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.Comment: 52 pages, 5 figures, 11 table