PSYCHOLOGICAL EXPECTED UTILITY THEORY AND …pages.stern.nyu.edu/~dbackus/Exotic/1Other/CaplinLeahy antic QJE … · portfolio, tend to increase anxiety in the period before ” nal

PSYCHOLOGICAL EXPECTED UTILITY THEORY ANDANTICIPATORY FEELINGS

ANDREW CAPLIN AND JOHN LEAHY

We extend expected utility theory to situations in which agents experiencefeelings of anticipation prior to the resolution of uncertainty We show how theseanticipatory feelings may result in time inconsistency We provide an examplefrom portfolio theory to illustrate the potential impact of anticipation on assetprices

I INTRODUCTION

We all experience feelings related to our uncertainty aboutthe future such as hopefulness anxiety and suspense Psy-chologists have long recognized the importance of these anticipa-tory emotions with anxiety theory being one of the most dynamicelds of psychological research

Economists in contrast have paid little attention to theanticipatory emotions and what attention has been paid has beenlimited to the case of a certain future as in Jevons [1905] andLoewenstein [1987]1 Loewenstein builds a model to explain whyone might bring forward an unpleasant experience to shorten theperiod of dread yet delay a pleasant experience in order to savorit Since his model is deterministic it is ill-suited to capturinganticipatory emotions such as anxiety that are predicated on anuncertain future

In this paper we provide a new model of decision makingunder uncertainty in which we allow for a quite general class ofanticipatory emotions While our general theory is relatively un-structured it nevertheless delivers novel results in almost allareas of application in part due to the time inconsistency ofindividual preferences Time inconsistency arises naturally in thepresence of anticipation As time passes so do anticipatory emo-tions and preferences may change as a result

We thank Edward Glaeser Colin Camerer Daniel Cohen Vincent Craw-ford Jon Elster Nico Frijda Daniel Gilbert Simon Gilchrist David LaibsonGeorge Loewenstein Mark Machina Sendhil Mullainathan Yaw Nyarko Efe OkMatthew Rabin Bob Rosenthal Ben Slugowski Charles Wilson and Ruth Wyattfor valuable comments Caplin thanks the C V Starr Center at New YorkUniversity and Leahy thanks the National Science Foundation and the SloanFoundation for nancial support

1 Elster and Loewenstein [1992] provide a rich yet informal discussion ofthe importance of utility from anticipation as well as utility from memory

copy 2001 by the President and Fellows of Harvard College and the Massachusetts Institute ofTechnologyThe Quarterly Journal of Economics February 2001

55

We begin in Section II with a brief and highly selectivesurvey of some of the relevant psychological literature on antici-pation We focus our discussion on the nature and determinantsof anxiety since this has been a particularly active area of re-search For our purposes the most important conclusions are thatanxiety is anticipatory and that the desire to reduce anxietymotivates many decisions

In Section III we show how to extend the expected utilitymodel to incorporate anticipation Our approach is to expand thestandard prize space to include anticipatory emotions such assuspense and anxiety and to model how lotteries over futurephysical prizes inuence these emotions We then place our pref-erences into a two-period decision problem and prove that opti-mal strategies exist Because we expand the state space to in-clude states of mind we refer to our model as the psychologicalexpected utility model

In Section IV we specialize the model and focus on the port-folio decisions of an anxious saver We argue that the incorpora-tion of anxiety into asset pricing models may help explain boththe equity premium puzzle and the risk-free rate puzzle Safeassets by providing secure returns may reduce anxiety evenbefore nal consumption takes place They therefore provide anextra benet in addition to the smoothing of nal consumptionacross states serving to reduce the risk-free rate Stocks andother risky assets however by increasing the variance of theportfolio tend to increase anxiety in the period before nal con-sumption takes place Hence owning stocks involves an extra costin addition to increasing the variance of nal consumption whichincreases their required return

Anxiety complements risk aversion in our discussion of therisk-free rate puzzle and the equity premium puzzle The discus-sion in Section IV however also points out several differencesbetween anxiety and risk aversion One is that anxiety mayrespond more directly to possibilities than to probabilities so thatagents may appear to ldquooverreactrdquo to small probability eventsAnother is that anxiety is an anticipatory emotion whereas riskaversion is a static concept Hence there will be a time prole toanxiety that is absent in attitudes toward risk Finally we dis-cuss the interaction between anxiety and attention and showhow agents may avoid anxiety by putting their heads in the sandwith the obvious consequences for the quality of decision making

Section V discusses other applications and extensions of the

56 QUARTERLY JOURNAL OF ECONOMICS

framework Section VI discusses the relationship between ourwork and prior work in decision theory Section VII briey dis-cusses some of the policy implications of the model Section VIIIcontains concluding remarks

II AVERSIVE FEELINGS ABOUT FUTURE LOTTERIESTHEORY AND EVIDENCE

To motivate our model we present evidence from the psycho-logical literature on the anxiety worry and fear constellation ofemotions We rst outline qualitative theories of anxiety anddiscuss the experimental evidence on the determinants of anxi-ety We then present evidence that people make choices that areaimed at lowering their level of anxiety

IIA Determinants of Anxiety

Two agreed principles of anxiety theory are that the emotionis anticipatory and aversive According to the glossary of theDiagnostic and Statistical Manual of Mental Disorders [AmericanPsychiatric Association 1987] the term anxiety denotes ldquoappre-hension tension or uneasiness that stems from the anticipationof dangerrdquo [p 392] Recent work on worry is even more clear-cutin this regard2 ldquoWorry is a cognitive phenomenon it is concernedwith future events where there is uncertainty about the outcomethe future being thought about is a negative one and this isaccompanied by feelings of anxietyrdquo [MacLeod Williams andBekerian 1991 p 478]

Research indicates that these anticipatory feelings can beacute Andrykowski Redd and Hateld [1985] for exampledocument that many patients who are due to receive chemother-apy experience bouts of vomiting and related noxious symptomsduring the 24 hours prior to treatment In some cases the antic-ipation of an event may be worse than the event itself Lazarus[1966] provides a survey of experiments demonstrating that cer-tain forms of physical pain such as pinpricks do not producemeasurable psychological-stress reactions beyond those producedby the mere anticipation of such conditions3

2 As Eysenck [1997] points out Aristotle was already clear on the subjectldquoLet fear then be a kind of pain or disturbance resulting from the imagination ofimpending danger either destructive or painfulrdquo [Aristotle in Eysenck]

3 Whereas much anxiety is purely anticipatory there is also evidence thatanxiety can be learned In their study of patientsrsquo levels of anxiety prior to their

57PSYCHOLOGICAL EXPECTED UTILITY THEORY

It is now widely believed that the anticipatory and unpleas-ant nature of fear are two aspects of an innate mammalian ldquofearsystemrdquo Many theorists view fear as a ldquobasic emotionrdquo with aprofound evolutionary role in species preservation4 In work withboth rats and humans LeDoux [1993] has established the impor-tant role of the amygdala in the preconscious evaluation of astimulus as representing a potential threat This evaluationserves to trigger a set of internal and external responses that aidin the further evaluation of the frightening stimulus with con-scious feelings of fear and anxiety representing but one part ofthis overall system In this vision the aversive nature of anxietyis connected to the appropriate ldquoightrdquo response

The fact that there are important neurological and physio-logical concomitants of anxiety has proved very important inestablishing higher measurement standards in the eld of anxi-ety research than in most other branches of psychological theoryIn the early experimental literature skin conductance and pulserate were among the key measures used in addition to self-reported data The arsenal of available measures is currentlyundergoing rapid expansion as experimentalists manipulate theenvironment to induce fear and then measure as many aspects aspossible of the bodily and neurological response5

IIB Anxiety and Choices

Experimentalists have uncovered many regularities in thedeterminants of anxiety One is that an extended waiting periodbefore a stressful event results in a markedly greater buildup ofanxiety than does a shorter waiting period [Nomikos et al 1968]This suggests that it may be better to undertake an anxiety-inducing task immediately in order to shorten the duration of theanxiety A number of studies support this intuition Cook andBarnes [1964] performed some early experiments linking feelings

rst six doses of chemotherapy Jacobsen Bovberg and Redd [1996] are inter-ested in the dynamic pattern of anxiety Their results are broadly supportive of asimple model of learning theory whereby a bad experience in an earlier chemo-therapy session results in elevated anxiety prior to subsequent sessions

4 The origin of this work is Darwinrsquos theory of mammalian facial expressionsas dening of emotions In support of this it has been found that there istremendous cross-cultural agreement about which facial expressions convey fearas opposed to other emotions such as elation

