A Powerful Test Needs to Be Size-Correct: Response to “Robust Inference for Consumption-Based Asset Pricing with Power”

Statistical tests need to be size-correct, i.e., their rejection frequencies under the null hypothesis should not exceed the nominal significance level, before we can talk about their power. It is well established in the weak identification literature that commonly used t-tests (such as the Fama–MacBeth/Shanken and generalized method of moments (GMM) t-tests) exhibit size distortion when identification conditions are at risk, while identification-robust tests remain size-correct. Furthermore, this literature has also produced tests that are both size-correct and optimal in terms of power. Therefore, these robust tests should be recommended over t-tests, and not vice versa.