science and Engineering Workforce Drawn fromthe Far Upper Tail of the Math Ability Distributionrsquorsquo mimeo UCSB 2005

Westfall Jacob Leaf Van Boven John Chambers and Charles Judd lsquolsquoPerceivingPolitical Polarization in the United States Party Identity Strength andAttitude Extremity Exacerbate the Perceived Partisan DividersquorsquoPsychological Science 10 (2015) 145ndash158

Wolsko Christopher Bernadette Park Charles Judd and Bernd WittenbrinklsquolsquoFraming Interethnic Ideology Effects of Multicultural and Color-BlindPerspectives on Judgments of Groups and Individualsrsquorsquo Journal ofPersonality and Social Psychology 78 (2000) 635ndash654

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Page 23: I. Introduction · uneducated at the beginning of the 20th century, and as high achievers at the beginning of the 21st (Madon et al. 2001). Social science has produced three broad

tested positive This analysis formalizes Tversky andKahnemanrsquos (1983) verbal account of base rate neglect23

The same mechanism may underlie several other instanceswhere DMs overweight diagnostic information When assessingan employeersquos skill level an employer attributes high perfor-mance to high skill because high performance is the distinctivemark of a talented employee Because he neglects the possibilitythat some talented employees perform poorly and that somenontalented ones perform well (perhaps due to stochasticity inthe environment) the employer has too much faith in skill andneglects the role of luck in accounting for the output Similarlywhen assessing the performance of firms in a hot sector of theeconomy (eg G = internet) an investor recalls highly successfulfirms in that sector (t = return of Google Amazon etc) He ne-glects the possibility of firms being unsuccessful because lack ofsuccess is statistically nondiagnostic and psychologically nonrep-resentative of a growing sectormdasheven if it is likely This causesexcessive optimism (in that the expectation of growth is unrea-sonably high) and overconfidence (in that the variability in earn-ings growth considered possible is truncated) True the hot sectormay have better growth opportunities on average but represen-tativeness exaggerates this feature and induces the investor toneglect a significant risk of failure

IV Evidence on Representativeness and Stereotypes

Testing our model requires evaluating the beliefs individualshold about a target group against the true distribution of thattarget group over an attribute space An ideal data set would

23 Our account is distinct from a mechanical underweighting of base rates inBayes rule as in Grether (1980) and Bodoh-Creed Benjamin and Rabin (2013) Inthose models upon receiving the test results the DM can update his beliefs in thewrong direction he can be less confident that a person is healthy after a negativetest than under his prior which cannot happen in our model Although this predic-tion of our model seems consistent with introspection we are not aware of experi-mental evidence on this point Griffin and Tversky (1992) present evidenceconsistent with pure neglect of base rates but in a significantly different tasknamely inferring the bias of a coin from a history of coin flips Such experimentsare hard to compare with the predictions of our model because subjects are asked togenerate distributions of different numbers of coin flips in their minds which is amuch more involved task than to recall types of a given distribution Their assess-ments then might be wrong for other reasons See Bodoh-Creed Benjamin andRabin (2013) for a detailed discussion

STEREOTYPES 1775

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consist of naturally defined groups with known distributions overa given space of types and a corresponding set of beliefs about thedistribution of each group over that space of types This wouldallow us to test for exaggeration of true differences betweengroups and to ask whether this exaggeration is well predictedby overweighting representative types To identify a causal rolefor representativeness or context dependence we would need ex-ogenous variation in either the comparison group ndashG or in thedistributions over the type spaces This is unavailable in existingdata sets Accordingly we take a two-pronged approach First wecreate a controlled laboratory environment that allows us toinduce the exogenous variation in representative types that weneed to test causality then we reanalyze existing field evidence tocheck for consistency with our predictions

In testing our model we focus on the two main implicationsof representativeness-based stereotypes

Context dependence the stereotype of a target group de-pends on the characteristics of the reference group it iscompared to

Kernel of truth stereotypes depend on group character-istics andmdashin most (precisely characterized) settingsmdashare slanted toward representative types

We test the first property with a lab experiment (SectionIVA) We then turn to survey data on beliefs about US politicalgroups (Section IVB) for an empirical analysis that explores thesecond property The survey data are more tightly linked to ourinterest in social stereotypes The laboratory experiment allowsus to directly test the role of representativeness in generatingcontext dependent beliefs Online Appendixes F and G provideall details and additional results for the experiments and fieldevidence

IVA Lab Evidence on Representativeness and ContextDependence

The influence of the representativeness heuristic on recalland on beliefs has been extensively documented in the lab(Kahneman and Tversky 1972 1973) Our goal is to considerhow representativeness as formalized in equation (2) gives riseto context-dependent beliefs To our knowledge the possibility

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that representativeness may generate context dependence hasnot been tested before

To assess this prediction we perform a controlled laboratoryexperiment that allows us to isolate representativeness frommany confounding factorsmdashhistorical sociological or other-wisemdashthat may affect stereotype formation in the real worldWe construct our own groups of ordinary objects creating atarget group G and a comparison group ndashG We hold thetarget group G fixed and explore how participant impressions ofit change as we change the comparison group ndashG and thusrepresentativeness

We conducted several experiments in the laboratory and onAmazon Mechanical Turk Each involves a basic three-stepdesign First participants are shown the target group and a ran-domly assigned comparison group for 15 seconds In this timedifferences between groups can be noticed but the groupsrsquo precisecompositions cannot be memorized The second step consists of afew filler questions which briefly draw the participantsrsquo cognitivebandwidth away from their observation Finally participants areasked to assess the groups they saw Participants are incentiv-ized to provide accurate answers

We randomly assign participants to either the Control or theRepresentativeness condition In the Control condition G and ndashGhave nearly identical distributions so that all types are similarlyrepresentative for each group In the Representativeness condi-tion ndashG is changed in such a way that a certain type becomes veryrepresentative for G Context dependence implies that the assess-ment of G should now overweight this representative type eventhough the distribution of G itself has not changed

We ran six experiments of this form with design changesfocused on reducing participant confusion and removing con-founds We describe the final and most refined version of theseexperiments here In an attempt to provide a overview of the re-sults while remaining concise we provide the results from pooledspecifications that use all data collected In Online Appendix Fwe offer additional details and report all experiments conductedWe also give instructions and materials for each experiment thefull data set is available by request

Consider first the experiment illustrated in Figure II Agroup of 25 cartoon girls is presented next to a group of 25 cartoonboys in T-shirts of different colors blue green or purple In theControl condition (Figure II Panel a) the groups have identical

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color distributions (13 purple 12 green) so no color is represen-tative of either group The Representativeness condition (Panel b)compares the same group of girls with a different group of boysfor whom green shirts are replaced with blue shirts Now onlygirls wear green and only boys wear blue These colors althoughstill not the most frequent for either group are now most repre-sentative For each group girls and boys participants are asked anumber of questions concerning the frequency of T-shirts of dif-ferent colors worn by that group

Applying our model in the control condition the type space isT frac14 fgreen purpleg and the groups are G = girls and ndashG = boysGiven that the color distributions are identical across groups both

types are equally representativegreengirls

greenboysfrac14 1 frac14

purplegirls

purpleboys As a result

assessment of G should be correct on average stcontrolgreengirls frac14 greengirls

and stcontrolpurplegirls frac14 purplegirls for any weighing function (the same is

true about assessments of ndashG)In the treatment condition the distribution of shirt colors re-

mains the same for girls For boys green shirts are changed intoblue Thus the type space changes to T frac14 fgreen purple bluegand the representative color for girls becomes greengreengirls

greenboysfrac14 1 gt 1 frac14

purplegirls

purpleboys while that for boys becomes blue As

a result in the treatment condition subjects should inflate the

frequency of green shirts relative to the truth sttreatmentgreengirls

gt greengirls (the same should happen to assessments of blueshirts for boys) We also expect the assessed frequency of greenshirts to go up relative to the control condition namely

sttreatmentgreengirls gt stcontrol

greengirls Critically the only factor that varies

across treatments is the representativeness of the 12-colorshirt Thus if we see differences across conditions the causalrole of representativeness-based recall in shaping group judg-ments is clear24

24 We vary which colors are used in which roles across participants Someparticipants saw this particular color distribution while others see for examplegreen as the modal color and purple as the diagnostic color for boys in theRepresentativeness condition and blue as the diagnostic color for girls in theRepresentativeness condition We vary the colors across the roles to avoid con-founding the characteristics of any particular color with its diagnosticity

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FIG

UR

EII

T-S

hir

tsE

xp

erim

ent

Fig

ure

sap

pea

red

inco

lor

top

art

icip

an

tsin

the

exp

erim

ent

For

clari

ty

we

have

ad

ded

ale

tter

toea

chT

-sh

irt

toid

enti

fyth

eco

lor

for

the

read

er

lsquolsquoGrsquorsquo

ind

icate

sgre

en

lsquolsquoPrsquorsquo

ind

icate

sp

urp

le

lsquolsquoBrsquorsquo

ind

icate

sblu

eT

hes

ele

tter

sd

idn

otap

pea

rto

part

icip

an

tsan

dare

for

read

erre

fere

nce

only

P

lease

see

onli

ne

ver

sion

ofp

ubli

shed

art

icle

for

colo

rfi

gu

reex

act

lyas

itap

pea

red

top

art

icip

an

ts

STEREOTYPES 1779

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We collected data from 301 participants using this T-shirtsdesign25 Since the number of green and purple shirts is verysimilar we first ask each participant the simplest question ofwhich shirt color is modal Next we ask participants to assessthe share of green and purple shirts

Consistent with the role of representativeness participantsassigned to the Representativeness condition are 105 percentagepoints more likely to recall the less frequent color (green for girlsor blue for boys) as the modal color when it is representative of agroup (35 of participants guess the less frequent color is modalin the Control condition this proportion increases to 46 in theRepresentativeness condition p = 01 estimated from a probitregression reported in Online Appendix F)

We now turn to subjectsrsquo estimates of how many T-shirts ofeach color they saw in each group In both conditions the truedifference in counts is 1 (13 purple shirts 12 green or blue shirts)In the Control condition participants on average believe they saw054 more purple shirts than green or blue shirts In theRepresentativeness condition participants believe they saw072 fewer purple shirts than green or blue shirts (the acrosstreatment difference is significant with p = 01 from OLS regres-sion reported in Online Appendix F)

In total we collected data for six experiments of this generalstructure gathering evidence from more than 1000 participantsAs we describe in Online Appendix F although there is substan-tial variation across experiments when we pool all of the data wefind significant aggregate treatment effects in line with a role ofrepresentativeness in judgment We employ four different unor-dered types designs similar to the T-shirts experiment using sixsamples (four online and two in the laboratory) with 741 partic-ipants We find effects in the predicted direction for five of the sixsamples Using a probit regression that pools the data for theseunordered type experiments we find that participants are 93 per-centage points more likely to guess that the less frequent type ismodal when it is representative than when it is not (p = 002) Wealso run a family of ordered types experiments (two designs fivesamples 402 participants) Unlike the simpler T-shirts style

25 Throughout our analysis we exclude any participant who participated in aprevious version of the experiment and any participant who self-identified as color-blind In Online Appendix F we show that our results are unchanged if we includethese additional observations

QUARTERLY JOURNAL OF ECONOMICS1780

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design the theoretical predictions for the ordered types designsare more sensitive to the specific assumptions one makes aboutthe weighting function of the DM26 We find effects in the pre-dicted direction for three of the five samples As we discuss inmore detail in Online Appendix F the ordered types resultsvary by platform with consistently stronger results on AmazonMechanical Turk than in the laboratory samples Pooling all or-dered types experiments participants are 93 percentage pointsmore likely to guess that the group of interest has a greater av-erage than the comparison group when the right tail is represen-tative (p = 062) Given our simple experimental setting withgroups of mundane objects we interpret our resultsmdasha signifi-cant and reasonably sized impact on average beliefsmdashas an im-portant proof of concept the presence of representative typesbiases ex post assessment

IVB Empirical Evidence on Political Stereotypes

We examine two data sets on political preferences and be-liefs about political preferences in the United States We inves-tigate the roles of representativeness and context dependence byseparately testing for hypotheses that allow us to assess the lead-ing theories of stereotypes

First we test whether beliefs are correct or depart systemat-ically from the truth The statistical discrimination approachbuilds on the assumption that people hold rational expectationsof group traits Comparing beliefs to the truth allows us to assessthe validity of this assumption in our data

Second we test if beliefs depart from the truth by exagger-ating (mean) differences among groups per the kernel of truthhypothesis This is an implicit test of context dependence be-cause it implies that beliefs about the target groups are shapednot only by that grouprsquos characteristics but also by those of thereference group27

Third we test if distortions in beliefs can be accounted for bythe overweighting of highly representative types (defined astypes that are relatively more frequent in the target relative to

26 This is due in part to our choice to not study MLRP distributions We moti-vate and discuss this design decision in Online Appendix F

27 Of course unlike in the laboratory experiment in this setting we cannot testfor context dependence by exogenously varying the reference group

STEREOTYPES 1781

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the reference group) The second and third tests address the keypredictions of our model

1 The Data We have two data sets on political preferences andbeliefs about political preferences The first data set from GrahamNosek and Haidt (GNH 2012) contains data from the MoralFoundations Questionnaire Respondents (1174 self-identified lib-erals and 500 self-identified conservatives) answer questions abouttheir position on a subset of 45 issues 20 moral relevance state-ments (eg lsquolsquowhen you decide whether something is right orwrong to what extent are the following considerations relevantto your thinkingrsquorsquo) and 25 moral judgments (eg lsquolsquoindicate theextent to which you would agree or disagreersquorsquo) For each issue arandomly determined subset of participants states their own posi-tion another subset states their belief on the position of a lsquolsquotypicalliberalrsquorsquo and a third subset states their belief on the position of alsquolsquotypical conservativersquorsquo The data thus include the distribution overpositions for both liberal and conservatives as well as the averagebelieved typical position of liberals and of conservatives on the 45issues Each position is elicited on 1ndash6 scale

The second data set comes from the American NationalElection Survey (ANES) and contains data from more than20000 respondents between 1964 and 201228 The surveycovers political issues of the day such as the optimal amount ofgovernment spending and service provision (1984ndash2000) or theplace of women in society (1972ndash1998) We focus on the 10 issuesthat ask participants to respond on a 1ndash7 scale (rather than justindicate binary agreement or disagreement) all 10 issues areasked in multiple years Participants are asked to provide theirown position on the scale and their believed position of theDemocratic and Republican parties (lsquolsquoWhere would you placethe Democratic [Republican] party on this scalersquorsquo) The data in-clude for each issue-year observation the distribution of partic-ipant positions for self-identified liberals and self-identifiedconservatives as well as the distribution of believed typical posi-tions of the Democratic and Republican parties

28 These data are publicly available at httpwwwelectionstudiesorgstudy-pagesanes_timeseries_cdfanes_timeseries_cdfhtm

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2 Empirical Strategy Our analysis focuses on beliefs abouttwo groups Conservatives and Liberals The types are the possi-ble positions for each issue (1 2 6 7) For the GNH data weinterpret beliefs about the lsquolsquotypicalrsquorsquo element of a group to coincidewith the believed average position in that group Similarly forthe ANES data we use the believed party positions as a proxy forbelieved mean of each group29 We then take as a benchmark thehypothesis that individuals hold accurate beliefs about eachgroup and in particular that believed mean position shouldequal true mean position at least on average across subjectsThe accurate beliefs hypothesis underlies the most common eco-nomic model of stereotyping statistical discrimination

To assess our representativeness-based model we perform aregression exercise To test our model in a linear regressionframework we rely on linear approximations of the weightingfunction Our model then yields two regression specifications

PROPOSITION 4 Let G 2 fconservative liberal g and assume

ht h tG

tG

be a differentiable and strictly increasing weight-

ing function as in Definition 2 The following hold as a first-order approximation around identical distributions G

Gfrac14 1

(i) Kernel of truth regression There exists a constant gt 0such that

EstethtjGTHORN frac14 EethtjGTHORNeth1thorn THORN EethtjGTHORNeth5THORN

(ii) Representativeness regression Denote H frac14 fT 2 Tg

the right tail of types and RconsH frac14

PHtconsPHtlib

as the average

representativeness of right tail types for conservatives

29 This assumption is consistent with the authorsrsquo interpretation of the GNHdata (GNH 2012) and with previous studies using ANES (eg Westfall et al 2015)Furthermore to the extent that this assumption holds equally well for most issueswithin a data set our focus on cross-issue differences should allow us to test thepredictions of our model even with an imperfect proxy for beliefs of mean positionsFinally the data provide some insight into whether subjects are reporting (per-ceived) modal or mean types As we show the modal type is a poor prediction ofstated beliefs while a distorted mean slanted toward representative types is anaccurate prediction of stated beliefs

STEREOTYPES 1783

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Under the further approximation where tcons

tlibampRcons

H for

t 2 H

EstethtjconsTHORN frac14 EethtjconsTHORN thorn consethR

consH 1THORNeth6THORN

EstethtjlibTHORN frac14 EethtjlibTHORN libethR

consH 1THORNeth7THORN

where lcons and llib are positive constants

The first regression allows us to test for the kernel of truthhypothesis and the second set of regressions allows us to test forthe role of representativeness

Equation (5) says that respondents in our model inflate theaverage position of a group say the conservatives if and only ifthe group has a higher average position than the other groupnamely the liberals Formally EstethtjconsTHORN gt EethtjconsTHORN if and onlyif EethtjconsTHORN gt EethtjlibTHORN Because in our measurement scale highertypes mean lsquolsquomore conservativersquorsquo we expect (i) believed conserva-tive average to be higher than the truth and (ii) the extent ofoverstatement to decrease in the average liberal position EethtjlibTHORNConversely we expect the average liberal position to be lowerthan the truth the more so the higher the average conservativeposition EethtjconsTHORN

As previously discussed the basis of these predictions is con-text dependence information about the distribution of ndashG is rel-evant for the beliefs about G This context dependence isinconsistent with rational expectations in which only thegrouprsquos own means should affect beliefs We test the hypothesisthat the true mean EethtjGTHORN is a significant predictor of the believedmean E

stethtjGTHORN with a positive sign and the other grouprsquos truemean EethtjGTHORN is a predictor of the believed mean with a negativesign

Equations (6) and (7) say that repondentsrsquo assessment bias isshaped by representativeness When the right tail is more repre-sentative for conservatives (Rcons

H 1 positive and large) partici-pants should inflate the average conservative position more(higher E

stethtjconsTHORN EethtjconsTHORN) and deflate the average liberal po-sition more (lower E

stethtjlibTHORN EethtjlibTHORN) We test the hypothesisthat the inflation in conservative positions is positively associatedwith the representativeness of the right tail for the conservativesand the inflation in liberal positions is negatively associated with

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it Once again the representativeness of the right tail is com-puted using the true distribution of positions

In equations (6) and (7) in many cases the representative tailis also the most likely one As a consequence these tests cannotdistinguish a representativeness-based from a likelihood-basedmodel of distorted beliefs We perform two additional testsFirst we run versions of equations (6) and (7) in which we controlfor the likelihood of tails (see Table A4 in Online Appendix G)Second we compute numerically the predictions of a representa-tiveness-based model of stereotypes and a likelihood-based modelof stereotypes We then assess which of these two is better able tomatch the data on beliefs

3 Empirical Results To begin we illustrate the structure ofthe data and the nature of our predictions with two simple exam-ples from the GNH data set focusing on beliefs about conserva-tives In example 1 participants are asked about their agreementwith the statement lsquolsquoIt can never be right to kill a human beingrsquorsquoIn example 2 participants are asked about the moral relevance oflsquolsquowhether or not someone cared for someone weak or vulnerablersquorsquoAs can be seen in Figure III in example 1 the modal position(strongly disagree (1)) and most representative positions(strongly disagree (1)) coincide for conservatives In contrast inexample 2 in Figure III the most representative types (slightlyrelevant (3) not at all relevant (1)) are not most likely for theconservative group Following Proposition 1 we predict that be-liefs will be distorted in the direction of the most representativetypes Thus we expect more exaggeration in example 2 than inexample 1 since in example 2 the most representative types (inthe left tail) are far from the modal type whereas in example 1they coincide This is what we find the conservative position isexaggerated by only 009 positions in Example 1 (true mean 299believed mean 290) but by 106 positions in Example 2 (truemean 421 believed mean 315)

In the full data sets we treat each (issue year) pair as anobservation and we cluster standard errors at the issue level Forthe GNH data we have 45 observations 45 issues measured inthe same year For the ANES data we have 66 observations 10issues measured in multiple years To begin we simply docu-ment systematic exaggeration in both data sets This is a primaryfocus of the original analysis in GNH (2012) and also in Westfall

STEREOTYPES 1785

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FIGURE III

Two Examples

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et al (2015)rsquos analysis of the ANES data30 Figure IV shows thatthe believed difference between typical conservative and typicalliberal positions is larger than the true difference in mean posi-tions for 109 of the 111 observations The data for both GNH(squares) and ANES (triangles) lie above the 45-degree line(dashed)31 Average exaggeration is 062 positions on the scale(066 in the GNH data 059 in the ANES data)32

The systematic and significant exaggeration of mean differ-ences suggests that the benchmark model of accurate beliefs ismissing something important Indeed this exaggeration reflectsthe fact that believed means are typically more extreme than truemeans First note that the kernel of truth regression (equation(5)) generates exaggeration of mean differences just as docu-mented in Figure IV

EstethtjGTHORN E

stethtjGTHORN frac14 eth1thorn 2THORN frac12EethtjGTHORN EethtjGTHORN

To bring this prediction to the data we regress the believedmean position for each group EBethtjGTHORN on the true mean of thegroup EethtjGTHORN and the true mean of the comparison groupEethtjGTHORN across issues We do this for each group (liberals con-servatives) in each data set separately We also present pooledspecifications that combine the data sets to make a prediction fora given group (liberals conservatives) In these pooled specifica-tions we include a dummy variable indicating whether theobservation came from the ANES data set For all specificationswe cluster observations at the issue level33 The results from re-gression are shown in Table I In every specification we find thatEethtjGTHORN is a significant predictor of EBethtjGTHORN with the predicted pos-itive sign Crucially for five of the six specifications the mean of

30 Chambers and Melnyk (2006) also find evidence of exaggeration of truedifferences in beliefs about political positions

31 For convenience we recode all issues so that the high end of the scale (67)represents the stereotypically more conservative position

32 A natural question to ask is how beliefs vary across liberals and conserva-tives That is do beliefs about a group G depend on membership in G versus ndashG Ourmodel does not speak to this issue However in Online Appendix G we show thatthe results we document below hold for both beliefs held by conservatives and be-liefs held by liberals see Tables A9 A10 and A11

33 In general the results presented below for the ANES data are not largelyimpacted by the decision to cluster at the issue level Similar results are obtained ifthe data are not clustered

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the comparison group EethtjGTHORN is also a significant predictor ofE

BethtjGTHORN with the predicted negative signAlthough these results provide strong evidence of context

dependence and are consistent with our model they do not pindown a role for representativeness of types Our next test relatesthe magnitude of representativeness of tail types to the magni-tude of belief distortions

To this end we implement the regressions in equations (6)and (7) Following Proposition 4 we compute the average repre-

sentativeness of tail types for conservatives RconsH frac14

PtT2tconsPtT2tlib

We

again test the hypothesis that RconsH is a significant predictor of Est

ethtjconsTHORN with a positive sign and a predictor of EstethtjlibTHORN with a

negative sign Table II shows that conditional on true mean RconsH

predicts believed mean for each group G as expected The firstthree specifications display the results for predicting beliefs heldabout conservatives In both data sets the average representa-tiveness of tail types for conservatives is a significant positivepredictor of beliefs held about conservatives The final three spe-cifications display the results for predicting beliefs held about

FIGURE IV

Exaggeration of Differences

QUARTERLY JOURNAL OF ECONOMICS1788

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liberals We find that the average representativeness of tail typesfor conservatives is a negative predictor of beliefs held about lib-erals This effect is significant in the GNH data and marginallysignificant in the ANES data

We present several additional results in Online Appendix GTo further examine the role of representativeness in driving be-liefs we first show the results of Table II carry through when we

TABLE II

AVERAGE REPRESENTATIVENESS OF TAIL POSITIONS PREDICTS BELIEFS

OLS Predicting Believed Mean of Group G for Each Issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position

of group G for issue

078 024 051 072 018 041

(006) (008) (009) (005) (005) (010)

Avg rep of tail types for

conservatives RconsH

019 055 025 014 012 024

(007) (022) (008) (006) (007) (005)

Constant 101 260 184 093 271 201

(026) (045) (029) (022) (025) (032)

R2 082 048 060 091 031 070

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

TABLE I

INFORMATION ABOUT ndashG PREDICTS BELIEFS ABOUT G

OLS predicting believed mean of group G for each issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position of

conservatives for issue

102 098 096 021 019 025

(0097) (0133) (0076) (0060) (0116) (0060)

True mean position of

liberals for issue

035 086 058 0987 039 073

(0106) (0134) (0131) (0066) (0106) (0135)

Constant 151 335 235 069 258 156

(0195) (0269) (0279) (0122) (0249) (0270)

R2 083 053 066 092 032 068

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

STEREOTYPES 1789

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control for the average likelihood on the tail positions (see Table A4in Online Appendix G) Most tellingly we use the model to predictbeliefs across issues and compare those to the data For simplicitywe use the rank-based truncation specification to predict mean be-liefs when stereotypes include the d most representative types ford frac14 1 T We compare these predictions to those of a model inwhich beliefs are obtained by restricting the distribution to the dmost likely types Our benchmark for both models is predicting thebelieved mean from the entire distribution where d = T We showthat the predictions of the rank-based truncation model with d = 4or 5 compare favorably to both a likelihood-based truncation model(with any d) and the accurate beliefs benchmark Interestingly thisresult suggests that stereotypical beliefs are well approximated byneglecting the least representative types (as opposed to focusingonly on the most representative types) and so represent a moderatethough systematic departure from the standard benchmarkFinally we show that the results we document above hold forboth beliefs held by conservatives and beliefs held by liberals (seeTables A9 A10 and A11 in Online Appendix G)

V Conclusion

We present a model of stereotypical thinking in which DMsmaking predictions about a group overweight the grouprsquos mostdistinctive types These overweighted types are not the mostlikely ones given the DMrsquos data but the most representativeones in the sense of being the most diagnostic of the group rela-tive to other groups Representativeness implies that what ismost distinctive of a group depends on what group it is comparedwith We present experimental evidence that confirms this con-text dependence in recall-based assessments of groups Finallywe evaluated the predictions of the model using political data fromexisting large-scale surveys We find context dependence to be akey feature of beliefs Given the richness of the political data wecan go a step further and identify a role for representativeness inparticular As the representativeness of tail types increases beliefsof a group are distorted in the direction of that tail

Our approach provides a parsimonious and psychologicallyfounded account of how DMs generate simplified representationsof reality from social groups to stock returns and offers a unifiedaccount of disparate pieces of evidence relating to this type of

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uncertainty The model captures the central fact that stereotypeshighlight the greatest difference between groups thus explainingwhy some stereotypes are very accurate while others lack valid-ity Still stereotypes often have a kernel of truth when they arebased on systematicmdasheven if smallmdashdifferences between groupsThis logic allows us to describe a number of heuristics and psy-chological biases many of which arise in the context of predictionproblems Generically our model generates overreaction to diag-nostic information

Our model is based on representativeness and does not cap-ture all the features of stereotypical thinking However it cap-tures perhaps the central feature when we think of a group wefocus on what is most distinctive about it and neglect or under-weight the rest

Saeuroıd Business School University of Oxford

Ohio State University and Harvard Business School

Universita Bocconi and Innocenzo Gasparini Institute

for Economic Research

Harvard University

Supplementary Material

An Online Appendix for this article can be found at QJEonline (qjeoxfordjournalorg)

References

Adorno Theodor Else Frenkel-Brunswik Daniel Levinson and Nevitt SanfordThe Authoritarian Personality (New York Harper amp Row 1950)

Arrow Kenneth lsquolsquoThe Theory of Discriminationrsquorsquo in Discrimination in LaborMarkets Orley Ashenfelter and Albert Rees eds (Princeton NJPrinceton University Press 1973)

Ashton Michael and Victoria Esses lsquolsquoStereotype Accuracy Estimating theAcademic Performance of Ethnic Groupsrsquorsquo Personality and SocialPsychology Bulletin 25 (1999) 225ndash236

Barberis Nicholas Andrei Shleifer and Robert Vishny lsquolsquoA Model of InvestorSentimentrsquorsquo Journal of Financial Economics 49 (1998) 307ndash343

Bayer Sylvia lsquolsquoThe Accuracy of Academic Gender Stereotypesrsquorsquo Sex Roles 40(1999) 787ndash813

Benjamin Dan James Choi and Joshua Strickland lsquolsquoSocial Identity andPreferencesrsquorsquo American Economic Review 100 (2010) 1913ndash1928

Benjamin Dan Matthew Rabin and Collin Raymond lsquolsquoA Model of Non-Belief inthe Law of Large Numbersrsquorsquo Journal of the European Economic Association15 (2015) 515ndash544

Bertrand Marianne lsquolsquoNew Perspectives on Genderrsquorsquo Handbook of LaborEconomics 4 (2011) 1543ndash1590

Bodoh-Creed Aaron Dan Benjamin and Matthew Rabin lsquolsquoThe Dynamics of Base-Rate Neglectrsquorsquo mimeo Haas Business School 2013

STEREOTYPES 1791

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

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Bohnet Iris Alexandra van Geen and Max Bazerman lsquolsquoWhen PerformanceTrumps Gender Bias Joint versus Separate Evaluationrsquorsquo ManagementScience 5 (2016) 1225ndash1234

Bordalo Pedro Nicola Gennaioli and Andrei Shleifer lsquolsquoSalience Theory of Choiceunder Riskrsquorsquo Quarterly Journal of Economics 127 (2012) 1243ndash1285

mdashmdashmdash lsquolsquoSalience and Consumer Choicersquorsquo Journal of Political Economy 121(2013) 803ndash843

Briton Nancy and Judith Hall lsquolsquoBeliefs about Female and Male NonverbalCommunicationrsquorsquo Sex Roles 32 (1995) 79ndash90

Buser Thomas Muriel Niederle and Hessel Oosterbeek lsquolsquoGenderCompetitiveness and Career Choicesrsquorsquo Quarterly Journal of Economics 129(2014) 1409ndash1447

Carrell Scott Marianne Page and James West lsquolsquoSex and Science How ProfessorGender Perpetuates the Gender Gaprsquorsquo Quarterly Journal of Economics 125(2010) 1101ndash1144

Chambers John and Darya Melnyk lsquolsquoWhy Do I Hate Thee ConflictMisperceptions and Intergroup Mistrustrsquorsquo Personality and SocialPsychology Bulletin 32 (2006) 1295ndash1311

Chan Wayne Robert R McCrae Filip De Fruyt Lee Jussim CorinnaE Lockenhoff Marleen De Bolle Paul T Costa Jr Angelina R SutinAnu Realo Juri Allik Katsuharu Nakazato Yoshiko ShimonakaMartina Hrebıckova Sylvie Graf Michelle Yik Marina Brunner-SciarraNora Leibovich De Figueora Vanina Schmidt Chang-kyo Ahn Hyun-nie Ahn Maria E Aguilar-Vafaie Jerzy Siuta Barbara SzmigielskaThomas R Cain Janet T Crawford Khairul Anwar Mastor Jean-Pierre Rolland Florence Nansubuga Daniel R MiramontezVeronica Benet-Martınez Jerome Rossier Denis Bratko Iris MarusicJamin Halberstadt Mami Yamaguchi Goran Knezevic Thomas A MartinMirona Gheorghiu Peter B Smith Claudio Barbaranelli Lei WangJane Shakespeare-Finch Margarida P Lima Waldemar KlinkoszAndrzej Sekowski Lidia Alcalay Franco Simonetti Tatyana V AvdeyevaV S Pramila and Antonio Terracciano lsquolsquoStereotypes of Age Differences inPersonality Traits Universal and Accuratersquorsquo Journal of Personality andSocial Psychology 103 (2012) 1050ndash1066

Chen Yan Sherry Xin Liu Tracy Xiao and Margaret Shih lsquolsquoWhich Hat to WearImpact of Natural Identities on Coordination and Cooperationrsquorsquo Games andEconomic Behavior 84 (2014) 58ndash86

Coffman Katherine lsquolsquoEvidence on Self-Stereotyping and the Contribution ofIdeasrsquorsquo Quarterly Journal of Economics 129 (2014) 1625ndash1660

Cunningham Tom lsquolsquoComparisons and Choicersquorsquo mimeo Stockholm University2013

Diekman Amanda Alice Eagly and Patrick Kulesa lsquolsquoAccuracy and Bias in theStereotypes about the Social and Political Attitudes of Women and MenrsquorsquoJournal of Experimental Social Psychology 38 (2002) 268ndash282

Eccles Jacquelynne S Janis E Jacobs and Rena D Harold lsquolsquoGender RoleStereotypes Expectancy Effects and Parentsrsquo Socialization of GenderDifferencesrsquorsquo Journal of Social Issues 46 (1990) 183ndash201

Fryer Roland and Matthew Jackson lsquolsquoA Categorical Model of Cognition andBiased Decision-Makingrsquorsquo BE Journal of Theoretical Economics 8 (2008)1ndash42

Fryer Roland and Steven Levitt lsquolsquoAn Empirical Analysis of the Gender Gap inMathematicsrsquorsquo American Economic Journal Applied Economics 2 (2010)210ndash240

Gennaioli Nicola and Andrei Shleifer lsquolsquoWhat Comes to Mindrsquorsquo Quarterly Journalof Economics 125 (2010) 1399ndash1433

Gennaioli Nicola Andrei Shleifer and Robert Vishny lsquolsquoNeglected RisksFinancial Innovation and Financial Fragilityrsquorsquo Journal of FinancialEconomics 104 (2012) 452ndash468

Gilens Martin lsquolsquoRace and Poverty in America Public Misperceptions and theAmerican News Mediarsquorsquo Public Opinion Quarterly 60 (1996) 515ndash541

Glaeser Edward lsquolsquoThe Political Economy of Hatredrsquorsquo Quarterly Journal ofEconomics 120 (2005) 45ndash86

QUARTERLY JOURNAL OF ECONOMICS1792

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Glover Dyland Amanda Pallais and William Pariente lsquolsquoDiscrimination as a Self-Fulfilling Prophecy Evidence from French Grocery Storesrsquorsquo mimeo HarvardUniversity 2015

Goldin Claudia Lawrence Katz and Ilyana Kuziemko lsquolsquoThe Homecoming ofAmerican College Women The Reversal of the College Gender GaprsquorsquoJournal of Economic Perspectives 20 (2006) 133ndash156

Graham Jesse Brian Nosek and Jonathan Haidt lsquolsquoThe Moral Stereotypes ofLiberals and Conservatives Exaggeration of Differences across thePolitical Spectrumrsquorsquo PLoS One 7 (2012) 1ndash13

Grether David lsquolsquoBayes Rule as a Descriptive Model The RepresentativenessHeuristicrsquorsquo Quarterly Journal of Economics 95 (1980) 537ndash557

Griffin Dale and Amos Tversky lsquolsquoThe Weighing of Evidence and theDeterminants of Confidencersquorsquo Cognitive Psychology 24 (1992) 411ndash435

Guiso Luigi Ferdinando Monte Paola Sapienza and Luigi Zingales lsquolsquoCultureGender and Mathrsquorsquo Science 320 (2008) 1164ndash1165

Hilton James and William Von Hippel lsquolsquoStereotypesrsquorsquo Annual Review ofPsychology 47 (1996) 237ndash271

Hyde Janet Sara Lindberg Marcia Linn Amy Ellis and Caroline WilliamslsquolsquoGender Similarities Characterize Math Performancersquorsquo Science 321 (2008)494ndash495

Judd Charles and Bernardette Park lsquolsquoDefinition and Assessment of Accuracy inSocial Stereotypesrsquorsquo Psychological Review 100 (1993) 109ndash128

Jussim Lee Jarret Crawford Stephanie Anglin John Chambers Sean Stevensand Florette Cohen lsquolsquoStereotype Accuracy One of the Largest and MostReplicable Effects in All of Social Psychologyrsquorsquo in The Handbook ofPrejudice Stereotyping and Discrimination Todd Nelson ed (MahwahNJ Lawrence Erlbaum 2015)

Kahneman Daniel and Amos Tversky lsquolsquoSubjective Probability A Judgment ofRepresentativenessrsquorsquo Cognitive Psychology 3 (1972) 430ndash454

mdashmdashmdash lsquolsquoOn the Psychology of Predictionrsquorsquo Psychological Review 80 (1973) 237ndash251

Kaplowitz Stan Bradley Fisher and Clifford Broman lsquolsquoHow Accurate ArePerceptions of Social Statistics about Blacks and Whitesrsquorsquo Public OpinionQuarterly 67 (2003) 237ndash243

Kersten Daniel Pascal Mamassian and Alan Yuille lsquolsquoObject Perception asBayesian Inferencersquorsquo Annual Review of Psychology 55 (2004) 271ndash304

Klein Richard Kate A Ratliff Michelangelo Vianello Reginald B Adams JrStepan Bahnik Michael J Bernstein Konrad Bocian Mark J BrandtBeach Brooks Claudia Chloe Brumbaugh Zeynep CemalcilarJesse Chandler Winnee Cheong William E Davis Thierry DevosMatthew Eisner Natalia Frankowska David Furrow Elisa Maria GallianiFred Hasselman Joshua A Hicks James F Hovermale S Jane HuntJeffrey R Huntsinger Hans IJzerman Melissa-Sue John Jennifer A Joy-Gaba Heather Barry Kappes Lacy E Krueger Jaime Kurtz CarmelA Levitan Robyn Mallett Wendy L Morris Anthony J Nelson JasonA Nier Grant Packard Ronaldo Pilati Abraham M RutchickKathleen Schmidt Jeanine L Skorinko Robert Smith Troy G SteinerJustin Storbeck Lyn M Van Swol Donna Thompson Anna van rsquot VeerLeigh Ann Vaughn Marek Vranka Aaron Wichman Julie A Woodzickaand Brian A Nosek lsquolsquoInvestigating Variation in Replicability A ManyLabs Replication Projectrsquorsquo Social Psychology 45 (2014) 142ndash152

Lundberg Shelly and Richard Startz lsquolsquoPrivate Discrimination and SocialIntervention in Competitive Labor Marketsrsquorsquo American Economic Review73 (1983) 340ndash347

Madon Stephanie Max Guyll Kathy Aboufadel Eulices Montiel Alison SmithPolly Palumbo and Lee Jussim lsquolsquoEthnic and National Stereotypes ThePrinceton Trilogy Revisited and Revisedrsquorsquo Personality and SocialPsychological Bulletin 27 (2001) 996ndash1010

Martin Carol lsquolsquoA Ratio Measure of Sex Stereotypingrsquorsquo Journal of Personality andSocial Psychology 52 (1987) 489ndash499

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ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

McCauley Clark Krishna Thangavelu and Paul Rozin lsquolsquoSex Stereotyping ofOccupations in Relation to Television Representations and Census FactsrsquorsquoBasic and Applied Social Psychology 9 (1988) 197ndash212

Mullainathan Sendhil lsquolsquoThinking through Categoriesrsquorsquo mimeo HarvardUniversity 2002

Ortoleva Pietro and Erik Snowberg lsquolsquoOverconfidence in Political BehaviorrsquorsquoAmerican Economic Review 105 (2015) 504ndash535

Phelps Edmund lsquolsquoThe Statistical Theory of Racism and Sexismrsquorsquo AmericanEconomic Review 62 (1972) 659ndash661

Pope Devin and Justin Sydnor lsquolsquoGeographic Variation in the Gender Differencesin Test Scoresrsquorsquo Journal of Economic Perspectives 24 (2010) 95ndash108

Rabin Matthew lsquolsquoInference by Believers in the Law of Small NumbersrsquorsquoQuarterly Journal of Economics 117 (2002) 775ndash816

Rabin Matthew and Joel Schrag lsquolsquoFirst Impressions Matter A Model ofConfirmatory Biasrsquorsquo Quarterly Journal of Economics 114 (1999) 37ndash82

Rabin Matthew and Dimitri Vayanos lsquolsquoThe Gamblerrsquos and Hot-Hand FallaciesTheory and Applicationsrsquorsquo Review of Economic Studies 77 (2010) 730ndash778

Reuben Ernesto Paola Sapienza and Luigi Zingales lsquolsquoHow Stereotypes ImpairWomenrsquos Careers in Sciencersquorsquo Proceedings of the National Academy ofSciences 111 (2014) 4403ndash4408

Rosch Eleanor lsquolsquoNatural Categoriesrsquorsquo Cognitive Psychology 4 (1973) 328ndash350Ryan Carey S lsquolsquoAccuracy of Black and White College Studentsrsquo In-Group and

Out-Group Stereotypesrsquorsquo Personality and Social Psychology Bulletin 22(1996) 1114ndash1127

Schneider David The Psychology of Stereotyping (New York Guilford Press2004)

Schneider David Albert Hastorf and Phoebe Ellsworth Person Perception(Reading MA Addison-Wesley 1979)

Shih Margaret Todd Pittinsky and Nalini Ambady lsquolsquoStereotype SusceptibilityIdentity Salience and Shifts in Quantitative Performancersquorsquo PsychologicalScience 10 (1999) 80ndash83

Shih Margaret Todd Pittinsky and Amy Trahan lsquolsquoDomain-Specific Effects ofStereotypes on Performancersquorsquo Self and Identity 5 (2006) 1ndash14

Steele Claude Whistling Vivaldi How Stereotypes Affect Us and What We CanDo (New York Norton 2010)

Tenenbaum Joshua and Thomas Griffiths lsquolsquoThe Rational Basis ofRepresentativenessrsquorsquo 23rd Annual Conference of the Cognitive ScienceSociety (2001) 1036ndash1041

Tversky Amos and Daniel Kahneman lsquolsquoExtensional versus Intuitive ReasoningThe Conjunction Fallacy in Probability Judgmentrsquorsquo Psychological Review 90(1983) 293ndash315

Weinberger Catherin lsquolsquoIs the Science and Engineering Workforce Drawn fromthe Far Upper Tail of the Math Ability Distributionrsquorsquo mimeo UCSB 2005

Westfall Jacob Leaf Van Boven John Chambers and Charles Judd lsquolsquoPerceivingPolitical Polarization in the United States Party Identity Strength andAttitude Extremity Exacerbate the Perceived Partisan DividersquorsquoPsychological Science 10 (2015) 145ndash158

Wolsko Christopher Bernadette Park Charles Judd and Bernd WittenbrinklsquolsquoFraming Interethnic Ideology Effects of Multicultural and Color-BlindPerspectives on Judgments of Groups and Individualsrsquorsquo Journal ofPersonality and Social Psychology 78 (2000) 635ndash654

QUARTERLY JOURNAL OF ECONOMICS1794

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ibrary on October 28 2016

httpqjeoxfordjournalsorgD

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Page 24: I. Introduction · uneducated at the beginning of the 20th century, and as high achievers at the beginning of the 21st (Madon et al. 2001). Social science has produced three broad

consist of naturally defined groups with known distributions overa given space of types and a corresponding set of beliefs about thedistribution of each group over that space of types This wouldallow us to test for exaggeration of true differences betweengroups and to ask whether this exaggeration is well predictedby overweighting representative types To identify a causal rolefor representativeness or context dependence we would need ex-ogenous variation in either the comparison group ndashG or in thedistributions over the type spaces This is unavailable in existingdata sets Accordingly we take a two-pronged approach First wecreate a controlled laboratory environment that allows us toinduce the exogenous variation in representative types that weneed to test causality then we reanalyze existing field evidence tocheck for consistency with our predictions

In testing our model we focus on the two main implicationsof representativeness-based stereotypes

Context dependence the stereotype of a target group de-pends on the characteristics of the reference group it iscompared to

Kernel of truth stereotypes depend on group character-istics andmdashin most (precisely characterized) settingsmdashare slanted toward representative types

We test the first property with a lab experiment (SectionIVA) We then turn to survey data on beliefs about US politicalgroups (Section IVB) for an empirical analysis that explores thesecond property The survey data are more tightly linked to ourinterest in social stereotypes The laboratory experiment allowsus to directly test the role of representativeness in generatingcontext dependent beliefs Online Appendixes F and G provideall details and additional results for the experiments and fieldevidence

IVA Lab Evidence on Representativeness and ContextDependence

The influence of the representativeness heuristic on recalland on beliefs has been extensively documented in the lab(Kahneman and Tversky 1972 1973) Our goal is to considerhow representativeness as formalized in equation (2) gives riseto context-dependent beliefs To our knowledge the possibility

QUARTERLY JOURNAL OF ECONOMICS1776

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that representativeness may generate context dependence hasnot been tested before

To assess this prediction we perform a controlled laboratoryexperiment that allows us to isolate representativeness frommany confounding factorsmdashhistorical sociological or other-wisemdashthat may affect stereotype formation in the real worldWe construct our own groups of ordinary objects creating atarget group G and a comparison group ndashG We hold thetarget group G fixed and explore how participant impressions ofit change as we change the comparison group ndashG and thusrepresentativeness

We conducted several experiments in the laboratory and onAmazon Mechanical Turk Each involves a basic three-stepdesign First participants are shown the target group and a ran-domly assigned comparison group for 15 seconds In this timedifferences between groups can be noticed but the groupsrsquo precisecompositions cannot be memorized The second step consists of afew filler questions which briefly draw the participantsrsquo cognitivebandwidth away from their observation Finally participants areasked to assess the groups they saw Participants are incentiv-ized to provide accurate answers

We randomly assign participants to either the Control or theRepresentativeness condition In the Control condition G and ndashGhave nearly identical distributions so that all types are similarlyrepresentative for each group In the Representativeness condi-tion ndashG is changed in such a way that a certain type becomes veryrepresentative for G Context dependence implies that the assess-ment of G should now overweight this representative type eventhough the distribution of G itself has not changed

We ran six experiments of this form with design changesfocused on reducing participant confusion and removing con-founds We describe the final and most refined version of theseexperiments here In an attempt to provide a overview of the re-sults while remaining concise we provide the results from pooledspecifications that use all data collected In Online Appendix Fwe offer additional details and report all experiments conductedWe also give instructions and materials for each experiment thefull data set is available by request

Consider first the experiment illustrated in Figure II Agroup of 25 cartoon girls is presented next to a group of 25 cartoonboys in T-shirts of different colors blue green or purple In theControl condition (Figure II Panel a) the groups have identical

STEREOTYPES 1777

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color distributions (13 purple 12 green) so no color is represen-tative of either group The Representativeness condition (Panel b)compares the same group of girls with a different group of boysfor whom green shirts are replaced with blue shirts Now onlygirls wear green and only boys wear blue These colors althoughstill not the most frequent for either group are now most repre-sentative For each group girls and boys participants are asked anumber of questions concerning the frequency of T-shirts of dif-ferent colors worn by that group

Applying our model in the control condition the type space isT frac14 fgreen purpleg and the groups are G = girls and ndashG = boysGiven that the color distributions are identical across groups both

types are equally representativegreengirls

greenboysfrac14 1 frac14

purplegirls

purpleboys As a result

assessment of G should be correct on average stcontrolgreengirls frac14 greengirls

and stcontrolpurplegirls frac14 purplegirls for any weighing function (the same is

true about assessments of ndashG)In the treatment condition the distribution of shirt colors re-

mains the same for girls For boys green shirts are changed intoblue Thus the type space changes to T frac14 fgreen purple bluegand the representative color for girls becomes greengreengirls

greenboysfrac14 1 gt 1 frac14

purplegirls

purpleboys while that for boys becomes blue As

a result in the treatment condition subjects should inflate the

frequency of green shirts relative to the truth sttreatmentgreengirls

gt greengirls (the same should happen to assessments of blueshirts for boys) We also expect the assessed frequency of greenshirts to go up relative to the control condition namely

sttreatmentgreengirls gt stcontrol

greengirls Critically the only factor that varies

across treatments is the representativeness of the 12-colorshirt Thus if we see differences across conditions the causalrole of representativeness-based recall in shaping group judg-ments is clear24

24 We vary which colors are used in which roles across participants Someparticipants saw this particular color distribution while others see for examplegreen as the modal color and purple as the diagnostic color for boys in theRepresentativeness condition and blue as the diagnostic color for girls in theRepresentativeness condition We vary the colors across the roles to avoid con-founding the characteristics of any particular color with its diagnosticity

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FIG

UR

EII

T-S

hir

tsE

xp

erim

ent

Fig

ure

sap

pea

red

inco

lor

top

art

icip

an

tsin

the

exp

erim

ent

For

clari

ty

we

have

ad

ded

ale

tter

toea

chT

-sh

irt

toid

enti

fyth

eco

lor

for

the

read

er

lsquolsquoGrsquorsquo

ind

icate

sgre

en

lsquolsquoPrsquorsquo

ind

icate

sp

urp

le

lsquolsquoBrsquorsquo

ind

icate

sblu

eT

hes

ele

tter

sd

idn

otap

pea

rto

part

icip

an

tsan

dare

for

read

erre

fere

nce

only

P

lease

see

onli

ne

ver

sion

ofp

ubli

shed

art

icle

for

colo

rfi

gu

reex

act

lyas

itap

pea

red

top

art

icip

an

ts

STEREOTYPES 1779

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We collected data from 301 participants using this T-shirtsdesign25 Since the number of green and purple shirts is verysimilar we first ask each participant the simplest question ofwhich shirt color is modal Next we ask participants to assessthe share of green and purple shirts

Consistent with the role of representativeness participantsassigned to the Representativeness condition are 105 percentagepoints more likely to recall the less frequent color (green for girlsor blue for boys) as the modal color when it is representative of agroup (35 of participants guess the less frequent color is modalin the Control condition this proportion increases to 46 in theRepresentativeness condition p = 01 estimated from a probitregression reported in Online Appendix F)

We now turn to subjectsrsquo estimates of how many T-shirts ofeach color they saw in each group In both conditions the truedifference in counts is 1 (13 purple shirts 12 green or blue shirts)In the Control condition participants on average believe they saw054 more purple shirts than green or blue shirts In theRepresentativeness condition participants believe they saw072 fewer purple shirts than green or blue shirts (the acrosstreatment difference is significant with p = 01 from OLS regres-sion reported in Online Appendix F)

In total we collected data for six experiments of this generalstructure gathering evidence from more than 1000 participantsAs we describe in Online Appendix F although there is substan-tial variation across experiments when we pool all of the data wefind significant aggregate treatment effects in line with a role ofrepresentativeness in judgment We employ four different unor-dered types designs similar to the T-shirts experiment using sixsamples (four online and two in the laboratory) with 741 partic-ipants We find effects in the predicted direction for five of the sixsamples Using a probit regression that pools the data for theseunordered type experiments we find that participants are 93 per-centage points more likely to guess that the less frequent type ismodal when it is representative than when it is not (p = 002) Wealso run a family of ordered types experiments (two designs fivesamples 402 participants) Unlike the simpler T-shirts style

25 Throughout our analysis we exclude any participant who participated in aprevious version of the experiment and any participant who self-identified as color-blind In Online Appendix F we show that our results are unchanged if we includethese additional observations

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design the theoretical predictions for the ordered types designsare more sensitive to the specific assumptions one makes aboutthe weighting function of the DM26 We find effects in the pre-dicted direction for three of the five samples As we discuss inmore detail in Online Appendix F the ordered types resultsvary by platform with consistently stronger results on AmazonMechanical Turk than in the laboratory samples Pooling all or-dered types experiments participants are 93 percentage pointsmore likely to guess that the group of interest has a greater av-erage than the comparison group when the right tail is represen-tative (p = 062) Given our simple experimental setting withgroups of mundane objects we interpret our resultsmdasha signifi-cant and reasonably sized impact on average beliefsmdashas an im-portant proof of concept the presence of representative typesbiases ex post assessment

IVB Empirical Evidence on Political Stereotypes

We examine two data sets on political preferences and be-liefs about political preferences in the United States We inves-tigate the roles of representativeness and context dependence byseparately testing for hypotheses that allow us to assess the lead-ing theories of stereotypes

First we test whether beliefs are correct or depart systemat-ically from the truth The statistical discrimination approachbuilds on the assumption that people hold rational expectationsof group traits Comparing beliefs to the truth allows us to assessthe validity of this assumption in our data

Second we test if beliefs depart from the truth by exagger-ating (mean) differences among groups per the kernel of truthhypothesis This is an implicit test of context dependence be-cause it implies that beliefs about the target groups are shapednot only by that grouprsquos characteristics but also by those of thereference group27

Third we test if distortions in beliefs can be accounted for bythe overweighting of highly representative types (defined astypes that are relatively more frequent in the target relative to

26 This is due in part to our choice to not study MLRP distributions We moti-vate and discuss this design decision in Online Appendix F

27 Of course unlike in the laboratory experiment in this setting we cannot testfor context dependence by exogenously varying the reference group

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the reference group) The second and third tests address the keypredictions of our model

1 The Data We have two data sets on political preferences andbeliefs about political preferences The first data set from GrahamNosek and Haidt (GNH 2012) contains data from the MoralFoundations Questionnaire Respondents (1174 self-identified lib-erals and 500 self-identified conservatives) answer questions abouttheir position on a subset of 45 issues 20 moral relevance state-ments (eg lsquolsquowhen you decide whether something is right orwrong to what extent are the following considerations relevantto your thinkingrsquorsquo) and 25 moral judgments (eg lsquolsquoindicate theextent to which you would agree or disagreersquorsquo) For each issue arandomly determined subset of participants states their own posi-tion another subset states their belief on the position of a lsquolsquotypicalliberalrsquorsquo and a third subset states their belief on the position of alsquolsquotypical conservativersquorsquo The data thus include the distribution overpositions for both liberal and conservatives as well as the averagebelieved typical position of liberals and of conservatives on the 45issues Each position is elicited on 1ndash6 scale

The second data set comes from the American NationalElection Survey (ANES) and contains data from more than20000 respondents between 1964 and 201228 The surveycovers political issues of the day such as the optimal amount ofgovernment spending and service provision (1984ndash2000) or theplace of women in society (1972ndash1998) We focus on the 10 issuesthat ask participants to respond on a 1ndash7 scale (rather than justindicate binary agreement or disagreement) all 10 issues areasked in multiple years Participants are asked to provide theirown position on the scale and their believed position of theDemocratic and Republican parties (lsquolsquoWhere would you placethe Democratic [Republican] party on this scalersquorsquo) The data in-clude for each issue-year observation the distribution of partic-ipant positions for self-identified liberals and self-identifiedconservatives as well as the distribution of believed typical posi-tions of the Democratic and Republican parties

28 These data are publicly available at httpwwwelectionstudiesorgstudy-pagesanes_timeseries_cdfanes_timeseries_cdfhtm

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2 Empirical Strategy Our analysis focuses on beliefs abouttwo groups Conservatives and Liberals The types are the possi-ble positions for each issue (1 2 6 7) For the GNH data weinterpret beliefs about the lsquolsquotypicalrsquorsquo element of a group to coincidewith the believed average position in that group Similarly forthe ANES data we use the believed party positions as a proxy forbelieved mean of each group29 We then take as a benchmark thehypothesis that individuals hold accurate beliefs about eachgroup and in particular that believed mean position shouldequal true mean position at least on average across subjectsThe accurate beliefs hypothesis underlies the most common eco-nomic model of stereotyping statistical discrimination

To assess our representativeness-based model we perform aregression exercise To test our model in a linear regressionframework we rely on linear approximations of the weightingfunction Our model then yields two regression specifications

PROPOSITION 4 Let G 2 fconservative liberal g and assume

ht h tG

tG

be a differentiable and strictly increasing weight-

ing function as in Definition 2 The following hold as a first-order approximation around identical distributions G

Gfrac14 1

(i) Kernel of truth regression There exists a constant gt 0such that

EstethtjGTHORN frac14 EethtjGTHORNeth1thorn THORN EethtjGTHORNeth5THORN

(ii) Representativeness regression Denote H frac14 fT 2 Tg

the right tail of types and RconsH frac14

PHtconsPHtlib

as the average

representativeness of right tail types for conservatives

29 This assumption is consistent with the authorsrsquo interpretation of the GNHdata (GNH 2012) and with previous studies using ANES (eg Westfall et al 2015)Furthermore to the extent that this assumption holds equally well for most issueswithin a data set our focus on cross-issue differences should allow us to test thepredictions of our model even with an imperfect proxy for beliefs of mean positionsFinally the data provide some insight into whether subjects are reporting (per-ceived) modal or mean types As we show the modal type is a poor prediction ofstated beliefs while a distorted mean slanted toward representative types is anaccurate prediction of stated beliefs

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Under the further approximation where tcons

tlibampRcons

H for

t 2 H

EstethtjconsTHORN frac14 EethtjconsTHORN thorn consethR

consH 1THORNeth6THORN

EstethtjlibTHORN frac14 EethtjlibTHORN libethR

consH 1THORNeth7THORN

where lcons and llib are positive constants

The first regression allows us to test for the kernel of truthhypothesis and the second set of regressions allows us to test forthe role of representativeness

Equation (5) says that respondents in our model inflate theaverage position of a group say the conservatives if and only ifthe group has a higher average position than the other groupnamely the liberals Formally EstethtjconsTHORN gt EethtjconsTHORN if and onlyif EethtjconsTHORN gt EethtjlibTHORN Because in our measurement scale highertypes mean lsquolsquomore conservativersquorsquo we expect (i) believed conserva-tive average to be higher than the truth and (ii) the extent ofoverstatement to decrease in the average liberal position EethtjlibTHORNConversely we expect the average liberal position to be lowerthan the truth the more so the higher the average conservativeposition EethtjconsTHORN

As previously discussed the basis of these predictions is con-text dependence information about the distribution of ndashG is rel-evant for the beliefs about G This context dependence isinconsistent with rational expectations in which only thegrouprsquos own means should affect beliefs We test the hypothesisthat the true mean EethtjGTHORN is a significant predictor of the believedmean E

stethtjGTHORN with a positive sign and the other grouprsquos truemean EethtjGTHORN is a predictor of the believed mean with a negativesign

Equations (6) and (7) say that repondentsrsquo assessment bias isshaped by representativeness When the right tail is more repre-sentative for conservatives (Rcons

H 1 positive and large) partici-pants should inflate the average conservative position more(higher E

stethtjconsTHORN EethtjconsTHORN) and deflate the average liberal po-sition more (lower E

stethtjlibTHORN EethtjlibTHORN) We test the hypothesisthat the inflation in conservative positions is positively associatedwith the representativeness of the right tail for the conservativesand the inflation in liberal positions is negatively associated with

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it Once again the representativeness of the right tail is com-puted using the true distribution of positions

In equations (6) and (7) in many cases the representative tailis also the most likely one As a consequence these tests cannotdistinguish a representativeness-based from a likelihood-basedmodel of distorted beliefs We perform two additional testsFirst we run versions of equations (6) and (7) in which we controlfor the likelihood of tails (see Table A4 in Online Appendix G)Second we compute numerically the predictions of a representa-tiveness-based model of stereotypes and a likelihood-based modelof stereotypes We then assess which of these two is better able tomatch the data on beliefs

3 Empirical Results To begin we illustrate the structure ofthe data and the nature of our predictions with two simple exam-ples from the GNH data set focusing on beliefs about conserva-tives In example 1 participants are asked about their agreementwith the statement lsquolsquoIt can never be right to kill a human beingrsquorsquoIn example 2 participants are asked about the moral relevance oflsquolsquowhether or not someone cared for someone weak or vulnerablersquorsquoAs can be seen in Figure III in example 1 the modal position(strongly disagree (1)) and most representative positions(strongly disagree (1)) coincide for conservatives In contrast inexample 2 in Figure III the most representative types (slightlyrelevant (3) not at all relevant (1)) are not most likely for theconservative group Following Proposition 1 we predict that be-liefs will be distorted in the direction of the most representativetypes Thus we expect more exaggeration in example 2 than inexample 1 since in example 2 the most representative types (inthe left tail) are far from the modal type whereas in example 1they coincide This is what we find the conservative position isexaggerated by only 009 positions in Example 1 (true mean 299believed mean 290) but by 106 positions in Example 2 (truemean 421 believed mean 315)

In the full data sets we treat each (issue year) pair as anobservation and we cluster standard errors at the issue level Forthe GNH data we have 45 observations 45 issues measured inthe same year For the ANES data we have 66 observations 10issues measured in multiple years To begin we simply docu-ment systematic exaggeration in both data sets This is a primaryfocus of the original analysis in GNH (2012) and also in Westfall

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FIGURE III

Two Examples

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et al (2015)rsquos analysis of the ANES data30 Figure IV shows thatthe believed difference between typical conservative and typicalliberal positions is larger than the true difference in mean posi-tions for 109 of the 111 observations The data for both GNH(squares) and ANES (triangles) lie above the 45-degree line(dashed)31 Average exaggeration is 062 positions on the scale(066 in the GNH data 059 in the ANES data)32

The systematic and significant exaggeration of mean differ-ences suggests that the benchmark model of accurate beliefs ismissing something important Indeed this exaggeration reflectsthe fact that believed means are typically more extreme than truemeans First note that the kernel of truth regression (equation(5)) generates exaggeration of mean differences just as docu-mented in Figure IV

EstethtjGTHORN E

stethtjGTHORN frac14 eth1thorn 2THORN frac12EethtjGTHORN EethtjGTHORN

To bring this prediction to the data we regress the believedmean position for each group EBethtjGTHORN on the true mean of thegroup EethtjGTHORN and the true mean of the comparison groupEethtjGTHORN across issues We do this for each group (liberals con-servatives) in each data set separately We also present pooledspecifications that combine the data sets to make a prediction fora given group (liberals conservatives) In these pooled specifica-tions we include a dummy variable indicating whether theobservation came from the ANES data set For all specificationswe cluster observations at the issue level33 The results from re-gression are shown in Table I In every specification we find thatEethtjGTHORN is a significant predictor of EBethtjGTHORN with the predicted pos-itive sign Crucially for five of the six specifications the mean of

30 Chambers and Melnyk (2006) also find evidence of exaggeration of truedifferences in beliefs about political positions

31 For convenience we recode all issues so that the high end of the scale (67)represents the stereotypically more conservative position

32 A natural question to ask is how beliefs vary across liberals and conserva-tives That is do beliefs about a group G depend on membership in G versus ndashG Ourmodel does not speak to this issue However in Online Appendix G we show thatthe results we document below hold for both beliefs held by conservatives and be-liefs held by liberals see Tables A9 A10 and A11

33 In general the results presented below for the ANES data are not largelyimpacted by the decision to cluster at the issue level Similar results are obtained ifthe data are not clustered

STEREOTYPES 1787

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the comparison group EethtjGTHORN is also a significant predictor ofE

BethtjGTHORN with the predicted negative signAlthough these results provide strong evidence of context

dependence and are consistent with our model they do not pindown a role for representativeness of types Our next test relatesthe magnitude of representativeness of tail types to the magni-tude of belief distortions

To this end we implement the regressions in equations (6)and (7) Following Proposition 4 we compute the average repre-

sentativeness of tail types for conservatives RconsH frac14

PtT2tconsPtT2tlib

We

again test the hypothesis that RconsH is a significant predictor of Est

ethtjconsTHORN with a positive sign and a predictor of EstethtjlibTHORN with a

negative sign Table II shows that conditional on true mean RconsH

predicts believed mean for each group G as expected The firstthree specifications display the results for predicting beliefs heldabout conservatives In both data sets the average representa-tiveness of tail types for conservatives is a significant positivepredictor of beliefs held about conservatives The final three spe-cifications display the results for predicting beliefs held about

FIGURE IV

Exaggeration of Differences

QUARTERLY JOURNAL OF ECONOMICS1788

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liberals We find that the average representativeness of tail typesfor conservatives is a negative predictor of beliefs held about lib-erals This effect is significant in the GNH data and marginallysignificant in the ANES data

We present several additional results in Online Appendix GTo further examine the role of representativeness in driving be-liefs we first show the results of Table II carry through when we

TABLE II

AVERAGE REPRESENTATIVENESS OF TAIL POSITIONS PREDICTS BELIEFS

OLS Predicting Believed Mean of Group G for Each Issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position

of group G for issue

078 024 051 072 018 041

(006) (008) (009) (005) (005) (010)

Avg rep of tail types for

conservatives RconsH

019 055 025 014 012 024

(007) (022) (008) (006) (007) (005)

