The impact of a Hausman pretest on the asymptotic size of a hypothesis test

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

This paper investigates the asymptotic size properties of a two-stage test in the linear instrumental variables model when in the first stage a Hausman (1978) specification test is used as a pretest of exogeneity of a regressor. In the second stage, a simple hypothesis about a component of the structural parameter vector is tested, using a t-statistic that is based on either the ordinary least squares (OLS) or the two-stage least squares estimator (2SLS), depending on the outcome of the Hausman pretest. The asymptotic size of the two-stage test is derived in a model where weak instruments are ruled out by imposing a positive lower bound on the strength of the instruments. The asymptotic size equals 1 for empirically relevant choices of the parameter space. The size distortion is caused by a discontinuity of the asymptotic distribution of the test statistic in the correlation parameter between the structural and reduced form error terms. The Hausman pretest does not have sufficient power against correlations that are local to zero while the OLS-based t-statistic takes on large values for such nonzero correlations. Instead of using the two-stage procedure, the recommendation then is to use a t-statistic based on the 2SLS estimator or, if weak instruments are a concern, the conditional likelihood ratio test by Moreira (2003).

Original languageEnglish (US)
Pages (from-to)369-382
Number of pages14
JournalEconometric Theory
Volume26
Issue number2
DOIs
StatePublished - Apr 1 2010

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statistics
Pre-test
Hypothesis test
Statistics
Ordinary least squares
Weak instruments
Values
Discontinuity
Instrumental variables
Asymptotic distribution
Size distortion
Likelihood ratio test
Specification test
Reduced form
Structural parameters
Least squares estimator
Estimator
Two-stage least squares
Test statistic
Lower bounds

All Science Journal Classification (ASJC) codes

  • Social Sciences (miscellaneous)
  • Economics and Econometrics

Cite this

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The impact of a Hausman pretest on the asymptotic size of a hypothesis test. / Guggenberger, Patrik.

In: Econometric Theory, Vol. 26, No. 2, 01.04.2010, p. 369-382.

Research output: Contribution to journalArticle

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