Efficient Estimation of Linear Panel Data Models with Sample Selection and Fixed Effects

For linear panel data models with endogenous selectivity, the popular pooled ordinary least squares with bias correction and its minimum distance variant can suffer from severe efficiency loss in the presence of large random effects. To resolve this problem, we algebraically derive an efficient estimator based on the moment restrictions used by the pooled ordinary least squares and make the estimator feasible under the conventional error-component assumption. The efficient estimation involves heavy computation, and we propose a convenient suboptimal estimator based on a novel common weighting transformation. We also consider partial and full aggregation of information in pairwise differences, where unobserved fixed effects are completely eliminated. Efficient estimation based on pairwise differences is discussed, and a computationally affordable method of estimating nuisance higher-order moments is proposed. Analytic standard errors are provided for all considered estimators. Simulations suggest that a convenient suboptimal estimator and the fully-aggregated pairwise-differencing estimator exhibit remarkable performances. The methods are applied to estimating earnings equation for married women using the Korean Labor and Income Panel Study data.