Identification and Estimation of Group-Level Partial Effects

This paper presents identification and estimation results for causal effects of group-level variables when agents select into groups. I specify a triangular system of equations to model outcome determination and group selection, accommodating general nonseparable models. Using conditional independence and completeness assumptions, I show that the group-level distribution of individual characteristics is a valid control function, conditional on which group-level variables of interest become exogenous. Building on this result, I identify average effects under a common support condition. The key identifying requirements are more plausible in settings where a rich array of individual characteristics are observed. For the identified parameter, I construct a kernel-based estimator and prove its consistency. Although the identification argument uses completeness, the estimation procedure does not involve solving for an ill-posed integral equation.