Template-Type: ReDIF-Paper 1.0 Series: Tinbergen Institute Discussion Papers Creation-Date: 2013-12-12 Number: 13-197/III Author-Name: Kazumitsu Nawata Author-Workplace-Name: University of Tokyo, Japan Author-Name: Michael McAleer Author-Workplace-Name: National Tsing Hua University, Taiwan, Erasmus University Rotterdam, the Netherlands, Complutense University of Madrid, Spain Title: The Maximum Number of Parameters for the Hausman Test When the Estimators are from Different Sets of Equations Abstract: This discussion paper led to a publication in 'Economics Letters' (2014). Vol. 123(3), pages 291-294.
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 File-Url: http://papers.tinbergen.nl/13197.pdf File-Format: application/pdf File-Size: 122595 bytes Handle: RePEc:tin:wpaper:20130197