Efficient Estimation of Semiparametric Conditional Moment Models with Possibly Nonsmooth Residuals

34 Pages Posted: 31 Oct 2008 Last revised: 16 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 16, 2009

Abstract

This paper considers semiparametric efficient estimation of conditional moment models with possibly nonsmooth residuals in unknown parametric components (theta) and unknown functions (h) of endogenous variables. We show that: (1) the penalized sieve minimum distance (PSMD) estimator (theta\hat,h\hat) can simultaneously achieve root-n asymptotic normality of theta\hat and nonparametric optimal convergence rate of h\hat, allowing for noncompact function parameter spaces; (2) a simple weighted bootstrap procedure consistently estimates the limiting distribution of the PSMD theta\hat; (3) the semiparametric efficiency bound formula of Ai and Chen (2003) remains valid for conditional models with nonsmooth residuals, and the optimally weighted PSMD estimator achieves the bound; (4) the centered, profiled optimally weighted PSMD criterion is asymptotically chi-square distributed. We illustrate our theories using a partially linear quantile instrumental variables (IV) regression, a Monte Carlo study, and an empirical estimation of the shape-invariant quantile IV Engel curves.

Keywords: Penalized sieve minimum distance, Nonsmooth generalized residuals, Nonlinear nonparametric endogeneity, Weighted bootstrap, Semiparametric efficiency, Confidence region, Partially linear quantile IV regression, Shape-invariant quantile IV Engel curves

JEL Classification: C14, C22

Suggested Citation

Chen, Xiaohong and Pouzo, Demian, Efficient Estimation of Semiparametric Conditional Moment Models with Possibly Nonsmooth Residuals (July 16, 2009). Cowles Foundation Discussion Paper No. 1640R, Available at SSRN: https://ssrn.com/abstract=1267230

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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