5 See Gerritsen et al [1996] for an application of this methodology to socialfear and Cacciopo et al [1993] for a rich discussion of studies that attempt todistinguish fear responses from other emotional responses


of anxiety to choice behavior They offered subjects a choice be-tween a large immediate electric shock and a lesser shock thatwould be delayed by eight seconds They found that many sub-jects chose the larger shock rather than waiting anxiously for thesmaller shock A similar pattern was identied by Loewenstein[1987] who used a survey technique to conrm that many sub-jects would prefer an immediate electric shock over a shock de-layed by 24 hours

There has also been a signicant volume of research onwhether additional information about an upcoming event willserve to raise or to lower anxiety The pioneering work in thisarea is due to Janis [1958] who believed that providing informa-tion prior to a medical procedure would stimulate the ldquowork ofworryingrdquo that would initially raise anxiety but subsequentlylower anxiety (and possibly speed recovery) Consistent with thistheory Klusman [1975] reported results of an experiment inwhich childbirth information generally lowered anxiety and low-ered patient self-reports of pain

It is now widely accepted that not all individuals want orbenet from information and that information actually serves toraise anxiety in some cases In one of a number of similar studiesMiller and Mangan [1983] performed an experiment on subjectswho were about to undergo a stressful medical procedure (colos-copy) The patients rst completed a questionnaire upon the basisof which they were categorized as either ldquobluntersrdquo or ldquomonitorsrdquoblunters answered the survey in a manner suggestive of informa-tion avoidance while monitorsrsquo answers suggested a pattern ofinformation gathering Voluminous prior information about theprocedure was then provided to half of the monitors and half ofthe blunters with minimal information given to the others Theresults conrmed the theory that more information lowered theanxiety level of the monitors but raised the anxiety level of theblunters6

Given that information inuences anxiety it is not surpris-ing that people often collect information in a way that reducesanxiety The desire of some subjects to avoid information inanxiety-inducing situations was conrmed experimentally by

6 The discovery of widely divergent anxiety responses to information is partof a broader analysis of differences in anxiety responses across individuals Thedistinction between anxiety-inducing external states of the world and anxiety-proneness as an individual trait has been central in the recent theoretical lit-erature [Spielberger 1972]


Averill and Rosenn [1972] (see Section V below for details) Morerecently these ndings have moved out of the laboratory and intothe eld In a study by Lerman et al [1998] subjects who hadearlier given a blood sample were told that their blood sample hadbeen analyzed to identify whether or not they were carriers of oneof two genetic mutations that indicate susceptibility to breastcancer later in life Subjects were then asked whether or not theywanted to know the result of the test Despite the clear planningadvantage of knowing onersquos status a large set of experimentalsubjects reject this information Of the 396 individuals who wereincluded in the study 227 chose to receive the information whilethe remaining 169 declined

IIC Toward a Decision-Theoretic Framework

The psychological research on anxiety needs to be placed in adecision-theoretic setting in order to ask and answer the manyimportant policy questions that are raised The framework mustrespect the qualitative ndings that anxiety is anticipatory andaversive Where possible the level of anxiety should be related tobeliefs in a manner that ts with the experimental evidence andthe theory should therefore have no difculty in matching thendings concerning how anxiety inuences choices Finally themodel should allow us to develop decision-theoretic and game-theoretic approaches in order to identify welfare-enhancing poli-cies in settings in which anxiety matters Our model is designedto accomplish these broad objectives not only for the case ofanxious feelings but also for the broader class of anticipatoryemotions

III THE GENERAL FRAMEWORK

The model has three components The rst is a denition ofthe relevant prize space We replace the standard prize spacewith a space of ldquopsychological statesrdquo comprising a complete (formodel purposes) description of the individualrsquos state of mind Anindividual can experience many different mental states such asanxiety or excitement and it is these that we connect to theagentrsquos level of utility and well-being The second component ofthe model is a formal description of the space of lotteries in thephysical world and of the manner in which uncertainty aboutthese lotteries resolves over time The nal component is a map-ping that connects physical lotteries with mental states We refer


to the complete model as the psychological expected utility modelAfter presenting the basic model we develop the correspondingdecision-theoretic framework and prove that optimal strategiesexist

IIIA The General Model of Individual Preferences

We model an agentrsquos state of mind as a vector of real num-bers Formally there are two periods and two spaces Xt Rntt = 12 that represent the possible psychological states in eachof the two periods Let X denote the product space X1 3 X2 Thespace of psychological lotteries P(X) is the space of all Borelprobability distributions on X We endow X with the producttopology and P(X) with the topology of weak convergence Sinceeach space Xt is separable X is separable and P(X) is separableand metrizable (by the Prohorov metric)

Note that P(X) is a mixture space for l [ [01] and p q [P(X) there exists an element of P(X) which we shall denote p l qthat assigns to each Borel measurable subset A X the proba-bility l p( A) + (1 2 l )q( A)

We assume that the decision maker has a preference relationsdened on psychological lotteries P(X) that satises standardaxioms for choice under uncertainty including a substitutionaxiom

ASSUMPTION 1 Make the following assumptions on s

(i) s is complete and transitive

(ii) for all p q r [ P(X) and l [ [01] p sq implies p l r

s q l r

(iii) given p q r [ P(X) such that p sq and q

s r thereexist l 1 l 2 [ [01] such that p l 1r

s q and p l 2r aq(iv) for all p q [ P(X) ( p1p2) = (q1q2) implies that p

q(v)

s is continuous in the topology of weak convergence7

Assumption 1(ii) is the substitution axiom which we assume

7 A binary relation sdened on a mixture space V is continuous if for all xy z [ V

l [ [01] x l y s z

andl [ [01] z s xl y

are closed


holds on the space of psychological lotteries Assumption 1(iv) issufcient for the additive separability of preferences over timewhich we assume for convenience

Assumption 1 is sufcient to ensure that there exists anexpected utility representation of

s (see Fishburn [1982] Theo-rem 101 and p 73) Let Erf denote the expectation of the randomvariable f with respect to the measure r

PROPOSITION 1 Given Assumption 1 there exists a bounded con-tinuous function U X reg R such that for p q [ P(X) p

sq if and only if EpU ugrave EqU In addition the function U X regR has a time additive representation

U(x) 5 u1(x1) 1 u2(x2)

where u t Xt reg R for t [ 12

Turning to the physical lotteries the basic data are twospaces describing all of the physical prizes that the agent mayreceive in each period Zt [ Rmt t [ 12 Since our concern isanticipation the timing of physical and psychological lotteriesand utility is important We take as our convention that theperiod t psychological state is realized at the end of period timmediately after the physical state for the period is realizedHence there is no time for anticipation within a period Given thetwo-period setup this means that the agent will only experiencefeelings of anticipation in the rst period Those feelings will onlyconcern the second-period uncertainty that remains unresolvedafter the outcome of the rst-period lottery has been realizedSince there are no anticipatory feelings in the second period wemake the simplifying assumption that the physical and psycho-logical reward spaces are the same in the second period Z2 = X2This is equivalent to assuming that only the actual physical prizein period 2 inuences that periodrsquos psychological state

The rst period is more subtle To capture anticipatory emo-tions we allow the psychological prize in period 1 to depend notonly on the physical prize received in the rst period but also onthe remaining uncertainty concerning the physical prize that willbe realized in the second period To capture this we follow themethods of Kreps and Porteus [1978] to formalize evolving un-certainty Let Z1 be the space of physical prizes in period 1 andL2 the space of Borel probability distributions over period 2prizes Dene Y1 = Z1 3 L2 and let L1 be the space of Borel


probability measures over Y1 We endow Y1 with the producttopology and L1 with the topology of weak convergence It can beshown that both L1 and Y1 are separable metrizable spaces (seeKreps and Porteus [1978])

The elements of Y1 can be thought of as the pure outcomes inthe rst period these pure outcomes include a prize from Z1 anda lottery over future prizes from L2 Each such outcome deter-mines just how much uncertainty regarding the second-periodprize remains to be resolved in the second period Thus a lotteryl1 [ L1 species the period 1 view of the likely state of knowledgeat the end of the period In this way a lottery l1 [ L1 encodes thetiming of the resolution of uncertainty Following Kreps andPorteus we refer to each element l1 [ L1 as a temporal lottery

To complete our model of preferences we dene the functionf Y1 reg X1 which gives the psychological state that results froman agent facing the outcome y1 [ Y1 We assume that f iscontinuous

We are now in a position to dene the utility function overtemporal lotteries This utility function is induced by the map-ping f and the utility function over psychological prizes Giveny1 = ( z1l2) [ Y1

(1) V1( y1) 5 u1( f ( y1)) 1 El2[u2( x2)]

