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.
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- 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.
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Econometric Society, vol. 47(1), pages 153-61, January.
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"Specification Tests in Econometrics,"
185, Massachusetts Institute of Technology (MIT), Department of Economics.
- Kazumitsu Nawata, 2013. "A new estimator of the Box-Cox transformation model using moment conditions," Economics Bulletin, AccessEcon, vol. 33(3), pages 2287-2297.
- Holly, Alberto, 1982. "A Remark on Hausman's Specification Test," Econometrica, Econometric Society, vol. 50(3), pages 749-59, May.
- Hausman, Jerry A. & Taylor, William E., 1981. "A generalized specification test," Economics Letters, Elsevier, vol. 8(3), pages 239-245.
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