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Semiparametric inference on average causal effects from observational data isbased on assumptions yielding identification of the effects. In practice,several distinct identifying assumptions may be plausible; an analyst has tomake a delicate choice between these models. In this paper, we study threeidentifying assumptions based on the potential outcome framework: the back-doorassumption, which uses pre-treatment covariates, the front-door assumption,which uses mediators, and the two-door assumption using pre-treatmentcovariates and mediators simultaneously. We provide the efficient influencefunctions and the corresponding semiparametric efficiency bounds that holdunder these assumptions, and their combinations. We demonstrate that neither ofthe identification models provides uniformly the most efficient estimation andgive conditions under which some bounds are lower than others. We show whensemiparametric estimating equation estimators based on influence functionsattain the bounds, and study the robustness of the estimators tomisspecification of the nuisance models. The theory is complemented withsimulation experiments on the finite sample behavior of the estimators. Theresults obtained are relevant for an analyst facing a choice between severalplausible identifying assumptions and corresponding estimators. Our resultsshow that this choice implies a trade-off between efficiency and robustness tomisspecification of the nuisance models.

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