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As I understand it, the synthetic control method (SCM)-a method that builds on difference-in-differences (DD) estimation-can be used to evaluate the causal effect of shocks or interventions [see 1]. This method may be used in circumstances where only a few units are subject to the intervention while a larger set of units are not subject to the intervention. To compare treated units with controls, outcomes from the control units are weighted so as to construct a counterfactual "synthetic control" which could be compared with the treated unit. The synthetic control is constructed so as to match the pre-intervention characteristic of the treated unit.

However, in all applications of the SCM that I have seen, one often considers, for example, cases where a number of states or regions in a nation are treated, while all other states or regions serve as control units.

My question is whether it is possible to use the SCM if there is only one group treated and if anyone has done this? For example, suppose there is a policy reform on 1 January 2000 which only applies to all children born at or after that date. Thus children born on or after 1 January 2000 are treated while all other children are controls. Here a DD estimation seems to be the best way to evaluate the effect of the reform on treated children. However, could the SCM be applied to study the same reform? For example, could the control units be divided in e.g. ten smaller control units (e.g., children born before 1 January 2000 with different levels of income), which are then weighted to form a more suitable counterfactual?

[1] Abadie, A., Diamond, A., & Hainmueller, J. (2010). Synthetic control methods for comparative case studies: Estimating the effect of California’s tobacco control program. Journal of the American Statistical Association, 105(490), 493-505.

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Yes it is possible. There is a whole literature regarding so called N-of-1 trials. That term is mostly used to describe patient studies or case series. However, the approach can be generalized to community-based research where the community or the state is the basic unit of sampling/randomization. You can also call these types of studies a "pre/post" study.

Data obtained from the "pre" period serve as an historical control, then the crossover period to active intervention begins the collection of "post" period data. The limitations of this approach are noted and they're substantial. For instance, period and cohort effects are all completely aliased. Depending on the sample, age may be aliased as well (such as in studies of students within a particular grade level).

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