Constant 101 260 184 093 271 201

(026) (045) (029) (022) (025) (032)

R2 082 048 060 091 031 070

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

TABLE I

INFORMATION ABOUT ndashG PREDICTS BELIEFS ABOUT G

OLS predicting believed mean of group G for each issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position of

conservatives for issue

102 098 096 021 019 025

(0097) (0133) (0076) (0060) (0116) (0060)

True mean position of

liberals for issue

035 086 058 0987 039 073

(0106) (0134) (0131) (0066) (0106) (0135)

Constant 151 335 235 069 258 156

(0195) (0269) (0279) (0122) (0249) (0270)

R2 083 053 066 092 032 068

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

STEREOTYPES 1789

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control for the average likelihood on the tail positions (see Table A4in Online Appendix G) Most tellingly we use the model to predictbeliefs across issues and compare those to the data For simplicitywe use the rank-based truncation specification to predict mean be-liefs when stereotypes include the d most representative types ford frac14 1 T We compare these predictions to those of a model inwhich beliefs are obtained by restricting the distribution to the dmost likely types Our benchmark for both models is predicting thebelieved mean from the entire distribution where d = T We showthat the predictions of the rank-based truncation model with d = 4or 5 compare favorably to both a likelihood-based truncation model(with any d) and the accurate beliefs benchmark Interestingly thisresult suggests that stereotypical beliefs are well approximated byneglecting the least representative types (as opposed to focusingonly on the most representative types) and so represent a moderatethough systematic departure from the standard benchmarkFinally we show that the results we document above hold forboth beliefs held by conservatives and beliefs held by liberals (seeTables A9 A10 and A11 in Online Appendix G)

V Conclusion

We present a model of stereotypical thinking in which DMsmaking predictions about a group overweight the grouprsquos mostdistinctive types These overweighted types are not the mostlikely ones given the DMrsquos data but the most representativeones in the sense of being the most diagnostic of the group rela-tive to other groups Representativeness implies that what ismost distinctive of a group depends on what group it is comparedwith We present experimental evidence that confirms this con-text dependence in recall-based assessments of groups Finallywe evaluated the predictions of the model using political data fromexisting large-scale surveys We find context dependence to be akey feature of beliefs Given the richness of the political data wecan go a step further and identify a role for representativeness inparticular As the representativeness of tail types increases beliefsof a group are distorted in the direction of that tail

Our approach provides a parsimonious and psychologicallyfounded account of how DMs generate simplified representationsof reality from social groups to stock returns and offers a unifiedaccount of disparate pieces of evidence relating to this type of

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uncertainty The model captures the central fact that stereotypeshighlight the greatest difference between groups thus explainingwhy some stereotypes are very accurate while others lack valid-ity Still stereotypes often have a kernel of truth when they arebased on systematicmdasheven if smallmdashdifferences between groupsThis logic allows us to describe a number of heuristics and psy-chological biases many of which arise in the context of predictionproblems Generically our model generates overreaction to diag-nostic information

Our model is based on representativeness and does not cap-ture all the features of stereotypical thinking However it cap-tures perhaps the central feature when we think of a group wefocus on what is most distinctive about it and neglect or under-weight the rest

Saeuroıd Business School University of Oxford

Ohio State University and Harvard Business School

Universita Bocconi and Innocenzo Gasparini Institute

for Economic Research

Harvard University

Supplementary Material

An Online Appendix for this article can be found at QJEonline (qjeoxfordjournalorg)

References

Adorno Theodor Else Frenkel-Brunswik Daniel Levinson and Nevitt SanfordThe Authoritarian Personality (New York Harper amp Row 1950)

Arrow Kenneth lsquolsquoThe Theory of Discriminationrsquorsquo in Discrimination in LaborMarkets Orley Ashenfelter and Albert Rees eds (Princeton NJPrinceton University Press 1973)

Ashton Michael and Victoria Esses lsquolsquoStereotype Accuracy Estimating theAcademic Performance of Ethnic Groupsrsquorsquo Personality and SocialPsychology Bulletin 25 (1999) 225ndash236

Barberis Nicholas Andrei Shleifer and Robert Vishny lsquolsquoA Model of InvestorSentimentrsquorsquo Journal of Financial Economics 49 (1998) 307ndash343

Bayer Sylvia lsquolsquoThe Accuracy of Academic Gender Stereotypesrsquorsquo Sex Roles 40(1999) 787ndash813

Benjamin Dan James Choi and Joshua Strickland lsquolsquoSocial Identity andPreferencesrsquorsquo American Economic Review 100 (2010) 1913ndash1928

Benjamin Dan Matthew Rabin and Collin Raymond lsquolsquoA Model of Non-Belief inthe Law of Large Numbersrsquorsquo Journal of the European Economic Association15 (2015) 515ndash544

Bertrand Marianne lsquolsquoNew Perspectives on Genderrsquorsquo Handbook of LaborEconomics 4 (2011) 1543ndash1590

Bodoh-Creed Aaron Dan Benjamin and Matthew Rabin lsquolsquoThe Dynamics of Base-Rate Neglectrsquorsquo mimeo Haas Business School 2013

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ibrary on October 28 2016

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Bohnet Iris Alexandra van Geen and Max Bazerman lsquolsquoWhen PerformanceTrumps Gender Bias Joint versus Separate Evaluationrsquorsquo ManagementScience 5 (2016) 1225ndash1234

Bordalo Pedro Nicola Gennaioli and Andrei Shleifer lsquolsquoSalience Theory of Choiceunder Riskrsquorsquo Quarterly Journal of Economics 127 (2012) 1243ndash1285

mdashmdashmdash lsquolsquoSalience and Consumer Choicersquorsquo Journal of Political Economy 121(2013) 803ndash843

Briton Nancy and Judith Hall lsquolsquoBeliefs about Female and Male NonverbalCommunicationrsquorsquo Sex Roles 32 (1995) 79ndash90

Buser Thomas Muriel Niederle and Hessel Oosterbeek lsquolsquoGenderCompetitiveness and Career Choicesrsquorsquo Quarterly Journal of Economics 129(2014) 1409ndash1447

Carrell Scott Marianne Page and James West lsquolsquoSex and Science How ProfessorGender Perpetuates the Gender Gaprsquorsquo Quarterly Journal of Economics 125(2010) 1101ndash1144

Chambers John and Darya Melnyk lsquolsquoWhy Do I Hate Thee ConflictMisperceptions and Intergroup Mistrustrsquorsquo Personality and SocialPsychology Bulletin 32 (2006) 1295ndash1311

Chan Wayne Robert R McCrae Filip De Fruyt Lee Jussim CorinnaE Lockenhoff Marleen De Bolle Paul T Costa Jr Angelina R SutinAnu Realo Juri Allik Katsuharu Nakazato Yoshiko ShimonakaMartina Hrebıckova Sylvie Graf Michelle Yik Marina Brunner-SciarraNora Leibovich De Figueora Vanina Schmidt Chang-kyo Ahn Hyun-nie Ahn Maria E Aguilar-Vafaie Jerzy Siuta Barbara SzmigielskaThomas R Cain Janet T Crawford Khairul Anwar Mastor Jean-Pierre Rolland Florence Nansubuga Daniel R MiramontezVeronica Benet-Martınez Jerome Rossier Denis Bratko Iris MarusicJamin Halberstadt Mami Yamaguchi Goran Knezevic Thomas A MartinMirona Gheorghiu Peter B Smith Claudio Barbaranelli Lei WangJane Shakespeare-Finch Margarida P Lima Waldemar KlinkoszAndrzej Sekowski Lidia Alcalay Franco Simonetti Tatyana V AvdeyevaV S Pramila and Antonio Terracciano lsquolsquoStereotypes of Age Differences inPersonality Traits Universal and Accuratersquorsquo Journal of Personality andSocial Psychology 103 (2012) 1050ndash1066

Chen Yan Sherry Xin Liu Tracy Xiao and Margaret Shih lsquolsquoWhich Hat to WearImpact of Natural Identities on Coordination and Cooperationrsquorsquo Games andEconomic Behavior 84 (2014) 58ndash86

Coffman Katherine lsquolsquoEvidence on Self-Stereotyping and the Contribution ofIdeasrsquorsquo Quarterly Journal of Economics 129 (2014) 1625ndash1660

Cunningham Tom lsquolsquoComparisons and Choicersquorsquo mimeo Stockholm University2013

Diekman Amanda Alice Eagly and Patrick Kulesa lsquolsquoAccuracy and Bias in theStereotypes about the Social and Political Attitudes of Women and MenrsquorsquoJournal of Experimental Social Psychology 38 (2002) 268ndash282

Eccles Jacquelynne S Janis E Jacobs and Rena D Harold lsquolsquoGender RoleStereotypes Expectancy Effects and Parentsrsquo Socialization of GenderDifferencesrsquorsquo Journal of Social Issues 46 (1990) 183ndash201

Fryer Roland and Matthew Jackson lsquolsquoA Categorical Model of Cognition andBiased Decision-Makingrsquorsquo BE Journal of Theoretical Economics 8 (2008)1ndash42

Fryer Roland and Steven Levitt lsquolsquoAn Empirical Analysis of the Gender Gap inMathematicsrsquorsquo American Economic Journal Applied Economics 2 (2010)210ndash240

Gennaioli Nicola and Andrei Shleifer lsquolsquoWhat Comes to Mindrsquorsquo Quarterly Journalof Economics 125 (2010) 1399ndash1433

Gennaioli Nicola Andrei Shleifer and Robert Vishny lsquolsquoNeglected RisksFinancial Innovation and Financial Fragilityrsquorsquo Journal of FinancialEconomics 104 (2012) 452ndash468

Gilens Martin lsquolsquoRace and Poverty in America Public Misperceptions and theAmerican News Mediarsquorsquo Public Opinion Quarterly 60 (1996) 515ndash541

Glaeser Edward lsquolsquoThe Political Economy of Hatredrsquorsquo Quarterly Journal ofEconomics 120 (2005) 45ndash86

QUARTERLY JOURNAL OF ECONOMICS1792

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

Glover Dyland Amanda Pallais and William Pariente lsquolsquoDiscrimination as a Self-Fulfilling Prophecy Evidence from French Grocery Storesrsquorsquo mimeo HarvardUniversity 2015

Goldin Claudia Lawrence Katz and Ilyana Kuziemko lsquolsquoThe Homecoming ofAmerican College Women The Reversal of the College Gender GaprsquorsquoJournal of Economic Perspectives 20 (2006) 133ndash156

Graham Jesse Brian Nosek and Jonathan Haidt lsquolsquoThe Moral Stereotypes ofLiberals and Conservatives Exaggeration of Differences across thePolitical Spectrumrsquorsquo PLoS One 7 (2012) 1ndash13

Grether David lsquolsquoBayes Rule as a Descriptive Model The RepresentativenessHeuristicrsquorsquo Quarterly Journal of Economics 95 (1980) 537ndash557

Griffin Dale and Amos Tversky lsquolsquoThe Weighing of Evidence and theDeterminants of Confidencersquorsquo Cognitive Psychology 24 (1992) 411ndash435

Guiso Luigi Ferdinando Monte Paola Sapienza and Luigi Zingales lsquolsquoCultureGender and Mathrsquorsquo Science 320 (2008) 1164ndash1165

Hilton James and William Von Hippel lsquolsquoStereotypesrsquorsquo Annual Review ofPsychology 47 (1996) 237ndash271

Hyde Janet Sara Lindberg Marcia Linn Amy Ellis and Caroline WilliamslsquolsquoGender Similarities Characterize Math Performancersquorsquo Science 321 (2008)494ndash495

Judd Charles and Bernardette Park lsquolsquoDefinition and Assessment of Accuracy inSocial Stereotypesrsquorsquo Psychological Review 100 (1993) 109ndash128

Jussim Lee Jarret Crawford Stephanie Anglin John Chambers Sean Stevensand Florette Cohen lsquolsquoStereotype Accuracy One of the Largest and MostReplicable Effects in All of Social Psychologyrsquorsquo in The Handbook ofPrejudice Stereotyping and Discrimination Todd Nelson ed (MahwahNJ Lawrence Erlbaum 2015)

Kahneman Daniel and Amos Tversky lsquolsquoSubjective Probability A Judgment ofRepresentativenessrsquorsquo Cognitive Psychology 3 (1972) 430ndash454

mdashmdashmdash lsquolsquoOn the Psychology of Predictionrsquorsquo Psychological Review 80 (1973) 237ndash251

Kaplowitz Stan Bradley Fisher and Clifford Broman lsquolsquoHow Accurate ArePerceptions of Social Statistics about Blacks and Whitesrsquorsquo Public OpinionQuarterly 67 (2003) 237ndash243

Kersten Daniel Pascal Mamassian and Alan Yuille lsquolsquoObject Perception asBayesian Inferencersquorsquo Annual Review of Psychology 55 (2004) 271ndash304

Klein Richard Kate A Ratliff Michelangelo Vianello Reginald B Adams JrStepan Bahnik Michael J Bernstein Konrad Bocian Mark J BrandtBeach Brooks Claudia Chloe Brumbaugh Zeynep CemalcilarJesse Chandler Winnee Cheong William E Davis Thierry DevosMatthew Eisner Natalia Frankowska David Furrow Elisa Maria GallianiFred Hasselman Joshua A Hicks James F Hovermale S Jane HuntJeffrey R Huntsinger Hans IJzerman Melissa-Sue John Jennifer A Joy-Gaba Heather Barry Kappes Lacy E Krueger Jaime Kurtz CarmelA Levitan Robyn Mallett Wendy L Morris Anthony J Nelson JasonA Nier Grant Packard Ronaldo Pilati Abraham M RutchickKathleen Schmidt Jeanine L Skorinko Robert Smith Troy G SteinerJustin Storbeck Lyn M Van Swol Donna Thompson Anna van rsquot VeerLeigh Ann Vaughn Marek Vranka Aaron Wichman Julie A Woodzickaand Brian A Nosek lsquolsquoInvestigating Variation in Replicability A ManyLabs Replication Projectrsquorsquo Social Psychology 45 (2014) 142ndash152

Lundberg Shelly and Richard Startz lsquolsquoPrivate Discrimination and SocialIntervention in Competitive Labor Marketsrsquorsquo American Economic Review73 (1983) 340ndash347

Madon Stephanie Max Guyll Kathy Aboufadel Eulices Montiel Alison SmithPolly Palumbo and Lee Jussim lsquolsquoEthnic and National Stereotypes ThePrinceton Trilogy Revisited and Revisedrsquorsquo Personality and SocialPsychological Bulletin 27 (2001) 996ndash1010

Martin Carol lsquolsquoA Ratio Measure of Sex Stereotypingrsquorsquo Journal of Personality andSocial Psychology 52 (1987) 489ndash499

STEREOTYPES 1793

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

McCauley Clark Krishna Thangavelu and Paul Rozin lsquolsquoSex Stereotyping ofOccupations in Relation to Television Representations and Census FactsrsquorsquoBasic and Applied Social Psychology 9 (1988) 197ndash212

Mullainathan Sendhil lsquolsquoThinking through Categoriesrsquorsquo mimeo HarvardUniversity 2002

Ortoleva Pietro and Erik Snowberg lsquolsquoOverconfidence in Political BehaviorrsquorsquoAmerican Economic Review 105 (2015) 504ndash535

Phelps Edmund lsquolsquoThe Statistical Theory of Racism and Sexismrsquorsquo AmericanEconomic Review 62 (1972) 659ndash661

Pope Devin and Justin Sydnor lsquolsquoGeographic Variation in the Gender Differencesin Test Scoresrsquorsquo Journal of Economic Perspectives 24 (2010) 95ndash108

Rabin Matthew lsquolsquoInference by Believers in the Law of Small NumbersrsquorsquoQuarterly Journal of Economics 117 (2002) 775ndash816

Rabin Matthew and Joel Schrag lsquolsquoFirst Impressions Matter A Model ofConfirmatory Biasrsquorsquo Quarterly Journal of Economics 114 (1999) 37ndash82

Rabin Matthew and Dimitri Vayanos lsquolsquoThe Gamblerrsquos and Hot-Hand FallaciesTheory and Applicationsrsquorsquo Review of Economic Studies 77 (2010) 730ndash778

Reuben Ernesto Paola Sapienza and Luigi Zingales lsquolsquoHow Stereotypes ImpairWomenrsquos Careers in Sciencersquorsquo Proceedings of the National Academy ofSciences 111 (2014) 4403ndash4408

Rosch Eleanor lsquolsquoNatural Categoriesrsquorsquo Cognitive Psychology 4 (1973) 328ndash350Ryan Carey S lsquolsquoAccuracy of Black and White College Studentsrsquo In-Group and

Out-Group Stereotypesrsquorsquo Personality and Social Psychology Bulletin 22(1996) 1114ndash1127

Schneider David The Psychology of Stereotyping (New York Guilford Press2004)

Schneider David Albert Hastorf and Phoebe Ellsworth Person Perception(Reading MA Addison-Wesley 1979)

Shih Margaret Todd Pittinsky and Nalini Ambady lsquolsquoStereotype SusceptibilityIdentity Salience and Shifts in Quantitative Performancersquorsquo PsychologicalScience 10 (1999) 80ndash83

Shih Margaret Todd Pittinsky and Amy Trahan lsquolsquoDomain-Specific Effects ofStereotypes on Performancersquorsquo Self and Identity 5 (2006) 1ndash14

Steele Claude Whistling Vivaldi How Stereotypes Affect Us and What We CanDo (New York Norton 2010)

Tenenbaum Joshua and Thomas Griffiths lsquolsquoThe Rational Basis ofRepresentativenessrsquorsquo 23rd Annual Conference of the Cognitive ScienceSociety (2001) 1036ndash1041

Tversky Amos and Daniel Kahneman lsquolsquoExtensional versus Intuitive ReasoningThe Conjunction Fallacy in Probability Judgmentrsquorsquo Psychological Review 90(1983) 293ndash315

Weinberger Catherin lsquolsquoIs the Science and Engineering Workforce Drawn fromthe Far Upper Tail of the Math Ability Distributionrsquorsquo mimeo UCSB 2005

Westfall Jacob Leaf Van Boven John Chambers and Charles Judd lsquolsquoPerceivingPolitical Polarization in the United States Party Identity Strength andAttitude Extremity Exacerbate the Perceived Partisan DividersquorsquoPsychological Science 10 (2015) 145ndash158

Wolsko Christopher Bernadette Park Charles Judd and Bernd WittenbrinklsquolsquoFraming Interethnic Ideology Effects of Multicultural and Color-BlindPerspectives on Judgments of Groups and Individualsrsquorsquo Journal ofPersonality and Social Psychology 78 (2000) 635ndash654

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Page 25: I. Introduction · uneducated at the beginning of the 20th century, and as high achievers at the beginning of the 21st (Madon et al. 2001). Social science has produced three broad

that representativeness may generate context dependence hasnot been tested before

To assess this prediction we perform a controlled laboratoryexperiment that allows us to isolate representativeness frommany confounding factorsmdashhistorical sociological or other-wisemdashthat may affect stereotype formation in the real worldWe construct our own groups of ordinary objects creating atarget group G and a comparison group ndashG We hold thetarget group G fixed and explore how participant impressions ofit change as we change the comparison group ndashG and thusrepresentativeness

We conducted several experiments in the laboratory and onAmazon Mechanical Turk Each involves a basic three-stepdesign First participants are shown the target group and a ran-domly assigned comparison group for 15 seconds In this timedifferences between groups can be noticed but the groupsrsquo precisecompositions cannot be memorized The second step consists of afew filler questions which briefly draw the participantsrsquo cognitivebandwidth away from their observation Finally participants areasked to assess the groups they saw Participants are incentiv-ized to provide accurate answers

We randomly assign participants to either the Control or theRepresentativeness condition In the Control condition G and ndashGhave nearly identical distributions so that all types are similarlyrepresentative for each group In the Representativeness condi-tion ndashG is changed in such a way that a certain type becomes veryrepresentative for G Context dependence implies that the assess-ment of G should now overweight this representative type eventhough the distribution of G itself has not changed

We ran six experiments of this form with design changesfocused on reducing participant confusion and removing con-founds We describe the final and most refined version of theseexperiments here In an attempt to provide a overview of the re-sults while remaining concise we provide the results from pooledspecifications that use all data collected In Online Appendix Fwe offer additional details and report all experiments conductedWe also give instructions and materials for each experiment thefull data set is available by request

Consider first the experiment illustrated in Figure II Agroup of 25 cartoon girls is presented next to a group of 25 cartoonboys in T-shirts of different colors blue green or purple In theControl condition (Figure II Panel a) the groups have identical

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color distributions (13 purple 12 green) so no color is represen-tative of either group The Representativeness condition (Panel b)compares the same group of girls with a different group of boysfor whom green shirts are replaced with blue shirts Now onlygirls wear green and only boys wear blue These colors althoughstill not the most frequent for either group are now most repre-sentative For each group girls and boys participants are asked anumber of questions concerning the frequency of T-shirts of dif-ferent colors worn by that group

Applying our model in the control condition the type space isT frac14 fgreen purpleg and the groups are G = girls and ndashG = boysGiven that the color distributions are identical across groups both

types are equally representativegreengirls

greenboysfrac14 1 frac14

purplegirls

purpleboys As a result

assessment of G should be correct on average stcontrolgreengirls frac14 greengirls

and stcontrolpurplegirls frac14 purplegirls for any weighing function (the same is

true about assessments of ndashG)In the treatment condition the distribution of shirt colors re-

mains the same for girls For boys green shirts are changed intoblue Thus the type space changes to T frac14 fgreen purple bluegand the representative color for girls becomes greengreengirls

greenboysfrac14 1 gt 1 frac14

purplegirls

purpleboys while that for boys becomes blue As

a result in the treatment condition subjects should inflate the

frequency of green shirts relative to the truth sttreatmentgreengirls

gt greengirls (the same should happen to assessments of blueshirts for boys) We also expect the assessed frequency of greenshirts to go up relative to the control condition namely

sttreatmentgreengirls gt stcontrol

greengirls Critically the only factor that varies

across treatments is the representativeness of the 12-colorshirt Thus if we see differences across conditions the causalrole of representativeness-based recall in shaping group judg-ments is clear24

24 We vary which colors are used in which roles across participants Someparticipants saw this particular color distribution while others see for examplegreen as the modal color and purple as the diagnostic color for boys in theRepresentativeness condition and blue as the diagnostic color for girls in theRepresentativeness condition We vary the colors across the roles to avoid con-founding the characteristics of any particular color with its diagnosticity

QUARTERLY JOURNAL OF ECONOMICS1778

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FIG

UR

EII

T-S

hir

tsE

xp

erim

ent

Fig

ure

sap

pea

red

inco

lor

top

art

icip

an

tsin

the

exp

erim

ent

For

clari

ty

we

have

ad

ded

ale

tter

toea

chT

-sh

irt

toid

enti

fyth

eco

lor

for

the

read

er

lsquolsquoGrsquorsquo

ind

icate

sgre

en

lsquolsquoPrsquorsquo

ind

icate

sp

urp

le

lsquolsquoBrsquorsquo

ind

icate

sblu

eT

hes

ele

tter

sd

idn

otap

pea

rto

part

icip

an

tsan

dare

for

read

erre

fere

nce

only

P

lease

see

onli

ne

ver

sion

ofp

ubli

shed

art

icle

for

colo

rfi

gu

reex

act

lyas

itap

pea

red

top

art

icip

an

ts

STEREOTYPES 1779

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We collected data from 301 participants using this T-shirtsdesign25 Since the number of green and purple shirts is verysimilar we first ask each participant the simplest question ofwhich shirt color is modal Next we ask participants to assessthe share of green and purple shirts

Consistent with the role of representativeness participantsassigned to the Representativeness condition are 105 percentagepoints more likely to recall the less frequent color (green for girlsor blue for boys) as the modal color when it is representative of agroup (35 of participants guess the less frequent color is modalin the Control condition this proportion increases to 46 in theRepresentativeness condition p = 01 estimated from a probitregression reported in Online Appendix F)

We now turn to subjectsrsquo estimates of how many T-shirts ofeach color they saw in each group In both conditions the truedifference in counts is 1 (13 purple shirts 12 green or blue shirts)In the Control condition participants on average believe they saw054 more purple shirts than green or blue shirts In theRepresentativeness condition participants believe they saw072 fewer purple shirts than green or blue shirts (the acrosstreatment difference is significant with p = 01 from OLS regres-sion reported in Online Appendix F)

In total we collected data for six experiments of this generalstructure gathering evidence from more than 1000 participantsAs we describe in Online Appendix F although there is substan-tial variation across experiments when we pool all of the data wefind significant aggregate treatment effects in line with a role ofrepresentativeness in judgment We employ four different unor-dered types designs similar to the T-shirts experiment using sixsamples (four online and two in the laboratory) with 741 partic-ipants We find effects in the predicted direction for five of the sixsamples Using a probit regression that pools the data for theseunordered type experiments we find that participants are 93 per-centage points more likely to guess that the less frequent type ismodal when it is representative than when it is not (p = 002) Wealso run a family of ordered types experiments (two designs fivesamples 402 participants) Unlike the simpler T-shirts style

25 Throughout our analysis we exclude any participant who participated in aprevious version of the experiment and any participant who self-identified as color-blind In Online Appendix F we show that our results are unchanged if we includethese additional observations

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design the theoretical predictions for the ordered types designsare more sensitive to the specific assumptions one makes aboutthe weighting function of the DM26 We find effects in the pre-dicted direction for three of the five samples As we discuss inmore detail in Online Appendix F the ordered types resultsvary by platform with consistently stronger results on AmazonMechanical Turk than in the laboratory samples Pooling all or-dered types experiments participants are 93 percentage pointsmore likely to guess that the group of interest has a greater av-erage than the comparison group when the right tail is represen-tative (p = 062) Given our simple experimental setting withgroups of mundane objects we interpret our resultsmdasha signifi-cant and reasonably sized impact on average beliefsmdashas an im-portant proof of concept the presence of representative typesbiases ex post assessment

IVB Empirical Evidence on Political Stereotypes

We examine two data sets on political preferences and be-liefs about political preferences in the United States We inves-tigate the roles of representativeness and context dependence byseparately testing for hypotheses that allow us to assess the lead-ing theories of stereotypes

First we test whether beliefs are correct or depart systemat-ically from the truth The statistical discrimination approachbuilds on the assumption that people hold rational expectationsof group traits Comparing beliefs to the truth allows us to assessthe validity of this assumption in our data

Second we test if beliefs depart from the truth by exagger-ating (mean) differences among groups per the kernel of truthhypothesis This is an implicit test of context dependence be-cause it implies that beliefs about the target groups are shapednot only by that grouprsquos characteristics but also by those of thereference group27

Third we test if distortions in beliefs can be accounted for bythe overweighting of highly representative types (defined astypes that are relatively more frequent in the target relative to

26 This is due in part to our choice to not study MLRP distributions We moti-vate and discuss this design decision in Online Appendix F

27 Of course unlike in the laboratory experiment in this setting we cannot testfor context dependence by exogenously varying the reference group

STEREOTYPES 1781

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the reference group) The second and third tests address the keypredictions of our model

1 The Data We have two data sets on political preferences andbeliefs about political preferences The first data set from GrahamNosek and Haidt (GNH 2012) contains data from the MoralFoundations Questionnaire Respondents (1174 self-identified lib-erals and 500 self-identified conservatives) answer questions abouttheir position on a subset of 45 issues 20 moral relevance state-ments (eg lsquolsquowhen you decide whether something is right orwrong to what extent are the following considerations relevantto your thinkingrsquorsquo) and 25 moral judgments (eg lsquolsquoindicate theextent to which you would agree or disagreersquorsquo) For each issue arandomly determined subset of participants states their own posi-tion another subset states their belief on the position of a lsquolsquotypicalliberalrsquorsquo and a third subset states their belief on the position of alsquolsquotypical conservativersquorsquo The data thus include the distribution overpositions for both liberal and conservatives as well as the averagebelieved typical position of liberals and of conservatives on the 45issues Each position is elicited on 1ndash6 scale

The second data set comes from the American NationalElection Survey (ANES) and contains data from more than20000 respondents between 1964 and 201228 The surveycovers political issues of the day such as the optimal amount ofgovernment spending and service provision (1984ndash2000) or theplace of women in society (1972ndash1998) We focus on the 10 issuesthat ask participants to respond on a 1ndash7 scale (rather than justindicate binary agreement or disagreement) all 10 issues areasked in multiple years Participants are asked to provide theirown position on the scale and their believed position of theDemocratic and Republican parties (lsquolsquoWhere would you placethe Democratic [Republican] party on this scalersquorsquo) The data in-clude for each issue-year observation the distribution of partic-ipant positions for self-identified liberals and self-identifiedconservatives as well as the distribution of believed typical posi-tions of the Democratic and Republican parties

28 These data are publicly available at httpwwwelectionstudiesorgstudy-pagesanes_timeseries_cdfanes_timeseries_cdfhtm

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2 Empirical Strategy Our analysis focuses on beliefs abouttwo groups Conservatives and Liberals The types are the possi-ble positions for each issue (1 2 6 7) For the GNH data weinterpret beliefs about the lsquolsquotypicalrsquorsquo element of a group to coincidewith the believed average position in that group Similarly forthe ANES data we use the believed party positions as a proxy forbelieved mean of each group29 We then take as a benchmark thehypothesis that individuals hold accurate beliefs about eachgroup and in particular that believed mean position shouldequal true mean position at least on average across subjectsThe accurate beliefs hypothesis underlies the most common eco-nomic model of stereotyping statistical discrimination

To assess our representativeness-based model we perform aregression exercise To test our model in a linear regressionframework we rely on linear approximations of the weightingfunction Our model then yields two regression specifications

PROPOSITION 4 Let G 2 fconservative liberal g and assume

ht h tG

tG

be a differentiable and strictly increasing weight-

ing function as in Definition 2 The following hold as a first-order approximation around identical distributions G

Gfrac14 1

(i) Kernel of truth regression There exists a constant gt 0such that

EstethtjGTHORN frac14 EethtjGTHORNeth1thorn THORN EethtjGTHORNeth5THORN

(ii) Representativeness regression Denote H frac14 fT 2 Tg

the right tail of types and RconsH frac14

PHtconsPHtlib

as the average

representativeness of right tail types for conservatives

29 This assumption is consistent with the authorsrsquo interpretation of the GNHdata (GNH 2012) and with previous studies using ANES (eg Westfall et al 2015)Furthermore to the extent that this assumption holds equally well for most issueswithin a data set our focus on cross-issue differences should allow us to test thepredictions of our model even with an imperfect proxy for beliefs of mean positionsFinally the data provide some insight into whether subjects are reporting (per-ceived) modal or mean types As we show the modal type is a poor prediction ofstated beliefs while a distorted mean slanted toward representative types is anaccurate prediction of stated beliefs

STEREOTYPES 1783

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Under the further approximation where tcons

tlibampRcons

H for

t 2 H

EstethtjconsTHORN frac14 EethtjconsTHORN thorn consethR

consH 1THORNeth6THORN

EstethtjlibTHORN frac14 EethtjlibTHORN libethR

consH 1THORNeth7THORN

where lcons and llib are positive constants

The first regression allows us to test for the kernel of truthhypothesis and the second set of regressions allows us to test forthe role of representativeness

Equation (5) says that respondents in our model inflate theaverage position of a group say the conservatives if and only ifthe group has a higher average position than the other groupnamely the liberals Formally EstethtjconsTHORN gt EethtjconsTHORN if and onlyif EethtjconsTHORN gt EethtjlibTHORN Because in our measurement scale highertypes mean lsquolsquomore conservativersquorsquo we expect (i) believed conserva-tive average to be higher than the truth and (ii) the extent ofoverstatement to decrease in the average liberal position EethtjlibTHORNConversely we expect the average liberal position to be lowerthan the truth the more so the higher the average conservativeposition EethtjconsTHORN

As previously discussed the basis of these predictions is con-text dependence information about the distribution of ndashG is rel-evant for the beliefs about G This context dependence isinconsistent with rational expectations in which only thegrouprsquos own means should affect beliefs We test the hypothesisthat the true mean EethtjGTHORN is a significant predictor of the believedmean E

stethtjGTHORN with a positive sign and the other grouprsquos truemean EethtjGTHORN is a predictor of the believed mean with a negativesign

Equations (6) and (7) say that repondentsrsquo assessment bias isshaped by representativeness When the right tail is more repre-sentative for conservatives (Rcons

H 1 positive and large) partici-pants should inflate the average conservative position more(higher E

stethtjconsTHORN EethtjconsTHORN) and deflate the average liberal po-sition more (lower E

stethtjlibTHORN EethtjlibTHORN) We test the hypothesisthat the inflation in conservative positions is positively associatedwith the representativeness of the right tail for the conservativesand the inflation in liberal positions is negatively associated with

QUARTERLY JOURNAL OF ECONOMICS1784

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it Once again the representativeness of the right tail is com-puted using the true distribution of positions

In equations (6) and (7) in many cases the representative tailis also the most likely one As a consequence these tests cannotdistinguish a representativeness-based from a likelihood-basedmodel of distorted beliefs We perform two additional testsFirst we run versions of equations (6) and (7) in which we controlfor the likelihood of tails (see Table A4 in Online Appendix G)Second we compute numerically the predictions of a representa-tiveness-based model of stereotypes and a likelihood-based modelof stereotypes We then assess which of these two is better able tomatch the data on beliefs

3 Empirical Results To begin we illustrate the structure ofthe data and the nature of our predictions with two simple exam-ples from the GNH data set focusing on beliefs about conserva-tives In example 1 participants are asked about their agreementwith the statement lsquolsquoIt can never be right to kill a human beingrsquorsquoIn example 2 participants are asked about the moral relevance oflsquolsquowhether or not someone cared for someone weak or vulnerablersquorsquoAs can be seen in Figure III in example 1 the modal position(strongly disagree (1)) and most representative positions(strongly disagree (1)) coincide for conservatives In contrast inexample 2 in Figure III the most representative types (slightlyrelevant (3) not at all relevant (1)) are not most likely for theconservative group Following Proposition 1 we predict that be-liefs will be distorted in the direction of the most representativetypes Thus we expect more exaggeration in example 2 than inexample 1 since in example 2 the most representative types (inthe left tail) are far from the modal type whereas in example 1they coincide This is what we find the conservative position isexaggerated by only 009 positions in Example 1 (true mean 299believed mean 290) but by 106 positions in Example 2 (truemean 421 believed mean 315)

In the full data sets we treat each (issue year) pair as anobservation and we cluster standard errors at the issue level Forthe GNH data we have 45 observations 45 issues measured inthe same year For the ANES data we have 66 observations 10issues measured in multiple years To begin we simply docu-ment systematic exaggeration in both data sets This is a primaryfocus of the original analysis in GNH (2012) and also in Westfall

STEREOTYPES 1785

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FIGURE III

Two Examples

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et al (2015)rsquos analysis of the ANES data30 Figure IV shows thatthe believed difference between typical conservative and typicalliberal positions is larger than the true difference in mean posi-tions for 109 of the 111 observations The data for both GNH(squares) and ANES (triangles) lie above the 45-degree line(dashed)31 Average exaggeration is 062 positions on the scale(066 in the GNH data 059 in the ANES data)32

The systematic and significant exaggeration of mean differ-ences suggests that the benchmark model of accurate beliefs ismissing something important Indeed this exaggeration reflectsthe fact that believed means are typically more extreme than truemeans First note that the kernel of truth regression (equation(5)) generates exaggeration of mean differences just as docu-mented in Figure IV

EstethtjGTHORN E

stethtjGTHORN frac14 eth1thorn 2THORN frac12EethtjGTHORN EethtjGTHORN

To bring this prediction to the data we regress the believedmean position for each group EBethtjGTHORN on the true mean of thegroup EethtjGTHORN and the true mean of the comparison groupEethtjGTHORN across issues We do this for each group (liberals con-servatives) in each data set separately We also present pooledspecifications that combine the data sets to make a prediction fora given group (liberals conservatives) In these pooled specifica-tions we include a dummy variable indicating whether theobservation came from the ANES data set For all specificationswe cluster observations at the issue level33 The results from re-gression are shown in Table I In every specification we find thatEethtjGTHORN is a significant predictor of EBethtjGTHORN with the predicted pos-itive sign Crucially for five of the six specifications the mean of

30 Chambers and Melnyk (2006) also find evidence of exaggeration of truedifferences in beliefs about political positions

31 For convenience we recode all issues so that the high end of the scale (67)represents the stereotypically more conservative position

32 A natural question to ask is how beliefs vary across liberals and conserva-tives That is do beliefs about a group G depend on membership in G versus ndashG Ourmodel does not speak to this issue However in Online Appendix G we show thatthe results we document below hold for both beliefs held by conservatives and be-liefs held by liberals see Tables A9 A10 and A11

33 In general the results presented below for the ANES data are not largelyimpacted by the decision to cluster at the issue level Similar results are obtained ifthe data are not clustered

STEREOTYPES 1787

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the comparison group EethtjGTHORN is also a significant predictor ofE

BethtjGTHORN with the predicted negative signAlthough these results provide strong evidence of context

dependence and are consistent with our model they do not pindown a role for representativeness of types Our next test relatesthe magnitude of representativeness of tail types to the magni-tude of belief distortions

To this end we implement the regressions in equations (6)and (7) Following Proposition 4 we compute the average repre-

sentativeness of tail types for conservatives RconsH frac14

PtT2tconsPtT2tlib

We

again test the hypothesis that RconsH is a significant predictor of Est

ethtjconsTHORN with a positive sign and a predictor of EstethtjlibTHORN with a

negative sign Table II shows that conditional on true mean RconsH

predicts believed mean for each group G as expected The firstthree specifications display the results for predicting beliefs heldabout conservatives In both data sets the average representa-tiveness of tail types for conservatives is a significant positivepredictor of beliefs held about conservatives The final three spe-cifications display the results for predicting beliefs held about

FIGURE IV

Exaggeration of Differences

QUARTERLY JOURNAL OF ECONOMICS1788

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liberals We find that the average representativeness of tail typesfor conservatives is a negative predictor of beliefs held about lib-erals This effect is significant in the GNH data and marginallysignificant in the ANES data

We present several additional results in Online Appendix GTo further examine the role of representativeness in driving be-liefs we first show the results of Table II carry through when we

TABLE II

AVERAGE REPRESENTATIVENESS OF TAIL POSITIONS PREDICTS BELIEFS

OLS Predicting Believed Mean of Group G for Each Issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position

of group G for issue

078 024 051 072 018 041

(006) (008) (009) (005) (005) (010)

Avg rep of tail types for

conservatives RconsH

019 055 025 014 012 024

(007) (022) (008) (006) (007) (005)

Constant 101 260 184 093 271 201

(026) (045) (029) (022) (025) (032)

R2 082 048 060 091 031 070

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

TABLE I

INFORMATION ABOUT ndashG PREDICTS BELIEFS ABOUT G

OLS predicting believed mean of group G for each issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position of

conservatives for issue

102 098 096 021 019 025

(0097) (0133) (0076) (0060) (0116) (0060)

True mean position of

liberals for issue

035 086 058 0987 039 073

(0106) (0134) (0131) (0066) (0106) (0135)

Constant 151 335 235 069 258 156

(0195) (0269) (0279) (0122) (0249) (0270)

R2 083 053 066 092 032 068

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

STEREOTYPES 1789

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control for the average likelihood on the tail positions (see Table A4in Online Appendix G) Most tellingly we use the model to predictbeliefs across issues and compare those to the data For simplicitywe use the rank-based truncation specification to predict mean be-liefs when stereotypes include the d most representative types ford frac14 1 T We compare these predictions to those of a model inwhich beliefs are obtained by restricting the distribution to the dmost likely types Our benchmark for both models is predicting thebelieved mean from the entire distribution where d = T We showthat the predictions of the rank-based truncation model with d = 4or 5 compare favorably to both a likelihood-based truncation model(with any d) and the accurate beliefs benchmark Interestingly thisresult suggests that stereotypical beliefs are well approximated byneglecting the least representative types (as opposed to focusingonly on the most representative types) and so represent a moderatethough systematic departure from the standard benchmarkFinally we show that the results we document above hold forboth beliefs held by conservatives and beliefs held by liberals (seeTables A9 A10 and A11 in Online Appendix G)

V Conclusion

We present a model of stereotypical thinking in which DMsmaking predictions about a group overweight the grouprsquos mostdistinctive types These overweighted types are not the mostlikely ones given the DMrsquos data but the most representativeones in the sense of being the most diagnostic of the group rela-tive to other groups Representativeness implies that what ismost distinctive of a group depends on what group it is comparedwith We present experimental evidence that confirms this con-text dependence in recall-based assessments of groups Finallywe evaluated the predictions of the model using political data fromexisting large-scale surveys We find context dependence to be akey feature of beliefs Given the richness of the political data wecan go a step further and identify a role for representativeness inparticular As the representativeness of tail types increases beliefsof a group are distorted in the direction of that tail

Our approach provides a parsimonious and psychologicallyfounded account of how DMs generate simplified representationsof reality from social groups to stock returns and offers a unifiedaccount of disparate pieces of evidence relating to this type of

QUARTERLY JOURNAL OF ECONOMICS1790

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uncertainty The model captures the central fact that stereotypeshighlight the greatest difference between groups thus explainingwhy some stereotypes are very accurate while others lack valid-ity Still stereotypes often have a kernel of truth when they arebased on systematicmdasheven if smallmdashdifferences between groupsThis logic allows us to describe a number of heuristics and psy-chological biases many of which arise in the context of predictionproblems Generically our model generates overreaction to diag-nostic information

Our model is based on representativeness and does not cap-ture all the features of stereotypical thinking However it cap-tures perhaps the central feature when we think of a group wefocus on what is most distinctive about it and neglect or under-weight the rest

Saeuroıd Business School University of Oxford

Ohio State University and Harvard Business School

Universita Bocconi and Innocenzo Gasparini Institute

for Economic Research

Harvard University

Supplementary Material

An Online Appendix for this article can be found at QJEonline (qjeoxfordjournalorg)

References

Adorno Theodor Else Frenkel-Brunswik Daniel Levinson and Nevitt SanfordThe Authoritarian Personality (New York Harper amp Row 1950)

Arrow Kenneth lsquolsquoThe Theory of Discriminationrsquorsquo in Discrimination in LaborMarkets Orley Ashenfelter and Albert Rees eds (Princeton NJPrinceton University Press 1973)

Ashton Michael and Victoria Esses lsquolsquoStereotype Accuracy Estimating theAcademic Performance of Ethnic Groupsrsquorsquo Personality and SocialPsychology Bulletin 25 (1999) 225ndash236

Barberis Nicholas Andrei Shleifer and Robert Vishny lsquolsquoA Model of InvestorSentimentrsquorsquo Journal of Financial Economics 49 (1998) 307ndash343

Bayer Sylvia lsquolsquoThe Accuracy of Academic Gender Stereotypesrsquorsquo Sex Roles 40(1999) 787ndash813

Benjamin Dan James Choi and Joshua Strickland lsquolsquoSocial Identity andPreferencesrsquorsquo American Economic Review 100 (2010) 1913ndash1928

Benjamin Dan Matthew Rabin and Collin Raymond lsquolsquoA Model of Non-Belief inthe Law of Large Numbersrsquorsquo Journal of the European Economic Association15 (2015) 515ndash544

Bertrand Marianne lsquolsquoNew Perspectives on Genderrsquorsquo Handbook of LaborEconomics 4 (2011) 1543ndash1590

Bodoh-Creed Aaron Dan Benjamin and Matthew Rabin lsquolsquoThe Dynamics of Base-Rate Neglectrsquorsquo mimeo Haas Business School 2013

STEREOTYPES 1791

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

Bohnet Iris Alexandra van Geen and Max Bazerman lsquolsquoWhen PerformanceTrumps Gender Bias Joint versus Separate Evaluationrsquorsquo ManagementScience 5 (2016) 1225ndash1234

Bordalo Pedro Nicola Gennaioli and Andrei Shleifer lsquolsquoSalience Theory of Choiceunder Riskrsquorsquo Quarterly Journal of Economics 127 (2012) 1243ndash1285

mdashmdashmdash lsquolsquoSalience and Consumer Choicersquorsquo Journal of Political Economy 121(2013) 803ndash843

Briton Nancy and Judith Hall lsquolsquoBeliefs about Female and Male NonverbalCommunicationrsquorsquo Sex Roles 32 (1995) 79ndash90

Buser Thomas Muriel Niederle and Hessel Oosterbeek lsquolsquoGenderCompetitiveness and Career Choicesrsquorsquo Quarterly Journal of Economics 129(2014) 1409ndash1447

Carrell Scott Marianne Page and James West lsquolsquoSex and Science How ProfessorGender Perpetuates the Gender Gaprsquorsquo Quarterly Journal of Economics 125(2010) 1101ndash1144

Chambers John and Darya Melnyk lsquolsquoWhy Do I Hate Thee ConflictMisperceptions and Intergroup Mistrustrsquorsquo Personality and SocialPsychology Bulletin 32 (2006) 1295ndash1311

Chan Wayne Robert R McCrae Filip De Fruyt Lee Jussim CorinnaE Lockenhoff Marleen De Bolle Paul T Costa Jr Angelina R SutinAnu Realo Juri Allik Katsuharu Nakazato Yoshiko ShimonakaMartina Hrebıckova Sylvie Graf Michelle Yik Marina Brunner-SciarraNora Leibovich De Figueora Vanina Schmidt Chang-kyo Ahn Hyun-nie Ahn Maria E Aguilar-Vafaie Jerzy Siuta Barbara SzmigielskaThomas R Cain Janet T Crawford Khairul Anwar Mastor Jean-Pierre Rolland Florence Nansubuga Daniel R MiramontezVeronica Benet-Martınez Jerome Rossier Denis Bratko Iris MarusicJamin Halberstadt Mami Yamaguchi Goran Knezevic Thomas A MartinMirona Gheorghiu Peter B Smith Claudio Barbaranelli Lei WangJane Shakespeare-Finch Margarida P Lima Waldemar KlinkoszAndrzej Sekowski Lidia Alcalay Franco Simonetti Tatyana V AvdeyevaV S Pramila and Antonio Terracciano lsquolsquoStereotypes of Age Differences inPersonality Traits Universal and Accuratersquorsquo Journal of Personality andSocial Psychology 103 (2012) 1050ndash1066

Chen Yan Sherry Xin Liu Tracy Xiao and Margaret Shih lsquolsquoWhich Hat to WearImpact of Natural Identities on Coordination and Cooperationrsquorsquo Games andEconomic Behavior 84 (2014) 58ndash86

Coffman Katherine lsquolsquoEvidence on Self-Stereotyping and the Contribution ofIdeasrsquorsquo Quarterly Journal of Economics 129 (2014) 1625ndash1660

Cunningham Tom lsquolsquoComparisons and Choicersquorsquo mimeo Stockholm University2013

Diekman Amanda Alice Eagly and Patrick Kulesa lsquolsquoAccuracy and Bias in theStereotypes about the Social and Political Attitudes of Women and MenrsquorsquoJournal of Experimental Social Psychology 38 (2002) 268ndash282

Eccles Jacquelynne S Janis E Jacobs and Rena D Harold lsquolsquoGender RoleStereotypes Expectancy Effects and Parentsrsquo Socialization of GenderDifferencesrsquorsquo Journal of Social Issues 46 (1990) 183ndash201

Fryer Roland and Matthew Jackson lsquolsquoA Categorical Model of Cognition andBiased Decision-Makingrsquorsquo BE Journal of Theoretical Economics 8 (2008)1ndash42

Fryer Roland and Steven Levitt lsquolsquoAn Empirical Analysis of the Gender Gap inMathematicsrsquorsquo American Economic Journal Applied Economics 2 (2010)210ndash240

Gennaioli Nicola and Andrei Shleifer lsquolsquoWhat Comes to Mindrsquorsquo Quarterly Journalof Economics 125 (2010) 1399ndash1433

Gennaioli Nicola Andrei Shleifer and Robert Vishny lsquolsquoNeglected RisksFinancial Innovation and Financial Fragilityrsquorsquo Journal of FinancialEconomics 104 (2012) 452ndash468

Gilens Martin lsquolsquoRace and Poverty in America Public Misperceptions and theAmerican News Mediarsquorsquo Public Opinion Quarterly 60 (1996) 515ndash541

Glaeser Edward lsquolsquoThe Political Economy of Hatredrsquorsquo Quarterly Journal ofEconomics 120 (2005) 45ndash86

QUARTERLY JOURNAL OF ECONOMICS1792

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

Glover Dyland Amanda Pallais and William Pariente lsquolsquoDiscrimination as a Self-Fulfilling Prophecy Evidence from French Grocery Storesrsquorsquo mimeo HarvardUniversity 2015

Goldin Claudia Lawrence Katz and Ilyana Kuziemko lsquolsquoThe Homecoming ofAmerican College Women The Reversal of the College Gender GaprsquorsquoJournal of Economic Perspectives 20 (2006) 133ndash156

Graham Jesse Brian Nosek and Jonathan Haidt lsquolsquoThe Moral Stereotypes ofLiberals and Conservatives Exaggeration of Differences across thePolitical Spectrumrsquorsquo PLoS One 7 (2012) 1ndash13

Grether David lsquolsquoBayes Rule as a Descriptive Model The RepresentativenessHeuristicrsquorsquo Quarterly Journal of Economics 95 (1980) 537ndash557

Griffin Dale and Amos Tversky lsquolsquoThe Weighing of Evidence and theDeterminants of Confidencersquorsquo Cognitive Psychology 24 (1992) 411ndash435

Guiso Luigi Ferdinando Monte Paola Sapienza and Luigi Zingales lsquolsquoCultureGender and Mathrsquorsquo Science 320 (2008) 1164ndash1165

Hilton James and William Von Hippel lsquolsquoStereotypesrsquorsquo Annual Review ofPsychology 47 (1996) 237ndash271

Hyde Janet Sara Lindberg Marcia Linn Amy Ellis and Caroline WilliamslsquolsquoGender Similarities Characterize Math Performancersquorsquo Science 321 (2008)494ndash495

Judd Charles and Bernardette Park lsquolsquoDefinition and Assessment of Accuracy inSocial Stereotypesrsquorsquo Psychological Review 100 (1993) 109ndash128

Jussim Lee Jarret Crawford Stephanie Anglin John Chambers Sean Stevensand Florette Cohen lsquolsquoStereotype Accuracy One of the Largest and MostReplicable Effects in All of Social Psychologyrsquorsquo in The Handbook ofPrejudice Stereotyping and Discrimination Todd Nelson ed (MahwahNJ Lawrence Erlbaum 2015)

Kahneman Daniel and Amos Tversky lsquolsquoSubjective Probability A Judgment ofRepresentativenessrsquorsquo Cognitive Psychology 3 (1972) 430ndash454

mdashmdashmdash lsquolsquoOn the Psychology of Predictionrsquorsquo Psychological Review 80 (1973) 237ndash251

Kaplowitz Stan Bradley Fisher and Clifford Broman lsquolsquoHow Accurate ArePerceptions of Social Statistics about Blacks and Whitesrsquorsquo Public OpinionQuarterly 67 (2003) 237ndash243

Kersten Daniel Pascal Mamassian and Alan Yuille lsquolsquoObject Perception asBayesian Inferencersquorsquo Annual Review of Psychology 55 (2004) 271ndash304

Klein Richard Kate A Ratliff Michelangelo Vianello Reginald B Adams JrStepan Bahnik Michael J Bernstein Konrad Bocian Mark J BrandtBeach Brooks Claudia Chloe Brumbaugh Zeynep CemalcilarJesse Chandler Winnee Cheong William E Davis Thierry DevosMatthew Eisner Natalia Frankowska David Furrow Elisa Maria GallianiFred Hasselman Joshua A Hicks James F Hovermale S Jane HuntJeffrey R Huntsinger Hans IJzerman Melissa-Sue John Jennifer A Joy-Gaba Heather Barry Kappes Lacy E Krueger Jaime Kurtz CarmelA Levitan Robyn Mallett Wendy L Morris Anthony J Nelson JasonA Nier Grant Packard Ronaldo Pilati Abraham M RutchickKathleen Schmidt Jeanine L Skorinko Robert Smith Troy G SteinerJustin Storbeck Lyn M Van Swol Donna Thompson Anna van rsquot VeerLeigh Ann Vaughn Marek Vranka Aaron Wichman Julie A Woodzickaand Brian A Nosek lsquolsquoInvestigating Variation in Replicability A ManyLabs Replication Projectrsquorsquo Social Psychology 45 (2014) 142ndash152

Lundberg Shelly and Richard Startz lsquolsquoPrivate Discrimination and SocialIntervention in Competitive Labor Marketsrsquorsquo American Economic Review73 (1983) 340ndash347

Madon Stephanie Max Guyll Kathy Aboufadel Eulices Montiel Alison SmithPolly Palumbo and Lee Jussim lsquolsquoEthnic and National Stereotypes ThePrinceton Trilogy Revisited and Revisedrsquorsquo Personality and SocialPsychological Bulletin 27 (2001) 996ndash1010

Martin Carol lsquolsquoA Ratio Measure of Sex Stereotypingrsquorsquo Journal of Personality andSocial Psychology 52 (1987) 489ndash499

STEREOTYPES 1793

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

McCauley Clark Krishna Thangavelu and Paul Rozin lsquolsquoSex Stereotyping ofOccupations in Relation to Television Representations and Census FactsrsquorsquoBasic and Applied Social Psychology 9 (1988) 197ndash212

Mullainathan Sendhil lsquolsquoThinking through Categoriesrsquorsquo mimeo HarvardUniversity 2002

Ortoleva Pietro and Erik Snowberg lsquolsquoOverconfidence in Political BehaviorrsquorsquoAmerican Economic Review 105 (2015) 504ndash535

Phelps Edmund lsquolsquoThe Statistical Theory of Racism and Sexismrsquorsquo AmericanEconomic Review 62 (1972) 659ndash661

Pope Devin and Justin Sydnor lsquolsquoGeographic Variation in the Gender Differencesin Test Scoresrsquorsquo Journal of Economic Perspectives 24 (2010) 95ndash108

Rabin Matthew lsquolsquoInference by Believers in the Law of Small NumbersrsquorsquoQuarterly Journal of Economics 117 (2002) 775ndash816

Rabin Matthew and Joel Schrag lsquolsquoFirst Impressions Matter A Model ofConfirmatory Biasrsquorsquo Quarterly Journal of Economics 114 (1999) 37ndash82

Rabin Matthew and Dimitri Vayanos lsquolsquoThe Gamblerrsquos and Hot-Hand FallaciesTheory and Applicationsrsquorsquo Review of Economic Studies 77 (2010) 730ndash778

Reuben Ernesto Paola Sapienza and Luigi Zingales lsquolsquoHow Stereotypes ImpairWomenrsquos Careers in Sciencersquorsquo Proceedings of the National Academy ofSciences 111 (2014) 4403ndash4408

Rosch Eleanor lsquolsquoNatural Categoriesrsquorsquo Cognitive Psychology 4 (1973) 328ndash350Ryan Carey S lsquolsquoAccuracy of Black and White College Studentsrsquo In-Group and

Out-Group Stereotypesrsquorsquo Personality and Social Psychology Bulletin 22(1996) 1114ndash1127

Schneider David The Psychology of Stereotyping (New York Guilford Press2004)

Schneider David Albert Hastorf and Phoebe Ellsworth Person Perception(Reading MA Addison-Wesley 1979)

Shih Margaret Todd Pittinsky and Nalini Ambady lsquolsquoStereotype SusceptibilityIdentity Salience and Shifts in Quantitative Performancersquorsquo PsychologicalScience 10 (1999) 80ndash83

Shih Margaret Todd Pittinsky and Amy Trahan lsquolsquoDomain-Specific Effects ofStereotypes on Performancersquorsquo Self and Identity 5 (2006) 1ndash14

Steele Claude Whistling Vivaldi How Stereotypes Affect Us and What We CanDo (New York Norton 2010)

Tenenbaum Joshua and Thomas Griffiths lsquolsquoThe Rational Basis ofRepresentativenessrsquorsquo 23rd Annual Conference of the Cognitive ScienceSociety (2001) 1036ndash1041

Tversky Amos and Daniel Kahneman lsquolsquoExtensional versus Intuitive ReasoningThe Conjunction Fallacy in Probability Judgmentrsquorsquo Psychological Review 90(1983) 293ndash315

Weinberger Catherin lsquolsquoIs the Science and Engineering Workforce Drawn fromthe Far Upper Tail of the Math Ability Distributionrsquorsquo mimeo UCSB 2005

Westfall Jacob Leaf Van Boven John Chambers and Charles Judd lsquolsquoPerceivingPolitical Polarization in the United States Party Identity Strength andAttitude Extremity Exacerbate the Perceived Partisan DividersquorsquoPsychological Science 10 (2015) 145ndash158

Wolsko Christopher Bernadette Park Charles Judd and Bernd WittenbrinklsquolsquoFraming Interethnic Ideology Effects of Multicultural and Color-BlindPerspectives on Judgments of Groups and Individualsrsquorsquo Journal ofPersonality and Social Psychology 78 (2000) 635ndash654

QUARTERLY JOURNAL OF ECONOMICS1794

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ibrary on October 28 2016

httpqjeoxfordjournalsorgD

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Page 26: I. Introduction · uneducated at the beginning of the 20th century, and as high achievers at the beginning of the 21st (Madon et al. 2001). Social science has produced three broad

color distributions (13 purple 12 green) so no color is represen-tative of either group The Representativeness condition (Panel b)compares the same group of girls with a different group of boysfor whom green shirts are replaced with blue shirts Now onlygirls wear green and only boys wear blue These colors althoughstill not the most frequent for either group are now most repre-sentative For each group girls and boys participants are asked anumber of questions concerning the frequency of T-shirts of dif-ferent colors worn by that group

Applying our model in the control condition the type space isT frac14 fgreen purpleg and the groups are G = girls and ndashG = boysGiven that the color distributions are identical across groups both

types are equally representativegreengirls

greenboysfrac14 1 frac14

purplegirls

purpleboys As a result

assessment of G should be correct on average stcontrolgreengirls frac14 greengirls

and stcontrolpurplegirls frac14 purplegirls for any weighing function (the same is

true about assessments of ndashG)In the treatment condition the distribution of shirt colors re-

mains the same for girls For boys green shirts are changed intoblue Thus the type space changes to T frac14 fgreen purple bluegand the representative color for girls becomes greengreengirls

greenboysfrac14 1 gt 1 frac14

purplegirls

purpleboys while that for boys becomes blue As

a result in the treatment condition subjects should inflate the

frequency of green shirts relative to the truth sttreatmentgreengirls

gt greengirls (the same should happen to assessments of blueshirts for boys) We also expect the assessed frequency of greenshirts to go up relative to the control condition namely

sttreatmentgreengirls gt stcontrol

greengirls Critically the only factor that varies

across treatments is the representativeness of the 12-colorshirt Thus if we see differences across conditions the causalrole of representativeness-based recall in shaping group judg-ments is clear24

24 We vary which colors are used in which roles across participants Someparticipants saw this particular color distribution while others see for examplegreen as the modal color and purple as the diagnostic color for boys in theRepresentativeness condition and blue as the diagnostic color for girls in theRepresentativeness condition We vary the colors across the roles to avoid con-founding the characteristics of any particular color with its diagnosticity

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FIG

UR

EII

T-S

hir

tsE

xp

erim

ent

Fig

ure

sap

pea

red

inco

lor

top

art

icip

an

tsin

the

exp

erim

ent

For

clari

ty

we

have

ad

ded

ale

tter

toea

chT

-sh

irt

toid

enti

fyth

eco

lor

for

the

read

er

lsquolsquoGrsquorsquo

ind

icate

sgre

en

lsquolsquoPrsquorsquo

ind

icate

sp

urp

le

lsquolsquoBrsquorsquo

ind

icate

sblu

eT

hes

ele

tter

sd

idn

otap

pea

rto

part

icip

an

tsan

dare

for

read

erre

fere

nce

only

P

lease

see

onli

ne

ver

sion

ofp

ubli

shed

art

icle

for

colo

rfi

gu

reex

act

lyas

itap

pea

red

top

art

icip

an

ts

STEREOTYPES 1779

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We collected data from 301 participants using this T-shirtsdesign25 Since the number of green and purple shirts is verysimilar we first ask each participant the simplest question ofwhich shirt color is modal Next we ask participants to assessthe share of green and purple shirts

Consistent with the role of representativeness participantsassigned to the Representativeness condition are 105 percentagepoints more likely to recall the less frequent color (green for girlsor blue for boys) as the modal color when it is representative of agroup (35 of participants guess the less frequent color is modalin the Control condition this proportion increases to 46 in theRepresentativeness condition p = 01 estimated from a probitregression reported in Online Appendix F)

We now turn to subjectsrsquo estimates of how many T-shirts ofeach color they saw in each group In both conditions the truedifference in counts is 1 (13 purple shirts 12 green or blue shirts)In the Control condition participants on average believe they saw054 more purple shirts than green or blue shirts In theRepresentativeness condition participants believe they saw072 fewer purple shirts than green or blue shirts (the acrosstreatment difference is significant with p = 01 from OLS regres-sion reported in Online Appendix F)

In total we collected data for six experiments of this generalstructure gathering evidence from more than 1000 participantsAs we describe in Online Appendix F although there is substan-tial variation across experiments when we pool all of the data wefind significant aggregate treatment effects in line with a role ofrepresentativeness in judgment We employ four different unor-dered types designs similar to the T-shirts experiment using sixsamples (four online and two in the laboratory) with 741 partic-ipants We find effects in the predicted direction for five of the sixsamples Using a probit regression that pools the data for theseunordered type experiments we find that participants are 93 per-centage points more likely to guess that the less frequent type ismodal when it is representative than when it is not (p = 002) Wealso run a family of ordered types experiments (two designs fivesamples 402 participants) Unlike the simpler T-shirts style

25 Throughout our analysis we exclude any participant who participated in aprevious version of the experiment and any participant who self-identified as color-blind In Online Appendix F we show that our results are unchanged if we includethese additional observations

QUARTERLY JOURNAL OF ECONOMICS1780

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design the theoretical predictions for the ordered types designsare more sensitive to the specific assumptions one makes aboutthe weighting function of the DM26 We find effects in the pre-dicted direction for three of the five samples As we discuss inmore detail in Online Appendix F the ordered types resultsvary by platform with consistently stronger results on AmazonMechanical Turk than in the laboratory samples Pooling all or-dered types experiments participants are 93 percentage pointsmore likely to guess that the group of interest has a greater av-erage than the comparison group when the right tail is represen-tative (p = 062) Given our simple experimental setting withgroups of mundane objects we interpret our resultsmdasha signifi-cant and reasonably sized impact on average beliefsmdashas an im-portant proof of concept the presence of representative typesbiases ex post assessment

IVB Empirical Evidence on Political Stereotypes

We examine two data sets on political preferences and be-liefs about political preferences in the United States We inves-tigate the roles of representativeness and context dependence byseparately testing for hypotheses that allow us to assess the lead-ing theories of stereotypes

First we test whether beliefs are correct or depart systemat-ically from the truth The statistical discrimination approachbuilds on the assumption that people hold rational expectationsof group traits Comparing beliefs to the truth allows us to assessthe validity of this assumption in our data

Second we test if beliefs depart from the truth by exagger-ating (mean) differences among groups per the kernel of truthhypothesis This is an implicit test of context dependence be-cause it implies that beliefs about the target groups are shapednot only by that grouprsquos characteristics but also by those of thereference group27

Third we test if distortions in beliefs can be accounted for bythe overweighting of highly representative types (defined astypes that are relatively more frequent in the target relative to

26 This is due in part to our choice to not study MLRP distributions We moti-vate and discuss this design decision in Online Appendix F

27 Of course unlike in the laboratory experiment in this setting we cannot testfor context dependence by exogenously varying the reference group

STEREOTYPES 1781

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the reference group) The second and third tests address the keypredictions of our model

1 The Data We have two data sets on political preferences andbeliefs about political preferences The first data set from GrahamNosek and Haidt (GNH 2012) contains data from the MoralFoundations Questionnaire Respondents (1174 self-identified lib-erals and 500 self-identified conservatives) answer questions abouttheir position on a subset of 45 issues 20 moral relevance state-ments (eg lsquolsquowhen you decide whether something is right orwrong to what extent are the following considerations relevantto your thinkingrsquorsquo) and 25 moral judgments (eg lsquolsquoindicate theextent to which you would agree or disagreersquorsquo) For each issue arandomly determined subset of participants states their own posi-tion another subset states their belief on the position of a lsquolsquotypicalliberalrsquorsquo and a third subset states their belief on the position of alsquolsquotypical conservativersquorsquo The data thus include the distribution overpositions for both liberal and conservatives as well as the averagebelieved typical position of liberals and of conservatives on the 45issues Each position is elicited on 1ndash6 scale

