Local identification of nonparametric and semiparametric models

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.

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Nonparametric Euler equation identification and estimation

Escanciano¹,

Hoderlein²,

Lewbel³

et al. 2015

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We consider nonparametric identi…cation and estimation of pricing kernels, or equivalently of marginal utility functions up to scale, in consumption based asset pricing Euler equations.Ours is the …rst paper to prove nonparametric identi…cation of Euler equations under low level conditions (without imposing functional restrictions or just assuming completeness). We also propose a novel nonparametric estimator based on our identi…cation analysis, which combines standard kernel estimation with the computation of a matrix eigenvector problem. Our estimator avoids the ill-posed inverse issues associated with existing nonparametric instrumental variables based Euler equation estimators. We derive limiting distributions for our estimator and for relevant associated functionals. We provide a Monte Carlo analysis and an empirical application to US household-level consumption data.

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Local identification of nonparametric and semiparametric models

Cited by 8 publications

References 38 publications

Convergence of the risk for nonparametric IV quantile regression and nonparametric IV regression with full independence

Convergence of the risk for nonparametric IV quantile regression and nonparametric IV regression with full independence

Constrained conditional moment restriction models

Nonparametric Euler equation identification and estimation

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