Scholarships at a score cutoff: a natural experiment

Question

A scholarship is awarded to every student who scores at least 80 on an entrance exam. You want the causal effect of the scholarship on eventual graduation, but you cannot randomize who gets money.

Explain how a regression discontinuity design uses the cutoff to estimate the effect, why it can be treated as almost random, the key assumption it needs, and its main limitation.

Accepted Answer

The problem with the obvious comparison. Simply comparing scholarship winners to non-winners is hopeless: winners scored higher, so they were stronger students to begin with and would graduate more often anyway. The score is a confounder tangled up with getting the money. The regression discontinuity idea. Zoom in on students right around the cutoff. A student who scored 79 and one who scored 81 are, for all practical purposes, the same kind of student. Whether they landed just below or just above 80 comes down to a lucky guess, a generous grader, or a good night's sleep, essentially noise. S…

Scholarships at a score cutoff: a natural experiment

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