Causal Orderings

Abstract

It is a commonplace of elementary instruction in economics that endogenous variables are not generally causally ordered, implying that the question “What is the effect of y₁, on y₂?” where y, and y₂are endogenous variables is generally meaningless. The reason is that many possible interventions on the exogenous variables could have caused the hypothesized change y₁ and these interventions generate different values of y₂. Therefore, if all one knows about a hypothetical intervention on the values of the exogenous variables is that it induced the change Δy₁ in y₁, one cannot generally characterize the effect of the intervention on y₂. Sometimes, however, it happens that all the interventions on exogenous variables consistent with a given change in y, induce the same change in y₂. If so, y₁ is said tocausey₂. Essentially, the idea of causal orderings is related to that of statistical sufficiency: y₁ causes y₂if it aggregates the information contained in the exogenous variables that determine y₁ for the purpose of determining y₂.