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

Xiaohong Chen () and Demian Pouzo
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Demian Pouzo: Dept. of Economics, University of California, Berkeley

No 1897, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

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 (search for similar items in EconPapers)
Pages: 43 pages
Date: 2013-05
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (10)

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