What are the assumptions needed to be made for using the Synthetic Controls method?

Question

I am wondering what assumptions typically need to be made for the Synthetic Controls Method to work. It seems that I cannot find any concrete assumptions online and would like to understand what crucial assumptions there are. Thanks.

Answer 1

Main assumption about synthetic control method are as follows [(Nguyen, M. (2020). A Guide on Data Analysis. Bookdown. ch 27)][1]:

Donor subject is a good match for the synthetic control (i.e., gap between the dependent of the donor subject and that of the synthetic control should be 0 before treatment)

Only the treated subject undergoes the treatment and not any of the subjects in the donor pool.

No other changes to the subjects during the whole window.

The counterfactual outcome of the treatment group can be imputed in a linear combination of control groups.

[1]: https://bookdown.org/mike/data_analysis/synthetic-control.html#:~:text=Basically%2C%20we%20assume%20that%20the,not%20exposed%20to%20the%20treatment.&text=To%20make%20inference%2C%20we%20have,placebo%20effects%20in%20each%20iteration).

Answer 2

As phrased, this question doesn't have a coherent answer because "the Synthetic Controls method" isn't a single method—it's an infinite family of methods.

Honestly, this is why I recommend against using the term "synthetic controls". A synthetic control is just a fancy name for a regression where you're controlling for confounders.

You take a set of cases (e.g. countries or people). Then, you do a regression with the individual case you want to predict as the output, using the other test subjects as the input variables.

The reason this sometimes works is that maybe the other test subjects let you control for any unobserved variables that over time. e.g. maybe we can assume that if some unobserved variable affects the economy of Wisconsin, it'll also affect the economies of Minnesota and Iowa.

So, the assumptions are exactly the same as for the assumptions of whichever regression model you're using. In our example, you have to assume that controlling for the economies of Minnesota and Iowa is enough to remove any confounding.

If you'd like to understand the assumptions behind your regression models better, Statistical Rethinking covers causal inference much better than any econometrics textbook I've ever seen.