A reformulation of the Hausman test for regression models with pooled cross-section-time-series data

A Hausman test has been typically used to determine the consistency of the GLS estimator in static models with pooled cross-section-time-series data. Based on a GMM approach, we reformulate the Hausman test and find that it incorporates and tests only a limited set of moment restrictions. We also consider an alternative GMM statistic incorporating additional restrictions, which has power toward additional sources of model misspecification. Our Monte Carlo experiments demonstrate that while both the Hausman test and the alternative have good power detecting endogenous regressors, the alternative dominates if coefficients of regressors are nonstationary.