Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/79400
Authors: 
Horowitz, Joel
Lee, Sokbae
Year of Publication: 
2006
Series/Report no.: 
cemmap working paper, Centre for Microdata Methods and Practice CWP09/06
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.
Subjects: 
Statistical inverse , endogenous variable , instrumental variable , optimal rate , nonlinear integral equation , nonparametric regression
JEL: 
C13
C31
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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