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Unformatted text preview: Measuring the e/ects of segregation in the presence of social spillovers: a nonparametric approach 1 Bryan S. Graham y Guido W. Imbens z Geert Ridder \ October 19, 2010 Abstract: In this paper we nonparametrically analyze the e/ects of reallocating in- dividuals across social groups in the presence of social spillovers. Individuals are either &high¡or & low¡types. Own outcomes may vary with the fraction of high types in one¡s social group. We characterize the average outcome and inequality e/ects of small in- creases in segregation by type. We also provide a measure of average spillover strength. We generalize the setup used by Benabou (1996) and others to study sorting in the presence of social spillovers by incorporating unobserved individual- and group-level heterogeneity. We relate our reallocation estimands to this theory. For each estimand we provide conditions for nonparametric identi¢cation, propose estimators, and char- acterize their large sample properties. We also consider the social planner¡s problem. We illustrate our approach by studying the e/ects of sex segregation in classrooms on mathematics achievement. JEL Classification: C14, C31, D62, I21 Key Words: Social Interactions, Peer Group E/ects, Sorting, Segregation, Equity vs. E£ ciency Trade-o/, Allocation Problems, Semiparametric M-estimation. 1 We thank David Ahn, Susan Athey, Alan Auerbach, Alberto Bisin, Raj Chetty, Rajeev Dehejia, Steven Durlauf, Raquel Fern¤ndez, Jack Porter, Jim Powell, Paul Ruud and, especially, Emmanuel Saez for helpful discussions. We would also like to thank participants in numerous seminars and conferences for helpful questions and suggestions. Financial support was generously provided by the NSF (SES #0820361). y Department of Economics, New York University, 19 West 4 th Street 6FL, New York, NY 10012 and National Bureau of Economic Research. E-mail: [email protected] Web: https://files.nyu.edu/bsg1/public/ z Department of Economics, Harvard University, Littauer M-24, Cambridge, MA 02138 and the National Bureau of Economic Research. E-mail: [email protected] Web: http://www.economics.harvard.edu/faculty/imbens/imbens.html \ Department of Economics, University of Southern California, Kaprielian Hall, University Park Campus, Los Angeles, CA 90089. E-mail: [email protected] Web: http://www-rcf.usc.edu/~ridder/ 1 Introduction Debates about the social costs and bene&ts of segregation by socioeconomic status, ability, race or gender &gure prominently in discussions of education, housing and other areas of social policy. In the late-1960s Coleman et al. (1966) argued that racial isolation lowered the academic achievement of minority students. This claim immediately generated controversy, spawning a vast empirical literature in education, sociology and economics. Forty years later Rivkin and Welch (2006), surveying the resulting body of work, concluded that ¡the e/ect of integration on black students remains largely unsettled¢ (p. 1043). Scho&eld (1995), reviewing the education and sociologyremains largely unsettled¢ (p....
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