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 leverage a two-stage approach to conduct statistical inference on effects of interest. The proposed method is examined through a simulation study and a case study that investigates the effect of smoking on the blood level of cadmium using the National Health and Nutrition Examination Survey.

翻译：我们考虑了在存在未测量混杂的情况下，对平均处理效应以及依赖于可观测协变量的异质性处理效应的识别与推断。由于在缺乏强假设时，这些处理效应的点识别无法实现，我们通过利用差异效应（一种允许使用第二种处理来学习第一种处理效应的工具）来获得这些处理效应的边界。差异效应是指使用一种处理替代另一种处理所产生的效应。我们提供了在何种条件下，差异处理效应可用于点识别或部分识别处理效应。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边界，并利用两阶段方法对感兴趣的效应进行统计推断。通过模拟研究和一项利用国家健康与营养调查数据探究吸烟对血镉水平影响的案例研究，对所提出的方法进行了检验。