All simulators
Fuzzy RD
First-stage and reduced-form jumps; their ratio recovers the compliers' effect at the cutoff.
Day 76: Fuzzy RD as Local IVFIRST STAGE: P(treated | x)
REDUCED FORM: E[Y | x]
first-stage jump
0.643
reduced-form jump
1.933
fuzzy RD = ratio
3.00
truth 3.00
treated vs untreated near cutoff
3.70
Crossing the cutoff makes treatment available to compliers; always-takers are treated on both sides, never-takers on neither. Left: take-up jumps by the complier share (first stage). Right: outcomes jump by compliers' share × their effect (reduced form). The ratio recovers the compliers' effect at the cutoff; comparing treated and untreated units near the cutoff does not.