A Refresher on Theory and Explanation in Sociology

Micro-Macro Links in Sociology

Werner Raub

Workshop on Social Theory, Trust, Social Networks, and Social Capital II

National Chengchi University – NCCUApril 2011

Agenda for the twointroductory sessions

• Basic features of problem-driven and systematic (deductive) theory construction, model building and explanation in social science…

• … by way of examples

• Focus on micro-macro links in theory and research in sociology

• Some “take home messages”

1

Sociological theory according to the “analytical tradition”

• Sociology = research on social phenomena (i.e., macro-phenomena) and their social macro-conditions (“causes”); compare Durkheim’s “minimal program”

• Sociological theory explains social phenomena by showing how they come about as (often unintended) results of individual behavior that is affected by social conditions.

Useful tools for summarizing and reconstructing social science theory and research• Problems as a starting point for theory

formation and empirical research

P1 T1 E1 P2 ... Problem Theory Empirical Research New Problem

• Coleman’s scheme for macro-micro-macro transitions

• A scheme representing the structure of social science explanations

2

James Coleman (1926-1995)

Coleman’s scheme for macro-micro-macro transitions

Macro

Micro

Social conditions

Preferences, information

Individual effects

Macro outcomes

3

1 2

1: Bridge assumptions

2. Transformation rules

3. Behavioral theory

Coleman’s scheme and the structure of explanations in sociology I

1. General laws Explanans

2. Initial conditions:Social conditions

Deduction

Description of thephenomenon to be explained ExplanandumSocial phenomenon

Adequacy conditions for explanations

1. The explanandum is a logical consequence of the explanans.

2. The explanans contains at least one general law.

3. The explanans has empirical content (i.e., is testable).

4. The explanans is true/empirically supported.

(See Hempel & Oppenheim, Studies in the logic of explanation, 1948)

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Coleman’s scheme and the structure of explanations in sociology II

Behavioral theory(arrow 2)

Bridge assumptions(arrow 1)

Initial conditions• Macro-conditions (node A)• Micro-conditions (node B)

Individual effects(node C)

Transformation rules(arrow 3)

Additional boundaryconditions

Individual effects(node C)

Collective phenomena andprocesses (node D)

Three examples

• Two highly simplified examples from Coleman 1990, 1987

• Max Weber: the spirit of capitalism• Occurrence of a panic

• One more elaborate (though still highly stylized) example

• Schelling’s model of residential segregation

3

Max Weber: the spirit of capitalism

4

Macro

Micro

Protestant religious doctrine

Values Economic behavior

Capitalism

The panic example

5

Macro

Micro

Fire alarm in a crowded theater

Utility structure for alternative actions

Run to exit / transfer control conditionally

Panic or order

A somewhat more complex example:residential segregation

A sociologically uninformedcommon-sense theory

versus

Schelling’s models of segregation

6

Examples of segregation phenomena

• Segregation by ...• ethnicity (race)• religion• wealth

8

Residential segregation: a (very) rough definition• Consider a city with X% ‘Whites’ and Y% ‘Non-

Whites’• The city consists of a number of

neighborhoods.• ‘Perfect integration’ := Each neighborhood

consists of X% ‘Whites’ and Y% ‘Non-Whites’.• ‘Perfect segregration’ := Each neighborhood is

either 100% ‘White’ or 100% ‘Non-White’.• Roughly: A city is more integrated, the ‘closer’

the neighborhoods approximate the case of ‘perfect integration.’ And a city is more segregated the ‘closer’ the neighborhoods approximate the case of ‘perfect segregation.’

10

Data on residential segregation:United States, 1940-1960• Indices of residential segregation by race, 109 cities,

for 1940, 1950, 1960.

11

Source: JS Coleman, Resources for Social Change: Race in the US. NY: Wiley 1971, p. 9.

The indices are measures of the % of blacks who would have to move in order to achieve residential homogenization by race. An index of 0 would indicate no racial segregation among blocks. A score of 100 would mean that each block is either all white or all black.

