Invalidity of the Bootstrap and the m Out of n Bootstrap for Interval Endpoints Defined by Moment Inequalities

36 Pages Posted: 28 Jul 2008 Last revised: 19 Aug 2008

See all articles by Donald W. K. Andrews

Donald W. K. Andrews

Yale University - Cowles Foundation

Sukjin Han

University of Texas at Austin - Department of Economics

Date Written: July 28, 2008

Abstract

This paper analyzes the finite-sample and asymptotic properties of several bootstrap and m out of n bootstrap methods for constructing confidence interval (CI) endpoints in models defined by moment inequalities. In particular, we consider using these methods directly to construct CI endpoints. By considering two very simple models, the paper shows that neither the bootstrap nor the m out of n bootstrap is valid in finite samples or in a uniform asymptotic sense in general when applied directly to construct CI endpoints.

In contrast, other results in the literature show that other ways of applying the bootstrap, m out of n bootstrap, and subsampling do lead to uniformly asymptotically valid confidence sets in moment inequality models. Thus, the uniform asymptotic validity of resampling methods in moment inequality models depends on the way in which the resampling methods are employed.

Keywords: Bootstrap, Coverage probability, m out of n bootstrap, Moment inequality model, Partial identification, Subsampling

JEL Classification: C01

Suggested Citation

Andrews, Donald W. K. and Han, Sukjin, Invalidity of the Bootstrap and the m Out of n Bootstrap for Interval Endpoints Defined by Moment Inequalities (July 28, 2008). Cowles Foundation Discussion Paper No. 1671, Available at SSRN: https://ssrn.com/abstract=1182639 or http://dx.doi.org/10.2139/ssrn.1182639

Donald W. K. Andrews (Contact Author)

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States
203-432-3698 (Phone)
203-432-6167 (Fax)

Sukjin Han

University of Texas at Austin - Department of Economics ( email )

Austin, TX 78712
United States

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