Correct (and Incorrect) Inference with a Single Instrumental Variable: Practical Takeaways from the Weak Instruments Literature

Most empirical economists have encountered the warning that instrumental variables can be “weak,” but the underlying issues—what makes an instrument weak, why weakness distorts inference, and what to do about it—are less widely understood. This article offers an accessible introduction to the weak instruments problem for the common just-identified case of a single endogenous regressor and a single instrument. We explain why the usual two-stage least squares t-ratio and its “±1.96 times the standard error” confidence interval can yield incorrect inferences, much as homoskedasticity-only standard errors do when errors are not homoskedastic. We then describe practical, robust-to-weak-instrument solutions—including the Anderson-Rubin and tF methods—that deliver valid confidence intervals whatever the instrument's true strength, and we offer some do's and don'ts, notably why the popular “F greater than 10” rule has no theoretical justification in this setting.