Is there any downside to synthetic control compared to differences-in-differences model?

Question

Synthetic control seems to me to be simply a version of differences-in-differences model, where the assumption of parallel trends is satisfied by construction, since the synthetic control to the treatment is constructed in in such way that it is satisfied (weights are based on similarity to treatment in donor pool to control).

But if this is the case why would anyone bother with running differences-in-differences when synthetic control method is available? Is there any advantage that classic differences-in-differences has over synthetic control method?

Answer 1

I wouldn't say the assumption is "satisfied by construction". Parallel trends prior to treatment time is satisfied by construction, but the assumption is that the trend in the synthetic control is what would have happened in the treatment group in the absence of treatment. This is not testable.

Some people just think synthetic control is crazy. If you don't believe the diff-in-diff assumption for any one control, do you really believe it for a weighted average of controls?

The synthetic control may fit well prior to treatment due to overfitting (fitting the error term). In such a case, the synthetic control won't model the treatment group in the absence of treatment post-treatment.

Inference is hard with synthetic control. We must rely on permutation tests and placebo checks, which are prone to resulting in insignificance or just not being convincing.

Having said all that, synthetic control is a cool method that I like. Andersson 2019 is a particularly convincing application. https://www.aeaweb.org/articles?id=10.1257/pol.20170144