The Hausman Test Statistic can be Negative even Asymptotically
AbstractWe 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoArticle 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)
Contact details of provider:
Postal: Licher Straße 74, 35394 Gießen
Phone: +49 (0)641 99 22 001
Fax: +49 (0)641 99 22 009
Web page: http://wiwi.uni-giessen.de/home/oekonometrie/Jahrbuecher/
More information through EDIRC
Hausman test; negative chi-square statistic; nuisance parameter;
Find related papers by JEL classification:
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- J. A. Hausman, 1976.
"Specification Tests in Econometrics,"
185, Massachusetts Institute of Technology (MIT), Department of Economics.
- Hausman, Jerry A. & Taylor, William E., 1981. "A generalized specification test," Economics Letters, Elsevier, vol. 8(3), pages 239-245.
- 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.
- Pesaran, M.H. & Smith, R., 1992. "Estimating Long-Run Relationships From Dynamic Heterogeneous Panels," Cambridge Working Papers in Economics 9215, Faculty of Economics, University of Cambridge.
- Holly, Alberto, 1982. "A Remark on Hausman's Specification Test," Econometrica, Econometric Society, vol. 50(3), pages 749-59, May.
- 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.
- Bücker, Michael & Krämer, Walter & Arnold, Matthias, 2012. "A Hausman test for non-ignorability," Economics Letters, Elsevier, vol. 114(1), pages 23-25.
- 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.
- Björn Alecke & Timo Mitze & Gerhard Untiedt, 2010. "Internal migration, regional labour market dynamics and implications for German East-West disparities: results from a Panel VAR," Jahrbuch für Regionalwissenschaft, Springer, vol. 30(2), pages 159-189, September.
- 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.
- 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.
- Lehto, Eero, 2011. "Electricity prices in the Finnish retail market," Energy Policy, Elsevier, vol. 39(4), pages 2179-2192, April.
- Laura Magazzini & Giorgio Calzolari, 2010. "Negative variance estimates in panel data models," Working Papers 15/2010, University of Verona, Department of Economics.
- 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.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Peter Winker).
If references are entirely missing, you can add them using this form.