What to Do When You Can't Use 196 Confidence Intervals for IV

Working Paper: NBER ID: w31893

Authors: David S. Lee; Justin McCrary; Marcelo J. Moreira; Jack R. Porter; Luther Yap

Abstract: 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.

Keywords: instrumental variables; confidence intervals; causal inference

JEL Codes: C01; C26; J0

Causal Claims

Cause	Effect
Conventional 196 critical values for the t-ratio in IV models (C26)	Invalid inference (C20)
Low first-stage F-statistic (C29)	Invalid inference (C20)
v_tf procedure (Y20)	Valid inferences (C20)
v_tf intervals (C32)	Shorter than Anderson-Rubin intervals (C41)
v_tf method (C29)	Improves precision of statistical results (C46)
v_tf procedure (Y20)	Statistically significant results more frequently (C12)