Identification and Estimation of Social Interactions in Endogenous Peer Groups

Abstract: This paper studies a linear-in-means social interaction model with endogenous peer groups. The groups are endogenous because the unobservables that affect group formation and social interactions can be correlated. We characterize group formation using a many-to-one matching model, where each individual joins one group and each group contains many individuals. In this model, each individual chooses a group among the groups that she is eligible for. The groups formed in equilibrium depend on the observed and unobserved characteristics of all the individuals in the market, making it difficult to correct for the selection bias without simplification. Following the idea in the matching literature, we approximate the equilibrium in the finite model using the equilibrium in a limiting model, where the number of individuals in the market approaches infinity. Given the limiting equilibrium, each individual’s group only depends on her own characteristics. We then show that the formation of the groups follows a multivariate selection rule and the selection bias is a nonparametric function of the preference and qualification indices in group formation. We provide identification results for the parameters in group formation and social interactions when the unobservables are nonparametrically distributed. We propose a two-stage distribution-free estimation strategy, where in the first stage we estimate the group formation parameters and in the second stage we estimate the social interaction parameters, both by semiparametric estimators.