The Maximum Number of Parameters for the Hausman Test When the Estimators are from Different Sets of Equations
Hausman (1978) developed a widely-used model specification test that has passed the test of time. The test is based on two estimators, one being consistent under the null hypothesis but inconsistent under the alternative, and the other being consistent under both the null and alternative hypotheses. In this paper, we show that the asymptotic variance of the difference of the two estimators can be a singular matrix. Moreover, in calculating the Hausman test there is a maximum number of parameters which is the number of different equations that are used to obtain the two estimators. Three illustrative examples are used, namely an exogeneity test for the linear regression model, a test for the Box-Cox transformation, and a test for sample selection bias.
|Date of creation:||01 Jan 2014|
|Date of revision:|
|Contact details of provider:|| Postal: |
Phone: 64 3 369 3123 (Administrator)
Fax: 64 3 364 2635
Web page: http://www.econ.canterbury.ac.nz
More information through EDIRC
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.:
- Hausman, Jerry A. & Taylor, William E., 1981. "A generalized specification test," Economics Letters, Elsevier, vol. 8(3), pages 239-245.
- J. A. Hausman, 1976.
"Specification Tests in Econometrics,"
185, Massachusetts Institute of Technology (MIT), Department of Economics.
- Smith, Richard J., 1985. "Wald tests for the independence of stochastic variables and disturbance of a single linear stochastic simultaneous equation," Economics Letters, Elsevier, vol. 17(1-2), pages 87-90.
- Holly, Alberto, 1982. "A Remark on Hausman's Specification Test," Econometrica, Econometric Society, vol. 50(3), pages 749-59, May.
- Wu, De-Min, 1973. "Alternative Tests of Independence Between Stochastic Regressors and Disturbances," Econometrica, Econometric Society, vol. 41(4), pages 733-50, July.
- Heckman, James J, 1979.
"Sample Selection Bias as a Specification Error,"
Econometric Society, vol. 47(1), pages 153-61, January.
- Smith, Richard J, 1984. "A Note on Likelihood Ratio Tests for the Independence between a Subset of Stochastic Regressors and Disturbances," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 25(1), pages 263-69, February.
- Smith, Richard, 1983. "On the classical nature of the Wu-Hausman statistics for the independence of stochastic regressors and disturbance," Economics Letters, Elsevier, vol. 11(4), pages 357-364.
- Kazumitsu Nawata, 2013. "A new estimator of the Box-Cox transformation model using moment conditions," Economics Bulletin, AccessEcon, vol. 33(3), pages 2287-2297.
When requesting a correction, please mention this item's handle: RePEc:cbt:econwp:14/02. 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: (Albert Yee)
If references are entirely missing, you can add them using this form.