Asymptotically Efficient Estimation of Models Defined by Convex Moment Inequalities
2014; Wiley; Volume: 82; Issue: 1 Linguagem: Inglês
10.3982/ecta10017
ISSN1468-0262
Autores Tópico(s)Statistical Methods and Bayesian Inference
ResumoEconometricaVolume 82, Issue 1 p. 387-413 Asymptotically Efficient Estimation of Models Defined by Convex Moment Inequalities Hiroaki Kaido, Hiroaki Kaido Dept. of Economics, Boston University, 270 Bay State Road, Boston, MA 02215, U.S.A.; [email protected]Search for more papers by this authorAndres Santos, Andres Santos Dept. of Economics, University of California—San Diego, 9500 Gilman Drive MS 0508, La Jolla, CA 92093-0508, U.S.A.; [email protected] We would like to thank Francesca Molinari, James Stock, and two anonymous referees for valuable suggestions that helped greatly improve this paper. We are also indebted to Victor Chernozhukov, Mark Machina, Ulrich Müller, and numerous seminar participants for their helpful comments.Search for more papers by this author Hiroaki Kaido, Hiroaki Kaido Dept. of Economics, Boston University, 270 Bay State Road, Boston, MA 02215, U.S.A.; [email protected]Search for more papers by this authorAndres Santos, Andres Santos Dept. of Economics, University of California—San Diego, 9500 Gilman Drive MS 0508, La Jolla, CA 92093-0508, U.S.A.; [email protected] We would like to thank Francesca Molinari, James Stock, and two anonymous referees for valuable suggestions that helped greatly improve this paper. We are also indebted to Victor Chernozhukov, Mark Machina, Ulrich Müller, and numerous seminar participants for their helpful comments.Search for more papers by this author First published: 05 February 2014 https://doi.org/10.3982/ECTA10017Citations: 26 AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat Abstract This paper examines the efficient estimation of partially identified models defined by moment inequalities that are convex in the parameter of interest. In such a setting, the identified set is itself convex and hence fully characterized by its support function. We provide conditions under which, despite being an infinite dimensional parameter, the support function admits √n-consistent regular estimators. A semiparametric efficiency bound is then derived for its estimation, and it is shown that any regular estimator attaining it must also minimize a wide class of asymptotic loss functions. In addition, we show that the "plug-in" estimator is efficient, and devise a consistent bootstrap procedure for estimating its limiting distribution. The setting we examine is related to an incomplete linear model studied in Beresteanu and Molinari (2008) and Bontemps, Magnac, and Maurin (2012), which further enables us to establish the semiparametric efficiency of their proposed estimators for that problem. References Ai, C., and X. 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