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 these treatment effects is not achievable without strong assumptions, we obtain bounds on these 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. We provide conditions under which differential treatment effects can be used to point identify or partially identify treatment effects. Under these conditions, 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. The proposed method is examined through a simulation study and two case studies that investigate the effect of smoking on the blood level of lead and cadmium using the National Health and Nutrition Examination Survey, and the effect of soft drink consumption on the occurrence of physical fights in teenagers using the Youth Risk Behavior Surveillance System.

翻译：我们考虑了在存在未测量混杂因素时，平均治疗效应和基于可观测协变量的异质性治疗效应的识别与推断问题。由于缺乏强假设无法实现这些治疗效应的点识别，我们通过利用差异效应（一种允许使用第二种治疗来学习第一种治疗效果的工具）来获得这些治疗效应的界。差异效应是指使用一种治疗替代另一种治疗所产生的效应。我们给出了差异治疗效应可用于点识别或部分识别治疗效应的条件。在这些条件下，我们开发了一个灵活且易于实施的半参数框架来估计这些界，并建立了在支持集上进行统计推断的渐近性质。通过一项模拟研究和两项案例研究对所提方法进行了检验：其一利用国家健康与营养调查数据研究了吸烟对血液中铅和镉水平的影响；其二利用青少年风险行为监测系统研究了软饮料消费对青少年斗殴事件发生的影响。