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A New Perspective on Weak Instruments

Michael Keane and Timothy Neal

Abstract: It is well-understood that 2SLS has poor properties if instruments are exogenous but weak. We clarify these properties, explain weak instrument tests, and study how behavior of 2SLS depends on instrument strength. A common standard for acceptable instruments is a first-stage F-statistic of at least 10. But we show 2SLS has poor properties in that context: Besides having little power, 2SLS generates artificially low standard errors precisely in those samples where it generates estimates most contaminated by endogeneity. This problem persists even when instruments are very strong, causing one-tailed 2SLS t-tests to suffer from severe size distortions unless F approaches 10,000. The Anderson-Rubin test alleviates this problem, and should be used even with strong instruments. A first-stage F of 50 or more is necessary to give reasonable confidence that 2SLS will outperform OLS. Otherwise, OLS combined with controls for sources of endogeneity may be a superior research strategy to IV.

Keywords: Instrumental variables, weak instruments, 2SLS, endogeneity, Anderson-Rubin test, F-test, size distortions of tests



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