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

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Bookmark: http://trove.nla.gov.au/version/157832
Physical Description
  • preprint
Language
  • English

Edition details

Title
  • Estimation of nonparametric conditional moment models with possibly nonsmooth moments
Author
  • Xiaohong Chen
  • Demian Pouzo
Physical Description
  • preprint
Notes
  • This paper studies nonparametric estimation of conditional moment models in which the residual functions could be nonsmooth with respect to the unknown functions of endogenous variables. It is a problem of nonparametric nonlinear instrumental variables (IV) estimation, and a difficult nonlinear ill-posed inverse problem with an unknown operator. We first propose a penalized sieve minimum distance (SMD) estimator of the unknown functions that are iden­tified via the conditional moment models. We then establish its consistency and convergence rate (in strong metric), allowing for possibly non-compact function parameter spaces, possibly non-compact finite or infinite dimensional sieves with flexible lower semicompact or convex penalty, or finite dimensional linear sieves without penalty. Under relatively low-level sufficient conditions, and for both mildly and severely ill-posed problems, we show that the convergence rates for the nonlinear ill-posed inverse problems coincide with the known minimax optimal rates for the nonparametric mean IV regression. We illustrate the theory by two important ap­plications: root-n asymptotic normality of the plug-in penalized SMD estimator of a weighted average derivative of a nonparametric nonlinear IV regression, and the convergence rate of a nonparametric additive quantile IV regression. We also present a simulation study and an empirical estimation of a system of nonparametric quantile IV Engel curves.
  • Nonsmooth residuals, Nonlinear ill-posed inverse, Penalized sieve minimum distance, Modulus of continuity, Average derivative of a nonparametric nonlinear IV regression, Non-parametric additive quantile IV regression
  • RePEc:cwl:cwldpp:1650
  • RePEc:ifs:cemmap:12/​08
Language
  • English
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