The Hausman test and weak instruments

Jinyong Hahn, John Ham, Hyungsik Roger Moon

    Research output: Contribution to journalArticle

    Abstract

    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
    Volume160
    Issue number2
    DOIs
    StatePublished - Feb 1 2011

    Fingerprint

    Weak Instruments
    Structural Equations
    Consistent Test
    Heteroskedasticity
    Instrumental Variables
    Monte Carlo Experiment
    Weak instruments
    Hausman test
    Economics
    Valid
    Predict
    Structural equations

    Keywords

    • Hausman test
    • Weak instruments

    ASJC Scopus subject areas

    • Economics and Econometrics
    • Applied Mathematics
    • History and Philosophy of Science

    Cite this

    The Hausman test and weak instruments. / Hahn, Jinyong; Ham, John; Moon, Hyungsik Roger.

    In: Journal of Econometrics, Vol. 160, No. 2, 01.02.2011, p. 289-299.

    Research output: Contribution to journalArticle

    Hahn, Jinyong ; Ham, John ; Moon, Hyungsik Roger. / The Hausman test and weak instruments. In: Journal of Econometrics. 2011 ; Vol. 160, No. 2. pp. 289-299.
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