Confidence intervals for projections of partially identified parameters
Hiroaki Kaido,
Francesca Molinari and
Jörg Stoye
No CWP49/17, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies
Abstract:
We propose a bootstrap-based calibrated projection procedure to build con fidence intervals for single components and for smooth functions of a partially identi fied parameter vector in moment (in)equality models. The method controls asymptotic coverage uniformly over a large class of data generating processes. The extreme points of the calibrated projection confi dence interval are obtained by extremizing the value of the component (or function) of interest subject to a proper relaxation of studentized sample analogs of the moment (in)equality conditions. The degree of relaxation, or critical level, is calibrated so that the component (or function) of , not itself, is uniformly asymptotically covered with prespeci ed probability. This calibration is based on repeatedly checking feasibility of linear programming problems, rendering it computationally attractive. Nonetheless, the program defi ning an extreme point of the confi dence interval is generally nonlinear and potentially intricate. We provide an algorithm, based on the response surface method for global optimization, that approximates the solution rapidly and accurately. The algorithm is of independent interest for inference on optimal values of stochastic nonlinear programs. We establish its convergence under conditions satisfi ed by canonical examples in the moment (in)equalities literature. Our assumptions and those used in the leading alternative approach (a profi ling based method) are not nested. An extensive Monte Carlo analysis con rms the accuracy of the solution algorithm and the good statistical as well as computational performance of calibrated projection, including in comparison to other methods.
Keywords: Partial identi fication; Inference on projections; Moment inequalities; Uniform inference (search for similar items in EconPapers)
Date: 2017-11-10
New Economics Papers: this item is included in nep-ore
References: Add references at CitEc
Citations: View citations in EconPapers (5)
Downloads: (external link)
https://www.ifs.org.uk/uploads/CWP491717.pdf (application/pdf)
Our link check indicates that this URL is bad, the error code is: 404 Not Found (https://www.ifs.org.uk/uploads/CWP491717.pdf [302 Found]--> https://ifs.org.uk/uploads/CWP491717.pdf)
Related works:
Journal Article: Confidence Intervals for Projections of Partially Identified Parameters (2019)
Working Paper: Confidence Intervals for Projections of Partially Identified Parameters (2019)
Working Paper: Confi dence Intervals for Projections of Partially Identifi ed Parameters (2019)
Working Paper: Confidence intervals for projections of partially identified parameters (2017)
Working Paper: Confidence intervals for projections of partially identified parameters (2016)
Working Paper: Confi dence Intervals for Projections of Partially Identi fied Parameters (2016)
Working Paper: Confidence intervals for projections of partially identified parameters (2016)
Working Paper: Confidence Intervals for Projections of Partially Identified Parameters (2016)
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text
Persistent link: https://EconPapers.repec.org/RePEc:ifs:cemmap:49/17
Ordering information: This working paper can be ordered from
The Institute for Fiscal Studies 7 Ridgmount Street LONDON WC1E 7AE
mailbox@ifs.org.uk
Access Statistics for this paper
More papers in CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies The Institute for Fiscal Studies 7 Ridgmount Street LONDON WC1E 7AE. Contact information at EDIRC.
Bibliographic data for series maintained by Emma Hyman (emma_h@ifs.org.uk).