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Nonparametric instrumental variables estimation of a quantile regression model

Authors: Joel L. Horowitz and Sokbae Lee
Date: 01 July 2007
Type: Journal Article, Econometrica, Vol. 75, No. 4, pp. 1191-1208

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.

Previous version:
Joel L. Horowitz and Sokbae Lee June 2006, Nonparametric instrumental variables estimation of a quantile regression model, cemmap Working Paper, CWP09/06

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