Specification testing with grouped fixed effects

We propose a bootstrap generalized Hausman test for the correct specification of unobserved heterogeneity in fixed-effects panel data models. We consider as null hypotheses two scenarios in which the unobserved heterogeneity is either time-invariant or specified as additive individual and time effects. We contrast the standard fixed- effects estimators with the recently developed two-step grouped fixed-effects estimator, that is consistent in the presence of time-varying heterogeneity under minimal specification and distributional assumptions for the unobserved effects. The Hausman test exploits the general formulation for the variance of the vector of contrasts and critical values are computed via parametric percentile bootstrap, so as to account for the non-centrality of the asymptotic χ 2 distribution arising from the incidental parameters and approximation biases. Monte Carlo evidence shows that the test has correct size and good power in both linear and non linear specification.