Selection Bias Lives in Y(0)

Ten units, one targeting rule, and a naive comparison that is sometimes exactly right.

Set the rules of the world

What the data say

Naive gap E[Y|D=1] − E[Y|D=0]
ATT
ATC
ATE
E[Y(0)|D=1]
E[Y(0)|D=0]
Selection bias E[Y(0)|D=1] − E[Y(0)|D=0]
UnitXY(0)Y(1)τD