(i) X → Z → Y and (ii) X → M → Y ↓ Z In example (i), Z satisfies conditions (1) and (2) but is not a confounder. It is known as a mediator: it is the variable that explains the causal effect of X on Y. It is a disaster to control for Z if you are trying to find the causal effect of X on Y. If you look only at those individuals in the treatment and control groups for whom Z = 0, then you have completely blocked the effect of X, because it works by changing Z. So you will conclude that X has no effect on Y. This is exactly what Ezra Klein meant when he said, “Sometimes you end up
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