Semiparametric Estimation of Long-Term Treatment Effects

This paper studies the estimation of long-term treatment effects though the combination of short-term experimental and long-term observational datasets. In particular, we consider settings in which only short-term outcomes are observed in an experimental sample with exogenously assigned treatment, both short-term and long-term outcomes are observed in an observational sample where treatment assignment may be confounded, and the researcher is willing to assume that the causal relationships between treatment assignment and the short-term and long-term outcomes share the same unobserved confounding variables in the observational sample. We derive the efficient influence function for the average causal effect of treatment on long-term outcomes in each of the models that we consider and characterize the corresponding asymptotic semiparametric efficiency bounds.