Non-linear Panel Data Models with Expected a Posteriori Values of Correlated Random Effects

We develop a two step estimation procedure to estimate nonlinear panel data models. Most papers studying nonlinear panel data models assume all regressors to be exogenous or exogenous conditional on the unobserved heterogeneity. In this paper we relax this assumption. Our approach combines the “correlated random effect” and the “control function” approach to handle endogeneity of regressors that are correlated with the unobserved heterogeneity and a subset of which may not be independent of idiosyncratic component. The “control functions”are based on Expected ´a Posteriori values of the correlated random effects. Our framework suggests straight forward tests for correlation between unobserved heterogeneity and the covariates, and correlation between idiosyncratic component and the covariates. The static model is easily extend to estimate dynamic discrete choice model. Average partial effects (APEs) of covariates too are also easily obtained. The proposed estimator is used to investigate the impact of India’s National Rural Employment Guarantee Scheme (NREGS) on children’s educational outcomes via women’s labour force participation.

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