Panel Data Models with Nonadditive Unobserved Heterogeneity: Estimation and Inference

TL;DR

This paper develops bias-corrected fixed effects estimators for linear and nonlinear panel data models with random coefficients, addressing the incidental parameter problem and providing improved inference in moderately long panels.

Contribution

It introduces bias correction methods based on higher-order asymptotics for GMM estimators in panel data with nonadditive unobserved heterogeneity, applicable to both linear and nonlinear models.

Findings

Bias corrections effectively reduce estimation bias in short panels.

Empirical analysis reveals significant heterogeneity in price effects across states.

Method improves inference accuracy without increasing estimator variance.

Abstract

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.