A Differential Effect Approach to Partial Identification of Treatment Effects

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.