The second data set comes from the American NationalElection Survey (ANES) and contains data from more than20000 respondents between 1964 and 201228 The surveycovers political issues of the day such as the optimal amount ofgovernment spending and service provision (1984ndash2000) or theplace of women in society (1972ndash1998) We focus on the 10 issuesthat ask participants to respond on a 1ndash7 scale (rather than justindicate binary agreement or disagreement) all 10 issues areasked in multiple years Participants are asked to provide theirown position on the scale and their believed position of theDemocratic and Republican parties (lsquolsquoWhere would you placethe Democratic [Republican] party on this scalersquorsquo) The data in-clude for each issue-year observation the distribution of partic-ipant positions for self-identified liberals and self-identifiedconservatives as well as the distribution of believed typical posi-tions of the Democratic and Republican parties

28 These data are publicly available at httpwwwelectionstudiesorgstudy-pagesanes_timeseries_cdfanes_timeseries_cdfhtm

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2 Empirical Strategy Our analysis focuses on beliefs abouttwo groups Conservatives and Liberals The types are the possi-ble positions for each issue (1 2 6 7) For the GNH data weinterpret beliefs about the lsquolsquotypicalrsquorsquo element of a group to coincidewith the believed average position in that group Similarly forthe ANES data we use the believed party positions as a proxy forbelieved mean of each group29 We then take as a benchmark thehypothesis that individuals hold accurate beliefs about eachgroup and in particular that believed mean position shouldequal true mean position at least on average across subjectsThe accurate beliefs hypothesis underlies the most common eco-nomic model of stereotyping statistical discrimination

To assess our representativeness-based model we perform aregression exercise To test our model in a linear regressionframework we rely on linear approximations of the weightingfunction Our model then yields two regression specifications

PROPOSITION 4 Let G 2 fconservative liberal g and assume

ht h tG

tG

be a differentiable and strictly increasing weight-

ing function as in Definition 2 The following hold as a first-order approximation around identical distributions G

Gfrac14 1

(i) Kernel of truth regression There exists a constant gt 0such that

EstethtjGTHORN frac14 EethtjGTHORNeth1thorn THORN EethtjGTHORNeth5THORN

(ii) Representativeness regression Denote H frac14 fT 2 Tg

the right tail of types and RconsH frac14

PHtconsPHtlib

as the average

representativeness of right tail types for conservatives

29 This assumption is consistent with the authorsrsquo interpretation of the GNHdata (GNH 2012) and with previous studies using ANES (eg Westfall et al 2015)Furthermore to the extent that this assumption holds equally well for most issueswithin a data set our focus on cross-issue differences should allow us to test thepredictions of our model even with an imperfect proxy for beliefs of mean positionsFinally the data provide some insight into whether subjects are reporting (per-ceived) modal or mean types As we show the modal type is a poor prediction ofstated beliefs while a distorted mean slanted toward representative types is anaccurate prediction of stated beliefs

STEREOTYPES 1783

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Under the further approximation where tcons

tlibampRcons

H for

t 2 H

EstethtjconsTHORN frac14 EethtjconsTHORN thorn consethR

consH 1THORNeth6THORN

EstethtjlibTHORN frac14 EethtjlibTHORN libethR

consH 1THORNeth7THORN

where lcons and llib are positive constants

The first regression allows us to test for the kernel of truthhypothesis and the second set of regressions allows us to test forthe role of representativeness

Equation (5) says that respondents in our model inflate theaverage position of a group say the conservatives if and only ifthe group has a higher average position than the other groupnamely the liberals Formally EstethtjconsTHORN gt EethtjconsTHORN if and onlyif EethtjconsTHORN gt EethtjlibTHORN Because in our measurement scale highertypes mean lsquolsquomore conservativersquorsquo we expect (i) believed conserva-tive average to be higher than the truth and (ii) the extent ofoverstatement to decrease in the average liberal position EethtjlibTHORNConversely we expect the average liberal position to be lowerthan the truth the more so the higher the average conservativeposition EethtjconsTHORN

As previously discussed the basis of these predictions is con-text dependence information about the distribution of ndashG is rel-evant for the beliefs about G This context dependence isinconsistent with rational expectations in which only thegrouprsquos own means should affect beliefs We test the hypothesisthat the true mean EethtjGTHORN is a significant predictor of the believedmean E

stethtjGTHORN with a positive sign and the other grouprsquos truemean EethtjGTHORN is a predictor of the believed mean with a negativesign

Equations (6) and (7) say that repondentsrsquo assessment bias isshaped by representativeness When the right tail is more repre-sentative for conservatives (Rcons

H 1 positive and large) partici-pants should inflate the average conservative position more(higher E

stethtjconsTHORN EethtjconsTHORN) and deflate the average liberal po-sition more (lower E

stethtjlibTHORN EethtjlibTHORN) We test the hypothesisthat the inflation in conservative positions is positively associatedwith the representativeness of the right tail for the conservativesand the inflation in liberal positions is negatively associated with

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it Once again the representativeness of the right tail is com-puted using the true distribution of positions

In equations (6) and (7) in many cases the representative tailis also the most likely one As a consequence these tests cannotdistinguish a representativeness-based from a likelihood-basedmodel of distorted beliefs We perform two additional testsFirst we run versions of equations (6) and (7) in which we controlfor the likelihood of tails (see Table A4 in Online Appendix G)Second we compute numerically the predictions of a representa-tiveness-based model of stereotypes and a likelihood-based modelof stereotypes We then assess which of these two is better able tomatch the data on beliefs

3 Empirical Results To begin we illustrate the structure ofthe data and the nature of our predictions with two simple exam-ples from the GNH data set focusing on beliefs about conserva-tives In example 1 participants are asked about their agreementwith the statement lsquolsquoIt can never be right to kill a human beingrsquorsquoIn example 2 participants are asked about the moral relevance oflsquolsquowhether or not someone cared for someone weak or vulnerablersquorsquoAs can be seen in Figure III in example 1 the modal position(strongly disagree (1)) and most representative positions(strongly disagree (1)) coincide for conservatives In contrast inexample 2 in Figure III the most representative types (slightlyrelevant (3) not at all relevant (1)) are not most likely for theconservative group Following Proposition 1 we predict that be-liefs will be distorted in the direction of the most representativetypes Thus we expect more exaggeration in example 2 than inexample 1 since in example 2 the most representative types (inthe left tail) are far from the modal type whereas in example 1they coincide This is what we find the conservative position isexaggerated by only 009 positions in Example 1 (true mean 299believed mean 290) but by 106 positions in Example 2 (truemean 421 believed mean 315)

In the full data sets we treat each (issue year) pair as anobservation and we cluster standard errors at the issue level Forthe GNH data we have 45 observations 45 issues measured inthe same year For the ANES data we have 66 observations 10issues measured in multiple years To begin we simply docu-ment systematic exaggeration in both data sets This is a primaryfocus of the original analysis in GNH (2012) and also in Westfall

STEREOTYPES 1785

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FIGURE III

Two Examples

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et al (2015)rsquos analysis of the ANES data30 Figure IV shows thatthe believed difference between typical conservative and typicalliberal positions is larger than the true difference in mean posi-tions for 109 of the 111 observations The data for both GNH(squares) and ANES (triangles) lie above the 45-degree line(dashed)31 Average exaggeration is 062 positions on the scale(066 in the GNH data 059 in the ANES data)32

The systematic and significant exaggeration of mean differ-ences suggests that the benchmark model of accurate beliefs ismissing something important Indeed this exaggeration reflectsthe fact that believed means are typically more extreme than truemeans First note that the kernel of truth regression (equation(5)) generates exaggeration of mean differences just as docu-mented in Figure IV

EstethtjGTHORN E

stethtjGTHORN frac14 eth1thorn 2THORN frac12EethtjGTHORN EethtjGTHORN

To bring this prediction to the data we regress the believedmean position for each group EBethtjGTHORN on the true mean of thegroup EethtjGTHORN and the true mean of the comparison groupEethtjGTHORN across issues We do this for each group (liberals con-servatives) in each data set separately We also present pooledspecifications that combine the data sets to make a prediction fora given group (liberals conservatives) In these pooled specifica-tions we include a dummy variable indicating whether theobservation came from the ANES data set For all specificationswe cluster observations at the issue level33 The results from re-gression are shown in Table I In every specification we find thatEethtjGTHORN is a significant predictor of EBethtjGTHORN with the predicted pos-itive sign Crucially for five of the six specifications the mean of

30 Chambers and Melnyk (2006) also find evidence of exaggeration of truedifferences in beliefs about political positions

31 For convenience we recode all issues so that the high end of the scale (67)represents the stereotypically more conservative position

32 A natural question to ask is how beliefs vary across liberals and conserva-tives That is do beliefs about a group G depend on membership in G versus ndashG Ourmodel does not speak to this issue However in Online Appendix G we show thatthe results we document below hold for both beliefs held by conservatives and be-liefs held by liberals see Tables A9 A10 and A11

33 In general the results presented below for the ANES data are not largelyimpacted by the decision to cluster at the issue level Similar results are obtained ifthe data are not clustered

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the comparison group EethtjGTHORN is also a significant predictor ofE

BethtjGTHORN with the predicted negative signAlthough these results provide strong evidence of context

dependence and are consistent with our model they do not pindown a role for representativeness of types Our next test relatesthe magnitude of representativeness of tail types to the magni-tude of belief distortions

To this end we implement the regressions in equations (6)and (7) Following Proposition 4 we compute the average repre-

sentativeness of tail types for conservatives RconsH frac14

PtT2tconsPtT2tlib

We

again test the hypothesis that RconsH is a significant predictor of Est

ethtjconsTHORN with a positive sign and a predictor of EstethtjlibTHORN with a

negative sign Table II shows that conditional on true mean RconsH

predicts believed mean for each group G as expected The firstthree specifications display the results for predicting beliefs heldabout conservatives In both data sets the average representa-tiveness of tail types for conservatives is a significant positivepredictor of beliefs held about conservatives The final three spe-cifications display the results for predicting beliefs held about

FIGURE IV

Exaggeration of Differences

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liberals We find that the average representativeness of tail typesfor conservatives is a negative predictor of beliefs held about lib-erals This effect is significant in the GNH data and marginallysignificant in the ANES data

We present several additional results in Online Appendix GTo further examine the role of representativeness in driving be-liefs we first show the results of Table II carry through when we

TABLE II

AVERAGE REPRESENTATIVENESS OF TAIL POSITIONS PREDICTS BELIEFS

OLS Predicting Believed Mean of Group G for Each Issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position

of group G for issue

078 024 051 072 018 041

(006) (008) (009) (005) (005) (010)

Avg rep of tail types for

conservatives RconsH

019 055 025 014 012 024

(007) (022) (008) (006) (007) (005)

Constant 101 260 184 093 271 201

(026) (045) (029) (022) (025) (032)

R2 082 048 060 091 031 070

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

TABLE I

INFORMATION ABOUT ndashG PREDICTS BELIEFS ABOUT G

OLS predicting believed mean of group G for each issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position of

conservatives for issue

102 098 096 021 019 025

(0097) (0133) (0076) (0060) (0116) (0060)

True mean position of

liberals for issue

035 086 058 0987 039 073

(0106) (0134) (0131) (0066) (0106) (0135)

Constant 151 335 235 069 258 156

(0195) (0269) (0279) (0122) (0249) (0270)

R2 083 053 066 092 032 068

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

STEREOTYPES 1789

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control for the average likelihood on the tail positions (see Table A4in Online Appendix G) Most tellingly we use the model to predictbeliefs across issues and compare those to the data For simplicitywe use the rank-based truncation specification to predict mean be-liefs when stereotypes include the d most representative types ford frac14 1 T We compare these predictions to those of a model inwhich beliefs are obtained by restricting the distribution to the dmost likely types Our benchmark for both models is predicting thebelieved mean from the entire distribution where d = T We showthat the predictions of the rank-based truncation model with d = 4or 5 compare favorably to both a likelihood-based truncation model(with any d) and the accurate beliefs benchmark Interestingly thisresult suggests that stereotypical beliefs are well approximated byneglecting the least representative types (as opposed to focusingonly on the most representative types) and so represent a moderatethough systematic departure from the standard benchmarkFinally we show that the results we document above hold forboth beliefs held by conservatives and beliefs held by liberals (seeTables A9 A10 and A11 in Online Appendix G)

V Conclusion

We present a model of stereotypical thinking in which DMsmaking predictions about a group overweight the grouprsquos mostdistinctive types These overweighted types are not the mostlikely ones given the DMrsquos data but the most representativeones in the sense of being the most diagnostic of the group rela-tive to other groups Representativeness implies that what ismost distinctive of a group depends on what group it is comparedwith We present experimental evidence that confirms this con-text dependence in recall-based assessments of groups Finallywe evaluated the predictions of the model using political data fromexisting large-scale surveys We find context dependence to be akey feature of beliefs Given the richness of the political data wecan go a step further and identify a role for representativeness inparticular As the representativeness of tail types increases beliefsof a group are distorted in the direction of that tail

Our approach provides a parsimonious and psychologicallyfounded account of how DMs generate simplified representationsof reality from social groups to stock returns and offers a unifiedaccount of disparate pieces of evidence relating to this type of

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uncertainty The model captures the central fact that stereotypeshighlight the greatest difference between groups thus explainingwhy some stereotypes are very accurate while others lack valid-ity Still stereotypes often have a kernel of truth when they arebased on systematicmdasheven if smallmdashdifferences between groupsThis logic allows us to describe a number of heuristics and psy-chological biases many of which arise in the context of predictionproblems Generically our model generates overreaction to diag-nostic information

Our model is based on representativeness and does not cap-ture all the features of stereotypical thinking However it cap-tures perhaps the central feature when we think of a group wefocus on what is most distinctive about it and neglect or under-weight the rest

Saeuroıd Business School University of Oxford

Ohio State University and Harvard Business School

Universita Bocconi and Innocenzo Gasparini Institute

for Economic Research

Harvard University

Supplementary Material

An Online Appendix for this article can be found at QJEonline (qjeoxfordjournalorg)

References

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Arrow Kenneth lsquolsquoThe Theory of Discriminationrsquorsquo in Discrimination in LaborMarkets Orley Ashenfelter and Albert Rees eds (Princeton NJPrinceton University Press 1973)

Ashton Michael and Victoria Esses lsquolsquoStereotype Accuracy Estimating theAcademic Performance of Ethnic Groupsrsquorsquo Personality and SocialPsychology Bulletin 25 (1999) 225ndash236

Barberis Nicholas Andrei Shleifer and Robert Vishny lsquolsquoA Model of InvestorSentimentrsquorsquo Journal of Financial Economics 49 (1998) 307ndash343

Bayer Sylvia lsquolsquoThe Accuracy of Academic Gender Stereotypesrsquorsquo Sex Roles 40(1999) 787ndash813

Benjamin Dan James Choi and Joshua Strickland lsquolsquoSocial Identity andPreferencesrsquorsquo American Economic Review 100 (2010) 1913ndash1928

Benjamin Dan Matthew Rabin and Collin Raymond lsquolsquoA Model of Non-Belief inthe Law of Large Numbersrsquorsquo Journal of the European Economic Association15 (2015) 515ndash544

Bertrand Marianne lsquolsquoNew Perspectives on Genderrsquorsquo Handbook of LaborEconomics 4 (2011) 1543ndash1590

Bodoh-Creed Aaron Dan Benjamin and Matthew Rabin lsquolsquoThe Dynamics of Base-Rate Neglectrsquorsquo mimeo Haas Business School 2013

STEREOTYPES 1791

at Harvard L

ibrary on October 28 2016

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Bohnet Iris Alexandra van Geen and Max Bazerman lsquolsquoWhen PerformanceTrumps Gender Bias Joint versus Separate Evaluationrsquorsquo ManagementScience 5 (2016) 1225ndash1234

Bordalo Pedro Nicola Gennaioli and Andrei Shleifer lsquolsquoSalience Theory of Choiceunder Riskrsquorsquo Quarterly Journal of Economics 127 (2012) 1243ndash1285

mdashmdashmdash lsquolsquoSalience and Consumer Choicersquorsquo Journal of Political Economy 121(2013) 803ndash843

Briton Nancy and Judith Hall lsquolsquoBeliefs about Female and Male NonverbalCommunicationrsquorsquo Sex Roles 32 (1995) 79ndash90

Buser Thomas Muriel Niederle and Hessel Oosterbeek lsquolsquoGenderCompetitiveness and Career Choicesrsquorsquo Quarterly Journal of Economics 129(2014) 1409ndash1447

Carrell Scott Marianne Page and James West lsquolsquoSex and Science How ProfessorGender Perpetuates the Gender Gaprsquorsquo Quarterly Journal of Economics 125(2010) 1101ndash1144

Chambers John and Darya Melnyk lsquolsquoWhy Do I Hate Thee ConflictMisperceptions and Intergroup Mistrustrsquorsquo Personality and SocialPsychology Bulletin 32 (2006) 1295ndash1311

Chan Wayne Robert R McCrae Filip De Fruyt Lee Jussim CorinnaE Lockenhoff Marleen De Bolle Paul T Costa Jr Angelina R SutinAnu Realo Juri Allik Katsuharu Nakazato Yoshiko ShimonakaMartina Hrebıckova Sylvie Graf Michelle Yik Marina Brunner-SciarraNora Leibovich De Figueora Vanina Schmidt Chang-kyo Ahn Hyun-nie Ahn Maria E Aguilar-Vafaie Jerzy Siuta Barbara SzmigielskaThomas R Cain Janet T Crawford Khairul Anwar Mastor Jean-Pierre Rolland Florence Nansubuga Daniel R MiramontezVeronica Benet-Martınez Jerome Rossier Denis Bratko Iris MarusicJamin Halberstadt Mami Yamaguchi Goran Knezevic Thomas A MartinMirona Gheorghiu Peter B Smith Claudio Barbaranelli Lei WangJane Shakespeare-Finch Margarida P Lima Waldemar KlinkoszAndrzej Sekowski Lidia Alcalay Franco Simonetti Tatyana V AvdeyevaV S Pramila and Antonio Terracciano lsquolsquoStereotypes of Age Differences inPersonality Traits Universal and Accuratersquorsquo Journal of Personality andSocial Psychology 103 (2012) 1050ndash1066

Chen Yan Sherry Xin Liu Tracy Xiao and Margaret Shih lsquolsquoWhich Hat to WearImpact of Natural Identities on Coordination and Cooperationrsquorsquo Games andEconomic Behavior 84 (2014) 58ndash86

Coffman Katherine lsquolsquoEvidence on Self-Stereotyping and the Contribution ofIdeasrsquorsquo Quarterly Journal of Economics 129 (2014) 1625ndash1660

Cunningham Tom lsquolsquoComparisons and Choicersquorsquo mimeo Stockholm University2013

Diekman Amanda Alice Eagly and Patrick Kulesa lsquolsquoAccuracy and Bias in theStereotypes about the Social and Political Attitudes of Women and MenrsquorsquoJournal of Experimental Social Psychology 38 (2002) 268ndash282

Eccles Jacquelynne S Janis E Jacobs and Rena D Harold lsquolsquoGender RoleStereotypes Expectancy Effects and Parentsrsquo Socialization of GenderDifferencesrsquorsquo Journal of Social Issues 46 (1990) 183ndash201

Fryer Roland and Matthew Jackson lsquolsquoA Categorical Model of Cognition andBiased Decision-Makingrsquorsquo BE Journal of Theoretical Economics 8 (2008)1ndash42

Fryer Roland and Steven Levitt lsquolsquoAn Empirical Analysis of the Gender Gap inMathematicsrsquorsquo American Economic Journal Applied Economics 2 (2010)210ndash240

Gennaioli Nicola and Andrei Shleifer lsquolsquoWhat Comes to Mindrsquorsquo Quarterly Journalof Economics 125 (2010) 1399ndash1433

Gennaioli Nicola Andrei Shleifer and Robert Vishny lsquolsquoNeglected RisksFinancial Innovation and Financial Fragilityrsquorsquo Journal of FinancialEconomics 104 (2012) 452ndash468

Gilens Martin lsquolsquoRace and Poverty in America Public Misperceptions and theAmerican News Mediarsquorsquo Public Opinion Quarterly 60 (1996) 515ndash541

Glaeser Edward lsquolsquoThe Political Economy of Hatredrsquorsquo Quarterly Journal ofEconomics 120 (2005) 45ndash86

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Glover Dyland Amanda Pallais and William Pariente lsquolsquoDiscrimination as a Self-Fulfilling Prophecy Evidence from French Grocery Storesrsquorsquo mimeo HarvardUniversity 2015

Goldin Claudia Lawrence Katz and Ilyana Kuziemko lsquolsquoThe Homecoming ofAmerican College Women The Reversal of the College Gender GaprsquorsquoJournal of Economic Perspectives 20 (2006) 133ndash156

Graham Jesse Brian Nosek and Jonathan Haidt lsquolsquoThe Moral Stereotypes ofLiberals and Conservatives Exaggeration of Differences across thePolitical Spectrumrsquorsquo PLoS One 7 (2012) 1ndash13

Grether David lsquolsquoBayes Rule as a Descriptive Model The RepresentativenessHeuristicrsquorsquo Quarterly Journal of Economics 95 (1980) 537ndash557

Griffin Dale and Amos Tversky lsquolsquoThe Weighing of Evidence and theDeterminants of Confidencersquorsquo Cognitive Psychology 24 (1992) 411ndash435

Guiso Luigi Ferdinando Monte Paola Sapienza and Luigi Zingales lsquolsquoCultureGender and Mathrsquorsquo Science 320 (2008) 1164ndash1165

Hilton James and William Von Hippel lsquolsquoStereotypesrsquorsquo Annual Review ofPsychology 47 (1996) 237ndash271

Hyde Janet Sara Lindberg Marcia Linn Amy Ellis and Caroline WilliamslsquolsquoGender Similarities Characterize Math Performancersquorsquo Science 321 (2008)494ndash495

Judd Charles and Bernardette Park lsquolsquoDefinition and Assessment of Accuracy inSocial Stereotypesrsquorsquo Psychological Review 100 (1993) 109ndash128

Jussim Lee Jarret Crawford Stephanie Anglin John Chambers Sean Stevensand Florette Cohen lsquolsquoStereotype Accuracy One of the Largest and MostReplicable Effects in All of Social Psychologyrsquorsquo in The Handbook ofPrejudice Stereotyping and Discrimination Todd Nelson ed (MahwahNJ Lawrence Erlbaum 2015)

Kahneman Daniel and Amos Tversky lsquolsquoSubjective Probability A Judgment ofRepresentativenessrsquorsquo Cognitive Psychology 3 (1972) 430ndash454

mdashmdashmdash lsquolsquoOn the Psychology of Predictionrsquorsquo Psychological Review 80 (1973) 237ndash251

Kaplowitz Stan Bradley Fisher and Clifford Broman lsquolsquoHow Accurate ArePerceptions of Social Statistics about Blacks and Whitesrsquorsquo Public OpinionQuarterly 67 (2003) 237ndash243

Kersten Daniel Pascal Mamassian and Alan Yuille lsquolsquoObject Perception asBayesian Inferencersquorsquo Annual Review of Psychology 55 (2004) 271ndash304

Klein Richard Kate A Ratliff Michelangelo Vianello Reginald B Adams JrStepan Bahnik Michael J Bernstein Konrad Bocian Mark J BrandtBeach Brooks Claudia Chloe Brumbaugh Zeynep CemalcilarJesse Chandler Winnee Cheong William E Davis Thierry DevosMatthew Eisner Natalia Frankowska David Furrow Elisa Maria GallianiFred Hasselman Joshua A Hicks James F Hovermale S Jane HuntJeffrey R Huntsinger Hans IJzerman Melissa-Sue John Jennifer A Joy-Gaba Heather Barry Kappes Lacy E Krueger Jaime Kurtz CarmelA Levitan Robyn Mallett Wendy L Morris Anthony J Nelson JasonA Nier Grant Packard Ronaldo Pilati Abraham M RutchickKathleen Schmidt Jeanine L Skorinko Robert Smith Troy G SteinerJustin Storbeck Lyn M Van Swol Donna Thompson Anna van rsquot VeerLeigh Ann Vaughn Marek Vranka Aaron Wichman Julie A Woodzickaand Brian A Nosek lsquolsquoInvestigating Variation in Replicability A ManyLabs Replication Projectrsquorsquo Social Psychology 45 (2014) 142ndash152

Lundberg Shelly and Richard Startz lsquolsquoPrivate Discrimination and SocialIntervention in Competitive Labor Marketsrsquorsquo American Economic Review73 (1983) 340ndash347

Madon Stephanie Max Guyll Kathy Aboufadel Eulices Montiel Alison SmithPolly Palumbo and Lee Jussim lsquolsquoEthnic and National Stereotypes ThePrinceton Trilogy Revisited and Revisedrsquorsquo Personality and SocialPsychological Bulletin 27 (2001) 996ndash1010

Martin Carol lsquolsquoA Ratio Measure of Sex Stereotypingrsquorsquo Journal of Personality andSocial Psychology 52 (1987) 489ndash499

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httpqjeoxfordjournalsorgD

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McCauley Clark Krishna Thangavelu and Paul Rozin lsquolsquoSex Stereotyping ofOccupations in Relation to Television Representations and Census FactsrsquorsquoBasic and Applied Social Psychology 9 (1988) 197ndash212

Mullainathan Sendhil lsquolsquoThinking through Categoriesrsquorsquo mimeo HarvardUniversity 2002

Ortoleva Pietro and Erik Snowberg lsquolsquoOverconfidence in Political BehaviorrsquorsquoAmerican Economic Review 105 (2015) 504ndash535

Phelps Edmund lsquolsquoThe Statistical Theory of Racism and Sexismrsquorsquo AmericanEconomic Review 62 (1972) 659ndash661

Pope Devin and Justin Sydnor lsquolsquoGeographic Variation in the Gender Differencesin Test Scoresrsquorsquo Journal of Economic Perspectives 24 (2010) 95ndash108

Rabin Matthew lsquolsquoInference by Believers in the Law of Small NumbersrsquorsquoQuarterly Journal of Economics 117 (2002) 775ndash816

Rabin Matthew and Joel Schrag lsquolsquoFirst Impressions Matter A Model ofConfirmatory Biasrsquorsquo Quarterly Journal of Economics 114 (1999) 37ndash82

Rabin Matthew and Dimitri Vayanos lsquolsquoThe Gamblerrsquos and Hot-Hand FallaciesTheory and Applicationsrsquorsquo Review of Economic Studies 77 (2010) 730ndash778

Reuben Ernesto Paola Sapienza and Luigi Zingales lsquolsquoHow Stereotypes ImpairWomenrsquos Careers in Sciencersquorsquo Proceedings of the National Academy ofSciences 111 (2014) 4403ndash4408

Rosch Eleanor lsquolsquoNatural Categoriesrsquorsquo Cognitive Psychology 4 (1973) 328ndash350Ryan Carey S lsquolsquoAccuracy of Black and White College Studentsrsquo In-Group and

Out-Group Stereotypesrsquorsquo Personality and Social Psychology Bulletin 22(1996) 1114ndash1127

Schneider David The Psychology of Stereotyping (New York Guilford Press2004)

Schneider David Albert Hastorf and Phoebe Ellsworth Person Perception(Reading MA Addison-Wesley 1979)

Shih Margaret Todd Pittinsky and Nalini Ambady lsquolsquoStereotype SusceptibilityIdentity Salience and Shifts in Quantitative Performancersquorsquo PsychologicalScience 10 (1999) 80ndash83

Shih Margaret Todd Pittinsky and Amy Trahan lsquolsquoDomain-Specific Effects ofStereotypes on Performancersquorsquo Self and Identity 5 (2006) 1ndash14

Steele Claude Whistling Vivaldi How Stereotypes Affect Us and What We CanDo (New York Norton 2010)

Tenenbaum Joshua and Thomas Griffiths lsquolsquoThe Rational Basis ofRepresentativenessrsquorsquo 23rd Annual Conference of the Cognitive ScienceSociety (2001) 1036ndash1041

Tversky Amos and Daniel Kahneman lsquolsquoExtensional versus Intuitive ReasoningThe Conjunction Fallacy in Probability Judgmentrsquorsquo Psychological Review 90(1983) 293ndash315

Weinberger Catherin lsquolsquoIs the Science and Engineering Workforce Drawn fromthe Far Upper Tail of the Math Ability Distributionrsquorsquo mimeo UCSB 2005

Westfall Jacob Leaf Van Boven John Chambers and Charles Judd lsquolsquoPerceivingPolitical Polarization in the United States Party Identity Strength andAttitude Extremity Exacerbate the Perceived Partisan DividersquorsquoPsychological Science 10 (2015) 145ndash158

Wolsko Christopher Bernadette Park Charles Judd and Bernd WittenbrinklsquolsquoFraming Interethnic Ideology Effects of Multicultural and Color-BlindPerspectives on Judgments of Groups and Individualsrsquorsquo Journal ofPersonality and Social Psychology 78 (2000) 635ndash654

QUARTERLY JOURNAL OF ECONOMICS1794

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ibrary on October 28 2016

httpqjeoxfordjournalsorgD

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Page 27: I. Introduction · uneducated at the beginning of the 20th century, and as high achievers at the beginning of the 21st (Madon et al. 2001). Social science has produced three broad

FIG

UR

EII

T-S

hir

tsE

xp

erim

ent

Fig

ure

sap

pea

red

inco

lor

top

art

icip

an

tsin

the

exp

erim

ent

For

clari

ty

we

have

ad

ded

ale

tter

toea

chT

-sh

irt

toid

enti

fyth

eco

lor

for

the

read

er

lsquolsquoGrsquorsquo

ind

icate

sgre

en

lsquolsquoPrsquorsquo

ind

icate

sp

urp

le

lsquolsquoBrsquorsquo

ind

icate

sblu

eT

hes

ele

tter

sd

idn

otap

pea

rto

part

icip

an

tsan

dare

for

read

erre

fere

nce

only

P

lease

see

onli

ne

ver

sion

ofp

ubli

shed

art

icle

for

colo

rfi

gu

reex

act

lyas

itap

pea

red

top

art

icip

an

ts

STEREOTYPES 1779

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ibrary on October 28 2016

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ownloaded from

We collected data from 301 participants using this T-shirtsdesign25 Since the number of green and purple shirts is verysimilar we first ask each participant the simplest question ofwhich shirt color is modal Next we ask participants to assessthe share of green and purple shirts

Consistent with the role of representativeness participantsassigned to the Representativeness condition are 105 percentagepoints more likely to recall the less frequent color (green for girlsor blue for boys) as the modal color when it is representative of agroup (35 of participants guess the less frequent color is modalin the Control condition this proportion increases to 46 in theRepresentativeness condition p = 01 estimated from a probitregression reported in Online Appendix F)

We now turn to subjectsrsquo estimates of how many T-shirts ofeach color they saw in each group In both conditions the truedifference in counts is 1 (13 purple shirts 12 green or blue shirts)In the Control condition participants on average believe they saw054 more purple shirts than green or blue shirts In theRepresentativeness condition participants believe they saw072 fewer purple shirts than green or blue shirts (the acrosstreatment difference is significant with p = 01 from OLS regres-sion reported in Online Appendix F)

In total we collected data for six experiments of this generalstructure gathering evidence from more than 1000 participantsAs we describe in Online Appendix F although there is substan-tial variation across experiments when we pool all of the data wefind significant aggregate treatment effects in line with a role ofrepresentativeness in judgment We employ four different unor-dered types designs similar to the T-shirts experiment using sixsamples (four online and two in the laboratory) with 741 partic-ipants We find effects in the predicted direction for five of the sixsamples Using a probit regression that pools the data for theseunordered type experiments we find that participants are 93 per-centage points more likely to guess that the less frequent type ismodal when it is representative than when it is not (p = 002) Wealso run a family of ordered types experiments (two designs fivesamples 402 participants) Unlike the simpler T-shirts style

25 Throughout our analysis we exclude any participant who participated in aprevious version of the experiment and any participant who self-identified as color-blind In Online Appendix F we show that our results are unchanged if we includethese additional observations

QUARTERLY JOURNAL OF ECONOMICS1780

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design the theoretical predictions for the ordered types designsare more sensitive to the specific assumptions one makes aboutthe weighting function of the DM26 We find effects in the pre-dicted direction for three of the five samples As we discuss inmore detail in Online Appendix F the ordered types resultsvary by platform with consistently stronger results on AmazonMechanical Turk than in the laboratory samples Pooling all or-dered types experiments participants are 93 percentage pointsmore likely to guess that the group of interest has a greater av-erage than the comparison group when the right tail is represen-tative (p = 062) Given our simple experimental setting withgroups of mundane objects we interpret our resultsmdasha signifi-cant and reasonably sized impact on average beliefsmdashas an im-portant proof of concept the presence of representative typesbiases ex post assessment

IVB Empirical Evidence on Political Stereotypes

We examine two data sets on political preferences and be-liefs about political preferences in the United States We inves-tigate the roles of representativeness and context dependence byseparately testing for hypotheses that allow us to assess the lead-ing theories of stereotypes

First we test whether beliefs are correct or depart systemat-ically from the truth The statistical discrimination approachbuilds on the assumption that people hold rational expectationsof group traits Comparing beliefs to the truth allows us to assessthe validity of this assumption in our data

Second we test if beliefs depart from the truth by exagger-ating (mean) differences among groups per the kernel of truthhypothesis This is an implicit test of context dependence be-cause it implies that beliefs about the target groups are shapednot only by that grouprsquos characteristics but also by those of thereference group27

Third we test if distortions in beliefs can be accounted for bythe overweighting of highly representative types (defined astypes that are relatively more frequent in the target relative to

26 This is due in part to our choice to not study MLRP distributions We moti-vate and discuss this design decision in Online Appendix F

27 Of course unlike in the laboratory experiment in this setting we cannot testfor context dependence by exogenously varying the reference group

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the reference group) The second and third tests address the keypredictions of our model

1 The Data We have two data sets on political preferences andbeliefs about political preferences The first data set from GrahamNosek and Haidt (GNH 2012) contains data from the MoralFoundations Questionnaire Respondents (1174 self-identified lib-erals and 500 self-identified conservatives) answer questions abouttheir position on a subset of 45 issues 20 moral relevance state-ments (eg lsquolsquowhen you decide whether something is right orwrong to what extent are the following considerations relevantto your thinkingrsquorsquo) and 25 moral judgments (eg lsquolsquoindicate theextent to which you would agree or disagreersquorsquo) For each issue arandomly determined subset of participants states their own posi-tion another subset states their belief on the position of a lsquolsquotypicalliberalrsquorsquo and a third subset states their belief on the position of alsquolsquotypical conservativersquorsquo The data thus include the distribution overpositions for both liberal and conservatives as well as the averagebelieved typical position of liberals and of conservatives on the 45issues Each position is elicited on 1ndash6 scale

The second data set comes from the American NationalElection Survey (ANES) and contains data from more than20000 respondents between 1964 and 201228 The surveycovers political issues of the day such as the optimal amount ofgovernment spending and service provision (1984ndash2000) or theplace of women in society (1972ndash1998) We focus on the 10 issuesthat ask participants to respond on a 1ndash7 scale (rather than justindicate binary agreement or disagreement) all 10 issues areasked in multiple years Participants are asked to provide theirown position on the scale and their believed position of theDemocratic and Republican parties (lsquolsquoWhere would you placethe Democratic [Republican] party on this scalersquorsquo) The data in-clude for each issue-year observation the distribution of partic-ipant positions for self-identified liberals and self-identifiedconservatives as well as the distribution of believed typical posi-tions of the Democratic and Republican parties

28 These data are publicly available at httpwwwelectionstudiesorgstudy-pagesanes_timeseries_cdfanes_timeseries_cdfhtm

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2 Empirical Strategy Our analysis focuses on beliefs abouttwo groups Conservatives and Liberals The types are the possi-ble positions for each issue (1 2 6 7) For the GNH data weinterpret beliefs about the lsquolsquotypicalrsquorsquo element of a group to coincidewith the believed average position in that group Similarly forthe ANES data we use the believed party positions as a proxy forbelieved mean of each group29 We then take as a benchmark thehypothesis that individuals hold accurate beliefs about eachgroup and in particular that believed mean position shouldequal true mean position at least on average across subjectsThe accurate beliefs hypothesis underlies the most common eco-nomic model of stereotyping statistical discrimination

To assess our representativeness-based model we perform aregression exercise To test our model in a linear regressionframework we rely on linear approximations of the weightingfunction Our model then yields two regression specifications

PROPOSITION 4 Let G 2 fconservative liberal g and assume

ht h tG

tG

be a differentiable and strictly increasing weight-

ing function as in Definition 2 The following hold as a first-order approximation around identical distributions G

Gfrac14 1

(i) Kernel of truth regression There exists a constant gt 0such that

EstethtjGTHORN frac14 EethtjGTHORNeth1thorn THORN EethtjGTHORNeth5THORN

(ii) Representativeness regression Denote H frac14 fT 2 Tg

the right tail of types and RconsH frac14

PHtconsPHtlib

as the average

representativeness of right tail types for conservatives

29 This assumption is consistent with the authorsrsquo interpretation of the GNHdata (GNH 2012) and with previous studies using ANES (eg Westfall et al 2015)Furthermore to the extent that this assumption holds equally well for most issueswithin a data set our focus on cross-issue differences should allow us to test thepredictions of our model even with an imperfect proxy for beliefs of mean positionsFinally the data provide some insight into whether subjects are reporting (per-ceived) modal or mean types As we show the modal type is a poor prediction ofstated beliefs while a distorted mean slanted toward representative types is anaccurate prediction of stated beliefs

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Under the further approximation where tcons

tlibampRcons

H for

t 2 H

EstethtjconsTHORN frac14 EethtjconsTHORN thorn consethR

consH 1THORNeth6THORN

EstethtjlibTHORN frac14 EethtjlibTHORN libethR

consH 1THORNeth7THORN

where lcons and llib are positive constants

The first regression allows us to test for the kernel of truthhypothesis and the second set of regressions allows us to test forthe role of representativeness

Equation (5) says that respondents in our model inflate theaverage position of a group say the conservatives if and only ifthe group has a higher average position than the other groupnamely the liberals Formally EstethtjconsTHORN gt EethtjconsTHORN if and onlyif EethtjconsTHORN gt EethtjlibTHORN Because in our measurement scale highertypes mean lsquolsquomore conservativersquorsquo we expect (i) believed conserva-tive average to be higher than the truth and (ii) the extent ofoverstatement to decrease in the average liberal position EethtjlibTHORNConversely we expect the average liberal position to be lowerthan the truth the more so the higher the average conservativeposition EethtjconsTHORN

As previously discussed the basis of these predictions is con-text dependence information about the distribution of ndashG is rel-evant for the beliefs about G This context dependence isinconsistent with rational expectations in which only thegrouprsquos own means should affect beliefs We test the hypothesisthat the true mean EethtjGTHORN is a significant predictor of the believedmean E

stethtjGTHORN with a positive sign and the other grouprsquos truemean EethtjGTHORN is a predictor of the believed mean with a negativesign

Equations (6) and (7) say that repondentsrsquo assessment bias isshaped by representativeness When the right tail is more repre-sentative for conservatives (Rcons

H 1 positive and large) partici-pants should inflate the average conservative position more(higher E

stethtjconsTHORN EethtjconsTHORN) and deflate the average liberal po-sition more (lower E

stethtjlibTHORN EethtjlibTHORN) We test the hypothesisthat the inflation in conservative positions is positively associatedwith the representativeness of the right tail for the conservativesand the inflation in liberal positions is negatively associated with

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it Once again the representativeness of the right tail is com-puted using the true distribution of positions

In equations (6) and (7) in many cases the representative tailis also the most likely one As a consequence these tests cannotdistinguish a representativeness-based from a likelihood-basedmodel of distorted beliefs We perform two additional testsFirst we run versions of equations (6) and (7) in which we controlfor the likelihood of tails (see Table A4 in Online Appendix G)Second we compute numerically the predictions of a representa-tiveness-based model of stereotypes and a likelihood-based modelof stereotypes We then assess which of these two is better able tomatch the data on beliefs

3 Empirical Results To begin we illustrate the structure ofthe data and the nature of our predictions with two simple exam-ples from the GNH data set focusing on beliefs about conserva-tives In example 1 participants are asked about their agreementwith the statement lsquolsquoIt can never be right to kill a human beingrsquorsquoIn example 2 participants are asked about the moral relevance oflsquolsquowhether or not someone cared for someone weak or vulnerablersquorsquoAs can be seen in Figure III in example 1 the modal position(strongly disagree (1)) and most representative positions(strongly disagree (1)) coincide for conservatives In contrast inexample 2 in Figure III the most representative types (slightlyrelevant (3) not at all relevant (1)) are not most likely for theconservative group Following Proposition 1 we predict that be-liefs will be distorted in the direction of the most representativetypes Thus we expect more exaggeration in example 2 than inexample 1 since in example 2 the most representative types (inthe left tail) are far from the modal type whereas in example 1they coincide This is what we find the conservative position isexaggerated by only 009 positions in Example 1 (true mean 299believed mean 290) but by 106 positions in Example 2 (truemean 421 believed mean 315)

In the full data sets we treat each (issue year) pair as anobservation and we cluster standard errors at the issue level Forthe GNH data we have 45 observations 45 issues measured inthe same year For the ANES data we have 66 observations 10issues measured in multiple years To begin we simply docu-ment systematic exaggeration in both data sets This is a primaryfocus of the original analysis in GNH (2012) and also in Westfall

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FIGURE III

Two Examples

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et al (2015)rsquos analysis of the ANES data30 Figure IV shows thatthe believed difference between typical conservative and typicalliberal positions is larger than the true difference in mean posi-tions for 109 of the 111 observations The data for both GNH(squares) and ANES (triangles) lie above the 45-degree line(dashed)31 Average exaggeration is 062 positions on the scale(066 in the GNH data 059 in the ANES data)32

The systematic and significant exaggeration of mean differ-ences suggests that the benchmark model of accurate beliefs ismissing something important Indeed this exaggeration reflectsthe fact that believed means are typically more extreme than truemeans First note that the kernel of truth regression (equation(5)) generates exaggeration of mean differences just as docu-mented in Figure IV

EstethtjGTHORN E

stethtjGTHORN frac14 eth1thorn 2THORN frac12EethtjGTHORN EethtjGTHORN

To bring this prediction to the data we regress the believedmean position for each group EBethtjGTHORN on the true mean of thegroup EethtjGTHORN and the true mean of the comparison groupEethtjGTHORN across issues We do this for each group (liberals con-servatives) in each data set separately We also present pooledspecifications that combine the data sets to make a prediction fora given group (liberals conservatives) In these pooled specifica-tions we include a dummy variable indicating whether theobservation came from the ANES data set For all specificationswe cluster observations at the issue level33 The results from re-gression are shown in Table I In every specification we find thatEethtjGTHORN is a significant predictor of EBethtjGTHORN with the predicted pos-itive sign Crucially for five of the six specifications the mean of

30 Chambers and Melnyk (2006) also find evidence of exaggeration of truedifferences in beliefs about political positions

31 For convenience we recode all issues so that the high end of the scale (67)represents the stereotypically more conservative position

32 A natural question to ask is how beliefs vary across liberals and conserva-tives That is do beliefs about a group G depend on membership in G versus ndashG Ourmodel does not speak to this issue However in Online Appendix G we show thatthe results we document below hold for both beliefs held by conservatives and be-liefs held by liberals see Tables A9 A10 and A11

33 In general the results presented below for the ANES data are not largelyimpacted by the decision to cluster at the issue level Similar results are obtained ifthe data are not clustered

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the comparison group EethtjGTHORN is also a significant predictor ofE

BethtjGTHORN with the predicted negative signAlthough these results provide strong evidence of context

dependence and are consistent with our model they do not pindown a role for representativeness of types Our next test relatesthe magnitude of representativeness of tail types to the magni-tude of belief distortions

To this end we implement the regressions in equations (6)and (7) Following Proposition 4 we compute the average repre-

sentativeness of tail types for conservatives RconsH frac14

PtT2tconsPtT2tlib

We

again test the hypothesis that RconsH is a significant predictor of Est

ethtjconsTHORN with a positive sign and a predictor of EstethtjlibTHORN with a

negative sign Table II shows that conditional on true mean RconsH

predicts believed mean for each group G as expected The firstthree specifications display the results for predicting beliefs heldabout conservatives In both data sets the average representa-tiveness of tail types for conservatives is a significant positivepredictor of beliefs held about conservatives The final three spe-cifications display the results for predicting beliefs held about

FIGURE IV

Exaggeration of Differences

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liberals We find that the average representativeness of tail typesfor conservatives is a negative predictor of beliefs held about lib-erals This effect is significant in the GNH data and marginallysignificant in the ANES data

We present several additional results in Online Appendix GTo further examine the role of representativeness in driving be-liefs we first show the results of Table II carry through when we

TABLE II

AVERAGE REPRESENTATIVENESS OF TAIL POSITIONS PREDICTS BELIEFS

OLS Predicting Believed Mean of Group G for Each Issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position

of group G for issue

078 024 051 072 018 041

(006) (008) (009) (005) (005) (010)

Avg rep of tail types for

conservatives RconsH

019 055 025 014 012 024

(007) (022) (008) (006) (007) (005)

Constant 101 260 184 093 271 201

(026) (045) (029) (022) (025) (032)

R2 082 048 060 091 031 070

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

TABLE I

INFORMATION ABOUT ndashG PREDICTS BELIEFS ABOUT G

OLS predicting believed mean of group G for each issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position of

conservatives for issue

102 098 096 021 019 025

(0097) (0133) (0076) (0060) (0116) (0060)

True mean position of

liberals for issue

035 086 058 0987 039 073

(0106) (0134) (0131) (0066) (0106) (0135)

Constant 151 335 235 069 258 156

(0195) (0269) (0279) (0122) (0249) (0270)

R2 083 053 066 092 032 068

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

STEREOTYPES 1789

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control for the average likelihood on the tail positions (see Table A4in Online Appendix G) Most tellingly we use the model to predictbeliefs across issues and compare those to the data For simplicitywe use the rank-based truncation specification to predict mean be-liefs when stereotypes include the d most representative types ford frac14 1 T We compare these predictions to those of a model inwhich beliefs are obtained by restricting the distribution to the dmost likely types Our benchmark for both models is predicting thebelieved mean from the entire distribution where d = T We showthat the predictions of the rank-based truncation model with d = 4or 5 compare favorably to both a likelihood-based truncation model(with any d) and the accurate beliefs benchmark Interestingly thisresult suggests that stereotypical beliefs are well approximated byneglecting the least representative types (as opposed to focusingonly on the most representative types) and so represent a moderatethough systematic departure from the standard benchmarkFinally we show that the results we document above hold forboth beliefs held by conservatives and beliefs held by liberals (seeTables A9 A10 and A11 in Online Appendix G)

V Conclusion

We present a model of stereotypical thinking in which DMsmaking predictions about a group overweight the grouprsquos mostdistinctive types These overweighted types are not the mostlikely ones given the DMrsquos data but the most representativeones in the sense of being the most diagnostic of the group rela-tive to other groups Representativeness implies that what ismost distinctive of a group depends on what group it is comparedwith We present experimental evidence that confirms this con-text dependence in recall-based assessments of groups Finallywe evaluated the predictions of the model using political data fromexisting large-scale surveys We find context dependence to be akey feature of beliefs Given the richness of the political data wecan go a step further and identify a role for representativeness inparticular As the representativeness of tail types increases beliefsof a group are distorted in the direction of that tail

Our approach provides a parsimonious and psychologicallyfounded account of how DMs generate simplified representationsof reality from social groups to stock returns and offers a unifiedaccount of disparate pieces of evidence relating to this type of

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uncertainty The model captures the central fact that stereotypeshighlight the greatest difference between groups thus explainingwhy some stereotypes are very accurate while others lack valid-ity Still stereotypes often have a kernel of truth when they arebased on systematicmdasheven if smallmdashdifferences between groupsThis logic allows us to describe a number of heuristics and psy-chological biases many of which arise in the context of predictionproblems Generically our model generates overreaction to diag-nostic information

Our model is based on representativeness and does not cap-ture all the features of stereotypical thinking However it cap-tures perhaps the central feature when we think of a group wefocus on what is most distinctive about it and neglect or under-weight the rest

Saeuroıd Business School University of Oxford

Ohio State University and Harvard Business School

Universita Bocconi and Innocenzo Gasparini Institute

for Economic Research

Harvard University

Supplementary Material

An Online Appendix for this article can be found at QJEonline (qjeoxfordjournalorg)

References

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Arrow Kenneth lsquolsquoThe Theory of Discriminationrsquorsquo in Discrimination in LaborMarkets Orley Ashenfelter and Albert Rees eds (Princeton NJPrinceton University Press 1973)

Ashton Michael and Victoria Esses lsquolsquoStereotype Accuracy Estimating theAcademic Performance of Ethnic Groupsrsquorsquo Personality and SocialPsychology Bulletin 25 (1999) 225ndash236

Barberis Nicholas Andrei Shleifer and Robert Vishny lsquolsquoA Model of InvestorSentimentrsquorsquo Journal of Financial Economics 49 (1998) 307ndash343

Bayer Sylvia lsquolsquoThe Accuracy of Academic Gender Stereotypesrsquorsquo Sex Roles 40(1999) 787ndash813

Benjamin Dan James Choi and Joshua Strickland lsquolsquoSocial Identity andPreferencesrsquorsquo American Economic Review 100 (2010) 1913ndash1928

Benjamin Dan Matthew Rabin and Collin Raymond lsquolsquoA Model of Non-Belief inthe Law of Large Numbersrsquorsquo Journal of the European Economic Association15 (2015) 515ndash544

Bertrand Marianne lsquolsquoNew Perspectives on Genderrsquorsquo Handbook of LaborEconomics 4 (2011) 1543ndash1590

Bodoh-Creed Aaron Dan Benjamin and Matthew Rabin lsquolsquoThe Dynamics of Base-Rate Neglectrsquorsquo mimeo Haas Business School 2013

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Bohnet Iris Alexandra van Geen and Max Bazerman lsquolsquoWhen PerformanceTrumps Gender Bias Joint versus Separate Evaluationrsquorsquo ManagementScience 5 (2016) 1225ndash1234

Bordalo Pedro Nicola Gennaioli and Andrei Shleifer lsquolsquoSalience Theory of Choiceunder Riskrsquorsquo Quarterly Journal of Economics 127 (2012) 1243ndash1285

mdashmdashmdash lsquolsquoSalience and Consumer Choicersquorsquo Journal of Political Economy 121(2013) 803ndash843

Briton Nancy and Judith Hall lsquolsquoBeliefs about Female and Male NonverbalCommunicationrsquorsquo Sex Roles 32 (1995) 79ndash90

Buser Thomas Muriel Niederle and Hessel Oosterbeek lsquolsquoGenderCompetitiveness and Career Choicesrsquorsquo Quarterly Journal of Economics 129(2014) 1409ndash1447

Carrell Scott Marianne Page and James West lsquolsquoSex and Science How ProfessorGender Perpetuates the Gender Gaprsquorsquo Quarterly Journal of Economics 125(2010) 1101ndash1144

Chambers John and Darya Melnyk lsquolsquoWhy Do I Hate Thee ConflictMisperceptions and Intergroup Mistrustrsquorsquo Personality and SocialPsychology Bulletin 32 (2006) 1295ndash1311

Chan Wayne Robert R McCrae Filip De Fruyt Lee Jussim CorinnaE Lockenhoff Marleen De Bolle Paul T Costa Jr Angelina R SutinAnu Realo Juri Allik Katsuharu Nakazato Yoshiko ShimonakaMartina Hrebıckova Sylvie Graf Michelle Yik Marina Brunner-SciarraNora Leibovich De Figueora Vanina Schmidt Chang-kyo Ahn Hyun-nie Ahn Maria E Aguilar-Vafaie Jerzy Siuta Barbara SzmigielskaThomas R Cain Janet T Crawford Khairul Anwar Mastor Jean-Pierre Rolland Florence Nansubuga Daniel R MiramontezVeronica Benet-Martınez Jerome Rossier Denis Bratko Iris MarusicJamin Halberstadt Mami Yamaguchi Goran Knezevic Thomas A MartinMirona Gheorghiu Peter B Smith Claudio Barbaranelli Lei WangJane Shakespeare-Finch Margarida P Lima Waldemar KlinkoszAndrzej Sekowski Lidia Alcalay Franco Simonetti Tatyana V AvdeyevaV S Pramila and Antonio Terracciano lsquolsquoStereotypes of Age Differences inPersonality Traits Universal and Accuratersquorsquo Journal of Personality andSocial Psychology 103 (2012) 1050ndash1066

Chen Yan Sherry Xin Liu Tracy Xiao and Margaret Shih lsquolsquoWhich Hat to WearImpact of Natural Identities on Coordination and Cooperationrsquorsquo Games andEconomic Behavior 84 (2014) 58ndash86

Coffman Katherine lsquolsquoEvidence on Self-Stereotyping and the Contribution ofIdeasrsquorsquo Quarterly Journal of Economics 129 (2014) 1625ndash1660

Cunningham Tom lsquolsquoComparisons and Choicersquorsquo mimeo Stockholm University2013

Diekman Amanda Alice Eagly and Patrick Kulesa lsquolsquoAccuracy and Bias in theStereotypes about the Social and Political Attitudes of Women and MenrsquorsquoJournal of Experimental Social Psychology 38 (2002) 268ndash282

Eccles Jacquelynne S Janis E Jacobs and Rena D Harold lsquolsquoGender RoleStereotypes Expectancy Effects and Parentsrsquo Socialization of GenderDifferencesrsquorsquo Journal of Social Issues 46 (1990) 183ndash201

Fryer Roland and Matthew Jackson lsquolsquoA Categorical Model of Cognition andBiased Decision-Makingrsquorsquo BE Journal of Theoretical Economics 8 (2008)1ndash42

Fryer Roland and Steven Levitt lsquolsquoAn Empirical Analysis of the Gender Gap inMathematicsrsquorsquo American Economic Journal Applied Economics 2 (2010)210ndash240

Gennaioli Nicola and Andrei Shleifer lsquolsquoWhat Comes to Mindrsquorsquo Quarterly Journalof Economics 125 (2010) 1399ndash1433

Gennaioli Nicola Andrei Shleifer and Robert Vishny lsquolsquoNeglected RisksFinancial Innovation and Financial Fragilityrsquorsquo Journal of FinancialEconomics 104 (2012) 452ndash468

Gilens Martin lsquolsquoRace and Poverty in America Public Misperceptions and theAmerican News Mediarsquorsquo Public Opinion Quarterly 60 (1996) 515ndash541

Glaeser Edward lsquolsquoThe Political Economy of Hatredrsquorsquo Quarterly Journal ofEconomics 120 (2005) 45ndash86

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Glover Dyland Amanda Pallais and William Pariente lsquolsquoDiscrimination as a Self-Fulfilling Prophecy Evidence from French Grocery Storesrsquorsquo mimeo HarvardUniversity 2015

Goldin Claudia Lawrence Katz and Ilyana Kuziemko lsquolsquoThe Homecoming ofAmerican College Women The Reversal of the College Gender GaprsquorsquoJournal of Economic Perspectives 20 (2006) 133ndash156

Graham Jesse Brian Nosek and Jonathan Haidt lsquolsquoThe Moral Stereotypes ofLiberals and Conservatives Exaggeration of Differences across thePolitical Spectrumrsquorsquo PLoS One 7 (2012) 1ndash13

Grether David lsquolsquoBayes Rule as a Descriptive Model The RepresentativenessHeuristicrsquorsquo Quarterly Journal of Economics 95 (1980) 537ndash557

Griffin Dale and Amos Tversky lsquolsquoThe Weighing of Evidence and theDeterminants of Confidencersquorsquo Cognitive Psychology 24 (1992) 411ndash435

Guiso Luigi Ferdinando Monte Paola Sapienza and Luigi Zingales lsquolsquoCultureGender and Mathrsquorsquo Science 320 (2008) 1164ndash1165

Hilton James and William Von Hippel lsquolsquoStereotypesrsquorsquo Annual Review ofPsychology 47 (1996) 237ndash271

Hyde Janet Sara Lindberg Marcia Linn Amy Ellis and Caroline WilliamslsquolsquoGender Similarities Characterize Math Performancersquorsquo Science 321 (2008)494ndash495

Judd Charles and Bernardette Park lsquolsquoDefinition and Assessment of Accuracy inSocial Stereotypesrsquorsquo Psychological Review 100 (1993) 109ndash128

Jussim Lee Jarret Crawford Stephanie Anglin John Chambers Sean Stevensand Florette Cohen lsquolsquoStereotype Accuracy One of the Largest and MostReplicable Effects in All of Social Psychologyrsquorsquo in The Handbook ofPrejudice Stereotyping and Discrimination Todd Nelson ed (MahwahNJ Lawrence Erlbaum 2015)

Kahneman Daniel and Amos Tversky lsquolsquoSubjective Probability A Judgment ofRepresentativenessrsquorsquo Cognitive Psychology 3 (1972) 430ndash454

mdashmdashmdash lsquolsquoOn the Psychology of Predictionrsquorsquo Psychological Review 80 (1973) 237ndash251

Kaplowitz Stan Bradley Fisher and Clifford Broman lsquolsquoHow Accurate ArePerceptions of Social Statistics about Blacks and Whitesrsquorsquo Public OpinionQuarterly 67 (2003) 237ndash243

Kersten Daniel Pascal Mamassian and Alan Yuille lsquolsquoObject Perception asBayesian Inferencersquorsquo Annual Review of Psychology 55 (2004) 271ndash304

Klein Richard Kate A Ratliff Michelangelo Vianello Reginald B Adams JrStepan Bahnik Michael J Bernstein Konrad Bocian Mark J BrandtBeach Brooks Claudia Chloe Brumbaugh Zeynep CemalcilarJesse Chandler Winnee Cheong William E Davis Thierry DevosMatthew Eisner Natalia Frankowska David Furrow Elisa Maria GallianiFred Hasselman Joshua A Hicks James F Hovermale S Jane HuntJeffrey R Huntsinger Hans IJzerman Melissa-Sue John Jennifer A Joy-Gaba Heather Barry Kappes Lacy E Krueger Jaime Kurtz CarmelA Levitan Robyn Mallett Wendy L Morris Anthony J Nelson JasonA Nier Grant Packard Ronaldo Pilati Abraham M RutchickKathleen Schmidt Jeanine L Skorinko Robert Smith Troy G SteinerJustin Storbeck Lyn M Van Swol Donna Thompson Anna van rsquot VeerLeigh Ann Vaughn Marek Vranka Aaron Wichman Julie A Woodzickaand Brian A Nosek lsquolsquoInvestigating Variation in Replicability A ManyLabs Replication Projectrsquorsquo Social Psychology 45 (2014) 142ndash152

Lundberg Shelly and Richard Startz lsquolsquoPrivate Discrimination and SocialIntervention in Competitive Labor Marketsrsquorsquo American Economic Review73 (1983) 340ndash347

Madon Stephanie Max Guyll Kathy Aboufadel Eulices Montiel Alison SmithPolly Palumbo and Lee Jussim lsquolsquoEthnic and National Stereotypes ThePrinceton Trilogy Revisited and Revisedrsquorsquo Personality and SocialPsychological Bulletin 27 (2001) 996ndash1010

Martin Carol lsquolsquoA Ratio Measure of Sex Stereotypingrsquorsquo Journal of Personality andSocial Psychology 52 (1987) 489ndash499

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McCauley Clark Krishna Thangavelu and Paul Rozin lsquolsquoSex Stereotyping ofOccupations in Relation to Television Representations and Census FactsrsquorsquoBasic and Applied Social Psychology 9 (1988) 197ndash212

Mullainathan Sendhil lsquolsquoThinking through Categoriesrsquorsquo mimeo HarvardUniversity 2002

Ortoleva Pietro and Erik Snowberg lsquolsquoOverconfidence in Political BehaviorrsquorsquoAmerican Economic Review 105 (2015) 504ndash535

Phelps Edmund lsquolsquoThe Statistical Theory of Racism and Sexismrsquorsquo AmericanEconomic Review 62 (1972) 659ndash661

Pope Devin and Justin Sydnor lsquolsquoGeographic Variation in the Gender Differencesin Test Scoresrsquorsquo Journal of Economic Perspectives 24 (2010) 95ndash108

Rabin Matthew lsquolsquoInference by Believers in the Law of Small NumbersrsquorsquoQuarterly Journal of Economics 117 (2002) 775ndash816

Rabin Matthew and Joel Schrag lsquolsquoFirst Impressions Matter A Model ofConfirmatory Biasrsquorsquo Quarterly Journal of Economics 114 (1999) 37ndash82

Rabin Matthew and Dimitri Vayanos lsquolsquoThe Gamblerrsquos and Hot-Hand FallaciesTheory and Applicationsrsquorsquo Review of Economic Studies 77 (2010) 730ndash778

Reuben Ernesto Paola Sapienza and Luigi Zingales lsquolsquoHow Stereotypes ImpairWomenrsquos Careers in Sciencersquorsquo Proceedings of the National Academy ofSciences 111 (2014) 4403ndash4408

Rosch Eleanor lsquolsquoNatural Categoriesrsquorsquo Cognitive Psychology 4 (1973) 328ndash350Ryan Carey S lsquolsquoAccuracy of Black and White College Studentsrsquo In-Group and

Out-Group Stereotypesrsquorsquo Personality and Social Psychology Bulletin 22(1996) 1114ndash1127

Schneider David The Psychology of Stereotyping (New York Guilford Press2004)

Schneider David Albert Hastorf and Phoebe Ellsworth Person Perception(Reading MA Addison-Wesley 1979)

Shih Margaret Todd Pittinsky and Nalini Ambady lsquolsquoStereotype SusceptibilityIdentity Salience and Shifts in Quantitative Performancersquorsquo PsychologicalScience 10 (1999) 80ndash83

Shih Margaret Todd Pittinsky and Amy Trahan lsquolsquoDomain-Specific Effects ofStereotypes on Performancersquorsquo Self and Identity 5 (2006) 1ndash14

Steele Claude Whistling Vivaldi How Stereotypes Affect Us and What We CanDo (New York Norton 2010)

Tenenbaum Joshua and Thomas Griffiths lsquolsquoThe Rational Basis ofRepresentativenessrsquorsquo 23rd Annual Conference of the Cognitive ScienceSociety (2001) 1036ndash1041

Tversky Amos and Daniel Kahneman lsquolsquoExtensional versus Intuitive ReasoningThe Conjunction Fallacy in Probability Judgmentrsquorsquo Psychological Review 90(1983) 293ndash315

Weinberger Catherin lsquolsquoIs the Science and Engineering Workforce Drawn fromthe Far Upper Tail of the Math Ability Distributionrsquorsquo mimeo UCSB 2005

Westfall Jacob Leaf Van Boven John Chambers and Charles Judd lsquolsquoPerceivingPolitical Polarization in the United States Party Identity Strength andAttitude Extremity Exacerbate the Perceived Partisan DividersquorsquoPsychological Science 10 (2015) 145ndash158

Wolsko Christopher Bernadette Park Charles Judd and Bernd WittenbrinklsquolsquoFraming Interethnic Ideology Effects of Multicultural and Color-BlindPerspectives on Judgments of Groups and Individualsrsquorsquo Journal ofPersonality and Social Psychology 78 (2000) 635ndash654

QUARTERLY JOURNAL OF ECONOMICS1794

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Page 28: I. Introduction · uneducated at the beginning of the 20th century, and as high achievers at the beginning of the 21st (Madon et al. 2001). Social science has produced three broad

We collected data from 301 participants using this T-shirtsdesign25 Since the number of green and purple shirts is verysimilar we first ask each participant the simplest question ofwhich shirt color is modal Next we ask participants to assessthe share of green and purple shirts

Consistent with the role of representativeness participantsassigned to the Representativeness condition are 105 percentagepoints more likely to recall the less frequent color (green for girlsor blue for boys) as the modal color when it is representative of agroup (35 of participants guess the less frequent color is modalin the Control condition this proportion increases to 46 in theRepresentativeness condition p = 01 estimated from a probitregression reported in Online Appendix F)

