Bootstrapping the Hausman Test in Panel Data Models

Abstract

In the article, 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 the coverage of the bootstrapped HT is second-order correct.

The asymptotic versus 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 to 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.

Heteroscedasticity or serial correlation in the idiosyncratic part of the error does not hamper advantages of the bootstrapped version of HT, if a heteroscedasticity robust version of the HT and the wild bootstrap are used. But, the power penalty is not negligible if a heteroscedasticity robust approach is used in the homoscedastic panel data model.

Keywords:

• Bootstrap
• Edgeworth expansion
• Hausman test
• Monte carlo
• Panel data

Mathematics Subject Classification:

• 62E17
• 62F03
• 62F40
• 65C05

Notes

In the HC ₃ version of the heteroscedasticity robust covariance matrix, the estimated errors are adjusted for leverage h_it , so has to be used for (see Davidson and Flachaire, 2001).

Let denotes testing region for the statistic of the nominal size α and sample size n, then coverage error is defined by .

See, for example, Barlow (2010), Campos (2003), Dawson (2003), Eicher and Schreiber (2010), and Hammermann and Flanagan (2007).

The results for different values of correlation between the time-averaged explanatory variable and the individual-specific effect (different intensity of fixed effects) are available from the authors upon request.

The Rademacher distribution gives generally better results than the two-point distribution suggested by Mammen (1993); see Davidson and Flachaire (2001).

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