  This paper considers fixed effects estimation and inference in linear and
nonlinear 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 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
estimator has an asymptotic bias of the same order as the asymptotic variance.
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.
