Michael Keane and Timothy Neal
Abstract: We provide a simple survey of the literature on weak instruments, aimed at giving practical advice to applied researchers. It is well-known that 2SLS has poor properties if instruments are exogenous but “weak.” We clarify these properties, explain weak instrument tests, and examine how behavior of 2SLS depends on instrument strength. A common standard for “strong” instruments is a first-stage F -statistic of at least 10. But 2SLS has some poor properties in that context: It has low power, and the 2SLS standard error estimate tends to be artificially small in samples where the 2SLS parameter estimate is most contaminated by the OLS bias. This causes t-tests to give very misleading results. Surprisingly, this problem persists even if the first-stage F is in the thousands. Robust tests like Anderson-Rubin greatly alleviate these problems, and should be used in lieu of the t-test even with strong instruments. In many realistic settings a first-stage F well above 10 may be necessary to give high confidence that 2SLS will outperform OLS. For example, in the archetypal application of estimating returns to education, we argue one needs F of at least 50.
Keywords: Instrumental variables, weak instruments, 2SLS, endogeneity, F-test, size distortion, Anderson-Rubin test, conditional t-test, conditional LR test, Fuller, JIVE