I have a problem that I have not seen in the literature or discussed online. I am trying to design an experiment where there will be very few treated geographic units, perhaps only one. You can think of these as states of the US for the purpose of this question. In the non-experimental setting, synthetic cohort methods (like -synth- and -synth_runner- and -npsynth-) have been used to create Frankenstein control group(s) for causal inference. My situation is different since I can choose the treated unit(s). In doing that, there are several challenges that I am facing:
- Is the SC method still the best way to approach this question?
- How to do power calculation via simulation, when the SC estimation takes a considerable amount of time (especially with the nested optimization option, many covariates and half dozen outcomes)?
- What criteria should be used to select the treated unit? Good RMSE between the treated and their SC on historical data? Lack of significant false positives in false placebo tests, when you vary the timing of the test?
- When an additional unit gets assigned to treatment, it is pulled out from the set of potential donors, which alters how well the method works for the other treated units if that unit was heavily weighted and there is no suitable substitute.
- If there are reasons to worry about spillovers between treated and control units, is there a way to make the selection process deal with this? In doing ordinary SC, I would often exclude nearby units from the set of potential donors.
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