Estimation of Nonparametric Conditional Moment Models with Possibly Nonsmooth Generalized Residuals

51 Pages Posted: 17 Jul 2009

See all articles by Xiaohong Chen

Xiaohong Chen

Yale University - Cowles Foundation

Demian Pouzo

University of California, Berkeley - Department of Economics

Multiple version iconThere are 2 versions of this paper

Date Written: July 17, 2009

Abstract

This paper studies nonparametric estimation of conditional moment models in which the generalized residual functions can be nonsmooth in the unknown functions of endogenous variables. This is a nonparametric nonlinear instrumental variables (IV) problem. We propose a class of penalized sieve minimum distance (PSMD) estimators which are minimizers of a penalized empirical minimum distance criterion over a collection of sieve spaces that are dense in the infinite dimensional function parameter space. Some of the PSMD procedures use slowly growing finite dimensional sieves with flexible penalties or without any penalty; some use large dimensional sieves with lower semicompact and/or convex penalties. We establish their consistency and the convergence rates in Banach space norms (such as a sup-norm or a root mean squared norm), allowing for possibly non-compact infinite dimensional parameter spaces. For both mildly and severely ill-posed nonlinear inverse problems, our convergence rates in Hilbert space norms (such as a root mean squared norm) achieve the known minimax optimal rate for the nonparametric mean IV regression. We illustrate the theory with a nonparametric additive quantile IV regression. We present a simulation study and an empirical application of estimating nonparametric quantile IV Engel curves.

Keywords: Nonlinear ill-posed inverse, Penalized sieve minimum distance, Modulus of continuity, Convergence rate, Nonparametric additive quantile IV, Quantile IV Engel curves

JEL Classification: C13, C14, D12

Suggested Citation

Chen, Xiaohong and Pouzo, Demian, Estimation of Nonparametric Conditional Moment Models with Possibly Nonsmooth Generalized Residuals (July 17, 2009). Cowles Foundation Discussion Paper No. 1650R, Yale Economics Department Working Paper No. 47R, Available at SSRN: https://ssrn.com/abstract=1435496 or http://dx.doi.org/10.2139/ssrn.1435496

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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