V1 looks like a standard time-separable expected utility functionexcept for the presence of l2 in rst-period utility Given any twotemporal lotteries l1 l 91 [ L1 l1

s l 91 if and only if El1V1( y1)

ugrave El19 V1( y1)As we will see in Section IV it is f that gives the theory

structure It is in this mapping that we capture different psycho-logical attitudes toward uncertainty8

IIIB A General Decision Problem

We consider decision problems with the following generalstructure Given an initial state s1 [ S1 the agent chooses anaction a [ A1 from a feasible set G 1(s1) A1 The initial stateand action determine the physical payoff in the rst period ac-cording to a payoff function h S1 3 A1 reg Z1 Between the rst

8 The nature of the model as a formulation of anticipatory feelings is cap-tured in the assumption that the period t feelings are based purely on the currentphysical prize and uncertainty that is as yet unresolved The past prizes and pastpsychological states play no role in determining current feelings


and the second period a new exogenous state s2 [ S2 is realizedaccording to the Markov transition function Q(Bs)

Q(Bs) 5 Prs2 [ B u s1 5 s

Finally in the second period the agent chooses a lottery oversecond-period prizes from a feasible set that may depend bothupon the earlier action choice and the new informationG 2( a 1s2) L29 After this all remaining uncertainty is resolvedand the second-period payoff is realized We make standard sim-plifying assumptions on the various data of the problem

ASSUMPTION 2 The spaces A1 S1 and S2 are subsets of nite-dimensional Euclidean spaces The choice correspondencesG 1 and G 2 are compact valued and continuous The functionh S1 3 A1 reg Z1 is continuous in the second argument

We dene strategies in the standard fashion A period 2policy is a measurable function p 2 A1 3 S2 reg L2 withp 2( a 1s2) [ G 2( a 1s2) We let P 2 denote the set of such policies Anoverall strategy is a combination of an initial choice a 1 [ G 1(s1)and a second-period policy p 2 [ P 2

The lottery over second-period prizes that the agent antici-pates at the end of period 1 depends both on the distribution ofsecond-period exogenous shocks and on the strategy selected inthe second period We denote this lottery by l ( a 1 p 2 u s1) [ L2

l ( a 1 p 2 u s1) E p 2( a 1s2)Q(ds2s1)

Here p 2 gives the second-period prize distribution conditional onthe second-period state Integrating over second-period statesyields l

The dependence of the rst-period temporal lottery on thesecond-period strategy gives rise to the time inconsistency ofoptimal choices and requires us to take a stand on the appropri-ate denition of optimal strategies in the presence of timeinconsistency

9 Whether or not mixed strategies are allowed in period 2 is determined bythe nature of the correspondence G 2( a 1s2)


IIIC Optimal Strategies Denition and Existence

Our approach to the denition of optimal strategies in thepresence of time inconsistency is to exploit the recursive structureof the optimization problem The appropriate standard of ratio-nality in period 2 is straightforward we know that the agent inthe second period will make a decision that is optimal for thatperiod alone Let J2( a 1s2) denote the value of an optimal policyconditional on the second-period state and rst-period action Inthe second period the agent chooses a lottery from G 2 that maxi-mizes expected utility

J2( a 1s2) 5 maxl2 [ G 2( a 1s2)

E l2[u2( z2)]

We dene the second-period choice correspondence in the naturalmanner as

G2( a 1s2) 5 l2 [ G 2( a 1s2) u J2( a 1s2) 5 E l2[u2( z2)]

An optimal policy in period 2 is a measurable selection fromG2( a 1s2) Let P 2 denote the set of optimal period 2 policies Notethat with our assumptions the theorem of the maximum and astandard measurable selection theorem guarantee that P 2 isnonempty [Hinderer 1970]

The subtle point in the denition of optimal strategies con-cerns the nature of the period 1 choice There may be more thanone optimal policy in the second period and the method of select-ing among such indifferent policies may impact the payoff in therst period Without time consistency there is no presumptionthat indifference extends back from period 2 to period 1 Follow-ing Strotz [1955] we assume that the agent is able to select anyfuture strategy provided that there is no future contingency inwhich there is some alternative strategy that is strictly preferred

Given an initial state s1 [ S1 we refer to strategies p =( a 1 p 2) with p 2 [ P 2 as consistent strategies The (nonempty) setof such strategies is denoted P C(s1) Let J1(s1) denote the value ofan optimal strategy in the rst period then

(2) J1(s1) 5 supa 1[ G (s1)

p 2[ P 2

u1( f ( h (s1 a 1) l ( a 1 p 2u s1))

1 E l ( a 1 p 2 u s1)[u2( z2)]

An optimal strategy is a choice ( a 1 p 2) [ P C(s1) that maximizes


(2) A slight adaptation of a theorem of Harris [1985] shows thatan optimal strategy exists

PROPOSITION 2 An optimal strategy exists

Proof If we consider the decision-maker in period 1 and inperiod 2 as two separate individuals our solution concept isequivalent to selecting the subgame perfect equilibrium that isbest from the period 1 perspective It is easy to conrm that ourmodel satises all of the assumptions of Theorem 1 in Harris[1985] This Theorem states that the set of subgame perfectequilibria compact Since our objectives are continuous an opti-mum exists

IV ASSET PRICES AND ANXIETY

The model of Section III is relatively unstructured In orderto gain insight into the implications of anxiety it is useful toconsider a specic application One area of economics in which wemight expect anxiety to play an important role is portfolio choiceBelow we present a simple model and explore the implications ofanxiety for asset pricing

IVA The Model

Consider a two-period Lucas tree model of consumption andsaving [Stokey and Lucas 1989 p 300] A representative agent isborn with an endowment of a consumption good equal to w1 Theconsumption good is nonstorable The agent is also endowed withN productive assets each in xed supply (normalized to unity)that yield random quantities of a consumption good in the secondperiod Asset n [ N yields sn units of the consumption good inperiod 2

In each period there are spot markets for the consumptiongood and for shares in the assets Given the xed supplies ofgoods and assets the competitive equilibrium in this economy istrivial rst-period consumption is equal to the endowment c1 =w1 second-period consumption is equal to the random output ofthe assets c2 = S sn and the consumer willingly holds all of theassets The question is what prices support this allocation

Our point of departure from the standard model is that inaddition to valuing consumption the utility of the representativeagent depends on the anxiety associated with holding risky as-sets To make the connection with our model explicit we dene


the physical prize spaces to be Z1 = Z2 = R corresponding tounits of consumption ct [ Zt It follows that the space of tempo-ral lotteries is the set of pairs y1 = (c1l2) [ Y1 where l2

represents a lottery over second-period consumption levels Thenal component of the model is the mapping f Y1 reg X1

describing the relationship between temporal lotteries and themental state in period 1 We assume that f (c1l2) = (c1a(l2))where a L2 reg R is a differentiable function that measures theanxiety associated with the lottery l2 [ L2

With this formalization the induced expected utility function(1) takes the form

V1(c1l2) 5 u1(c1a(l2)) 1 b El2[u2(c2)]

In general l2 depends on the portfolio that the agent holds Let udenote the vector of portfolio shares held by the agent and u n theshare of asset n All shares will be unity in equilibrium Denel2( u ) to be the distribution of the random variable S n sn u n and leta( u ) be the differentiable composite mapping a(l2( u )) that asso-ciates with each portfolio the corresponding level of anxiety

The agent chooses the level of rst-period consumption andthe asset portfolio to maximize utility subject to the budgetconstraint

c1 1 On

pnu n 5 w1 1 On

pn

where pn is the price of asset n in terms of the consumption goodin period 1

The rst-order condition for asset n is

(3)shy u1

shy c1pn 5

shy u1

shy adad u n

1 b E l2sn

shy u2

shy c2

By reducing consumption by pn units in the rst period the agentcan purchase one unit of asset n thereby raising consumption bysn units in the second period The portfolio adjustment howeveralso has an effect on the level of anxiety in the rst periodreected in the rst term on the right-hand side of (3)

Rearranging (3) and plugging in the equilibrium conditionspins down the price of the asset

pn 5( shy shy a)u1(w1a(1))( shy shy u n)a(1) 1 b E l2sn( shy shy c2)u2( S n sn)

( shy shy c1)u1(w1 a(1))


where 1 is the vector consisting of all ones Since anxiety isaversive shy u1 shy a is negative It is immediate that an asset thatcauses anxiety has a lower price and a higher required rate ofreturn We now discuss the properties of the anxiety function

IVB Anxiety Risk and the Equity Premium

Suppose that anxiety is decreasing in the mean and increas-ing in the riskiness of second-period consumption10 Suppose forsimplicity that this relationship is linear

a(l2) 5 2 a E l2c2 1 g varl2(c2)

where a and g are positive parameters Since c2 = S sn u n itfollows that

dd u n

a(1) 5 2 a E l2sn 1 2 g covl2(c2sn)

