Implementation-neutral causation in structural models

Analysts associated with the Cowles Commission attached great importance to the distinction between structural and reduced-form models: in their view structural models, but not reduced-form models, allow the analysis of causal relations. They did not present clear justification for this view. Here we show that this insight is correct, and make the demonstration of it precise. Causal relations are shown to depend on parameter restrictions that are explicit in the structural form, but not in the reduced form when the coefficients are interpreted as unrestricted constants. The requisite parameter restrictions are those associated with implementation-neutral causation. A graphical procedure is outlined that identifies causal orderings and also the ordering based on implementation-neutral causation. The same procedure applied to reduced form models produces the implementation-neutral causal ordering only if the parameter restrictions are explicitly incorporated in the reduced form. The analysis is applied in investigating the validity of the causal Markov condition.