Ulric B. and Evelyn L. Bray Social Sciences Seminar

Abstract: This paper studies a social interaction model with endogenous group formation. We characterize group formation by a two-sided many-to-one matching model, where individuals choose among groups according to their preferences, and each group ranks individuals based on their qualifications and admits those with the highest qualifications given the capacity. Following the many-to-one matching literature, we show that an equilibrium in a finite market can be approximated by the equilibrium in a limiting market as the number of individuals approaches infinity, and in the limit the group that an individual joins only depends on her own characteristics. Based on the limiting approximation, we derive the selection bias as a group-specific nonparametric function of the preference and qualification indices in group formation. Under an exchangeable assumption on the unobservables, we show that the social effects can be identified by controlling for the selection bias as in a sample selection model. The excluded variables in group formation also provide instruments that can help resolve the reflection problem, even in the most challenging scenario where the adjacency matrix is given by group averages (Manski, 1993). We propose a multi-stage distribution-free estimation strategy based on our constructive identification results. The proposed estimator is root-n consistent and asymptotically normal and performs well in simulations.

Written with Xiaoting Sun