Synthetic Control

By the end of this lesson, you should be able to: explain when synthetic control is the right tool, build a synthetic control from a donor pool, explain why its weights are restricted, read its estimate, and recognise when it can't be trusted.

One treated unit, and nothing to compare it with

Difference-in-differences needs a comparison group that moves like the treated group. When the treatment hits a single large unit, like one city, one state or one country, there's often no single unit that's a good match. Every other city is bigger, smaller, growing faster or slower.

Synthetic control builds the comparison instead of picking it. It takes a weighted average of untreated units, called the donor pool, choosing weights so the average tracks the treated unit as closely as possible before the change. After the change, that weighted average, the "synthetic" unit, shows what would have happened without it.

The classic example: California's tobacco programme

In 1988, California voters passed Proposition 99. It raised the cigarette tax by 25 cents a pack, funded anti-smoking education and media campaigns, and encouraged local clean-air rules.1 What did it do to smoking?

No single state is a good comparison for California. So Abadie, Diamond and Hainmueller built a synthetic California from other states. They left out states that ran their own large tobacco programmes or raised cigarette taxes by 50 cents or more during the period, which left 38 donor states. The best match for California's cigarette sales before 1988 turned out to be a mix of just five:

Before 1988, synthetic California's cigarette sales tracked real California's closely. After 1988, the two paths separated. By 2000, annual cigarette sales per person in California were about 26 packs lower than in synthetic California.