We now turn to subjectsrsquo estimates of how many T-shirts ofeach color they saw in each group In both conditions the truedifference in counts is 1 (13 purple shirts 12 green or blue shirts)In the Control condition participants on average believe they saw054 more purple shirts than green or blue shirts In theRepresentativeness condition participants believe they saw072 fewer purple shirts than green or blue shirts (the acrosstreatment difference is significant with p = 01 from OLS regres-sion reported in Online Appendix F)

In total we collected data for six experiments of this generalstructure gathering evidence from more than 1000 participantsAs we describe in Online Appendix F although there is substan-tial variation across experiments when we pool all of the data wefind significant aggregate treatment effects in line with a role ofrepresentativeness in judgment We employ four different unor-dered types designs similar to the T-shirts experiment using sixsamples (four online and two in the laboratory) with 741 partic-ipants We find effects in the predicted direction for five of the sixsamples Using a probit regression that pools the data for theseunordered type experiments we find that participants are 93 per-centage points more likely to guess that the less frequent type ismodal when it is representative than when it is not (p = 002) Wealso run a family of ordered types experiments (two designs fivesamples 402 participants) Unlike the simpler T-shirts style

25 Throughout our analysis we exclude any participant who participated in aprevious version of the experiment and any participant who self-identified as color-blind In Online Appendix F we show that our results are unchanged if we includethese additional observations

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design the theoretical predictions for the ordered types designsare more sensitive to the specific assumptions one makes aboutthe weighting function of the DM26 We find effects in the pre-dicted direction for three of the five samples As we discuss inmore detail in Online Appendix F the ordered types resultsvary by platform with consistently stronger results on AmazonMechanical Turk than in the laboratory samples Pooling all or-dered types experiments participants are 93 percentage pointsmore likely to guess that the group of interest has a greater av-erage than the comparison group when the right tail is represen-tative (p = 062) Given our simple experimental setting withgroups of mundane objects we interpret our resultsmdasha signifi-cant and reasonably sized impact on average beliefsmdashas an im-portant proof of concept the presence of representative typesbiases ex post assessment

IVB Empirical Evidence on Political Stereotypes

We examine two data sets on political preferences and be-liefs about political preferences in the United States We inves-tigate the roles of representativeness and context dependence byseparately testing for hypotheses that allow us to assess the lead-ing theories of stereotypes

First we test whether beliefs are correct or depart systemat-ically from the truth The statistical discrimination approachbuilds on the assumption that people hold rational expectationsof group traits Comparing beliefs to the truth allows us to assessthe validity of this assumption in our data

Second we test if beliefs depart from the truth by exagger-ating (mean) differences among groups per the kernel of truthhypothesis This is an implicit test of context dependence be-cause it implies that beliefs about the target groups are shapednot only by that grouprsquos characteristics but also by those of thereference group27

Third we test if distortions in beliefs can be accounted for bythe overweighting of highly representative types (defined astypes that are relatively more frequent in the target relative to

26 This is due in part to our choice to not study MLRP distributions We moti-vate and discuss this design decision in Online Appendix F

27 Of course unlike in the laboratory experiment in this setting we cannot testfor context dependence by exogenously varying the reference group

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the reference group) The second and third tests address the keypredictions of our model

1 The Data We have two data sets on political preferences andbeliefs about political preferences The first data set from GrahamNosek and Haidt (GNH 2012) contains data from the MoralFoundations Questionnaire Respondents (1174 self-identified lib-erals and 500 self-identified conservatives) answer questions abouttheir position on a subset of 45 issues 20 moral relevance state-ments (eg lsquolsquowhen you decide whether something is right orwrong to what extent are the following considerations relevantto your thinkingrsquorsquo) and 25 moral judgments (eg lsquolsquoindicate theextent to which you would agree or disagreersquorsquo) For each issue arandomly determined subset of participants states their own posi-tion another subset states their belief on the position of a lsquolsquotypicalliberalrsquorsquo and a third subset states their belief on the position of alsquolsquotypical conservativersquorsquo The data thus include the distribution overpositions for both liberal and conservatives as well as the averagebelieved typical position of liberals and of conservatives on the 45issues Each position is elicited on 1ndash6 scale

The second data set comes from the American NationalElection Survey (ANES) and contains data from more than20000 respondents between 1964 and 201228 The surveycovers political issues of the day such as the optimal amount ofgovernment spending and service provision (1984ndash2000) or theplace of women in society (1972ndash1998) We focus on the 10 issuesthat ask participants to respond on a 1ndash7 scale (rather than justindicate binary agreement or disagreement) all 10 issues areasked in multiple years Participants are asked to provide theirown position on the scale and their believed position of theDemocratic and Republican parties (lsquolsquoWhere would you placethe Democratic [Republican] party on this scalersquorsquo) The data in-clude for each issue-year observation the distribution of partic-ipant positions for self-identified liberals and self-identifiedconservatives as well as the distribution of believed typical posi-tions of the Democratic and Republican parties

28 These data are publicly available at httpwwwelectionstudiesorgstudy-pagesanes_timeseries_cdfanes_timeseries_cdfhtm

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2 Empirical Strategy Our analysis focuses on beliefs abouttwo groups Conservatives and Liberals The types are the possi-ble positions for each issue (1 2 6 7) For the GNH data weinterpret beliefs about the lsquolsquotypicalrsquorsquo element of a group to coincidewith the believed average position in that group Similarly forthe ANES data we use the believed party positions as a proxy forbelieved mean of each group29 We then take as a benchmark thehypothesis that individuals hold accurate beliefs about eachgroup and in particular that believed mean position shouldequal true mean position at least on average across subjectsThe accurate beliefs hypothesis underlies the most common eco-nomic model of stereotyping statistical discrimination

To assess our representativeness-based model we perform aregression exercise To test our model in a linear regressionframework we rely on linear approximations of the weightingfunction Our model then yields two regression specifications

PROPOSITION 4 Let G 2 fconservative liberal g and assume

ht h tG

tG

be a differentiable and strictly increasing weight-

ing function as in Definition 2 The following hold as a first-order approximation around identical distributions G

Gfrac14 1

(i) Kernel of truth regression There exists a constant gt 0such that

EstethtjGTHORN frac14 EethtjGTHORNeth1thorn THORN EethtjGTHORNeth5THORN

(ii) Representativeness regression Denote H frac14 fT 2 Tg

the right tail of types and RconsH frac14

PHtconsPHtlib

as the average

representativeness of right tail types for conservatives

29 This assumption is consistent with the authorsrsquo interpretation of the GNHdata (GNH 2012) and with previous studies using ANES (eg Westfall et al 2015)Furthermore to the extent that this assumption holds equally well for most issueswithin a data set our focus on cross-issue differences should allow us to test thepredictions of our model even with an imperfect proxy for beliefs of mean positionsFinally the data provide some insight into whether subjects are reporting (per-ceived) modal or mean types As we show the modal type is a poor prediction ofstated beliefs while a distorted mean slanted toward representative types is anaccurate prediction of stated beliefs

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Under the further approximation where tcons

tlibampRcons

H for

t 2 H

EstethtjconsTHORN frac14 EethtjconsTHORN thorn consethR

consH 1THORNeth6THORN

EstethtjlibTHORN frac14 EethtjlibTHORN libethR

consH 1THORNeth7THORN

where lcons and llib are positive constants

The first regression allows us to test for the kernel of truthhypothesis and the second set of regressions allows us to test forthe role of representativeness

Equation (5) says that respondents in our model inflate theaverage position of a group say the conservatives if and only ifthe group has a higher average position than the other groupnamely the liberals Formally EstethtjconsTHORN gt EethtjconsTHORN if and onlyif EethtjconsTHORN gt EethtjlibTHORN Because in our measurement scale highertypes mean lsquolsquomore conservativersquorsquo we expect (i) believed conserva-tive average to be higher than the truth and (ii) the extent ofoverstatement to decrease in the average liberal position EethtjlibTHORNConversely we expect the average liberal position to be lowerthan the truth the more so the higher the average conservativeposition EethtjconsTHORN

As previously discussed the basis of these predictions is con-text dependence information about the distribution of ndashG is rel-evant for the beliefs about G This context dependence isinconsistent with rational expectations in which only thegrouprsquos own means should affect beliefs We test the hypothesisthat the true mean EethtjGTHORN is a significant predictor of the believedmean E

stethtjGTHORN with a positive sign and the other grouprsquos truemean EethtjGTHORN is a predictor of the believed mean with a negativesign

Equations (6) and (7) say that repondentsrsquo assessment bias isshaped by representativeness When the right tail is more repre-sentative for conservatives (Rcons

H 1 positive and large) partici-pants should inflate the average conservative position more(higher E

stethtjconsTHORN EethtjconsTHORN) and deflate the average liberal po-sition more (lower E

stethtjlibTHORN EethtjlibTHORN) We test the hypothesisthat the inflation in conservative positions is positively associatedwith the representativeness of the right tail for the conservativesand the inflation in liberal positions is negatively associated with

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it Once again the representativeness of the right tail is com-puted using the true distribution of positions

In equations (6) and (7) in many cases the representative tailis also the most likely one As a consequence these tests cannotdistinguish a representativeness-based from a likelihood-basedmodel of distorted beliefs We perform two additional testsFirst we run versions of equations (6) and (7) in which we controlfor the likelihood of tails (see Table A4 in Online Appendix G)Second we compute numerically the predictions of a representa-tiveness-based model of stereotypes and a likelihood-based modelof stereotypes We then assess which of these two is better able tomatch the data on beliefs

3 Empirical Results To begin we illustrate the structure ofthe data and the nature of our predictions with two simple exam-ples from the GNH data set focusing on beliefs about conserva-tives In example 1 participants are asked about their agreementwith the statement lsquolsquoIt can never be right to kill a human beingrsquorsquoIn example 2 participants are asked about the moral relevance oflsquolsquowhether or not someone cared for someone weak or vulnerablersquorsquoAs can be seen in Figure III in example 1 the modal position(strongly disagree (1)) and most representative positions(strongly disagree (1)) coincide for conservatives In contrast inexample 2 in Figure III the most representative types (slightlyrelevant (3) not at all relevant (1)) are not most likely for theconservative group Following Proposition 1 we predict that be-liefs will be distorted in the direction of the most representativetypes Thus we expect more exaggeration in example 2 than inexample 1 since in example 2 the most representative types (inthe left tail) are far from the modal type whereas in example 1they coincide This is what we find the conservative position isexaggerated by only 009 positions in Example 1 (true mean 299believed mean 290) but by 106 positions in Example 2 (truemean 421 believed mean 315)

In the full data sets we treat each (issue year) pair as anobservation and we cluster standard errors at the issue level Forthe GNH data we have 45 observations 45 issues measured inthe same year For the ANES data we have 66 observations 10issues measured in multiple years To begin we simply docu-ment systematic exaggeration in both data sets This is a primaryfocus of the original analysis in GNH (2012) and also in Westfall

STEREOTYPES 1785

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FIGURE III

Two Examples

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et al (2015)rsquos analysis of the ANES data30 Figure IV shows thatthe believed difference between typical conservative and typicalliberal positions is larger than the true difference in mean posi-tions for 109 of the 111 observations The data for both GNH(squares) and ANES (triangles) lie above the 45-degree line(dashed)31 Average exaggeration is 062 positions on the scale(066 in the GNH data 059 in the ANES data)32

The systematic and significant exaggeration of mean differ-ences suggests that the benchmark model of accurate beliefs ismissing something important Indeed this exaggeration reflectsthe fact that believed means are typically more extreme than truemeans First note that the kernel of truth regression (equation(5)) generates exaggeration of mean differences just as docu-mented in Figure IV

EstethtjGTHORN E

stethtjGTHORN frac14 eth1thorn 2THORN frac12EethtjGTHORN EethtjGTHORN

To bring this prediction to the data we regress the believedmean position for each group EBethtjGTHORN on the true mean of thegroup EethtjGTHORN and the true mean of the comparison groupEethtjGTHORN across issues We do this for each group (liberals con-servatives) in each data set separately We also present pooledspecifications that combine the data sets to make a prediction fora given group (liberals conservatives) In these pooled specifica-tions we include a dummy variable indicating whether theobservation came from the ANES data set For all specificationswe cluster observations at the issue level33 The results from re-gression are shown in Table I In every specification we find thatEethtjGTHORN is a significant predictor of EBethtjGTHORN with the predicted pos-itive sign Crucially for five of the six specifications the mean of

30 Chambers and Melnyk (2006) also find evidence of exaggeration of truedifferences in beliefs about political positions

31 For convenience we recode all issues so that the high end of the scale (67)represents the stereotypically more conservative position

32 A natural question to ask is how beliefs vary across liberals and conserva-tives That is do beliefs about a group G depend on membership in G versus ndashG Ourmodel does not speak to this issue However in Online Appendix G we show thatthe results we document below hold for both beliefs held by conservatives and be-liefs held by liberals see Tables A9 A10 and A11

33 In general the results presented below for the ANES data are not largelyimpacted by the decision to cluster at the issue level Similar results are obtained ifthe data are not clustered

STEREOTYPES 1787

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the comparison group EethtjGTHORN is also a significant predictor ofE

BethtjGTHORN with the predicted negative signAlthough these results provide strong evidence of context

dependence and are consistent with our model they do not pindown a role for representativeness of types Our next test relatesthe magnitude of representativeness of tail types to the magni-tude of belief distortions

To this end we implement the regressions in equations (6)and (7) Following Proposition 4 we compute the average repre-

sentativeness of tail types for conservatives RconsH frac14

PtT2tconsPtT2tlib

We

again test the hypothesis that RconsH is a significant predictor of Est

ethtjconsTHORN with a positive sign and a predictor of EstethtjlibTHORN with a

negative sign Table II shows that conditional on true mean RconsH

predicts believed mean for each group G as expected The firstthree specifications display the results for predicting beliefs heldabout conservatives In both data sets the average representa-tiveness of tail types for conservatives is a significant positivepredictor of beliefs held about conservatives The final three spe-cifications display the results for predicting beliefs held about

FIGURE IV

Exaggeration of Differences

QUARTERLY JOURNAL OF ECONOMICS1788

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liberals We find that the average representativeness of tail typesfor conservatives is a negative predictor of beliefs held about lib-erals This effect is significant in the GNH data and marginallysignificant in the ANES data

We present several additional results in Online Appendix GTo further examine the role of representativeness in driving be-liefs we first show the results of Table II carry through when we

TABLE II

AVERAGE REPRESENTATIVENESS OF TAIL POSITIONS PREDICTS BELIEFS

OLS Predicting Believed Mean of Group G for Each Issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position

of group G for issue

078 024 051 072 018 041

(006) (008) (009) (005) (005) (010)

Avg rep of tail types for

conservatives RconsH

019 055 025 014 012 024

(007) (022) (008) (006) (007) (005)

Constant 101 260 184 093 271 201

(026) (045) (029) (022) (025) (032)

R2 082 048 060 091 031 070

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

TABLE I

INFORMATION ABOUT ndashG PREDICTS BELIEFS ABOUT G

OLS predicting believed mean of group G for each issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position of

conservatives for issue

102 098 096 021 019 025

(0097) (0133) (0076) (0060) (0116) (0060)

True mean position of

liberals for issue

035 086 058 0987 039 073

(0106) (0134) (0131) (0066) (0106) (0135)

Constant 151 335 235 069 258 156

(0195) (0269) (0279) (0122) (0249) (0270)

R2 083 053 066 092 032 068

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

STEREOTYPES 1789

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control for the average likelihood on the tail positions (see Table A4in Online Appendix G) Most tellingly we use the model to predictbeliefs across issues and compare those to the data For simplicitywe use the rank-based truncation specification to predict mean be-liefs when stereotypes include the d most representative types ford frac14 1 T We compare these predictions to those of a model inwhich beliefs are obtained by restricting the distribution to the dmost likely types Our benchmark for both models is predicting thebelieved mean from the entire distribution where d = T We showthat the predictions of the rank-based truncation model with d = 4or 5 compare favorably to both a likelihood-based truncation model(with any d) and the accurate beliefs benchmark Interestingly thisresult suggests that stereotypical beliefs are well approximated byneglecting the least representative types (as opposed to focusingonly on the most representative types) and so represent a moderatethough systematic departure from the standard benchmarkFinally we show that the results we document above hold forboth beliefs held by conservatives and beliefs held by liberals (seeTables A9 A10 and A11 in Online Appendix G)

V Conclusion

We present a model of stereotypical thinking in which DMsmaking predictions about a group overweight the grouprsquos mostdistinctive types These overweighted types are not the mostlikely ones given the DMrsquos data but the most representativeones in the sense of being the most diagnostic of the group rela-tive to other groups Representativeness implies that what ismost distinctive of a group depends on what group it is comparedwith We present experimental evidence that confirms this con-text dependence in recall-based assessments of groups Finallywe evaluated the predictions of the model using political data fromexisting large-scale surveys We find context dependence to be akey feature of beliefs Given the richness of the political data wecan go a step further and identify a role for representativeness inparticular As the representativeness of tail types increases beliefsof a group are distorted in the direction of that tail

Our approach provides a parsimonious and psychologicallyfounded account of how DMs generate simplified representationsof reality from social groups to stock returns and offers a unifiedaccount of disparate pieces of evidence relating to this type of

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uncertainty The model captures the central fact that stereotypeshighlight the greatest difference between groups thus explainingwhy some stereotypes are very accurate while others lack valid-ity Still stereotypes often have a kernel of truth when they arebased on systematicmdasheven if smallmdashdifferences between groupsThis logic allows us to describe a number of heuristics and psy-chological biases many of which arise in the context of predictionproblems Generically our model generates overreaction to diag-nostic information

Our model is based on representativeness and does not cap-ture all the features of stereotypical thinking However it cap-tures perhaps the central feature when we think of a group wefocus on what is most distinctive about it and neglect or under-weight the rest

Saeuroıd Business School University of Oxford

Ohio State University and Harvard Business School

Universita Bocconi and Innocenzo Gasparini Institute

for Economic Research

Harvard University

Supplementary Material

An Online Appendix for this article can be found at QJEonline (qjeoxfordjournalorg)

References

Adorno Theodor Else Frenkel-Brunswik Daniel Levinson and Nevitt SanfordThe Authoritarian Personality (New York Harper amp Row 1950)

Arrow Kenneth lsquolsquoThe Theory of Discriminationrsquorsquo in Discrimination in LaborMarkets Orley Ashenfelter and Albert Rees eds (Princeton NJPrinceton University Press 1973)

Ashton Michael and Victoria Esses lsquolsquoStereotype Accuracy Estimating theAcademic Performance of Ethnic Groupsrsquorsquo Personality and SocialPsychology Bulletin 25 (1999) 225ndash236

Barberis Nicholas Andrei Shleifer and Robert Vishny lsquolsquoA Model of InvestorSentimentrsquorsquo Journal of Financial Economics 49 (1998) 307ndash343

Bayer Sylvia lsquolsquoThe Accuracy of Academic Gender Stereotypesrsquorsquo Sex Roles 40(1999) 787ndash813

Benjamin Dan James Choi and Joshua Strickland lsquolsquoSocial Identity andPreferencesrsquorsquo American Economic Review 100 (2010) 1913ndash1928

Benjamin Dan Matthew Rabin and Collin Raymond lsquolsquoA Model of Non-Belief inthe Law of Large Numbersrsquorsquo Journal of the European Economic Association15 (2015) 515ndash544

Bertrand Marianne lsquolsquoNew Perspectives on Genderrsquorsquo Handbook of LaborEconomics 4 (2011) 1543ndash1590

Bodoh-Creed Aaron Dan Benjamin and Matthew Rabin lsquolsquoThe Dynamics of Base-Rate Neglectrsquorsquo mimeo Haas Business School 2013

STEREOTYPES 1791

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Bohnet Iris Alexandra van Geen and Max Bazerman lsquolsquoWhen PerformanceTrumps Gender Bias Joint versus Separate Evaluationrsquorsquo ManagementScience 5 (2016) 1225ndash1234

Bordalo Pedro Nicola Gennaioli and Andrei Shleifer lsquolsquoSalience Theory of Choiceunder Riskrsquorsquo Quarterly Journal of Economics 127 (2012) 1243ndash1285

mdashmdashmdash lsquolsquoSalience and Consumer Choicersquorsquo Journal of Political Economy 121(2013) 803ndash843

Briton Nancy and Judith Hall lsquolsquoBeliefs about Female and Male NonverbalCommunicationrsquorsquo Sex Roles 32 (1995) 79ndash90

Buser Thomas Muriel Niederle and Hessel Oosterbeek lsquolsquoGenderCompetitiveness and Career Choicesrsquorsquo Quarterly Journal of Economics 129(2014) 1409ndash1447

Carrell Scott Marianne Page and James West lsquolsquoSex and Science How ProfessorGender Perpetuates the Gender Gaprsquorsquo Quarterly Journal of Economics 125(2010) 1101ndash1144

Chambers John and Darya Melnyk lsquolsquoWhy Do I Hate Thee ConflictMisperceptions and Intergroup Mistrustrsquorsquo Personality and SocialPsychology Bulletin 32 (2006) 1295ndash1311

Chan Wayne Robert R McCrae Filip De Fruyt Lee Jussim CorinnaE Lockenhoff Marleen De Bolle Paul T Costa Jr Angelina R SutinAnu Realo Juri Allik Katsuharu Nakazato Yoshiko ShimonakaMartina Hrebıckova Sylvie Graf Michelle Yik Marina Brunner-SciarraNora Leibovich De Figueora Vanina Schmidt Chang-kyo Ahn Hyun-nie Ahn Maria E Aguilar-Vafaie Jerzy Siuta Barbara SzmigielskaThomas R Cain Janet T Crawford Khairul Anwar Mastor Jean-Pierre Rolland Florence Nansubuga Daniel R MiramontezVeronica Benet-Martınez Jerome Rossier Denis Bratko Iris MarusicJamin Halberstadt Mami Yamaguchi Goran Knezevic Thomas A MartinMirona Gheorghiu Peter B Smith Claudio Barbaranelli Lei WangJane Shakespeare-Finch Margarida P Lima Waldemar KlinkoszAndrzej Sekowski Lidia Alcalay Franco Simonetti Tatyana V AvdeyevaV S Pramila and Antonio Terracciano lsquolsquoStereotypes of Age Differences inPersonality Traits Universal and Accuratersquorsquo Journal of Personality andSocial Psychology 103 (2012) 1050ndash1066

Chen Yan Sherry Xin Liu Tracy Xiao and Margaret Shih lsquolsquoWhich Hat to WearImpact of Natural Identities on Coordination and Cooperationrsquorsquo Games andEconomic Behavior 84 (2014) 58ndash86

Coffman Katherine lsquolsquoEvidence on Self-Stereotyping and the Contribution ofIdeasrsquorsquo Quarterly Journal of Economics 129 (2014) 1625ndash1660

Cunningham Tom lsquolsquoComparisons and Choicersquorsquo mimeo Stockholm University2013

Diekman Amanda Alice Eagly and Patrick Kulesa lsquolsquoAccuracy and Bias in theStereotypes about the Social and Political Attitudes of Women and MenrsquorsquoJournal of Experimental Social Psychology 38 (2002) 268ndash282

Eccles Jacquelynne S Janis E Jacobs and Rena D Harold lsquolsquoGender RoleStereotypes Expectancy Effects and Parentsrsquo Socialization of GenderDifferencesrsquorsquo Journal of Social Issues 46 (1990) 183ndash201

Fryer Roland and Matthew Jackson lsquolsquoA Categorical Model of Cognition andBiased Decision-Makingrsquorsquo BE Journal of Theoretical Economics 8 (2008)1ndash42

Fryer Roland and Steven Levitt lsquolsquoAn Empirical Analysis of the Gender Gap inMathematicsrsquorsquo American Economic Journal Applied Economics 2 (2010)210ndash240

Gennaioli Nicola and Andrei Shleifer lsquolsquoWhat Comes to Mindrsquorsquo Quarterly Journalof Economics 125 (2010) 1399ndash1433

Gennaioli Nicola Andrei Shleifer and Robert Vishny lsquolsquoNeglected RisksFinancial Innovation and Financial Fragilityrsquorsquo Journal of FinancialEconomics 104 (2012) 452ndash468

Gilens Martin lsquolsquoRace and Poverty in America Public Misperceptions and theAmerican News Mediarsquorsquo Public Opinion Quarterly 60 (1996) 515ndash541

Glaeser Edward lsquolsquoThe Political Economy of Hatredrsquorsquo Quarterly Journal ofEconomics 120 (2005) 45ndash86

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Glover Dyland Amanda Pallais and William Pariente lsquolsquoDiscrimination as a Self-Fulfilling Prophecy Evidence from French Grocery Storesrsquorsquo mimeo HarvardUniversity 2015

Goldin Claudia Lawrence Katz and Ilyana Kuziemko lsquolsquoThe Homecoming ofAmerican College Women The Reversal of the College Gender GaprsquorsquoJournal of Economic Perspectives 20 (2006) 133ndash156

Graham Jesse Brian Nosek and Jonathan Haidt lsquolsquoThe Moral Stereotypes ofLiberals and Conservatives Exaggeration of Differences across thePolitical Spectrumrsquorsquo PLoS One 7 (2012) 1ndash13

Grether David lsquolsquoBayes Rule as a Descriptive Model The RepresentativenessHeuristicrsquorsquo Quarterly Journal of Economics 95 (1980) 537ndash557

Griffin Dale and Amos Tversky lsquolsquoThe Weighing of Evidence and theDeterminants of Confidencersquorsquo Cognitive Psychology 24 (1992) 411ndash435

Guiso Luigi Ferdinando Monte Paola Sapienza and Luigi Zingales lsquolsquoCultureGender and Mathrsquorsquo Science 320 (2008) 1164ndash1165

Hilton James and William Von Hippel lsquolsquoStereotypesrsquorsquo Annual Review ofPsychology 47 (1996) 237ndash271

Hyde Janet Sara Lindberg Marcia Linn Amy Ellis and Caroline WilliamslsquolsquoGender Similarities Characterize Math Performancersquorsquo Science 321 (2008)494ndash495

Judd Charles and Bernardette Park lsquolsquoDefinition and Assessment of Accuracy inSocial Stereotypesrsquorsquo Psychological Review 100 (1993) 109ndash128

Jussim Lee Jarret Crawford Stephanie Anglin John Chambers Sean Stevensand Florette Cohen lsquolsquoStereotype Accuracy One of the Largest and MostReplicable Effects in All of Social Psychologyrsquorsquo in The Handbook ofPrejudice Stereotyping and Discrimination Todd Nelson ed (MahwahNJ Lawrence Erlbaum 2015)

Kahneman Daniel and Amos Tversky lsquolsquoSubjective Probability A Judgment ofRepresentativenessrsquorsquo Cognitive Psychology 3 (1972) 430ndash454

mdashmdashmdash lsquolsquoOn the Psychology of Predictionrsquorsquo Psychological Review 80 (1973) 237ndash251

Kaplowitz Stan Bradley Fisher and Clifford Broman lsquolsquoHow Accurate ArePerceptions of Social Statistics about Blacks and Whitesrsquorsquo Public OpinionQuarterly 67 (2003) 237ndash243

Kersten Daniel Pascal Mamassian and Alan Yuille lsquolsquoObject Perception asBayesian Inferencersquorsquo Annual Review of Psychology 55 (2004) 271ndash304

Klein Richard Kate A Ratliff Michelangelo Vianello Reginald B Adams JrStepan Bahnik Michael J Bernstein Konrad Bocian Mark J BrandtBeach Brooks Claudia Chloe Brumbaugh Zeynep CemalcilarJesse Chandler Winnee Cheong William E Davis Thierry DevosMatthew Eisner Natalia Frankowska David Furrow Elisa Maria GallianiFred Hasselman Joshua A Hicks James F Hovermale S Jane HuntJeffrey R Huntsinger Hans IJzerman Melissa-Sue John Jennifer A Joy-Gaba Heather Barry Kappes Lacy E Krueger Jaime Kurtz CarmelA Levitan Robyn Mallett Wendy L Morris Anthony J Nelson JasonA Nier Grant Packard Ronaldo Pilati Abraham M RutchickKathleen Schmidt Jeanine L Skorinko Robert Smith Troy G SteinerJustin Storbeck Lyn M Van Swol Donna Thompson Anna van rsquot VeerLeigh Ann Vaughn Marek Vranka Aaron Wichman Julie A Woodzickaand Brian A Nosek lsquolsquoInvestigating Variation in Replicability A ManyLabs Replication Projectrsquorsquo Social Psychology 45 (2014) 142ndash152

Lundberg Shelly and Richard Startz lsquolsquoPrivate Discrimination and SocialIntervention in Competitive Labor Marketsrsquorsquo American Economic Review73 (1983) 340ndash347

Madon Stephanie Max Guyll Kathy Aboufadel Eulices Montiel Alison SmithPolly Palumbo and Lee Jussim lsquolsquoEthnic and National Stereotypes ThePrinceton Trilogy Revisited and Revisedrsquorsquo Personality and SocialPsychological Bulletin 27 (2001) 996ndash1010

Martin Carol lsquolsquoA Ratio Measure of Sex Stereotypingrsquorsquo Journal of Personality andSocial Psychology 52 (1987) 489ndash499

STEREOTYPES 1793

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ibrary on October 28 2016

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McCauley Clark Krishna Thangavelu and Paul Rozin lsquolsquoSex Stereotyping ofOccupations in Relation to Television Representations and Census FactsrsquorsquoBasic and Applied Social Psychology 9 (1988) 197ndash212

Mullainathan Sendhil lsquolsquoThinking through Categoriesrsquorsquo mimeo HarvardUniversity 2002

Ortoleva Pietro and Erik Snowberg lsquolsquoOverconfidence in Political BehaviorrsquorsquoAmerican Economic Review 105 (2015) 504ndash535

Phelps Edmund lsquolsquoThe Statistical Theory of Racism and Sexismrsquorsquo AmericanEconomic Review 62 (1972) 659ndash661

Pope Devin and Justin Sydnor lsquolsquoGeographic Variation in the Gender Differencesin Test Scoresrsquorsquo Journal of Economic Perspectives 24 (2010) 95ndash108

Rabin Matthew lsquolsquoInference by Believers in the Law of Small NumbersrsquorsquoQuarterly Journal of Economics 117 (2002) 775ndash816

Rabin Matthew and Joel Schrag lsquolsquoFirst Impressions Matter A Model ofConfirmatory Biasrsquorsquo Quarterly Journal of Economics 114 (1999) 37ndash82

Rabin Matthew and Dimitri Vayanos lsquolsquoThe Gamblerrsquos and Hot-Hand FallaciesTheory and Applicationsrsquorsquo Review of Economic Studies 77 (2010) 730ndash778

Reuben Ernesto Paola Sapienza and Luigi Zingales lsquolsquoHow Stereotypes ImpairWomenrsquos Careers in Sciencersquorsquo Proceedings of the National Academy ofSciences 111 (2014) 4403ndash4408

Rosch Eleanor lsquolsquoNatural Categoriesrsquorsquo Cognitive Psychology 4 (1973) 328ndash350Ryan Carey S lsquolsquoAccuracy of Black and White College Studentsrsquo In-Group and

Out-Group Stereotypesrsquorsquo Personality and Social Psychology Bulletin 22(1996) 1114ndash1127

Schneider David The Psychology of Stereotyping (New York Guilford Press2004)

Schneider David Albert Hastorf and Phoebe Ellsworth Person Perception(Reading MA Addison-Wesley 1979)

Shih Margaret Todd Pittinsky and Nalini Ambady lsquolsquoStereotype SusceptibilityIdentity Salience and Shifts in Quantitative Performancersquorsquo PsychologicalScience 10 (1999) 80ndash83

Shih Margaret Todd Pittinsky and Amy Trahan lsquolsquoDomain-Specific Effects ofStereotypes on Performancersquorsquo Self and Identity 5 (2006) 1ndash14

Steele Claude Whistling Vivaldi How Stereotypes Affect Us and What We CanDo (New York Norton 2010)

Tenenbaum Joshua and Thomas Griffiths lsquolsquoThe Rational Basis ofRepresentativenessrsquorsquo 23rd Annual Conference of the Cognitive ScienceSociety (2001) 1036ndash1041

Tversky Amos and Daniel Kahneman lsquolsquoExtensional versus Intuitive ReasoningThe Conjunction Fallacy in Probability Judgmentrsquorsquo Psychological Review 90(1983) 293ndash315

Weinberger Catherin lsquolsquoIs the Science and Engineering Workforce Drawn fromthe Far Upper Tail of the Math Ability Distributionrsquorsquo mimeo UCSB 2005

Westfall Jacob Leaf Van Boven John Chambers and Charles Judd lsquolsquoPerceivingPolitical Polarization in the United States Party Identity Strength andAttitude Extremity Exacerbate the Perceived Partisan DividersquorsquoPsychological Science 10 (2015) 145ndash158

Wolsko Christopher Bernadette Park Charles Judd and Bernd WittenbrinklsquolsquoFraming Interethnic Ideology Effects of Multicultural and Color-BlindPerspectives on Judgments of Groups and Individualsrsquorsquo Journal ofPersonality and Social Psychology 78 (2000) 635ndash654

QUARTERLY JOURNAL OF ECONOMICS1794

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Page 29: I. Introduction · uneducated at the beginning of the 20th century, and as high achievers at the beginning of the 21st (Madon et al. 2001). Social science has produced three broad

design the theoretical predictions for the ordered types designsare more sensitive to the specific assumptions one makes aboutthe weighting function of the DM26 We find effects in the pre-dicted direction for three of the five samples As we discuss inmore detail in Online Appendix F the ordered types resultsvary by platform with consistently stronger results on AmazonMechanical Turk than in the laboratory samples Pooling all or-dered types experiments participants are 93 percentage pointsmore likely to guess that the group of interest has a greater av-erage than the comparison group when the right tail is represen-tative (p = 062) Given our simple experimental setting withgroups of mundane objects we interpret our resultsmdasha signifi-cant and reasonably sized impact on average beliefsmdashas an im-portant proof of concept the presence of representative typesbiases ex post assessment

IVB Empirical Evidence on Political Stereotypes

We examine two data sets on political preferences and be-liefs about political preferences in the United States We inves-tigate the roles of representativeness and context dependence byseparately testing for hypotheses that allow us to assess the lead-ing theories of stereotypes

First we test whether beliefs are correct or depart systemat-ically from the truth The statistical discrimination approachbuilds on the assumption that people hold rational expectationsof group traits Comparing beliefs to the truth allows us to assessthe validity of this assumption in our data

Second we test if beliefs depart from the truth by exagger-ating (mean) differences among groups per the kernel of truthhypothesis This is an implicit test of context dependence be-cause it implies that beliefs about the target groups are shapednot only by that grouprsquos characteristics but also by those of thereference group27

Third we test if distortions in beliefs can be accounted for bythe overweighting of highly representative types (defined astypes that are relatively more frequent in the target relative to

26 This is due in part to our choice to not study MLRP distributions We moti-vate and discuss this design decision in Online Appendix F

27 Of course unlike in the laboratory experiment in this setting we cannot testfor context dependence by exogenously varying the reference group

STEREOTYPES 1781

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the reference group) The second and third tests address the keypredictions of our model

1 The Data We have two data sets on political preferences andbeliefs about political preferences The first data set from GrahamNosek and Haidt (GNH 2012) contains data from the MoralFoundations Questionnaire Respondents (1174 self-identified lib-erals and 500 self-identified conservatives) answer questions abouttheir position on a subset of 45 issues 20 moral relevance state-ments (eg lsquolsquowhen you decide whether something is right orwrong to what extent are the following considerations relevantto your thinkingrsquorsquo) and 25 moral judgments (eg lsquolsquoindicate theextent to which you would agree or disagreersquorsquo) For each issue arandomly determined subset of participants states their own posi-tion another subset states their belief on the position of a lsquolsquotypicalliberalrsquorsquo and a third subset states their belief on the position of alsquolsquotypical conservativersquorsquo The data thus include the distribution overpositions for both liberal and conservatives as well as the averagebelieved typical position of liberals and of conservatives on the 45issues Each position is elicited on 1ndash6 scale

The second data set comes from the American NationalElection Survey (ANES) and contains data from more than20000 respondents between 1964 and 201228 The surveycovers political issues of the day such as the optimal amount ofgovernment spending and service provision (1984ndash2000) or theplace of women in society (1972ndash1998) We focus on the 10 issuesthat ask participants to respond on a 1ndash7 scale (rather than justindicate binary agreement or disagreement) all 10 issues areasked in multiple years Participants are asked to provide theirown position on the scale and their believed position of theDemocratic and Republican parties (lsquolsquoWhere would you placethe Democratic [Republican] party on this scalersquorsquo) The data in-clude for each issue-year observation the distribution of partic-ipant positions for self-identified liberals and self-identifiedconservatives as well as the distribution of believed typical posi-tions of the Democratic and Republican parties

28 These data are publicly available at httpwwwelectionstudiesorgstudy-pagesanes_timeseries_cdfanes_timeseries_cdfhtm

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2 Empirical Strategy Our analysis focuses on beliefs abouttwo groups Conservatives and Liberals The types are the possi-ble positions for each issue (1 2 6 7) For the GNH data weinterpret beliefs about the lsquolsquotypicalrsquorsquo element of a group to coincidewith the believed average position in that group Similarly forthe ANES data we use the believed party positions as a proxy forbelieved mean of each group29 We then take as a benchmark thehypothesis that individuals hold accurate beliefs about eachgroup and in particular that believed mean position shouldequal true mean position at least on average across subjectsThe accurate beliefs hypothesis underlies the most common eco-nomic model of stereotyping statistical discrimination

To assess our representativeness-based model we perform aregression exercise To test our model in a linear regressionframework we rely on linear approximations of the weightingfunction Our model then yields two regression specifications

PROPOSITION 4 Let G 2 fconservative liberal g and assume

ht h tG

tG

be a differentiable and strictly increasing weight-

ing function as in Definition 2 The following hold as a first-order approximation around identical distributions G

Gfrac14 1

(i) Kernel of truth regression There exists a constant gt 0such that

EstethtjGTHORN frac14 EethtjGTHORNeth1thorn THORN EethtjGTHORNeth5THORN

(ii) Representativeness regression Denote H frac14 fT 2 Tg

the right tail of types and RconsH frac14

PHtconsPHtlib

as the average

representativeness of right tail types for conservatives

29 This assumption is consistent with the authorsrsquo interpretation of the GNHdata (GNH 2012) and with previous studies using ANES (eg Westfall et al 2015)Furthermore to the extent that this assumption holds equally well for most issueswithin a data set our focus on cross-issue differences should allow us to test thepredictions of our model even with an imperfect proxy for beliefs of mean positionsFinally the data provide some insight into whether subjects are reporting (per-ceived) modal or mean types As we show the modal type is a poor prediction ofstated beliefs while a distorted mean slanted toward representative types is anaccurate prediction of stated beliefs

STEREOTYPES 1783

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Under the further approximation where tcons

tlibampRcons

H for

t 2 H

EstethtjconsTHORN frac14 EethtjconsTHORN thorn consethR

consH 1THORNeth6THORN

EstethtjlibTHORN frac14 EethtjlibTHORN libethR

consH 1THORNeth7THORN

where lcons and llib are positive constants

The first regression allows us to test for the kernel of truthhypothesis and the second set of regressions allows us to test forthe role of representativeness

Equation (5) says that respondents in our model inflate theaverage position of a group say the conservatives if and only ifthe group has a higher average position than the other groupnamely the liberals Formally EstethtjconsTHORN gt EethtjconsTHORN if and onlyif EethtjconsTHORN gt EethtjlibTHORN Because in our measurement scale highertypes mean lsquolsquomore conservativersquorsquo we expect (i) believed conserva-tive average to be higher than the truth and (ii) the extent ofoverstatement to decrease in the average liberal position EethtjlibTHORNConversely we expect the average liberal position to be lowerthan the truth the more so the higher the average conservativeposition EethtjconsTHORN

As previously discussed the basis of these predictions is con-text dependence information about the distribution of ndashG is rel-evant for the beliefs about G This context dependence isinconsistent with rational expectations in which only thegrouprsquos own means should affect beliefs We test the hypothesisthat the true mean EethtjGTHORN is a significant predictor of the believedmean E

stethtjGTHORN with a positive sign and the other grouprsquos truemean EethtjGTHORN is a predictor of the believed mean with a negativesign

Equations (6) and (7) say that repondentsrsquo assessment bias isshaped by representativeness When the right tail is more repre-sentative for conservatives (Rcons

H 1 positive and large) partici-pants should inflate the average conservative position more(higher E

stethtjconsTHORN EethtjconsTHORN) and deflate the average liberal po-sition more (lower E

stethtjlibTHORN EethtjlibTHORN) We test the hypothesisthat the inflation in conservative positions is positively associatedwith the representativeness of the right tail for the conservativesand the inflation in liberal positions is negatively associated with

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it Once again the representativeness of the right tail is com-puted using the true distribution of positions

In equations (6) and (7) in many cases the representative tailis also the most likely one As a consequence these tests cannotdistinguish a representativeness-based from a likelihood-basedmodel of distorted beliefs We perform two additional testsFirst we run versions of equations (6) and (7) in which we controlfor the likelihood of tails (see Table A4 in Online Appendix G)Second we compute numerically the predictions of a representa-tiveness-based model of stereotypes and a likelihood-based modelof stereotypes We then assess which of these two is better able tomatch the data on beliefs

3 Empirical Results To begin we illustrate the structure ofthe data and the nature of our predictions with two simple exam-ples from the GNH data set focusing on beliefs about conserva-tives In example 1 participants are asked about their agreementwith the statement lsquolsquoIt can never be right to kill a human beingrsquorsquoIn example 2 participants are asked about the moral relevance oflsquolsquowhether or not someone cared for someone weak or vulnerablersquorsquoAs can be seen in Figure III in example 1 the modal position(strongly disagree (1)) and most representative positions(strongly disagree (1)) coincide for conservatives In contrast inexample 2 in Figure III the most representative types (slightlyrelevant (3) not at all relevant (1)) are not most likely for theconservative group Following Proposition 1 we predict that be-liefs will be distorted in the direction of the most representativetypes Thus we expect more exaggeration in example 2 than inexample 1 since in example 2 the most representative types (inthe left tail) are far from the modal type whereas in example 1they coincide This is what we find the conservative position isexaggerated by only 009 positions in Example 1 (true mean 299believed mean 290) but by 106 positions in Example 2 (truemean 421 believed mean 315)

In the full data sets we treat each (issue year) pair as anobservation and we cluster standard errors at the issue level Forthe GNH data we have 45 observations 45 issues measured inthe same year For the ANES data we have 66 observations 10issues measured in multiple years To begin we simply docu-ment systematic exaggeration in both data sets This is a primaryfocus of the original analysis in GNH (2012) and also in Westfall

STEREOTYPES 1785

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FIGURE III

Two Examples

QUARTERLY JOURNAL OF ECONOMICS1786

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et al (2015)rsquos analysis of the ANES data30 Figure IV shows thatthe believed difference between typical conservative and typicalliberal positions is larger than the true difference in mean posi-tions for 109 of the 111 observations The data for both GNH(squares) and ANES (triangles) lie above the 45-degree line(dashed)31 Average exaggeration is 062 positions on the scale(066 in the GNH data 059 in the ANES data)32

The systematic and significant exaggeration of mean differ-ences suggests that the benchmark model of accurate beliefs ismissing something important Indeed this exaggeration reflectsthe fact that believed means are typically more extreme than truemeans First note that the kernel of truth regression (equation(5)) generates exaggeration of mean differences just as docu-mented in Figure IV

EstethtjGTHORN E

stethtjGTHORN frac14 eth1thorn 2THORN frac12EethtjGTHORN EethtjGTHORN

To bring this prediction to the data we regress the believedmean position for each group EBethtjGTHORN on the true mean of thegroup EethtjGTHORN and the true mean of the comparison groupEethtjGTHORN across issues We do this for each group (liberals con-servatives) in each data set separately We also present pooledspecifications that combine the data sets to make a prediction fora given group (liberals conservatives) In these pooled specifica-tions we include a dummy variable indicating whether theobservation came from the ANES data set For all specificationswe cluster observations at the issue level33 The results from re-gression are shown in Table I In every specification we find thatEethtjGTHORN is a significant predictor of EBethtjGTHORN with the predicted pos-itive sign Crucially for five of the six specifications the mean of

30 Chambers and Melnyk (2006) also find evidence of exaggeration of truedifferences in beliefs about political positions

31 For convenience we recode all issues so that the high end of the scale (67)represents the stereotypically more conservative position

32 A natural question to ask is how beliefs vary across liberals and conserva-tives That is do beliefs about a group G depend on membership in G versus ndashG Ourmodel does not speak to this issue However in Online Appendix G we show thatthe results we document below hold for both beliefs held by conservatives and be-liefs held by liberals see Tables A9 A10 and A11

33 In general the results presented below for the ANES data are not largelyimpacted by the decision to cluster at the issue level Similar results are obtained ifthe data are not clustered

STEREOTYPES 1787

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the comparison group EethtjGTHORN is also a significant predictor ofE

BethtjGTHORN with the predicted negative signAlthough these results provide strong evidence of context

dependence and are consistent with our model they do not pindown a role for representativeness of types Our next test relatesthe magnitude of representativeness of tail types to the magni-tude of belief distortions

To this end we implement the regressions in equations (6)and (7) Following Proposition 4 we compute the average repre-

sentativeness of tail types for conservatives RconsH frac14

PtT2tconsPtT2tlib

We

again test the hypothesis that RconsH is a significant predictor of Est

ethtjconsTHORN with a positive sign and a predictor of EstethtjlibTHORN with a

negative sign Table II shows that conditional on true mean RconsH

predicts believed mean for each group G as expected The firstthree specifications display the results for predicting beliefs heldabout conservatives In both data sets the average representa-tiveness of tail types for conservatives is a significant positivepredictor of beliefs held about conservatives The final three spe-cifications display the results for predicting beliefs held about

FIGURE IV

Exaggeration of Differences

QUARTERLY JOURNAL OF ECONOMICS1788

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liberals We find that the average representativeness of tail typesfor conservatives is a negative predictor of beliefs held about lib-erals This effect is significant in the GNH data and marginallysignificant in the ANES data

We present several additional results in Online Appendix GTo further examine the role of representativeness in driving be-liefs we first show the results of Table II carry through when we

TABLE II

AVERAGE REPRESENTATIVENESS OF TAIL POSITIONS PREDICTS BELIEFS

OLS Predicting Believed Mean of Group G for Each Issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position

of group G for issue

078 024 051 072 018 041

(006) (008) (009) (005) (005) (010)

Avg rep of tail types for

conservatives RconsH

019 055 025 014 012 024

(007) (022) (008) (006) (007) (005)

Constant 101 260 184 093 271 201

(026) (045) (029) (022) (025) (032)

R2 082 048 060 091 031 070

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

TABLE I

INFORMATION ABOUT ndashG PREDICTS BELIEFS ABOUT G

OLS predicting believed mean of group G for each issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position of

conservatives for issue

102 098 096 021 019 025

(0097) (0133) (0076) (0060) (0116) (0060)

True mean position of

liberals for issue

035 086 058 0987 039 073

(0106) (0134) (0131) (0066) (0106) (0135)

Constant 151 335 235 069 258 156

(0195) (0269) (0279) (0122) (0249) (0270)

R2 083 053 066 092 032 068

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

STEREOTYPES 1789

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control for the average likelihood on the tail positions (see Table A4in Online Appendix G) Most tellingly we use the model to predictbeliefs across issues and compare those to the data For simplicitywe use the rank-based truncation specification to predict mean be-liefs when stereotypes include the d most representative types ford frac14 1 T We compare these predictions to those of a model inwhich beliefs are obtained by restricting the distribution to the dmost likely types Our benchmark for both models is predicting thebelieved mean from the entire distribution where d = T We showthat the predictions of the rank-based truncation model with d = 4or 5 compare favorably to both a likelihood-based truncation model(with any d) and the accurate beliefs benchmark Interestingly thisresult suggests that stereotypical beliefs are well approximated byneglecting the least representative types (as opposed to focusingonly on the most representative types) and so represent a moderatethough systematic departure from the standard benchmarkFinally we show that the results we document above hold forboth beliefs held by conservatives and beliefs held by liberals (seeTables A9 A10 and A11 in Online Appendix G)

V Conclusion

We present a model of stereotypical thinking in which DMsmaking predictions about a group overweight the grouprsquos mostdistinctive types These overweighted types are not the mostlikely ones given the DMrsquos data but the most representativeones in the sense of being the most diagnostic of the group rela-tive to other groups Representativeness implies that what ismost distinctive of a group depends on what group it is comparedwith We present experimental evidence that confirms this con-text dependence in recall-based assessments of groups Finallywe evaluated the predictions of the model using political data fromexisting large-scale surveys We find context dependence to be akey feature of beliefs Given the richness of the political data wecan go a step further and identify a role for representativeness inparticular As the representativeness of tail types increases beliefsof a group are distorted in the direction of that tail

Our approach provides a parsimonious and psychologicallyfounded account of how DMs generate simplified representationsof reality from social groups to stock returns and offers a unifiedaccount of disparate pieces of evidence relating to this type of

QUARTERLY JOURNAL OF ECONOMICS1790

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uncertainty The model captures the central fact that stereotypeshighlight the greatest difference between groups thus explainingwhy some stereotypes are very accurate while others lack valid-ity Still stereotypes often have a kernel of truth when they arebased on systematicmdasheven if smallmdashdifferences between groupsThis logic allows us to describe a number of heuristics and psy-chological biases many of which arise in the context of predictionproblems Generically our model generates overreaction to diag-nostic information

Our model is based on representativeness and does not cap-ture all the features of stereotypical thinking However it cap-tures perhaps the central feature when we think of a group wefocus on what is most distinctive about it and neglect or under-weight the rest

Saeuroıd Business School University of Oxford

Ohio State University and Harvard Business School

Universita Bocconi and Innocenzo Gasparini Institute

for Economic Research

Harvard University

Supplementary Material

An Online Appendix for this article can be found at QJEonline (qjeoxfordjournalorg)

References

Adorno Theodor Else Frenkel-Brunswik Daniel Levinson and Nevitt SanfordThe Authoritarian Personality (New York Harper amp Row 1950)

Arrow Kenneth lsquolsquoThe Theory of Discriminationrsquorsquo in Discrimination in LaborMarkets Orley Ashenfelter and Albert Rees eds (Princeton NJPrinceton University Press 1973)

Ashton Michael and Victoria Esses lsquolsquoStereotype Accuracy Estimating theAcademic Performance of Ethnic Groupsrsquorsquo Personality and SocialPsychology Bulletin 25 (1999) 225ndash236

Barberis Nicholas Andrei Shleifer and Robert Vishny lsquolsquoA Model of InvestorSentimentrsquorsquo Journal of Financial Economics 49 (1998) 307ndash343

Bayer Sylvia lsquolsquoThe Accuracy of Academic Gender Stereotypesrsquorsquo Sex Roles 40(1999) 787ndash813

Benjamin Dan James Choi and Joshua Strickland lsquolsquoSocial Identity andPreferencesrsquorsquo American Economic Review 100 (2010) 1913ndash1928

Benjamin Dan Matthew Rabin and Collin Raymond lsquolsquoA Model of Non-Belief inthe Law of Large Numbersrsquorsquo Journal of the European Economic Association15 (2015) 515ndash544

Bertrand Marianne lsquolsquoNew Perspectives on Genderrsquorsquo Handbook of LaborEconomics 4 (2011) 1543ndash1590

Bodoh-Creed Aaron Dan Benjamin and Matthew Rabin lsquolsquoThe Dynamics of Base-Rate Neglectrsquorsquo mimeo Haas Business School 2013

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Bohnet Iris Alexandra van Geen and Max Bazerman lsquolsquoWhen PerformanceTrumps Gender Bias Joint versus Separate Evaluationrsquorsquo ManagementScience 5 (2016) 1225ndash1234

Bordalo Pedro Nicola Gennaioli and Andrei Shleifer lsquolsquoSalience Theory of Choiceunder Riskrsquorsquo Quarterly Journal of Economics 127 (2012) 1243ndash1285

mdashmdashmdash lsquolsquoSalience and Consumer Choicersquorsquo Journal of Political Economy 121(2013) 803ndash843

Briton Nancy and Judith Hall lsquolsquoBeliefs about Female and Male NonverbalCommunicationrsquorsquo Sex Roles 32 (1995) 79ndash90

Buser Thomas Muriel Niederle and Hessel Oosterbeek lsquolsquoGenderCompetitiveness and Career Choicesrsquorsquo Quarterly Journal of Economics 129(2014) 1409ndash1447

Carrell Scott Marianne Page and James West lsquolsquoSex and Science How ProfessorGender Perpetuates the Gender Gaprsquorsquo Quarterly Journal of Economics 125(2010) 1101ndash1144

Chambers John and Darya Melnyk lsquolsquoWhy Do I Hate Thee ConflictMisperceptions and Intergroup Mistrustrsquorsquo Personality and SocialPsychology Bulletin 32 (2006) 1295ndash1311

Chan Wayne Robert R McCrae Filip De Fruyt Lee Jussim CorinnaE Lockenhoff Marleen De Bolle Paul T Costa Jr Angelina R SutinAnu Realo Juri Allik Katsuharu Nakazato Yoshiko ShimonakaMartina Hrebıckova Sylvie Graf Michelle Yik Marina Brunner-SciarraNora Leibovich De Figueora Vanina Schmidt Chang-kyo Ahn Hyun-nie Ahn Maria E Aguilar-Vafaie Jerzy Siuta Barbara SzmigielskaThomas R Cain Janet T Crawford Khairul Anwar Mastor Jean-Pierre Rolland Florence Nansubuga Daniel R MiramontezVeronica Benet-Martınez Jerome Rossier Denis Bratko Iris MarusicJamin Halberstadt Mami Yamaguchi Goran Knezevic Thomas A MartinMirona Gheorghiu Peter B Smith Claudio Barbaranelli Lei WangJane Shakespeare-Finch Margarida P Lima Waldemar KlinkoszAndrzej Sekowski Lidia Alcalay Franco Simonetti Tatyana V AvdeyevaV S Pramila and Antonio Terracciano lsquolsquoStereotypes of Age Differences inPersonality Traits Universal and Accuratersquorsquo Journal of Personality andSocial Psychology 103 (2012) 1050ndash1066

Chen Yan Sherry Xin Liu Tracy Xiao and Margaret Shih lsquolsquoWhich Hat to WearImpact of Natural Identities on Coordination and Cooperationrsquorsquo Games andEconomic Behavior 84 (2014) 58ndash86

Coffman Katherine lsquolsquoEvidence on Self-Stereotyping and the Contribution ofIdeasrsquorsquo Quarterly Journal of Economics 129 (2014) 1625ndash1660

Cunningham Tom lsquolsquoComparisons and Choicersquorsquo mimeo Stockholm University2013

Diekman Amanda Alice Eagly and Patrick Kulesa lsquolsquoAccuracy and Bias in theStereotypes about the Social and Political Attitudes of Women and MenrsquorsquoJournal of Experimental Social Psychology 38 (2002) 268ndash282

Eccles Jacquelynne S Janis E Jacobs and Rena D Harold lsquolsquoGender RoleStereotypes Expectancy Effects and Parentsrsquo Socialization of GenderDifferencesrsquorsquo Journal of Social Issues 46 (1990) 183ndash201

Fryer Roland and Matthew Jackson lsquolsquoA Categorical Model of Cognition andBiased Decision-Makingrsquorsquo BE Journal of Theoretical Economics 8 (2008)1ndash42

Fryer Roland and Steven Levitt lsquolsquoAn Empirical Analysis of the Gender Gap inMathematicsrsquorsquo American Economic Journal Applied Economics 2 (2010)210ndash240

Gennaioli Nicola and Andrei Shleifer lsquolsquoWhat Comes to Mindrsquorsquo Quarterly Journalof Economics 125 (2010) 1399ndash1433

Gennaioli Nicola Andrei Shleifer and Robert Vishny lsquolsquoNeglected RisksFinancial Innovation and Financial Fragilityrsquorsquo Journal of FinancialEconomics 104 (2012) 452ndash468

Gilens Martin lsquolsquoRace and Poverty in America Public Misperceptions and theAmerican News Mediarsquorsquo Public Opinion Quarterly 60 (1996) 515ndash541

Glaeser Edward lsquolsquoThe Political Economy of Hatredrsquorsquo Quarterly Journal ofEconomics 120 (2005) 45ndash86

QUARTERLY JOURNAL OF ECONOMICS1792

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

Glover Dyland Amanda Pallais and William Pariente lsquolsquoDiscrimination as a Self-Fulfilling Prophecy Evidence from French Grocery Storesrsquorsquo mimeo HarvardUniversity 2015

Goldin Claudia Lawrence Katz and Ilyana Kuziemko lsquolsquoThe Homecoming ofAmerican College Women The Reversal of the College Gender GaprsquorsquoJournal of Economic Perspectives 20 (2006) 133ndash156

Graham Jesse Brian Nosek and Jonathan Haidt lsquolsquoThe Moral Stereotypes ofLiberals and Conservatives Exaggeration of Differences across thePolitical Spectrumrsquorsquo PLoS One 7 (2012) 1ndash13

Grether David lsquolsquoBayes Rule as a Descriptive Model The RepresentativenessHeuristicrsquorsquo Quarterly Journal of Economics 95 (1980) 537ndash557

Griffin Dale and Amos Tversky lsquolsquoThe Weighing of Evidence and theDeterminants of Confidencersquorsquo Cognitive Psychology 24 (1992) 411ndash435

Guiso Luigi Ferdinando Monte Paola Sapienza and Luigi Zingales lsquolsquoCultureGender and Mathrsquorsquo Science 320 (2008) 1164ndash1165

Hilton James and William Von Hippel lsquolsquoStereotypesrsquorsquo Annual Review ofPsychology 47 (1996) 237ndash271

Hyde Janet Sara Lindberg Marcia Linn Amy Ellis and Caroline WilliamslsquolsquoGender Similarities Characterize Math Performancersquorsquo Science 321 (2008)494ndash495

Judd Charles and Bernardette Park lsquolsquoDefinition and Assessment of Accuracy inSocial Stereotypesrsquorsquo Psychological Review 100 (1993) 109ndash128

Jussim Lee Jarret Crawford Stephanie Anglin John Chambers Sean Stevensand Florette Cohen lsquolsquoStereotype Accuracy One of the Largest and MostReplicable Effects in All of Social Psychologyrsquorsquo in The Handbook ofPrejudice Stereotyping and Discrimination Todd Nelson ed (MahwahNJ Lawrence Erlbaum 2015)

Kahneman Daniel and Amos Tversky lsquolsquoSubjective Probability A Judgment ofRepresentativenessrsquorsquo Cognitive Psychology 3 (1972) 430ndash454

mdashmdashmdash lsquolsquoOn the Psychology of Predictionrsquorsquo Psychological Review 80 (1973) 237ndash251

Kaplowitz Stan Bradley Fisher and Clifford Broman lsquolsquoHow Accurate ArePerceptions of Social Statistics about Blacks and Whitesrsquorsquo Public OpinionQuarterly 67 (2003) 237ndash243

Kersten Daniel Pascal Mamassian and Alan Yuille lsquolsquoObject Perception asBayesian Inferencersquorsquo Annual Review of Psychology 55 (2004) 271ndash304

Klein Richard Kate A Ratliff Michelangelo Vianello Reginald B Adams JrStepan Bahnik Michael J Bernstein Konrad Bocian Mark J BrandtBeach Brooks Claudia Chloe Brumbaugh Zeynep CemalcilarJesse Chandler Winnee Cheong William E Davis Thierry DevosMatthew Eisner Natalia Frankowska David Furrow Elisa Maria GallianiFred Hasselman Joshua A Hicks James F Hovermale S Jane HuntJeffrey R Huntsinger Hans IJzerman Melissa-Sue John Jennifer A Joy-Gaba Heather Barry Kappes Lacy E Krueger Jaime Kurtz CarmelA Levitan Robyn Mallett Wendy L Morris Anthony J Nelson JasonA Nier Grant Packard Ronaldo Pilati Abraham M RutchickKathleen Schmidt Jeanine L Skorinko Robert Smith Troy G SteinerJustin Storbeck Lyn M Van Swol Donna Thompson Anna van rsquot VeerLeigh Ann Vaughn Marek Vranka Aaron Wichman Julie A Woodzickaand Brian A Nosek lsquolsquoInvestigating Variation in Replicability A ManyLabs Replication Projectrsquorsquo Social Psychology 45 (2014) 142ndash152

Lundberg Shelly and Richard Startz lsquolsquoPrivate Discrimination and SocialIntervention in Competitive Labor Marketsrsquorsquo American Economic Review73 (1983) 340ndash347

Madon Stephanie Max Guyll Kathy Aboufadel Eulices Montiel Alison SmithPolly Palumbo and Lee Jussim lsquolsquoEthnic and National Stereotypes ThePrinceton Trilogy Revisited and Revisedrsquorsquo Personality and SocialPsychological Bulletin 27 (2001) 996ndash1010

Martin Carol lsquolsquoA Ratio Measure of Sex Stereotypingrsquorsquo Journal of Personality andSocial Psychology 52 (1987) 489ndash499

STEREOTYPES 1793

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ibrary on October 28 2016

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McCauley Clark Krishna Thangavelu and Paul Rozin lsquolsquoSex Stereotyping ofOccupations in Relation to Television Representations and Census FactsrsquorsquoBasic and Applied Social Psychology 9 (1988) 197ndash212

Mullainathan Sendhil lsquolsquoThinking through Categoriesrsquorsquo mimeo HarvardUniversity 2002

Ortoleva Pietro and Erik Snowberg lsquolsquoOverconfidence in Political BehaviorrsquorsquoAmerican Economic Review 105 (2015) 504ndash535

Phelps Edmund lsquolsquoThe Statistical Theory of Racism and Sexismrsquorsquo AmericanEconomic Review 62 (1972) 659ndash661

Pope Devin and Justin Sydnor lsquolsquoGeographic Variation in the Gender Differencesin Test Scoresrsquorsquo Journal of Economic Perspectives 24 (2010) 95ndash108

Rabin Matthew lsquolsquoInference by Believers in the Law of Small NumbersrsquorsquoQuarterly Journal of Economics 117 (2002) 775ndash816

Rabin Matthew and Joel Schrag lsquolsquoFirst Impressions Matter A Model ofConfirmatory Biasrsquorsquo Quarterly Journal of Economics 114 (1999) 37ndash82

Rabin Matthew and Dimitri Vayanos lsquolsquoThe Gamblerrsquos and Hot-Hand FallaciesTheory and Applicationsrsquorsquo Review of Economic Studies 77 (2010) 730ndash778

Reuben Ernesto Paola Sapienza and Luigi Zingales lsquolsquoHow Stereotypes ImpairWomenrsquos Careers in Sciencersquorsquo Proceedings of the National Academy ofSciences 111 (2014) 4403ndash4408

Rosch Eleanor lsquolsquoNatural Categoriesrsquorsquo Cognitive Psychology 4 (1973) 328ndash350Ryan Carey S lsquolsquoAccuracy of Black and White College Studentsrsquo In-Group and

Out-Group Stereotypesrsquorsquo Personality and Social Psychology Bulletin 22(1996) 1114ndash1127

Schneider David The Psychology of Stereotyping (New York Guilford Press2004)

Schneider David Albert Hastorf and Phoebe Ellsworth Person Perception(Reading MA Addison-Wesley 1979)

Shih Margaret Todd Pittinsky and Nalini Ambady lsquolsquoStereotype SusceptibilityIdentity Salience and Shifts in Quantitative Performancersquorsquo PsychologicalScience 10 (1999) 80ndash83

Shih Margaret Todd Pittinsky and Amy Trahan lsquolsquoDomain-Specific Effects ofStereotypes on Performancersquorsquo Self and Identity 5 (2006) 1ndash14

Steele Claude Whistling Vivaldi How Stereotypes Affect Us and What We CanDo (New York Norton 2010)

Tenenbaum Joshua and Thomas Griffiths lsquolsquoThe Rational Basis ofRepresentativenessrsquorsquo 23rd Annual Conference of the Cognitive ScienceSociety (2001) 1036ndash1041

Tversky Amos and Daniel Kahneman lsquolsquoExtensional versus Intuitive ReasoningThe Conjunction Fallacy in Probability Judgmentrsquorsquo Psychological Review 90(1983) 293ndash315

Weinberger Catherin lsquolsquoIs the Science and Engineering Workforce Drawn fromthe Far Upper Tail of the Math Ability Distributionrsquorsquo mimeo UCSB 2005

