Your observation is super insightful. One of the major communication obstacles I have encountered with potential outcome (PO) folks is the notion that causal effects and counterfactuals, Y_x, are PROPERTIES OF OUR MODEL. They cannot swallow it because, in the PO framework
of Rubin (1974) there is no such a beast as a MODEL. All he had were conditional probabilities of potential outcomes {Y(0),Y(1)}.
Subsequently, those who entered #causalinference through a PO-
education suffer from the same deficiency -- no model.
#Bookofwhy. (cont....)
Instead, the potential outcome Y(1) is defined in the context of a real-life RCT, not a model of how a population responds to RCT. Hard-core PO folks, including Rubin's disciples in economics continue to operate in this model-blind conception. DAG-using Epidemiologists
have advanced towards model-hood, but not all the way. Since Robins and Greenland works (1986) were rooted in Rubin's PO, many epidemiologists today still view DAGs as tools for serving the RCT conception of potential outcomes, not as a mathematical object (cont.
that DEFINES potential outcomes. This explains why @_MiguelHernan depicts it as black magic when I assert that an ideal intervention is defined as a property of one's model. This conceptual barrier continues to impede communication until ..(YES)... a metamorphosis occurs...
eg, estimate Mary's salary had she not quit school