Nonparametric instrumental variables estimation of a quantile regression model
Joel L. Horowitz () and
Sokbae (Simon) Lee ()
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Joel L. Horowitz: Institute for Fiscal Studies and Northwestern University
No CWP09/06, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies
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.
Keywords: Statistical inverse; endogenous variable; instrumental variable; optimal rate; nonlinear integral equation; nonparametric regression (search for similar items in EconPapers)
JEL-codes: C13 C31 (search for similar items in EconPapers)
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Journal Article: Nonparametric Instrumental Variables Estimation of a Quantile Regression Model (2007)
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Persistent link: https://EconPapers.repec.org/RePEc:ifs:cemmap:09/06
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