Valid t-ratio Inference for IV

TL;DR

This paper demonstrates that the common F > 10 threshold for IV t-ratio inference is anti-conservative, proposing corrected thresholds and a new test to improve inference accuracy in econometric analysis.

Contribution

It derives the correct F threshold for valid t-ratio inference in IV models and introduces the tF procedure for F-dependent critical values.

Findings

F > 10 threshold is anti-conservative for 5% tests

Corrected thresholds significantly alter previous significance conclusions

Introduces the tF procedure for more accurate inference

Abstract

In the single IV model, current practice relies on the first-stage F exceeding some threshold (e.g., 10) as a criterion for trusting t-ratio inferences, even though this yields an anti-conservative test. We show that a true 5 percent test instead requires an F greater than 104.7. Maintaining 10 as a threshold requires replacing the critical value 1.96 with 3.43. We re-examine 57 AER papers and find that corrected inference causes half of the initially presumed statistically significant results to be insignificant. We introduce a more powerful test, the tF procedure, which provides F-dependent adjusted t-ratio critical values.