Bias Correction in Panel Data Models with Individual Specific Parameters

In correlated random coefficient models, standard OLS and IV estimators do not estimate the average population effect. This problem can be fixed with panel data by estimating a different coefficient for each individual, and then using the sample moment of the individual coefficients to estimate the corresponding population moment of interest. These estimates, however, can be severily biased in short panels due to the incidental parameters problem. The bias arises if some of the regressors are endogenous, or if the moments to estimate are nonlinear functions of the coefficients, e.g., variances of the individual effects. This paper introduces a class of bias-corrected fixed effects estimators for these correlated random coefficient models, which do not impose restrictions on the coefficients heterogeneity. The new estimators are based on moment conditions that can be nonlinear functions in parameters and variables, encompassing both linear and nonlinear random coefficients 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 moments of the individual-specific coefficients. The asymptotic distribution of the bias-corrected estimators are centered at the true parameter values under asymptotic sequences where n = o(T^{3}). 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