Template-type: ReDIF-Paper 1.0
Author-Name: Kazumitsu Nawata 
Author-Email: nawata@tmi.t.u-tokyo.ac.jp
Author-Workplace-Name: Graduate School of Engineering, University of Tokyo 
Author-Name: Michael McAleer
Author-Person: pmc90 
Author-Workplace-Name: Econometric Institute, Erasmus School of Economics, Erasmus University Rotterdam and Tinbergen Institute,
	The Netherlands, Department of Quantitative Economics, Complutense University of Madrid, and Institute of
	Economic Research, Kyoto University. 
Title: The Maximum Number of Parameters for the Hausman Test When the Estimators are from Different Sets of Equations
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. 


Classification-JEL:  C2; C5; I18. 

Keywords: : Hausman test, specification test, number of parameters, instrumental variable (IV) model, Box-Cox 
	model, Sample selection bias. 

Note: 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. 


Length: 14 pages 
Creation-Date: 2013-12  
Number: 2013-39 
X-File-Ref: http://america.sim.ucm.es/repec/ucm/ref/doicae1339.txt
File-URL: https://eprints.ucm.es/id/eprint/23988/1/1339.pdf
File-Format: Application/pdf
Handle: RePEc:ucm:doicae:1339