Testing for Weak Instruments in Linear IV Regression

73 Pages Posted: 2 Apr 2003 Last revised: 13 Oct 2021

See all articles by James H. Stock

James H. Stock

Harvard University - Department of Economics; National Bureau of Economic Research (NBER); Harvard University - Harvard Kennedy School (HKS)

Motohiro Yogo

Princeton University - Department of Economics; National Bureau of Economic Research

Multiple version iconThere are 2 versions of this paper

Date Written: November 2002

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. A technical contribution is to justify sequential asymptotic approximations for IV statistics with many weak instruments.

Suggested Citation

Stock, James H. and Yogo, Motohiro, Testing for Weak Instruments in Linear IV Regression (November 2002). Available at SSRN: https://ssrn.com/abstract=346941

James H. Stock (Contact Author)

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Motohiro Yogo

Princeton University - Department of Economics ( email )

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