All simulators
ATE, ATT, ATC & CATE
A heterogeneous effect τ(x) averaged over three different populations — and when they coincide.
Day 33: Estimands: ATE, ATT, ATC & CATEeffect τ(x)density of x among enrolleesdensity among non-enrolleesdensity in population
share enrolled p
0.50
check p·ATT + (1−p)·ATC
2.500
ATE = 2.500
The effect τ(x) (orange) depends on prior earnings rank x. Who enrols depends on x too. ATT averages τ(x) over the treated's distribution (blue), ATC over the controls' (violet), ATE over everyone's (flat). They coincide only if τ is flat or enrolment ignores x.