Total Causal Effect

Given an SCM \(\mathcal{M}\), a total causal effect (, , p. 91, Definition 6.12) from \(X\) to \(Y\) exists if and only if we have statistical dependence between \(X\) and \(Y\) after applying \(do(X=N_X)\) in \(\mathcal{M}\) for some random variable \(N_X\).

The relation to the graph \(\mathcal{G}\) induced by \(\mathcal{M}\) is that no directed path between \(X,Y\) implies there is no total causal effect, and sometimes a directed path may exist without a total causal effect.