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Type: cemmap Working Papers Authors: Joel Horowitz and Sokbae 'Simon' Lee ISSN: 1753-9196
Volume, issue, pages: 34 pp.
JEL classification: C13, C31 Keywords: Statistical inverse, endogenous variable, instrumental variable, optimal rate, nonlinear integral equation, nonparametric regression
Now published in: Econometrica [Details]
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. Search |
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