Econometrica: Jul 2007, Volume 75, Issue 4

Nonparametric Instrumental Variables Estimation of a Quantile Regression Model
p. 1191-1208

Joel L. Horowitz, Sokbae Lee

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.

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Supplemental Material

Supplement to ?Nonparametric Instrumental Variables Estimation of a Quantile Regression Model?

This appendix provides proofs of Theorems 1-3. Theorems 4-5 can be proved by following the same steps after conditioning on Z .

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