In the Synthetic Controls Method, the treatment effect for a time $t$ is given to be the difference in outcomes for the treated unit and control unit, in the post-treatment period. In this regard, I think this is the ATT instead of the ATE, but cannot fully explain to myself why. Can anyone give a give way to reason? thanks!
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The treatment effect is the ATT because the control units are weighted to resemble the treated unit, creating a synthetic control unit with the same history as the treated unit except that it did not receive the treatment. That is, the final distribution of both the actually treated unit and the weighted synthetic control is that of the treated unit, so the effect is only generalizable to a unit with a history like that of the treated unit.
