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：我们考虑在存在未测到的混淆因素的情况下，针对可观测协变量的平均处理效应和异质处理效应的识别和推断。由于在没有强假设的情况下无法点识别这些处理效应，因此我们通过利用差分效应来获得这些处理效应的上下界，差分效应是使用第二种处理来学习第一种处理效应的工具。我们提供了可以使用差分处理效应来点识别或部分识别处理效应的条件。在这些条件下，我们开发了一种灵活且易于实现的半参数框架来估计上下界并确定用于进行统计推断的支持的渐近特性。所提出的方法通过使用美国国民健康和营养调查研究的吸烟对铅和镉血液水平的影响以及使用青少年风险行为监测系统研究软饮料摄入对身体战斗发生率的影响的两个案例研究进行了检验。