In this article, we review quantile models with endogeneity. We focus on models that achieve identification through the use of instrumental variables and discuss conditions under which partial and point identification are obtained. We discuss key conditions, which include monotonicity and full-rank-type conditions, in detail. In providing this review, we update the identification results of Chernozhukov and Hansen (2005). We illustrate the modelling assumptions through economically motivated examples. We also briefly review the literature on estimation and inference.
Centre for microdata methods and practice