What is causal effect of treatment (e.g. ads) on outcome (e.g. sales)?
Di = 1{unit i is treated} (e.g. user i is exposed to ad) Y;(d): i’s potential/counterfactual outcome (e.g. purchase) if Di — d
Causal treatment effect of Di = 1 for i is 11(1) Y;(0) AY;
Definition
So-called Causal Effects are features of distribution of AY; across i, e.g.,
Average Treatment Effect (ATE)-=E(AY;) (E is across i) • ATE on treated=E(AY;ID; = 1) • Quantile/Distributional TE=Percentiles of AY;
Why not whole distribution of AY;? (Fundamental Problem of Causality)
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