Two-Stage Estimators for Unbalanced Panel Data Under Endogenous Selection with Weak Instrumental Variables Condition

This paper proposes the novel two-stage estimators for unbalanced panel data that incorporate endogenous sample selection. Contrary to conventional methods, we rely on a weaker assumption which not requires sample selection to be random and ignorable. The first stage uses a bilateral truncated selection equation where we accommodate a weak instrumental variable (IV). This is due to the recognition that original selection is impacted on unobservable heterogeneity, so that unidentifiable endogenous selections problem exits, which causes optimal IV extremely difficult to acquire. The second stage develops Wooldridge's (2019) model to account for the correlation between unobservable heterogeneity in the main model with covariates and the heterogeneity in the selection mechanism. Simulations demonstrate the efficacy of our estimators in a variety of contexts. And an empirical application in financial panel data concludes a more accurate result than previous literature, also proves the advancement of our method.