Westfall Jacob Leaf Van Boven John Chambers and Charles Judd lsquolsquoPerceivingPolitical Polarization in the United States Party Identity Strength andAttitude Extremity Exacerbate the Perceived Partisan DividersquorsquoPsychological Science 10 (2015) 145ndash158

Wolsko Christopher Bernadette Park Charles Judd and Bernd WittenbrinklsquolsquoFraming Interethnic Ideology Effects of Multicultural and Color-BlindPerspectives on Judgments of Groups and Individualsrsquorsquo Journal ofPersonality and Social Psychology 78 (2000) 635ndash654

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Page 30: I. Introduction · uneducated at the beginning of the 20th century, and as high achievers at the beginning of the 21st (Madon et al. 2001). Social science has produced three broad

the reference group) The second and third tests address the keypredictions of our model

1 The Data We have two data sets on political preferences andbeliefs about political preferences The first data set from GrahamNosek and Haidt (GNH 2012) contains data from the MoralFoundations Questionnaire Respondents (1174 self-identified lib-erals and 500 self-identified conservatives) answer questions abouttheir position on a subset of 45 issues 20 moral relevance state-ments (eg lsquolsquowhen you decide whether something is right orwrong to what extent are the following considerations relevantto your thinkingrsquorsquo) and 25 moral judgments (eg lsquolsquoindicate theextent to which you would agree or disagreersquorsquo) For each issue arandomly determined subset of participants states their own posi-tion another subset states their belief on the position of a lsquolsquotypicalliberalrsquorsquo and a third subset states their belief on the position of alsquolsquotypical conservativersquorsquo The data thus include the distribution overpositions for both liberal and conservatives as well as the averagebelieved typical position of liberals and of conservatives on the 45issues Each position is elicited on 1ndash6 scale

The second data set comes from the American NationalElection Survey (ANES) and contains data from more than20000 respondents between 1964 and 201228 The surveycovers political issues of the day such as the optimal amount ofgovernment spending and service provision (1984ndash2000) or theplace of women in society (1972ndash1998) We focus on the 10 issuesthat ask participants to respond on a 1ndash7 scale (rather than justindicate binary agreement or disagreement) all 10 issues areasked in multiple years Participants are asked to provide theirown position on the scale and their believed position of theDemocratic and Republican parties (lsquolsquoWhere would you placethe Democratic [Republican] party on this scalersquorsquo) The data in-clude for each issue-year observation the distribution of partic-ipant positions for self-identified liberals and self-identifiedconservatives as well as the distribution of believed typical posi-tions of the Democratic and Republican parties

28 These data are publicly available at httpwwwelectionstudiesorgstudy-pagesanes_timeseries_cdfanes_timeseries_cdfhtm

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2 Empirical Strategy Our analysis focuses on beliefs abouttwo groups Conservatives and Liberals The types are the possi-ble positions for each issue (1 2 6 7) For the GNH data weinterpret beliefs about the lsquolsquotypicalrsquorsquo element of a group to coincidewith the believed average position in that group Similarly forthe ANES data we use the believed party positions as a proxy forbelieved mean of each group29 We then take as a benchmark thehypothesis that individuals hold accurate beliefs about eachgroup and in particular that believed mean position shouldequal true mean position at least on average across subjectsThe accurate beliefs hypothesis underlies the most common eco-nomic model of stereotyping statistical discrimination

To assess our representativeness-based model we perform aregression exercise To test our model in a linear regressionframework we rely on linear approximations of the weightingfunction Our model then yields two regression specifications

PROPOSITION 4 Let G 2 fconservative liberal g and assume

ht h tG

tG

be a differentiable and strictly increasing weight-

ing function as in Definition 2 The following hold as a first-order approximation around identical distributions G

Gfrac14 1

(i) Kernel of truth regression There exists a constant gt 0such that

EstethtjGTHORN frac14 EethtjGTHORNeth1thorn THORN EethtjGTHORNeth5THORN

(ii) Representativeness regression Denote H frac14 fT 2 Tg

the right tail of types and RconsH frac14

PHtconsPHtlib

as the average

representativeness of right tail types for conservatives

29 This assumption is consistent with the authorsrsquo interpretation of the GNHdata (GNH 2012) and with previous studies using ANES (eg Westfall et al 2015)Furthermore to the extent that this assumption holds equally well for most issueswithin a data set our focus on cross-issue differences should allow us to test thepredictions of our model even with an imperfect proxy for beliefs of mean positionsFinally the data provide some insight into whether subjects are reporting (per-ceived) modal or mean types As we show the modal type is a poor prediction ofstated beliefs while a distorted mean slanted toward representative types is anaccurate prediction of stated beliefs

STEREOTYPES 1783

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Under the further approximation where tcons

tlibampRcons

H for

t 2 H

EstethtjconsTHORN frac14 EethtjconsTHORN thorn consethR

consH 1THORNeth6THORN

EstethtjlibTHORN frac14 EethtjlibTHORN libethR

consH 1THORNeth7THORN

where lcons and llib are positive constants

The first regression allows us to test for the kernel of truthhypothesis and the second set of regressions allows us to test forthe role of representativeness

Equation (5) says that respondents in our model inflate theaverage position of a group say the conservatives if and only ifthe group has a higher average position than the other groupnamely the liberals Formally EstethtjconsTHORN gt EethtjconsTHORN if and onlyif EethtjconsTHORN gt EethtjlibTHORN Because in our measurement scale highertypes mean lsquolsquomore conservativersquorsquo we expect (i) believed conserva-tive average to be higher than the truth and (ii) the extent ofoverstatement to decrease in the average liberal position EethtjlibTHORNConversely we expect the average liberal position to be lowerthan the truth the more so the higher the average conservativeposition EethtjconsTHORN

As previously discussed the basis of these predictions is con-text dependence information about the distribution of ndashG is rel-evant for the beliefs about G This context dependence isinconsistent with rational expectations in which only thegrouprsquos own means should affect beliefs We test the hypothesisthat the true mean EethtjGTHORN is a significant predictor of the believedmean E

stethtjGTHORN with a positive sign and the other grouprsquos truemean EethtjGTHORN is a predictor of the believed mean with a negativesign

Equations (6) and (7) say that repondentsrsquo assessment bias isshaped by representativeness When the right tail is more repre-sentative for conservatives (Rcons

H 1 positive and large) partici-pants should inflate the average conservative position more(higher E

stethtjconsTHORN EethtjconsTHORN) and deflate the average liberal po-sition more (lower E

stethtjlibTHORN EethtjlibTHORN) We test the hypothesisthat the inflation in conservative positions is positively associatedwith the representativeness of the right tail for the conservativesand the inflation in liberal positions is negatively associated with

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it Once again the representativeness of the right tail is com-puted using the true distribution of positions

In equations (6) and (7) in many cases the representative tailis also the most likely one As a consequence these tests cannotdistinguish a representativeness-based from a likelihood-basedmodel of distorted beliefs We perform two additional testsFirst we run versions of equations (6) and (7) in which we controlfor the likelihood of tails (see Table A4 in Online Appendix G)Second we compute numerically the predictions of a representa-tiveness-based model of stereotypes and a likelihood-based modelof stereotypes We then assess which of these two is better able tomatch the data on beliefs

3 Empirical Results To begin we illustrate the structure ofthe data and the nature of our predictions with two simple exam-ples from the GNH data set focusing on beliefs about conserva-tives In example 1 participants are asked about their agreementwith the statement lsquolsquoIt can never be right to kill a human beingrsquorsquoIn example 2 participants are asked about the moral relevance oflsquolsquowhether or not someone cared for someone weak or vulnerablersquorsquoAs can be seen in Figure III in example 1 the modal position(strongly disagree (1)) and most representative positions(strongly disagree (1)) coincide for conservatives In contrast inexample 2 in Figure III the most representative types (slightlyrelevant (3) not at all relevant (1)) are not most likely for theconservative group Following Proposition 1 we predict that be-liefs will be distorted in the direction of the most representativetypes Thus we expect more exaggeration in example 2 than inexample 1 since in example 2 the most representative types (inthe left tail) are far from the modal type whereas in example 1they coincide This is what we find the conservative position isexaggerated by only 009 positions in Example 1 (true mean 299believed mean 290) but by 106 positions in Example 2 (truemean 421 believed mean 315)

In the full data sets we treat each (issue year) pair as anobservation and we cluster standard errors at the issue level Forthe GNH data we have 45 observations 45 issues measured inthe same year For the ANES data we have 66 observations 10issues measured in multiple years To begin we simply docu-ment systematic exaggeration in both data sets This is a primaryfocus of the original analysis in GNH (2012) and also in Westfall

STEREOTYPES 1785

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FIGURE III

Two Examples

QUARTERLY JOURNAL OF ECONOMICS1786

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et al (2015)rsquos analysis of the ANES data30 Figure IV shows thatthe believed difference between typical conservative and typicalliberal positions is larger than the true difference in mean posi-tions for 109 of the 111 observations The data for both GNH(squares) and ANES (triangles) lie above the 45-degree line(dashed)31 Average exaggeration is 062 positions on the scale(066 in the GNH data 059 in the ANES data)32

The systematic and significant exaggeration of mean differ-ences suggests that the benchmark model of accurate beliefs ismissing something important Indeed this exaggeration reflectsthe fact that believed means are typically more extreme than truemeans First note that the kernel of truth regression (equation(5)) generates exaggeration of mean differences just as docu-mented in Figure IV

EstethtjGTHORN E

stethtjGTHORN frac14 eth1thorn 2THORN frac12EethtjGTHORN EethtjGTHORN

To bring this prediction to the data we regress the believedmean position for each group EBethtjGTHORN on the true mean of thegroup EethtjGTHORN and the true mean of the comparison groupEethtjGTHORN across issues We do this for each group (liberals con-servatives) in each data set separately We also present pooledspecifications that combine the data sets to make a prediction fora given group (liberals conservatives) In these pooled specifica-tions we include a dummy variable indicating whether theobservation came from the ANES data set For all specificationswe cluster observations at the issue level33 The results from re-gression are shown in Table I In every specification we find thatEethtjGTHORN is a significant predictor of EBethtjGTHORN with the predicted pos-itive sign Crucially for five of the six specifications the mean of

30 Chambers and Melnyk (2006) also find evidence of exaggeration of truedifferences in beliefs about political positions

31 For convenience we recode all issues so that the high end of the scale (67)represents the stereotypically more conservative position

32 A natural question to ask is how beliefs vary across liberals and conserva-tives That is do beliefs about a group G depend on membership in G versus ndashG Ourmodel does not speak to this issue However in Online Appendix G we show thatthe results we document below hold for both beliefs held by conservatives and be-liefs held by liberals see Tables A9 A10 and A11

33 In general the results presented below for the ANES data are not largelyimpacted by the decision to cluster at the issue level Similar results are obtained ifthe data are not clustered

STEREOTYPES 1787

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the comparison group EethtjGTHORN is also a significant predictor ofE

BethtjGTHORN with the predicted negative signAlthough these results provide strong evidence of context

dependence and are consistent with our model they do not pindown a role for representativeness of types Our next test relatesthe magnitude of representativeness of tail types to the magni-tude of belief distortions

To this end we implement the regressions in equations (6)and (7) Following Proposition 4 we compute the average repre-

sentativeness of tail types for conservatives RconsH frac14

PtT2tconsPtT2tlib

We

again test the hypothesis that RconsH is a significant predictor of Est

ethtjconsTHORN with a positive sign and a predictor of EstethtjlibTHORN with a

negative sign Table II shows that conditional on true mean RconsH

predicts believed mean for each group G as expected The firstthree specifications display the results for predicting beliefs heldabout conservatives In both data sets the average representa-tiveness of tail types for conservatives is a significant positivepredictor of beliefs held about conservatives The final three spe-cifications display the results for predicting beliefs held about

FIGURE IV

Exaggeration of Differences

QUARTERLY JOURNAL OF ECONOMICS1788

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liberals We find that the average representativeness of tail typesfor conservatives is a negative predictor of beliefs held about lib-erals This effect is significant in the GNH data and marginallysignificant in the ANES data

We present several additional results in Online Appendix GTo further examine the role of representativeness in driving be-liefs we first show the results of Table II carry through when we

TABLE II

AVERAGE REPRESENTATIVENESS OF TAIL POSITIONS PREDICTS BELIEFS

OLS Predicting Believed Mean of Group G for Each Issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position

of group G for issue

078 024 051 072 018 041

(006) (008) (009) (005) (005) (010)

Avg rep of tail types for

conservatives RconsH

019 055 025 014 012 024

(007) (022) (008) (006) (007) (005)

Constant 101 260 184 093 271 201

(026) (045) (029) (022) (025) (032)

R2 082 048 060 091 031 070

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

TABLE I

INFORMATION ABOUT ndashG PREDICTS BELIEFS ABOUT G

OLS predicting believed mean of group G for each issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position of

conservatives for issue

102 098 096 021 019 025

(0097) (0133) (0076) (0060) (0116) (0060)

True mean position of

liberals for issue

035 086 058 0987 039 073

(0106) (0134) (0131) (0066) (0106) (0135)

Constant 151 335 235 069 258 156

(0195) (0269) (0279) (0122) (0249) (0270)

R2 083 053 066 092 032 068

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

STEREOTYPES 1789

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control for the average likelihood on the tail positions (see Table A4in Online Appendix G) Most tellingly we use the model to predictbeliefs across issues and compare those to the data For simplicitywe use the rank-based truncation specification to predict mean be-liefs when stereotypes include the d most representative types ford frac14 1 T We compare these predictions to those of a model inwhich beliefs are obtained by restricting the distribution to the dmost likely types Our benchmark for both models is predicting thebelieved mean from the entire distribution where d = T We showthat the predictions of the rank-based truncation model with d = 4or 5 compare favorably to both a likelihood-based truncation model(with any d) and the accurate beliefs benchmark Interestingly thisresult suggests that stereotypical beliefs are well approximated byneglecting the least representative types (as opposed to focusingonly on the most representative types) and so represent a moderatethough systematic departure from the standard benchmarkFinally we show that the results we document above hold forboth beliefs held by conservatives and beliefs held by liberals (seeTables A9 A10 and A11 in Online Appendix G)

V Conclusion

We present a model of stereotypical thinking in which DMsmaking predictions about a group overweight the grouprsquos mostdistinctive types These overweighted types are not the mostlikely ones given the DMrsquos data but the most representativeones in the sense of being the most diagnostic of the group rela-tive to other groups Representativeness implies that what ismost distinctive of a group depends on what group it is comparedwith We present experimental evidence that confirms this con-text dependence in recall-based assessments of groups Finallywe evaluated the predictions of the model using political data fromexisting large-scale surveys We find context dependence to be akey feature of beliefs Given the richness of the political data wecan go a step further and identify a role for representativeness inparticular As the representativeness of tail types increases beliefsof a group are distorted in the direction of that tail

Our approach provides a parsimonious and psychologicallyfounded account of how DMs generate simplified representationsof reality from social groups to stock returns and offers a unifiedaccount of disparate pieces of evidence relating to this type of

QUARTERLY JOURNAL OF ECONOMICS1790

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uncertainty The model captures the central fact that stereotypeshighlight the greatest difference between groups thus explainingwhy some stereotypes are very accurate while others lack valid-ity Still stereotypes often have a kernel of truth when they arebased on systematicmdasheven if smallmdashdifferences between groupsThis logic allows us to describe a number of heuristics and psy-chological biases many of which arise in the context of predictionproblems Generically our model generates overreaction to diag-nostic information

Our model is based on representativeness and does not cap-ture all the features of stereotypical thinking However it cap-tures perhaps the central feature when we think of a group wefocus on what is most distinctive about it and neglect or under-weight the rest

Saeuroıd Business School University of Oxford

Ohio State University and Harvard Business School

Universita Bocconi and Innocenzo Gasparini Institute

for Economic Research

Harvard University

Supplementary Material

An Online Appendix for this article can be found at QJEonline (qjeoxfordjournalorg)

References

Adorno Theodor Else Frenkel-Brunswik Daniel Levinson and Nevitt SanfordThe Authoritarian Personality (New York Harper amp Row 1950)

Arrow Kenneth lsquolsquoThe Theory of Discriminationrsquorsquo in Discrimination in LaborMarkets Orley Ashenfelter and Albert Rees eds (Princeton NJPrinceton University Press 1973)

Ashton Michael and Victoria Esses lsquolsquoStereotype Accuracy Estimating theAcademic Performance of Ethnic Groupsrsquorsquo Personality and SocialPsychology Bulletin 25 (1999) 225ndash236

Barberis Nicholas Andrei Shleifer and Robert Vishny lsquolsquoA Model of InvestorSentimentrsquorsquo Journal of Financial Economics 49 (1998) 307ndash343

Bayer Sylvia lsquolsquoThe Accuracy of Academic Gender Stereotypesrsquorsquo Sex Roles 40(1999) 787ndash813

Benjamin Dan James Choi and Joshua Strickland lsquolsquoSocial Identity andPreferencesrsquorsquo American Economic Review 100 (2010) 1913ndash1928

Benjamin Dan Matthew Rabin and Collin Raymond lsquolsquoA Model of Non-Belief inthe Law of Large Numbersrsquorsquo Journal of the European Economic Association15 (2015) 515ndash544

Bertrand Marianne lsquolsquoNew Perspectives on Genderrsquorsquo Handbook of LaborEconomics 4 (2011) 1543ndash1590

Bodoh-Creed Aaron Dan Benjamin and Matthew Rabin lsquolsquoThe Dynamics of Base-Rate Neglectrsquorsquo mimeo Haas Business School 2013

STEREOTYPES 1791

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Bohnet Iris Alexandra van Geen and Max Bazerman lsquolsquoWhen PerformanceTrumps Gender Bias Joint versus Separate Evaluationrsquorsquo ManagementScience 5 (2016) 1225ndash1234

Bordalo Pedro Nicola Gennaioli and Andrei Shleifer lsquolsquoSalience Theory of Choiceunder Riskrsquorsquo Quarterly Journal of Economics 127 (2012) 1243ndash1285

mdashmdashmdash lsquolsquoSalience and Consumer Choicersquorsquo Journal of Political Economy 121(2013) 803ndash843

Briton Nancy and Judith Hall lsquolsquoBeliefs about Female and Male NonverbalCommunicationrsquorsquo Sex Roles 32 (1995) 79ndash90

Buser Thomas Muriel Niederle and Hessel Oosterbeek lsquolsquoGenderCompetitiveness and Career Choicesrsquorsquo Quarterly Journal of Economics 129(2014) 1409ndash1447

Carrell Scott Marianne Page and James West lsquolsquoSex and Science How ProfessorGender Perpetuates the Gender Gaprsquorsquo Quarterly Journal of Economics 125(2010) 1101ndash1144

Chambers John and Darya Melnyk lsquolsquoWhy Do I Hate Thee ConflictMisperceptions and Intergroup Mistrustrsquorsquo Personality and SocialPsychology Bulletin 32 (2006) 1295ndash1311

Chan Wayne Robert R McCrae Filip De Fruyt Lee Jussim CorinnaE Lockenhoff Marleen De Bolle Paul T Costa Jr Angelina R SutinAnu Realo Juri Allik Katsuharu Nakazato Yoshiko ShimonakaMartina Hrebıckova Sylvie Graf Michelle Yik Marina Brunner-SciarraNora Leibovich De Figueora Vanina Schmidt Chang-kyo Ahn Hyun-nie Ahn Maria E Aguilar-Vafaie Jerzy Siuta Barbara SzmigielskaThomas R Cain Janet T Crawford Khairul Anwar Mastor Jean-Pierre Rolland Florence Nansubuga Daniel R MiramontezVeronica Benet-Martınez Jerome Rossier Denis Bratko Iris MarusicJamin Halberstadt Mami Yamaguchi Goran Knezevic Thomas A MartinMirona Gheorghiu Peter B Smith Claudio Barbaranelli Lei WangJane Shakespeare-Finch Margarida P Lima Waldemar KlinkoszAndrzej Sekowski Lidia Alcalay Franco Simonetti Tatyana V AvdeyevaV S Pramila and Antonio Terracciano lsquolsquoStereotypes of Age Differences inPersonality Traits Universal and Accuratersquorsquo Journal of Personality andSocial Psychology 103 (2012) 1050ndash1066

Chen Yan Sherry Xin Liu Tracy Xiao and Margaret Shih lsquolsquoWhich Hat to WearImpact of Natural Identities on Coordination and Cooperationrsquorsquo Games andEconomic Behavior 84 (2014) 58ndash86

Coffman Katherine lsquolsquoEvidence on Self-Stereotyping and the Contribution ofIdeasrsquorsquo Quarterly Journal of Economics 129 (2014) 1625ndash1660

Cunningham Tom lsquolsquoComparisons and Choicersquorsquo mimeo Stockholm University2013

Diekman Amanda Alice Eagly and Patrick Kulesa lsquolsquoAccuracy and Bias in theStereotypes about the Social and Political Attitudes of Women and MenrsquorsquoJournal of Experimental Social Psychology 38 (2002) 268ndash282

Eccles Jacquelynne S Janis E Jacobs and Rena D Harold lsquolsquoGender RoleStereotypes Expectancy Effects and Parentsrsquo Socialization of GenderDifferencesrsquorsquo Journal of Social Issues 46 (1990) 183ndash201

Fryer Roland and Matthew Jackson lsquolsquoA Categorical Model of Cognition andBiased Decision-Makingrsquorsquo BE Journal of Theoretical Economics 8 (2008)1ndash42

Fryer Roland and Steven Levitt lsquolsquoAn Empirical Analysis of the Gender Gap inMathematicsrsquorsquo American Economic Journal Applied Economics 2 (2010)210ndash240

Gennaioli Nicola and Andrei Shleifer lsquolsquoWhat Comes to Mindrsquorsquo Quarterly Journalof Economics 125 (2010) 1399ndash1433

Gennaioli Nicola Andrei Shleifer and Robert Vishny lsquolsquoNeglected RisksFinancial Innovation and Financial Fragilityrsquorsquo Journal of FinancialEconomics 104 (2012) 452ndash468

Gilens Martin lsquolsquoRace and Poverty in America Public Misperceptions and theAmerican News Mediarsquorsquo Public Opinion Quarterly 60 (1996) 515ndash541

Glaeser Edward lsquolsquoThe Political Economy of Hatredrsquorsquo Quarterly Journal ofEconomics 120 (2005) 45ndash86

QUARTERLY JOURNAL OF ECONOMICS1792

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ibrary on October 28 2016

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Glover Dyland Amanda Pallais and William Pariente lsquolsquoDiscrimination as a Self-Fulfilling Prophecy Evidence from French Grocery Storesrsquorsquo mimeo HarvardUniversity 2015

Goldin Claudia Lawrence Katz and Ilyana Kuziemko lsquolsquoThe Homecoming ofAmerican College Women The Reversal of the College Gender GaprsquorsquoJournal of Economic Perspectives 20 (2006) 133ndash156

Graham Jesse Brian Nosek and Jonathan Haidt lsquolsquoThe Moral Stereotypes ofLiberals and Conservatives Exaggeration of Differences across thePolitical Spectrumrsquorsquo PLoS One 7 (2012) 1ndash13

Grether David lsquolsquoBayes Rule as a Descriptive Model The RepresentativenessHeuristicrsquorsquo Quarterly Journal of Economics 95 (1980) 537ndash557

Griffin Dale and Amos Tversky lsquolsquoThe Weighing of Evidence and theDeterminants of Confidencersquorsquo Cognitive Psychology 24 (1992) 411ndash435

Guiso Luigi Ferdinando Monte Paola Sapienza and Luigi Zingales lsquolsquoCultureGender and Mathrsquorsquo Science 320 (2008) 1164ndash1165

Hilton James and William Von Hippel lsquolsquoStereotypesrsquorsquo Annual Review ofPsychology 47 (1996) 237ndash271

Hyde Janet Sara Lindberg Marcia Linn Amy Ellis and Caroline WilliamslsquolsquoGender Similarities Characterize Math Performancersquorsquo Science 321 (2008)494ndash495

Judd Charles and Bernardette Park lsquolsquoDefinition and Assessment of Accuracy inSocial Stereotypesrsquorsquo Psychological Review 100 (1993) 109ndash128

Jussim Lee Jarret Crawford Stephanie Anglin John Chambers Sean Stevensand Florette Cohen lsquolsquoStereotype Accuracy One of the Largest and MostReplicable Effects in All of Social Psychologyrsquorsquo in The Handbook ofPrejudice Stereotyping and Discrimination Todd Nelson ed (MahwahNJ Lawrence Erlbaum 2015)

Kahneman Daniel and Amos Tversky lsquolsquoSubjective Probability A Judgment ofRepresentativenessrsquorsquo Cognitive Psychology 3 (1972) 430ndash454

mdashmdashmdash lsquolsquoOn the Psychology of Predictionrsquorsquo Psychological Review 80 (1973) 237ndash251

Kaplowitz Stan Bradley Fisher and Clifford Broman lsquolsquoHow Accurate ArePerceptions of Social Statistics about Blacks and Whitesrsquorsquo Public OpinionQuarterly 67 (2003) 237ndash243

Kersten Daniel Pascal Mamassian and Alan Yuille lsquolsquoObject Perception asBayesian Inferencersquorsquo Annual Review of Psychology 55 (2004) 271ndash304

Klein Richard Kate A Ratliff Michelangelo Vianello Reginald B Adams JrStepan Bahnik Michael J Bernstein Konrad Bocian Mark J BrandtBeach Brooks Claudia Chloe Brumbaugh Zeynep CemalcilarJesse Chandler Winnee Cheong William E Davis Thierry DevosMatthew Eisner Natalia Frankowska David Furrow Elisa Maria GallianiFred Hasselman Joshua A Hicks James F Hovermale S Jane HuntJeffrey R Huntsinger Hans IJzerman Melissa-Sue John Jennifer A Joy-Gaba Heather Barry Kappes Lacy E Krueger Jaime Kurtz CarmelA Levitan Robyn Mallett Wendy L Morris Anthony J Nelson JasonA Nier Grant Packard Ronaldo Pilati Abraham M RutchickKathleen Schmidt Jeanine L Skorinko Robert Smith Troy G SteinerJustin Storbeck Lyn M Van Swol Donna Thompson Anna van rsquot VeerLeigh Ann Vaughn Marek Vranka Aaron Wichman Julie A Woodzickaand Brian A Nosek lsquolsquoInvestigating Variation in Replicability A ManyLabs Replication Projectrsquorsquo Social Psychology 45 (2014) 142ndash152

Lundberg Shelly and Richard Startz lsquolsquoPrivate Discrimination and SocialIntervention in Competitive Labor Marketsrsquorsquo American Economic Review73 (1983) 340ndash347

Madon Stephanie Max Guyll Kathy Aboufadel Eulices Montiel Alison SmithPolly Palumbo and Lee Jussim lsquolsquoEthnic and National Stereotypes ThePrinceton Trilogy Revisited and Revisedrsquorsquo Personality and SocialPsychological Bulletin 27 (2001) 996ndash1010

Martin Carol lsquolsquoA Ratio Measure of Sex Stereotypingrsquorsquo Journal of Personality andSocial Psychology 52 (1987) 489ndash499

STEREOTYPES 1793

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ibrary on October 28 2016

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McCauley Clark Krishna Thangavelu and Paul Rozin lsquolsquoSex Stereotyping ofOccupations in Relation to Television Representations and Census FactsrsquorsquoBasic and Applied Social Psychology 9 (1988) 197ndash212

Mullainathan Sendhil lsquolsquoThinking through Categoriesrsquorsquo mimeo HarvardUniversity 2002

Ortoleva Pietro and Erik Snowberg lsquolsquoOverconfidence in Political BehaviorrsquorsquoAmerican Economic Review 105 (2015) 504ndash535

Phelps Edmund lsquolsquoThe Statistical Theory of Racism and Sexismrsquorsquo AmericanEconomic Review 62 (1972) 659ndash661

Pope Devin and Justin Sydnor lsquolsquoGeographic Variation in the Gender Differencesin Test Scoresrsquorsquo Journal of Economic Perspectives 24 (2010) 95ndash108

Rabin Matthew lsquolsquoInference by Believers in the Law of Small NumbersrsquorsquoQuarterly Journal of Economics 117 (2002) 775ndash816

Rabin Matthew and Joel Schrag lsquolsquoFirst Impressions Matter A Model ofConfirmatory Biasrsquorsquo Quarterly Journal of Economics 114 (1999) 37ndash82

Rabin Matthew and Dimitri Vayanos lsquolsquoThe Gamblerrsquos and Hot-Hand FallaciesTheory and Applicationsrsquorsquo Review of Economic Studies 77 (2010) 730ndash778

Reuben Ernesto Paola Sapienza and Luigi Zingales lsquolsquoHow Stereotypes ImpairWomenrsquos Careers in Sciencersquorsquo Proceedings of the National Academy ofSciences 111 (2014) 4403ndash4408

Rosch Eleanor lsquolsquoNatural Categoriesrsquorsquo Cognitive Psychology 4 (1973) 328ndash350Ryan Carey S lsquolsquoAccuracy of Black and White College Studentsrsquo In-Group and

Out-Group Stereotypesrsquorsquo Personality and Social Psychology Bulletin 22(1996) 1114ndash1127

Schneider David The Psychology of Stereotyping (New York Guilford Press2004)

Schneider David Albert Hastorf and Phoebe Ellsworth Person Perception(Reading MA Addison-Wesley 1979)

Shih Margaret Todd Pittinsky and Nalini Ambady lsquolsquoStereotype SusceptibilityIdentity Salience and Shifts in Quantitative Performancersquorsquo PsychologicalScience 10 (1999) 80ndash83

Shih Margaret Todd Pittinsky and Amy Trahan lsquolsquoDomain-Specific Effects ofStereotypes on Performancersquorsquo Self and Identity 5 (2006) 1ndash14

Steele Claude Whistling Vivaldi How Stereotypes Affect Us and What We CanDo (New York Norton 2010)

Tenenbaum Joshua and Thomas Griffiths lsquolsquoThe Rational Basis ofRepresentativenessrsquorsquo 23rd Annual Conference of the Cognitive ScienceSociety (2001) 1036ndash1041

Tversky Amos and Daniel Kahneman lsquolsquoExtensional versus Intuitive ReasoningThe Conjunction Fallacy in Probability Judgmentrsquorsquo Psychological Review 90(1983) 293ndash315

Weinberger Catherin lsquolsquoIs the Science and Engineering Workforce Drawn fromthe Far Upper Tail of the Math Ability Distributionrsquorsquo mimeo UCSB 2005

Westfall Jacob Leaf Van Boven John Chambers and Charles Judd lsquolsquoPerceivingPolitical Polarization in the United States Party Identity Strength andAttitude Extremity Exacerbate the Perceived Partisan DividersquorsquoPsychological Science 10 (2015) 145ndash158

Wolsko Christopher Bernadette Park Charles Judd and Bernd WittenbrinklsquolsquoFraming Interethnic Ideology Effects of Multicultural and Color-BlindPerspectives on Judgments of Groups and Individualsrsquorsquo Journal ofPersonality and Social Psychology 78 (2000) 635ndash654

QUARTERLY JOURNAL OF ECONOMICS1794

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Page 31: I. Introduction · uneducated at the beginning of the 20th century, and as high achievers at the beginning of the 21st (Madon et al. 2001). Social science has produced three broad

2 Empirical Strategy Our analysis focuses on beliefs abouttwo groups Conservatives and Liberals The types are the possi-ble positions for each issue (1 2 6 7) For the GNH data weinterpret beliefs about the lsquolsquotypicalrsquorsquo element of a group to coincidewith the believed average position in that group Similarly forthe ANES data we use the believed party positions as a proxy forbelieved mean of each group29 We then take as a benchmark thehypothesis that individuals hold accurate beliefs about eachgroup and in particular that believed mean position shouldequal true mean position at least on average across subjectsThe accurate beliefs hypothesis underlies the most common eco-nomic model of stereotyping statistical discrimination

To assess our representativeness-based model we perform aregression exercise To test our model in a linear regressionframework we rely on linear approximations of the weightingfunction Our model then yields two regression specifications

PROPOSITION 4 Let G 2 fconservative liberal g and assume

ht h tG

tG

be a differentiable and strictly increasing weight-

ing function as in Definition 2 The following hold as a first-order approximation around identical distributions G

Gfrac14 1

(i) Kernel of truth regression There exists a constant gt 0such that

EstethtjGTHORN frac14 EethtjGTHORNeth1thorn THORN EethtjGTHORNeth5THORN

(ii) Representativeness regression Denote H frac14 fT 2 Tg

the right tail of types and RconsH frac14

PHtconsPHtlib

as the average

representativeness of right tail types for conservatives

29 This assumption is consistent with the authorsrsquo interpretation of the GNHdata (GNH 2012) and with previous studies using ANES (eg Westfall et al 2015)Furthermore to the extent that this assumption holds equally well for most issueswithin a data set our focus on cross-issue differences should allow us to test thepredictions of our model even with an imperfect proxy for beliefs of mean positionsFinally the data provide some insight into whether subjects are reporting (per-ceived) modal or mean types As we show the modal type is a poor prediction ofstated beliefs while a distorted mean slanted toward representative types is anaccurate prediction of stated beliefs

STEREOTYPES 1783

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Under the further approximation where tcons

tlibampRcons

H for

t 2 H

EstethtjconsTHORN frac14 EethtjconsTHORN thorn consethR

consH 1THORNeth6THORN

EstethtjlibTHORN frac14 EethtjlibTHORN libethR

consH 1THORNeth7THORN

where lcons and llib are positive constants

The first regression allows us to test for the kernel of truthhypothesis and the second set of regressions allows us to test forthe role of representativeness

Equation (5) says that respondents in our model inflate theaverage position of a group say the conservatives if and only ifthe group has a higher average position than the other groupnamely the liberals Formally EstethtjconsTHORN gt EethtjconsTHORN if and onlyif EethtjconsTHORN gt EethtjlibTHORN Because in our measurement scale highertypes mean lsquolsquomore conservativersquorsquo we expect (i) believed conserva-tive average to be higher than the truth and (ii) the extent ofoverstatement to decrease in the average liberal position EethtjlibTHORNConversely we expect the average liberal position to be lowerthan the truth the more so the higher the average conservativeposition EethtjconsTHORN

As previously discussed the basis of these predictions is con-text dependence information about the distribution of ndashG is rel-evant for the beliefs about G This context dependence isinconsistent with rational expectations in which only thegrouprsquos own means should affect beliefs We test the hypothesisthat the true mean EethtjGTHORN is a significant predictor of the believedmean E

stethtjGTHORN with a positive sign and the other grouprsquos truemean EethtjGTHORN is a predictor of the believed mean with a negativesign

Equations (6) and (7) say that repondentsrsquo assessment bias isshaped by representativeness When the right tail is more repre-sentative for conservatives (Rcons

H 1 positive and large) partici-pants should inflate the average conservative position more(higher E

stethtjconsTHORN EethtjconsTHORN) and deflate the average liberal po-sition more (lower E

stethtjlibTHORN EethtjlibTHORN) We test the hypothesisthat the inflation in conservative positions is positively associatedwith the representativeness of the right tail for the conservativesand the inflation in liberal positions is negatively associated with

QUARTERLY JOURNAL OF ECONOMICS1784

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it Once again the representativeness of the right tail is com-puted using the true distribution of positions

In equations (6) and (7) in many cases the representative tailis also the most likely one As a consequence these tests cannotdistinguish a representativeness-based from a likelihood-basedmodel of distorted beliefs We perform two additional testsFirst we run versions of equations (6) and (7) in which we controlfor the likelihood of tails (see Table A4 in Online Appendix G)Second we compute numerically the predictions of a representa-tiveness-based model of stereotypes and a likelihood-based modelof stereotypes We then assess which of these two is better able tomatch the data on beliefs

3 Empirical Results To begin we illustrate the structure ofthe data and the nature of our predictions with two simple exam-ples from the GNH data set focusing on beliefs about conserva-tives In example 1 participants are asked about their agreementwith the statement lsquolsquoIt can never be right to kill a human beingrsquorsquoIn example 2 participants are asked about the moral relevance oflsquolsquowhether or not someone cared for someone weak or vulnerablersquorsquoAs can be seen in Figure III in example 1 the modal position(strongly disagree (1)) and most representative positions(strongly disagree (1)) coincide for conservatives In contrast inexample 2 in Figure III the most representative types (slightlyrelevant (3) not at all relevant (1)) are not most likely for theconservative group Following Proposition 1 we predict that be-liefs will be distorted in the direction of the most representativetypes Thus we expect more exaggeration in example 2 than inexample 1 since in example 2 the most representative types (inthe left tail) are far from the modal type whereas in example 1they coincide This is what we find the conservative position isexaggerated by only 009 positions in Example 1 (true mean 299believed mean 290) but by 106 positions in Example 2 (truemean 421 believed mean 315)

In the full data sets we treat each (issue year) pair as anobservation and we cluster standard errors at the issue level Forthe GNH data we have 45 observations 45 issues measured inthe same year For the ANES data we have 66 observations 10issues measured in multiple years To begin we simply docu-ment systematic exaggeration in both data sets This is a primaryfocus of the original analysis in GNH (2012) and also in Westfall

STEREOTYPES 1785

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FIGURE III

Two Examples

QUARTERLY JOURNAL OF ECONOMICS1786

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et al (2015)rsquos analysis of the ANES data30 Figure IV shows thatthe believed difference between typical conservative and typicalliberal positions is larger than the true difference in mean posi-tions for 109 of the 111 observations The data for both GNH(squares) and ANES (triangles) lie above the 45-degree line(dashed)31 Average exaggeration is 062 positions on the scale(066 in the GNH data 059 in the ANES data)32

The systematic and significant exaggeration of mean differ-ences suggests that the benchmark model of accurate beliefs ismissing something important Indeed this exaggeration reflectsthe fact that believed means are typically more extreme than truemeans First note that the kernel of truth regression (equation(5)) generates exaggeration of mean differences just as docu-mented in Figure IV

EstethtjGTHORN E

stethtjGTHORN frac14 eth1thorn 2THORN frac12EethtjGTHORN EethtjGTHORN

To bring this prediction to the data we regress the believedmean position for each group EBethtjGTHORN on the true mean of thegroup EethtjGTHORN and the true mean of the comparison groupEethtjGTHORN across issues We do this for each group (liberals con-servatives) in each data set separately We also present pooledspecifications that combine the data sets to make a prediction fora given group (liberals conservatives) In these pooled specifica-tions we include a dummy variable indicating whether theobservation came from the ANES data set For all specificationswe cluster observations at the issue level33 The results from re-gression are shown in Table I In every specification we find thatEethtjGTHORN is a significant predictor of EBethtjGTHORN with the predicted pos-itive sign Crucially for five of the six specifications the mean of

30 Chambers and Melnyk (2006) also find evidence of exaggeration of truedifferences in beliefs about political positions

31 For convenience we recode all issues so that the high end of the scale (67)represents the stereotypically more conservative position

32 A natural question to ask is how beliefs vary across liberals and conserva-tives That is do beliefs about a group G depend on membership in G versus ndashG Ourmodel does not speak to this issue However in Online Appendix G we show thatthe results we document below hold for both beliefs held by conservatives and be-liefs held by liberals see Tables A9 A10 and A11

33 In general the results presented below for the ANES data are not largelyimpacted by the decision to cluster at the issue level Similar results are obtained ifthe data are not clustered

STEREOTYPES 1787

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the comparison group EethtjGTHORN is also a significant predictor ofE

BethtjGTHORN with the predicted negative signAlthough these results provide strong evidence of context

dependence and are consistent with our model they do not pindown a role for representativeness of types Our next test relatesthe magnitude of representativeness of tail types to the magni-tude of belief distortions

To this end we implement the regressions in equations (6)and (7) Following Proposition 4 we compute the average repre-

sentativeness of tail types for conservatives RconsH frac14

PtT2tconsPtT2tlib

We

again test the hypothesis that RconsH is a significant predictor of Est

ethtjconsTHORN with a positive sign and a predictor of EstethtjlibTHORN with a

negative sign Table II shows that conditional on true mean RconsH

predicts believed mean for each group G as expected The firstthree specifications display the results for predicting beliefs heldabout conservatives In both data sets the average representa-tiveness of tail types for conservatives is a significant positivepredictor of beliefs held about conservatives The final three spe-cifications display the results for predicting beliefs held about

FIGURE IV

Exaggeration of Differences

QUARTERLY JOURNAL OF ECONOMICS1788

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liberals We find that the average representativeness of tail typesfor conservatives is a negative predictor of beliefs held about lib-erals This effect is significant in the GNH data and marginallysignificant in the ANES data

We present several additional results in Online Appendix GTo further examine the role of representativeness in driving be-liefs we first show the results of Table II carry through when we

TABLE II

AVERAGE REPRESENTATIVENESS OF TAIL POSITIONS PREDICTS BELIEFS

OLS Predicting Believed Mean of Group G for Each Issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position

of group G for issue

078 024 051 072 018 041

(006) (008) (009) (005) (005) (010)

Avg rep of tail types for

conservatives RconsH

019 055 025 014 012 024

(007) (022) (008) (006) (007) (005)

Constant 101 260 184 093 271 201

(026) (045) (029) (022) (025) (032)

R2 082 048 060 091 031 070

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

TABLE I

INFORMATION ABOUT ndashG PREDICTS BELIEFS ABOUT G

OLS predicting believed mean of group G for each issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position of

conservatives for issue

102 098 096 021 019 025

(0097) (0133) (0076) (0060) (0116) (0060)

True mean position of

liberals for issue

035 086 058 0987 039 073

(0106) (0134) (0131) (0066) (0106) (0135)

Constant 151 335 235 069 258 156

(0195) (0269) (0279) (0122) (0249) (0270)

R2 083 053 066 092 032 068

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

STEREOTYPES 1789

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control for the average likelihood on the tail positions (see Table A4in Online Appendix G) Most tellingly we use the model to predictbeliefs across issues and compare those to the data For simplicitywe use the rank-based truncation specification to predict mean be-liefs when stereotypes include the d most representative types ford frac14 1 T We compare these predictions to those of a model inwhich beliefs are obtained by restricting the distribution to the dmost likely types Our benchmark for both models is predicting thebelieved mean from the entire distribution where d = T We showthat the predictions of the rank-based truncation model with d = 4or 5 compare favorably to both a likelihood-based truncation model(with any d) and the accurate beliefs benchmark Interestingly thisresult suggests that stereotypical beliefs are well approximated byneglecting the least representative types (as opposed to focusingonly on the most representative types) and so represent a moderatethough systematic departure from the standard benchmarkFinally we show that the results we document above hold forboth beliefs held by conservatives and beliefs held by liberals (seeTables A9 A10 and A11 in Online Appendix G)

V Conclusion

We present a model of stereotypical thinking in which DMsmaking predictions about a group overweight the grouprsquos mostdistinctive types These overweighted types are not the mostlikely ones given the DMrsquos data but the most representativeones in the sense of being the most diagnostic of the group rela-tive to other groups Representativeness implies that what ismost distinctive of a group depends on what group it is comparedwith We present experimental evidence that confirms this con-text dependence in recall-based assessments of groups Finallywe evaluated the predictions of the model using political data fromexisting large-scale surveys We find context dependence to be akey feature of beliefs Given the richness of the political data wecan go a step further and identify a role for representativeness inparticular As the representativeness of tail types increases beliefsof a group are distorted in the direction of that tail

Our approach provides a parsimonious and psychologicallyfounded account of how DMs generate simplified representationsof reality from social groups to stock returns and offers a unifiedaccount of disparate pieces of evidence relating to this type of

QUARTERLY JOURNAL OF ECONOMICS1790

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uncertainty The model captures the central fact that stereotypeshighlight the greatest difference between groups thus explainingwhy some stereotypes are very accurate while others lack valid-ity Still stereotypes often have a kernel of truth when they arebased on systematicmdasheven if smallmdashdifferences between groupsThis logic allows us to describe a number of heuristics and psy-chological biases many of which arise in the context of predictionproblems Generically our model generates overreaction to diag-nostic information

Our model is based on representativeness and does not cap-ture all the features of stereotypical thinking However it cap-tures perhaps the central feature when we think of a group wefocus on what is most distinctive about it and neglect or under-weight the rest

Saeuroıd Business School University of Oxford

Ohio State University and Harvard Business School

Universita Bocconi and Innocenzo Gasparini Institute

for Economic Research

Harvard University

Supplementary Material

An Online Appendix for this article can be found at QJEonline (qjeoxfordjournalorg)

References

Adorno Theodor Else Frenkel-Brunswik Daniel Levinson and Nevitt SanfordThe Authoritarian Personality (New York Harper amp Row 1950)

Arrow Kenneth lsquolsquoThe Theory of Discriminationrsquorsquo in Discrimination in LaborMarkets Orley Ashenfelter and Albert Rees eds (Princeton NJPrinceton University Press 1973)

Ashton Michael and Victoria Esses lsquolsquoStereotype Accuracy Estimating theAcademic Performance of Ethnic Groupsrsquorsquo Personality and SocialPsychology Bulletin 25 (1999) 225ndash236

Barberis Nicholas Andrei Shleifer and Robert Vishny lsquolsquoA Model of InvestorSentimentrsquorsquo Journal of Financial Economics 49 (1998) 307ndash343

Bayer Sylvia lsquolsquoThe Accuracy of Academic Gender Stereotypesrsquorsquo Sex Roles 40(1999) 787ndash813

Benjamin Dan James Choi and Joshua Strickland lsquolsquoSocial Identity andPreferencesrsquorsquo American Economic Review 100 (2010) 1913ndash1928

Benjamin Dan Matthew Rabin and Collin Raymond lsquolsquoA Model of Non-Belief inthe Law of Large Numbersrsquorsquo Journal of the European Economic Association15 (2015) 515ndash544

Bertrand Marianne lsquolsquoNew Perspectives on Genderrsquorsquo Handbook of LaborEconomics 4 (2011) 1543ndash1590

Bodoh-Creed Aaron Dan Benjamin and Matthew Rabin lsquolsquoThe Dynamics of Base-Rate Neglectrsquorsquo mimeo Haas Business School 2013

STEREOTYPES 1791

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ibrary on October 28 2016

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Bohnet Iris Alexandra van Geen and Max Bazerman lsquolsquoWhen PerformanceTrumps Gender Bias Joint versus Separate Evaluationrsquorsquo ManagementScience 5 (2016) 1225ndash1234

Bordalo Pedro Nicola Gennaioli and Andrei Shleifer lsquolsquoSalience Theory of Choiceunder Riskrsquorsquo Quarterly Journal of Economics 127 (2012) 1243ndash1285

mdashmdashmdash lsquolsquoSalience and Consumer Choicersquorsquo Journal of Political Economy 121(2013) 803ndash843

Briton Nancy and Judith Hall lsquolsquoBeliefs about Female and Male NonverbalCommunicationrsquorsquo Sex Roles 32 (1995) 79ndash90

Buser Thomas Muriel Niederle and Hessel Oosterbeek lsquolsquoGenderCompetitiveness and Career Choicesrsquorsquo Quarterly Journal of Economics 129(2014) 1409ndash1447

Carrell Scott Marianne Page and James West lsquolsquoSex and Science How ProfessorGender Perpetuates the Gender Gaprsquorsquo Quarterly Journal of Economics 125(2010) 1101ndash1144

Chambers John and Darya Melnyk lsquolsquoWhy Do I Hate Thee ConflictMisperceptions and Intergroup Mistrustrsquorsquo Personality and SocialPsychology Bulletin 32 (2006) 1295ndash1311

Chan Wayne Robert R McCrae Filip De Fruyt Lee Jussim CorinnaE Lockenhoff Marleen De Bolle Paul T Costa Jr Angelina R SutinAnu Realo Juri Allik Katsuharu Nakazato Yoshiko ShimonakaMartina Hrebıckova Sylvie Graf Michelle Yik Marina Brunner-SciarraNora Leibovich De Figueora Vanina Schmidt Chang-kyo Ahn Hyun-nie Ahn Maria E Aguilar-Vafaie Jerzy Siuta Barbara SzmigielskaThomas R Cain Janet T Crawford Khairul Anwar Mastor Jean-Pierre Rolland Florence Nansubuga Daniel R MiramontezVeronica Benet-Martınez Jerome Rossier Denis Bratko Iris MarusicJamin Halberstadt Mami Yamaguchi Goran Knezevic Thomas A MartinMirona Gheorghiu Peter B Smith Claudio Barbaranelli Lei WangJane Shakespeare-Finch Margarida P Lima Waldemar KlinkoszAndrzej Sekowski Lidia Alcalay Franco Simonetti Tatyana V AvdeyevaV S Pramila and Antonio Terracciano lsquolsquoStereotypes of Age Differences inPersonality Traits Universal and Accuratersquorsquo Journal of Personality andSocial Psychology 103 (2012) 1050ndash1066

Chen Yan Sherry Xin Liu Tracy Xiao and Margaret Shih lsquolsquoWhich Hat to WearImpact of Natural Identities on Coordination and Cooperationrsquorsquo Games andEconomic Behavior 84 (2014) 58ndash86

Coffman Katherine lsquolsquoEvidence on Self-Stereotyping and the Contribution ofIdeasrsquorsquo Quarterly Journal of Economics 129 (2014) 1625ndash1660

Cunningham Tom lsquolsquoComparisons and Choicersquorsquo mimeo Stockholm University2013

Diekman Amanda Alice Eagly and Patrick Kulesa lsquolsquoAccuracy and Bias in theStereotypes about the Social and Political Attitudes of Women and MenrsquorsquoJournal of Experimental Social Psychology 38 (2002) 268ndash282

Eccles Jacquelynne S Janis E Jacobs and Rena D Harold lsquolsquoGender RoleStereotypes Expectancy Effects and Parentsrsquo Socialization of GenderDifferencesrsquorsquo Journal of Social Issues 46 (1990) 183ndash201

Fryer Roland and Matthew Jackson lsquolsquoA Categorical Model of Cognition andBiased Decision-Makingrsquorsquo BE Journal of Theoretical Economics 8 (2008)1ndash42

Fryer Roland and Steven Levitt lsquolsquoAn Empirical Analysis of the Gender Gap inMathematicsrsquorsquo American Economic Journal Applied Economics 2 (2010)210ndash240

Gennaioli Nicola and Andrei Shleifer lsquolsquoWhat Comes to Mindrsquorsquo Quarterly Journalof Economics 125 (2010) 1399ndash1433

Gennaioli Nicola Andrei Shleifer and Robert Vishny lsquolsquoNeglected RisksFinancial Innovation and Financial Fragilityrsquorsquo Journal of FinancialEconomics 104 (2012) 452ndash468

Gilens Martin lsquolsquoRace and Poverty in America Public Misperceptions and theAmerican News Mediarsquorsquo Public Opinion Quarterly 60 (1996) 515ndash541

Glaeser Edward lsquolsquoThe Political Economy of Hatredrsquorsquo Quarterly Journal ofEconomics 120 (2005) 45ndash86

QUARTERLY JOURNAL OF ECONOMICS1792

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ibrary on October 28 2016

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Glover Dyland Amanda Pallais and William Pariente lsquolsquoDiscrimination as a Self-Fulfilling Prophecy Evidence from French Grocery Storesrsquorsquo mimeo HarvardUniversity 2015

Goldin Claudia Lawrence Katz and Ilyana Kuziemko lsquolsquoThe Homecoming ofAmerican College Women The Reversal of the College Gender GaprsquorsquoJournal of Economic Perspectives 20 (2006) 133ndash156

Graham Jesse Brian Nosek and Jonathan Haidt lsquolsquoThe Moral Stereotypes ofLiberals and Conservatives Exaggeration of Differences across thePolitical Spectrumrsquorsquo PLoS One 7 (2012) 1ndash13

Grether David lsquolsquoBayes Rule as a Descriptive Model The RepresentativenessHeuristicrsquorsquo Quarterly Journal of Economics 95 (1980) 537ndash557

Griffin Dale and Amos Tversky lsquolsquoThe Weighing of Evidence and theDeterminants of Confidencersquorsquo Cognitive Psychology 24 (1992) 411ndash435

Guiso Luigi Ferdinando Monte Paola Sapienza and Luigi Zingales lsquolsquoCultureGender and Mathrsquorsquo Science 320 (2008) 1164ndash1165

Hilton James and William Von Hippel lsquolsquoStereotypesrsquorsquo Annual Review ofPsychology 47 (1996) 237ndash271

Hyde Janet Sara Lindberg Marcia Linn Amy Ellis and Caroline WilliamslsquolsquoGender Similarities Characterize Math Performancersquorsquo Science 321 (2008)494ndash495

Judd Charles and Bernardette Park lsquolsquoDefinition and Assessment of Accuracy inSocial Stereotypesrsquorsquo Psychological Review 100 (1993) 109ndash128

Jussim Lee Jarret Crawford Stephanie Anglin John Chambers Sean Stevensand Florette Cohen lsquolsquoStereotype Accuracy One of the Largest and MostReplicable Effects in All of Social Psychologyrsquorsquo in The Handbook ofPrejudice Stereotyping and Discrimination Todd Nelson ed (MahwahNJ Lawrence Erlbaum 2015)

Kahneman Daniel and Amos Tversky lsquolsquoSubjective Probability A Judgment ofRepresentativenessrsquorsquo Cognitive Psychology 3 (1972) 430ndash454

mdashmdashmdash lsquolsquoOn the Psychology of Predictionrsquorsquo Psychological Review 80 (1973) 237ndash251

Kaplowitz Stan Bradley Fisher and Clifford Broman lsquolsquoHow Accurate ArePerceptions of Social Statistics about Blacks and Whitesrsquorsquo Public OpinionQuarterly 67 (2003) 237ndash243

Kersten Daniel Pascal Mamassian and Alan Yuille lsquolsquoObject Perception asBayesian Inferencersquorsquo Annual Review of Psychology 55 (2004) 271ndash304

Klein Richard Kate A Ratliff Michelangelo Vianello Reginald B Adams JrStepan Bahnik Michael J Bernstein Konrad Bocian Mark J BrandtBeach Brooks Claudia Chloe Brumbaugh Zeynep CemalcilarJesse Chandler Winnee Cheong William E Davis Thierry DevosMatthew Eisner Natalia Frankowska David Furrow Elisa Maria GallianiFred Hasselman Joshua A Hicks James F Hovermale S Jane HuntJeffrey R Huntsinger Hans IJzerman Melissa-Sue John Jennifer A Joy-Gaba Heather Barry Kappes Lacy E Krueger Jaime Kurtz CarmelA Levitan Robyn Mallett Wendy L Morris Anthony J Nelson JasonA Nier Grant Packard Ronaldo Pilati Abraham M RutchickKathleen Schmidt Jeanine L Skorinko Robert Smith Troy G SteinerJustin Storbeck Lyn M Van Swol Donna Thompson Anna van rsquot VeerLeigh Ann Vaughn Marek Vranka Aaron Wichman Julie A Woodzickaand Brian A Nosek lsquolsquoInvestigating Variation in Replicability A ManyLabs Replication Projectrsquorsquo Social Psychology 45 (2014) 142ndash152

Lundberg Shelly and Richard Startz lsquolsquoPrivate Discrimination and SocialIntervention in Competitive Labor Marketsrsquorsquo American Economic Review73 (1983) 340ndash347

Madon Stephanie Max Guyll Kathy Aboufadel Eulices Montiel Alison SmithPolly Palumbo and Lee Jussim lsquolsquoEthnic and National Stereotypes ThePrinceton Trilogy Revisited and Revisedrsquorsquo Personality and SocialPsychological Bulletin 27 (2001) 996ndash1010

Martin Carol lsquolsquoA Ratio Measure of Sex Stereotypingrsquorsquo Journal of Personality andSocial Psychology 52 (1987) 489ndash499

STEREOTYPES 1793

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ibrary on October 28 2016

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McCauley Clark Krishna Thangavelu and Paul Rozin lsquolsquoSex Stereotyping ofOccupations in Relation to Television Representations and Census FactsrsquorsquoBasic and Applied Social Psychology 9 (1988) 197ndash212

Mullainathan Sendhil lsquolsquoThinking through Categoriesrsquorsquo mimeo HarvardUniversity 2002

Ortoleva Pietro and Erik Snowberg lsquolsquoOverconfidence in Political BehaviorrsquorsquoAmerican Economic Review 105 (2015) 504ndash535

Phelps Edmund lsquolsquoThe Statistical Theory of Racism and Sexismrsquorsquo AmericanEconomic Review 62 (1972) 659ndash661

Pope Devin and Justin Sydnor lsquolsquoGeographic Variation in the Gender Differencesin Test Scoresrsquorsquo Journal of Economic Perspectives 24 (2010) 95ndash108

Rabin Matthew lsquolsquoInference by Believers in the Law of Small NumbersrsquorsquoQuarterly Journal of Economics 117 (2002) 775ndash816

Rabin Matthew and Joel Schrag lsquolsquoFirst Impressions Matter A Model ofConfirmatory Biasrsquorsquo Quarterly Journal of Economics 114 (1999) 37ndash82

Rabin Matthew and Dimitri Vayanos lsquolsquoThe Gamblerrsquos and Hot-Hand FallaciesTheory and Applicationsrsquorsquo Review of Economic Studies 77 (2010) 730ndash778

Reuben Ernesto Paola Sapienza and Luigi Zingales lsquolsquoHow Stereotypes ImpairWomenrsquos Careers in Sciencersquorsquo Proceedings of the National Academy ofSciences 111 (2014) 4403ndash4408

Rosch Eleanor lsquolsquoNatural Categoriesrsquorsquo Cognitive Psychology 4 (1973) 328ndash350Ryan Carey S lsquolsquoAccuracy of Black and White College Studentsrsquo In-Group and

Out-Group Stereotypesrsquorsquo Personality and Social Psychology Bulletin 22(1996) 1114ndash1127

Schneider David The Psychology of Stereotyping (New York Guilford Press2004)

Schneider David Albert Hastorf and Phoebe Ellsworth Person Perception(Reading MA Addison-Wesley 1979)

Shih Margaret Todd Pittinsky and Nalini Ambady lsquolsquoStereotype SusceptibilityIdentity Salience and Shifts in Quantitative Performancersquorsquo PsychologicalScience 10 (1999) 80ndash83

Shih Margaret Todd Pittinsky and Amy Trahan lsquolsquoDomain-Specific Effects ofStereotypes on Performancersquorsquo Self and Identity 5 (2006) 1ndash14

Steele Claude Whistling Vivaldi How Stereotypes Affect Us and What We CanDo (New York Norton 2010)

Tenenbaum Joshua and Thomas Griffiths lsquolsquoThe Rational Basis ofRepresentativenessrsquorsquo 23rd Annual Conference of the Cognitive ScienceSociety (2001) 1036ndash1041

Tversky Amos and Daniel Kahneman lsquolsquoExtensional versus Intuitive ReasoningThe Conjunction Fallacy in Probability Judgmentrsquorsquo Psychological Review 90(1983) 293ndash315

Weinberger Catherin lsquolsquoIs the Science and Engineering Workforce Drawn fromthe Far Upper Tail of the Math Ability Distributionrsquorsquo mimeo UCSB 2005

Westfall Jacob Leaf Van Boven John Chambers and Charles Judd lsquolsquoPerceivingPolitical Polarization in the United States Party Identity Strength andAttitude Extremity Exacerbate the Perceived Partisan DividersquorsquoPsychological Science 10 (2015) 145ndash158

Wolsko Christopher Bernadette Park Charles Judd and Bernd WittenbrinklsquolsquoFraming Interethnic Ideology Effects of Multicultural and Color-BlindPerspectives on Judgments of Groups and Individualsrsquorsquo Journal ofPersonality and Social Psychology 78 (2000) 635ndash654

QUARTERLY JOURNAL OF ECONOMICS1794

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Page 32: I. Introduction · uneducated at the beginning of the 20th century, and as high achievers at the beginning of the 21st (Madon et al. 2001). Social science has produced three broad

Under the further approximation where tcons

tlibampRcons

H for

t 2 H

EstethtjconsTHORN frac14 EethtjconsTHORN thorn consethR

consH 1THORNeth6THORN

EstethtjlibTHORN frac14 EethtjlibTHORN libethR

consH 1THORNeth7THORN

where lcons and llib are positive constants

The first regression allows us to test for the kernel of truthhypothesis and the second set of regressions allows us to test forthe role of representativeness

Equation (5) says that respondents in our model inflate theaverage position of a group say the conservatives if and only ifthe group has a higher average position than the other groupnamely the liberals Formally EstethtjconsTHORN gt EethtjconsTHORN if and onlyif EethtjconsTHORN gt EethtjlibTHORN Because in our measurement scale highertypes mean lsquolsquomore conservativersquorsquo we expect (i) believed conserva-tive average to be higher than the truth and (ii) the extent ofoverstatement to decrease in the average liberal position EethtjlibTHORNConversely we expect the average liberal position to be lowerthan the truth the more so the higher the average conservativeposition EethtjconsTHORN

As previously discussed the basis of these predictions is con-text dependence information about the distribution of ndashG is rel-evant for the beliefs about G This context dependence isinconsistent with rational expectations in which only thegrouprsquos own means should affect beliefs We test the hypothesisthat the true mean EethtjGTHORN is a significant predictor of the believedmean E

stethtjGTHORN with a positive sign and the other grouprsquos truemean EethtjGTHORN is a predictor of the believed mean with a negativesign

Equations (6) and (7) say that repondentsrsquo assessment bias isshaped by representativeness When the right tail is more repre-sentative for conservatives (Rcons

H 1 positive and large) partici-pants should inflate the average conservative position more(higher E

stethtjconsTHORN EethtjconsTHORN) and deflate the average liberal po-sition more (lower E

stethtjlibTHORN EethtjlibTHORN) We test the hypothesisthat the inflation in conservative positions is positively associatedwith the representativeness of the right tail for the conservativesand the inflation in liberal positions is negatively associated with

QUARTERLY JOURNAL OF ECONOMICS1784

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it Once again the representativeness of the right tail is com-puted using the true distribution of positions

In equations (6) and (7) in many cases the representative tailis also the most likely one As a consequence these tests cannotdistinguish a representativeness-based from a likelihood-basedmodel of distorted beliefs We perform two additional testsFirst we run versions of equations (6) and (7) in which we controlfor the likelihood of tails (see Table A4 in Online Appendix G)Second we compute numerically the predictions of a representa-tiveness-based model of stereotypes and a likelihood-based modelof stereotypes We then assess which of these two is better able tomatch the data on beliefs

3 Empirical Results To begin we illustrate the structure ofthe data and the nature of our predictions with two simple exam-ples from the GNH data set focusing on beliefs about conserva-tives In example 1 participants are asked about their agreementwith the statement lsquolsquoIt can never be right to kill a human beingrsquorsquoIn example 2 participants are asked about the moral relevance oflsquolsquowhether or not someone cared for someone weak or vulnerablersquorsquoAs can be seen in Figure III in example 1 the modal position(strongly disagree (1)) and most representative positions(strongly disagree (1)) coincide for conservatives In contrast inexample 2 in Figure III the most representative types (slightlyrelevant (3) not at all relevant (1)) are not most likely for theconservative group Following Proposition 1 we predict that be-liefs will be distorted in the direction of the most representativetypes Thus we expect more exaggeration in example 2 than inexample 1 since in example 2 the most representative types (inthe left tail) are far from the modal type whereas in example 1they coincide This is what we find the conservative position isexaggerated by only 009 positions in Example 1 (true mean 299believed mean 290) but by 106 positions in Example 2 (truemean 421 believed mean 315)

In the full data sets we treat each (issue year) pair as anobservation and we cluster standard errors at the issue level Forthe GNH data we have 45 observations 45 issues measured inthe same year For the ANES data we have 66 observations 10issues measured in multiple years To begin we simply docu-ment systematic exaggeration in both data sets This is a primaryfocus of the original analysis in GNH (2012) and also in Westfall

STEREOTYPES 1785

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FIGURE III

Two Examples

QUARTERLY JOURNAL OF ECONOMICS1786

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et al (2015)rsquos analysis of the ANES data30 Figure IV shows thatthe believed difference between typical conservative and typicalliberal positions is larger than the true difference in mean posi-tions for 109 of the 111 observations The data for both GNH(squares) and ANES (triangles) lie above the 45-degree line(dashed)31 Average exaggeration is 062 positions on the scale(066 in the GNH data 059 in the ANES data)32

The systematic and significant exaggeration of mean differ-ences suggests that the benchmark model of accurate beliefs ismissing something important Indeed this exaggeration reflectsthe fact that believed means are typically more extreme than truemeans First note that the kernel of truth regression (equation(5)) generates exaggeration of mean differences just as docu-mented in Figure IV

