Econometrica Vol. 75 No. 4 2007
Nonparametric Instrumental Variables Estimation of a Quantile Regression Model
Abstract
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.
- DOI
- 10.1111/j.1468-0262.2007.00786.x
- Volume
- 75
- Issue
- 4
- Pages
- 1191-1208
- Language
- en
- Sources
- bibtex:phds-export.bib openalex crossref