Identication-Robust Subvector Inference

This paper introduces identi…cation-robust subvector tests and con…dence sets (CS’s) that have asymptotic size equal to their nominal size and are asymptotically e¢ cient under strong identi…cation. Hence, inference is as good asymptotically as standard methods under standard regularity conditions, but also is identi…cation robust. The results do not require special structure on the models under consideration, or strong identi…cation 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( )-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( )-type test in the second step. The two-step tests are closely related to Bonferroni tests, but are not asymptotically conservative and achieve asymptotic e¢ ciency under strong identi…cation. Keywords: Asymptotics, con…dence set, identi…cation-robust, inference, instrumental variables, moment condition, robust, test. JEL Classi…cation Numbers: C10, C12. The author gratefully acknowledges the research support of the National Science Foundation via grant SES1355504. The author thanks Koohyun Kwon for constructing the …gures and Jaewon Lee for a very careful proofreading of the paper. The author thanks Isaiah Andrews, Angelo Melino, Charlie Saunders, and Katsumi Shimotsu for helpful comments.