Nonparametric instrumental variables estimation of a quantile regression model

• 成果类型: Article
• 署名作者: Horowitz, Joel L.; Lee, Sokbae
• 署名单位: Northwestern University; University of London; University College London
• 刊物名称: ECONOMETRICA
• ISSN/ISSBN: 0012-9682
• DOI: 10.1111/j.1468-0262.2007.00786.x
• 发表日期: 2007
• 页码: 1191-1208
• 关键词: ABSOLUTE DEVIATIONS ESTIMATORS; STRUCTURAL EQUATION MODELS; nonseparable models; regularization; CONVERGENCE; inference

摘要

We consider nonparametric estimation of a regression function that is identified by requiring a specified quantile of the regression error conditional on an instrumental variable to be zero. The resulting estimating equation is a nonlinear integral equation of the first kind, which generates an ill-posed inverse problem. The integral operator and distribution of the instrumental variable are unknown and must be estimated nonparametrically. We show that the estimator is mean-square consistent, derive its rate of convergence in probability, and give conditions under which this rate is optimal in a minimax sense. The results of Monte Carlo experiments show that the estimator behaves well in finite samples.