In this paper we analyze the causal effects of reallocating individuals across social groups in the presence of social interactions or spillovers. We consider the case where individuals are either ‘high’ or ‘low’ types. Own outcomes may depend on the fraction of high types in one’s social group. We characterize the average outcome effect and inter-type inequality effects of ‘local’ increases in segregation. We relate our estimands to the theory of sorting in the presence of social interactions. For each estimand we provide conditions for identification, propose nonparametric estimators, and characterize their large sample properties. Finally we consider the social planner’s problems, characterizing the structure of average outcome-maximizing and -minimizing allocations of individuals to groups.
Joint work with Bryan S. Graham (University of California – Berkeley) and Guido W. Imbens (Harvard University), April 2009.