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Sieve Wald and QLR Inferences on Semi/nonparametric Conditional Moment Models

Xiaohong Chen () and Demian Pouzo

Papers from arXiv.org

Abstract: This paper considers inference on functionals of semi/nonparametric conditional moment restrictions with possibly nonsmooth generalized residuals, which include all of the (nonlinear) nonparametric instrumental variables (IV) as special cases. These models are often ill-posed and hence it is difficult to verify whether a (possibly nonlinear) functional is root-$n$ estimable or not. We provide computationally simple, unified inference procedures that are asymptotically valid regardless of whether a functional is root-$n$ estimable or not. We establish the following new useful results: (1) the asymptotic normality of a plug-in penalized sieve minimum distance (PSMD) estimator of a (possibly nonlinear) functional; (2) the consistency of simple sieve variance estimators for the plug-in PSMD estimator, and hence the asymptotic chi-square distribution of the sieve Wald statistic; (3) the asymptotic chi-square distribution of an optimally weighted sieve quasi likelihood ratio (QLR) test under the null hypothesis; (4) the asymptotic tight distribution of a non-optimally weighted sieve QLR statistic under the null; (5) the consistency of generalized residual bootstrap sieve Wald and QLR tests; (6) local power properties of sieve Wald and QLR tests and of their bootstrap versions; (7) asymptotic properties of sieve Wald and SQLR for functionals of increasing dimension. Simulation studies and an empirical illustration of a nonparametric quantile IV regression are presented.

Date: 2014-11, Revised 2015-03
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http://arxiv.org/pdf/1411.1144 Latest version (application/pdf)

Related works:
Journal Article: Sieve Wald and QLR Inferences on Semi/Nonparametric Conditional Moment Models (2015) Downloads
Working Paper: Sieve Wald and QLR Inferences on Semi/nonparametric Conditional Moment Models (2014) Downloads
Working Paper: Sieve Wald and QLR Inferences on Semi/nonparametric Conditional Moment Models (2014) Downloads
Working Paper: Sieve Wald and QLR Inferences on Semi/nonparametric Conditional Moment Models (2014) Downloads
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