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COMPARISON OF INFERENTIAL METHODS IN PARTIALLY IDENTIFIED MODELS IN TERMS OF ERROR IN COVERAGE PROBABILITY

Published online by Cambridge University Press:  13 November 2014

Federico A. Bugni
Federico A. Bugni*
Affiliation:
Duke University
*
*Address correspondence to Federico Bugni, Department of Economics, Duke University, 213 Social Sciences, Box 90097, Durham, NC, 27708; phone: 919-660-1887; e-mail: [email protected].
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Abstract

This paper considers the problem of coverage of the elements of the identified set in a class of partially identified econometric models with a prespecified probability. In order to conduct inference in partially identified econometric models defined by moment (in)equalities, the literature has proposed three methods: bootstrap, subsampling, and asymptotic approximation. The objective of this paper is to compare these methods in terms of the rate at which they achieve the desired coverage level, i.e., in terms of the rate at which the error in the coverage probability (ECP) converges to zero.

Under certain conditions, we show that the ECP of the bootstrap and the ECP of the asymptotic approximation converge to zero at the same rate, which is a faster rate than that of the ECP of subsampling methods. As a consequence, under these conditions, the bootstrap and the asymptotic approximation produce inference that is more precise than subsampling. A Monte Carlo simulation study confirms that these results are relevant in finite samples.

Type
ARTICLES
Information
Econometric Theory , Volume 32 , Issue 1 , February 2016 , pp. 187 - 242
Copyright
Copyright © Cambridge University Press 2014 

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