What are natural experiments such as regression discontinuity and synthetic control?
They are designs in which something outside anyone’s choice splits units into comparable groups. John Snow compared houses supplied by two water companies. A regression discontinuity compares units just either side of a rule’s threshold. A synthetic control builds a weighted twin from untreated regions. Mendelian randomisation uses genes dealt out at conception.
Last time's quick check: parallel trends means that without the change, the treated and comparison groups would have kept moving together. In 1854 cholera struck London again. Most experts blamed bad air. The physician John Snow suspected the water. Two companies supplied the same streets of South London. The Southwark and Vauxhall Company drew its water from the Thames downstream of the city's sewage. The Lambeth Company had moved its intake upstream in 1852.
Houses side by side, rich and poor alike, got different water by an accident of history, and most residents didn't even know which company supplied them. Snow counted the deaths: 315 for every 10,000 houses supplied by Southwark and Vauxhall; 37 for every 10,000 supplied by Lambeth. Nobody designed that experiment. A water company did.
Some rules create sharp lines. Suppose a grant went only to farms above 50 hectares. A farm of 49 hectares and one of 51 are nearly identical, apart from the grant. Compare farms just either side of the line, and you have something close to a randomised trial, for farms near the threshold.
That's a regression discontinuity design. It only tells you about units near the line, and it fails if farms can shift themselves across it, for instance by renting a little extra land to qualify. Sometimes only one place is treated: a single country or region changes a policy, and there's no natural twin. So you build one. Combine other regions, weighted so that together they track the treated region's past as closely as possible, and use that synthetic twin to show what would have happened.
Researchers did this for California's 1988 tobacco control programme, building a synthetic California from other US states. After the programme began, cigarette sales in the real California fell well below those of its twin. And remember the cows from Module 2. Genes are dealt out at conception, before anyone decides anything, so they can act as a natural lottery for a trait like milk yield.
That's Mendelian randomisation. Natural experiments share one thing: something outside anyone's choice split the units into comparable groups. The work is arguing that the split really was as good as random, for the question you're asking. Next: what happens when one farm's treatment reaches its neighbour.
A design that uses a sharp rule. Suppose a grant went only to farms above 50 hectares: farms of 49 and 51 hectares are nearly identical apart from the grant, so comparing farms just either side of the line is close to a randomised trial for farms near the threshold. It fails if farms can shift across the line, for instance by renting a little extra land.
When only one place is treated, you build its twin: combine other regions, weighted so that together they track the treated region’s past as closely as possible. Researchers did this for California’s 1988 tobacco control programme, and after it began, cigarette sales in the real California fell well below those of its synthetic twin.
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