The Hausman Test Statistic can be Negative even Asymptotically
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.
If 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.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 228 (2008)
Issue (Month): 4 (August)
|Contact details of provider:|| Web page: https://www.degruyter.com|
|Order Information:||Web: https://www.degruyter.com/view/j/jbnst|
References listed on IDEAS
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.:
- 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.
- Hausman, Jerry A, 1978.
"Specification Tests in Econometrics,"
Econometric Society, vol. 46(6), pages 1251-1271, November.
- Holly, Alberto, 1982. "A Remark on Hausman's Specification Test," Econometrica, Econometric Society, vol. 50(3), pages 749-759, May.
- Hausman, Jerry A. & Taylor, William E., 1981. "A generalized specification test," Economics Letters, Elsevier, vol. 8(3), pages 239-245.
When requesting a correction, please mention this item's handle: RePEc:jns:jbstat:v:228:y:2008:i:4:p:394-405. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Peter Golla)
If references are entirely missing, you can add them using this form.