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Nonparametric instrumental variables estimation of a quantile regression model

Horowitz, J.; Lee, S.; (2006) Nonparametric instrumental variables estimation of a quantile regression model. (cemmap Working Papers CWP09/). Institute for Fiscal Studies: London, UK. Green open access

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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.

Type: Working / discussion paper
Title: Nonparametric instrumental variables estimation of a quantile regression model
Open access status: An open access version is available from UCL Discovery
Publisher version: http://www.cemmap.ac.uk/publications.php
Language: English
Additional information: Please see http://eprints.ucl.ac.uk/12659/ for a version published in Econometrica
Keywords: JEL classification: C13, C31
UCL classification: UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of SandHS > Dept of Economics
URI: https://discovery.ucl.ac.uk/id/eprint/14679
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