Forecasted counterfactual as quasi synthetic control

Question

I’ve been curious about a synthetic control inspired design and wanted to get some feedback.

Vanilla synthetic control: Takes a treatment group and a control group then infers some optimal weighting of each control unit (0.25A + 0.75B) such that the treatment group and synthetic control group are negligibly different.

CausalImpact: Google model where there are still an initial control and treatment group, but the weights are dynamic given time series data on both treatment and initial control groups. Thus the synthetic control group is robust against effects time and continues to be representative of the treatment group.

So my question is— why not just forecast the treatment group to get a counterfactual then compare fact-counterfactual for each randomization unit and get the distribution over lift?

Does this already have a name or is it a somewhat novel approach?

Answer 1

Synthetic controls make better use of the data

In CausalImpact, the synthetic counterfactual is built using the covariates of the control group. This makes use of the fact that we have data for the control group even after the experiment has begun. If one were to use just the treatment group, one would have to extrapolate into the future which can be more challenging. Nonetheless, the approach of forecasting the treatment group is also well known in the literature. For some arguments in favor of the synthetic control method see for example Section 4 in Abadie 2021 .

Ultimately it depends on the task - if extrapolation into the future can be argued to be simple and the control group is not very similar to the treatment group, it may be the better idea. If there is a suitable control group, synthetic controls provide a way to make use of their post-treatment covariates which helps the forecast.