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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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Nawata , Kazumitsu and McAleer, Michael (2013) The Maximum Number of Parameters for the Hausman Test When the Estimators are from Different Sets of Equations. [ Documentos de Trabajo del Instituto Complutense de Análisis Económico (ICAE); nº 39, 2013, ] (Unpublished)

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Official URL: http://eprints.ucm.es/23988/


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Abstract

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.


Item Type:Working Paper or Technical Report
Additional Information:

JEL 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.

Uncontrolled Keywords:Hausman test, Specification test, Number of parameters, Instrumental variable (IV) model, Box-Cox model, Sample selection bias.
Subjects:Social sciences > Economics > Econometrics
Series Name:Documentos de Trabajo del Instituto Complutense de Análisis Económico (ICAE)
Volume:2013
Number:39
ID Code:23988
Deposited On:18 Dec 2013 12:13
Last Modified:09 Jan 2014 11:45

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