Comparing Causal Frameworks: Potential Outcomes, Structural Models, Graphs, and Abstractions

Abstract: The aim of this paper is to make clear and precise the relationship between the Rubin causal model (RCM) and structural causal model (SCM) frameworks for causal inference. Adopting a neutral logical perspective, and drawing on previous work, we show what is required for an RCM to be representable by an SCM. A key result then shows that every RCM -- including those that violate algebraic principles implied by the SCM framework -- emerges as an abstraction of some representable RCM. Finally, we illustrate the power of this conciliatory perspective by pinpointing an important role for SCM principles in classic applications of RCMs; conversely, we offer a characterization of the algebraic constraints implied by a graph, helping to substantiate further comparisons between the two frameworks.