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Efficient Estimation of Semiparametric Conditional Moment Models with Possibly Nonsmooth Residuals

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

No 1640R, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

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 (search for similar items in EconPapers)
JEL-codes: C14 C22 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm
Date: 2008-02, Revised 2009-07
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Published in Journal of Econometrics (September 2009), 152: 46-60

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Related works:
Journal Article: Efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals (2009) Downloads
Working Paper: Efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals (2009) Downloads
Working Paper: Efficient Estimation of Semiparametric Conditional Moment Models with Possibly Nonsmooth Residuals (2008) Downloads
Working Paper: Efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals (2008) Downloads
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