EstethtjGTHORN E

stethtjGTHORN frac14 eth1thorn 2THORN frac12EethtjGTHORN EethtjGTHORN

To bring this prediction to the data we regress the believedmean position for each group EBethtjGTHORN on the true mean of thegroup EethtjGTHORN and the true mean of the comparison groupEethtjGTHORN across issues We do this for each group (liberals con-servatives) in each data set separately We also present pooledspecifications that combine the data sets to make a prediction fora given group (liberals conservatives) In these pooled specifica-tions we include a dummy variable indicating whether theobservation came from the ANES data set For all specificationswe cluster observations at the issue level33 The results from re-gression are shown in Table I In every specification we find thatEethtjGTHORN is a significant predictor of EBethtjGTHORN with the predicted pos-itive sign Crucially for five of the six specifications the mean of

30 Chambers and Melnyk (2006) also find evidence of exaggeration of truedifferences in beliefs about political positions

31 For convenience we recode all issues so that the high end of the scale (67)represents the stereotypically more conservative position

32 A natural question to ask is how beliefs vary across liberals and conserva-tives That is do beliefs about a group G depend on membership in G versus ndashG Ourmodel does not speak to this issue However in Online Appendix G we show thatthe results we document below hold for both beliefs held by conservatives and be-liefs held by liberals see Tables A9 A10 and A11

33 In general the results presented below for the ANES data are not largelyimpacted by the decision to cluster at the issue level Similar results are obtained ifthe data are not clustered

STEREOTYPES 1787

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the comparison group EethtjGTHORN is also a significant predictor ofE

BethtjGTHORN with the predicted negative signAlthough these results provide strong evidence of context

dependence and are consistent with our model they do not pindown a role for representativeness of types Our next test relatesthe magnitude of representativeness of tail types to the magni-tude of belief distortions

To this end we implement the regressions in equations (6)and (7) Following Proposition 4 we compute the average repre-

sentativeness of tail types for conservatives RconsH frac14

PtT2tconsPtT2tlib

We

again test the hypothesis that RconsH is a significant predictor of Est

ethtjconsTHORN with a positive sign and a predictor of EstethtjlibTHORN with a

negative sign Table II shows that conditional on true mean RconsH

predicts believed mean for each group G as expected The firstthree specifications display the results for predicting beliefs heldabout conservatives In both data sets the average representa-tiveness of tail types for conservatives is a significant positivepredictor of beliefs held about conservatives The final three spe-cifications display the results for predicting beliefs held about

FIGURE IV

Exaggeration of Differences

QUARTERLY JOURNAL OF ECONOMICS1788

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liberals We find that the average representativeness of tail typesfor conservatives is a negative predictor of beliefs held about lib-erals This effect is significant in the GNH data and marginallysignificant in the ANES data

We present several additional results in Online Appendix GTo further examine the role of representativeness in driving be-liefs we first show the results of Table II carry through when we

TABLE II

AVERAGE REPRESENTATIVENESS OF TAIL POSITIONS PREDICTS BELIEFS

OLS Predicting Believed Mean of Group G for Each Issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position

of group G for issue

078 024 051 072 018 041

(006) (008) (009) (005) (005) (010)

Avg rep of tail types for

conservatives RconsH

019 055 025 014 012 024

(007) (022) (008) (006) (007) (005)

Constant 101 260 184 093 271 201

(026) (045) (029) (022) (025) (032)

R2 082 048 060 091 031 070

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

TABLE I

INFORMATION ABOUT ndashG PREDICTS BELIEFS ABOUT G

OLS predicting believed mean of group G for each issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position of

conservatives for issue

102 098 096 021 019 025

(0097) (0133) (0076) (0060) (0116) (0060)

True mean position of

liberals for issue

035 086 058 0987 039 073

(0106) (0134) (0131) (0066) (0106) (0135)

Constant 151 335 235 069 258 156

(0195) (0269) (0279) (0122) (0249) (0270)

R2 083 053 066 092 032 068

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

STEREOTYPES 1789

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control for the average likelihood on the tail positions (see Table A4in Online Appendix G) Most tellingly we use the model to predictbeliefs across issues and compare those to the data For simplicitywe use the rank-based truncation specification to predict mean be-liefs when stereotypes include the d most representative types ford frac14 1 T We compare these predictions to those of a model inwhich beliefs are obtained by restricting the distribution to the dmost likely types Our benchmark for both models is predicting thebelieved mean from the entire distribution where d = T We showthat the predictions of the rank-based truncation model with d = 4or 5 compare favorably to both a likelihood-based truncation model(with any d) and the accurate beliefs benchmark Interestingly thisresult suggests that stereotypical beliefs are well approximated byneglecting the least representative types (as opposed to focusingonly on the most representative types) and so represent a moderatethough systematic departure from the standard benchmarkFinally we show that the results we document above hold forboth beliefs held by conservatives and beliefs held by liberals (seeTables A9 A10 and A11 in Online Appendix G)

V Conclusion

We present a model of stereotypical thinking in which DMsmaking predictions about a group overweight the grouprsquos mostdistinctive types These overweighted types are not the mostlikely ones given the DMrsquos data but the most representativeones in the sense of being the most diagnostic of the group rela-tive to other groups Representativeness implies that what ismost distinctive of a group depends on what group it is comparedwith We present experimental evidence that confirms this con-text dependence in recall-based assessments of groups Finallywe evaluated the predictions of the model using political data fromexisting large-scale surveys We find context dependence to be akey feature of beliefs Given the richness of the political data wecan go a step further and identify a role for representativeness inparticular As the representativeness of tail types increases beliefsof a group are distorted in the direction of that tail

Our approach provides a parsimonious and psychologicallyfounded account of how DMs generate simplified representationsof reality from social groups to stock returns and offers a unifiedaccount of disparate pieces of evidence relating to this type of

QUARTERLY JOURNAL OF ECONOMICS1790

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uncertainty The model captures the central fact that stereotypeshighlight the greatest difference between groups thus explainingwhy some stereotypes are very accurate while others lack valid-ity Still stereotypes often have a kernel of truth when they arebased on systematicmdasheven if smallmdashdifferences between groupsThis logic allows us to describe a number of heuristics and psy-chological biases many of which arise in the context of predictionproblems Generically our model generates overreaction to diag-nostic information

Our model is based on representativeness and does not cap-ture all the features of stereotypical thinking However it cap-tures perhaps the central feature when we think of a group wefocus on what is most distinctive about it and neglect or under-weight the rest

Saeuroıd Business School University of Oxford

Ohio State University and Harvard Business School

Universita Bocconi and Innocenzo Gasparini Institute

for Economic Research

Harvard University

Supplementary Material

An Online Appendix for this article can be found at QJEonline (qjeoxfordjournalorg)

References

Adorno Theodor Else Frenkel-Brunswik Daniel Levinson and Nevitt SanfordThe Authoritarian Personality (New York Harper amp Row 1950)

Arrow Kenneth lsquolsquoThe Theory of Discriminationrsquorsquo in Discrimination in LaborMarkets Orley Ashenfelter and Albert Rees eds (Princeton NJPrinceton University Press 1973)

Ashton Michael and Victoria Esses lsquolsquoStereotype Accuracy Estimating theAcademic Performance of Ethnic Groupsrsquorsquo Personality and SocialPsychology Bulletin 25 (1999) 225ndash236

Barberis Nicholas Andrei Shleifer and Robert Vishny lsquolsquoA Model of InvestorSentimentrsquorsquo Journal of Financial Economics 49 (1998) 307ndash343

Bayer Sylvia lsquolsquoThe Accuracy of Academic Gender Stereotypesrsquorsquo Sex Roles 40(1999) 787ndash813

Benjamin Dan James Choi and Joshua Strickland lsquolsquoSocial Identity andPreferencesrsquorsquo American Economic Review 100 (2010) 1913ndash1928

Benjamin Dan Matthew Rabin and Collin Raymond lsquolsquoA Model of Non-Belief inthe Law of Large Numbersrsquorsquo Journal of the European Economic Association15 (2015) 515ndash544

Bertrand Marianne lsquolsquoNew Perspectives on Genderrsquorsquo Handbook of LaborEconomics 4 (2011) 1543ndash1590

Bodoh-Creed Aaron Dan Benjamin and Matthew Rabin lsquolsquoThe Dynamics of Base-Rate Neglectrsquorsquo mimeo Haas Business School 2013

STEREOTYPES 1791

at Harvard L

ibrary on October 28 2016

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Bohnet Iris Alexandra van Geen and Max Bazerman lsquolsquoWhen PerformanceTrumps Gender Bias Joint versus Separate Evaluationrsquorsquo ManagementScience 5 (2016) 1225ndash1234

Bordalo Pedro Nicola Gennaioli and Andrei Shleifer lsquolsquoSalience Theory of Choiceunder Riskrsquorsquo Quarterly Journal of Economics 127 (2012) 1243ndash1285

mdashmdashmdash lsquolsquoSalience and Consumer Choicersquorsquo Journal of Political Economy 121(2013) 803ndash843

Briton Nancy and Judith Hall lsquolsquoBeliefs about Female and Male NonverbalCommunicationrsquorsquo Sex Roles 32 (1995) 79ndash90

Buser Thomas Muriel Niederle and Hessel Oosterbeek lsquolsquoGenderCompetitiveness and Career Choicesrsquorsquo Quarterly Journal of Economics 129(2014) 1409ndash1447

Carrell Scott Marianne Page and James West lsquolsquoSex and Science How ProfessorGender Perpetuates the Gender Gaprsquorsquo Quarterly Journal of Economics 125(2010) 1101ndash1144

Chambers John and Darya Melnyk lsquolsquoWhy Do I Hate Thee ConflictMisperceptions and Intergroup Mistrustrsquorsquo Personality and SocialPsychology Bulletin 32 (2006) 1295ndash1311

Chan Wayne Robert R McCrae Filip De Fruyt Lee Jussim CorinnaE Lockenhoff Marleen De Bolle Paul T Costa Jr Angelina R SutinAnu Realo Juri Allik Katsuharu Nakazato Yoshiko ShimonakaMartina Hrebıckova Sylvie Graf Michelle Yik Marina Brunner-SciarraNora Leibovich De Figueora Vanina Schmidt Chang-kyo Ahn Hyun-nie Ahn Maria E Aguilar-Vafaie Jerzy Siuta Barbara SzmigielskaThomas R Cain Janet T Crawford Khairul Anwar Mastor Jean-Pierre Rolland Florence Nansubuga Daniel R MiramontezVeronica Benet-Martınez Jerome Rossier Denis Bratko Iris MarusicJamin Halberstadt Mami Yamaguchi Goran Knezevic Thomas A MartinMirona Gheorghiu Peter B Smith Claudio Barbaranelli Lei WangJane Shakespeare-Finch Margarida P Lima Waldemar KlinkoszAndrzej Sekowski Lidia Alcalay Franco Simonetti Tatyana V AvdeyevaV S Pramila and Antonio Terracciano lsquolsquoStereotypes of Age Differences inPersonality Traits Universal and Accuratersquorsquo Journal of Personality andSocial Psychology 103 (2012) 1050ndash1066

Chen Yan Sherry Xin Liu Tracy Xiao and Margaret Shih lsquolsquoWhich Hat to WearImpact of Natural Identities on Coordination and Cooperationrsquorsquo Games andEconomic Behavior 84 (2014) 58ndash86

Coffman Katherine lsquolsquoEvidence on Self-Stereotyping and the Contribution ofIdeasrsquorsquo Quarterly Journal of Economics 129 (2014) 1625ndash1660

Cunningham Tom lsquolsquoComparisons and Choicersquorsquo mimeo Stockholm University2013

Diekman Amanda Alice Eagly and Patrick Kulesa lsquolsquoAccuracy and Bias in theStereotypes about the Social and Political Attitudes of Women and MenrsquorsquoJournal of Experimental Social Psychology 38 (2002) 268ndash282

Eccles Jacquelynne S Janis E Jacobs and Rena D Harold lsquolsquoGender RoleStereotypes Expectancy Effects and Parentsrsquo Socialization of GenderDifferencesrsquorsquo Journal of Social Issues 46 (1990) 183ndash201

Fryer Roland and Matthew Jackson lsquolsquoA Categorical Model of Cognition andBiased Decision-Makingrsquorsquo BE Journal of Theoretical Economics 8 (2008)1ndash42

Fryer Roland and Steven Levitt lsquolsquoAn Empirical Analysis of the Gender Gap inMathematicsrsquorsquo American Economic Journal Applied Economics 2 (2010)210ndash240

Gennaioli Nicola and Andrei Shleifer lsquolsquoWhat Comes to Mindrsquorsquo Quarterly Journalof Economics 125 (2010) 1399ndash1433

Gennaioli Nicola Andrei Shleifer and Robert Vishny lsquolsquoNeglected RisksFinancial Innovation and Financial Fragilityrsquorsquo Journal of FinancialEconomics 104 (2012) 452ndash468

Gilens Martin lsquolsquoRace and Poverty in America Public Misperceptions and theAmerican News Mediarsquorsquo Public Opinion Quarterly 60 (1996) 515ndash541

Glaeser Edward lsquolsquoThe Political Economy of Hatredrsquorsquo Quarterly Journal ofEconomics 120 (2005) 45ndash86

QUARTERLY JOURNAL OF ECONOMICS1792

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

Glover Dyland Amanda Pallais and William Pariente lsquolsquoDiscrimination as a Self-Fulfilling Prophecy Evidence from French Grocery Storesrsquorsquo mimeo HarvardUniversity 2015

Goldin Claudia Lawrence Katz and Ilyana Kuziemko lsquolsquoThe Homecoming ofAmerican College Women The Reversal of the College Gender GaprsquorsquoJournal of Economic Perspectives 20 (2006) 133ndash156

Graham Jesse Brian Nosek and Jonathan Haidt lsquolsquoThe Moral Stereotypes ofLiberals and Conservatives Exaggeration of Differences across thePolitical Spectrumrsquorsquo PLoS One 7 (2012) 1ndash13

Grether David lsquolsquoBayes Rule as a Descriptive Model The RepresentativenessHeuristicrsquorsquo Quarterly Journal of Economics 95 (1980) 537ndash557

Griffin Dale and Amos Tversky lsquolsquoThe Weighing of Evidence and theDeterminants of Confidencersquorsquo Cognitive Psychology 24 (1992) 411ndash435

Guiso Luigi Ferdinando Monte Paola Sapienza and Luigi Zingales lsquolsquoCultureGender and Mathrsquorsquo Science 320 (2008) 1164ndash1165

Hilton James and William Von Hippel lsquolsquoStereotypesrsquorsquo Annual Review ofPsychology 47 (1996) 237ndash271

Hyde Janet Sara Lindberg Marcia Linn Amy Ellis and Caroline WilliamslsquolsquoGender Similarities Characterize Math Performancersquorsquo Science 321 (2008)494ndash495

Judd Charles and Bernardette Park lsquolsquoDefinition and Assessment of Accuracy inSocial Stereotypesrsquorsquo Psychological Review 100 (1993) 109ndash128

Jussim Lee Jarret Crawford Stephanie Anglin John Chambers Sean Stevensand Florette Cohen lsquolsquoStereotype Accuracy One of the Largest and MostReplicable Effects in All of Social Psychologyrsquorsquo in The Handbook ofPrejudice Stereotyping and Discrimination Todd Nelson ed (MahwahNJ Lawrence Erlbaum 2015)

Kahneman Daniel and Amos Tversky lsquolsquoSubjective Probability A Judgment ofRepresentativenessrsquorsquo Cognitive Psychology 3 (1972) 430ndash454

mdashmdashmdash lsquolsquoOn the Psychology of Predictionrsquorsquo Psychological Review 80 (1973) 237ndash251

Kaplowitz Stan Bradley Fisher and Clifford Broman lsquolsquoHow Accurate ArePerceptions of Social Statistics about Blacks and Whitesrsquorsquo Public OpinionQuarterly 67 (2003) 237ndash243

Kersten Daniel Pascal Mamassian and Alan Yuille lsquolsquoObject Perception asBayesian Inferencersquorsquo Annual Review of Psychology 55 (2004) 271ndash304

Klein Richard Kate A Ratliff Michelangelo Vianello Reginald B Adams JrStepan Bahnik Michael J Bernstein Konrad Bocian Mark J BrandtBeach Brooks Claudia Chloe Brumbaugh Zeynep CemalcilarJesse Chandler Winnee Cheong William E Davis Thierry DevosMatthew Eisner Natalia Frankowska David Furrow Elisa Maria GallianiFred Hasselman Joshua A Hicks James F Hovermale S Jane HuntJeffrey R Huntsinger Hans IJzerman Melissa-Sue John Jennifer A Joy-Gaba Heather Barry Kappes Lacy E Krueger Jaime Kurtz CarmelA Levitan Robyn Mallett Wendy L Morris Anthony J Nelson JasonA Nier Grant Packard Ronaldo Pilati Abraham M RutchickKathleen Schmidt Jeanine L Skorinko Robert Smith Troy G SteinerJustin Storbeck Lyn M Van Swol Donna Thompson Anna van rsquot VeerLeigh Ann Vaughn Marek Vranka Aaron Wichman Julie A Woodzickaand Brian A Nosek lsquolsquoInvestigating Variation in Replicability A ManyLabs Replication Projectrsquorsquo Social Psychology 45 (2014) 142ndash152

Lundberg Shelly and Richard Startz lsquolsquoPrivate Discrimination and SocialIntervention in Competitive Labor Marketsrsquorsquo American Economic Review73 (1983) 340ndash347

Madon Stephanie Max Guyll Kathy Aboufadel Eulices Montiel Alison SmithPolly Palumbo and Lee Jussim lsquolsquoEthnic and National Stereotypes ThePrinceton Trilogy Revisited and Revisedrsquorsquo Personality and SocialPsychological Bulletin 27 (2001) 996ndash1010

Martin Carol lsquolsquoA Ratio Measure of Sex Stereotypingrsquorsquo Journal of Personality andSocial Psychology 52 (1987) 489ndash499

STEREOTYPES 1793

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

McCauley Clark Krishna Thangavelu and Paul Rozin lsquolsquoSex Stereotyping ofOccupations in Relation to Television Representations and Census FactsrsquorsquoBasic and Applied Social Psychology 9 (1988) 197ndash212

Mullainathan Sendhil lsquolsquoThinking through Categoriesrsquorsquo mimeo HarvardUniversity 2002

Ortoleva Pietro and Erik Snowberg lsquolsquoOverconfidence in Political BehaviorrsquorsquoAmerican Economic Review 105 (2015) 504ndash535

Phelps Edmund lsquolsquoThe Statistical Theory of Racism and Sexismrsquorsquo AmericanEconomic Review 62 (1972) 659ndash661

Pope Devin and Justin Sydnor lsquolsquoGeographic Variation in the Gender Differencesin Test Scoresrsquorsquo Journal of Economic Perspectives 24 (2010) 95ndash108

Rabin Matthew lsquolsquoInference by Believers in the Law of Small NumbersrsquorsquoQuarterly Journal of Economics 117 (2002) 775ndash816

Rabin Matthew and Joel Schrag lsquolsquoFirst Impressions Matter A Model ofConfirmatory Biasrsquorsquo Quarterly Journal of Economics 114 (1999) 37ndash82

Rabin Matthew and Dimitri Vayanos lsquolsquoThe Gamblerrsquos and Hot-Hand FallaciesTheory and Applicationsrsquorsquo Review of Economic Studies 77 (2010) 730ndash778

Reuben Ernesto Paola Sapienza and Luigi Zingales lsquolsquoHow Stereotypes ImpairWomenrsquos Careers in Sciencersquorsquo Proceedings of the National Academy ofSciences 111 (2014) 4403ndash4408

Rosch Eleanor lsquolsquoNatural Categoriesrsquorsquo Cognitive Psychology 4 (1973) 328ndash350Ryan Carey S lsquolsquoAccuracy of Black and White College Studentsrsquo In-Group and

Out-Group Stereotypesrsquorsquo Personality and Social Psychology Bulletin 22(1996) 1114ndash1127

Schneider David The Psychology of Stereotyping (New York Guilford Press2004)

Schneider David Albert Hastorf and Phoebe Ellsworth Person Perception(Reading MA Addison-Wesley 1979)

Shih Margaret Todd Pittinsky and Nalini Ambady lsquolsquoStereotype SusceptibilityIdentity Salience and Shifts in Quantitative Performancersquorsquo PsychologicalScience 10 (1999) 80ndash83

Shih Margaret Todd Pittinsky and Amy Trahan lsquolsquoDomain-Specific Effects ofStereotypes on Performancersquorsquo Self and Identity 5 (2006) 1ndash14

Steele Claude Whistling Vivaldi How Stereotypes Affect Us and What We CanDo (New York Norton 2010)

Tenenbaum Joshua and Thomas Griffiths lsquolsquoThe Rational Basis ofRepresentativenessrsquorsquo 23rd Annual Conference of the Cognitive ScienceSociety (2001) 1036ndash1041

Tversky Amos and Daniel Kahneman lsquolsquoExtensional versus Intuitive ReasoningThe Conjunction Fallacy in Probability Judgmentrsquorsquo Psychological Review 90(1983) 293ndash315

Weinberger Catherin lsquolsquoIs the Science and Engineering Workforce Drawn fromthe Far Upper Tail of the Math Ability Distributionrsquorsquo mimeo UCSB 2005

Westfall Jacob Leaf Van Boven John Chambers and Charles Judd lsquolsquoPerceivingPolitical Polarization in the United States Party Identity Strength andAttitude Extremity Exacerbate the Perceived Partisan DividersquorsquoPsychological Science 10 (2015) 145ndash158

Wolsko Christopher Bernadette Park Charles Judd and Bernd WittenbrinklsquolsquoFraming Interethnic Ideology Effects of Multicultural and Color-BlindPerspectives on Judgments of Groups and Individualsrsquorsquo Journal ofPersonality and Social Psychology 78 (2000) 635ndash654

QUARTERLY JOURNAL OF ECONOMICS1794

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httpqjeoxfordjournalsorgD

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Page 33: I. Introduction · uneducated at the beginning of the 20th century, and as high achievers at the beginning of the 21st (Madon et al. 2001). Social science has produced three broad

it Once again the representativeness of the right tail is com-puted using the true distribution of positions

In equations (6) and (7) in many cases the representative tailis also the most likely one As a consequence these tests cannotdistinguish a representativeness-based from a likelihood-basedmodel of distorted beliefs We perform two additional testsFirst we run versions of equations (6) and (7) in which we controlfor the likelihood of tails (see Table A4 in Online Appendix G)Second we compute numerically the predictions of a representa-tiveness-based model of stereotypes and a likelihood-based modelof stereotypes We then assess which of these two is better able tomatch the data on beliefs

3 Empirical Results To begin we illustrate the structure ofthe data and the nature of our predictions with two simple exam-ples from the GNH data set focusing on beliefs about conserva-tives In example 1 participants are asked about their agreementwith the statement lsquolsquoIt can never be right to kill a human beingrsquorsquoIn example 2 participants are asked about the moral relevance oflsquolsquowhether or not someone cared for someone weak or vulnerablersquorsquoAs can be seen in Figure III in example 1 the modal position(strongly disagree (1)) and most representative positions(strongly disagree (1)) coincide for conservatives In contrast inexample 2 in Figure III the most representative types (slightlyrelevant (3) not at all relevant (1)) are not most likely for theconservative group Following Proposition 1 we predict that be-liefs will be distorted in the direction of the most representativetypes Thus we expect more exaggeration in example 2 than inexample 1 since in example 2 the most representative types (inthe left tail) are far from the modal type whereas in example 1they coincide This is what we find the conservative position isexaggerated by only 009 positions in Example 1 (true mean 299believed mean 290) but by 106 positions in Example 2 (truemean 421 believed mean 315)

In the full data sets we treat each (issue year) pair as anobservation and we cluster standard errors at the issue level Forthe GNH data we have 45 observations 45 issues measured inthe same year For the ANES data we have 66 observations 10issues measured in multiple years To begin we simply docu-ment systematic exaggeration in both data sets This is a primaryfocus of the original analysis in GNH (2012) and also in Westfall

STEREOTYPES 1785

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FIGURE III

Two Examples

QUARTERLY JOURNAL OF ECONOMICS1786

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et al (2015)rsquos analysis of the ANES data30 Figure IV shows thatthe believed difference between typical conservative and typicalliberal positions is larger than the true difference in mean posi-tions for 109 of the 111 observations The data for both GNH(squares) and ANES (triangles) lie above the 45-degree line(dashed)31 Average exaggeration is 062 positions on the scale(066 in the GNH data 059 in the ANES data)32

The systematic and significant exaggeration of mean differ-ences suggests that the benchmark model of accurate beliefs ismissing something important Indeed this exaggeration reflectsthe fact that believed means are typically more extreme than truemeans First note that the kernel of truth regression (equation(5)) generates exaggeration of mean differences just as docu-mented in Figure IV

EstethtjGTHORN E

stethtjGTHORN frac14 eth1thorn 2THORN frac12EethtjGTHORN EethtjGTHORN

To bring this prediction to the data we regress the believedmean position for each group EBethtjGTHORN on the true mean of thegroup EethtjGTHORN and the true mean of the comparison groupEethtjGTHORN across issues We do this for each group (liberals con-servatives) in each data set separately We also present pooledspecifications that combine the data sets to make a prediction fora given group (liberals conservatives) In these pooled specifica-tions we include a dummy variable indicating whether theobservation came from the ANES data set For all specificationswe cluster observations at the issue level33 The results from re-gression are shown in Table I In every specification we find thatEethtjGTHORN is a significant predictor of EBethtjGTHORN with the predicted pos-itive sign Crucially for five of the six specifications the mean of

30 Chambers and Melnyk (2006) also find evidence of exaggeration of truedifferences in beliefs about political positions

31 For convenience we recode all issues so that the high end of the scale (67)represents the stereotypically more conservative position

32 A natural question to ask is how beliefs vary across liberals and conserva-tives That is do beliefs about a group G depend on membership in G versus ndashG Ourmodel does not speak to this issue However in Online Appendix G we show thatthe results we document below hold for both beliefs held by conservatives and be-liefs held by liberals see Tables A9 A10 and A11

33 In general the results presented below for the ANES data are not largelyimpacted by the decision to cluster at the issue level Similar results are obtained ifthe data are not clustered

STEREOTYPES 1787

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the comparison group EethtjGTHORN is also a significant predictor ofE

BethtjGTHORN with the predicted negative signAlthough these results provide strong evidence of context

dependence and are consistent with our model they do not pindown a role for representativeness of types Our next test relatesthe magnitude of representativeness of tail types to the magni-tude of belief distortions

To this end we implement the regressions in equations (6)and (7) Following Proposition 4 we compute the average repre-

sentativeness of tail types for conservatives RconsH frac14

PtT2tconsPtT2tlib

We

again test the hypothesis that RconsH is a significant predictor of Est

ethtjconsTHORN with a positive sign and a predictor of EstethtjlibTHORN with a

negative sign Table II shows that conditional on true mean RconsH

predicts believed mean for each group G as expected The firstthree specifications display the results for predicting beliefs heldabout conservatives In both data sets the average representa-tiveness of tail types for conservatives is a significant positivepredictor of beliefs held about conservatives The final three spe-cifications display the results for predicting beliefs held about

FIGURE IV

Exaggeration of Differences

QUARTERLY JOURNAL OF ECONOMICS1788

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liberals We find that the average representativeness of tail typesfor conservatives is a negative predictor of beliefs held about lib-erals This effect is significant in the GNH data and marginallysignificant in the ANES data

We present several additional results in Online Appendix GTo further examine the role of representativeness in driving be-liefs we first show the results of Table II carry through when we

TABLE II

AVERAGE REPRESENTATIVENESS OF TAIL POSITIONS PREDICTS BELIEFS

OLS Predicting Believed Mean of Group G for Each Issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position

of group G for issue

078 024 051 072 018 041

(006) (008) (009) (005) (005) (010)

Avg rep of tail types for

conservatives RconsH

019 055 025 014 012 024

(007) (022) (008) (006) (007) (005)

Constant 101 260 184 093 271 201

(026) (045) (029) (022) (025) (032)

R2 082 048 060 091 031 070

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

TABLE I

INFORMATION ABOUT ndashG PREDICTS BELIEFS ABOUT G

OLS predicting believed mean of group G for each issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position of

conservatives for issue

102 098 096 021 019 025

(0097) (0133) (0076) (0060) (0116) (0060)

True mean position of

liberals for issue

035 086 058 0987 039 073

(0106) (0134) (0131) (0066) (0106) (0135)

Constant 151 335 235 069 258 156

(0195) (0269) (0279) (0122) (0249) (0270)

R2 083 053 066 092 032 068

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

STEREOTYPES 1789

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control for the average likelihood on the tail positions (see Table A4in Online Appendix G) Most tellingly we use the model to predictbeliefs across issues and compare those to the data For simplicitywe use the rank-based truncation specification to predict mean be-liefs when stereotypes include the d most representative types ford frac14 1 T We compare these predictions to those of a model inwhich beliefs are obtained by restricting the distribution to the dmost likely types Our benchmark for both models is predicting thebelieved mean from the entire distribution where d = T We showthat the predictions of the rank-based truncation model with d = 4or 5 compare favorably to both a likelihood-based truncation model(with any d) and the accurate beliefs benchmark Interestingly thisresult suggests that stereotypical beliefs are well approximated byneglecting the least representative types (as opposed to focusingonly on the most representative types) and so represent a moderatethough systematic departure from the standard benchmarkFinally we show that the results we document above hold forboth beliefs held by conservatives and beliefs held by liberals (seeTables A9 A10 and A11 in Online Appendix G)

V Conclusion

We present a model of stereotypical thinking in which DMsmaking predictions about a group overweight the grouprsquos mostdistinctive types These overweighted types are not the mostlikely ones given the DMrsquos data but the most representativeones in the sense of being the most diagnostic of the group rela-tive to other groups Representativeness implies that what ismost distinctive of a group depends on what group it is comparedwith We present experimental evidence that confirms this con-text dependence in recall-based assessments of groups Finallywe evaluated the predictions of the model using political data fromexisting large-scale surveys We find context dependence to be akey feature of beliefs Given the richness of the political data wecan go a step further and identify a role for representativeness inparticular As the representativeness of tail types increases beliefsof a group are distorted in the direction of that tail

Our approach provides a parsimonious and psychologicallyfounded account of how DMs generate simplified representationsof reality from social groups to stock returns and offers a unifiedaccount of disparate pieces of evidence relating to this type of

QUARTERLY JOURNAL OF ECONOMICS1790

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uncertainty The model captures the central fact that stereotypeshighlight the greatest difference between groups thus explainingwhy some stereotypes are very accurate while others lack valid-ity Still stereotypes often have a kernel of truth when they arebased on systematicmdasheven if smallmdashdifferences between groupsThis logic allows us to describe a number of heuristics and psy-chological biases many of which arise in the context of predictionproblems Generically our model generates overreaction to diag-nostic information

Our model is based on representativeness and does not cap-ture all the features of stereotypical thinking However it cap-tures perhaps the central feature when we think of a group wefocus on what is most distinctive about it and neglect or under-weight the rest

Saeuroıd Business School University of Oxford

Ohio State University and Harvard Business School

Universita Bocconi and Innocenzo Gasparini Institute

for Economic Research

Harvard University

Supplementary Material

An Online Appendix for this article can be found at QJEonline (qjeoxfordjournalorg)

References

Adorno Theodor Else Frenkel-Brunswik Daniel Levinson and Nevitt SanfordThe Authoritarian Personality (New York Harper amp Row 1950)

Arrow Kenneth lsquolsquoThe Theory of Discriminationrsquorsquo in Discrimination in LaborMarkets Orley Ashenfelter and Albert Rees eds (Princeton NJPrinceton University Press 1973)

Ashton Michael and Victoria Esses lsquolsquoStereotype Accuracy Estimating theAcademic Performance of Ethnic Groupsrsquorsquo Personality and SocialPsychology Bulletin 25 (1999) 225ndash236

Barberis Nicholas Andrei Shleifer and Robert Vishny lsquolsquoA Model of InvestorSentimentrsquorsquo Journal of Financial Economics 49 (1998) 307ndash343

Bayer Sylvia lsquolsquoThe Accuracy of Academic Gender Stereotypesrsquorsquo Sex Roles 40(1999) 787ndash813

Benjamin Dan James Choi and Joshua Strickland lsquolsquoSocial Identity andPreferencesrsquorsquo American Economic Review 100 (2010) 1913ndash1928

Benjamin Dan Matthew Rabin and Collin Raymond lsquolsquoA Model of Non-Belief inthe Law of Large Numbersrsquorsquo Journal of the European Economic Association15 (2015) 515ndash544

Bertrand Marianne lsquolsquoNew Perspectives on Genderrsquorsquo Handbook of LaborEconomics 4 (2011) 1543ndash1590

Bodoh-Creed Aaron Dan Benjamin and Matthew Rabin lsquolsquoThe Dynamics of Base-Rate Neglectrsquorsquo mimeo Haas Business School 2013

STEREOTYPES 1791

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

Bohnet Iris Alexandra van Geen and Max Bazerman lsquolsquoWhen PerformanceTrumps Gender Bias Joint versus Separate Evaluationrsquorsquo ManagementScience 5 (2016) 1225ndash1234

Bordalo Pedro Nicola Gennaioli and Andrei Shleifer lsquolsquoSalience Theory of Choiceunder Riskrsquorsquo Quarterly Journal of Economics 127 (2012) 1243ndash1285

mdashmdashmdash lsquolsquoSalience and Consumer Choicersquorsquo Journal of Political Economy 121(2013) 803ndash843

Briton Nancy and Judith Hall lsquolsquoBeliefs about Female and Male NonverbalCommunicationrsquorsquo Sex Roles 32 (1995) 79ndash90

Buser Thomas Muriel Niederle and Hessel Oosterbeek lsquolsquoGenderCompetitiveness and Career Choicesrsquorsquo Quarterly Journal of Economics 129(2014) 1409ndash1447

Carrell Scott Marianne Page and James West lsquolsquoSex and Science How ProfessorGender Perpetuates the Gender Gaprsquorsquo Quarterly Journal of Economics 125(2010) 1101ndash1144

Chambers John and Darya Melnyk lsquolsquoWhy Do I Hate Thee ConflictMisperceptions and Intergroup Mistrustrsquorsquo Personality and SocialPsychology Bulletin 32 (2006) 1295ndash1311

Chan Wayne Robert R McCrae Filip De Fruyt Lee Jussim CorinnaE Lockenhoff Marleen De Bolle Paul T Costa Jr Angelina R SutinAnu Realo Juri Allik Katsuharu Nakazato Yoshiko ShimonakaMartina Hrebıckova Sylvie Graf Michelle Yik Marina Brunner-SciarraNora Leibovich De Figueora Vanina Schmidt Chang-kyo Ahn Hyun-nie Ahn Maria E Aguilar-Vafaie Jerzy Siuta Barbara SzmigielskaThomas R Cain Janet T Crawford Khairul Anwar Mastor Jean-Pierre Rolland Florence Nansubuga Daniel R MiramontezVeronica Benet-Martınez Jerome Rossier Denis Bratko Iris MarusicJamin Halberstadt Mami Yamaguchi Goran Knezevic Thomas A MartinMirona Gheorghiu Peter B Smith Claudio Barbaranelli Lei WangJane Shakespeare-Finch Margarida P Lima Waldemar KlinkoszAndrzej Sekowski Lidia Alcalay Franco Simonetti Tatyana V AvdeyevaV S Pramila and Antonio Terracciano lsquolsquoStereotypes of Age Differences inPersonality Traits Universal and Accuratersquorsquo Journal of Personality andSocial Psychology 103 (2012) 1050ndash1066

Chen Yan Sherry Xin Liu Tracy Xiao and Margaret Shih lsquolsquoWhich Hat to WearImpact of Natural Identities on Coordination and Cooperationrsquorsquo Games andEconomic Behavior 84 (2014) 58ndash86

Coffman Katherine lsquolsquoEvidence on Self-Stereotyping and the Contribution ofIdeasrsquorsquo Quarterly Journal of Economics 129 (2014) 1625ndash1660

Cunningham Tom lsquolsquoComparisons and Choicersquorsquo mimeo Stockholm University2013

Diekman Amanda Alice Eagly and Patrick Kulesa lsquolsquoAccuracy and Bias in theStereotypes about the Social and Political Attitudes of Women and MenrsquorsquoJournal of Experimental Social Psychology 38 (2002) 268ndash282

Eccles Jacquelynne S Janis E Jacobs and Rena D Harold lsquolsquoGender RoleStereotypes Expectancy Effects and Parentsrsquo Socialization of GenderDifferencesrsquorsquo Journal of Social Issues 46 (1990) 183ndash201

Fryer Roland and Matthew Jackson lsquolsquoA Categorical Model of Cognition andBiased Decision-Makingrsquorsquo BE Journal of Theoretical Economics 8 (2008)1ndash42

Fryer Roland and Steven Levitt lsquolsquoAn Empirical Analysis of the Gender Gap inMathematicsrsquorsquo American Economic Journal Applied Economics 2 (2010)210ndash240

Gennaioli Nicola and Andrei Shleifer lsquolsquoWhat Comes to Mindrsquorsquo Quarterly Journalof Economics 125 (2010) 1399ndash1433

Gennaioli Nicola Andrei Shleifer and Robert Vishny lsquolsquoNeglected RisksFinancial Innovation and Financial Fragilityrsquorsquo Journal of FinancialEconomics 104 (2012) 452ndash468

Gilens Martin lsquolsquoRace and Poverty in America Public Misperceptions and theAmerican News Mediarsquorsquo Public Opinion Quarterly 60 (1996) 515ndash541

Glaeser Edward lsquolsquoThe Political Economy of Hatredrsquorsquo Quarterly Journal ofEconomics 120 (2005) 45ndash86

QUARTERLY JOURNAL OF ECONOMICS1792

at Harvard L

ibrary on October 28 2016

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Glover Dyland Amanda Pallais and William Pariente lsquolsquoDiscrimination as a Self-Fulfilling Prophecy Evidence from French Grocery Storesrsquorsquo mimeo HarvardUniversity 2015

Goldin Claudia Lawrence Katz and Ilyana Kuziemko lsquolsquoThe Homecoming ofAmerican College Women The Reversal of the College Gender GaprsquorsquoJournal of Economic Perspectives 20 (2006) 133ndash156

Graham Jesse Brian Nosek and Jonathan Haidt lsquolsquoThe Moral Stereotypes ofLiberals and Conservatives Exaggeration of Differences across thePolitical Spectrumrsquorsquo PLoS One 7 (2012) 1ndash13

Grether David lsquolsquoBayes Rule as a Descriptive Model The RepresentativenessHeuristicrsquorsquo Quarterly Journal of Economics 95 (1980) 537ndash557

Griffin Dale and Amos Tversky lsquolsquoThe Weighing of Evidence and theDeterminants of Confidencersquorsquo Cognitive Psychology 24 (1992) 411ndash435

Guiso Luigi Ferdinando Monte Paola Sapienza and Luigi Zingales lsquolsquoCultureGender and Mathrsquorsquo Science 320 (2008) 1164ndash1165

Hilton James and William Von Hippel lsquolsquoStereotypesrsquorsquo Annual Review ofPsychology 47 (1996) 237ndash271

Hyde Janet Sara Lindberg Marcia Linn Amy Ellis and Caroline WilliamslsquolsquoGender Similarities Characterize Math Performancersquorsquo Science 321 (2008)494ndash495

Judd Charles and Bernardette Park lsquolsquoDefinition and Assessment of Accuracy inSocial Stereotypesrsquorsquo Psychological Review 100 (1993) 109ndash128

Jussim Lee Jarret Crawford Stephanie Anglin John Chambers Sean Stevensand Florette Cohen lsquolsquoStereotype Accuracy One of the Largest and MostReplicable Effects in All of Social Psychologyrsquorsquo in The Handbook ofPrejudice Stereotyping and Discrimination Todd Nelson ed (MahwahNJ Lawrence Erlbaum 2015)

Kahneman Daniel and Amos Tversky lsquolsquoSubjective Probability A Judgment ofRepresentativenessrsquorsquo Cognitive Psychology 3 (1972) 430ndash454

mdashmdashmdash lsquolsquoOn the Psychology of Predictionrsquorsquo Psychological Review 80 (1973) 237ndash251

Kaplowitz Stan Bradley Fisher and Clifford Broman lsquolsquoHow Accurate ArePerceptions of Social Statistics about Blacks and Whitesrsquorsquo Public OpinionQuarterly 67 (2003) 237ndash243

Kersten Daniel Pascal Mamassian and Alan Yuille lsquolsquoObject Perception asBayesian Inferencersquorsquo Annual Review of Psychology 55 (2004) 271ndash304

Klein Richard Kate A Ratliff Michelangelo Vianello Reginald B Adams JrStepan Bahnik Michael J Bernstein Konrad Bocian Mark J BrandtBeach Brooks Claudia Chloe Brumbaugh Zeynep CemalcilarJesse Chandler Winnee Cheong William E Davis Thierry DevosMatthew Eisner Natalia Frankowska David Furrow Elisa Maria GallianiFred Hasselman Joshua A Hicks James F Hovermale S Jane HuntJeffrey R Huntsinger Hans IJzerman Melissa-Sue John Jennifer A Joy-Gaba Heather Barry Kappes Lacy E Krueger Jaime Kurtz CarmelA Levitan Robyn Mallett Wendy L Morris Anthony J Nelson JasonA Nier Grant Packard Ronaldo Pilati Abraham M RutchickKathleen Schmidt Jeanine L Skorinko Robert Smith Troy G SteinerJustin Storbeck Lyn M Van Swol Donna Thompson Anna van rsquot VeerLeigh Ann Vaughn Marek Vranka Aaron Wichman Julie A Woodzickaand Brian A Nosek lsquolsquoInvestigating Variation in Replicability A ManyLabs Replication Projectrsquorsquo Social Psychology 45 (2014) 142ndash152

Lundberg Shelly and Richard Startz lsquolsquoPrivate Discrimination and SocialIntervention in Competitive Labor Marketsrsquorsquo American Economic Review73 (1983) 340ndash347

Madon Stephanie Max Guyll Kathy Aboufadel Eulices Montiel Alison SmithPolly Palumbo and Lee Jussim lsquolsquoEthnic and National Stereotypes ThePrinceton Trilogy Revisited and Revisedrsquorsquo Personality and SocialPsychological Bulletin 27 (2001) 996ndash1010

Martin Carol lsquolsquoA Ratio Measure of Sex Stereotypingrsquorsquo Journal of Personality andSocial Psychology 52 (1987) 489ndash499

STEREOTYPES 1793

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

McCauley Clark Krishna Thangavelu and Paul Rozin lsquolsquoSex Stereotyping ofOccupations in Relation to Television Representations and Census FactsrsquorsquoBasic and Applied Social Psychology 9 (1988) 197ndash212

Mullainathan Sendhil lsquolsquoThinking through Categoriesrsquorsquo mimeo HarvardUniversity 2002

Ortoleva Pietro and Erik Snowberg lsquolsquoOverconfidence in Political BehaviorrsquorsquoAmerican Economic Review 105 (2015) 504ndash535

Phelps Edmund lsquolsquoThe Statistical Theory of Racism and Sexismrsquorsquo AmericanEconomic Review 62 (1972) 659ndash661

Pope Devin and Justin Sydnor lsquolsquoGeographic Variation in the Gender Differencesin Test Scoresrsquorsquo Journal of Economic Perspectives 24 (2010) 95ndash108

Rabin Matthew lsquolsquoInference by Believers in the Law of Small NumbersrsquorsquoQuarterly Journal of Economics 117 (2002) 775ndash816

Rabin Matthew and Joel Schrag lsquolsquoFirst Impressions Matter A Model ofConfirmatory Biasrsquorsquo Quarterly Journal of Economics 114 (1999) 37ndash82

Rabin Matthew and Dimitri Vayanos lsquolsquoThe Gamblerrsquos and Hot-Hand FallaciesTheory and Applicationsrsquorsquo Review of Economic Studies 77 (2010) 730ndash778

Reuben Ernesto Paola Sapienza and Luigi Zingales lsquolsquoHow Stereotypes ImpairWomenrsquos Careers in Sciencersquorsquo Proceedings of the National Academy ofSciences 111 (2014) 4403ndash4408

Rosch Eleanor lsquolsquoNatural Categoriesrsquorsquo Cognitive Psychology 4 (1973) 328ndash350Ryan Carey S lsquolsquoAccuracy of Black and White College Studentsrsquo In-Group and

Out-Group Stereotypesrsquorsquo Personality and Social Psychology Bulletin 22(1996) 1114ndash1127

Schneider David The Psychology of Stereotyping (New York Guilford Press2004)

Schneider David Albert Hastorf and Phoebe Ellsworth Person Perception(Reading MA Addison-Wesley 1979)

Shih Margaret Todd Pittinsky and Nalini Ambady lsquolsquoStereotype SusceptibilityIdentity Salience and Shifts in Quantitative Performancersquorsquo PsychologicalScience 10 (1999) 80ndash83

Shih Margaret Todd Pittinsky and Amy Trahan lsquolsquoDomain-Specific Effects ofStereotypes on Performancersquorsquo Self and Identity 5 (2006) 1ndash14

Steele Claude Whistling Vivaldi How Stereotypes Affect Us and What We CanDo (New York Norton 2010)

Tenenbaum Joshua and Thomas Griffiths lsquolsquoThe Rational Basis ofRepresentativenessrsquorsquo 23rd Annual Conference of the Cognitive ScienceSociety (2001) 1036ndash1041

Tversky Amos and Daniel Kahneman lsquolsquoExtensional versus Intuitive ReasoningThe Conjunction Fallacy in Probability Judgmentrsquorsquo Psychological Review 90(1983) 293ndash315

Weinberger Catherin lsquolsquoIs the Science and Engineering Workforce Drawn fromthe Far Upper Tail of the Math Ability Distributionrsquorsquo mimeo UCSB 2005

Westfall Jacob Leaf Van Boven John Chambers and Charles Judd lsquolsquoPerceivingPolitical Polarization in the United States Party Identity Strength andAttitude Extremity Exacerbate the Perceived Partisan DividersquorsquoPsychological Science 10 (2015) 145ndash158

Wolsko Christopher Bernadette Park Charles Judd and Bernd WittenbrinklsquolsquoFraming Interethnic Ideology Effects of Multicultural and Color-BlindPerspectives on Judgments of Groups and Individualsrsquorsquo Journal ofPersonality and Social Psychology 78 (2000) 635ndash654

QUARTERLY JOURNAL OF ECONOMICS1794

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

Page 34: I. Introduction · uneducated at the beginning of the 20th century, and as high achievers at the beginning of the 21st (Madon et al. 2001). Social science has produced three broad

FIGURE III

Two Examples

QUARTERLY JOURNAL OF ECONOMICS1786

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

et al (2015)rsquos analysis of the ANES data30 Figure IV shows thatthe believed difference between typical conservative and typicalliberal positions is larger than the true difference in mean posi-tions for 109 of the 111 observations The data for both GNH(squares) and ANES (triangles) lie above the 45-degree line(dashed)31 Average exaggeration is 062 positions on the scale(066 in the GNH data 059 in the ANES data)32

The systematic and significant exaggeration of mean differ-ences suggests that the benchmark model of accurate beliefs ismissing something important Indeed this exaggeration reflectsthe fact that believed means are typically more extreme than truemeans First note that the kernel of truth regression (equation(5)) generates exaggeration of mean differences just as docu-mented in Figure IV

EstethtjGTHORN E

stethtjGTHORN frac14 eth1thorn 2THORN frac12EethtjGTHORN EethtjGTHORN

To bring this prediction to the data we regress the believedmean position for each group EBethtjGTHORN on the true mean of thegroup EethtjGTHORN and the true mean of the comparison groupEethtjGTHORN across issues We do this for each group (liberals con-servatives) in each data set separately We also present pooledspecifications that combine the data sets to make a prediction fora given group (liberals conservatives) In these pooled specifica-tions we include a dummy variable indicating whether theobservation came from the ANES data set For all specificationswe cluster observations at the issue level33 The results from re-gression are shown in Table I In every specification we find thatEethtjGTHORN is a significant predictor of EBethtjGTHORN with the predicted pos-itive sign Crucially for five of the six specifications the mean of

30 Chambers and Melnyk (2006) also find evidence of exaggeration of truedifferences in beliefs about political positions

31 For convenience we recode all issues so that the high end of the scale (67)represents the stereotypically more conservative position

32 A natural question to ask is how beliefs vary across liberals and conserva-tives That is do beliefs about a group G depend on membership in G versus ndashG Ourmodel does not speak to this issue However in Online Appendix G we show thatthe results we document below hold for both beliefs held by conservatives and be-liefs held by liberals see Tables A9 A10 and A11

33 In general the results presented below for the ANES data are not largelyimpacted by the decision to cluster at the issue level Similar results are obtained ifthe data are not clustered

STEREOTYPES 1787

at Harvard L

ibrary on October 28 2016

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ownloaded from

the comparison group EethtjGTHORN is also a significant predictor ofE

BethtjGTHORN with the predicted negative signAlthough these results provide strong evidence of context

dependence and are consistent with our model they do not pindown a role for representativeness of types Our next test relatesthe magnitude of representativeness of tail types to the magni-tude of belief distortions

To this end we implement the regressions in equations (6)and (7) Following Proposition 4 we compute the average repre-

sentativeness of tail types for conservatives RconsH frac14

PtT2tconsPtT2tlib

We

again test the hypothesis that RconsH is a significant predictor of Est

ethtjconsTHORN with a positive sign and a predictor of EstethtjlibTHORN with a

negative sign Table II shows that conditional on true mean RconsH

predicts believed mean for each group G as expected The firstthree specifications display the results for predicting beliefs heldabout conservatives In both data sets the average representa-tiveness of tail types for conservatives is a significant positivepredictor of beliefs held about conservatives The final three spe-cifications display the results for predicting beliefs held about

FIGURE IV

Exaggeration of Differences

QUARTERLY JOURNAL OF ECONOMICS1788

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ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

liberals We find that the average representativeness of tail typesfor conservatives is a negative predictor of beliefs held about lib-erals This effect is significant in the GNH data and marginallysignificant in the ANES data

We present several additional results in Online Appendix GTo further examine the role of representativeness in driving be-liefs we first show the results of Table II carry through when we

TABLE II

AVERAGE REPRESENTATIVENESS OF TAIL POSITIONS PREDICTS BELIEFS

OLS Predicting Believed Mean of Group G for Each Issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position

of group G for issue

078 024 051 072 018 041

(006) (008) (009) (005) (005) (010)

Avg rep of tail types for

conservatives RconsH

019 055 025 014 012 024

(007) (022) (008) (006) (007) (005)

Constant 101 260 184 093 271 201

(026) (045) (029) (022) (025) (032)

R2 082 048 060 091 031 070

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

TABLE I

INFORMATION ABOUT ndashG PREDICTS BELIEFS ABOUT G

OLS predicting believed mean of group G for each issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position of

conservatives for issue

102 098 096 021 019 025

(0097) (0133) (0076) (0060) (0116) (0060)

True mean position of

liberals for issue

035 086 058 0987 039 073

(0106) (0134) (0131) (0066) (0106) (0135)

Constant 151 335 235 069 258 156

(0195) (0269) (0279) (0122) (0249) (0270)

R2 083 053 066 092 032 068

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

STEREOTYPES 1789

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ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

control for the average likelihood on the tail positions (see Table A4in Online Appendix G) Most tellingly we use the model to predictbeliefs across issues and compare those to the data For simplicitywe use the rank-based truncation specification to predict mean be-liefs when stereotypes include the d most representative types ford frac14 1 T We compare these predictions to those of a model inwhich beliefs are obtained by restricting the distribution to the dmost likely types Our benchmark for both models is predicting thebelieved mean from the entire distribution where d = T We showthat the predictions of the rank-based truncation model with d = 4or 5 compare favorably to both a likelihood-based truncation model(with any d) and the accurate beliefs benchmark Interestingly thisresult suggests that stereotypical beliefs are well approximated byneglecting the least representative types (as opposed to focusingonly on the most representative types) and so represent a moderatethough systematic departure from the standard benchmarkFinally we show that the results we document above hold forboth beliefs held by conservatives and beliefs held by liberals (seeTables A9 A10 and A11 in Online Appendix G)

V Conclusion

We present a model of stereotypical thinking in which DMsmaking predictions about a group overweight the grouprsquos mostdistinctive types These overweighted types are not the mostlikely ones given the DMrsquos data but the most representativeones in the sense of being the most diagnostic of the group rela-tive to other groups Representativeness implies that what ismost distinctive of a group depends on what group it is comparedwith We present experimental evidence that confirms this con-text dependence in recall-based assessments of groups Finallywe evaluated the predictions of the model using political data fromexisting large-scale surveys We find context dependence to be akey feature of beliefs Given the richness of the political data wecan go a step further and identify a role for representativeness inparticular As the representativeness of tail types increases beliefsof a group are distorted in the direction of that tail

Our approach provides a parsimonious and psychologicallyfounded account of how DMs generate simplified representationsof reality from social groups to stock returns and offers a unifiedaccount of disparate pieces of evidence relating to this type of

QUARTERLY JOURNAL OF ECONOMICS1790

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ibrary on October 28 2016

httpqjeoxfordjournalsorgD

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uncertainty The model captures the central fact that stereotypeshighlight the greatest difference between groups thus explainingwhy some stereotypes are very accurate while others lack valid-ity Still stereotypes often have a kernel of truth when they arebased on systematicmdasheven if smallmdashdifferences between groupsThis logic allows us to describe a number of heuristics and psy-chological biases many of which arise in the context of predictionproblems Generically our model generates overreaction to diag-nostic information

Our model is based on representativeness and does not cap-ture all the features of stereotypical thinking However it cap-tures perhaps the central feature when we think of a group wefocus on what is most distinctive about it and neglect or under-weight the rest

Saeuroıd Business School University of Oxford

Ohio State University and Harvard Business School

Universita Bocconi and Innocenzo Gasparini Institute

for Economic Research

Harvard University

Supplementary Material

An Online Appendix for this article can be found at QJEonline (qjeoxfordjournalorg)

References

Adorno Theodor Else Frenkel-Brunswik Daniel Levinson and Nevitt SanfordThe Authoritarian Personality (New York Harper amp Row 1950)

Arrow Kenneth lsquolsquoThe Theory of Discriminationrsquorsquo in Discrimination in LaborMarkets Orley Ashenfelter and Albert Rees eds (Princeton NJPrinceton University Press 1973)

Ashton Michael and Victoria Esses lsquolsquoStereotype Accuracy Estimating theAcademic Performance of Ethnic Groupsrsquorsquo Personality and SocialPsychology Bulletin 25 (1999) 225ndash236

Barberis Nicholas Andrei Shleifer and Robert Vishny lsquolsquoA Model of InvestorSentimentrsquorsquo Journal of Financial Economics 49 (1998) 307ndash343

Bayer Sylvia lsquolsquoThe Accuracy of Academic Gender Stereotypesrsquorsquo Sex Roles 40(1999) 787ndash813

Benjamin Dan James Choi and Joshua Strickland lsquolsquoSocial Identity andPreferencesrsquorsquo American Economic Review 100 (2010) 1913ndash1928

Benjamin Dan Matthew Rabin and Collin Raymond lsquolsquoA Model of Non-Belief inthe Law of Large Numbersrsquorsquo Journal of the European Economic Association15 (2015) 515ndash544

Bertrand Marianne lsquolsquoNew Perspectives on Genderrsquorsquo Handbook of LaborEconomics 4 (2011) 1543ndash1590

Bodoh-Creed Aaron Dan Benjamin and Matthew Rabin lsquolsquoThe Dynamics of Base-Rate Neglectrsquorsquo mimeo Haas Business School 2013

STEREOTYPES 1791

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

Bohnet Iris Alexandra van Geen and Max Bazerman lsquolsquoWhen PerformanceTrumps Gender Bias Joint versus Separate Evaluationrsquorsquo ManagementScience 5 (2016) 1225ndash1234

Bordalo Pedro Nicola Gennaioli and Andrei Shleifer lsquolsquoSalience Theory of Choiceunder Riskrsquorsquo Quarterly Journal of Economics 127 (2012) 1243ndash1285

mdashmdashmdash lsquolsquoSalience and Consumer Choicersquorsquo Journal of Political Economy 121(2013) 803ndash843

Briton Nancy and Judith Hall lsquolsquoBeliefs about Female and Male NonverbalCommunicationrsquorsquo Sex Roles 32 (1995) 79ndash90

Buser Thomas Muriel Niederle and Hessel Oosterbeek lsquolsquoGenderCompetitiveness and Career Choicesrsquorsquo Quarterly Journal of Economics 129(2014) 1409ndash1447

Carrell Scott Marianne Page and James West lsquolsquoSex and Science How ProfessorGender Perpetuates the Gender Gaprsquorsquo Quarterly Journal of Economics 125(2010) 1101ndash1144

Chambers John and Darya Melnyk lsquolsquoWhy Do I Hate Thee ConflictMisperceptions and Intergroup Mistrustrsquorsquo Personality and SocialPsychology Bulletin 32 (2006) 1295ndash1311

Chan Wayne Robert R McCrae Filip De Fruyt Lee Jussim CorinnaE Lockenhoff Marleen De Bolle Paul T Costa Jr Angelina R SutinAnu Realo Juri Allik Katsuharu Nakazato Yoshiko ShimonakaMartina Hrebıckova Sylvie Graf Michelle Yik Marina Brunner-SciarraNora Leibovich De Figueora Vanina Schmidt Chang-kyo Ahn Hyun-nie Ahn Maria E Aguilar-Vafaie Jerzy Siuta Barbara SzmigielskaThomas R Cain Janet T Crawford Khairul Anwar Mastor Jean-Pierre Rolland Florence Nansubuga Daniel R MiramontezVeronica Benet-Martınez Jerome Rossier Denis Bratko Iris MarusicJamin Halberstadt Mami Yamaguchi Goran Knezevic Thomas A MartinMirona Gheorghiu Peter B Smith Claudio Barbaranelli Lei WangJane Shakespeare-Finch Margarida P Lima Waldemar KlinkoszAndrzej Sekowski Lidia Alcalay Franco Simonetti Tatyana V AvdeyevaV S Pramila and Antonio Terracciano lsquolsquoStereotypes of Age Differences inPersonality Traits Universal and Accuratersquorsquo Journal of Personality andSocial Psychology 103 (2012) 1050ndash1066

Chen Yan Sherry Xin Liu Tracy Xiao and Margaret Shih lsquolsquoWhich Hat to WearImpact of Natural Identities on Coordination and Cooperationrsquorsquo Games andEconomic Behavior 84 (2014) 58ndash86

Coffman Katherine lsquolsquoEvidence on Self-Stereotyping and the Contribution ofIdeasrsquorsquo Quarterly Journal of Economics 129 (2014) 1625ndash1660

Cunningham Tom lsquolsquoComparisons and Choicersquorsquo mimeo Stockholm University2013

Diekman Amanda Alice Eagly and Patrick Kulesa lsquolsquoAccuracy and Bias in theStereotypes about the Social and Political Attitudes of Women and MenrsquorsquoJournal of Experimental Social Psychology 38 (2002) 268ndash282

Eccles Jacquelynne S Janis E Jacobs and Rena D Harold lsquolsquoGender RoleStereotypes Expectancy Effects and Parentsrsquo Socialization of GenderDifferencesrsquorsquo Journal of Social Issues 46 (1990) 183ndash201

Fryer Roland and Matthew Jackson lsquolsquoA Categorical Model of Cognition andBiased Decision-Makingrsquorsquo BE Journal of Theoretical Economics 8 (2008)1ndash42

Fryer Roland and Steven Levitt lsquolsquoAn Empirical Analysis of the Gender Gap inMathematicsrsquorsquo American Economic Journal Applied Economics 2 (2010)210ndash240

Gennaioli Nicola and Andrei Shleifer lsquolsquoWhat Comes to Mindrsquorsquo Quarterly Journalof Economics 125 (2010) 1399ndash1433

Gennaioli Nicola Andrei Shleifer and Robert Vishny lsquolsquoNeglected RisksFinancial Innovation and Financial Fragilityrsquorsquo Journal of FinancialEconomics 104 (2012) 452ndash468

Gilens Martin lsquolsquoRace and Poverty in America Public Misperceptions and theAmerican News Mediarsquorsquo Public Opinion Quarterly 60 (1996) 515ndash541

Glaeser Edward lsquolsquoThe Political Economy of Hatredrsquorsquo Quarterly Journal ofEconomics 120 (2005) 45ndash86

QUARTERLY JOURNAL OF ECONOMICS1792

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

Glover Dyland Amanda Pallais and William Pariente lsquolsquoDiscrimination as a Self-Fulfilling Prophecy Evidence from French Grocery Storesrsquorsquo mimeo HarvardUniversity 2015

Goldin Claudia Lawrence Katz and Ilyana Kuziemko lsquolsquoThe Homecoming ofAmerican College Women The Reversal of the College Gender GaprsquorsquoJournal of Economic Perspectives 20 (2006) 133ndash156

Graham Jesse Brian Nosek and Jonathan Haidt lsquolsquoThe Moral Stereotypes ofLiberals and Conservatives Exaggeration of Differences across thePolitical Spectrumrsquorsquo PLoS One 7 (2012) 1ndash13

Grether David lsquolsquoBayes Rule as a Descriptive Model The RepresentativenessHeuristicrsquorsquo Quarterly Journal of Economics 95 (1980) 537ndash557

Griffin Dale and Amos Tversky lsquolsquoThe Weighing of Evidence and theDeterminants of Confidencersquorsquo Cognitive Psychology 24 (1992) 411ndash435

Guiso Luigi Ferdinando Monte Paola Sapienza and Luigi Zingales lsquolsquoCultureGender and Mathrsquorsquo Science 320 (2008) 1164ndash1165

Hilton James and William Von Hippel lsquolsquoStereotypesrsquorsquo Annual Review ofPsychology 47 (1996) 237ndash271

Hyde Janet Sara Lindberg Marcia Linn Amy Ellis and Caroline WilliamslsquolsquoGender Similarities Characterize Math Performancersquorsquo Science 321 (2008)494ndash495

Judd Charles and Bernardette Park lsquolsquoDefinition and Assessment of Accuracy inSocial Stereotypesrsquorsquo Psychological Review 100 (1993) 109ndash128

Jussim Lee Jarret Crawford Stephanie Anglin John Chambers Sean Stevensand Florette Cohen lsquolsquoStereotype Accuracy One of the Largest and MostReplicable Effects in All of Social Psychologyrsquorsquo in The Handbook ofPrejudice Stereotyping and Discrimination Todd Nelson ed (MahwahNJ Lawrence Erlbaum 2015)

Kahneman Daniel and Amos Tversky lsquolsquoSubjective Probability A Judgment ofRepresentativenessrsquorsquo Cognitive Psychology 3 (1972) 430ndash454

mdashmdashmdash lsquolsquoOn the Psychology of Predictionrsquorsquo Psychological Review 80 (1973) 237ndash251

Kaplowitz Stan Bradley Fisher and Clifford Broman lsquolsquoHow Accurate ArePerceptions of Social Statistics about Blacks and Whitesrsquorsquo Public OpinionQuarterly 67 (2003) 237ndash243

Kersten Daniel Pascal Mamassian and Alan Yuille lsquolsquoObject Perception asBayesian Inferencersquorsquo Annual Review of Psychology 55 (2004) 271ndash304

Klein Richard Kate A Ratliff Michelangelo Vianello Reginald B Adams JrStepan Bahnik Michael J Bernstein Konrad Bocian Mark J BrandtBeach Brooks Claudia Chloe Brumbaugh Zeynep CemalcilarJesse Chandler Winnee Cheong William E Davis Thierry DevosMatthew Eisner Natalia Frankowska David Furrow Elisa Maria GallianiFred Hasselman Joshua A Hicks James F Hovermale S Jane HuntJeffrey R Huntsinger Hans IJzerman Melissa-Sue John Jennifer A Joy-Gaba Heather Barry Kappes Lacy E Krueger Jaime Kurtz CarmelA Levitan Robyn Mallett Wendy L Morris Anthony J Nelson JasonA Nier Grant Packard Ronaldo Pilati Abraham M RutchickKathleen Schmidt Jeanine L Skorinko Robert Smith Troy G SteinerJustin Storbeck Lyn M Van Swol Donna Thompson Anna van rsquot VeerLeigh Ann Vaughn Marek Vranka Aaron Wichman Julie A Woodzickaand Brian A Nosek lsquolsquoInvestigating Variation in Replicability A ManyLabs Replication Projectrsquorsquo Social Psychology 45 (2014) 142ndash152

