= Average treatment effect on the treated
{title2=ATT}
The <average treatment effect on the treated> is $\mathbb E[Y(1)-Y(0)\mid A=1]$, averaging over those who actually receive treatment. Their untreated <potential outcomes> are counterfactual. This can differ from the <average treatment effect> when effects vary and treatment uptake changes the population mix. Under <conditional exchangeability>, <consistency in causal inference> and adequate untreated overlap, it equals $\mathbb E[Y\mid A=1]-\mathbb E[\mathbb E(Y\mid A=0,X)\mid A=1]$. The second term standardizes untreated outcomes to the treated covariate distribution rather than using the crude untreated mean.
Back to article page
