Sieve Quasi Likelihood Ratio Inference on Semi/Nonparametric Conditional Moment Models

Posted: 30 May 2013

See all articles by Xiaohong Chen

Xiaohong Chen

Yale University - Cowles Foundation

Demian Pouzo

University of California, Berkeley - Department of Economics

Date Written: May 29, 2013

Abstract

This paper considers inference on functionals of semi/nonparametric conditional moment restrictions with possibly nonsmooth generalized residuals. These models belong to the difficult (nonlinear) ill-posed inverse problems with unknown operators, and include all of the (nonlinear) nonparametric instrumental variables (IV) as special cases. For these models it is generally difficult to verify whether a functional is regular (i.e., root-n estimable) or irregular (i.e., slower than root-n estimable). In this paper we provide computationally simple, unified inference procedures that are asymptotically valid regardless of whether a functional is regular or irregular. We establish the following new results: (1) the asymptotic normality of the plug-in penalized sieve minimum distance (PSMD) estimators of the (possibly irregular) functionals; (2) the consistency of sieve variance estimators of the plug-in PSMD estimators; (3) the asymptotic chi-square distribution of an optimally weighted sieve quasi likelihood ratio (SQLR) statistic; (4) the asymptotic tight distribution of a possibly non-optimally weighted SQLR statistic; (5) the consistency of the nonparametric bootstrap and the weighted bootstrap (possibly non-optimally weighted) SQLR and sieve Wald statistics, which are proved under virtually the same conditions as those for the original-sample statistics. Small simulation studies and an empirical illustration of a nonparametric quantile IV regression are presented.

Keywords: Nonlinear nonparametric instrumental variables, Penalized sieve minimum distance, Irregular functional, Sieve Riesz representer, Sieve quasi likelihood ratio, Asymptotic normality, Bootstrap, Sieve variance estimator

Suggested Citation

Chen, Xiaohong and Pouzo, Demian, Sieve Quasi Likelihood Ratio Inference on Semi/Nonparametric Conditional Moment Models (May 29, 2013). Cowles Foundation Discussion Paper No. 1897, Available at SSRN: https://ssrn.com/abstract=2271617 or http://dx.doi.org/10.2139/ssrn.2271617

Xiaohong Chen (Contact Author)

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States

Demian Pouzo

University of California, Berkeley - Department of Economics ( email )

549 Evans Hall #3880
Berkeley, CA 94720-3880
United States

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