(i) In the context of potential outcomes with a sample of size n, let [yi(0), yi(1)] denote the pair of potential outcomes for unit i. Define the averages

and define the sample average treatment effect (SATE) as SATE = Y̅(̅1̅)̅ – Y̅(̅0̅)̅. Can you compute the SATE given the typical program evaluation data set?

(ii) Let y̅₀ and y̅₁ be the sample averages of the observed y_i for the control and treated groups, respectively. Show how these differ from y̅(̅0̅)̅ and y̅(̅1̅)̅.

Transcribed Image Text:

y(0) = n-y,(0) y(1) = ny.(1) Σ i=1"