Thus we have two equations: ab = rZY and a = rZX. If we divide the first equation by the second, we get the causal effect of X on Y: b = rZY/rZX. In this way, instrumental variables allow us to perform the same kind of magic trick that we did with front-door adjustment: we have found the effect of X on Y even without being able to control for, or collect data on, the confounder, U.