The rst term reects the effect on anxiety of an increase in theholding of asset n through the mean of consumption and thesecond term the effect through the variance

In this formulation the presence of anxiety helps to explainboth the risk-free rate puzzle and the equity premium puzzle Fora riskless asset in which sn is constant dad u n = 2 a sn lt 0 Itfollows that the price of the riskless asset is greater than the price

b El2snS shy u2

shy c2Y shy u1

shy c1D

that it would take in the standard model In this view the agentis purchasing ldquopeace of mindrdquo along with the asset and thisjusties the low risk-free rate11

Since stocks are risky their purchase will tend to increaseboth the mean and the variance of second-period consumptionThe sign of dad u n will depend on how these two effects balanceout If g is sufciently large relative to a the effect through thevariance will dominate and dad u n will be positive In this case

10 That anxiety would be decreasing in the mean and increasing in thevariance of consumption is implicit in most characterizations of anxiety Forexample Lazarus [1966] denes threat as the variable that induces anxiety andconcludes that the ldquodegree of threat is a function primarily of amount imminenceand likelihood of the anticipated harmrdquo [p 43]

11 Hogarth and Kunreuther [1995] found that people refer to peace of mindrather than probabilities when defending purchases of warranties They tend onlyto think about probabilities if these gures are given to them


anxiety will reduce the price of stocks and increase their returnrelative to the standard model Here stock ownership entailspsychic costs The agent has to live with the anxiety that accom-panies the holding of a risky portfolio12

Many discussions of risk appear to confuse anxiety and riskaversion13 We believe that it is important to distinguish betweenthese two phenomena Anxiety is an anticipatory emotion expe-rienced prior to the resolution of uncertainty It is related to thefeeling of living with uncertainty In contrast risk aversion is astatic concept pertaining to the curvature of the utility functionwithin a period

By ignoring anxiety conventional measures of risk aversionunderestimate the effect of uncertainty on asset prices For ex-ample the measure of risk aversion that Barsky et al [1997]obtain from their survey concerns a static gamble A typicalquestion that they ask is whether agents would prefer a job thatguarantees their current income for the rest of their life to alottery between a job that will double their income and a job thatwill cut their income by a third In terms of our model they arelearning only about the curvature of the utility function oversecond-period consumption levels and not the anxiety that work-ers may associate with living with the possibility that their wagemight change As we have seen such an approach will underes-timate the equity premium14

IVC Possibility not Probability

The analysis above shows how an anxious individual mayappear more risk averse Anxiety however also differs from risk

12 Our explanation of the equity premium and risk-free rate puzzles sharesimportant common elements with the work of Epstein and Zin [1989] Farmer[1990] and Weil [1990] based on application of the Kreps-Porteus model In factthe Kreps-Porteus model is a special case of our model in which preferences aretime consistent In addition to highlighting the role of anticipation and timeinconsistency the critical difference between the models lies in the assignment ofutility to specic periods in our model The lack of specicity concerning theassignment of utility across periods in the Kreps-Porteus model means that thereare many different psychological expected utility models that reduce to the sameKreps-Porteus model See Caplin and Leahy [1999] for more on this last point andan application to welfare

13 For example in a section titled ldquoYour Attitude Toward Risk A Question-nairerdquo TIAA-CREF recommends a portfolio allocation on the basis of four ques-tions one of which is ldquoHow would you rate your ability to tolerate the stress ofinvestment volatilityrdquo [TIAA-CREF 1999 p 19]

14 Loewenstein et al [1999] refer to an experiment by Weber and Clore whofound that subjects who were made anxious through hypnosis appeared signi-cantly more risk averse than a control group These subjects appeared to associatetheir feelings of anxiety with the uncertainty of outcomes for the gamble options


aversion in important ways15 In particular it may explain whyagents appear to overreact to small probability events

Harless and Camerer [1994] in a metastudy of laboratoryexperiments on risk taking report that the expected utility modelperforms remarkably well if agents are choosing from gambleswith the same support and quite poorly if the gambles are ofdifferent support Behavior is generally consistent with the modelwhen the probability of an event changes from 34 to 35 percent orfrom 50 to 51 percent but deviates markedly if the probabilitychanges from 0 to 1 percent

The introduction of anticipatory emotions can help to explainthis failure of the expected utility model Damasio [1994] positsthat anticipatory emotions arise in reaction to mental images ofthe outcome of a decision and that these mental images arediscrete If this is the case then changes in probability withinsome broad midrange of values may have little effect on antici-patory emotions and therefore little effect on the rankings oflotteries Changing the probability of an outcome from zero tosome small positive number however may have a large effect onanticipation

This view nds empirical support in the work of MonatAverill and Lazarus [1972] and Bankhart and Elliot [1974] Intheir experiments subjects were informed that they would receivea painful electric shock at a certain point in time with varyingdegrees of certainty Measures of anxiety such as heart rate andskin conductance showed little sensitivity to the probability of theshock unless this probability was zero In the words of Loewen-stein et al [1999] many decisions are sensitive ldquoto the possibilityrather than probability of negative outcomesrdquo

The implications for asset prices are immediate If anxietyreacts to possibilities then asset prices will tend to ldquooverreactrdquo tosmall probability events For example the announcement thatthe Federal Reserve is concerned with ination will focus inves-torsrsquo attention on the possibility of an increase in interest ratesThis will have an effect on investor anxiety independent of thelikelihood of a rate increase

IVD The Time Course of Anxiety

As mentioned above anxiety is an anticipatory emotionwhereas risk aversion is a static concept It follows that one of the

15 Loewenstein et al [1999] discuss these differences extensively


places that the two should differ is in their timing The literaturein experimental psychology suggests that once an individual isfully aware of an upcoming threat the time path of anxiety tendsto be U-shaped [Breznitz 1984] There is intense fear when anindividual is rst informed of an upcoming threat This fear thendiminishes for a while before rising sharply in anticipation of theimpact Moreover an extended waiting period prior to a stressfulevent occurs results in a markedly greater buildup of anxietythan does a shorter waiting period [Nomikos et al 1968]

These studies suggest a complex relationship between thetime that a threat is recognized T0 the time that a threat isexpected to materialize T the current time t and anxiety a Allelse equal newly announced risks (t = T0) should cause greateranxiety than recently announced risks Moreover the buildupprior to impact rises as t approaches T and is greater the longerthe period of anticipation (T 2 T0) There is no analogous rolefor T0 in the analysis of risk

IVE Attention

An experiment of Averill and Rosenn [1972] provides agraphic illustration of the connection between anxiety and atten-tion Subjects were told that there would be an electric shockcoming and that they could switch at will between listening toone of two channels of a tape recorder One channel would broad-cast a warning signal directly before the shock The second chan-nel played music so that listening to it precluded hearing thewarning signal The subjects were divided into two groups Therst group was told that even if they heard the signal they wouldbe unable to avoid the shock The second group was told that ifthey heard the warning signal they would be able to avoid theshock if they immediately pressed a button In the rst group 50percent of the subjects chose to listen to the warning even thoughevasion was impossible In the second group 23 percent of thesubjects chose to listen to the music even though this made itinevitable that they would receive the shock)

The desire to ldquoput onersquos head in the sandrdquo appears general Insummarizing the experimental literature Miller [1987] writesldquoThe evidence indicates that the way in which individuals selec-tively attend to and process threat-relevant cues in a givensituation determine how stressed and anxious they become inthat situationrdquo [p 345]

The most direct asset market application concerns a possible


desire on the part of an anxious investor to avoid information Ifthis desire is important it may dominate the possible planningadvantages involved in paying detailed attention to the currentstate of the portfolio

One area in which such avoidant behavior might have prac-tical implications is saving for retirement Bernheim [1995] offersa sobering assessment of the savings of the baby boom genera-tion arguing that most households are far from adequatelyprepared for retirement He further argues that the low levelsof accumulated wealth are unlikely to reect standard life-cycleconsiderations and are more likely to reect psychological is-sues and in particular psychological impediments to adequateplanning16

A vision of how anxiety and attention interact may aid inunderstanding planning problems in the period leading up toretirement Thinking about all of the nancial and life-stylechanges in the retirement period is likely to be anxiety-inducingGiven that this anxiety is aversive there will be a strongtemptation to avoid thinking about let alone planning for retire-ment until it is too close to avoid ldquoOut of mind out of sightrdquomay increase utility today but at the cost of reducing welfaretomorrow17

