  When estimating treatment effects, the golden 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, the
key to validate the use of observational data is hard to verify 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 method 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 a simple estimator to estimate the average treatment effect of interest
using both the observational data and the experimental data.
