Social Interactions in Endogenous Groups

Abstract: This paper investigates social interactions in endogenous groups. We specify a two-sided many-to-one matching model, where individuals select groups based on preferences, while groups admit individuals based on qualifications until reaching capacities. Endogenous formation of groups leads to selection bias in peer effect estimation, which is complicated by equilibrium effects and alternative groups. We propose novel methods to simplify selection bias and develop a sieve OLS estimator for peer effects that is \sqrt{n}-consistent and asymptotically normal. Using Chilean data, we find that ignoring selection into high schools leads to overestimated peer influence and distorts the estimation of school effectiveness.