Testing for Weak Instruments in Linear IV Regression

Abstract

TECHNICAL WORKING PAPER SERIES TESTING FOR WEAK INSTRUMENTS IN LINEAR IV REGRESSION James H. Stock Motohiro Yogo Technical Working Paper 284 http://www.nber.org/papers/T0284 NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambridge, MA 02138 October 2002 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. This research was supported by NSF grants SBR-9730489 and SBR-0214131. The views expressed in this paper are those of the authors and not necessarily those of the National Bureau of Economic Research. © 2002 by James H. Stock and Motohiro Yogo. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. Testing for Weak Instruments in Linear IV Regression James H. Stock and Motohiro Yogo NBER Technical Working Paper No. 284 October 2002 JEL No. C2, C3 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 …

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