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The Maximum Number of Parameters for the Hausman Test When the Estimators are from Different Sets of Equations

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dc.contributor.authorNawata , Kazumitsu
dc.contributor.authorMcAleer, Michael
dc.date.accessioned2023-06-19T23:53:51Z
dc.date.available2023-06-19T23:53:51Z
dc.date.issued2013-12
dc.descriptionJEL classifications: C2; C5; I18. This paper was supported by a Grant-in-Aid for Scientific Research “Analyses of the Large Scale Medical Survey Data and the Policy Evaluations in Japan (Grant Number: 24330067)” of the Japan Society of Science for the first author, and Australian Research Council and the National Science Council, Taiwan for the second author.
dc.description.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.
dc.description.facultyFac. de Ciencias Económicas y Empresariales
dc.description.facultyInstituto Complutense de Análisis Económico (ICAE)
dc.description.refereedFALSE
dc.description.sponsorshipThe Japan Society of Science
dc.description.sponsorshipAustralian Research Council
dc.description.sponsorshipthe National Science Council, Taiwan
dc.description.statusunpub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/23988
dc.identifier.relatedurlhttps://www.ucm.es/icae
dc.identifier.urihttps://hdl.handle.net/20.500.14352/41534
dc.issue.number39
dc.language.isoeng
dc.page.total14
dc.relation.ispartofseriesDocumentos de Trabajo del Instituto Complutense de Análisis Económico (ICAE)
dc.rightsAtribución-NoComercial 3.0 España
dc.rights.accessRightsopen access
dc.rights.urihttps://creativecommons.org/licenses/by-nc/3.0/es/
dc.subject.keywordHausman test
dc.subject.keywordSpecification test
dc.subject.keywordNumber of parameters
dc.subject.keywordInstrumental variable (IV) model
dc.subject.keywordBox-Cox model
dc.subject.keywordSample selection bias.
dc.subject.ucmEconometría (Economía)
dc.subject.unesco5302 Econometría
dc.titleThe Maximum Number of Parameters for the Hausman Test When the Estimators are from Different Sets of Equations
dc.typetechnical report
dc.volume.number2013
dcterms.referencesBickel, P.J. and K.A. Doksum (1981) “An Analysis of Transformations Revisited,” Journal of the American Statistical Association 76, 296-311. Box, G.E.P., and D.R. Cox (1964) “An Analysis of Transformations,” Journal of the Royal Statistical Society B 26, 211-252. Durbin, J. (1954) “Errors in Variables,” Review of the International Statistical Institute, 22, 23-32. Hausman, J. (1978) “Specification Tests in Econometrics”, Econometrica, 46, 1251-72. Hausman, J.A. and W. Taylor (l980) “Comparing Specification Tests and Classical Tests,” MIT Department of Economics Discussion Paper No. 226. Hausman, J.A. and W. Taylor (1981) “A Generalized Specification Test,” Economics Letters, 8, 239–245. Heckman, J. (1976) “The Common Structure of Statistical Models of Truncation, Sample Selection Bias and Limited Dependent Variables and a Simple Estimator for such Models,” Annals of Econometric and Social Measurement, 5, 475-492. Heckman, J. (1979) “Sample Selection Bias as a Specification Error,” Econometrica, 47, 153-161. Holly, A. (1982) “A Remark on Hausman's Specification Test,” Econometrica, 50, 749-759. Ichimura, H. and L.-F. Lee (1991), “Semiparametric Least Squares Estimation of Multiple Index Models: Single Equation Estimation”, in International Symposia in Economic Theory and Econometrics, W.A. Barnett, J. Powell, and G. Tauchen (eds.), Cambridge University Press, pp. 3-49. Nawata K. (2013). “A New Estimator of the Box-Cox Transformation Model Using Moment Conditions,” Economics Bulletin, 33, 2287-2297. Smith, R. J., (1983) “On the Classical Nature of the Wu-Hausman Statistics for the Independence of Stochastic Regressors and Disturbance,” Economics Letters, 11, 357-364. Smith, R. J., (1984) “A Note on Likelihood Ratio Tests for the Independence Between a Subset of Stochastic Regressors and Disturbances,” International Economic Review, 25, 263-269. Smith, R.J. (1985) “Wald Tests for the Independence of Stochastic Variables and Disturbance of a Single Linear Stochastic Simultaneous Equation,” Economics Letters, 17, 87-90. Wu. D.M. (1973) “Alternative Tests of Independence Between Stochastic Regressors and Disturbances,” Econometrica, 41, 733-750.
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