Lundberg Shelly and Richard Startz lsquolsquoPrivate Discrimination and SocialIntervention in Competitive Labor Marketsrsquorsquo American Economic Review73 (1983) 340ndash347

Madon Stephanie Max Guyll Kathy Aboufadel Eulices Montiel Alison SmithPolly Palumbo and Lee Jussim lsquolsquoEthnic and National Stereotypes ThePrinceton Trilogy Revisited and Revisedrsquorsquo Personality and SocialPsychological Bulletin 27 (2001) 996ndash1010

Martin Carol lsquolsquoA Ratio Measure of Sex Stereotypingrsquorsquo Journal of Personality andSocial Psychology 52 (1987) 489ndash499

STEREOTYPES 1793

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

McCauley Clark Krishna Thangavelu and Paul Rozin lsquolsquoSex Stereotyping ofOccupations in Relation to Television Representations and Census FactsrsquorsquoBasic and Applied Social Psychology 9 (1988) 197ndash212

Mullainathan Sendhil lsquolsquoThinking through Categoriesrsquorsquo mimeo HarvardUniversity 2002

Ortoleva Pietro and Erik Snowberg lsquolsquoOverconfidence in Political BehaviorrsquorsquoAmerican Economic Review 105 (2015) 504ndash535

Phelps Edmund lsquolsquoThe Statistical Theory of Racism and Sexismrsquorsquo AmericanEconomic Review 62 (1972) 659ndash661

Pope Devin and Justin Sydnor lsquolsquoGeographic Variation in the Gender Differencesin Test Scoresrsquorsquo Journal of Economic Perspectives 24 (2010) 95ndash108

Rabin Matthew lsquolsquoInference by Believers in the Law of Small NumbersrsquorsquoQuarterly Journal of Economics 117 (2002) 775ndash816

Rabin Matthew and Joel Schrag lsquolsquoFirst Impressions Matter A Model ofConfirmatory Biasrsquorsquo Quarterly Journal of Economics 114 (1999) 37ndash82

Rabin Matthew and Dimitri Vayanos lsquolsquoThe Gamblerrsquos and Hot-Hand FallaciesTheory and Applicationsrsquorsquo Review of Economic Studies 77 (2010) 730ndash778

Reuben Ernesto Paola Sapienza and Luigi Zingales lsquolsquoHow Stereotypes ImpairWomenrsquos Careers in Sciencersquorsquo Proceedings of the National Academy ofSciences 111 (2014) 4403ndash4408

Rosch Eleanor lsquolsquoNatural Categoriesrsquorsquo Cognitive Psychology 4 (1973) 328ndash350Ryan Carey S lsquolsquoAccuracy of Black and White College Studentsrsquo In-Group and

Out-Group Stereotypesrsquorsquo Personality and Social Psychology Bulletin 22(1996) 1114ndash1127

Schneider David The Psychology of Stereotyping (New York Guilford Press2004)

Schneider David Albert Hastorf and Phoebe Ellsworth Person Perception(Reading MA Addison-Wesley 1979)

Shih Margaret Todd Pittinsky and Nalini Ambady lsquolsquoStereotype SusceptibilityIdentity Salience and Shifts in Quantitative Performancersquorsquo PsychologicalScience 10 (1999) 80ndash83

Shih Margaret Todd Pittinsky and Amy Trahan lsquolsquoDomain-Specific Effects ofStereotypes on Performancersquorsquo Self and Identity 5 (2006) 1ndash14

Steele Claude Whistling Vivaldi How Stereotypes Affect Us and What We CanDo (New York Norton 2010)

Tenenbaum Joshua and Thomas Griffiths lsquolsquoThe Rational Basis ofRepresentativenessrsquorsquo 23rd Annual Conference of the Cognitive ScienceSociety (2001) 1036ndash1041

Tversky Amos and Daniel Kahneman lsquolsquoExtensional versus Intuitive ReasoningThe Conjunction Fallacy in Probability Judgmentrsquorsquo Psychological Review 90(1983) 293ndash315

Weinberger Catherin lsquolsquoIs the Science and Engineering Workforce Drawn fromthe Far Upper Tail of the Math Ability Distributionrsquorsquo mimeo UCSB 2005

Westfall Jacob Leaf Van Boven John Chambers and Charles Judd lsquolsquoPerceivingPolitical Polarization in the United States Party Identity Strength andAttitude Extremity Exacerbate the Perceived Partisan DividersquorsquoPsychological Science 10 (2015) 145ndash158

Wolsko Christopher Bernadette Park Charles Judd and Bernd WittenbrinklsquolsquoFraming Interethnic Ideology Effects of Multicultural and Color-BlindPerspectives on Judgments of Groups and Individualsrsquorsquo Journal ofPersonality and Social Psychology 78 (2000) 635ndash654

QUARTERLY JOURNAL OF ECONOMICS1794

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

Page 35: I. Introduction · uneducated at the beginning of the 20th century, and as high achievers at the beginning of the 21st (Madon et al. 2001). Social science has produced three broad

et al (2015)rsquos analysis of the ANES data30 Figure IV shows thatthe believed difference between typical conservative and typicalliberal positions is larger than the true difference in mean posi-tions for 109 of the 111 observations The data for both GNH(squares) and ANES (triangles) lie above the 45-degree line(dashed)31 Average exaggeration is 062 positions on the scale(066 in the GNH data 059 in the ANES data)32

The systematic and significant exaggeration of mean differ-ences suggests that the benchmark model of accurate beliefs ismissing something important Indeed this exaggeration reflectsthe fact that believed means are typically more extreme than truemeans First note that the kernel of truth regression (equation(5)) generates exaggeration of mean differences just as docu-mented in Figure IV

EstethtjGTHORN E

stethtjGTHORN frac14 eth1thorn 2THORN frac12EethtjGTHORN EethtjGTHORN

To bring this prediction to the data we regress the believedmean position for each group EBethtjGTHORN on the true mean of thegroup EethtjGTHORN and the true mean of the comparison groupEethtjGTHORN across issues We do this for each group (liberals con-servatives) in each data set separately We also present pooledspecifications that combine the data sets to make a prediction fora given group (liberals conservatives) In these pooled specifica-tions we include a dummy variable indicating whether theobservation came from the ANES data set For all specificationswe cluster observations at the issue level33 The results from re-gression are shown in Table I In every specification we find thatEethtjGTHORN is a significant predictor of EBethtjGTHORN with the predicted pos-itive sign Crucially for five of the six specifications the mean of

30 Chambers and Melnyk (2006) also find evidence of exaggeration of truedifferences in beliefs about political positions

31 For convenience we recode all issues so that the high end of the scale (67)represents the stereotypically more conservative position

32 A natural question to ask is how beliefs vary across liberals and conserva-tives That is do beliefs about a group G depend on membership in G versus ndashG Ourmodel does not speak to this issue However in Online Appendix G we show thatthe results we document below hold for both beliefs held by conservatives and be-liefs held by liberals see Tables A9 A10 and A11

33 In general the results presented below for the ANES data are not largelyimpacted by the decision to cluster at the issue level Similar results are obtained ifthe data are not clustered

STEREOTYPES 1787

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

the comparison group EethtjGTHORN is also a significant predictor ofE

BethtjGTHORN with the predicted negative signAlthough these results provide strong evidence of context

dependence and are consistent with our model they do not pindown a role for representativeness of types Our next test relatesthe magnitude of representativeness of tail types to the magni-tude of belief distortions

To this end we implement the regressions in equations (6)and (7) Following Proposition 4 we compute the average repre-

sentativeness of tail types for conservatives RconsH frac14

PtT2tconsPtT2tlib

We

again test the hypothesis that RconsH is a significant predictor of Est

ethtjconsTHORN with a positive sign and a predictor of EstethtjlibTHORN with a

negative sign Table II shows that conditional on true mean RconsH

predicts believed mean for each group G as expected The firstthree specifications display the results for predicting beliefs heldabout conservatives In both data sets the average representa-tiveness of tail types for conservatives is a significant positivepredictor of beliefs held about conservatives The final three spe-cifications display the results for predicting beliefs held about

FIGURE IV

Exaggeration of Differences

QUARTERLY JOURNAL OF ECONOMICS1788

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

liberals We find that the average representativeness of tail typesfor conservatives is a negative predictor of beliefs held about lib-erals This effect is significant in the GNH data and marginallysignificant in the ANES data

We present several additional results in Online Appendix GTo further examine the role of representativeness in driving be-liefs we first show the results of Table II carry through when we

TABLE II

AVERAGE REPRESENTATIVENESS OF TAIL POSITIONS PREDICTS BELIEFS

OLS Predicting Believed Mean of Group G for Each Issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position

of group G for issue

078 024 051 072 018 041

(006) (008) (009) (005) (005) (010)

Avg rep of tail types for

conservatives RconsH

019 055 025 014 012 024

(007) (022) (008) (006) (007) (005)

Constant 101 260 184 093 271 201

(026) (045) (029) (022) (025) (032)

R2 082 048 060 091 031 070

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

TABLE I

INFORMATION ABOUT ndashG PREDICTS BELIEFS ABOUT G

OLS predicting believed mean of group G for each issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position of

conservatives for issue

102 098 096 021 019 025

(0097) (0133) (0076) (0060) (0116) (0060)

True mean position of

liberals for issue

035 086 058 0987 039 073

(0106) (0134) (0131) (0066) (0106) (0135)

Constant 151 335 235 069 258 156

(0195) (0269) (0279) (0122) (0249) (0270)

R2 083 053 066 092 032 068

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

STEREOTYPES 1789

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

control for the average likelihood on the tail positions (see Table A4in Online Appendix G) Most tellingly we use the model to predictbeliefs across issues and compare those to the data For simplicitywe use the rank-based truncation specification to predict mean be-liefs when stereotypes include the d most representative types ford frac14 1 T We compare these predictions to those of a model inwhich beliefs are obtained by restricting the distribution to the dmost likely types Our benchmark for both models is predicting thebelieved mean from the entire distribution where d = T We showthat the predictions of the rank-based truncation model with d = 4or 5 compare favorably to both a likelihood-based truncation model(with any d) and the accurate beliefs benchmark Interestingly thisresult suggests that stereotypical beliefs are well approximated byneglecting the least representative types (as opposed to focusingonly on the most representative types) and so represent a moderatethough systematic departure from the standard benchmarkFinally we show that the results we document above hold forboth beliefs held by conservatives and beliefs held by liberals (seeTables A9 A10 and A11 in Online Appendix G)

V Conclusion

We present a model of stereotypical thinking in which DMsmaking predictions about a group overweight the grouprsquos mostdistinctive types These overweighted types are not the mostlikely ones given the DMrsquos data but the most representativeones in the sense of being the most diagnostic of the group rela-tive to other groups Representativeness implies that what ismost distinctive of a group depends on what group it is comparedwith We present experimental evidence that confirms this con-text dependence in recall-based assessments of groups Finallywe evaluated the predictions of the model using political data fromexisting large-scale surveys We find context dependence to be akey feature of beliefs Given the richness of the political data wecan go a step further and identify a role for representativeness inparticular As the representativeness of tail types increases beliefsof a group are distorted in the direction of that tail

Our approach provides a parsimonious and psychologicallyfounded account of how DMs generate simplified representationsof reality from social groups to stock returns and offers a unifiedaccount of disparate pieces of evidence relating to this type of

QUARTERLY JOURNAL OF ECONOMICS1790

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

uncertainty The model captures the central fact that stereotypeshighlight the greatest difference between groups thus explainingwhy some stereotypes are very accurate while others lack valid-ity Still stereotypes often have a kernel of truth when they arebased on systematicmdasheven if smallmdashdifferences between groupsThis logic allows us to describe a number of heuristics and psy-chological biases many of which arise in the context of predictionproblems Generically our model generates overreaction to diag-nostic information

Our model is based on representativeness and does not cap-ture all the features of stereotypical thinking However it cap-tures perhaps the central feature when we think of a group wefocus on what is most distinctive about it and neglect or under-weight the rest

Saeuroıd Business School University of Oxford

Ohio State University and Harvard Business School

Universita Bocconi and Innocenzo Gasparini Institute

for Economic Research

Harvard University

Supplementary Material

An Online Appendix for this article can be found at QJEonline (qjeoxfordjournalorg)

References

Adorno Theodor Else Frenkel-Brunswik Daniel Levinson and Nevitt SanfordThe Authoritarian Personality (New York Harper amp Row 1950)

Arrow Kenneth lsquolsquoThe Theory of Discriminationrsquorsquo in Discrimination in LaborMarkets Orley Ashenfelter and Albert Rees eds (Princeton NJPrinceton University Press 1973)

Ashton Michael and Victoria Esses lsquolsquoStereotype Accuracy Estimating theAcademic Performance of Ethnic Groupsrsquorsquo Personality and SocialPsychology Bulletin 25 (1999) 225ndash236

Barberis Nicholas Andrei Shleifer and Robert Vishny lsquolsquoA Model of InvestorSentimentrsquorsquo Journal of Financial Economics 49 (1998) 307ndash343

Bayer Sylvia lsquolsquoThe Accuracy of Academic Gender Stereotypesrsquorsquo Sex Roles 40(1999) 787ndash813

Benjamin Dan James Choi and Joshua Strickland lsquolsquoSocial Identity andPreferencesrsquorsquo American Economic Review 100 (2010) 1913ndash1928

Benjamin Dan Matthew Rabin and Collin Raymond lsquolsquoA Model of Non-Belief inthe Law of Large Numbersrsquorsquo Journal of the European Economic Association15 (2015) 515ndash544

Bertrand Marianne lsquolsquoNew Perspectives on Genderrsquorsquo Handbook of LaborEconomics 4 (2011) 1543ndash1590

Bodoh-Creed Aaron Dan Benjamin and Matthew Rabin lsquolsquoThe Dynamics of Base-Rate Neglectrsquorsquo mimeo Haas Business School 2013

STEREOTYPES 1791

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

Bohnet Iris Alexandra van Geen and Max Bazerman lsquolsquoWhen PerformanceTrumps Gender Bias Joint versus Separate Evaluationrsquorsquo ManagementScience 5 (2016) 1225ndash1234

Bordalo Pedro Nicola Gennaioli and Andrei Shleifer lsquolsquoSalience Theory of Choiceunder Riskrsquorsquo Quarterly Journal of Economics 127 (2012) 1243ndash1285

mdashmdashmdash lsquolsquoSalience and Consumer Choicersquorsquo Journal of Political Economy 121(2013) 803ndash843

Briton Nancy and Judith Hall lsquolsquoBeliefs about Female and Male NonverbalCommunicationrsquorsquo Sex Roles 32 (1995) 79ndash90

Buser Thomas Muriel Niederle and Hessel Oosterbeek lsquolsquoGenderCompetitiveness and Career Choicesrsquorsquo Quarterly Journal of Economics 129(2014) 1409ndash1447

Carrell Scott Marianne Page and James West lsquolsquoSex and Science How ProfessorGender Perpetuates the Gender Gaprsquorsquo Quarterly Journal of Economics 125(2010) 1101ndash1144

Chambers John and Darya Melnyk lsquolsquoWhy Do I Hate Thee ConflictMisperceptions and Intergroup Mistrustrsquorsquo Personality and SocialPsychology Bulletin 32 (2006) 1295ndash1311

Chan Wayne Robert R McCrae Filip De Fruyt Lee Jussim CorinnaE Lockenhoff Marleen De Bolle Paul T Costa Jr Angelina R SutinAnu Realo Juri Allik Katsuharu Nakazato Yoshiko ShimonakaMartina Hrebıckova Sylvie Graf Michelle Yik Marina Brunner-SciarraNora Leibovich De Figueora Vanina Schmidt Chang-kyo Ahn Hyun-nie Ahn Maria E Aguilar-Vafaie Jerzy Siuta Barbara SzmigielskaThomas R Cain Janet T Crawford Khairul Anwar Mastor Jean-Pierre Rolland Florence Nansubuga Daniel R MiramontezVeronica Benet-Martınez Jerome Rossier Denis Bratko Iris MarusicJamin Halberstadt Mami Yamaguchi Goran Knezevic Thomas A MartinMirona Gheorghiu Peter B Smith Claudio Barbaranelli Lei WangJane Shakespeare-Finch Margarida P Lima Waldemar KlinkoszAndrzej Sekowski Lidia Alcalay Franco Simonetti Tatyana V AvdeyevaV S Pramila and Antonio Terracciano lsquolsquoStereotypes of Age Differences inPersonality Traits Universal and Accuratersquorsquo Journal of Personality andSocial Psychology 103 (2012) 1050ndash1066

Chen Yan Sherry Xin Liu Tracy Xiao and Margaret Shih lsquolsquoWhich Hat to WearImpact of Natural Identities on Coordination and Cooperationrsquorsquo Games andEconomic Behavior 84 (2014) 58ndash86

Coffman Katherine lsquolsquoEvidence on Self-Stereotyping and the Contribution ofIdeasrsquorsquo Quarterly Journal of Economics 129 (2014) 1625ndash1660

Cunningham Tom lsquolsquoComparisons and Choicersquorsquo mimeo Stockholm University2013

Diekman Amanda Alice Eagly and Patrick Kulesa lsquolsquoAccuracy and Bias in theStereotypes about the Social and Political Attitudes of Women and MenrsquorsquoJournal of Experimental Social Psychology 38 (2002) 268ndash282

Eccles Jacquelynne S Janis E Jacobs and Rena D Harold lsquolsquoGender RoleStereotypes Expectancy Effects and Parentsrsquo Socialization of GenderDifferencesrsquorsquo Journal of Social Issues 46 (1990) 183ndash201

Fryer Roland and Matthew Jackson lsquolsquoA Categorical Model of Cognition andBiased Decision-Makingrsquorsquo BE Journal of Theoretical Economics 8 (2008)1ndash42

Fryer Roland and Steven Levitt lsquolsquoAn Empirical Analysis of the Gender Gap inMathematicsrsquorsquo American Economic Journal Applied Economics 2 (2010)210ndash240

Gennaioli Nicola and Andrei Shleifer lsquolsquoWhat Comes to Mindrsquorsquo Quarterly Journalof Economics 125 (2010) 1399ndash1433

Gennaioli Nicola Andrei Shleifer and Robert Vishny lsquolsquoNeglected RisksFinancial Innovation and Financial Fragilityrsquorsquo Journal of FinancialEconomics 104 (2012) 452ndash468

Gilens Martin lsquolsquoRace and Poverty in America Public Misperceptions and theAmerican News Mediarsquorsquo Public Opinion Quarterly 60 (1996) 515ndash541

Glaeser Edward lsquolsquoThe Political Economy of Hatredrsquorsquo Quarterly Journal ofEconomics 120 (2005) 45ndash86

QUARTERLY JOURNAL OF ECONOMICS1792

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

Glover Dyland Amanda Pallais and William Pariente lsquolsquoDiscrimination as a Self-Fulfilling Prophecy Evidence from French Grocery Storesrsquorsquo mimeo HarvardUniversity 2015

Goldin Claudia Lawrence Katz and Ilyana Kuziemko lsquolsquoThe Homecoming ofAmerican College Women The Reversal of the College Gender GaprsquorsquoJournal of Economic Perspectives 20 (2006) 133ndash156

Graham Jesse Brian Nosek and Jonathan Haidt lsquolsquoThe Moral Stereotypes ofLiberals and Conservatives Exaggeration of Differences across thePolitical Spectrumrsquorsquo PLoS One 7 (2012) 1ndash13

Grether David lsquolsquoBayes Rule as a Descriptive Model The RepresentativenessHeuristicrsquorsquo Quarterly Journal of Economics 95 (1980) 537ndash557

Griffin Dale and Amos Tversky lsquolsquoThe Weighing of Evidence and theDeterminants of Confidencersquorsquo Cognitive Psychology 24 (1992) 411ndash435

Guiso Luigi Ferdinando Monte Paola Sapienza and Luigi Zingales lsquolsquoCultureGender and Mathrsquorsquo Science 320 (2008) 1164ndash1165

Hilton James and William Von Hippel lsquolsquoStereotypesrsquorsquo Annual Review ofPsychology 47 (1996) 237ndash271

Hyde Janet Sara Lindberg Marcia Linn Amy Ellis and Caroline WilliamslsquolsquoGender Similarities Characterize Math Performancersquorsquo Science 321 (2008)494ndash495

Judd Charles and Bernardette Park lsquolsquoDefinition and Assessment of Accuracy inSocial Stereotypesrsquorsquo Psychological Review 100 (1993) 109ndash128

Jussim Lee Jarret Crawford Stephanie Anglin John Chambers Sean Stevensand Florette Cohen lsquolsquoStereotype Accuracy One of the Largest and MostReplicable Effects in All of Social Psychologyrsquorsquo in The Handbook ofPrejudice Stereotyping and Discrimination Todd Nelson ed (MahwahNJ Lawrence Erlbaum 2015)

Kahneman Daniel and Amos Tversky lsquolsquoSubjective Probability A Judgment ofRepresentativenessrsquorsquo Cognitive Psychology 3 (1972) 430ndash454

mdashmdashmdash lsquolsquoOn the Psychology of Predictionrsquorsquo Psychological Review 80 (1973) 237ndash251

Kaplowitz Stan Bradley Fisher and Clifford Broman lsquolsquoHow Accurate ArePerceptions of Social Statistics about Blacks and Whitesrsquorsquo Public OpinionQuarterly 67 (2003) 237ndash243

Kersten Daniel Pascal Mamassian and Alan Yuille lsquolsquoObject Perception asBayesian Inferencersquorsquo Annual Review of Psychology 55 (2004) 271ndash304

Klein Richard Kate A Ratliff Michelangelo Vianello Reginald B Adams JrStepan Bahnik Michael J Bernstein Konrad Bocian Mark J BrandtBeach Brooks Claudia Chloe Brumbaugh Zeynep CemalcilarJesse Chandler Winnee Cheong William E Davis Thierry DevosMatthew Eisner Natalia Frankowska David Furrow Elisa Maria GallianiFred Hasselman Joshua A Hicks James F Hovermale S Jane HuntJeffrey R Huntsinger Hans IJzerman Melissa-Sue John Jennifer A Joy-Gaba Heather Barry Kappes Lacy E Krueger Jaime Kurtz CarmelA Levitan Robyn Mallett Wendy L Morris Anthony J Nelson JasonA Nier Grant Packard Ronaldo Pilati Abraham M RutchickKathleen Schmidt Jeanine L Skorinko Robert Smith Troy G SteinerJustin Storbeck Lyn M Van Swol Donna Thompson Anna van rsquot VeerLeigh Ann Vaughn Marek Vranka Aaron Wichman Julie A Woodzickaand Brian A Nosek lsquolsquoInvestigating Variation in Replicability A ManyLabs Replication Projectrsquorsquo Social Psychology 45 (2014) 142ndash152

Lundberg Shelly and Richard Startz lsquolsquoPrivate Discrimination and SocialIntervention in Competitive Labor Marketsrsquorsquo American Economic Review73 (1983) 340ndash347

Madon Stephanie Max Guyll Kathy Aboufadel Eulices Montiel Alison SmithPolly Palumbo and Lee Jussim lsquolsquoEthnic and National Stereotypes ThePrinceton Trilogy Revisited and Revisedrsquorsquo Personality and SocialPsychological Bulletin 27 (2001) 996ndash1010

Martin Carol lsquolsquoA Ratio Measure of Sex Stereotypingrsquorsquo Journal of Personality andSocial Psychology 52 (1987) 489ndash499

STEREOTYPES 1793

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

McCauley Clark Krishna Thangavelu and Paul Rozin lsquolsquoSex Stereotyping ofOccupations in Relation to Television Representations and Census FactsrsquorsquoBasic and Applied Social Psychology 9 (1988) 197ndash212

Mullainathan Sendhil lsquolsquoThinking through Categoriesrsquorsquo mimeo HarvardUniversity 2002

Ortoleva Pietro and Erik Snowberg lsquolsquoOverconfidence in Political BehaviorrsquorsquoAmerican Economic Review 105 (2015) 504ndash535

Phelps Edmund lsquolsquoThe Statistical Theory of Racism and Sexismrsquorsquo AmericanEconomic Review 62 (1972) 659ndash661

Pope Devin and Justin Sydnor lsquolsquoGeographic Variation in the Gender Differencesin Test Scoresrsquorsquo Journal of Economic Perspectives 24 (2010) 95ndash108

Rabin Matthew lsquolsquoInference by Believers in the Law of Small NumbersrsquorsquoQuarterly Journal of Economics 117 (2002) 775ndash816

Rabin Matthew and Joel Schrag lsquolsquoFirst Impressions Matter A Model ofConfirmatory Biasrsquorsquo Quarterly Journal of Economics 114 (1999) 37ndash82

Rabin Matthew and Dimitri Vayanos lsquolsquoThe Gamblerrsquos and Hot-Hand FallaciesTheory and Applicationsrsquorsquo Review of Economic Studies 77 (2010) 730ndash778

Reuben Ernesto Paola Sapienza and Luigi Zingales lsquolsquoHow Stereotypes ImpairWomenrsquos Careers in Sciencersquorsquo Proceedings of the National Academy ofSciences 111 (2014) 4403ndash4408

Rosch Eleanor lsquolsquoNatural Categoriesrsquorsquo Cognitive Psychology 4 (1973) 328ndash350Ryan Carey S lsquolsquoAccuracy of Black and White College Studentsrsquo In-Group and

Out-Group Stereotypesrsquorsquo Personality and Social Psychology Bulletin 22(1996) 1114ndash1127

Schneider David The Psychology of Stereotyping (New York Guilford Press2004)

Schneider David Albert Hastorf and Phoebe Ellsworth Person Perception(Reading MA Addison-Wesley 1979)

Shih Margaret Todd Pittinsky and Nalini Ambady lsquolsquoStereotype SusceptibilityIdentity Salience and Shifts in Quantitative Performancersquorsquo PsychologicalScience 10 (1999) 80ndash83

Shih Margaret Todd Pittinsky and Amy Trahan lsquolsquoDomain-Specific Effects ofStereotypes on Performancersquorsquo Self and Identity 5 (2006) 1ndash14

Steele Claude Whistling Vivaldi How Stereotypes Affect Us and What We CanDo (New York Norton 2010)

Tenenbaum Joshua and Thomas Griffiths lsquolsquoThe Rational Basis ofRepresentativenessrsquorsquo 23rd Annual Conference of the Cognitive ScienceSociety (2001) 1036ndash1041

Tversky Amos and Daniel Kahneman lsquolsquoExtensional versus Intuitive ReasoningThe Conjunction Fallacy in Probability Judgmentrsquorsquo Psychological Review 90(1983) 293ndash315

Weinberger Catherin lsquolsquoIs the Science and Engineering Workforce Drawn fromthe Far Upper Tail of the Math Ability Distributionrsquorsquo mimeo UCSB 2005

Westfall Jacob Leaf Van Boven John Chambers and Charles Judd lsquolsquoPerceivingPolitical Polarization in the United States Party Identity Strength andAttitude Extremity Exacerbate the Perceived Partisan DividersquorsquoPsychological Science 10 (2015) 145ndash158

Wolsko Christopher Bernadette Park Charles Judd and Bernd WittenbrinklsquolsquoFraming Interethnic Ideology Effects of Multicultural and Color-BlindPerspectives on Judgments of Groups and Individualsrsquorsquo Journal ofPersonality and Social Psychology 78 (2000) 635ndash654

QUARTERLY JOURNAL OF ECONOMICS1794

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ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

Page 36: I. Introduction · uneducated at the beginning of the 20th century, and as high achievers at the beginning of the 21st (Madon et al. 2001). Social science has produced three broad

the comparison group EethtjGTHORN is also a significant predictor ofE

BethtjGTHORN with the predicted negative signAlthough these results provide strong evidence of context

dependence and are consistent with our model they do not pindown a role for representativeness of types Our next test relatesthe magnitude of representativeness of tail types to the magni-tude of belief distortions

To this end we implement the regressions in equations (6)and (7) Following Proposition 4 we compute the average repre-

sentativeness of tail types for conservatives RconsH frac14

PtT2tconsPtT2tlib

We

again test the hypothesis that RconsH is a significant predictor of Est

ethtjconsTHORN with a positive sign and a predictor of EstethtjlibTHORN with a

negative sign Table II shows that conditional on true mean RconsH

predicts believed mean for each group G as expected The firstthree specifications display the results for predicting beliefs heldabout conservatives In both data sets the average representa-tiveness of tail types for conservatives is a significant positivepredictor of beliefs held about conservatives The final three spe-cifications display the results for predicting beliefs held about

FIGURE IV

Exaggeration of Differences

QUARTERLY JOURNAL OF ECONOMICS1788

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httpqjeoxfordjournalsorgD

ownloaded from

liberals We find that the average representativeness of tail typesfor conservatives is a negative predictor of beliefs held about lib-erals This effect is significant in the GNH data and marginallysignificant in the ANES data

We present several additional results in Online Appendix GTo further examine the role of representativeness in driving be-liefs we first show the results of Table II carry through when we

TABLE II

AVERAGE REPRESENTATIVENESS OF TAIL POSITIONS PREDICTS BELIEFS

OLS Predicting Believed Mean of Group G for Each Issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position

of group G for issue

078 024 051 072 018 041

(006) (008) (009) (005) (005) (010)

Avg rep of tail types for

conservatives RconsH

019 055 025 014 012 024

(007) (022) (008) (006) (007) (005)

Constant 101 260 184 093 271 201

(026) (045) (029) (022) (025) (032)

R2 082 048 060 091 031 070

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

TABLE I

INFORMATION ABOUT ndashG PREDICTS BELIEFS ABOUT G

OLS predicting believed mean of group G for each issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position of

conservatives for issue

102 098 096 021 019 025

(0097) (0133) (0076) (0060) (0116) (0060)

True mean position of

liberals for issue

035 086 058 0987 039 073

(0106) (0134) (0131) (0066) (0106) (0135)

Constant 151 335 235 069 258 156

(0195) (0269) (0279) (0122) (0249) (0270)

R2 083 053 066 092 032 068

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

STEREOTYPES 1789

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ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

control for the average likelihood on the tail positions (see Table A4in Online Appendix G) Most tellingly we use the model to predictbeliefs across issues and compare those to the data For simplicitywe use the rank-based truncation specification to predict mean be-liefs when stereotypes include the d most representative types ford frac14 1 T We compare these predictions to those of a model inwhich beliefs are obtained by restricting the distribution to the dmost likely types Our benchmark for both models is predicting thebelieved mean from the entire distribution where d = T We showthat the predictions of the rank-based truncation model with d = 4or 5 compare favorably to both a likelihood-based truncation model(with any d) and the accurate beliefs benchmark Interestingly thisresult suggests that stereotypical beliefs are well approximated byneglecting the least representative types (as opposed to focusingonly on the most representative types) and so represent a moderatethough systematic departure from the standard benchmarkFinally we show that the results we document above hold forboth beliefs held by conservatives and beliefs held by liberals (seeTables A9 A10 and A11 in Online Appendix G)

V Conclusion

We present a model of stereotypical thinking in which DMsmaking predictions about a group overweight the grouprsquos mostdistinctive types These overweighted types are not the mostlikely ones given the DMrsquos data but the most representativeones in the sense of being the most diagnostic of the group rela-tive to other groups Representativeness implies that what ismost distinctive of a group depends on what group it is comparedwith We present experimental evidence that confirms this con-text dependence in recall-based assessments of groups Finallywe evaluated the predictions of the model using political data fromexisting large-scale surveys We find context dependence to be akey feature of beliefs Given the richness of the political data wecan go a step further and identify a role for representativeness inparticular As the representativeness of tail types increases beliefsof a group are distorted in the direction of that tail

Our approach provides a parsimonious and psychologicallyfounded account of how DMs generate simplified representationsof reality from social groups to stock returns and offers a unifiedaccount of disparate pieces of evidence relating to this type of

QUARTERLY JOURNAL OF ECONOMICS1790

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

uncertainty The model captures the central fact that stereotypeshighlight the greatest difference between groups thus explainingwhy some stereotypes are very accurate while others lack valid-ity Still stereotypes often have a kernel of truth when they arebased on systematicmdasheven if smallmdashdifferences between groupsThis logic allows us to describe a number of heuristics and psy-chological biases many of which arise in the context of predictionproblems Generically our model generates overreaction to diag-nostic information

Our model is based on representativeness and does not cap-ture all the features of stereotypical thinking However it cap-tures perhaps the central feature when we think of a group wefocus on what is most distinctive about it and neglect or under-weight the rest

Saeuroıd Business School University of Oxford

Ohio State University and Harvard Business School

Universita Bocconi and Innocenzo Gasparini Institute

for Economic Research

Harvard University

Supplementary Material

An Online Appendix for this article can be found at QJEonline (qjeoxfordjournalorg)

References

Adorno Theodor Else Frenkel-Brunswik Daniel Levinson and Nevitt SanfordThe Authoritarian Personality (New York Harper amp Row 1950)

Arrow Kenneth lsquolsquoThe Theory of Discriminationrsquorsquo in Discrimination in LaborMarkets Orley Ashenfelter and Albert Rees eds (Princeton NJPrinceton University Press 1973)

Ashton Michael and Victoria Esses lsquolsquoStereotype Accuracy Estimating theAcademic Performance of Ethnic Groupsrsquorsquo Personality and SocialPsychology Bulletin 25 (1999) 225ndash236

Barberis Nicholas Andrei Shleifer and Robert Vishny lsquolsquoA Model of InvestorSentimentrsquorsquo Journal of Financial Economics 49 (1998) 307ndash343

Bayer Sylvia lsquolsquoThe Accuracy of Academic Gender Stereotypesrsquorsquo Sex Roles 40(1999) 787ndash813

Benjamin Dan James Choi and Joshua Strickland lsquolsquoSocial Identity andPreferencesrsquorsquo American Economic Review 100 (2010) 1913ndash1928

Benjamin Dan Matthew Rabin and Collin Raymond lsquolsquoA Model of Non-Belief inthe Law of Large Numbersrsquorsquo Journal of the European Economic Association15 (2015) 515ndash544

Bertrand Marianne lsquolsquoNew Perspectives on Genderrsquorsquo Handbook of LaborEconomics 4 (2011) 1543ndash1590

Bodoh-Creed Aaron Dan Benjamin and Matthew Rabin lsquolsquoThe Dynamics of Base-Rate Neglectrsquorsquo mimeo Haas Business School 2013

STEREOTYPES 1791

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

Bohnet Iris Alexandra van Geen and Max Bazerman lsquolsquoWhen PerformanceTrumps Gender Bias Joint versus Separate Evaluationrsquorsquo ManagementScience 5 (2016) 1225ndash1234

Bordalo Pedro Nicola Gennaioli and Andrei Shleifer lsquolsquoSalience Theory of Choiceunder Riskrsquorsquo Quarterly Journal of Economics 127 (2012) 1243ndash1285

mdashmdashmdash lsquolsquoSalience and Consumer Choicersquorsquo Journal of Political Economy 121(2013) 803ndash843

Briton Nancy and Judith Hall lsquolsquoBeliefs about Female and Male NonverbalCommunicationrsquorsquo Sex Roles 32 (1995) 79ndash90

Buser Thomas Muriel Niederle and Hessel Oosterbeek lsquolsquoGenderCompetitiveness and Career Choicesrsquorsquo Quarterly Journal of Economics 129(2014) 1409ndash1447

Carrell Scott Marianne Page and James West lsquolsquoSex and Science How ProfessorGender Perpetuates the Gender Gaprsquorsquo Quarterly Journal of Economics 125(2010) 1101ndash1144

Chambers John and Darya Melnyk lsquolsquoWhy Do I Hate Thee ConflictMisperceptions and Intergroup Mistrustrsquorsquo Personality and SocialPsychology Bulletin 32 (2006) 1295ndash1311

Chan Wayne Robert R McCrae Filip De Fruyt Lee Jussim CorinnaE Lockenhoff Marleen De Bolle Paul T Costa Jr Angelina R SutinAnu Realo Juri Allik Katsuharu Nakazato Yoshiko ShimonakaMartina Hrebıckova Sylvie Graf Michelle Yik Marina Brunner-SciarraNora Leibovich De Figueora Vanina Schmidt Chang-kyo Ahn Hyun-nie Ahn Maria E Aguilar-Vafaie Jerzy Siuta Barbara SzmigielskaThomas R Cain Janet T Crawford Khairul Anwar Mastor Jean-Pierre Rolland Florence Nansubuga Daniel R MiramontezVeronica Benet-Martınez Jerome Rossier Denis Bratko Iris MarusicJamin Halberstadt Mami Yamaguchi Goran Knezevic Thomas A MartinMirona Gheorghiu Peter B Smith Claudio Barbaranelli Lei WangJane Shakespeare-Finch Margarida P Lima Waldemar KlinkoszAndrzej Sekowski Lidia Alcalay Franco Simonetti Tatyana V AvdeyevaV S Pramila and Antonio Terracciano lsquolsquoStereotypes of Age Differences inPersonality Traits Universal and Accuratersquorsquo Journal of Personality andSocial Psychology 103 (2012) 1050ndash1066

Chen Yan Sherry Xin Liu Tracy Xiao and Margaret Shih lsquolsquoWhich Hat to WearImpact of Natural Identities on Coordination and Cooperationrsquorsquo Games andEconomic Behavior 84 (2014) 58ndash86

Coffman Katherine lsquolsquoEvidence on Self-Stereotyping and the Contribution ofIdeasrsquorsquo Quarterly Journal of Economics 129 (2014) 1625ndash1660

Cunningham Tom lsquolsquoComparisons and Choicersquorsquo mimeo Stockholm University2013

Diekman Amanda Alice Eagly and Patrick Kulesa lsquolsquoAccuracy and Bias in theStereotypes about the Social and Political Attitudes of Women and MenrsquorsquoJournal of Experimental Social Psychology 38 (2002) 268ndash282

Eccles Jacquelynne S Janis E Jacobs and Rena D Harold lsquolsquoGender RoleStereotypes Expectancy Effects and Parentsrsquo Socialization of GenderDifferencesrsquorsquo Journal of Social Issues 46 (1990) 183ndash201

Fryer Roland and Matthew Jackson lsquolsquoA Categorical Model of Cognition andBiased Decision-Makingrsquorsquo BE Journal of Theoretical Economics 8 (2008)1ndash42

Fryer Roland and Steven Levitt lsquolsquoAn Empirical Analysis of the Gender Gap inMathematicsrsquorsquo American Economic Journal Applied Economics 2 (2010)210ndash240

Gennaioli Nicola and Andrei Shleifer lsquolsquoWhat Comes to Mindrsquorsquo Quarterly Journalof Economics 125 (2010) 1399ndash1433

Gennaioli Nicola Andrei Shleifer and Robert Vishny lsquolsquoNeglected RisksFinancial Innovation and Financial Fragilityrsquorsquo Journal of FinancialEconomics 104 (2012) 452ndash468

Gilens Martin lsquolsquoRace and Poverty in America Public Misperceptions and theAmerican News Mediarsquorsquo Public Opinion Quarterly 60 (1996) 515ndash541

Glaeser Edward lsquolsquoThe Political Economy of Hatredrsquorsquo Quarterly Journal ofEconomics 120 (2005) 45ndash86

QUARTERLY JOURNAL OF ECONOMICS1792

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

Glover Dyland Amanda Pallais and William Pariente lsquolsquoDiscrimination as a Self-Fulfilling Prophecy Evidence from French Grocery Storesrsquorsquo mimeo HarvardUniversity 2015

Goldin Claudia Lawrence Katz and Ilyana Kuziemko lsquolsquoThe Homecoming ofAmerican College Women The Reversal of the College Gender GaprsquorsquoJournal of Economic Perspectives 20 (2006) 133ndash156

Graham Jesse Brian Nosek and Jonathan Haidt lsquolsquoThe Moral Stereotypes ofLiberals and Conservatives Exaggeration of Differences across thePolitical Spectrumrsquorsquo PLoS One 7 (2012) 1ndash13

Grether David lsquolsquoBayes Rule as a Descriptive Model The RepresentativenessHeuristicrsquorsquo Quarterly Journal of Economics 95 (1980) 537ndash557

Griffin Dale and Amos Tversky lsquolsquoThe Weighing of Evidence and theDeterminants of Confidencersquorsquo Cognitive Psychology 24 (1992) 411ndash435

Guiso Luigi Ferdinando Monte Paola Sapienza and Luigi Zingales lsquolsquoCultureGender and Mathrsquorsquo Science 320 (2008) 1164ndash1165

Hilton James and William Von Hippel lsquolsquoStereotypesrsquorsquo Annual Review ofPsychology 47 (1996) 237ndash271

Hyde Janet Sara Lindberg Marcia Linn Amy Ellis and Caroline WilliamslsquolsquoGender Similarities Characterize Math Performancersquorsquo Science 321 (2008)494ndash495

Judd Charles and Bernardette Park lsquolsquoDefinition and Assessment of Accuracy inSocial Stereotypesrsquorsquo Psychological Review 100 (1993) 109ndash128

Jussim Lee Jarret Crawford Stephanie Anglin John Chambers Sean Stevensand Florette Cohen lsquolsquoStereotype Accuracy One of the Largest and MostReplicable Effects in All of Social Psychologyrsquorsquo in The Handbook ofPrejudice Stereotyping and Discrimination Todd Nelson ed (MahwahNJ Lawrence Erlbaum 2015)

Kahneman Daniel and Amos Tversky lsquolsquoSubjective Probability A Judgment ofRepresentativenessrsquorsquo Cognitive Psychology 3 (1972) 430ndash454

mdashmdashmdash lsquolsquoOn the Psychology of Predictionrsquorsquo Psychological Review 80 (1973) 237ndash251

Kaplowitz Stan Bradley Fisher and Clifford Broman lsquolsquoHow Accurate ArePerceptions of Social Statistics about Blacks and Whitesrsquorsquo Public OpinionQuarterly 67 (2003) 237ndash243

Kersten Daniel Pascal Mamassian and Alan Yuille lsquolsquoObject Perception asBayesian Inferencersquorsquo Annual Review of Psychology 55 (2004) 271ndash304

Klein Richard Kate A Ratliff Michelangelo Vianello Reginald B Adams JrStepan Bahnik Michael J Bernstein Konrad Bocian Mark J BrandtBeach Brooks Claudia Chloe Brumbaugh Zeynep CemalcilarJesse Chandler Winnee Cheong William E Davis Thierry DevosMatthew Eisner Natalia Frankowska David Furrow Elisa Maria GallianiFred Hasselman Joshua A Hicks James F Hovermale S Jane HuntJeffrey R Huntsinger Hans IJzerman Melissa-Sue John Jennifer A Joy-Gaba Heather Barry Kappes Lacy E Krueger Jaime Kurtz CarmelA Levitan Robyn Mallett Wendy L Morris Anthony J Nelson JasonA Nier Grant Packard Ronaldo Pilati Abraham M RutchickKathleen Schmidt Jeanine L Skorinko Robert Smith Troy G SteinerJustin Storbeck Lyn M Van Swol Donna Thompson Anna van rsquot VeerLeigh Ann Vaughn Marek Vranka Aaron Wichman Julie A Woodzickaand Brian A Nosek lsquolsquoInvestigating Variation in Replicability A ManyLabs Replication Projectrsquorsquo Social Psychology 45 (2014) 142ndash152

Lundberg Shelly and Richard Startz lsquolsquoPrivate Discrimination and SocialIntervention in Competitive Labor Marketsrsquorsquo American Economic Review73 (1983) 340ndash347

Madon Stephanie Max Guyll Kathy Aboufadel Eulices Montiel Alison SmithPolly Palumbo and Lee Jussim lsquolsquoEthnic and National Stereotypes ThePrinceton Trilogy Revisited and Revisedrsquorsquo Personality and SocialPsychological Bulletin 27 (2001) 996ndash1010

Martin Carol lsquolsquoA Ratio Measure of Sex Stereotypingrsquorsquo Journal of Personality andSocial Psychology 52 (1987) 489ndash499

STEREOTYPES 1793

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

McCauley Clark Krishna Thangavelu and Paul Rozin lsquolsquoSex Stereotyping ofOccupations in Relation to Television Representations and Census FactsrsquorsquoBasic and Applied Social Psychology 9 (1988) 197ndash212

Mullainathan Sendhil lsquolsquoThinking through Categoriesrsquorsquo mimeo HarvardUniversity 2002

Ortoleva Pietro and Erik Snowberg lsquolsquoOverconfidence in Political BehaviorrsquorsquoAmerican Economic Review 105 (2015) 504ndash535

Phelps Edmund lsquolsquoThe Statistical Theory of Racism and Sexismrsquorsquo AmericanEconomic Review 62 (1972) 659ndash661

Pope Devin and Justin Sydnor lsquolsquoGeographic Variation in the Gender Differencesin Test Scoresrsquorsquo Journal of Economic Perspectives 24 (2010) 95ndash108

Rabin Matthew lsquolsquoInference by Believers in the Law of Small NumbersrsquorsquoQuarterly Journal of Economics 117 (2002) 775ndash816

Rabin Matthew and Joel Schrag lsquolsquoFirst Impressions Matter A Model ofConfirmatory Biasrsquorsquo Quarterly Journal of Economics 114 (1999) 37ndash82

Rabin Matthew and Dimitri Vayanos lsquolsquoThe Gamblerrsquos and Hot-Hand FallaciesTheory and Applicationsrsquorsquo Review of Economic Studies 77 (2010) 730ndash778

Reuben Ernesto Paola Sapienza and Luigi Zingales lsquolsquoHow Stereotypes ImpairWomenrsquos Careers in Sciencersquorsquo Proceedings of the National Academy ofSciences 111 (2014) 4403ndash4408

Rosch Eleanor lsquolsquoNatural Categoriesrsquorsquo Cognitive Psychology 4 (1973) 328ndash350Ryan Carey S lsquolsquoAccuracy of Black and White College Studentsrsquo In-Group and

Out-Group Stereotypesrsquorsquo Personality and Social Psychology Bulletin 22(1996) 1114ndash1127

Schneider David The Psychology of Stereotyping (New York Guilford Press2004)

Schneider David Albert Hastorf and Phoebe Ellsworth Person Perception(Reading MA Addison-Wesley 1979)

Shih Margaret Todd Pittinsky and Nalini Ambady lsquolsquoStereotype SusceptibilityIdentity Salience and Shifts in Quantitative Performancersquorsquo PsychologicalScience 10 (1999) 80ndash83

Shih Margaret Todd Pittinsky and Amy Trahan lsquolsquoDomain-Specific Effects ofStereotypes on Performancersquorsquo Self and Identity 5 (2006) 1ndash14

Steele Claude Whistling Vivaldi How Stereotypes Affect Us and What We CanDo (New York Norton 2010)

Tenenbaum Joshua and Thomas Griffiths lsquolsquoThe Rational Basis ofRepresentativenessrsquorsquo 23rd Annual Conference of the Cognitive ScienceSociety (2001) 1036ndash1041

Tversky Amos and Daniel Kahneman lsquolsquoExtensional versus Intuitive ReasoningThe Conjunction Fallacy in Probability Judgmentrsquorsquo Psychological Review 90(1983) 293ndash315

Weinberger Catherin lsquolsquoIs the Science and Engineering Workforce Drawn fromthe Far Upper Tail of the Math Ability Distributionrsquorsquo mimeo UCSB 2005

Westfall Jacob Leaf Van Boven John Chambers and Charles Judd lsquolsquoPerceivingPolitical Polarization in the United States Party Identity Strength andAttitude Extremity Exacerbate the Perceived Partisan DividersquorsquoPsychological Science 10 (2015) 145ndash158

Wolsko Christopher Bernadette Park Charles Judd and Bernd WittenbrinklsquolsquoFraming Interethnic Ideology Effects of Multicultural and Color-BlindPerspectives on Judgments of Groups and Individualsrsquorsquo Journal ofPersonality and Social Psychology 78 (2000) 635ndash654

QUARTERLY JOURNAL OF ECONOMICS1794

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

Page 37: I. Introduction · uneducated at the beginning of the 20th century, and as high achievers at the beginning of the 21st (Madon et al. 2001). Social science has produced three broad

liberals We find that the average representativeness of tail typesfor conservatives is a negative predictor of beliefs held about lib-erals This effect is significant in the GNH data and marginallysignificant in the ANES data

We present several additional results in Online Appendix GTo further examine the role of representativeness in driving be-liefs we first show the results of Table II carry through when we

TABLE II

AVERAGE REPRESENTATIVENESS OF TAIL POSITIONS PREDICTS BELIEFS

OLS Predicting Believed Mean of Group G for Each Issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position

of group G for issue

078 024 051 072 018 041

(006) (008) (009) (005) (005) (010)

Avg rep of tail types for

conservatives RconsH

019 055 025 014 012 024

(007) (022) (008) (006) (007) (005)

Constant 101 260 184 093 271 201

(026) (045) (029) (022) (025) (032)

R2 082 048 060 091 031 070

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

TABLE I

INFORMATION ABOUT ndashG PREDICTS BELIEFS ABOUT G

OLS predicting believed mean of group G for each issue

G = conservatives G = liberals

GNH ANES Pooled GNH ANES Pooled

True mean position of

conservatives for issue

102 098 096 021 019 025

(0097) (0133) (0076) (0060) (0116) (0060)

True mean position of

liberals for issue

035 086 058 0987 039 073

(0106) (0134) (0131) (0066) (0106) (0135)

Constant 151 335 235 069 258 156

(0195) (0269) (0279) (0122) (0249) (0270)

R2 083 053 066 092 032 068

Obs (clusters) 45 (45) 66 (10) 111 (55) 45 (45) 66 (10) 111 (55)

Notes Standard errors in parentheses clustered at the issue level and denote sig-nificance at the 10 5 1 and 01 levels respectively In pooled specifications we include a dummyvariable indicating whether the observation came from ANES data set

STEREOTYPES 1789

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

control for the average likelihood on the tail positions (see Table A4in Online Appendix G) Most tellingly we use the model to predictbeliefs across issues and compare those to the data For simplicitywe use the rank-based truncation specification to predict mean be-liefs when stereotypes include the d most representative types ford frac14 1 T We compare these predictions to those of a model inwhich beliefs are obtained by restricting the distribution to the dmost likely types Our benchmark for both models is predicting thebelieved mean from the entire distribution where d = T We showthat the predictions of the rank-based truncation model with d = 4or 5 compare favorably to both a likelihood-based truncation model(with any d) and the accurate beliefs benchmark Interestingly thisresult suggests that stereotypical beliefs are well approximated byneglecting the least representative types (as opposed to focusingonly on the most representative types) and so represent a moderatethough systematic departure from the standard benchmarkFinally we show that the results we document above hold forboth beliefs held by conservatives and beliefs held by liberals (seeTables A9 A10 and A11 in Online Appendix G)

V Conclusion

We present a model of stereotypical thinking in which DMsmaking predictions about a group overweight the grouprsquos mostdistinctive types These overweighted types are not the mostlikely ones given the DMrsquos data but the most representativeones in the sense of being the most diagnostic of the group rela-tive to other groups Representativeness implies that what ismost distinctive of a group depends on what group it is comparedwith We present experimental evidence that confirms this con-text dependence in recall-based assessments of groups Finallywe evaluated the predictions of the model using political data fromexisting large-scale surveys We find context dependence to be akey feature of beliefs Given the richness of the political data wecan go a step further and identify a role for representativeness inparticular As the representativeness of tail types increases beliefsof a group are distorted in the direction of that tail

Our approach provides a parsimonious and psychologicallyfounded account of how DMs generate simplified representationsof reality from social groups to stock returns and offers a unifiedaccount of disparate pieces of evidence relating to this type of

QUARTERLY JOURNAL OF ECONOMICS1790

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

uncertainty The model captures the central fact that stereotypeshighlight the greatest difference between groups thus explainingwhy some stereotypes are very accurate while others lack valid-ity Still stereotypes often have a kernel of truth when they arebased on systematicmdasheven if smallmdashdifferences between groupsThis logic allows us to describe a number of heuristics and psy-chological biases many of which arise in the context of predictionproblems Generically our model generates overreaction to diag-nostic information

Our model is based on representativeness and does not cap-ture all the features of stereotypical thinking However it cap-tures perhaps the central feature when we think of a group wefocus on what is most distinctive about it and neglect or under-weight the rest

Saeuroıd Business School University of Oxford

Ohio State University and Harvard Business School

Universita Bocconi and Innocenzo Gasparini Institute

for Economic Research

Harvard University

Supplementary Material

An Online Appendix for this article can be found at QJEonline (qjeoxfordjournalorg)

References

Adorno Theodor Else Frenkel-Brunswik Daniel Levinson and Nevitt SanfordThe Authoritarian Personality (New York Harper amp Row 1950)

Arrow Kenneth lsquolsquoThe Theory of Discriminationrsquorsquo in Discrimination in LaborMarkets Orley Ashenfelter and Albert Rees eds (Princeton NJPrinceton University Press 1973)

Ashton Michael and Victoria Esses lsquolsquoStereotype Accuracy Estimating theAcademic Performance of Ethnic Groupsrsquorsquo Personality and SocialPsychology Bulletin 25 (1999) 225ndash236

Barberis Nicholas Andrei Shleifer and Robert Vishny lsquolsquoA Model of InvestorSentimentrsquorsquo Journal of Financial Economics 49 (1998) 307ndash343

Bayer Sylvia lsquolsquoThe Accuracy of Academic Gender Stereotypesrsquorsquo Sex Roles 40(1999) 787ndash813

Benjamin Dan James Choi and Joshua Strickland lsquolsquoSocial Identity andPreferencesrsquorsquo American Economic Review 100 (2010) 1913ndash1928

Benjamin Dan Matthew Rabin and Collin Raymond lsquolsquoA Model of Non-Belief inthe Law of Large Numbersrsquorsquo Journal of the European Economic Association15 (2015) 515ndash544

Bertrand Marianne lsquolsquoNew Perspectives on Genderrsquorsquo Handbook of LaborEconomics 4 (2011) 1543ndash1590

Bodoh-Creed Aaron Dan Benjamin and Matthew Rabin lsquolsquoThe Dynamics of Base-Rate Neglectrsquorsquo mimeo Haas Business School 2013

STEREOTYPES 1791

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

Bohnet Iris Alexandra van Geen and Max Bazerman lsquolsquoWhen PerformanceTrumps Gender Bias Joint versus Separate Evaluationrsquorsquo ManagementScience 5 (2016) 1225ndash1234

Bordalo Pedro Nicola Gennaioli and Andrei Shleifer lsquolsquoSalience Theory of Choiceunder Riskrsquorsquo Quarterly Journal of Economics 127 (2012) 1243ndash1285

mdashmdashmdash lsquolsquoSalience and Consumer Choicersquorsquo Journal of Political Economy 121(2013) 803ndash843

Briton Nancy and Judith Hall lsquolsquoBeliefs about Female and Male NonverbalCommunicationrsquorsquo Sex Roles 32 (1995) 79ndash90

Buser Thomas Muriel Niederle and Hessel Oosterbeek lsquolsquoGenderCompetitiveness and Career Choicesrsquorsquo Quarterly Journal of Economics 129(2014) 1409ndash1447

Carrell Scott Marianne Page and James West lsquolsquoSex and Science How ProfessorGender Perpetuates the Gender Gaprsquorsquo Quarterly Journal of Economics 125(2010) 1101ndash1144

Chambers John and Darya Melnyk lsquolsquoWhy Do I Hate Thee ConflictMisperceptions and Intergroup Mistrustrsquorsquo Personality and SocialPsychology Bulletin 32 (2006) 1295ndash1311

Chan Wayne Robert R McCrae Filip De Fruyt Lee Jussim CorinnaE Lockenhoff Marleen De Bolle Paul T Costa Jr Angelina R SutinAnu Realo Juri Allik Katsuharu Nakazato Yoshiko ShimonakaMartina Hrebıckova Sylvie Graf Michelle Yik Marina Brunner-SciarraNora Leibovich De Figueora Vanina Schmidt Chang-kyo Ahn Hyun-nie Ahn Maria E Aguilar-Vafaie Jerzy Siuta Barbara SzmigielskaThomas R Cain Janet T Crawford Khairul Anwar Mastor Jean-Pierre Rolland Florence Nansubuga Daniel R MiramontezVeronica Benet-Martınez Jerome Rossier Denis Bratko Iris MarusicJamin Halberstadt Mami Yamaguchi Goran Knezevic Thomas A MartinMirona Gheorghiu Peter B Smith Claudio Barbaranelli Lei WangJane Shakespeare-Finch Margarida P Lima Waldemar KlinkoszAndrzej Sekowski Lidia Alcalay Franco Simonetti Tatyana V AvdeyevaV S Pramila and Antonio Terracciano lsquolsquoStereotypes of Age Differences inPersonality Traits Universal and Accuratersquorsquo Journal of Personality andSocial Psychology 103 (2012) 1050ndash1066

Chen Yan Sherry Xin Liu Tracy Xiao and Margaret Shih lsquolsquoWhich Hat to WearImpact of Natural Identities on Coordination and Cooperationrsquorsquo Games andEconomic Behavior 84 (2014) 58ndash86

Coffman Katherine lsquolsquoEvidence on Self-Stereotyping and the Contribution ofIdeasrsquorsquo Quarterly Journal of Economics 129 (2014) 1625ndash1660

Cunningham Tom lsquolsquoComparisons and Choicersquorsquo mimeo Stockholm University2013

Diekman Amanda Alice Eagly and Patrick Kulesa lsquolsquoAccuracy and Bias in theStereotypes about the Social and Political Attitudes of Women and MenrsquorsquoJournal of Experimental Social Psychology 38 (2002) 268ndash282

Eccles Jacquelynne S Janis E Jacobs and Rena D Harold lsquolsquoGender RoleStereotypes Expectancy Effects and Parentsrsquo Socialization of GenderDifferencesrsquorsquo Journal of Social Issues 46 (1990) 183ndash201

Fryer Roland and Matthew Jackson lsquolsquoA Categorical Model of Cognition andBiased Decision-Makingrsquorsquo BE Journal of Theoretical Economics 8 (2008)1ndash42

Fryer Roland and Steven Levitt lsquolsquoAn Empirical Analysis of the Gender Gap inMathematicsrsquorsquo American Economic Journal Applied Economics 2 (2010)210ndash240

Gennaioli Nicola and Andrei Shleifer lsquolsquoWhat Comes to Mindrsquorsquo Quarterly Journalof Economics 125 (2010) 1399ndash1433

Gennaioli Nicola Andrei Shleifer and Robert Vishny lsquolsquoNeglected RisksFinancial Innovation and Financial Fragilityrsquorsquo Journal of FinancialEconomics 104 (2012) 452ndash468

Gilens Martin lsquolsquoRace and Poverty in America Public Misperceptions and theAmerican News Mediarsquorsquo Public Opinion Quarterly 60 (1996) 515ndash541

Glaeser Edward lsquolsquoThe Political Economy of Hatredrsquorsquo Quarterly Journal ofEconomics 120 (2005) 45ndash86

QUARTERLY JOURNAL OF ECONOMICS1792

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

Glover Dyland Amanda Pallais and William Pariente lsquolsquoDiscrimination as a Self-Fulfilling Prophecy Evidence from French Grocery Storesrsquorsquo mimeo HarvardUniversity 2015

Goldin Claudia Lawrence Katz and Ilyana Kuziemko lsquolsquoThe Homecoming ofAmerican College Women The Reversal of the College Gender GaprsquorsquoJournal of Economic Perspectives 20 (2006) 133ndash156

Graham Jesse Brian Nosek and Jonathan Haidt lsquolsquoThe Moral Stereotypes ofLiberals and Conservatives Exaggeration of Differences across thePolitical Spectrumrsquorsquo PLoS One 7 (2012) 1ndash13

Grether David lsquolsquoBayes Rule as a Descriptive Model The RepresentativenessHeuristicrsquorsquo Quarterly Journal of Economics 95 (1980) 537ndash557

Griffin Dale and Amos Tversky lsquolsquoThe Weighing of Evidence and theDeterminants of Confidencersquorsquo Cognitive Psychology 24 (1992) 411ndash435

Guiso Luigi Ferdinando Monte Paola Sapienza and Luigi Zingales lsquolsquoCultureGender and Mathrsquorsquo Science 320 (2008) 1164ndash1165

Hilton James and William Von Hippel lsquolsquoStereotypesrsquorsquo Annual Review ofPsychology 47 (1996) 237ndash271

Hyde Janet Sara Lindberg Marcia Linn Amy Ellis and Caroline WilliamslsquolsquoGender Similarities Characterize Math Performancersquorsquo Science 321 (2008)494ndash495

Judd Charles and Bernardette Park lsquolsquoDefinition and Assessment of Accuracy inSocial Stereotypesrsquorsquo Psychological Review 100 (1993) 109ndash128

Jussim Lee Jarret Crawford Stephanie Anglin John Chambers Sean Stevensand Florette Cohen lsquolsquoStereotype Accuracy One of the Largest and MostReplicable Effects in All of Social Psychologyrsquorsquo in The Handbook ofPrejudice Stereotyping and Discrimination Todd Nelson ed (MahwahNJ Lawrence Erlbaum 2015)

Kahneman Daniel and Amos Tversky lsquolsquoSubjective Probability A Judgment ofRepresentativenessrsquorsquo Cognitive Psychology 3 (1972) 430ndash454

mdashmdashmdash lsquolsquoOn the Psychology of Predictionrsquorsquo Psychological Review 80 (1973) 237ndash251

Kaplowitz Stan Bradley Fisher and Clifford Broman lsquolsquoHow Accurate ArePerceptions of Social Statistics about Blacks and Whitesrsquorsquo Public OpinionQuarterly 67 (2003) 237ndash243

Kersten Daniel Pascal Mamassian and Alan Yuille lsquolsquoObject Perception asBayesian Inferencersquorsquo Annual Review of Psychology 55 (2004) 271ndash304

Klein Richard Kate A Ratliff Michelangelo Vianello Reginald B Adams JrStepan Bahnik Michael J Bernstein Konrad Bocian Mark J BrandtBeach Brooks Claudia Chloe Brumbaugh Zeynep CemalcilarJesse Chandler Winnee Cheong William E Davis Thierry DevosMatthew Eisner Natalia Frankowska David Furrow Elisa Maria GallianiFred Hasselman Joshua A Hicks James F Hovermale S Jane HuntJeffrey R Huntsinger Hans IJzerman Melissa-Sue John Jennifer A Joy-Gaba Heather Barry Kappes Lacy E Krueger Jaime Kurtz CarmelA Levitan Robyn Mallett Wendy L Morris Anthony J Nelson JasonA Nier Grant Packard Ronaldo Pilati Abraham M RutchickKathleen Schmidt Jeanine L Skorinko Robert Smith Troy G SteinerJustin Storbeck Lyn M Van Swol Donna Thompson Anna van rsquot VeerLeigh Ann Vaughn Marek Vranka Aaron Wichman Julie A Woodzickaand Brian A Nosek lsquolsquoInvestigating Variation in Replicability A ManyLabs Replication Projectrsquorsquo Social Psychology 45 (2014) 142ndash152

Lundberg Shelly and Richard Startz lsquolsquoPrivate Discrimination and SocialIntervention in Competitive Labor Marketsrsquorsquo American Economic Review73 (1983) 340ndash347

Madon Stephanie Max Guyll Kathy Aboufadel Eulices Montiel Alison SmithPolly Palumbo and Lee Jussim lsquolsquoEthnic and National Stereotypes ThePrinceton Trilogy Revisited and Revisedrsquorsquo Personality and SocialPsychological Bulletin 27 (2001) 996ndash1010

Martin Carol lsquolsquoA Ratio Measure of Sex Stereotypingrsquorsquo Journal of Personality andSocial Psychology 52 (1987) 489ndash499

STEREOTYPES 1793

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

McCauley Clark Krishna Thangavelu and Paul Rozin lsquolsquoSex Stereotyping ofOccupations in Relation to Television Representations and Census FactsrsquorsquoBasic and Applied Social Psychology 9 (1988) 197ndash212

Mullainathan Sendhil lsquolsquoThinking through Categoriesrsquorsquo mimeo HarvardUniversity 2002

Ortoleva Pietro and Erik Snowberg lsquolsquoOverconfidence in Political BehaviorrsquorsquoAmerican Economic Review 105 (2015) 504ndash535

