Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/130090
Authors: 
Kaido, Hiroaki
Molinari, Francesca
Stoye, Jörg
Year of Publication: 
2016
Series/Report no.: 
cemmap working paper, Centre for Microdata Methods and Practice CWP02/16
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 Ø, instead of Ø 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 (in finite 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.
Subjects: 
Partial identification
Inference on projections
Moment inequalities
Uniform inference
Document Type: 
Working Paper

Files in This Item:
File
Size
953.67 kB





Items in EconStor are protected by copyright, with all rights reserved, unless otherwise indicated.