Identification-Robust Subvector Inference

This paper introduces identification-robust subvector tests and confidence sets (CS’s) that have asymptotic size equal to their nominal size and are asymptotically efficient under strong identification. Hence, inference is as good asymptotically as standard methods under standard regularity conditions, but also is identification robust. The results do not require special structure on the models under consideration, or strong identification of the nuisance parameters, as many existing methods do. We provide general results under high-level conditions that can be applied to moment condition, likelihood, and minimum distance models, among others. We verify these conditions under primitive conditions for moment condition models. In another paper, we do so for likelihood models. The results build on the approach of Chaudhuri and Zivot (2011), who introduce a C(α)-type Lagrange multiplier test and employ it in a Bonferroni subvector test. Here we consider two-step tests and CS’s that employ a C(α)-type test in the second step. The two-step tests are closely related to Bonferroni tests, but are not asymptotically conservative and achieve asymptotic efficiency under strong identification.