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 individual- and 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.
We thank David Ahn, Susan Athey, Alan Auerbach, Alberto Bisin, Raj Chetty, Rajeev Dehejia, Steven Durlauf, Raquel Fernández, 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). The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research.