Efficient estimation of models with conditional moment restrictions containing unknown functions

• 成果类型: Article
• 署名作者: Ai, CR; Chen, XH
• 署名单位: State University System of Florida; University of Florida; New York University
• 刊物名称: ECONOMETRICA
• ISSN/ISSBN: 0012-9682
• DOI: 10.1111/1468-0262.00470
• 发表日期: 2003
• 页码: 1795-1843
• 关键词: Asymptotic Normality; generalized-method; convergence-rates; sample properties; likelihood; bounds

摘要

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(-1/4) under certain metric; (ii) the estimator of theta is rootn 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 0 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.