Estimation of Nonparametric Conditional Moment Models with Possibly Nonsmooth Moments

Xiaohong Chen () and Demian Pouzo
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Demian Pouzo: Dept. of Economics, New York University

No 1650, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: This paper studies nonparametric estimation of conditional moment models in which the residual functions could be nonsmooth with respect to the unknown functions of endogenous variables. It is a problem of nonparametric nonlinear instrumental variables (IV) estimation, and a difficult nonlinear ill-posed inverse problem with an unknown operator. We first propose a penalized sieve minimum distance (SMD) estimator of the unknown functions that are iden­tified via the conditional moment models. We then establish its consistency and convergence rate (in strong metric), allowing for possibly non-compact function parameter spaces, possibly non-compact finite or infinite dimensional sieves with flexible lower semicompact or convex penalty, or finite dimensional linear sieves without penalty. Under relatively low-level sufficient conditions, and for both mildly and severely ill-posed problems, we show that the convergence rates for the nonlinear ill-posed inverse problems coincide with the known minimax optimal rates for the nonparametric mean IV regression. We illustrate the theory by two important ap­plications: root-n asymptotic normality of the plug-in penalized SMD estimator of a weighted average derivative of a nonparametric nonlinear IV regression, and the convergence rate of a nonparametric additive quantile IV regression. We also present a simulation study and an empirical estimation of a system of nonparametric quantile IV Engel curves.

Keywords: Nonsmooth residuals; Nonlinear ill-posed inverse; Penalized sieve minimum distance; Modulus of continuity; Average derivative of a nonparametric nonlinear IV regression; Non-parametric additive quantile IV regression (search for similar items in EconPapers)
JEL-codes: C13 C14 D12 (search for similar items in EconPapers)
Pages: 60 pages
Date: 2008-04, Revised 2008-10
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (13)

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Related works:
Working Paper: Estimation of Nonparametric Conditional Moment Models with Possibly Nonsmooth Moments (2008)
Working Paper: Estimation of nonparametric conditional moment models with possibly nonsmooth moments (2008)
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