Nonlinear Panel Data Models with Expected a Posteriori Values of Correlated Random Effects

Abstract

We develop a two step estimation procedure to estimate nonlinear panel data models. Our approach combines the “correlated random effect” and the “control function” approach to handel endogeneity of regressors that are correlated with both the unobserved heterogeneity as well as the idiosyncratic component. The novelty here lies in integrating out the unobserved heterogeneity on which the structural equations are conditioned. The integration is performed with respect to the posterior distribution of the individual effects obtained from the first stage reduced form estimation. Our framework suggests separate tests for correlation between unobserved heterogeneity and the covariates, and correlation between idiosyncratic component and the covariates. Average partial effects (APEs) of covariates are also easily obtained.