Estimating treatment effects using observational data and experimental data with non-overlapping support

When estimating treatment effects, the gold standard is to conduct a randomized experiment and then contrast outcomes associated with the treatment group and the control group. However, in many cases, randomized experiments are either conducted with a much smaller scale compared to the size of the target population or accompanied with certain ethical issues and thus hard to implement. Therefore, researchers usually rely on observational data to study causal connections. The downside is that the unconfoundedness assumption, which is the key to validating the use of observational data, is untestable and almost always violated. Hence, any conclusion drawn from observational data should be further analyzed with great care. Given the richness of observational data and usefulness of experimental data, researchers hope to develop credible methods to combine the strength of the two. In this paper, we consider a setting where the observational data contain the outcome of interest as well as a surrogate outcome, while the experimental data contain only the surrogate outcome. We propose an easy-to-implement estimator to estimate the average treatment effect of interest using both the observational data and the experimental data.