Synthetic Control for Health Policy

Difference-in-differences compares the treated unit to one or more controls under the assumption that their outcomes would have moved in parallel absent the policy, weighting controls equally or by a fixed rule. Synthetic control instead estimates data-driven weights so that a convex combination of donors reproduces the treated unit's pre-intervention path, then reads the effect as the post-period gap. This makes the comparator's quality visible through pre-period fit and avoids assuming parallel trends with an arbitrary control group. Abadie, Diamond and Hainmueller present it precisely as a more credible alternative when no single control matches the treated unit.

With only one treated unit there is no sampling distribution of treated outcomes to support conventional standard errors. Instead, inference is done by reassigning the policy to each donor, building a synthetic control for that placebo, and computing its gap. The treated unit's effect is judged significant if it is extreme relative to the distribution of placebo gaps, typically after scaling by pre-period fit. This permutation logic, introduced in the California tobacco study, asks how often a gap as large as the observed one arises by chance among units that were not actually treated.

Three things. First, a close pre-intervention fit: the synthetic unit should track the treated unit's outcome and predictors for many periods before the policy. Second, a clean donor pool of units that did not adopt the policy or a similar one and were not affected by spillovers. Third, robustness: the result should survive reasonable changes to the predictor set and donor pool and should pass placebo tests. When the pre-period fit is poor or no donor combination can reproduce the treated unit, Abadie and colleagues advise against drawing causal conclusions from the method.