The Econometric SocietyEdited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262
Econometrica: Jul, 2012, Volume 80, Issue 4
https://doi.org/10.3982/ECTA9604
p. 1741-1768
Federico A. Bugni, Ivan A. Canay, Patrik Guggenberger
This paper studies the behavior, under local misspecification, of several confidence sets (CSs) commonly used in the literature on inference in moment (in)equality models. We propose the amount of asymptotic confidence size distortion as a criterion to choose among competing inference methods. This criterion is then applied to compare across test statistics and critical values employed in the construction of CSs. We find two important results under weak assumptions. First, we show that CSs based on subsampling and generalized moment selection (Andrews and Soares (2010)) suffer from the same degree of asymptotic confidence size distortion, despite the fact that asymptotically the latter can lead to CSs with strictly smaller expected volume under correct model specification. Second, we show that the asymptotic confidence size of CSs based on the quasi‐likelihood ratio test statistic can be an arbitrary small fraction of the asymptotic confidence size of CSs based on the modified method of moments test statistic.
This supplement contains the Lemmas and their proofs that are used in the proofs of Theorems 3.1 and 3.2 of the paper in Sections S1 and S2; the proof of Corollary 3.1 in Section S2; a missing data example and Monte Carlo simulations in Section S3; the verification of Assumptions A.6 and A.7 in two leading examples in Section S4; a discussion of the intuition behind Theorem 3.2 in Section S5; and details of the computations carried out in Table 1 in Section S6.
