English, Article, Journal or magazine article edition: Efficient Estimation of Semiparametric Conditional Moment Models with Possibly Nonsmooth Residuals Xiaohong Chen; Demian Pouzo

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  • preprint
Language
  • English

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Title
  • Efficient Estimation of Semiparametric Conditional Moment Models with Possibly Nonsmooth Residuals
Author
  • Xiaohong Chen
  • Demian Pouzo
Physical Description
  • preprint
Notes
  • For semi/​nonparametric conditional moment models containing unknown parametric components θ and unknown functions of endogenous variables (h), Newey and Powell (2003) and Ai and Chen (2003) propose sieve minimum distance (SMD) estimation of (θ, h) and derive the large sample properties. This paper greatly extends their results by establishing the followings: (1) The penalized SMD (PSMD) estimator can simultaneously achieve root-n asymptotic normality of the parametric components and nonparametric optimal convergence rate of the nonparametric components, allowing for models with possibly nonsmooth residuals and/​or noncompact infinite dimensional parameter spaces. (2) A simple weighted bootstrap procedure can consistently estimate the limiting distribution of the PSMD estimator of the parametric components. (3) The semiparametric efficiency bound results of Ai and Chen (2003) remain valid for conditional models with nonsmooth residuals, and the optimally weighted PSMD estimator achieves the bounds. (4) The profiled optimally weighted PSMD criterion is asymptotically Chi-square distributed, which implies an alternative consistent estimation of confidence region of the efficient PSMD estimator of θ. All the theoretical results are stated in terms of any consistent nonparametric estimator of conditional mean functions. We illustrate our general theories using a partially linear quantile instrumental variables regression, a Monte Carlo study, and an empirical estimation of the shape-invariant quantile Engel curves with endogenous total expenditure.<
  • RePEc:ifs:cemmap:09/​08
  • For semi/​nonparametric conditional moment models containing unknown parametric components (theta) and unknown functions of endogenous variables (h), Newey and Powell (2003) and Ai and Chen (2003) propose sieve minimum distance (SMD) estimation of (theta, h) and derive the large sample prop­erties. This paper greatly extends their results by establishing the followings: (1) The penalized SMD (PSMD) estimator (hat{theta}, hat{h}) can simultaneously achieve root-n asymptotic normality of theta hat and nonpara­metric optimal convergence rate of hat{h}, allowing for models with possibly nonsmooth residuals and/​or noncompact infinite dimensional parameter spaces. (2) A simple weighted bootstrap procedure can con­sistently estimate the limiting distribution of the PSMD hat{theta}. (3) The semiparametric efficiency bound results of Ai and Chen (2003) remain valid for conditional models with nonsmooth residuals, and the optimally weighted PSMD estimator achieves the bounds. (4) The profiled optimally weighted PSMD criterion is asymptotically Chi-square distributed, which implies an alternative consistent estimation of confidence region of the efficient PSMD estimator of theta. All the theoretical results are stated in terms of any consistent nonparametric estimator of conditional mean functions. We illustrate our general theories using a partially linear quantile instrumental variables regression, a Monte Carlo study, and an empirical estimation of the shape-invariant quantile Engel curves with endogenous total expenditure.
  • Penalized sieve minimum distance, Nonsmooth generalized residuals, Nonparametric en­dogeneity, Weighted bootstrap, Semiparametric efficiency, Confidence region, Partially linear quantile IV regression
  • 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.
  • 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
  • RePEc:cwl:cwldpp:1640r
Language
  • English
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