Distortions of Asymptotic Confidence Size in Locally Misspecified Moment Inequality Models


  • Federico A. Bugni,

    1. Dept. of Economics, Duke University, Durham, NC 27708, U.S.A.; federico.bugni@duke.edu
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  • Ivan A. Canay,

    1. Dept. of Economics, Northwestern University, Evanston, IL 60208, U.S.A.; iacanay@northwestern.edu
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  • Patrik Guggenberger

    1. Dept. of Economics, University of California, San Diego, La Jolla, CA 92093, U.S.A.; pguggenberger@ucsd.edu
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    • This paper was previously circulated under the title “Asymptotic Distortions in Locally Misspecified Moment Inequality Models.” We thank a co-editor and three referees for very helpful comments and suggestions. We also thank seminar participants at various universities, the 2010 Econometric Society World Congress, the Cemmap/Cowles “Advancing Applied Microeconometrics” conference, the Econometrics Jamboree at Duke, and the 2011 Econometric Society North American Winter Meeting for helpful comments. Bugni, Canay, and Guggenberger thank the National Science Foundation for research support via Grants SES-1123771, SES-1123586, and SES-1021101, respectively. Guggenberger also thanks the Alfred P. Sloan Foundation for a 2009–2011 fellowship.


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.