Nonparametric Instrumental Variables Estimation of a Quantile Regression Model

Joel L. Horowitz and Sokbae (Simon) Lee

Econometrica, 2007, vol. 75, issue 4, 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. Copyright The Econometric Society 2007.

Date: 2007
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Working Paper: Nonparametric instrumental variables estimation of a quantile regression model (2006)
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