A Practical Guide to Weak Instruments

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 acceptable instruments is a ï¬ rst-stage F-statistic of at least 10. But 2SLS has poor properties in that context: It has very little power, and generates artiï¬ cially low standard errors precisely in those samples where it generates estimates most contaminated by endogeneity. This causes t-tests to give misleading results. In fact, the distribution of t-statistics is highly non-normal unless F is in the thousands. Anderson-Rubin and conditional t-tests greatly alleviate this problem, and should be used even with strong instruments. A ï¬ rst-stage F well above 10 is necessary to give high conï¬ dence that 2SLS will outperform OLS. Otherwise, OLS combined with controls for sources of endogeneity may be a superior research strategy to IV.