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Efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals

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Author Info
Chen, Xiaohong
Pouzo, Demian
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 can simultaneously achieve root-n asymptotic normality of and nonparametric optimal convergence rate of , allowing for noncompact function parameter spaces; (2) a simple weighted bootstrap procedure consistently estimates the limiting distribution of the PSMD ; (3) the semiparametric efficiency bound formula of [Ai, C., Chen, X., 2003. Efficient estimation of models with conditional moment restrictions containing unknown functions. Econometrica, 71, 1795-1843] 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.

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Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 152 (2009)
Issue (Month): 1 (September)
Pages: 46-60
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Handle: RePEc:eee:econom:v:152:y:2009:i:1:p:46-60

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Related research
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;

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  1. Chunrong Ai & Xiaohong Chen, 2009. "Semiparametric Efficiency Bound for Models of Sequential Moment Restrictions Containing Unknown Functions," Cowles Foundation Discussion Papers 1731, Cowles Foundation, Yale University. [Downloadable!]
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