Estimation of nonparametric conditional moment models with possibly nonsmooth moments

Xiaohong Chen () and Demian Pouzo
Additional contact information
Demian Pouzo: Institute for Fiscal Studies

No CWP12/08, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

Abstract:

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.

JEL-codes: C13 C14 D12 (search for similar items in EconPapers)
Date: 2008-04-25
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (16)

Downloads: (external link)
http://cemmap.ifs.org.uk/wps/cwp1208.pdf (application/pdf)

Related works:
Working Paper: Estimation of Nonparametric Conditional Moment Models with Possibly Nonsmooth Moments (2008)
Working Paper: Estimation of Nonparametric Conditional Moment Models with Possibly Nonsmooth Moments (2008)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ifs:cemmap:12/08

Ordering information: This working paper can be ordered from
The Institute for Fiscal Studies 7 Ridgmount Street LONDON WC1E 7AE

Access Statistics for this paper

More papers in CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies The Institute for Fiscal Studies 7 Ridgmount Street LONDON WC1E 7AE. Contact information at EDIRC.
Bibliographic data for series maintained by Emma Hyman ().