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Inference for functions of partially identified parameters in moment inequality models

Authors: Federico A. Bugni , Ivan A. Canay and Xiaoxia Shi
Date: 07 May 2014
Type: cemmap Working Paper, CWP22/14
DOI: 10.1920/wp.cem.2014.2214

Abstract

This paper introduces a bootstrap-based inference method for functions of the parameter vector in a moment (in)equality model. As a special case, our method yields marginal con fidence sets for individual coordinates of this parameter vector. Our inference method controls asymptotic size uniformly over a large class of data distributions. The current literature describes only two other procedures that deliver uniform size control for this type of problem: projection-based and subsampling inference. Relative to projection-based procedures, our method presents three advantages: (i) it weakly dominates in terms of fi nite sample power, (ii) it strictly dominates in terms of asymptotic power, and (iii) it is typically less computationally demanding. Relative to subsampling, our method presents two advantages: (i) it strictly dominates in terms of asymptotic power (for reasonable choices of subsample size), and (ii) it appears to be less sensitive to the choice of its tuning parameter than subsampling is to the choice of subsample size.

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New version:
Federico A. Bugni, Ivan A. Canay and Xiaoxia Shi September 2015, Inference for functions of partially identified parameters in moment inequality models, cemmap Working Paper, CWP54/15, Institute for Fiscal Studies
Previous version:
Federico A. Bugni, Ivan A. Canay and Xiaoxia Shi January 2014, Inference for functions of partially identified parameters in moment inequality models, cemmap Working Paper, CWP05/14, Institute for Fiscal Studies

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