Transcription of Testing for Weak Instruments in Linear IV Regression
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Testing for Weak Instruments in Linear IV Regression
Testing for Weak Instruments in Linear IV Regression August 2001 (This revision: February 2003) James H. Stock Department of Economics, Harvard University and the National Bureau of Economic Research and Motohiro Yogo* Department of Economics, Harvard University ABSTRACT Weak Instruments can produce biased IV estimators and hypothesis tests with large size distortions. But what, precisely, are weak Instruments , and how does one detect them in practice? This paper proposes quantitative definitions of weak Instruments based on the maximum IV estimator bias, or the maximum Wald test size distortion, when there are multiple endogenous regressors. We tabulate critical values that enable using the first-stage F-statistic (or, when there are multiple endogenous regressors, the Cragg-Donald (1993) statistic) to test whether given Instruments are weak. *Prepared for the Festschrift in honor of Thomas Rothenberg. We thank Alastair Hall, Jerry Hausman, Takesi Hayakawa, George Judge, Whitney Newey, and Jonathan Wright for helpful comments and/or suggestions.
obtained using weak instrument asymptotic distributions (Staiger and Stock (1997)), which are more accurate than Edgeworth approximations when the concentration parameter is small.1 This paper is part of a growing literature on detecting weak instruments, surveyed in Stock, Wright, and Yogo (2002) and Hahn and Hausman (2003). Cragg and Donald
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