Estimating the causal effect of a treatment or exposure for a subpopulation is of great interest in many biomedical and economical studies. Expected shortfall, also referred to as the super-quantile, is an attractive effect-size measure that can accommodate data heterogeneity and aggregate local information of effect over a certain region of interest of the outcome distribution. In this article, we propose the ComplieR Expected Shortfall Treatment Effect (CRESTE) model under an instrumental variable framework to quantity the CRESTE for a binary endogenous treatment variable. By utilizing the special characteristics of a binary instrumental variable and a specific formulation of Neyman-orthogonalization, we propose a two-step estimation procedure, which can be implemented by simply solving weighted least-squares regression and weighted quantile regression with estimated weights. We develop the asymptotic properties for the proposed estimator and use numerical simulations to confirm its validity and robust finite-sample performance. An illustrative analysis of a National Job Training Partnership Act study is presented to show the practical utility of the proposed method.

翻译：在许多生物医学和经济学研究中，估计治疗或暴露对某一子总体的因果效应具有重要意义。期望损失（亦称超分位数）作为一种效应量指标，既能适应数据异质性，又可聚合结果分布在特定感兴趣区域的局部信息。本文在工具变量框架下提出依从者期望损失处理效应（CRESTE）模型，用以量化二元内生治疗变量的CRESTE。通过利用二元工具变量的特殊性质及尼曼正交化的特定形式，我们提出了一种两步估计程序，该程序可通过求解带估计权重的加权最小二乘回归和加权分位数回归实现。我们发展了所提估计量的渐近性质，并通过数值模拟验证其有效性与稳健的有限样本表现。最后，通过对一项国家就业培训伙伴关系法案研究的实例分析，展示了所提方法的实际应用价值。