VI OTHER APPLICATIONS

VA Anticipatory Pleasure Savoring and Planning

While our discussion has focused on anxiety not all antici-patory emotions are aversive Loewenstein [1987] found thatthere was a general preference for delaying a kiss from a roman-tic ideal This is suggestive of a savoring motive whereby subjectsprefer to extend the period in which they can savor the anticipa-tion of an enjoyable prize According to our theory this savoringmotive should give rise to time inconsistency and a resultingdesire to use commitment devices to overcome the time inconsis-

16 Bernheim Skinner and Weinberg [1997] show that many households gothrough signicant reductions in food consumption upon retirement as if theirretirement came by surprise and caused a large reduction in perceived wealth

17 A related issue concerns the optimal supply of nancial education Bern-heim and Garrett [1996] have shown that savings and participation in nancialeducation counseling are strongly positively correlated It may well be that en-couraging or even ldquoforcingrdquo more households to participate in these programswould result in them being better prepared for retirement But would there be acost in terms of increased anxiety in the preretirement period


tency After all if you currently prefer to delay an experience inorder to savor it will you not feel the same way tomorrow

Caplin and Leahy [1997] provide another example of savor-ing which illuminates the commitment motive We consider afamily contemplating a future vacation to one of two locationsThe family is indifferent between the two locations given theinformation that they initially possess The twist is that theyenjoy thinking about the impending trip and nd it is easier toanticipate the vacation if they know which vacation they willtake This means that the householdrsquos preferences over possiblevacation lotteries will change over time In order to facilitateanticipation they would like to know their destination some timeprior to departure At the point of departure however all thatmatters is which vacation looks more promising at that datewhich may or may not coincide with the choice that they wouldhave made earlier Given this potential change in attitude weshow that the family may wish to commit to one of the locationsat an early stage by getting a nonrefundable airline ticket

VB Suspense and Gambling

Another positive anticipatory emotion is suspense In Caplinand Leahy [1997] we dene suspense as the pleasure experiencedimmediately prior to the anticipated resolution of uncertaintyand posit that it is positively related (up to a point) to the amountthat is at stake on the outcome of an event This provides a simplereason for agents to bet that their emotional favorite will win ina sporting event By betting on their favorite agents increasetheir stake in the outcome thereby heightening feelings of sus-pense Our prediction that agents will prefer to bet on theiremotional favorites nds strong support in the empirical analysisof Babad and Katz [1991] who study betting on soccer matches inIsrael

VC Moods and Risk-Taking Behavior

It has long been conjectured that personal mood impactsrisk-taking behavior a factor that is per force ignored in thestandard theory in which the individualrsquos attitude to risk issummarized by a xed function describing the expected utility ofwealth Isen [1993] notes one important effect Her experimentalresearch indicates that in many settings ldquofeeling goodrdquo gives riseto a higher degree of risk aversion in the sense that the individ-


ual in a good mood rejects as too risky gambles that are accept-able to subjects in a bad mood

Going beyond the experiments Isen [1993] has presented atheoretical explanation that ts in squarely with our model ofrational behavior ldquoThe relative risk aversion observed in positiveaffect subjects considering real risks can be interpreted in termsof affect maintenance People who are feeling happy risk losingthat state as well as any tangible stake if they lose a gambleTherefore with more to lose than controls they are more risk-averse than controlsrdquo [p 270] It is straightforward to use ourmodel of mental states to rationalize precisely this pattern ofbehavior by making the second-period mental state depend uponthe rst-period mental state More broadly our model offers hopefor analyzing the role of moods not only in individual decisionmaking but also in strategic settings18 Are there times duringthe bargaining process when it would make sense to try to inu-ence the mood of your opposite number

VI COMMENTS ON THE LITERATURE

VIA Why Retain the Substitution Axiom

Our approach to analyzing psychological aspects of decisionsis to retain the classical assumption of rationality in its fullforce19 We encode the anticipatory emotions as part of the prizespace and apply the standard substitution axiom on this richerdomain Pope [1985] provides an alternative vision of anticipationand the substitution axiom She believes that the introduction oftime invalidates the substitution axiom while we believe that itrestores it (provided that one uses the appropriate state space)

According to Pope [1985] when one allows for feelings in theperiod prior to the realization of a lottery the intuitive argumentin favor of the substitution axiom may be false Lottery A may bepreferred to lottery B but these lotteries may give rise to entirelydifferent anticipatory responses when mixed with lottery C

We agree with Pope that anticipatory feelings invalidate thestandard static version of the substitution axiom Rather thanabandon the axiom we choose instead to encode the prior feelings

18 See Frijda [1993] for a survey of the psychological literature on moods andmood dynamics

19 In this sense we lie within the tradition summarized in Section 2 ofRabinrsquos [1998] recent survey article on economics and psychology


as prizes in the lottery We believe that when the substitutionaxiom is applied on this larger psychological state space theaxiom regains its original appeal20 Rejection of the substitutionaxiom is valid only if one believes that there can be no completemodel of psychological states as when one is forced to introduceldquoanticipatory feelings about anticipatory feelings about rdquo andso on ad innitum

VIB PEU and Nonexpected Utility Theory

In contrast with our approach much recent progress in thetheory of choice under uncertainty has involved the rejection ofthe substitution axiom for lotteries and the development ofvarious nonexpected utility theories Many of these theories havebeen developed in response to the observed violations of thesubstitution axiom such as the Allais paradox In fact the chiefgoal of many nonexpected utility theories is to relax the substi-tution axiom as little as possible while nevertheless allowing forsome limited class of violations

One important advantage of our formulation over static non-expected utility models is that the latter theories attempt totelescope a dynamic pattern of feelings into a single static utilityfunction Many subtle phenomena in the psychology of risk-tak-ing require explicitly dynamic formulations For example whilethe models of disappointment due to Bell [1985] and Loomes andSugden [1986] are explicit concerning the way in which a givenlottery produces feelings of disappointment they remain staticAmong other things this means that the models do not include ananticipatory phase Have you ever felt disappointed about an out-come without having experienced prior feelings of hopefulness21

The model that is most directly related to ours is the dynamicnonexpected utility model of Kreps and Porteus [1978] This wasthe rst model to allow agents to have a preference for delayingthe receipt of information (see Grant Kajii and Polak [1998] foran exploration of this aspect of the model) In fact our model canbe seen in its reduced form as a generalization of their model in

20 In this respect at least one prominent nonexpected utility theoristagrees Machina wrote ldquoFor my part I will grant that separability may berational provided the descriptions of consequences are sufciently deep to incor-porate any relevant emotional states such as disappointment (eg at having won$0 when you might have won $5 million) regret and so onrdquo [Machina 1989 p1662]

21 Psychological recognition of the link between these two emotions can befound in the very interesting book by Ortony Clore and Collins [1988]


which we relax their assumption that preferences are time con-sistent This is an important generalization since time consis-tency appears to be a very unnatural assumption in cases withanticipatory emotions as we have seen

Caplin and Leahy [1999] provide further motivation for anexpected utility approach such as ours rather than a nonexpectedutility approach such as that of Kreps and Porteus We model adoctorrsquos decision on whether or not to provide a patient withdetailed information about an upcoming operation We show thatthe Kreps-Porteus model is not sufciently rich to model thedoctorrsquos decision The subtle point is that the doctor must be ableto decide what to do in the face of a superior understanding of thelottery that the patient is about to face The decision on whetheror not to provide information at this stage must be based on anassessment of whether or not to leave the patient with an illusionabout tomorrowrsquos lottery The Kreps-Porteus model is not richenough to cover preferences over illusions while such preferencescan be straightforwardly assessed in our psychological expectedutility theory

VII SOME POTENTIAL ISSUES FOR POLICY

Anticipatory emotions such as anxiety are a function ofagentsrsquo beliefs about the future This suggests that policy makersmight want to consider how policies affect beliefs especially pol-icies that involve the provision of information For example sup-pose that the Federal Reserve possesses a piece of bad news suchas the imminent failure of a large bank and that the Fed knowsthat in all likelihood it will be able to solve the problem before theproblem gets out of hand and affects other nancial institutionsor the economy as a whole Should the Fed release this informa-tion immediately or should it hold off until the trouble is pastBarring public misunderstanding of the news if agents are ex-pected utility maximizers then the Fed should provide the newsThe planning advantages of more information argue for immedi-ate disclosure of any information relevant to decision making

In a model with anxiety however the situation is morecomplex The Fed must weigh the planning advantages of supe-rior information against the possibility that an announcementwould needlessly cause investors to worry or worse to panic Ifthe Fed believes that it has the situation under control theoptimal policy would appear to be to suppress the information


The lost planning advantages would be small and since anxietydepends on possibility and not probability the potential reduc-tion in anxiety is large

