regression discontinuity design (RDD)

Many rules assign benefits by a sharp cutoff: scholarships above a test score, subsidies below an income line. Just on either side of that line sit people who are essentially identical except for one accident, which side of the threshold they landed on. Regression discontinuity design treats that knife-edge as a tiny natural experiment, reading the causal effect off the jump in outcomes exactly at the cutoff.

Let a running variable X assign treatment when it crosses a threshold c. In a sharp design treatment switches deterministically at c, and the local effect is the gap between the limits of the outcome's regression on X approached from above and from below. In a fuzzy design crossing c only changes the probability of treatment, and one scales the outcome jump by the treatment-probability jump, an instrumental-variables move. Estimation uses local linear regression within a data-driven bandwidth around c, balancing bias against variance.

Its credibility comes from a mild, partly testable assumption: everything other than treatment varies smoothly through the cutoff, so units cannot precisely manipulate which side they fall on (a McCrary density test probes this). The cost is external validity, RDD identifies the effect only for units near the threshold, a local average treatment effect that may not extend to those far from the boundary.