The Hausman Test Statistic can be Negative even Asymptotically
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Sven Schreiber
Summary
We show that under the alternative hypothesis the Hausman chi-square test statistic can be negative not only in small samples but even asymptotically. Therefore in large samples such a result is only compatible with the alternative and should be interpreted accordingly. Applying a known insight from finite samples, this can only occur if the different estimation precisions (often the residual variance estimates) under the null and the alternative both enter the test statistic. In finite samples, using the absolute value of the test statistic is a remedy that does not alter the null distribution and is thus admissible. Even for positive test statistics the relevant covariance matrix difference should be routinely checked for positive semi-definiteness, because we also show that otherwise test results may be misleading. Of course the preferable solution still is to impose the same nuisance parameter (i.e., residual variance) estimate under the null and alternative hypotheses, if the model context permits that with relative ease. We complement the likelihood-based exposition by a formal proof in an omitted-variable context, we present simulation evidence for the test of panel random effects, and we illustrate the problems with a panel homogeneity test.
© 2008 by Lucius & Lucius, Stuttgart
Artikel in diesem Heft
- Inhalt / Contents
- Abhandlungen / Original Papers
- Konjunktur und Generationenbilanz – eine Analyse anhand des HP-Filters / Business Cycle Effects on Generational Accounting – An Analysis using the HP-Filter
- Fiskalische Effekte der Kommunalverfassungsreformen der 1990er Jahre in Deutschland / Reforming Local Constitutions in Germany during the 1990s – Their Fiscal Effects
- The Effect of Reputation on Selling Prices in Auctions
- Capital Stock Approximation using Firm Level Panel Data
- Rational Ignorance is not Bliss: When do Lazy Voters Learn from Decentralised Policy Experiments?
- The Hausman Test Statistic can be Negative even Asymptotically
- Buchbesprechungen / Book Reviews
Artikel in diesem Heft
- Inhalt / Contents
- Abhandlungen / Original Papers
- Konjunktur und Generationenbilanz – eine Analyse anhand des HP-Filters / Business Cycle Effects on Generational Accounting – An Analysis using the HP-Filter
- Fiskalische Effekte der Kommunalverfassungsreformen der 1990er Jahre in Deutschland / Reforming Local Constitutions in Germany during the 1990s – Their Fiscal Effects
- The Effect of Reputation on Selling Prices in Auctions
- Capital Stock Approximation using Firm Level Panel Data
- Rational Ignorance is not Bliss: When do Lazy Voters Learn from Decentralised Policy Experiments?
- The Hausman Test Statistic can be Negative even Asymptotically
- Buchbesprechungen / Book Reviews