Policy makers might also be concerned with the actionsagents take to affect their own beliefs Consider an example fromthe medical arena If agents avoid information that makes themanxious they might be reluctant to go to the doctor or testthemselves for diseases such as breast cancer22 Such avoidantbehavior has clear implications for health and health-care costsIn response to the apparent pattern of avoidant behavior therehas recently been increased attention paid to new formats forsupplying medical advice and medical information to the generalpopulation23 A number of studies indicate that ldquopsychologically-appropriaterdquo forms of information-intervention can improvehealth-care outcomes and lower costs on the order of 20 percent[Fries 1998]

VIII CONCLUDING REMARKS

In this paper we have introduced the psychological expectedutility model and used it to analyze the impact on decision makingof anticipatory feelings The broader goal of our research agenda isto open up a variety of psychologically interesting phenomena torational analysis and in this respect our work has just begun

NEW YORK UNIVERSITY

BOSTON UNIVERSITY

REFERENCES

American Psychiatric Association (APA) Diagnostic and Statistical Manual ofMental Disorders 3rd edition (Washington DC APA 1987)

Andrykowski M W Redd and A Hateld ldquoDevelopment of Anticipatory Nau-sea A Prospective Analysisrdquo Journal of Consulting and Clinical PsychologyLIII (1985) 447ndash454

Averill J and M Rosenn ldquoVigilant and Nonvigilant Coping Strategies andPsychophysiological Stress Reactions during Anticipation of Electric ShockrdquoJournal of Personality and Social Psychology XXIII (1972) 128ndash141

Babad E and Y Katz ldquoWishful Thinking Against all Oddsrdquo Journal of AppliedSocial Psychology XXI (1991) 1921ndash1938

Bankhart C and R Elliot ldquoHeart Rate and Skin Conductance in Anticipation of

22 A study by Kash et al [1992] suggests that high levels of anxiety may beassociated with lower levels of compliance with self-examination guidelines inwomen with a family history of breast cancer

23 See Kahn [1999] for a study of the role of information in diabetic risktaking


Shocks with Varying Probability of Occurrencerdquo Psychophysiology XI (1974)160ndash174

Barsky R F T Juster M Kimball and M Shapiro ldquoPreference Parameters andBehavioral Heterogeneity An Experimental Approach in the Health andRetirement Studyrdquo Quarterly Journal of Economics CXII (1997) 537ndash580

Bell D ldquoDisappointment in Decision Making under Uncertaintyrdquo OperationsResearch XXXIII (1985) 1ndash27

Bernheim D ldquoDo Households Appreciate their Financial Vulnerabilities AnAnalysis of Actions Perceptions and Public Policyrdquo Tax Policy and EconomicGrowth (Washington DC American Council for Capital Formation 1995)

Bernheim D J Skinner and S Weinberg ldquoWhat Accounts for the Variation inRetirement Wealth among U S Householdsrdquo NBER Working Paper No6227 1997

Bernheim D and D Garrett ldquoThe Determinants and Consequences of FinancialEducation in the Workplace Evidence from a Survey of Householdsrdquo NBERWorking Paper No 5667 1996

Breznitz S Cry Wolf (Hillsdale NJ Lawrence Erlbaum Associates 1984)Cacciopo J D Klein G Berntson and E Hateld ldquoThe Psychophysiology of

Emotionrdquo in Handbook of Emotions M Lewis and J Haviland eds (NewYork Guilford Press 1993)

Caplin A and J Leahy ldquoPsychological Expected Utility Theory and AnticipatoryFeelingsrdquo Research Report 97-37 C V Starr Center New York University1997

Caplin A and J Leahy ldquoThe Supply of Information by a Concerned ExpertrdquoResearch Report 99-08 C V Starr Center New York University 1999

Cook J and L Barnes ldquoChoice of Delay of Inevitable Shockrdquo Journal of Abnor-mal and Social Psychology LXVIII (1964) 669ndash672

Damasio A Descartesrsquo Error Emotion Reason and the Human Brain (NewYork Putnam 1994)

Elster J and G Loewenstein ldquoUtility from Memory and from Anticipationrdquo inChoice over Time G Loewenstein and J Elster eds (New York Russell SageFoundation 1992)

Epstein L and S Zin ldquoSubstitution Risk Aversion and the Temporal Behaviorof Consumption and Asset Returns A Theoretical Frameworkrdquo Economet-rica LVII (1989) 937ndash969

Eysenck M Anxiety and Cognition A Unied Theory (Hove UK PsychologyPress 1997)

Farmer R ldquoRINCE Preferencesrdquo Quarterly Journal of Economics CV (1990)43ndash60

Fishburn P The Foundations of Expected Utility (Boston D Reidel 1982)Fries J ldquoReducing the Need and Demand for Medical Servicesrdquo Psychosomatic

Medicine LX (1998) 140ndash142Frijda N ldquoMoods Emotion Episodes and Emotionsrdquo in Handbook of Emotions

M Lewis and J Haviland eds (New York Guilford Press 1993)Gerritsen W C Heijnen V Wiegant B Bermond and N Frijda ldquoExperimental

Social Fear Immunological Hormonal and Autonomic Concomitantsrdquo Psy-chosomatic Medicine LVIII (1996) 273ndash286

Grant S A Kajii and B Polak ldquoIntrinsic Preference for Informationrdquo Journalof Economic Theory LXXXIII (1998) 233ndash259

Harless D and C Camerer ldquoThe Predictive Utility of Generalized ExpectedUtility Theoriesrdquo Econometrica LXII (1994) 1251ndash1289

Harris C ldquoExistence and Characterization of Perfect Equilibrium in Games ofPerfect Informationrdquo Econometrica LIII (1985) 613ndash628

Hinderer K Foundations of Non-Stationary Dynamic Programming with Dis-crete Time Parameter (New York Springer-Verlag 1970)

Hogarth R and H Kunreuther ldquoDecision Making under Ignorance Arguingwith Yourselfrdquo Journal of Risk and Uncertainty X (1995) 15ndash36

Isen A ldquoPositive Affect and Decision Makingrdquo in Handbook of Emotions MLewis and J Haviland eds (New York Guilford Press 1993)

Jacobsen P D Bovberg and W Redd ldquoAnticipatory Anxiety in Women Receiv-ing Chemotherapy for Breast Cancerrdquo Health Psychology XII (1996)469ndash 475


Janis I Psychological Stress (New York Wiley 1958)Jevons W Essays on Economics (London Macmillan 1905)Kahn M ldquoDiabetic Risk Taking The Role of Information Education and Medi-

cationrdquo mimeo Columbia University 1999Kash K J Holland M Halper and D Miller ldquoPsychological Distress and

Surveillance Behaviors of Women with a Family History of Breast CancerrdquoJournal of the National Cancer Institute LXXXIV (1992) 24ndash30

Klusman L ldquoReduction in Pain in Childbirth by the Alleviation of Anxiety duringPregnancyrdquo Journal of Consulting and Clinical Psychology XLIII (1975)162ndash165

Kreps D and E Porteus ldquoTemporal Resolution of Uncertainty and DynamicChoice Theoryrdquo Econometrica XLVI (1978) 185ndash200

Lazarus R Psychological Stress and the Coping Process (New York McGrawHill 1966)

LeDoux J ldquoEmotional Networks in the Brainrdquo in Handbook of Emotions MLewis and J Haviland eds (New York Guilford Press 1993)

Lerman C C Hughes S Lemon D Main C Snyder C Durham S Narod HLynch ldquoWhat You Donrsquot Know Can Hurt You Adverse Psychological Effectsin Members of BRCA1-Linked and BRCA2-Linked Families Who DeclineGenetic Testingrdquo Journal of Clinical Oncology XVI (1998) 1650ndash1654

Loewenstein G ldquoAnticipation and the Valuation of Delayed Consumptionrdquo Eco-nomic Journal XCVII (1987) 666ndash 684

Loewenstein G E Weber C Hsee and E Welch ldquoRisk as Feelingrdquo mimeoCarnegie Mellon University 1999

Loomes G and R Sugden ldquoDisappointment and Dynamic Consistency in Choiceunder Uncertaintyrdquo Review of Economic Studies LIII (1986) 271ndash282

Machina M ldquoDynamic Consistency and Non-Expected Utility Models of Choiceunder Uncertaintyrdquo Journal of Economic Literature XXVII (1989)1622ndash1668

MacLeod A J Williams and D Bekerian ldquoWorry is Reasonable the Role ofExplanations in Pessimism about Future Personal Eventsrdquo Journal of Ab-normal Psychology C (1991) 478ndash486

