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g 1, 2 and t 1, 2, and Fgtyis the cdf for the observed outcome Yi conditional on Gi g and Ti t, then

F

  • 0

11

  • y

F10F

1 00

  • F01y,

w h e r e F 0 0 1 i s t h e i n v e r s e f u n c t i o n o f F 0 0 , which exists under the strict monotonicity

a s s u m p t i o n . B e c a u s e F 1 1 1 y F 1 1 y , w e c a n estimate the entire distributions of both counterfactuals conditional on intervention, Gi Ti 1. Can apply to repeated cross sections or panel data. Of course, can also identify the average treatment effect

  • CIC EY111 EY110.

In particular,

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