Valid Two-Step Identification-Robust Confidence Sets for GMM

In models with potentially weak identification, researchers often decide whether to report a robust confidence set based on an initial assessment of model identification. Two-step procedures of this sort can generate large coverage distortions for reported confidence sets, and existing procedures for controlling these distortions are quite limited. This paper introduces a generally applicable approach to detecting weak identification and constructing two-step confidence sets in GMM. This approach controls coverage distortions under weak identification and indicates strong identification, with probability tending to 1 when the model is well identified.