Miller S ldquoMonitoring and Blunting Validation of a Questionnaire to AssessStyles of Information Seeking under Threatrdquo Journal of Personality andSocial Psychology LII (1987) 345ndash353

Miller S and C Mangan ldquoInteracting Effects of Information and Coping Style inAdapting to Gynecologic Stress Should the Doctor Tell Allrdquo Journal ofPersonality and Social Psychology XLV (1983) 223ndash236

Monat A J Averill and R Lazarus ldquoAnticipatory Stress and Coping Reactionsunder Various Conditions of Uncertaintyrdquo Journal of Personality and SocialPsychology XXIV (1972) 237ndash253

Nomikos M E Opton J Averill and R Lazarus ldquoSurprise and Suspense in theProduction of Stress Reactionrdquo Journal of Personality and Social PsychologyVIII (1968) 204ndash208

Ortony A G Clore and A Collins The Cognitive Structure of the Emotions(Cambridge Cambridge University Press 1988)

Pope R ldquoTiming Contradictions in von Neumann and Morgensternrsquos Axioms andin Savagersquos lsquoSure Thingrsquo Proofrdquo Theory and Decision XVIII (1985) 229ndash261

Rabin M ldquoPsychology and Economicsrdquo Journal of Economic Literature XXXVI(1998) 11ndash46

Spielberger C ldquoConceptual and Methodological Issues in Anxiety Researchrdquo inC Spielberger ed Anxiety Current Trends in Theory and Research Volume2 (New York Academic Press 1972)

Stokey Nancy and Robert Lucas Recursive Methods in Economic Dynamics(Cambridge MA Harvard University Press 1989)

Strotz Robert ldquoMyopia and Inconsistency in Dynamic Utility MaximizationrdquoReview of Economic Studies XXIII (1956) 165ndash180

TIAA-CREF ldquoBuilding Your Portfolio with TIAA-CREFrdquo (New York TIAA-CREF1999)

Weil P ldquoNonexpected Utility in Macroeconomicsrdquo Quarterly Journal of Econom-ics CV (1990) 29ndash 42


We begin in Section II with a brief and highly selectivesurvey of some of the relevant psychological literature on antici-pation We focus our discussion on the nature and determinantsof anxiety since this has been a particularly active area of re-search For our purposes the most important conclusions are thatanxiety is anticipatory and that the desire to reduce anxietymotivates many decisions

In Section III we show how to extend the expected utilitymodel to incorporate anticipation Our approach is to expand thestandard prize space to include anticipatory emotions such assuspense and anxiety and to model how lotteries over futurephysical prizes inuence these emotions We then place our pref-erences into a two-period decision problem and prove that opti-mal strategies exist Because we expand the state space to in-clude states of mind we refer to our model as the psychologicalexpected utility model

In Section IV we specialize the model and focus on the port-folio decisions of an anxious saver We argue that the incorpora-tion of anxiety into asset pricing models may help explain boththe equity premium puzzle and the risk-free rate puzzle Safeassets by providing secure returns may reduce anxiety evenbefore nal consumption takes place They therefore provide anextra benet in addition to the smoothing of nal consumptionacross states serving to reduce the risk-free rate Stocks andother risky assets however by increasing the variance of theportfolio tend to increase anxiety in the period before nal con-sumption takes place Hence owning stocks involves an extra costin addition to increasing the variance of nal consumption whichincreases their required return

Anxiety complements risk aversion in our discussion of therisk-free rate puzzle and the equity premium puzzle The discus-sion in Section IV however also points out several differencesbetween anxiety and risk aversion One is that anxiety mayrespond more directly to possibilities than to probabilities so thatagents may appear to ldquooverreactrdquo to small probability eventsAnother is that anxiety is an anticipatory emotion whereas riskaversion is a static concept Hence there will be a time prole toanxiety that is absent in attitudes toward risk Finally we dis-cuss the interaction between anxiety and attention and showhow agents may avoid anxiety by putting their heads in the sandwith the obvious consequences for the quality of decision making

Section V discusses other applications and extensions of the







































s q l r




q(v)




l [ [01] x l y s z


are closed







U(x) 5 u1(x1) 1 u2(x2)









(1) V1( y1) 5 u1( f ( y1)) 1 El2[u2( x2)]















l ( a 1 p 2 u s1) E p 2( a 1s2)Q(ds2s1)







J2( a 1s2) 5 maxl2 [ G 2( a 1s2)

E l2[u2( z2)]






(2) J1(s1) 5 supa 1[ G (s1)

p 2[ P 2

u1( f ( h (s1 a 1) l ( a 1 p 2u s1))

1 E l ( a 1 p 2 u s1)[u2( z2)]








IVA The Model









V1(c1l2) 5 u1(c1a(l2)) 1 b El2[u2(c2)]



c1 1 On

pnu n 5 w1 1 On

pn



(3)shy u1

shy c1pn 5

shy u1

shy adad u n

1 b E l2sn

shy u2

shy c2









a(l2) 5 2 a E l2c2 1 g varl2(c2)


dd u n




b El2snS shy u2

shy c2Y shy u1

shy c1D


























IVE Attention

















































NEW YORK UNIVERSITY

BOSTON UNIVERSITY

REFERENCES




































































































s q l r




q(v)




l [ [01] x l y s z


are closed







U(x) 5 u1(x1) 1 u2(x2)









(1) V1( y1) 5 u1( f ( y1)) 1 El2[u2( x2)]















l ( a 1 p 2 u s1) E p 2( a 1s2)Q(ds2s1)







J2( a 1s2) 5 maxl2 [ G 2( a 1s2)

E l2[u2( z2)]






(2) J1(s1) 5 supa 1[ G (s1)

p 2[ P 2

u1( f ( h (s1 a 1) l ( a 1 p 2u s1))

1 E l ( a 1 p 2 u s1)[u2( z2)]








IVA The Model









V1(c1l2) 5 u1(c1a(l2)) 1 b El2[u2(c2)]



c1 1 On

pnu n 5 w1 1 On

pn



(3)shy u1

shy c1pn 5

shy u1

shy adad u n

1 b E l2sn

shy u2

shy c2









a(l2) 5 2 a E l2c2 1 g varl2(c2)


dd u n




b El2snS shy u2

shy c2Y shy u1

shy c1D


























IVE Attention

















































NEW YORK UNIVERSITY

BOSTON UNIVERSITY

REFERENCES



























































































s q l r




q(v)




l [ [01] x l y s z


are closed







U(x) 5 u1(x1) 1 u2(x2)









(1) V1( y1) 5 u1( f ( y1)) 1 El2[u2( x2)]















l ( a 1 p 2 u s1) E p 2( a 1s2)Q(ds2s1)







J2( a 1s2) 5 maxl2 [ G 2( a 1s2)

E l2[u2( z2)]






(2) J1(s1) 5 supa 1[ G (s1)

p 2[ P 2

u1( f ( h (s1 a 1) l ( a 1 p 2u s1))

1 E l ( a 1 p 2 u s1)[u2( z2)]








IVA The Model









V1(c1l2) 5 u1(c1a(l2)) 1 b El2[u2(c2)]



c1 1 On

pnu n 5 w1 1 On

pn



(3)shy u1

shy c1pn 5

shy u1

shy adad u n

1 b E l2sn

shy u2

shy c2









a(l2) 5 2 a E l2c2 1 g varl2(c2)


dd u n




b El2snS shy u2

shy c2Y shy u1

shy c1D


























IVE Attention

















































NEW YORK UNIVERSITY

BOSTON UNIVERSITY

REFERENCES



















































































s q l r




q(v)




l [ [01] x l y s z


are closed







U(x) 5 u1(x1) 1 u2(x2)









(1) V1( y1) 5 u1( f ( y1)) 1 El2[u2( x2)]















l ( a 1 p 2 u s1) E p 2( a 1s2)Q(ds2s1)







J2( a 1s2) 5 maxl2 [ G 2( a 1s2)

E l2[u2( z2)]






(2) J1(s1) 5 supa 1[ G (s1)

p 2[ P 2

u1( f ( h (s1 a 1) l ( a 1 p 2u s1))

1 E l ( a 1 p 2 u s1)[u2( z2)]








IVA The Model









V1(c1l2) 5 u1(c1a(l2)) 1 b El2[u2(c2)]



c1 1 On

pnu n 5 w1 1 On

pn



(3)shy u1

shy c1pn 5

shy u1

shy adad u n

1 b E l2sn

shy u2

shy c2









a(l2) 5 2 a E l2c2 1 g varl2(c2)


dd u n




b El2snS shy u2

shy c2Y shy u1

shy c1D


























IVE Attention

















































NEW YORK UNIVERSITY

BOSTON UNIVERSITY

REFERENCES













































































s q l r




q(v)




l [ [01] x l y s z


are closed







U(x) 5 u1(x1) 1 u2(x2)









