Correlated random effects models with unbalanced panels

I propose some strategies for allowing unobserved heterogeneity to be correlated with observed covariates and sample selection for unbalanced panels. The methods are extensions of the Chamberlain Mundlak approach for balanced panels when explanatory variables are strictly exogenous conditional on unobserved effects. A byproduct is fully robust Hausman tests for unbalanced panels. Even for nonlinear models, in many cases the estimators can be implemented using standard software. The framework suggests straightforward tests for sample selection that is correlated with unobserved shocks while allowing selection to be correlated with the observed covariates and unobserved heterogeneity. (C) 2018 Elsevier B.V. All rights reserved.