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THE IMPACT OF A HAUSMAN PRETEST ON THEASYMPTOTIC SIZE OF A HYPOTHESIS TEST

Published online by Cambridge University Press:  18 August 2009

Patrik Guggenberger
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Abstract

This paper investigates the asymptotic size propertiesof a two-stage test in the linear instrumentalvariables model when in the first stage a Hausman(1978) specification test is used as a pretest ofexogeneity of a regressor. In the second stage, asimple hypothesis about a component of thestructural parameter vector is tested, using at-statistic that is based oneither the ordinary least squares (OLS) or thetwo-stage least squares estimator (2SLS), dependingon the outcome of the Hausman pretest. Theasymptotic size of the two-stage test is derived ina model where weak instruments are ruled out byimposing a positive lower bound on the strength ofthe instruments. The asymptotic size equals 1 forempirically relevant choices of the parameter space.The size distortion is caused by a discontinuity ofthe asymptotic distribution of the test statistic inthe correlation parameter between the structural andreduced form error terms. The Hausman pretest doesnot have sufficient power against correlations thatare local to zero while the OLS-basedt-statistic takes on large valuesfor such nonzero correlations. Instead of using thetwo-stage procedure, the recommendation then is touse a t-statistic based on the 2SLSestimator or, if weak instruments are a concern, theconditional likelihood ratio test by Moreira(2003).

Information

Type
Research Article
Information
Econometric Theory , Volume 26 , Issue 2 , April 2010 , pp. 369 - 382
Copyright
Copyright © Cambridge University Press 2009

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Footnotes

I would like to thank the Sloan Foundation for a2009 fellowship and the NSF for support undergrant number SES-0748922, co-editor Richard Smith,seminar participants, Don Andrews, Badi Baltagi,Ivan Canay, Gary Chamberlain, Victor Chernozhukov,Phoebus Dhrymes, Ivan Fernandez-Val, RaffaellaGiacomini, William Greene, Jinyong Hahn, BruceHansen, Jerry Hausman, Guido Imbens, DaleJorgenson, Anna Mikusheva, Marcelo Moreira, UlrichMüller, Whitney Newey, Pierre Perron, Jack Porter,Zhongjun Qu, John Rust, Jim Stock, and MichaelWolf for comments, and the Economics Department atHarvard and the Cowles Foundation at Yale fortheir hospitality.

References

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