Large-N and Large-T Properties of Panel Data Estimators and the Hausman Test

Abstract

This paper examines the asymptotic properties of the popular within, GLS estimators and the Hausman test for panel data models with both large numbers of cross-section (N) and time-series (T) observations. The model we consider includes the regressors with deterministic trends in mean as well as time invariant regressors. If a time-varying regressor is correlated with time invariant regressors, the time series of the time-varying regressor is not ergodic. Our asymptotic results are obtained considering the dependence of such non-ergodic time-varying regressors. We find that the within estimator is as efficient as the GLS estimator. Despite this asymptotic equivalence, however, the Hausman statistic, which is essentially a distance measure between the two estimators, is well defined and asymptotically chi square-distributed under the random effects assumption.