Discrete Choice with social interactions and endogenous memberships

Abstract- This paper tackles the issue of self-selection in social interactions models. I develop a theory of sorting and behavior, when the latter is subject to social influences, extending the model developed by Brock and Durlauf (2001a, 2003) to allow for equilibrium group formation. Individuals choose a group, and a behavior subject to an endogenous social effect. The latter turns out to be a segregating force, and stable equilibria are stratified. The sorting process may induce, inefficiently, multiple behavioral equilibria. Such a theory serves as a means to solve identification and selection problems that may undermine the empirical detection of social effects on individual behavior. I exploit the theoretical model to build a nonlinear (in the social effect) selection correction term. Such a term allows identification, and solves the selection problem that arises when individuals can choose the group whose effect the researcher is trying to disentangle. The resulting econometric model, although relying on strict parametric assumptions, indicates a viable alternative when reliable instrumental variables are not available, or randomized experiments not possible