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The Hausman Test Statistic can be Negative even Asymptotically

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  • Schreiber Sven

    () (Goethe University Frankfurt, House of Finance, Grüneburgplatz 1, 60323 Frankfurt am Main, Germany)

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 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.

Suggested Citation

  • Schreiber Sven, 2008. "The Hausman Test Statistic can be Negative even Asymptotically," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 228(4), pages 394-405, August.
  • Handle: RePEc:jns:jbstat:v:228:y:2008:i:4:p:394-405
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    References listed on IDEAS

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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.
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    Cited by:

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    6. Chang, C-L. & McAleer, M.J. & Tang, J-T., 2013. "International Technology Diffusion of Joint and Cross-border Patents," Econometric Institute Research Papers EI 2013-24, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    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.
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    11. Galina Besstremyannaya, 2015. "Heterogeneous effect of residency matching and prospective payment on labor returns and hospital scale economies," Discussion Papers 15-001, Stanford Institute for Economic Policy Research.
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    14. 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.
    15. Chia-Lin Chang & Michael McAleer & Ju-Ting Tang, 2015. "Joint and Cross-border Patents as Proxies for International Technology Diffusion," Tinbergen Institute Discussion Papers 15-053/III, Tinbergen Institute, revised 30 Jan 2017.
    16. Chia-Lin Chang & Michael McAleer & Ju-Ting Tang, "undated". "International Technology Diffusion of Joint and Cross-border Patents (Revised version)," Documentos de Trabajo del ICAE 2015-06, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico, revised May 2015.
    17. Mitze, Timo & Alecke, Björn & Untiedt, Gerhard, 2009. "Trade-FDI Linkages in a System of Gravity Equations for German Regional Data," Ruhr Economic Papers 84, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
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    19. Laura Magazzini & Giorgio Calzolari, 2010. "Negative variance estimates in panel data models," Working Papers 15/2010, University of Verona, Department of Economics.
    20. 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.
    21. Cristina Simón, 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.
    22. Lehto, Eero, 2011. "Electricity prices in the Finnish retail market," Energy Policy, Elsevier, vol. 39(4), pages 2179-2192, April.
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    24. F Marchionne & S Parekh, 2015. "Growth, Debt, and Inequality," Economic Issues Journal Articles, Economic Issues, vol. 20(2), pages 67-94, September.

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