Contrasting Identifying Assumptions of Average Causal Effects: Robustness and Semiparametric Efficiency

Semiparametric inference about average causal effects from observational data is based on assumptions yielding identification of the effects. In practice, several distinct identifying assumptions may be plausible; an analyst has to make a delicate choice between these models. In this paper, we study three identifying assumptions based on the potential outcome framework: the back-door assumption, which uses pre-treatment covariates, the front-door assumption, which uses mediators, and the two-door assumption using pre-treatment covariates and mediators simultaneously. We derive the efficient influence functions and the corresponding semiparametric efficiency bounds that hold under these assumptions, and their combinations. We compare the bounds and give conditions under which some bounds are lower than others. We also propose semiparametric estimators, quantify their efficiency and study their robustness to misspecification of the nuisance models. The theory is complemented with simulation experiments on the finite sample behavior of the estimators. The results obtained are relevant for an analyst facing a choice between several plausible identifying assumptions and corresponding estimators. Here, the choice is a trade-off between efficiency and robustness to misspecification of the nuisance models.