The Maximum Number of Parameters for the Hausman Test When the Estimators are from Different Sets of Equations
AbstractHausman (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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Bibliographic InfoPaper provided by University of Canterbury, Department of Economics and Finance in its series Working Papers in Economics with number 14/02.
Length: 14 pages
Date of creation: 01 Jan 2014
Date of revision:
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Hausman test; specification test; number of parameters; instrumental variable (IV) model; Box-Cox model; Sample selection bias;
Other versions of this item:
- Nawata, Kazumitsu & McAleer, Michael, 2014. "The maximum number of parameters for the Hausman test when the estimators are from different sets of equations," Economics Letters, Elsevier, vol. 123(3), pages 291-294.
- Nawata, K. & McAleer, M.J., 2013. "The maximum Number of parameters for the Hausman Test When the Estimators are from Different Sets of Equations," Econometric Institute Research Papers EI2013-35, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
- Kazumitsu Nawata & Michael McAleer, 2013. "The Maximum Number of Parameters for the Hausman Test When the Estimators are from Different Sets of Equations," Documentos del Instituto Complutense de AnÃ¡lisis EconÃ³mico 2013-39, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales.
- Kazumitsu Nawata & Michael McAleer, 2013. "The Maximum Number of Parameters for the Hausman Test When the Estimators are from Different Sets of Equations," Tinbergen Institute Discussion Papers 13-197/III, Tinbergen Institute.
- C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
- C5 - Mathematical and Quantitative Methods - - Econometric Modeling
- I18 - Health, Education, and Welfare - - Health - - - Government Policy; Regulation; Public Health
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"Specification Tests in Econometrics,"
185, Massachusetts Institute of Technology (MIT), Department of Economics.
- 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.
- Wu, De-Min, 1973. "Alternative Tests of Independence Between Stochastic Regressors and Disturbances," Econometrica, Econometric Society, vol. 41(4), pages 733-50, July.
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