Nonparametric instrumental variables estimation of a quantile regression model

Joel L. Horowitz*, Sokbae Lee

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

62 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1191-1208
Number of pages18
Issue number4
StatePublished - Jul 2007


  • Endogenous variable
  • Instrumental variable
  • Nonlinear integral equation
  • Nonparametric regression
  • Optimal rate
  • Statistical inverse

ASJC Scopus subject areas

  • Economics and Econometrics


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