Nber Working Paper Series Measuring the Effects of Segregation in the Presence of Social Spillovers: a Nonparametric Approach

In this paper we nonparametrically analyze the effects of reallocating individuals 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 effects of small increases 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 individualand group-level heterogeneity. We relate our reallocation estimands to this theory. For each estimand we provide conditions for nonparametric identification, propose estimators, and characterize their large sample properties. We also consider the social planner's problem. We illustrate our approach by studying the effects of sex segregation in classrooms on mathematics achievement. Bryan S. Graham New York University 19 W 4th Street, 6FL New York, NY 10012 and NBER [email protected] Guido W. Imbens Department of Economics Littauer Center Harvard University 1805 Cambridge Street Cambridge, MA 02138 and NBER [email protected] Geert Ridder Department of Economics University of Southern California Kaprielian Hall Los Angeles, CA 90089 [email protected]