Decentralization estimators for instrumental variable quantile regression models - Hiroaki Kaido; Kaspar Wüthrich (Centre for Microdata Methods and Practice (cemmap), 2019)
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.
Keywords: C21; C26; 330; instrumental variables; quantile regression; contraction mapping; fixed pointestimator; bootstrap