Data on residential segregation in the US, 2005-2009

• The New York Times offers a resource providing quite up to date and comprehensive data on residential segregation in the US, see:

http://projects.nytimes.com/census/2010/explorer

• Screening this site is recommended!

Residential segregation: some types of problems 1. Descriptive problems

- Trends over time- Cross-section: comparing North and South

2. Explanatory problems – our focusWhy is residential segregation rather stable over time?Why are there hardly any differences in residential segregation between North and South?

3. Problems of institutional designHow to reduce or mitigate residential segregation?

4. Normative problemsHow much residential segregation is normatively acceptable?What are acceptable costs of reducing or mitigating residential segregation?

12

Residential segregation: possible causes• Actors’ preferences and perceptions

– Prejudice– Perception of unwelcome by-effects

of integration

• Constraints– income inequality / prices on the

housing market– legislation

Etc.!

13

Common sense-theory

% of whites residentialapproving segregationintegration

14

The stability of residential segregation over time: sketch of an explanationCommon sense-theory:• percentage of whites residential

approving residential integration segregation

Antecedent condition:• In the US (North and South), the percentages of whites

approving residential integration has been appr. constant between 1940 and 1960.

______________________________________________• In the US (North and South), residential segregation has

been appr. constant between 1940 and 1960.

Note: We shall see that this explanation is not adequate!

15

Similarities in residential segregation between North and South: sketch of an explanation Common sense-theory:• percentage of whites residential

approving residential integration segregation

Antecedent condition:• In the US (between 1940 and 1960), there are no

systematic North-South differences in the percentage of whites approving residential integration.

______________________________________________• In the US (between 1940 and 1960), there are no

systematic North-South differences in residential segregation.

Note: We shall see that this explanation is not adequate!

16

Science as a systematic test of theories

17

The logic of empirical tests of theories

18

1 Propose a theory / hypothesis

2 Derive empirically testable implications

3 Compare these implications with data

4.1 Corroboration

of the theory

4.2 Refutation

of the theory

Table I-3 and I-25 combined. Indices of residential segregation by race, 109 cities, for 1940, 1950, 1960, and percentage of whites who approve residential segregation in 1942, 1956, June and December 1963, 1965, 1968ª

19

ª Source: For residential segregation see Table I-3. For attitudes towards residential integration the question asked was, “ If a Negro with the same income and education as yours moved into your block, would it make any difference to you?” Data on 1942, 1956, 1963 from Paul B. Sheatsley (1996, Table I, p. 222). Data on 1965, 1968 by personal communication from Paul B. Sheatsley (July 1, 1969) unpublished data from NORC surveys of October 1965 and April 1968.

An empirical test of the common sense- theory of residential segregation 1. Common sense-theory (hypothesis):

% of whites residentialapproving residential integration segregation

2. Implications: Trend: If the percentage of whites approving integration increases

in the US (North and South) between 1942 and 1956 as well as between 1956 and 1963, then residential segregation decreases in the US (North and South) in both periods. Comparison North-South: If the percentage of whites approving integration is higher in the North than in the South of the US in the forties, fifties, and sixties, then residential segregation is lower in the North than in the South of the US in all three periods.

3. Comparison with data (from Coleman, 1971 and Sheatsley, 1966).

4. Refutation of common sense theory of residential segregation.

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Schelling’s models of segregation

23

Thomas Schelling

24

Residential segregation:summary of the problem situation

25

Schelling’s game

1. Initial state (residential integration)

• Unidimensional town: from left to right, 70 pieces (households) are spread out in a line.

• Two ethnicities: each piece is black or white

• The color of each piece is decided by throwing a dice.

• 1,2,3: black piece• 4,5,6: white piece

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2. Definition of the neighborhood of a piece (neighborhood of a household)

• The neighborhood of a piece consists of the piece itself, the four pieces to the left, and the four pieces to the right

• Pieces near the end of the line have less neighbors (alternative: circle)

27

oo#o#oo##Neighborhood

Neighborhood and interdependence

• Neighborhood of a piece = neighborhood of a household

• Note: interdependence between households: if A and B are neighbors, (color of) A affects composition of B’s neighborhood and vice versa

• Interdependence as a social condition for residential segregation in addition to preferences and perceptions of actors

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3. Moving pieces I

• The game proceeds in rounds (segregation as a dynamic process).

• At the beginning of each round, each piece in a neighborhood where more than half of the neighbors have the opposite color is marked

• Preferences of households: avoid a minority situation

• Social condition: composition of neighborhoods

• Individual motives (avoiding a minority situation) versus collective effects (segregation)

• Order of moving: marked pieces move in turn, counting from left to right.

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Moving pieces – interpretation

• The preference of households to avoid a minority situation is consistent with different more specific assumptions:

• One prefers segregated over integrated neighborhoods (“white prejudice”)

• One prefers an integrated (50-50) neighborhood to any other other composition as long as one is not in the minority situation (“preference for residential integration”)

• One is indifferent with respect to to neighborhood composition as long as one is not in the minority situation

• Hence, Schelling’s rules and assumptions are consistent with the assumption of preferences for integration!

30

An observation on the “spirit” of Schelling’s models

• Schelling’s rules and assumptions are in a sense very “optimistic” with respect to “prospects for residential integration”

• He tries to show precisely that extreme residential segregation can emerge even under seemingly favorable conditions for integration

• Complex relationship between individual motives (avoiding minority situation) and collective effects (extreme residential segregation)

• Residential segregation as an unintended and unfavorable (suboptimal) outcome for the actors

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Moving pieces II

• How pieces move: a piece moves to the nearest point between two other pieces to the right or to the left where it is not a minority.

• Interpretation• Moves are costly; costs increase in

distance• No scarcity on the housing market• No legal or economic constraints to

choosing certain neighborhoods• No discrimination on the housing

market

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Moving pieces III

• If the neighborhood of a marked piece has changed such that not more than half of the neighbors have the opposite color when the turn to move comes, the marked piece does not move after all- Interdependence between households.

• End of a round: each piece that has been marked at the beginning of the round has had a turn to move

• End of the game: each piece has a neighborhood with at least half of the neighbors of the same color (or: there are no suitable places to move to)

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Example (compare Schelling 1969: 490, 1971: 149-151)

1. Start situation:

o#ooo##o#oo##oo###o##o##oo##oo##oo##o#o#oo###o##ooooo###ooo#oo##o#o##o

2. Situation after round 1

oooooooo####o#########oooo##ooo#o#o###o#########oooooooooooooooo######

3. Situation after round 2

oooooooo###############oooooooooo###############oooooooooooooooo######

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Important features of Schelling’s model

• The model shows that high levels of segregation can result from rather tolerant individual preferences

• High levels of segregation can result from both tolerant and intolerant preferences

• Schelling makes the micro-macro link explicit

• The model allows for derivation of new implications

35

“Changing support for integration” and “differences in support for integration”

• Background: the data on residential segregation for the United States

• Question: how to conceptualize “increasing support for integration within a region” and “differences in support for integration between regions” within Schelling’s model?

36

“Changing support for integration” and “differences in support for integration”• Consider the following preferences for

neighborhood composition that are all consistent with a 50%-threshold for moving:Most preferred is...1. complete segregation...2. much segregation...3. some segregation...4. perfect integration...and in all cases 1 – 4 one moves as soon as one

is in the minority position• Clearly, “support for integration” increases

when preferences shift from 1 to 4• NOTE: under each of the 4 types of preferences,

extreme segregation results

36

Schelling’s model versus the “common sense theory”• Schelling’s model improves on the common

sense-theory in two respects:• Empirically: Schelling’s model is consistent

with a ‘weak’ relation between prejudice and segregation.• Over time increasing support for integration

need not reduce segregation.• Two regions that differ with respect to

support for integration can be similar with respect to segregation levels.

• Theoretically: Schelling’s model (but not the common sense-theory) is consistent with the “minimal program of sociology”: explaining macro-phenomena as a result of macro-conditions and incentive-guided (goal-directed) behavior

37

Table I-3 and I-25 combined. Indices of residential segregation by race, 109 cities, for 1940, 1950, 1960, and percentage of whites who approve residential segregation in 1942, 1956, June and December 1963, 1965, 1968ª

38

ª Source: For residential segregation see Table I-3. For attitudes towards residential integration the question asked was, “ If a Negro with the same income and education as yours moved into your block, would it make any difference to you?” Data on 1942, 1956, 1963 from Paul B. Sheatsley (1996, Table I, p. 222). Data on 1965, 1968 by personal communication from Paul B. Sheatsley (July 1, 1969) unpublished data from NORC surveys of October 1965 and April 1968.

Some further questions on Schelling’s models• Does segregation always emerge? And how stable

is integration?• Integrated initial states

#0#0#0#0#0 ...0#0#0#0#0# ......

• Probability for such states is very small• These states are unstable under “external

shocks” such as “forced movements” or in- and out-migration of households

• Note: the final states in Schelling’s model are stable relative to such “external shocks

Schelling’s model: unrealistic and simplifying assumptions

1. One-dimensional town2. Order of moving3. Two groups of similar size4. Homogeneity assumption with respect to:

• Neighborhood size• Preferences of neighborhood

composition5. No scarcity on the housing market6. No legal or economic constraints to

choosing certain neighborhoods

Problem: derive implications of more realistic and less simplifying assumptions

39

A two-dimensional variant

40

Initial Situation Resulting Situation

Reconstruction of Schelling’s model

41

Schelling’s model and Coleman’s scheme

42

Social change in Coleman’s scheme

43

Recent literature on residential segregation

• Fossett, Mark (2011) Generative models of segregation: Investigating model-generated patterns of residential segregation by ethnicity and socioeconomic status, forthcoming in Journal of Mathematical Sociology 35(1) – up to date extension of Schelling-type models; will be available on Studion

• Bruch, Elizabeth & Robert Mare (2009) Segregation Dynamics, pp. 269-293 in Peter Hedström & Peter Bearman (eds.) The Oxford Handbook of Analytical Sociology, Oxford: Oxford University Press.

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Conclusions:

Some “take home messages” for theory construction and model building in sociology

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Some general features of theory construction

• The P-T-E-scheme: Sociology starts from Problems, Theories provide tentative solutions (answers) to these problems, and Empirical research is used to scrutinize (test) the adequacy of these answers. Research typically generates new problems, initiating a new P-T-E-sequence.

• The logical structure of theories, hypotheses, and explanations

• The logic of empirical tests of theories

46

Coleman’s scheme for macro-micro-macro transitions

Macro

Micro

Social conditions

Preferences, information

Individual effects

Macro outcomes

3

1 2

1: Bridge assumptions

2. Transformation rules

3. Behavioral theory

Coleman’s scheme and the structure of explanations in sociology II

Behavioral theory(arrow 2)

Bridge assumptions(arrow 1)

Initial conditions• Macro-conditions (node A)• Micro-conditions (node B)

Individual effects(node C)

Transformation rules(arrow 3)

Additional boundaryconditions

Individual effects(node C)

Collective phenomena andprocesses (node D)

A brief note on terminology: theory – hypothesis – explanation – testable implication

1. Two (different) meanings of “theory”(a) A set of hypotheses (other label for “hypothesis”:

proposition)• Note: sometimes, such a set of hypotheses is “structured” in

the sense that there are some “basic” hypotheses (often labeled “axioms”), while other hypotheses (sometimes labeled “lower-level hypotheses”) are implications of the basic hypotheses / axioms.

(b) An explanation

2. Two (different) meanings of “hypothesis”(a) An element of a theory in the sense of 1.a above.(b) An empirically testable implication that follows from a theory

and additional assumptions.

• Note: there is no “true” meaning of “theory” or of “hypothesis” (and in the literature you may encounter additional meanings not mentioned above). Often, you will have to conclude from the context, which meaning an author has in mind.

