The Hausman test and weak instruments

Jinyong Hahn, John C. Ham, Hyungsik Roger Moon

Research output: Contribution to journalArticlepeer-review


We consider the following problem. There is a structural equation of interest that contains an explanatory variable that theory predicts is endogenous. There are one or more instrumental variables that credibly are exogenous with regard to this structural equation, but which have limited explanatory power for the endogenous variable. Further, there is one or more potentially 'strong' instruments, which has much more explanatory power but which may not be exogenous. Hausman (1978) provided a test for the exogeneity of the second instrument when none of the instruments are weak. Here, we focus on how the standard Hausman test does in the presence of weak instruments using the StaigerStock asymptotics. It is natural to conjecture that the standard version of the Hausman test would be invalid in the weak instrument case, which we confirm. However, we provide a version of the Hausman test that is valid even in the presence of weak IV and illustrate how to implement the test in the presence of heteroskedasticity. We show that the situation we analyze occurs in several important economic examples. Our Monte Carlo experiments show that our procedure works relatively well in finite samples. We should note that our test is not consistent, although we believe that it is impossible to construct a consistent test with weak instruments.

Original languageEnglish (US)
Pages (from-to)289-299
Number of pages11
JournalJournal of Econometrics
Issue number2
StatePublished - Feb 2011


  • Hausman test
  • Weak instruments

ASJC Scopus subject areas

  • Economics and Econometrics


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