Regression Discontinuity Design
Causal effects from cutoffs, comparing people just above and just below a threshold.
Definition
Regression discontinuity: when treatment switches at a threshold of a running variable, units just above and just below the cutoff are as good as randomized.
Key equation
Effect = lim(x↓c) E[y|x] − lim(x↑c) E[y|x]
The intuition
A student at 49.9% and one at 50.1% are effectively identical except the scholarship, the jump in outcomes at the line IS the causal effect, locally. Credibility dies if people can manipulate their score across the cutoff.
Exam tip
Say 'local average treatment effect at the cutoff'. RDD buys internal validity at the price of generalizability, and examiners want that trade named.
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