Bias Correction in Panel Data Models with Individual Specific Parameters

In random coefficients linear IV models, fixed effects averages of the individual-specific coefficients are biased in short panels due to the finite-sample bias of IV estimators. This paper introduces a new class of bias-corrected semiparametric estimators for panel models where the response to the regressors can be individual-specific in an unrestricted way. These estimators are based on moment conditions that can be nonlinear functions in parameters and variables, encompassing both linear and nonlinear models and allowing for the presence of endogenous regressors. The corrections are derived from large-T expansions of the finite-sample bias, and reduce the order of this bias from O(T−1) to O(T−2) for model parameters and other quantities of interest, such as averages of the individual-specific parameters. The asymptotic distribution of the bias-corrected estimators are centered at the true parameter values in panels where n = o(T 3). In a Monte Carlo example for a linear IV model with both common and individualspecific coefficients, I find that estimators that do not account for parameter heterogeneity can be severely biased, and that bias corrections are effective in reducing the bias of fixed effects estimates. These methods are illustrated through an analysis of earnings equations for young men allowing the effect of the union status to be different for each individual. The results suggest the presence of important heterogeneity in the union premium. JEL Classification: C23; J31; J51.