Constrained conditional moment restriction models

Victor Chernozhukov, Whitney K. Newey and Andres Santos

No 59/15, CeMMAP working papers from Institute for Fiscal Studies

Abstract: This paper examines a general class of inferential problems in semiparametric and nonparametric models defined by conditional moment restrictions. We construct tests for the hypothesis that at least one element of the identified set satisfies a conjectured (Banach space) “equality” and/or (a Banach lattice) “inequality” constraint. Our procedure is applicable to identified and partially identified models, and is shown to control the level, and under some conditions the size, asymptotically uniformly in an appropriate class of distributions. The critical values are obtained by building a strong approximation to the statistic and then bootstrapping a (conservatively) relaxed form of the statistic. Sufficient conditions are provided, including strong approximations using Koltchinskii's coupling.Leading important special cases encompassed by the framework we study include: (i) Tests of shape restrictions for infinite dimensional parameters; (ii) Confidence regions for functionals that impose shape restrictions on the underlying parameter; (iii) Inference for functionals in semiparametric and nonparametric models defined by conditional moment (in)equalities; and (iv) Uniform inference in possibly nonlinear and severely ill-posed problems.

Date: 2015-09-22
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Citations: View citations in EconPapers (5)

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Related works:
Journal Article: Constrained Conditional Moment Restriction Models (2023)
Working Paper: Constrained conditional moment restriction models (2015)
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Persistent link: https://EconPapers.repec.org/RePEc:azt:cemmap:59/15

DOI: 10.1920/wp.cem.2015.5915

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