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Confi dence Intervals for Projections of Partially Identi fied Parameters

Author

Listed:
  • Hiroaki Kaido

    (Boston University)

  • Francesca Molinari

    (Cornell University)

  • Jorg Stoye

    (Cornell University)

Abstract
This paper proposes a bootstrap-based procedure to build con dence intervals for single components of a partially identi ed parameter vector, and for smooth functions of such components, in moment (in)equality models. The extreme points of our con dence 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, instead of itself, is uniformly asymptotically cov- ered with prespeci ed probability. Calibration of the critical level is based on repeatedly checking feasibility of linear programming problems, rendering it computationally attrac- tive. Computation of the extreme points of the con dence 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 nite sample) than the one used if projecting con dence regions designed to cover the entire parameter vector. Hence, our con dence interval is weakly shorter than the projection of established con dence 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 pro ling 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 pro ling based methods are not.

Suggested Citation

  • Hiroaki Kaido & Francesca Molinari & Jorg Stoye, 2016. "Confi dence Intervals for Projections of Partially Identi fied Parameters," Boston University - Department of Economics - Working Papers Series wp2016-001, Boston University - Department of Economics.
    • Handle: RePEc:bos:wpaper:wp2016-001
    as

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    File URL: http://people.bu.edu/hkaido/pdf/Projection.pdf
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Partial identi cation; Inference on projections; Moment inequalities; Uniform inference;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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