Sample selection in linear panel data models with heterogeneous coefficients

We propose a parametric estimation procedure for linear panel data models with sample selection and heterogeneous coefficients that are present in both outcome model and selection model. Our two‐step estimation procedure accounts for endogeneity from the selection process and endogeneity from correlation between the individual unobserved heterogeneity and the observed covariates using control function like methods. Conditional linear projections are used to establish a tractable approach that builds upon the original Heckman correction to sample selection. Monte Carlo simulations illustrate the finite sample properties of our estimator and demonstrate that our proposed estimator outperforms standard estimators. We apply the proposed approach to estimate gender differences in high‐stakes time‐constrained decisions using Elo ratings data from the World Chess Federation. When addressing both sources of endogeneity, we find a much larger gender skill gap and substantial differences across the genders in strategically selecting into time‐constrained matches.