What to do when you can't use '1.96' Confidence Intervals for IV

To address the well-established large-sample invalidity of the +/-1.96 critical values for the t-ratio in the single variable just-identified IV model, applied research typically qualifies the inference based on the first-stage-F (Staiger and Stock (1997) and Stock and Yogo (2005)). We fully extend this F-based approach to its logical conclusion by presenting new critical values for the t-ratio to additionally accommodate values of F that do not meet existing thresholds needed for validity. These new t-ratio critical values simultaneously fix the main problem of over-rejection (invalidity) and the under-appreciated possibility of under-rejection (conservativeness) that can occur when relying solely on the usual 1.96 critical value. We show that the corresponding new confidence intervals are generally expected to be substantially shorter than competing “robust to weak instrument” intervals, including those from the recommended benchmark of Anderson and Rubin (1949) (AR). In a sample of 89 specifications from 10 recent empirical studies drawn from five general interest journals, the new “VtF” intervals are shorter than AR intervals 100 percent of the time, and even more likely to produce statistically significant results than the usual +/-1.96 procedure.