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Chernozhukov, Victor
Newey, Whitney
Santos, Andres
Year of Publication: 
Series/Report no.: 
cemmap working paper, Centre for Microdata Methods and Practice CWP59/15
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.
Shape restrictions
inference on functionals
conditional moment (in)equality restrictions
instrumental variables
nonparametric and semiparametric models
Banach space
Banach lattice
Koltchinskii coupling
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Working Paper

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