Bootstrap Inference in Partially Identified Models Defined by Moment Inequalities: Coverage of the Identified Set


  • Federico A. Bugni

    1. Dept. of Economics, Duke University, 213 Social Sciences Building, Box 90097, Durham, NC 27708, U.S.A.;
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    • I am indebted to my advisors, Joel Horowitz, Rosa Matzkin, and Elie Tamer, for their guidance and support. I thank a co-editor and three anonymous referees for comments and suggestions that have significantly helped to improve this paper. I also thank Donald Andrews, Ivan Canay, Xiaohong Chen, Silvia Glaubach, Nenad Kos, Enno Mammen, Charles Manski, Adam Rosen, Viktor Subbotin, Xun Tang, and the participants of seminars at Oberwolfach, Northwestern, UCL, Brown, UPenn, UCLA, Columbia, NYU, Yale, Duke, and Michigan for their comments. Financial support from the Robert Eisner Memorial Fellowship and the Dissertation Year Fellowship is gratefully acknowledged. Any and all errors are my own.

  • We can also admit models defined by moment equalities by combining pairs of weak moment inequalities.

  • We deal with the objective of covering each element of the identified set with a prespecified probability in Bugni (2010a).


This paper introduces a novel bootstrap procedure to perform inference in a wide class of partially identified econometric models. We consider econometric models defined by finitely many weak moment inequalities,2 which encompass many applications of economic interest. The objective of our inferential procedure is to cover the identified set with a prespecified probability.3 We compare our bootstrap procedure, a competing asymptotic approximation, and subsampling procedures in terms of the rate at which they achieve the desired coverage level, also known as the error in the coverage probability. Under certain conditions, we show that our bootstrap procedure and the asymptotic approximation have the same order of error in the coverage probability, which is smaller than that obtained by using subsampling. This implies that inference based on our bootstrap and asymptotic approximation should eventually be more precise than inference based on subsampling. A Monte Carlo study confirms this finding in a small sample simulation.