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

Donald Andrews () and Sukjin Han

No 1671, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

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 (search for similar items in EconPapers)
JEL-codes: C01 (search for similar items in EconPapers)
Pages: 23 pages
Date: 2008-07
New Economics Papers: this item is included in nep-ecm
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Published in Econometrics Journal (2009), 12: S172-S199

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