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Decentralization estimators for instrumental variable quantile regression models

Hiroaki Kaido () and Kaspar Wüthrich ()

No CWP72/18, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

Abstract: The instrumental variable quantile regression (IVQR) model of Chernozhukov and Hansen (2005, 2006) is a exible 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 identi fication 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-fi nding 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.

Keywords: instrumental variables; quantile regression; contraction mapping; fixed point estimator; bootstrap. (search for similar items in EconPapers)
Date: 2018-12-31
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Working Paper: Decentralization Estimators for Instrumental Variable Quantile Regression Models (2019) Downloads
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