Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Jan, 2014, Volume 82, Issue 1

Asymptotically Efficient Estimation of Models Defined by Convex Moment Inequalities
p. 387-413

Hiroaki Kaido, Andres Santos

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 √‐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.

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Supplemental Material

Supplement to "Asymptotically Efficient Estimation of Models Defined by Convex Moment Inequalities"

This appendix includes all proofs of results stated in the main text, a more detailed discussion of the examples introduced in Section 2.1, and the results of our Monte Carlo study.  The proof of each main result is contained in its own Appendix, which also includes a discussion of the strategy of proof and the role of the auxiliary results.

Supplement to "Asymptotically Efficient Estimation of Models Defined by Convex Moment Inequalities"

This zip file contains the replication files for the manuscript.