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The Hausman Test Statistic can be Negative even Asymptotically

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  • Sven Schreiber

    ()
    (Universitaet Frankfurt)

Abstract

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 matric difference should be routinely checked for positive semi-definite-ness, 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.

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Bibliographic Info

Article provided by Justus-Liebig University Giessen, Department of Statistics and Economics in its journal Journal of Economics and Statistics.

Volume (Year): 228 (2008)
Issue (Month): 4 (August)
Pages: 394-405

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Handle: RePEc:jns:jbstat:v:228:y:2008:i:4:p:394-405

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Keywords: Hausman test; negative chi-square statistic; nuisance parameter;

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References

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  1. Pesaran, M. Hashem & Smith, Ron, 1995. "Estimating long-run relationships from dynamic heterogeneous panels," Journal of Econometrics, Elsevier, vol. 68(1), pages 79-113, July.
  2. Holly, Alberto, 1982. "A Remark on Hausman's Specification Test," Econometrica, Econometric Society, vol. 50(3), pages 749-59, May.
  3. Hausman, Jerry A, 1978. "Specification Tests in Econometrics," Econometrica, Econometric Society, vol. 46(6), pages 1251-71, November.
  4. Hausman, Jerry A. & Taylor, William E., 1981. "A generalized specification test," Economics Letters, Elsevier, vol. 8(3), pages 239-245.
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Cited by:
  1. Björn Alecke & Timo Mitze & Gerhard Untiedt, 2009. "Internal Migration, Regional Labour Market Dynamics and Implications for German East-West Disparities – Results from a Panel VAR," Ruhr Economic Papers 0096, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.
  2. Cristina Simon, 2012. "A panel data analysis of the effects of voluntary and involuntary separations on unit performance in," Working Papers Economia rh8-114-i, Instituto de Empresa, Area of Economic Environment.
  3. Lehto, Eero, 2011. "Electricity prices in the Finnish retail market," Energy Policy, Elsevier, vol. 39(4), pages 2179-2192, April.
  4. Mitze, Timo & Alecke, Björn & Untiedt, Gerhard, 2008. "Trade, FDI and Cross-Variable Linkages: A German (Macro-)Regional Perspective," MPRA Paper 12245, University Library of Munich, Germany.
  5. Timo Mitze & Björn Alecke & Gerhard Untiedt, 2009. "Trade-FDI Linkages in a System of Gravity Equations for German Regional Data," Ruhr Economic Papers 0084, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.
  6. Laura Magazzini & Giorgio Calzolari, 2010. "Negative variance estimates in panel data models," Working Papers 15/2010, University of Verona, Department of Economics.
  7. Francesco Marchionne & Alberto Zazzaro, 2013. "Rischio e concorrenza nel sistema bancario italiano durante la crisi finanziaria globale," Mo.Fi.R. Working Papers 86, Money and Finance Research group (Mo.Fi.R.) - Univ. Politecnica Marche - Dept. Economic and Social Sciences.
  8. Bücker, Michael & Krämer, Walter & Arnold, Matthias, 2012. "A Hausman test for non-ignorability," Economics Letters, Elsevier, vol. 114(1), pages 23-25.

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