  We propose a bootstrap generalized Hausman test for the correct specification
of unobserved heterogeneity in both linear and nonlinear 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-way 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 chi-square
distribution arising from the incidental parameters and approximation biases.
Monte Carlo evidence shows that the test has correct size and good power
properties. We provide two empirical applications to illustrate the proposed
test: the first one is based on a linear model for the determinants of the wage
of working women and the second analyzes the trade extensive margin.
