Scholarships at a score cutoff: a natural experiment
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.
Your answer
This one is open-ended. