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Chapter 54
INTERACTIONS-BASED MODELS
WILLIAM A BROCK' and STEVEN N DURLAUF**
Department of Economics, University of Wisconsin, 1180 Observatory Drive,
Madison, WI 53706-1393
Contents
Abstract 3299
Keywords 3299
1 Introduction 3300
1.1 Neighborhoods and inequality 3301
1.2 Spatial agglomeration 3302
1.3 Technology choice 3302
1.4 Preferences 3302
1.5 Behavior of political parties 3303
1.6 Social pathologies 3303
1.7 Information cascades 3304
1.8 Evolution of science 3304
1.9 Chapter objectives 3304
2 Binary choice with social interactions 3305
2.1 General framework 3305
2.2 Global interactions 3309
2.3 Local interactions 3312
2.4 Relationship to statistical mechanics 3314
2.5 Social planning problem 3315
2.6 Linear-in-means model 3318
3 Identification: basic issues 3318
3.1 Binary choice 3320
3.2 Linear-in-means model 3322
3.3 Instruments for unobservable expectations 3324
3.4 Identification of individual versus neighborhood contextual effects 3325
3.5 Nonlinear-in-means model 3326
3.6 Implications of self-selection for identification 3328
3.7 Implications of multiple equilibria for identification 3331
3.8 Dynamic models and rational expectations 3331
4 Further topics in identification 3335
4.1 Panel data 3335
4.1 1 Fixed effects 3336
4.1 2 Learning 3337
4.2 Duration data 3337
4.3 Nonparametric approaches 3340
4.3 1 Treatment effects 3340
4.3 2 Duration data 3346
5 Sampling properties 3348
5.1 Laws of large numbers 3348
5.2 Naive estimator 3349
5.3 Asymptotics for data generated by social planner 3349
5.4 Unobserved variables 3350
6 Statistical analysis with grouped data 3352
6.1 Differences in cross-group behavior 3353
6.2 Spatial patterns 3353
6.3 Ecological inference 3354
7 Evidence 3355
7.1 Analyses under assumption of correct specification 3355
7.1 1 Neighborhood effects in youth and adult outcomes 3355
7.2 Analyses which are robust to unobserved correlated heterogeneity 3356
7.2 1 Matching 3356
7.2 1 1 Gautreaux Assisted Housing Program 3357
7.2 1 2 Moving to Opportunity Demonstration 3358
7.2 1 3 Milwaukee School Voucher Program 3359
7.2 1 4 Classroom tracking 3360
7.2 1 5 Siblings 3361
7.2 2 Instrumental variables 3361
7.2 2 1 Neighborhood socioeconomic influences 3361
7.2 2 2 Catholic versus public schools 3362
8 Summary and conclusions 3362
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