Estimating Panel Data Models in the Presence of Endogeneity and Selection

We consider estimation of panel data models with sample selection when the equation of interest contains endogenous explanatory variables as well as unobserved heterogeneity. We offer a detailed analysis of the pooled two-stage least squares (pooled 2SLS) and fixed effects-2SLS (FE-2SLS) estimators and discuss complications in correcting for selection biases that arise when instruments are correlated with the unobserved effect. Assuming that appropriate instruments are available, we propose several tests for selection bias and two estimation procedures that correct for selection in the presence of endogenous regressors. The first correction procedure is valid under the assumption that the errors in the selection equation are normally distributed, while the second procedure drops the normality assumption and estimates the model parameters semiparametrically. In the proposed testing and correction procedures, the error terms may be heterogeneously distributed and serially dependent in both selection and primary equations. Correlation between the unobserved effects and explanatory and instrumental variables is permitted. To illustrate and study the performance of the proposed methods, we apply them to estimating earnings equations for females using the Panel Study of Income Dynamics data and perform Monte Carlo simulations.