All simulators
Compliers & the LATE
Three types with different effects: the Wald ratio equals the compliers' effect, not the ATE or ATT.
Day 63: LATE & Compliers (Imbens–Angrist)Compliers 50%
Always-takers 20%
Never-takers 30%
A school-voucher lottery with three types (no defiers). The instrument changes only compliers' treatment, so the Wald ratio equals their average effect, whatever always- and never-takers' effects are. ATE and ATT weight the types differently; a naive comparison also mixes in who chooses to enrol. Half of the population wins the lottery.