How many treated unit should we consider using synthetic control ?

[Phuc Nguyen]

There is a paper Arkhangelsky et al., (2021) on AER using synthetic control (SC) to overcome parallel problem in Diffrence-in-Difference.
However, the big hole of synthetic control is that it only deals with one treated unit (or small number). As Arkhangelsky described in his paper following the example of Albadie, 2010 that how anti-smoking legislation in California in 1999 affect cigarette sales. So in that case, they only have one treated unit is California.

My question is: how small the number of observations we should consider using synthetic control?
I am having around 700 firms (in 1 country). I want to examine the impact of anticorruption law of that country to firm performance of firms in this countries after this law. Should I use Synthetic control or Propensity macthing score in that case.

Thanks in advance.

[Jared Greathouse]

It's true SCM is typically used in situations where a few units are treated, but there's nothing stopping you from having 100 units treated if you have a dataset that supports that sort of design. I know commands like scul would likely take forever, but sdid or allsynth might not fare much better since so many are treated.