This paper presents some two-step estimators for a wide range of parametric panel data models with censored endogenous variables and sample selection bias. Our approach is to derive estimates of the unobserved heterogeneity responsible for the endogeneity/selection bias to include as additional explanatory variables in the primary equation. These are obtained through a decomposition of the reduced form residuals. The panel nature of the data allows adjustment, and testing, for two forms of endogeneity and/or sample selection bias. Furthermore, it incorporates roles for dynamics and state dependence in the reduced form. Finally, we provide an empirical illustration which features our procedure and highlights the ability to test several of the underlying assumptions.

Panel data, conditional maximum likelihood, endogenous regressors, sample selection, two-step estimation,
Journal of Econometrics
Erasmus School of Economics

Vella, F, & Verbeek, M.J.C.M. (1999). Two-step estimation of panel data models with censored endogenous variables and selection bias. Journal of Econometrics, 239–263. doi:10.1016/S0304-4076(98)00043-8