49

The logic of empirical tests of theories

18

1 Propose a theory / hypothesis

2 Derive empirically testable implications

3 Compare these implications with data

4.1 Corroboration

of the theory

4.2 Refutation

of the theory

The logic of empirical tests of theories

• Note: testing theories empirically is a complex enterprise involving more than “directly” confronting a theory or hypothesis with empirical findings:

• Theories have to be reconstructed in a systematic way so that testable implications can be derived.

• Derivation of testable implications: “sociology in action” (and science generally) typically involves argumentation, that is, the derivation of implications from assumptions – doing sociology (and science in general) is more than producing theories and empirical evidence, it is also about the links between theories and evidence.

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Theoretical models

• The “T” in a P-T-E scheme is often a theoretical model.

• A theoretical model comprises two elements (compare the explanations and the explanandum of a deductive explanation):1. A set of (often relatively abstract and

almost always simplified) assumptions.2. Implications of these assumptions

Note: a major task involved in model building is to show that these implications do indeed follow from the assumptions

52

Theoretical models

• After a model has been constructed (= the assumptions have been introduced) and analyzed (= implications/hypotheses have been derived), two further steps typically follow:1. Derivation of testable implications for empirical

research (note: this is part of the “E” in the P-T-E scheme) as well as derivation of policy implications

2. The method of decreasing abstraction – elaborating and improving the model in a stepwise fashion: step by step, simplified assumptions are replaced by more realistic ones, while checking the implications of more realistic assumptions (leading question: how robust are the implications of the model relative to modifications of assumptions of the model?)

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Assumptions on individuals: goal-directed (incentive guided) behavior

• Actors have:• Alternative actions,• Goals, i.e., they evaluate the possible

outcomes of their actions,• Expectations (or information) on the

“states of the world” (for example, expectations on certain “contingencies” or on the behavior of other actors).

• They choose the action that seems most appropriate, given their expectations, to realize their goals.

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What is taken into account at the macro level?

• Relations (networks) and interdependencies between actors

• Institutions (in the sense of organizations as well as rules and norms)

• Aggregate effects (frequencies, averages, variance distributions)

• Collective phenomena as unintended consequences of incentive-guided behavior.

Related research programs in the landscape of the social sciences1. Scottish moralists (A. Smith, D. Hume, etc.)2. (Contemporary) sociology

• Analytical sociology, broadly conceived

• US: J. Coleman, D. Heckathorn, M. Macy etc.

• Europe: R. Boudon, K.D. Opp, H. Esser, A. Diekmann, R.

Ziegler, J. Goldthorphe, P. Hedström, P. Abell, ICS, etc.

(structural-individualistic approach)

• Intersection of analytical sociology and network theory (R.

Burt, M. Granovetter, etc.)

• Social exchange theory (P. Blau, G. Homans, etc.)3. Political science

• Economic theory of politics; public choice (K. Arrow, A.

Downs, J. Buchanan & G. Tullock, M. Olson, W. Riker, P.

Ordeshook, etc.)

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Related research programs in the landscape of social sciences

. Economics

• Economic approach to human behavior (G. Becker etc.)

• New institutional economics (R. Coase, O. Williamson, D.

North, etc.)5. Also

• Social psychology: research on social dilemmas (R. Dawes

etc.)

• Interdisciplinary research on incentive-guided behavior,

bounded rationality, etc. (H. Simon, D. Kahneman, A.

Tversky, etc.)

• Game Theory and its application in various social sciences

(T. Schelling, R. Selten, J. Harsanyi, D. Kreps, etc.)

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Some books with a similar perspective on social science theory and research

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An advanced textbook and a handbook

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Some modern classics

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• Robert K. Merton, Social Theory and Social Structure, rev and enl. ed. New York: Free Press 1968 (original 1957)

Some modern classics

64

Some modern classics

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Coleman, Foundations of Social Theory

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Two recent books that elaborate on various topics that have been discussed

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