The properties of classical panel data estimators including fixed effect, first-differences, random effects, and generalized method of moments-instrumental variables estimators in both static as well as dynamic panel data models are investigated under sample selection. The correlation of the unobserved errors is shown not to be sufficient for the inconsistency of these estimators. A necessary condition for this to arise is the presence of common (and/or non-independent) non-deterministic covariates in the selection and outcome equations. When both equations do not have covariates in common and independent of each other, the fixed effects, and random effects estimators in static models with exogenous covariates are consistent. Furthermore, the first-differenced generalized method of moments estimator uncorrected for sample selection as well as the instrumental variables estimator uncorrected for sample selection are both consistent for autoregressive models even with endogenous covariates. The same results hold when both equations have no covariates in common but are correlated once we account for such correlation. Under the same circumstances, the system generalized method of moments estimator adding more moments from the levels equation has moderate bias. Alternatively, when both equations have common covariates the appropriate correction method is suggested. Serial correlation of the errors being a key determinant for that choice. The finite sample properties of the proposed estimators are evaluated using a Monte Carlo study. Two empirical illustrations are provided.