Regression Discontinuity: Learning From Cutoffs

How rules with sharp cutoffs, such as test score thresholds and class size limits, let economists compare people just above and just below the line.

Many rules use sharp cutoffs. A student with a test score of 80 or above gets a scholarship; a student with 79 does not. A town with more than a certain number of residents gets extra funding. These cutoffs create a powerful research opportunity called regression discontinuity.

The idea

Students who scored 79 and 81 are nearly identical in ability. Whether they landed just above or just below the line is largely a matter of luck on test day. So comparing students just above the cutoff with those just below is almost like a randomised experiment. If those just above do much better later, the scholarship is the likely reason.

The name comes from looking for a sudden jump, a discontinuity, in outcomes at the cutoff. Outcomes may rise smoothly with test scores in general, but if there is a sharp jump exactly at the threshold, that jump reveals the effect of crossing it.

Class size in Israel

A famous example comes from Joshua Angrist and Victor Lavy, who studied Israeli schools in the 1990s. Israel followed a rule, often called Maimonides’ rule after the medieval scholar, that classes could have no more than 40 pupils. A year group of 40 pupils formed one class of 40, but a year group of 41 was split into two classes of about 20 or 21. This created sharp, rule-driven changes in class size. Angrist and Lavy found that smaller classes led to higher test scores.

The election that barely went one way

Researchers use regression discontinuity to study close elections. A candidate who wins with 50.5 percent of the vote and one who loses with 49.5 percent are very similar, so comparing districts that barely elected one party with districts that barely elected the other reveals the effect of which party holds power.

Limits

The method estimates the effect only for people near the cutoff. A scholarship’s effect on students scoring around 80 may differ from its effect on students scoring 95. And if people can precisely manipulate which side of the line they fall on, for example by retaking a test until they pass, the comparison breaks down.

Applying the result to everyone

A regression discontinuity study reveals the effect for people close to the threshold. It is tempting to assume the same effect applies to everyone, but people far from the cutoff may respond very differently.

Key takeaways

Regression discontinuity compares people just above and just below a sharp cutoff.
People near the cutoff are very similar, so differences in outcomes reveal the rule's effect.
Angrist and Lavy used Israel's class size rule to show smaller classes raised test scores.
The results apply mainly near the cutoff and fail if people can manipulate their position.