Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/211092 
Year of Publication: 
2018
Series/Report no.: 
cemmap working paper No. CWP72/18
Publisher: 
Centre for Microdata Methods and Practice (cemmap), London
Abstract: 
The instrumental variable quantile regression (IVQR) model of Chernozhukov and Hansen (2005, 2006) is a flexible and powerful tool for evaluating the impact of endogenous covariates on the whole distribution of the outcome of interest. Estimation, however, is computationally burdensome because the GMM objective function is non-smooth and non-convex. This paper shows that the IVQR estimation problem can be decomposed into a set of conventional quantile regression sub-problems, which are convex and can be solved efficiently. This allows for reformulating the original estimation problem as the problem of finding the fixed point of a low dimensional map. This reformulation leads to new identification results and, most importantly, to practical, easy to implement, and computationally tractable estimators. We explore estimation algorithms based on the contraction mapping theorem and algorithms based on root-finding methods. We prove consistency and asymptotic normality of our estimators and establish the validity of a bootstrap procedure for estimating the limiting laws. Monte Carlo simulations support the estimator's enhanced computational tractability and demonstrate desirable finite sample properties.
Subjects: 
instrumental variables
quantile regression
contraction mapping
fixed point estimator
bootstrap
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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