Mastering 'Metrics: The Path from Cause to Effect

by Joshua D. Angrist

We’ve noted that the original randomizer (in this case, a KIPP offer) is called an instrumental variable or just an instrument for short. As we’ve seen, the link from the instrument to the causal variable of interest (in this case, the effect of lottery offers on KIPP attendance) is called the first-stage, because this is the first link in the chain. The direct effect of the instrument on outcomes, which runs the full length of the chain (in this case, the effect of offers on scores), is called the reduced form. Finally, the causal effect of interest—the second link in the chain—is determined by the ratio of reduced form to first-stage estimates. This causal effect is called a local average treatment effect (LATE for short).