Phelps Edmund lsquolsquoThe Statistical Theory of Racism and Sexismrsquorsquo AmericanEconomic Review 62 (1972) 659ndash661

Pope Devin and Justin Sydnor lsquolsquoGeographic Variation in the Gender Differencesin Test Scoresrsquorsquo Journal of Economic Perspectives 24 (2010) 95ndash108

Rabin Matthew lsquolsquoInference by Believers in the Law of Small NumbersrsquorsquoQuarterly Journal of Economics 117 (2002) 775ndash816

Rabin Matthew and Joel Schrag lsquolsquoFirst Impressions Matter A Model ofConfirmatory Biasrsquorsquo Quarterly Journal of Economics 114 (1999) 37ndash82

Rabin Matthew and Dimitri Vayanos lsquolsquoThe Gamblerrsquos and Hot-Hand FallaciesTheory and Applicationsrsquorsquo Review of Economic Studies 77 (2010) 730ndash778

Reuben Ernesto Paola Sapienza and Luigi Zingales lsquolsquoHow Stereotypes ImpairWomenrsquos Careers in Sciencersquorsquo Proceedings of the National Academy ofSciences 111 (2014) 4403ndash4408

Rosch Eleanor lsquolsquoNatural Categoriesrsquorsquo Cognitive Psychology 4 (1973) 328ndash350Ryan Carey S lsquolsquoAccuracy of Black and White College Studentsrsquo In-Group and

Out-Group Stereotypesrsquorsquo Personality and Social Psychology Bulletin 22(1996) 1114ndash1127

Schneider David The Psychology of Stereotyping (New York Guilford Press2004)

Schneider David Albert Hastorf and Phoebe Ellsworth Person Perception(Reading MA Addison-Wesley 1979)

Shih Margaret Todd Pittinsky and Nalini Ambady lsquolsquoStereotype SusceptibilityIdentity Salience and Shifts in Quantitative Performancersquorsquo PsychologicalScience 10 (1999) 80ndash83

Shih Margaret Todd Pittinsky and Amy Trahan lsquolsquoDomain-Specific Effects ofStereotypes on Performancersquorsquo Self and Identity 5 (2006) 1ndash14

Steele Claude Whistling Vivaldi How Stereotypes Affect Us and What We CanDo (New York Norton 2010)

Tenenbaum Joshua and Thomas Griffiths lsquolsquoThe Rational Basis ofRepresentativenessrsquorsquo 23rd Annual Conference of the Cognitive ScienceSociety (2001) 1036ndash1041

Tversky Amos and Daniel Kahneman lsquolsquoExtensional versus Intuitive ReasoningThe Conjunction Fallacy in Probability Judgmentrsquorsquo Psychological Review 90(1983) 293ndash315

Weinberger Catherin lsquolsquoIs the Science and Engineering Workforce Drawn fromthe Far Upper Tail of the Math Ability Distributionrsquorsquo mimeo UCSB 2005

Westfall Jacob Leaf Van Boven John Chambers and Charles Judd lsquolsquoPerceivingPolitical Polarization in the United States Party Identity Strength andAttitude Extremity Exacerbate the Perceived Partisan DividersquorsquoPsychological Science 10 (2015) 145ndash158

Wolsko Christopher Bernadette Park Charles Judd and Bernd WittenbrinklsquolsquoFraming Interethnic Ideology Effects of Multicultural and Color-BlindPerspectives on Judgments of Groups and Individualsrsquorsquo Journal ofPersonality and Social Psychology 78 (2000) 635ndash654

QUARTERLY JOURNAL OF ECONOMICS1794

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

Page 38: I. Introduction · uneducated at the beginning of the 20th century, and as high achievers at the beginning of the 21st (Madon et al. 2001). Social science has produced three broad

control for the average likelihood on the tail positions (see Table A4in Online Appendix G) Most tellingly we use the model to predictbeliefs across issues and compare those to the data For simplicitywe use the rank-based truncation specification to predict mean be-liefs when stereotypes include the d most representative types ford frac14 1 T We compare these predictions to those of a model inwhich beliefs are obtained by restricting the distribution to the dmost likely types Our benchmark for both models is predicting thebelieved mean from the entire distribution where d = T We showthat the predictions of the rank-based truncation model with d = 4or 5 compare favorably to both a likelihood-based truncation model(with any d) and the accurate beliefs benchmark Interestingly thisresult suggests that stereotypical beliefs are well approximated byneglecting the least representative types (as opposed to focusingonly on the most representative types) and so represent a moderatethough systematic departure from the standard benchmarkFinally we show that the results we document above hold forboth beliefs held by conservatives and beliefs held by liberals (seeTables A9 A10 and A11 in Online Appendix G)

V Conclusion

We present a model of stereotypical thinking in which DMsmaking predictions about a group overweight the grouprsquos mostdistinctive types These overweighted types are not the mostlikely ones given the DMrsquos data but the most representativeones in the sense of being the most diagnostic of the group rela-tive to other groups Representativeness implies that what ismost distinctive of a group depends on what group it is comparedwith We present experimental evidence that confirms this con-text dependence in recall-based assessments of groups Finallywe evaluated the predictions of the model using political data fromexisting large-scale surveys We find context dependence to be akey feature of beliefs Given the richness of the political data wecan go a step further and identify a role for representativeness inparticular As the representativeness of tail types increases beliefsof a group are distorted in the direction of that tail

Our approach provides a parsimonious and psychologicallyfounded account of how DMs generate simplified representationsof reality from social groups to stock returns and offers a unifiedaccount of disparate pieces of evidence relating to this type of

QUARTERLY JOURNAL OF ECONOMICS1790

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

uncertainty The model captures the central fact that stereotypeshighlight the greatest difference between groups thus explainingwhy some stereotypes are very accurate while others lack valid-ity Still stereotypes often have a kernel of truth when they arebased on systematicmdasheven if smallmdashdifferences between groupsThis logic allows us to describe a number of heuristics and psy-chological biases many of which arise in the context of predictionproblems Generically our model generates overreaction to diag-nostic information

Our model is based on representativeness and does not cap-ture all the features of stereotypical thinking However it cap-tures perhaps the central feature when we think of a group wefocus on what is most distinctive about it and neglect or under-weight the rest

Saeuroıd Business School University of Oxford

Ohio State University and Harvard Business School

Universita Bocconi and Innocenzo Gasparini Institute

for Economic Research

Harvard University

Supplementary Material

An Online Appendix for this article can be found at QJEonline (qjeoxfordjournalorg)

References

Adorno Theodor Else Frenkel-Brunswik Daniel Levinson and Nevitt SanfordThe Authoritarian Personality (New York Harper amp Row 1950)

Arrow Kenneth lsquolsquoThe Theory of Discriminationrsquorsquo in Discrimination in LaborMarkets Orley Ashenfelter and Albert Rees eds (Princeton NJPrinceton University Press 1973)

Ashton Michael and Victoria Esses lsquolsquoStereotype Accuracy Estimating theAcademic Performance of Ethnic Groupsrsquorsquo Personality and SocialPsychology Bulletin 25 (1999) 225ndash236

Barberis Nicholas Andrei Shleifer and Robert Vishny lsquolsquoA Model of InvestorSentimentrsquorsquo Journal of Financial Economics 49 (1998) 307ndash343

Bayer Sylvia lsquolsquoThe Accuracy of Academic Gender Stereotypesrsquorsquo Sex Roles 40(1999) 787ndash813

Benjamin Dan James Choi and Joshua Strickland lsquolsquoSocial Identity andPreferencesrsquorsquo American Economic Review 100 (2010) 1913ndash1928

Benjamin Dan Matthew Rabin and Collin Raymond lsquolsquoA Model of Non-Belief inthe Law of Large Numbersrsquorsquo Journal of the European Economic Association15 (2015) 515ndash544

Bertrand Marianne lsquolsquoNew Perspectives on Genderrsquorsquo Handbook of LaborEconomics 4 (2011) 1543ndash1590

Bodoh-Creed Aaron Dan Benjamin and Matthew Rabin lsquolsquoThe Dynamics of Base-Rate Neglectrsquorsquo mimeo Haas Business School 2013

STEREOTYPES 1791

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

Bohnet Iris Alexandra van Geen and Max Bazerman lsquolsquoWhen PerformanceTrumps Gender Bias Joint versus Separate Evaluationrsquorsquo ManagementScience 5 (2016) 1225ndash1234

Bordalo Pedro Nicola Gennaioli and Andrei Shleifer lsquolsquoSalience Theory of Choiceunder Riskrsquorsquo Quarterly Journal of Economics 127 (2012) 1243ndash1285

mdashmdashmdash lsquolsquoSalience and Consumer Choicersquorsquo Journal of Political Economy 121(2013) 803ndash843

Briton Nancy and Judith Hall lsquolsquoBeliefs about Female and Male NonverbalCommunicationrsquorsquo Sex Roles 32 (1995) 79ndash90

Buser Thomas Muriel Niederle and Hessel Oosterbeek lsquolsquoGenderCompetitiveness and Career Choicesrsquorsquo Quarterly Journal of Economics 129(2014) 1409ndash1447

Carrell Scott Marianne Page and James West lsquolsquoSex and Science How ProfessorGender Perpetuates the Gender Gaprsquorsquo Quarterly Journal of Economics 125(2010) 1101ndash1144

Chambers John and Darya Melnyk lsquolsquoWhy Do I Hate Thee ConflictMisperceptions and Intergroup Mistrustrsquorsquo Personality and SocialPsychology Bulletin 32 (2006) 1295ndash1311

Chan Wayne Robert R McCrae Filip De Fruyt Lee Jussim CorinnaE Lockenhoff Marleen De Bolle Paul T Costa Jr Angelina R SutinAnu Realo Juri Allik Katsuharu Nakazato Yoshiko ShimonakaMartina Hrebıckova Sylvie Graf Michelle Yik Marina Brunner-SciarraNora Leibovich De Figueora Vanina Schmidt Chang-kyo Ahn Hyun-nie Ahn Maria E Aguilar-Vafaie Jerzy Siuta Barbara SzmigielskaThomas R Cain Janet T Crawford Khairul Anwar Mastor Jean-Pierre Rolland Florence Nansubuga Daniel R MiramontezVeronica Benet-Martınez Jerome Rossier Denis Bratko Iris MarusicJamin Halberstadt Mami Yamaguchi Goran Knezevic Thomas A MartinMirona Gheorghiu Peter B Smith Claudio Barbaranelli Lei WangJane Shakespeare-Finch Margarida P Lima Waldemar KlinkoszAndrzej Sekowski Lidia Alcalay Franco Simonetti Tatyana V AvdeyevaV S Pramila and Antonio Terracciano lsquolsquoStereotypes of Age Differences inPersonality Traits Universal and Accuratersquorsquo Journal of Personality andSocial Psychology 103 (2012) 1050ndash1066

Chen Yan Sherry Xin Liu Tracy Xiao and Margaret Shih lsquolsquoWhich Hat to WearImpact of Natural Identities on Coordination and Cooperationrsquorsquo Games andEconomic Behavior 84 (2014) 58ndash86

Coffman Katherine lsquolsquoEvidence on Self-Stereotyping and the Contribution ofIdeasrsquorsquo Quarterly Journal of Economics 129 (2014) 1625ndash1660

Cunningham Tom lsquolsquoComparisons and Choicersquorsquo mimeo Stockholm University2013

Diekman Amanda Alice Eagly and Patrick Kulesa lsquolsquoAccuracy and Bias in theStereotypes about the Social and Political Attitudes of Women and MenrsquorsquoJournal of Experimental Social Psychology 38 (2002) 268ndash282

Eccles Jacquelynne S Janis E Jacobs and Rena D Harold lsquolsquoGender RoleStereotypes Expectancy Effects and Parentsrsquo Socialization of GenderDifferencesrsquorsquo Journal of Social Issues 46 (1990) 183ndash201

Fryer Roland and Matthew Jackson lsquolsquoA Categorical Model of Cognition andBiased Decision-Makingrsquorsquo BE Journal of Theoretical Economics 8 (2008)1ndash42

Fryer Roland and Steven Levitt lsquolsquoAn Empirical Analysis of the Gender Gap inMathematicsrsquorsquo American Economic Journal Applied Economics 2 (2010)210ndash240

Gennaioli Nicola and Andrei Shleifer lsquolsquoWhat Comes to Mindrsquorsquo Quarterly Journalof Economics 125 (2010) 1399ndash1433

Gennaioli Nicola Andrei Shleifer and Robert Vishny lsquolsquoNeglected RisksFinancial Innovation and Financial Fragilityrsquorsquo Journal of FinancialEconomics 104 (2012) 452ndash468

Gilens Martin lsquolsquoRace and Poverty in America Public Misperceptions and theAmerican News Mediarsquorsquo Public Opinion Quarterly 60 (1996) 515ndash541

Glaeser Edward lsquolsquoThe Political Economy of Hatredrsquorsquo Quarterly Journal ofEconomics 120 (2005) 45ndash86

QUARTERLY JOURNAL OF ECONOMICS1792

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

Glover Dyland Amanda Pallais and William Pariente lsquolsquoDiscrimination as a Self-Fulfilling Prophecy Evidence from French Grocery Storesrsquorsquo mimeo HarvardUniversity 2015

Goldin Claudia Lawrence Katz and Ilyana Kuziemko lsquolsquoThe Homecoming ofAmerican College Women The Reversal of the College Gender GaprsquorsquoJournal of Economic Perspectives 20 (2006) 133ndash156

Graham Jesse Brian Nosek and Jonathan Haidt lsquolsquoThe Moral Stereotypes ofLiberals and Conservatives Exaggeration of Differences across thePolitical Spectrumrsquorsquo PLoS One 7 (2012) 1ndash13

Grether David lsquolsquoBayes Rule as a Descriptive Model The RepresentativenessHeuristicrsquorsquo Quarterly Journal of Economics 95 (1980) 537ndash557

Griffin Dale and Amos Tversky lsquolsquoThe Weighing of Evidence and theDeterminants of Confidencersquorsquo Cognitive Psychology 24 (1992) 411ndash435

Guiso Luigi Ferdinando Monte Paola Sapienza and Luigi Zingales lsquolsquoCultureGender and Mathrsquorsquo Science 320 (2008) 1164ndash1165

Hilton James and William Von Hippel lsquolsquoStereotypesrsquorsquo Annual Review ofPsychology 47 (1996) 237ndash271

Hyde Janet Sara Lindberg Marcia Linn Amy Ellis and Caroline WilliamslsquolsquoGender Similarities Characterize Math Performancersquorsquo Science 321 (2008)494ndash495

Judd Charles and Bernardette Park lsquolsquoDefinition and Assessment of Accuracy inSocial Stereotypesrsquorsquo Psychological Review 100 (1993) 109ndash128

Jussim Lee Jarret Crawford Stephanie Anglin John Chambers Sean Stevensand Florette Cohen lsquolsquoStereotype Accuracy One of the Largest and MostReplicable Effects in All of Social Psychologyrsquorsquo in The Handbook ofPrejudice Stereotyping and Discrimination Todd Nelson ed (MahwahNJ Lawrence Erlbaum 2015)

Kahneman Daniel and Amos Tversky lsquolsquoSubjective Probability A Judgment ofRepresentativenessrsquorsquo Cognitive Psychology 3 (1972) 430ndash454

mdashmdashmdash lsquolsquoOn the Psychology of Predictionrsquorsquo Psychological Review 80 (1973) 237ndash251

Kaplowitz Stan Bradley Fisher and Clifford Broman lsquolsquoHow Accurate ArePerceptions of Social Statistics about Blacks and Whitesrsquorsquo Public OpinionQuarterly 67 (2003) 237ndash243

Kersten Daniel Pascal Mamassian and Alan Yuille lsquolsquoObject Perception asBayesian Inferencersquorsquo Annual Review of Psychology 55 (2004) 271ndash304

Klein Richard Kate A Ratliff Michelangelo Vianello Reginald B Adams JrStepan Bahnik Michael J Bernstein Konrad Bocian Mark J BrandtBeach Brooks Claudia Chloe Brumbaugh Zeynep CemalcilarJesse Chandler Winnee Cheong William E Davis Thierry DevosMatthew Eisner Natalia Frankowska David Furrow Elisa Maria GallianiFred Hasselman Joshua A Hicks James F Hovermale S Jane HuntJeffrey R Huntsinger Hans IJzerman Melissa-Sue John Jennifer A Joy-Gaba Heather Barry Kappes Lacy E Krueger Jaime Kurtz CarmelA Levitan Robyn Mallett Wendy L Morris Anthony J Nelson JasonA Nier Grant Packard Ronaldo Pilati Abraham M RutchickKathleen Schmidt Jeanine L Skorinko Robert Smith Troy G SteinerJustin Storbeck Lyn M Van Swol Donna Thompson Anna van rsquot VeerLeigh Ann Vaughn Marek Vranka Aaron Wichman Julie A Woodzickaand Brian A Nosek lsquolsquoInvestigating Variation in Replicability A ManyLabs Replication Projectrsquorsquo Social Psychology 45 (2014) 142ndash152

Lundberg Shelly and Richard Startz lsquolsquoPrivate Discrimination and SocialIntervention in Competitive Labor Marketsrsquorsquo American Economic Review73 (1983) 340ndash347

Madon Stephanie Max Guyll Kathy Aboufadel Eulices Montiel Alison SmithPolly Palumbo and Lee Jussim lsquolsquoEthnic and National Stereotypes ThePrinceton Trilogy Revisited and Revisedrsquorsquo Personality and SocialPsychological Bulletin 27 (2001) 996ndash1010

Martin Carol lsquolsquoA Ratio Measure of Sex Stereotypingrsquorsquo Journal of Personality andSocial Psychology 52 (1987) 489ndash499

STEREOTYPES 1793

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

McCauley Clark Krishna Thangavelu and Paul Rozin lsquolsquoSex Stereotyping ofOccupations in Relation to Television Representations and Census FactsrsquorsquoBasic and Applied Social Psychology 9 (1988) 197ndash212

Mullainathan Sendhil lsquolsquoThinking through Categoriesrsquorsquo mimeo HarvardUniversity 2002

Ortoleva Pietro and Erik Snowberg lsquolsquoOverconfidence in Political BehaviorrsquorsquoAmerican Economic Review 105 (2015) 504ndash535

Phelps Edmund lsquolsquoThe Statistical Theory of Racism and Sexismrsquorsquo AmericanEconomic Review 62 (1972) 659ndash661

Pope Devin and Justin Sydnor lsquolsquoGeographic Variation in the Gender Differencesin Test Scoresrsquorsquo Journal of Economic Perspectives 24 (2010) 95ndash108

Rabin Matthew lsquolsquoInference by Believers in the Law of Small NumbersrsquorsquoQuarterly Journal of Economics 117 (2002) 775ndash816

Rabin Matthew and Joel Schrag lsquolsquoFirst Impressions Matter A Model ofConfirmatory Biasrsquorsquo Quarterly Journal of Economics 114 (1999) 37ndash82

Rabin Matthew and Dimitri Vayanos lsquolsquoThe Gamblerrsquos and Hot-Hand FallaciesTheory and Applicationsrsquorsquo Review of Economic Studies 77 (2010) 730ndash778

Reuben Ernesto Paola Sapienza and Luigi Zingales lsquolsquoHow Stereotypes ImpairWomenrsquos Careers in Sciencersquorsquo Proceedings of the National Academy ofSciences 111 (2014) 4403ndash4408

Rosch Eleanor lsquolsquoNatural Categoriesrsquorsquo Cognitive Psychology 4 (1973) 328ndash350Ryan Carey S lsquolsquoAccuracy of Black and White College Studentsrsquo In-Group and

Out-Group Stereotypesrsquorsquo Personality and Social Psychology Bulletin 22(1996) 1114ndash1127

Schneider David The Psychology of Stereotyping (New York Guilford Press2004)

Schneider David Albert Hastorf and Phoebe Ellsworth Person Perception(Reading MA Addison-Wesley 1979)

Shih Margaret Todd Pittinsky and Nalini Ambady lsquolsquoStereotype SusceptibilityIdentity Salience and Shifts in Quantitative Performancersquorsquo PsychologicalScience 10 (1999) 80ndash83

Shih Margaret Todd Pittinsky and Amy Trahan lsquolsquoDomain-Specific Effects ofStereotypes on Performancersquorsquo Self and Identity 5 (2006) 1ndash14

Steele Claude Whistling Vivaldi How Stereotypes Affect Us and What We CanDo (New York Norton 2010)

Tenenbaum Joshua and Thomas Griffiths lsquolsquoThe Rational Basis ofRepresentativenessrsquorsquo 23rd Annual Conference of the Cognitive ScienceSociety (2001) 1036ndash1041

Tversky Amos and Daniel Kahneman lsquolsquoExtensional versus Intuitive ReasoningThe Conjunction Fallacy in Probability Judgmentrsquorsquo Psychological Review 90(1983) 293ndash315

Weinberger Catherin lsquolsquoIs the Science and Engineering Workforce Drawn fromthe Far Upper Tail of the Math Ability Distributionrsquorsquo mimeo UCSB 2005

Westfall Jacob Leaf Van Boven John Chambers and Charles Judd lsquolsquoPerceivingPolitical Polarization in the United States Party Identity Strength andAttitude Extremity Exacerbate the Perceived Partisan DividersquorsquoPsychological Science 10 (2015) 145ndash158

Wolsko Christopher Bernadette Park Charles Judd and Bernd WittenbrinklsquolsquoFraming Interethnic Ideology Effects of Multicultural and Color-BlindPerspectives on Judgments of Groups and Individualsrsquorsquo Journal ofPersonality and Social Psychology 78 (2000) 635ndash654

QUARTERLY JOURNAL OF ECONOMICS1794

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

Page 39: I. Introduction · uneducated at the beginning of the 20th century, and as high achievers at the beginning of the 21st (Madon et al. 2001). Social science has produced three broad

uncertainty The model captures the central fact that stereotypeshighlight the greatest difference between groups thus explainingwhy some stereotypes are very accurate while others lack valid-ity Still stereotypes often have a kernel of truth when they arebased on systematicmdasheven if smallmdashdifferences between groupsThis logic allows us to describe a number of heuristics and psy-chological biases many of which arise in the context of predictionproblems Generically our model generates overreaction to diag-nostic information

Our model is based on representativeness and does not cap-ture all the features of stereotypical thinking However it cap-tures perhaps the central feature when we think of a group wefocus on what is most distinctive about it and neglect or under-weight the rest

Saeuroıd Business School University of Oxford

Ohio State University and Harvard Business School

Universita Bocconi and Innocenzo Gasparini Institute

for Economic Research

Harvard University

Supplementary Material

An Online Appendix for this article can be found at QJEonline (qjeoxfordjournalorg)

References

Adorno Theodor Else Frenkel-Brunswik Daniel Levinson and Nevitt SanfordThe Authoritarian Personality (New York Harper amp Row 1950)

Arrow Kenneth lsquolsquoThe Theory of Discriminationrsquorsquo in Discrimination in LaborMarkets Orley Ashenfelter and Albert Rees eds (Princeton NJPrinceton University Press 1973)

Ashton Michael and Victoria Esses lsquolsquoStereotype Accuracy Estimating theAcademic Performance of Ethnic Groupsrsquorsquo Personality and SocialPsychology Bulletin 25 (1999) 225ndash236

Barberis Nicholas Andrei Shleifer and Robert Vishny lsquolsquoA Model of InvestorSentimentrsquorsquo Journal of Financial Economics 49 (1998) 307ndash343

Bayer Sylvia lsquolsquoThe Accuracy of Academic Gender Stereotypesrsquorsquo Sex Roles 40(1999) 787ndash813

Benjamin Dan James Choi and Joshua Strickland lsquolsquoSocial Identity andPreferencesrsquorsquo American Economic Review 100 (2010) 1913ndash1928

Benjamin Dan Matthew Rabin and Collin Raymond lsquolsquoA Model of Non-Belief inthe Law of Large Numbersrsquorsquo Journal of the European Economic Association15 (2015) 515ndash544

Bertrand Marianne lsquolsquoNew Perspectives on Genderrsquorsquo Handbook of LaborEconomics 4 (2011) 1543ndash1590

Bodoh-Creed Aaron Dan Benjamin and Matthew Rabin lsquolsquoThe Dynamics of Base-Rate Neglectrsquorsquo mimeo Haas Business School 2013

STEREOTYPES 1791

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

Bohnet Iris Alexandra van Geen and Max Bazerman lsquolsquoWhen PerformanceTrumps Gender Bias Joint versus Separate Evaluationrsquorsquo ManagementScience 5 (2016) 1225ndash1234

Bordalo Pedro Nicola Gennaioli and Andrei Shleifer lsquolsquoSalience Theory of Choiceunder Riskrsquorsquo Quarterly Journal of Economics 127 (2012) 1243ndash1285

mdashmdashmdash lsquolsquoSalience and Consumer Choicersquorsquo Journal of Political Economy 121(2013) 803ndash843

Briton Nancy and Judith Hall lsquolsquoBeliefs about Female and Male NonverbalCommunicationrsquorsquo Sex Roles 32 (1995) 79ndash90

Buser Thomas Muriel Niederle and Hessel Oosterbeek lsquolsquoGenderCompetitiveness and Career Choicesrsquorsquo Quarterly Journal of Economics 129(2014) 1409ndash1447

Carrell Scott Marianne Page and James West lsquolsquoSex and Science How ProfessorGender Perpetuates the Gender Gaprsquorsquo Quarterly Journal of Economics 125(2010) 1101ndash1144

Chambers John and Darya Melnyk lsquolsquoWhy Do I Hate Thee ConflictMisperceptions and Intergroup Mistrustrsquorsquo Personality and SocialPsychology Bulletin 32 (2006) 1295ndash1311

Chan Wayne Robert R McCrae Filip De Fruyt Lee Jussim CorinnaE Lockenhoff Marleen De Bolle Paul T Costa Jr Angelina R SutinAnu Realo Juri Allik Katsuharu Nakazato Yoshiko ShimonakaMartina Hrebıckova Sylvie Graf Michelle Yik Marina Brunner-SciarraNora Leibovich De Figueora Vanina Schmidt Chang-kyo Ahn Hyun-nie Ahn Maria E Aguilar-Vafaie Jerzy Siuta Barbara SzmigielskaThomas R Cain Janet T Crawford Khairul Anwar Mastor Jean-Pierre Rolland Florence Nansubuga Daniel R MiramontezVeronica Benet-Martınez Jerome Rossier Denis Bratko Iris MarusicJamin Halberstadt Mami Yamaguchi Goran Knezevic Thomas A MartinMirona Gheorghiu Peter B Smith Claudio Barbaranelli Lei WangJane Shakespeare-Finch Margarida P Lima Waldemar KlinkoszAndrzej Sekowski Lidia Alcalay Franco Simonetti Tatyana V AvdeyevaV S Pramila and Antonio Terracciano lsquolsquoStereotypes of Age Differences inPersonality Traits Universal and Accuratersquorsquo Journal of Personality andSocial Psychology 103 (2012) 1050ndash1066

Chen Yan Sherry Xin Liu Tracy Xiao and Margaret Shih lsquolsquoWhich Hat to WearImpact of Natural Identities on Coordination and Cooperationrsquorsquo Games andEconomic Behavior 84 (2014) 58ndash86

Coffman Katherine lsquolsquoEvidence on Self-Stereotyping and the Contribution ofIdeasrsquorsquo Quarterly Journal of Economics 129 (2014) 1625ndash1660

Cunningham Tom lsquolsquoComparisons and Choicersquorsquo mimeo Stockholm University2013

Diekman Amanda Alice Eagly and Patrick Kulesa lsquolsquoAccuracy and Bias in theStereotypes about the Social and Political Attitudes of Women and MenrsquorsquoJournal of Experimental Social Psychology 38 (2002) 268ndash282

Eccles Jacquelynne S Janis E Jacobs and Rena D Harold lsquolsquoGender RoleStereotypes Expectancy Effects and Parentsrsquo Socialization of GenderDifferencesrsquorsquo Journal of Social Issues 46 (1990) 183ndash201

Fryer Roland and Matthew Jackson lsquolsquoA Categorical Model of Cognition andBiased Decision-Makingrsquorsquo BE Journal of Theoretical Economics 8 (2008)1ndash42

Fryer Roland and Steven Levitt lsquolsquoAn Empirical Analysis of the Gender Gap inMathematicsrsquorsquo American Economic Journal Applied Economics 2 (2010)210ndash240

Gennaioli Nicola and Andrei Shleifer lsquolsquoWhat Comes to Mindrsquorsquo Quarterly Journalof Economics 125 (2010) 1399ndash1433

Gennaioli Nicola Andrei Shleifer and Robert Vishny lsquolsquoNeglected RisksFinancial Innovation and Financial Fragilityrsquorsquo Journal of FinancialEconomics 104 (2012) 452ndash468

Gilens Martin lsquolsquoRace and Poverty in America Public Misperceptions and theAmerican News Mediarsquorsquo Public Opinion Quarterly 60 (1996) 515ndash541

Glaeser Edward lsquolsquoThe Political Economy of Hatredrsquorsquo Quarterly Journal ofEconomics 120 (2005) 45ndash86

QUARTERLY JOURNAL OF ECONOMICS1792

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

Glover Dyland Amanda Pallais and William Pariente lsquolsquoDiscrimination as a Self-Fulfilling Prophecy Evidence from French Grocery Storesrsquorsquo mimeo HarvardUniversity 2015

Goldin Claudia Lawrence Katz and Ilyana Kuziemko lsquolsquoThe Homecoming ofAmerican College Women The Reversal of the College Gender GaprsquorsquoJournal of Economic Perspectives 20 (2006) 133ndash156

Graham Jesse Brian Nosek and Jonathan Haidt lsquolsquoThe Moral Stereotypes ofLiberals and Conservatives Exaggeration of Differences across thePolitical Spectrumrsquorsquo PLoS One 7 (2012) 1ndash13

Grether David lsquolsquoBayes Rule as a Descriptive Model The RepresentativenessHeuristicrsquorsquo Quarterly Journal of Economics 95 (1980) 537ndash557

Griffin Dale and Amos Tversky lsquolsquoThe Weighing of Evidence and theDeterminants of Confidencersquorsquo Cognitive Psychology 24 (1992) 411ndash435

Guiso Luigi Ferdinando Monte Paola Sapienza and Luigi Zingales lsquolsquoCultureGender and Mathrsquorsquo Science 320 (2008) 1164ndash1165

Hilton James and William Von Hippel lsquolsquoStereotypesrsquorsquo Annual Review ofPsychology 47 (1996) 237ndash271

Hyde Janet Sara Lindberg Marcia Linn Amy Ellis and Caroline WilliamslsquolsquoGender Similarities Characterize Math Performancersquorsquo Science 321 (2008)494ndash495

Judd Charles and Bernardette Park lsquolsquoDefinition and Assessment of Accuracy inSocial Stereotypesrsquorsquo Psychological Review 100 (1993) 109ndash128

Jussim Lee Jarret Crawford Stephanie Anglin John Chambers Sean Stevensand Florette Cohen lsquolsquoStereotype Accuracy One of the Largest and MostReplicable Effects in All of Social Psychologyrsquorsquo in The Handbook ofPrejudice Stereotyping and Discrimination Todd Nelson ed (MahwahNJ Lawrence Erlbaum 2015)

Kahneman Daniel and Amos Tversky lsquolsquoSubjective Probability A Judgment ofRepresentativenessrsquorsquo Cognitive Psychology 3 (1972) 430ndash454

mdashmdashmdash lsquolsquoOn the Psychology of Predictionrsquorsquo Psychological Review 80 (1973) 237ndash251

Kaplowitz Stan Bradley Fisher and Clifford Broman lsquolsquoHow Accurate ArePerceptions of Social Statistics about Blacks and Whitesrsquorsquo Public OpinionQuarterly 67 (2003) 237ndash243

Kersten Daniel Pascal Mamassian and Alan Yuille lsquolsquoObject Perception asBayesian Inferencersquorsquo Annual Review of Psychology 55 (2004) 271ndash304

Klein Richard Kate A Ratliff Michelangelo Vianello Reginald B Adams JrStepan Bahnik Michael J Bernstein Konrad Bocian Mark J BrandtBeach Brooks Claudia Chloe Brumbaugh Zeynep CemalcilarJesse Chandler Winnee Cheong William E Davis Thierry DevosMatthew Eisner Natalia Frankowska David Furrow Elisa Maria GallianiFred Hasselman Joshua A Hicks James F Hovermale S Jane HuntJeffrey R Huntsinger Hans IJzerman Melissa-Sue John Jennifer A Joy-Gaba Heather Barry Kappes Lacy E Krueger Jaime Kurtz CarmelA Levitan Robyn Mallett Wendy L Morris Anthony J Nelson JasonA Nier Grant Packard Ronaldo Pilati Abraham M RutchickKathleen Schmidt Jeanine L Skorinko Robert Smith Troy G SteinerJustin Storbeck Lyn M Van Swol Donna Thompson Anna van rsquot VeerLeigh Ann Vaughn Marek Vranka Aaron Wichman Julie A Woodzickaand Brian A Nosek lsquolsquoInvestigating Variation in Replicability A ManyLabs Replication Projectrsquorsquo Social Psychology 45 (2014) 142ndash152

Lundberg Shelly and Richard Startz lsquolsquoPrivate Discrimination and SocialIntervention in Competitive Labor Marketsrsquorsquo American Economic Review73 (1983) 340ndash347

Madon Stephanie Max Guyll Kathy Aboufadel Eulices Montiel Alison SmithPolly Palumbo and Lee Jussim lsquolsquoEthnic and National Stereotypes ThePrinceton Trilogy Revisited and Revisedrsquorsquo Personality and SocialPsychological Bulletin 27 (2001) 996ndash1010

Martin Carol lsquolsquoA Ratio Measure of Sex Stereotypingrsquorsquo Journal of Personality andSocial Psychology 52 (1987) 489ndash499

STEREOTYPES 1793

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

McCauley Clark Krishna Thangavelu and Paul Rozin lsquolsquoSex Stereotyping ofOccupations in Relation to Television Representations and Census FactsrsquorsquoBasic and Applied Social Psychology 9 (1988) 197ndash212

Mullainathan Sendhil lsquolsquoThinking through Categoriesrsquorsquo mimeo HarvardUniversity 2002

Ortoleva Pietro and Erik Snowberg lsquolsquoOverconfidence in Political BehaviorrsquorsquoAmerican Economic Review 105 (2015) 504ndash535

Phelps Edmund lsquolsquoThe Statistical Theory of Racism and Sexismrsquorsquo AmericanEconomic Review 62 (1972) 659ndash661

Pope Devin and Justin Sydnor lsquolsquoGeographic Variation in the Gender Differencesin Test Scoresrsquorsquo Journal of Economic Perspectives 24 (2010) 95ndash108

Rabin Matthew lsquolsquoInference by Believers in the Law of Small NumbersrsquorsquoQuarterly Journal of Economics 117 (2002) 775ndash816

Rabin Matthew and Joel Schrag lsquolsquoFirst Impressions Matter A Model ofConfirmatory Biasrsquorsquo Quarterly Journal of Economics 114 (1999) 37ndash82

Rabin Matthew and Dimitri Vayanos lsquolsquoThe Gamblerrsquos and Hot-Hand FallaciesTheory and Applicationsrsquorsquo Review of Economic Studies 77 (2010) 730ndash778

Reuben Ernesto Paola Sapienza and Luigi Zingales lsquolsquoHow Stereotypes ImpairWomenrsquos Careers in Sciencersquorsquo Proceedings of the National Academy ofSciences 111 (2014) 4403ndash4408

Rosch Eleanor lsquolsquoNatural Categoriesrsquorsquo Cognitive Psychology 4 (1973) 328ndash350Ryan Carey S lsquolsquoAccuracy of Black and White College Studentsrsquo In-Group and

Out-Group Stereotypesrsquorsquo Personality and Social Psychology Bulletin 22(1996) 1114ndash1127

Schneider David The Psychology of Stereotyping (New York Guilford Press2004)

Schneider David Albert Hastorf and Phoebe Ellsworth Person Perception(Reading MA Addison-Wesley 1979)

Shih Margaret Todd Pittinsky and Nalini Ambady lsquolsquoStereotype SusceptibilityIdentity Salience and Shifts in Quantitative Performancersquorsquo PsychologicalScience 10 (1999) 80ndash83

Shih Margaret Todd Pittinsky and Amy Trahan lsquolsquoDomain-Specific Effects ofStereotypes on Performancersquorsquo Self and Identity 5 (2006) 1ndash14

Steele Claude Whistling Vivaldi How Stereotypes Affect Us and What We CanDo (New York Norton 2010)

Tenenbaum Joshua and Thomas Griffiths lsquolsquoThe Rational Basis ofRepresentativenessrsquorsquo 23rd Annual Conference of the Cognitive ScienceSociety (2001) 1036ndash1041

Tversky Amos and Daniel Kahneman lsquolsquoExtensional versus Intuitive ReasoningThe Conjunction Fallacy in Probability Judgmentrsquorsquo Psychological Review 90(1983) 293ndash315

Weinberger Catherin lsquolsquoIs the Science and Engineering Workforce Drawn fromthe Far Upper Tail of the Math Ability Distributionrsquorsquo mimeo UCSB 2005

Westfall Jacob Leaf Van Boven John Chambers and Charles Judd lsquolsquoPerceivingPolitical Polarization in the United States Party Identity Strength andAttitude Extremity Exacerbate the Perceived Partisan DividersquorsquoPsychological Science 10 (2015) 145ndash158

Wolsko Christopher Bernadette Park Charles Judd and Bernd WittenbrinklsquolsquoFraming Interethnic Ideology Effects of Multicultural and Color-BlindPerspectives on Judgments of Groups and Individualsrsquorsquo Journal ofPersonality and Social Psychology 78 (2000) 635ndash654

QUARTERLY JOURNAL OF ECONOMICS1794

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

Page 40: I. Introduction · uneducated at the beginning of the 20th century, and as high achievers at the beginning of the 21st (Madon et al. 2001). Social science has produced three broad

Bohnet Iris Alexandra van Geen and Max Bazerman lsquolsquoWhen PerformanceTrumps Gender Bias Joint versus Separate Evaluationrsquorsquo ManagementScience 5 (2016) 1225ndash1234

Bordalo Pedro Nicola Gennaioli and Andrei Shleifer lsquolsquoSalience Theory of Choiceunder Riskrsquorsquo Quarterly Journal of Economics 127 (2012) 1243ndash1285

mdashmdashmdash lsquolsquoSalience and Consumer Choicersquorsquo Journal of Political Economy 121(2013) 803ndash843

Briton Nancy and Judith Hall lsquolsquoBeliefs about Female and Male NonverbalCommunicationrsquorsquo Sex Roles 32 (1995) 79ndash90

Buser Thomas Muriel Niederle and Hessel Oosterbeek lsquolsquoGenderCompetitiveness and Career Choicesrsquorsquo Quarterly Journal of Economics 129(2014) 1409ndash1447

Carrell Scott Marianne Page and James West lsquolsquoSex and Science How ProfessorGender Perpetuates the Gender Gaprsquorsquo Quarterly Journal of Economics 125(2010) 1101ndash1144

Chambers John and Darya Melnyk lsquolsquoWhy Do I Hate Thee ConflictMisperceptions and Intergroup Mistrustrsquorsquo Personality and SocialPsychology Bulletin 32 (2006) 1295ndash1311

Chan Wayne Robert R McCrae Filip De Fruyt Lee Jussim CorinnaE Lockenhoff Marleen De Bolle Paul T Costa Jr Angelina R SutinAnu Realo Juri Allik Katsuharu Nakazato Yoshiko ShimonakaMartina Hrebıckova Sylvie Graf Michelle Yik Marina Brunner-SciarraNora Leibovich De Figueora Vanina Schmidt Chang-kyo Ahn Hyun-nie Ahn Maria E Aguilar-Vafaie Jerzy Siuta Barbara SzmigielskaThomas R Cain Janet T Crawford Khairul Anwar Mastor Jean-Pierre Rolland Florence Nansubuga Daniel R MiramontezVeronica Benet-Martınez Jerome Rossier Denis Bratko Iris MarusicJamin Halberstadt Mami Yamaguchi Goran Knezevic Thomas A MartinMirona Gheorghiu Peter B Smith Claudio Barbaranelli Lei WangJane Shakespeare-Finch Margarida P Lima Waldemar KlinkoszAndrzej Sekowski Lidia Alcalay Franco Simonetti Tatyana V AvdeyevaV S Pramila and Antonio Terracciano lsquolsquoStereotypes of Age Differences inPersonality Traits Universal and Accuratersquorsquo Journal of Personality andSocial Psychology 103 (2012) 1050ndash1066

Chen Yan Sherry Xin Liu Tracy Xiao and Margaret Shih lsquolsquoWhich Hat to WearImpact of Natural Identities on Coordination and Cooperationrsquorsquo Games andEconomic Behavior 84 (2014) 58ndash86

Coffman Katherine lsquolsquoEvidence on Self-Stereotyping and the Contribution ofIdeasrsquorsquo Quarterly Journal of Economics 129 (2014) 1625ndash1660

Cunningham Tom lsquolsquoComparisons and Choicersquorsquo mimeo Stockholm University2013

Diekman Amanda Alice Eagly and Patrick Kulesa lsquolsquoAccuracy and Bias in theStereotypes about the Social and Political Attitudes of Women and MenrsquorsquoJournal of Experimental Social Psychology 38 (2002) 268ndash282

Eccles Jacquelynne S Janis E Jacobs and Rena D Harold lsquolsquoGender RoleStereotypes Expectancy Effects and Parentsrsquo Socialization of GenderDifferencesrsquorsquo Journal of Social Issues 46 (1990) 183ndash201

Fryer Roland and Matthew Jackson lsquolsquoA Categorical Model of Cognition andBiased Decision-Makingrsquorsquo BE Journal of Theoretical Economics 8 (2008)1ndash42

Fryer Roland and Steven Levitt lsquolsquoAn Empirical Analysis of the Gender Gap inMathematicsrsquorsquo American Economic Journal Applied Economics 2 (2010)210ndash240

Gennaioli Nicola and Andrei Shleifer lsquolsquoWhat Comes to Mindrsquorsquo Quarterly Journalof Economics 125 (2010) 1399ndash1433

Gennaioli Nicola Andrei Shleifer and Robert Vishny lsquolsquoNeglected RisksFinancial Innovation and Financial Fragilityrsquorsquo Journal of FinancialEconomics 104 (2012) 452ndash468

Gilens Martin lsquolsquoRace and Poverty in America Public Misperceptions and theAmerican News Mediarsquorsquo Public Opinion Quarterly 60 (1996) 515ndash541

Glaeser Edward lsquolsquoThe Political Economy of Hatredrsquorsquo Quarterly Journal ofEconomics 120 (2005) 45ndash86

QUARTERLY JOURNAL OF ECONOMICS1792

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

Glover Dyland Amanda Pallais and William Pariente lsquolsquoDiscrimination as a Self-Fulfilling Prophecy Evidence from French Grocery Storesrsquorsquo mimeo HarvardUniversity 2015

Goldin Claudia Lawrence Katz and Ilyana Kuziemko lsquolsquoThe Homecoming ofAmerican College Women The Reversal of the College Gender GaprsquorsquoJournal of Economic Perspectives 20 (2006) 133ndash156

Graham Jesse Brian Nosek and Jonathan Haidt lsquolsquoThe Moral Stereotypes ofLiberals and Conservatives Exaggeration of Differences across thePolitical Spectrumrsquorsquo PLoS One 7 (2012) 1ndash13

Grether David lsquolsquoBayes Rule as a Descriptive Model The RepresentativenessHeuristicrsquorsquo Quarterly Journal of Economics 95 (1980) 537ndash557

Griffin Dale and Amos Tversky lsquolsquoThe Weighing of Evidence and theDeterminants of Confidencersquorsquo Cognitive Psychology 24 (1992) 411ndash435

Guiso Luigi Ferdinando Monte Paola Sapienza and Luigi Zingales lsquolsquoCultureGender and Mathrsquorsquo Science 320 (2008) 1164ndash1165

Hilton James and William Von Hippel lsquolsquoStereotypesrsquorsquo Annual Review ofPsychology 47 (1996) 237ndash271

Hyde Janet Sara Lindberg Marcia Linn Amy Ellis and Caroline WilliamslsquolsquoGender Similarities Characterize Math Performancersquorsquo Science 321 (2008)494ndash495

Judd Charles and Bernardette Park lsquolsquoDefinition and Assessment of Accuracy inSocial Stereotypesrsquorsquo Psychological Review 100 (1993) 109ndash128

Jussim Lee Jarret Crawford Stephanie Anglin John Chambers Sean Stevensand Florette Cohen lsquolsquoStereotype Accuracy One of the Largest and MostReplicable Effects in All of Social Psychologyrsquorsquo in The Handbook ofPrejudice Stereotyping and Discrimination Todd Nelson ed (MahwahNJ Lawrence Erlbaum 2015)

Kahneman Daniel and Amos Tversky lsquolsquoSubjective Probability A Judgment ofRepresentativenessrsquorsquo Cognitive Psychology 3 (1972) 430ndash454

mdashmdashmdash lsquolsquoOn the Psychology of Predictionrsquorsquo Psychological Review 80 (1973) 237ndash251

Kaplowitz Stan Bradley Fisher and Clifford Broman lsquolsquoHow Accurate ArePerceptions of Social Statistics about Blacks and Whitesrsquorsquo Public OpinionQuarterly 67 (2003) 237ndash243

Kersten Daniel Pascal Mamassian and Alan Yuille lsquolsquoObject Perception asBayesian Inferencersquorsquo Annual Review of Psychology 55 (2004) 271ndash304

Klein Richard Kate A Ratliff Michelangelo Vianello Reginald B Adams JrStepan Bahnik Michael J Bernstein Konrad Bocian Mark J BrandtBeach Brooks Claudia Chloe Brumbaugh Zeynep CemalcilarJesse Chandler Winnee Cheong William E Davis Thierry DevosMatthew Eisner Natalia Frankowska David Furrow Elisa Maria GallianiFred Hasselman Joshua A Hicks James F Hovermale S Jane HuntJeffrey R Huntsinger Hans IJzerman Melissa-Sue John Jennifer A Joy-Gaba Heather Barry Kappes Lacy E Krueger Jaime Kurtz CarmelA Levitan Robyn Mallett Wendy L Morris Anthony J Nelson JasonA Nier Grant Packard Ronaldo Pilati Abraham M RutchickKathleen Schmidt Jeanine L Skorinko Robert Smith Troy G SteinerJustin Storbeck Lyn M Van Swol Donna Thompson Anna van rsquot VeerLeigh Ann Vaughn Marek Vranka Aaron Wichman Julie A Woodzickaand Brian A Nosek lsquolsquoInvestigating Variation in Replicability A ManyLabs Replication Projectrsquorsquo Social Psychology 45 (2014) 142ndash152

Lundberg Shelly and Richard Startz lsquolsquoPrivate Discrimination and SocialIntervention in Competitive Labor Marketsrsquorsquo American Economic Review73 (1983) 340ndash347

Madon Stephanie Max Guyll Kathy Aboufadel Eulices Montiel Alison SmithPolly Palumbo and Lee Jussim lsquolsquoEthnic and National Stereotypes ThePrinceton Trilogy Revisited and Revisedrsquorsquo Personality and SocialPsychological Bulletin 27 (2001) 996ndash1010

Martin Carol lsquolsquoA Ratio Measure of Sex Stereotypingrsquorsquo Journal of Personality andSocial Psychology 52 (1987) 489ndash499

STEREOTYPES 1793

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

McCauley Clark Krishna Thangavelu and Paul Rozin lsquolsquoSex Stereotyping ofOccupations in Relation to Television Representations and Census FactsrsquorsquoBasic and Applied Social Psychology 9 (1988) 197ndash212

Mullainathan Sendhil lsquolsquoThinking through Categoriesrsquorsquo mimeo HarvardUniversity 2002

Ortoleva Pietro and Erik Snowberg lsquolsquoOverconfidence in Political BehaviorrsquorsquoAmerican Economic Review 105 (2015) 504ndash535

Phelps Edmund lsquolsquoThe Statistical Theory of Racism and Sexismrsquorsquo AmericanEconomic Review 62 (1972) 659ndash661

Pope Devin and Justin Sydnor lsquolsquoGeographic Variation in the Gender Differencesin Test Scoresrsquorsquo Journal of Economic Perspectives 24 (2010) 95ndash108

Rabin Matthew lsquolsquoInference by Believers in the Law of Small NumbersrsquorsquoQuarterly Journal of Economics 117 (2002) 775ndash816

Rabin Matthew and Joel Schrag lsquolsquoFirst Impressions Matter A Model ofConfirmatory Biasrsquorsquo Quarterly Journal of Economics 114 (1999) 37ndash82

Rabin Matthew and Dimitri Vayanos lsquolsquoThe Gamblerrsquos and Hot-Hand FallaciesTheory and Applicationsrsquorsquo Review of Economic Studies 77 (2010) 730ndash778

Reuben Ernesto Paola Sapienza and Luigi Zingales lsquolsquoHow Stereotypes ImpairWomenrsquos Careers in Sciencersquorsquo Proceedings of the National Academy ofSciences 111 (2014) 4403ndash4408

Rosch Eleanor lsquolsquoNatural Categoriesrsquorsquo Cognitive Psychology 4 (1973) 328ndash350Ryan Carey S lsquolsquoAccuracy of Black and White College Studentsrsquo In-Group and

Out-Group Stereotypesrsquorsquo Personality and Social Psychology Bulletin 22(1996) 1114ndash1127

Schneider David The Psychology of Stereotyping (New York Guilford Press2004)

Schneider David Albert Hastorf and Phoebe Ellsworth Person Perception(Reading MA Addison-Wesley 1979)

Shih Margaret Todd Pittinsky and Nalini Ambady lsquolsquoStereotype SusceptibilityIdentity Salience and Shifts in Quantitative Performancersquorsquo PsychologicalScience 10 (1999) 80ndash83

Shih Margaret Todd Pittinsky and Amy Trahan lsquolsquoDomain-Specific Effects ofStereotypes on Performancersquorsquo Self and Identity 5 (2006) 1ndash14

Steele Claude Whistling Vivaldi How Stereotypes Affect Us and What We CanDo (New York Norton 2010)

Tenenbaum Joshua and Thomas Griffiths lsquolsquoThe Rational Basis ofRepresentativenessrsquorsquo 23rd Annual Conference of the Cognitive ScienceSociety (2001) 1036ndash1041

Tversky Amos and Daniel Kahneman lsquolsquoExtensional versus Intuitive ReasoningThe Conjunction Fallacy in Probability Judgmentrsquorsquo Psychological Review 90(1983) 293ndash315

Weinberger Catherin lsquolsquoIs the Science and Engineering Workforce Drawn fromthe Far Upper Tail of the Math Ability Distributionrsquorsquo mimeo UCSB 2005

Westfall Jacob Leaf Van Boven John Chambers and Charles Judd lsquolsquoPerceivingPolitical Polarization in the United States Party Identity Strength andAttitude Extremity Exacerbate the Perceived Partisan DividersquorsquoPsychological Science 10 (2015) 145ndash158

Wolsko Christopher Bernadette Park Charles Judd and Bernd WittenbrinklsquolsquoFraming Interethnic Ideology Effects of Multicultural and Color-BlindPerspectives on Judgments of Groups and Individualsrsquorsquo Journal ofPersonality and Social Psychology 78 (2000) 635ndash654

QUARTERLY JOURNAL OF ECONOMICS1794

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

Page 41: I. Introduction · uneducated at the beginning of the 20th century, and as high achievers at the beginning of the 21st (Madon et al. 2001). Social science has produced three broad

Glover Dyland Amanda Pallais and William Pariente lsquolsquoDiscrimination as a Self-Fulfilling Prophecy Evidence from French Grocery Storesrsquorsquo mimeo HarvardUniversity 2015

Goldin Claudia Lawrence Katz and Ilyana Kuziemko lsquolsquoThe Homecoming ofAmerican College Women The Reversal of the College Gender GaprsquorsquoJournal of Economic Perspectives 20 (2006) 133ndash156

Graham Jesse Brian Nosek and Jonathan Haidt lsquolsquoThe Moral Stereotypes ofLiberals and Conservatives Exaggeration of Differences across thePolitical Spectrumrsquorsquo PLoS One 7 (2012) 1ndash13

Grether David lsquolsquoBayes Rule as a Descriptive Model The RepresentativenessHeuristicrsquorsquo Quarterly Journal of Economics 95 (1980) 537ndash557

Griffin Dale and Amos Tversky lsquolsquoThe Weighing of Evidence and theDeterminants of Confidencersquorsquo Cognitive Psychology 24 (1992) 411ndash435

Guiso Luigi Ferdinando Monte Paola Sapienza and Luigi Zingales lsquolsquoCultureGender and Mathrsquorsquo Science 320 (2008) 1164ndash1165

Hilton James and William Von Hippel lsquolsquoStereotypesrsquorsquo Annual Review ofPsychology 47 (1996) 237ndash271

Hyde Janet Sara Lindberg Marcia Linn Amy Ellis and Caroline WilliamslsquolsquoGender Similarities Characterize Math Performancersquorsquo Science 321 (2008)494ndash495

Judd Charles and Bernardette Park lsquolsquoDefinition and Assessment of Accuracy inSocial Stereotypesrsquorsquo Psychological Review 100 (1993) 109ndash128

Jussim Lee Jarret Crawford Stephanie Anglin John Chambers Sean Stevensand Florette Cohen lsquolsquoStereotype Accuracy One of the Largest and MostReplicable Effects in All of Social Psychologyrsquorsquo in The Handbook ofPrejudice Stereotyping and Discrimination Todd Nelson ed (MahwahNJ Lawrence Erlbaum 2015)

Kahneman Daniel and Amos Tversky lsquolsquoSubjective Probability A Judgment ofRepresentativenessrsquorsquo Cognitive Psychology 3 (1972) 430ndash454

mdashmdashmdash lsquolsquoOn the Psychology of Predictionrsquorsquo Psychological Review 80 (1973) 237ndash251

Kaplowitz Stan Bradley Fisher and Clifford Broman lsquolsquoHow Accurate ArePerceptions of Social Statistics about Blacks and Whitesrsquorsquo Public OpinionQuarterly 67 (2003) 237ndash243

Kersten Daniel Pascal Mamassian and Alan Yuille lsquolsquoObject Perception asBayesian Inferencersquorsquo Annual Review of Psychology 55 (2004) 271ndash304

Klein Richard Kate A Ratliff Michelangelo Vianello Reginald B Adams JrStepan Bahnik Michael J Bernstein Konrad Bocian Mark J BrandtBeach Brooks Claudia Chloe Brumbaugh Zeynep CemalcilarJesse Chandler Winnee Cheong William E Davis Thierry DevosMatthew Eisner Natalia Frankowska David Furrow Elisa Maria GallianiFred Hasselman Joshua A Hicks James F Hovermale S Jane HuntJeffrey R Huntsinger Hans IJzerman Melissa-Sue John Jennifer A Joy-Gaba Heather Barry Kappes Lacy E Krueger Jaime Kurtz CarmelA Levitan Robyn Mallett Wendy L Morris Anthony J Nelson JasonA Nier Grant Packard Ronaldo Pilati Abraham M RutchickKathleen Schmidt Jeanine L Skorinko Robert Smith Troy G SteinerJustin Storbeck Lyn M Van Swol Donna Thompson Anna van rsquot VeerLeigh Ann Vaughn Marek Vranka Aaron Wichman Julie A Woodzickaand Brian A Nosek lsquolsquoInvestigating Variation in Replicability A ManyLabs Replication Projectrsquorsquo Social Psychology 45 (2014) 142ndash152

Lundberg Shelly and Richard Startz lsquolsquoPrivate Discrimination and SocialIntervention in Competitive Labor Marketsrsquorsquo American Economic Review73 (1983) 340ndash347

Madon Stephanie Max Guyll Kathy Aboufadel Eulices Montiel Alison SmithPolly Palumbo and Lee Jussim lsquolsquoEthnic and National Stereotypes ThePrinceton Trilogy Revisited and Revisedrsquorsquo Personality and SocialPsychological Bulletin 27 (2001) 996ndash1010

Martin Carol lsquolsquoA Ratio Measure of Sex Stereotypingrsquorsquo Journal of Personality andSocial Psychology 52 (1987) 489ndash499

STEREOTYPES 1793

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

McCauley Clark Krishna Thangavelu and Paul Rozin lsquolsquoSex Stereotyping ofOccupations in Relation to Television Representations and Census FactsrsquorsquoBasic and Applied Social Psychology 9 (1988) 197ndash212

Mullainathan Sendhil lsquolsquoThinking through Categoriesrsquorsquo mimeo HarvardUniversity 2002

Ortoleva Pietro and Erik Snowberg lsquolsquoOverconfidence in Political BehaviorrsquorsquoAmerican Economic Review 105 (2015) 504ndash535

Phelps Edmund lsquolsquoThe Statistical Theory of Racism and Sexismrsquorsquo AmericanEconomic Review 62 (1972) 659ndash661

Pope Devin and Justin Sydnor lsquolsquoGeographic Variation in the Gender Differencesin Test Scoresrsquorsquo Journal of Economic Perspectives 24 (2010) 95ndash108

Rabin Matthew lsquolsquoInference by Believers in the Law of Small NumbersrsquorsquoQuarterly Journal of Economics 117 (2002) 775ndash816

Rabin Matthew and Joel Schrag lsquolsquoFirst Impressions Matter A Model ofConfirmatory Biasrsquorsquo Quarterly Journal of Economics 114 (1999) 37ndash82

Rabin Matthew and Dimitri Vayanos lsquolsquoThe Gamblerrsquos and Hot-Hand FallaciesTheory and Applicationsrsquorsquo Review of Economic Studies 77 (2010) 730ndash778

Reuben Ernesto Paola Sapienza and Luigi Zingales lsquolsquoHow Stereotypes ImpairWomenrsquos Careers in Sciencersquorsquo Proceedings of the National Academy ofSciences 111 (2014) 4403ndash4408

Rosch Eleanor lsquolsquoNatural Categoriesrsquorsquo Cognitive Psychology 4 (1973) 328ndash350Ryan Carey S lsquolsquoAccuracy of Black and White College Studentsrsquo In-Group and

Out-Group Stereotypesrsquorsquo Personality and Social Psychology Bulletin 22(1996) 1114ndash1127

Schneider David The Psychology of Stereotyping (New York Guilford Press2004)

Schneider David Albert Hastorf and Phoebe Ellsworth Person Perception(Reading MA Addison-Wesley 1979)

Shih Margaret Todd Pittinsky and Nalini Ambady lsquolsquoStereotype SusceptibilityIdentity Salience and Shifts in Quantitative Performancersquorsquo PsychologicalScience 10 (1999) 80ndash83

Shih Margaret Todd Pittinsky and Amy Trahan lsquolsquoDomain-Specific Effects ofStereotypes on Performancersquorsquo Self and Identity 5 (2006) 1ndash14

Steele Claude Whistling Vivaldi How Stereotypes Affect Us and What We CanDo (New York Norton 2010)

Tenenbaum Joshua and Thomas Griffiths lsquolsquoThe Rational Basis ofRepresentativenessrsquorsquo 23rd Annual Conference of the Cognitive ScienceSociety (2001) 1036ndash1041

Tversky Amos and Daniel Kahneman lsquolsquoExtensional versus Intuitive ReasoningThe Conjunction Fallacy in Probability Judgmentrsquorsquo Psychological Review 90(1983) 293ndash315

Weinberger Catherin lsquolsquoIs the Science and Engineering Workforce Drawn fromthe Far Upper Tail of the Math Ability Distributionrsquorsquo mimeo UCSB 2005

Westfall Jacob Leaf Van Boven John Chambers and Charles Judd lsquolsquoPerceivingPolitical Polarization in the United States Party Identity Strength andAttitude Extremity Exacerbate the Perceived Partisan DividersquorsquoPsychological Science 10 (2015) 145ndash158

Wolsko Christopher Bernadette Park Charles Judd and Bernd WittenbrinklsquolsquoFraming Interethnic Ideology Effects of Multicultural and Color-BlindPerspectives on Judgments of Groups and Individualsrsquorsquo Journal ofPersonality and Social Psychology 78 (2000) 635ndash654

QUARTERLY JOURNAL OF ECONOMICS1794

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from

Page 42: I. Introduction · uneducated at the beginning of the 20th century, and as high achievers at the beginning of the 21st (Madon et al. 2001). Social science has produced three broad

McCauley Clark Krishna Thangavelu and Paul Rozin lsquolsquoSex Stereotyping ofOccupations in Relation to Television Representations and Census FactsrsquorsquoBasic and Applied Social Psychology 9 (1988) 197ndash212

Mullainathan Sendhil lsquolsquoThinking through Categoriesrsquorsquo mimeo HarvardUniversity 2002

Ortoleva Pietro and Erik Snowberg lsquolsquoOverconfidence in Political BehaviorrsquorsquoAmerican Economic Review 105 (2015) 504ndash535

Phelps Edmund lsquolsquoThe Statistical Theory of Racism and Sexismrsquorsquo AmericanEconomic Review 62 (1972) 659ndash661

Pope Devin and Justin Sydnor lsquolsquoGeographic Variation in the Gender Differencesin Test Scoresrsquorsquo Journal of Economic Perspectives 24 (2010) 95ndash108

Rabin Matthew lsquolsquoInference by Believers in the Law of Small NumbersrsquorsquoQuarterly Journal of Economics 117 (2002) 775ndash816

Rabin Matthew and Joel Schrag lsquolsquoFirst Impressions Matter A Model ofConfirmatory Biasrsquorsquo Quarterly Journal of Economics 114 (1999) 37ndash82

Rabin Matthew and Dimitri Vayanos lsquolsquoThe Gamblerrsquos and Hot-Hand FallaciesTheory and Applicationsrsquorsquo Review of Economic Studies 77 (2010) 730ndash778

Reuben Ernesto Paola Sapienza and Luigi Zingales lsquolsquoHow Stereotypes ImpairWomenrsquos Careers in Sciencersquorsquo Proceedings of the National Academy ofSciences 111 (2014) 4403ndash4408

Rosch Eleanor lsquolsquoNatural Categoriesrsquorsquo Cognitive Psychology 4 (1973) 328ndash350Ryan Carey S lsquolsquoAccuracy of Black and White College Studentsrsquo In-Group and

Out-Group Stereotypesrsquorsquo Personality and Social Psychology Bulletin 22(1996) 1114ndash1127

Schneider David The Psychology of Stereotyping (New York Guilford Press2004)

Schneider David Albert Hastorf and Phoebe Ellsworth Person Perception(Reading MA Addison-Wesley 1979)

Shih Margaret Todd Pittinsky and Nalini Ambady lsquolsquoStereotype SusceptibilityIdentity Salience and Shifts in Quantitative Performancersquorsquo PsychologicalScience 10 (1999) 80ndash83

Shih Margaret Todd Pittinsky and Amy Trahan lsquolsquoDomain-Specific Effects ofStereotypes on Performancersquorsquo Self and Identity 5 (2006) 1ndash14

Steele Claude Whistling Vivaldi How Stereotypes Affect Us and What We CanDo (New York Norton 2010)

Tenenbaum Joshua and Thomas Griffiths lsquolsquoThe Rational Basis ofRepresentativenessrsquorsquo 23rd Annual Conference of the Cognitive ScienceSociety (2001) 1036ndash1041

Tversky Amos and Daniel Kahneman lsquolsquoExtensional versus Intuitive ReasoningThe Conjunction Fallacy in Probability Judgmentrsquorsquo Psychological Review 90(1983) 293ndash315

Weinberger Catherin lsquolsquoIs the Science and Engineering Workforce Drawn fromthe Far Upper Tail of the Math Ability Distributionrsquorsquo mimeo UCSB 2005

Westfall Jacob Leaf Van Boven John Chambers and Charles Judd lsquolsquoPerceivingPolitical Polarization in the United States Party Identity Strength andAttitude Extremity Exacerbate the Perceived Partisan DividersquorsquoPsychological Science 10 (2015) 145ndash158

Wolsko Christopher Bernadette Park Charles Judd and Bernd WittenbrinklsquolsquoFraming Interethnic Ideology Effects of Multicultural and Color-BlindPerspectives on Judgments of Groups and Individualsrsquorsquo Journal ofPersonality and Social Psychology 78 (2000) 635ndash654

QUARTERLY JOURNAL OF ECONOMICS1794

at Harvard L

ibrary on October 28 2016

httpqjeoxfordjournalsorgD

ownloaded from