Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions

Chunrong Ai and Xiaohong Chen ()

Econometrica, 2003, vol. 71, issue 6, 1795-1843

Abstract: We propose an estimation method for models of conditional moment restrictions, which contain finite dimensional unknown parameters (theta) and infinite dimensional unknown functions (h). Our proposal is to approximate h with a sieve and to estimate theta and the sieve parameters jointly by applying the method of minimum distance. We show that: (i) the sieve estimator of h is consistent with a rate faster than n-super--1/4 under certain metric; (ii) the estimator of theta is root-n consistent and asymptotically normally distributed; (iii) the estimator for the asymptotic covariance of the theta estimator is consistent and easy to compute; and (iv) the optimally weighted minimum distance estimator of theta attains the semiparametric efficiency bound. We illustrate our results with two examples: a partially linear regression with an endogenous nonparametric part, and a partially additive IV regression with a link function. Copyright The Econometric Society 2003.

Date: 2003
References: Add references at CitEc
Citations: View citations in EconPapers (442)

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
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:ecm:emetrp:v:71:y:2003:i:6:p:1795-1843

Ordering information: This journal article can be ordered from
https://www.economet ... ordering-back-issues

Access Statistics for this article

Econometrica is currently edited by Guido Imbens

More articles in Econometrica from Econometric Society Contact information at EDIRC.
Bibliographic data for series maintained by Wiley Content Delivery ().