Bootstrapping the Hausman Test in Panel Data Models

In the paper it is shown that in panel data models the Hausman test (HT) statistic can be considerably refined using the bootstrap technique. Edgeworth expansion shows that coverage of the bootstrapped HT is second-order correct. The asymptotic vs. the bootstrapped HT are compared also by Monte Carlo simulations. At the null hypothesis and a nominal size of 0.05 the bootstrapped HT reduces the coverage error of the asymptotic HT by 10-40% of nominal size; for nominal sizes less than or equal to 0.025 the coverage error reduction is between 30% and 80% of nominal size. For the nonnull alternatives, the power of the asymptotic HT fictitiously increases by over 70% of the correct power for nominal sizes less than or equal 0.025; the bootstrapped HT reduces overrejection to less than one fourth of its value. The advantages of the bootstrapped HT increase with the number of explanatory variables. Heteroskedasticity or serial correlation in the idiosyncratic part of the error does not hamper advantages of the bootstrapped version of HT, if a heteroskedasticity robust version of the HT and wild bootstrap are used. But, the power penalty is not negligible if a heteroskedasticity robust approach is used in the homoskedastic panel data model