Understanding the causal effect of a treatment in randomized experiments with noncompliance is of fundamental interest in many domains. Within the instrumental variable (IV) framework, the causal treatment effect can only be reliably assessed for compliers, as they are the only subpopulation whose treatment assignment is influenced by the instrument. In this article, we study the conditional complier quantile treatment effect based on individual characteristics through stratified quantile regression models for compliers with and without treatment, which are flexible in capturing the interaction between treatment and covariates and include the past unified model as a special case. We introduce a tuning parameter-free method that directly utilizes the mixture structure in the compiler problem, departing from past approaches that relied on minimizing a weighted check function with nonparametric method-estimated weights. A novel iterated algorithm is proposed to solve discontinuous equations that involve unknown parameters in a complicated way. The consistency and asymptotic normality of the proposed estimators are established. Numerical results, including extensive simulation studies and real data analysis of the Oregon health insurance experiment and a job training study, show the practical utility of the proposed approach.
Ma et al. (Sun,) studied this question.