We consider identification and inference for the average treatment effect and heterogeneous treatment effect conditional on observable covariates in the presence of unmeasured confounding. Since point identification of average treatment effect and heterogeneous treatment effect is not achievable without strong assumptions, we obtain bounds on both average and heterogeneous treatment effects by leveraging differential effects, a tool that allows for using a second treatment to learn the effect of the first treatment. The differential effect is the effect of using one treatment in lieu of the other, and it could be identified in some observational studies in which treatments are not randomly assigned to units, where differences in outcomes may be due to biased assignments rather than treatment effects. With differential effects, we develop a flexible and easy-to-implement semi-parametric framework to estimate bounds and establish asymptotic properties over the support for conducting statistical inference. We provide conditions under which causal estimands are point identifiable as well in the proposed framework. The proposed method is examined by a simulation study and two case studies using datasets from National Health and Nutrition Examination Survey and Youth Risk Behavior Surveillance System.

翻译：我们考虑在存在未测量混杂因素的情况下，对平均治疗效应和以可观测协变量为条件的异质性治疗效应进行识别和推断。由于在缺乏强假设时无法实现平均治疗效应和异质性治疗效应的点识别，我们通过利用差分效应（一种允许使用第二种治疗来学习第一种治疗效应的工具）来获取平均和异质性治疗效应的界限。差分效应是指使用一种治疗替代另一种治疗的效应，它可以在某些治疗并非随机分配给个体的观测性研究中得到识别（在这些研究中，结果差异可能源于有偏的分配而非治疗效应）。基于差分效应，我们开发了一个灵活且易于实现的半参数框架来估计界限，并在进行统计推断时建立了支撑集上的渐近性质。我们在所提出的框架下提供了因果估计量可被点识别的条件。通过一项模拟研究以及使用来自国家健康与营养检查调查和青少年风险行为监测系统的数据集的两个案例研究，对所提出的方法进行了检验。