Panel Data Models with Nonadditive Unobserved Heterogeneity: Estimation and Inference

The main purpose of this paper is to estimate panel data models with endogenous regressors and nonadditive unobserved individual heterogeneity including, for example, linear and nonlinear models where all the parameters can vary across individuals. The quantities of interest are means, variances, and other moments of the individual parameters. Since estimates of these quantities based on individual by individual GMM estimation can be severely biased due to the incidental parameter problem, we develop bias corrections that give more accurate estimates in moderately long panels. These corrections, derived from large-T expansions of the finite-sample bias of fixed effects GMM estimators, reduce the order of the bias from O(T¡1) to O(T¡2) and center the asymptotic distributions at the true values in moderately long panels under asymptotic sequences where n = o(T3). An empirical example on cigarette demand based on Becker, Grossman and Murphy (1994) shows significant heterogeneity in the price effect across U.S. states.