(1) V1( y1) 5 u1( f ( y1)) 1 El2[u2( x2)]















l ( a 1 p 2 u s1) E p 2( a 1s2)Q(ds2s1)







J2( a 1s2) 5 maxl2 [ G 2( a 1s2)

E l2[u2( z2)]






(2) J1(s1) 5 supa 1[ G (s1)

p 2[ P 2

u1( f ( h (s1 a 1) l ( a 1 p 2u s1))

1 E l ( a 1 p 2 u s1)[u2( z2)]








IVA The Model









V1(c1l2) 5 u1(c1a(l2)) 1 b El2[u2(c2)]



c1 1 On

pnu n 5 w1 1 On

pn



(3)shy u1

shy c1pn 5

shy u1

shy adad u n

1 b E l2sn

shy u2

shy c2









a(l2) 5 2 a E l2c2 1 g varl2(c2)


dd u n




b El2snS shy u2

shy c2Y shy u1

shy c1D


























IVE Attention

















































NEW YORK UNIVERSITY

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REFERENCES







































































s q l r




q(v)




l [ [01] x l y s z


are closed







U(x) 5 u1(x1) 1 u2(x2)









(1) V1( y1) 5 u1( f ( y1)) 1 El2[u2( x2)]















l ( a 1 p 2 u s1) E p 2( a 1s2)Q(ds2s1)







J2( a 1s2) 5 maxl2 [ G 2( a 1s2)

E l2[u2( z2)]






(2) J1(s1) 5 supa 1[ G (s1)

p 2[ P 2

u1( f ( h (s1 a 1) l ( a 1 p 2u s1))

1 E l ( a 1 p 2 u s1)[u2( z2)]








IVA The Model









V1(c1l2) 5 u1(c1a(l2)) 1 b El2[u2(c2)]



c1 1 On

pnu n 5 w1 1 On

pn



(3)shy u1

shy c1pn 5

shy u1

shy adad u n

1 b E l2sn

shy u2

shy c2









a(l2) 5 2 a E l2c2 1 g varl2(c2)


dd u n




b El2snS shy u2

shy c2Y shy u1

shy c1D


























IVE Attention

















































NEW YORK UNIVERSITY

BOSTON UNIVERSITY

REFERENCES




































































U(x) 5 u1(x1) 1 u2(x2)









(1) V1( y1) 5 u1( f ( y1)) 1 El2[u2( x2)]















l ( a 1 p 2 u s1) E p 2( a 1s2)Q(ds2s1)







J2( a 1s2) 5 maxl2 [ G 2( a 1s2)

E l2[u2( z2)]






(2) J1(s1) 5 supa 1[ G (s1)

p 2[ P 2

u1( f ( h (s1 a 1) l ( a 1 p 2u s1))

1 E l ( a 1 p 2 u s1)[u2( z2)]








IVA The Model









V1(c1l2) 5 u1(c1a(l2)) 1 b El2[u2(c2)]



c1 1 On

pnu n 5 w1 1 On

pn



(3)shy u1

shy c1pn 5

shy u1

shy adad u n

1 b E l2sn

shy u2

shy c2









a(l2) 5 2 a E l2c2 1 g varl2(c2)


dd u n




b El2snS shy u2

shy c2Y shy u1

shy c1D


























IVE Attention

















































NEW YORK UNIVERSITY

BOSTON UNIVERSITY

REFERENCES



































































(1) V1( y1) 5 u1( f ( y1)) 1 El2[u2( x2)]















l ( a 1 p 2 u s1) E p 2( a 1s2)Q(ds2s1)







J2( a 1s2) 5 maxl2 [ G 2( a 1s2)

E l2[u2( z2)]






(2) J1(s1) 5 supa 1[ G (s1)

p 2[ P 2

u1( f ( h (s1 a 1) l ( a 1 p 2u s1))

1 E l ( a 1 p 2 u s1)[u2( z2)]








IVA The Model









V1(c1l2) 5 u1(c1a(l2)) 1 b El2[u2(c2)]



c1 1 On

pnu n 5 w1 1 On

pn



(3)shy u1

shy c1pn 5

shy u1

shy adad u n

1 b E l2sn

shy u2

shy c2









a(l2) 5 2 a E l2c2 1 g varl2(c2)


dd u n




b El2snS shy u2

shy c2Y shy u1

shy c1D


























IVE Attention

















































NEW YORK UNIVERSITY

BOSTON UNIVERSITY

REFERENCES





































































l ( a 1 p 2 u s1) E p 2( a 1s2)Q(ds2s1)







J2( a 1s2) 5 maxl2 [ G 2( a 1s2)

E l2[u2( z2)]






(2) J1(s1) 5 supa 1[ G (s1)

p 2[ P 2

u1( f ( h (s1 a 1) l ( a 1 p 2u s1))

1 E l ( a 1 p 2 u s1)[u2( z2)]








IVA The Model









V1(c1l2) 5 u1(c1a(l2)) 1 b El2[u2(c2)]



c1 1 On

pnu n 5 w1 1 On

pn



(3)shy u1

shy c1pn 5

shy u1

shy adad u n

1 b E l2sn

shy u2

shy c2









a(l2) 5 2 a E l2c2 1 g varl2(c2)


dd u n




b El2snS shy u2

shy c2Y shy u1

shy c1D


























IVE Attention

















































NEW YORK UNIVERSITY

BOSTON UNIVERSITY

REFERENCES

































































J2( a 1s2) 5 maxl2 [ G 2( a 1s2)

E l2[u2( z2)]






(2) J1(s1) 5 supa 1[ G (s1)

p 2[ P 2

u1( f ( h (s1 a 1) l ( a 1 p 2u s1))

1 E l ( a 1 p 2 u s1)[u2( z2)]








IVA The Model









V1(c1l2) 5 u1(c1a(l2)) 1 b El2[u2(c2)]



c1 1 On

pnu n 5 w1 1 On

pn



(3)shy u1

shy c1pn 5

shy u1

shy adad u n

1 b E l2sn

shy u2

shy c2









a(l2) 5 2 a E l2c2 1 g varl2(c2)


dd u n




b El2snS shy u2

shy c2Y shy u1

shy c1D


























IVE Attention

















































NEW YORK UNIVERSITY

BOSTON UNIVERSITY

REFERENCES




































































IVA The Model









V1(c1l2) 5 u1(c1a(l2)) 1 b El2[u2(c2)]



c1 1 On

pnu n 5 w1 1 On

pn



(3)shy u1

shy c1pn 5

shy u1

shy adad u n

1 b E l2sn

shy u2

shy c2









a(l2) 5 2 a E l2c2 1 g varl2(c2)


dd u n




b El2snS shy u2

shy c2Y shy u1

shy c1D


























IVE Attention

















































NEW YORK UNIVERSITY

BOSTON UNIVERSITY

REFERENCES



































































V1(c1l2) 5 u1(c1a(l2)) 1 b El2[u2(c2)]



c1 1 On

pnu n 5 w1 1 On

pn



(3)shy u1

shy c1pn 5

shy u1

shy adad u n

1 b E l2sn

shy u2

shy c2









a(l2) 5 2 a E l2c2 1 g varl2(c2)


dd u n




b El2snS shy u2

shy c2Y shy u1

shy c1D


























IVE Attention

















































NEW YORK UNIVERSITY

BOSTON UNIVERSITY

REFERENCES


































































a(l2) 5 2 a E l2c2 1 g varl2(c2)


dd u n




b El2snS shy u2

shy c2Y shy u1

shy c1D


























IVE Attention

















































NEW YORK UNIVERSITY

BOSTON UNIVERSITY

REFERENCES



















































































IVE Attention

















































NEW YORK UNIVERSITY

BOSTON UNIVERSITY

REFERENCES










































































IVE Attention

















































NEW YORK UNIVERSITY

BOSTON UNIVERSITY

REFERENCES

































































IVE Attention

















































NEW YORK UNIVERSITY

BOSTON UNIVERSITY

REFERENCES











































































































NEW YORK UNIVERSITY

BOSTON UNIVERSITY

REFERENCES


































































































NEW YORK UNIVERSITY

BOSTON UNIVERSITY

REFERENCES



























































































NEW YORK UNIVERSITY

BOSTON UNIVERSITY

REFERENCES

















































































NEW YORK UNIVERSITY

BOSTON UNIVERSITY

REFERENCES









































































NEW YORK UNIVERSITY

BOSTON UNIVERSITY

REFERENCES



































































NEW YORK UNIVERSITY

BOSTON UNIVERSITY

REFERENCES















































































































































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