Rubin Causal Model - Relations To Other Approaches

Relations To Other Approaches

In the view of Pearl (2000), the Rubin Causal Model (RCM) is subsumed by the Structural Equation Model (SEM) used in econometrics and the social sciences, in its extended nonparametric form. That view, which has long been argued by Heckman (2005) is presented formally in Pearl (2000). The key connection between the RCM and SEM rests on interpreting the "potential outcome" variable Y_x(u) to be the solution for variable Y in a modified structural model, in which the external intervention X=x is emulated by replacing the equation that determines X by the constant equation X=x. The variable u, which in the RCM stands for the identity of each experimental unit (e.g., a patient or an agricultural lot,) is represented in the SEM formulation by a vector of exogeneous variables (usually unobserved) that characterize that unit. With this interpretation, every theorem in RCM can be shown to be a theorem in SEM and vice versa. This interpretation has led to a complete axiomatization of RCM and, based on the derivations of Shpitser-Pearl (2006), a complete solution to the identification of causal effects, using graphs. Complete solution means that, for any subset X of variables and a set A of causal assumptions encoded in a graph G, it is possible to determine algorithmically whether the causal effect P(Y_x = y) can be estimated consistently from non-experimental data and, if so, what form the estimand of P(Y_x = y) should have. Using that estimand, it is possible then to estimate, from observational study, the average causal effect over the population:

From the perspective of Pearl and his colleagues, a major shortcoming of RCM is that all assumptions and background knowledge pertaining to a given problem must first be translated into the language of counterfactuals (e.g., ignorability) before analysis can commence. In SEM, by comparison, Pearl (2000) and Heckman (2008) hold that background knowledge is expressed directly in the vocabulary of ordinary scientific discourse, invoking cause-effect relationships among realizable, not hypothetical variables.

The Rubin causal model has also been connected to instrumental variables (Angrist, Imbens, and Rubin, 1996) and other techniques for causal inference. For more on the connections between the Rubin causal model, structural equation modeling, and other statistical methods for causal inference, see Morgan and Winship (2007) and Pearl (2009).