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 correc-
tions. These corrections are based on higher-order asymptotic expansions of the
GMM estimators and produce improved point and interval estimates in moder-
ately 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.
Keywords. Correlated random-coefficient model, panel data, instrumental vari-
ables, GMM, fixed effects, bias, incidental parameter problem, cigarette demand.
JEL classification. C23, J31, J51.