Con fidence Intervals for Projections of Partially Identi fied Parameters

74 Pages Posted: 16 Jan 2016

See all articles by Hiroaki Kaido

Hiroaki Kaido

Boston University - Department of Economics

Francesca Molinari

Cornell University - Department of Economics

Jörg Stoye

Cornell University - Department of Economics

Date Written: January 4, 2016

Abstract

This paper proposes a bootstrap-based procedure to build confidence intervals for single components of a partially identified parameter vector, and for smooth functions of such components, in moment (in)equality models. The extreme points of our confidence interval are obtained by maximizing/minimizing the value of the component (or function) of interest subject to the sample analog of the moment (in)equality conditions properly relaxed. The novelty is that the amount of relaxation, or critical level, is computed so that the component (or function) of theta, instead of theta itself, is uniformly asymptotically covered with prespecified probability. Calibration of the critical level is based on repeatedly checking feasibility of linear programming problems, rendering it computationally attractive. Computation of the extreme points of the confidence interval is based on a novel application of the response surface method for global optimization, which may prove of independent interest also for applications of other methods of inference in the moment (in)equalities literature.

The critical level is by construction smaller (infinite sample) than the one used if projecting confidence regions designed to cover the entire parameter vector. Hence, our confidence interval is weakly shorter than the projection of established confidence sets (Andrews and Soares, 2010), if one holds the choice of tuning parameters constant. We provide simple conditions under which the comparison is strict. Our inference method controls asymptotic coverage uniformly over a large class of data generating processes. Our assumptions and those used in the leading alternative approach (a profiling based method) are not nested. We explain why we employ some restrictions that are not required by other methods and provide examples of models for which our method is uniformly valid but profiling based methods are not.

Keywords: Partial identification; Inference on projections; Moment inequalities; Uniform inference

JEL Classification: C01, C15

Suggested Citation

Kaido, Hiroaki and Molinari, Francesca and Stoye, Jörg, Con fidence Intervals for Projections of Partially Identi fied Parameters (January 4, 2016). Available at SSRN: https://ssrn.com/abstract=2710987 or http://dx.doi.org/10.2139/ssrn.2710987

Hiroaki Kaido

Boston University - Department of Economics ( email )

595 Commonwealth Avenue
Boston, MA 02215
United States

Francesca Molinari

Cornell University - Department of Economics ( email )

414 Uris Hall
Ithaca, NY 14853-7601
United States
607-255-6367 (Phone)
607-255-2818 (Fax)

HOME PAGE: http://www.arts.cornell.edu/econ/fmolinari/

Jörg Stoye (Contact Author)

Cornell University - Department of Economics ( email )

414 Uris Hall
Ithaca, NY 14853-7601
United States

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