I want to use the Synthetic Control Method to estimate the effect of the adaption of a new ballot institution (treatment) on fiscal policy.
My sample consists of 20 units observed at 100 time points. 14 units adopted the new institution prior to begin of the sample and 2 never adopted the new institution. This leaves me with 4 units that changed the institution respectively received the treatment (treated units).
The Synthetic Control Method uses a weighted average of the units in the control group (or "donor pool"). Abadie et. al (2014) give some recommendations for empirical practice. One of those is that units affected by the treatment should be excluded from the donor pool. Another one is that the donor pool should consist of units with similar characteristics.
Should I refrain from including the 14 units that already had adopted the new institution in the donor pool? Why?
Note that the adoption of the new institution happened at different time points. While the earliest adoption could therefore be estimated by a donor pool of 5 units, the latest adoption only has a donor pool of 2 (the 2 units that still use the old ballot institution).
Also, would you estimate the effect of the adoption for every unit seperately (note again that there was staggered adoption) or is there a reason to use the Synthetic Control Method on an aggregate of the treated units?
References: Abadie, Alberto and Diamond, Alexis and Hainmueller, Jens, Comparative Politics and the Synthetic Control Method (February 1, 2014). American Journal of Political Science. 2014, Forthcoming; Formerly MIT Political Science Department Research Paper No. 2011-25. Available at SSRN: http://ssrn.com/abstract=1950298 or http://dx.doi.org/10.2139/ssrn.1950298