Panel data models with nonadditive unobserved heterogeneity : estimation and inference

This paper considers fixed effects estimation and inference in linear and non-linear panel data models with random coefficients and endogenous regressors. The quantities of interest - means, variances, and other moments of the random coefficients - are estimated by cross sectional sample moments of generalized method of moments (GMM) estimators applied separately to the time series of each individual. To deal with the incidental parameter problem introduced by the noise of the within-individual estimators in short panels, we develop bias corrections. These corrections are based on higher-order asymptotic expansions of the GMM estimators and produce improved point and interval estimates in moderately long panels. Under asymptotic sequences where the cross sectional and time series dimensions of the panel pass to infinity at the same rate, the uncorrected estimators have asymptotic biases of the same order as their asymptotic standard deviations. The bias corrections remove the bias without increasing variance. An empirical example on cigarette demand based on Becker, Grossman, and Murphy (1994) shows significant heterogeneity in the price effect across U.S. states.