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 covariateson 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 .
The instrumental variable quantile regression (IVQR) model ( Chernozhukov and Hansen , 2005 ) is a popular tool for estimating causal quantile effects with endogenous covariates. However, estimation is complicated by the non-smoothness and non-convexity of the IVQR GMM objective function . 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 reformulation leads to new identification results and to fast , easy to implement, and tuning-free estimators that do not require the availability of high-level black box optimization routines .
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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
tuning-free estimators that do not require the availability of high-level black box optimization routines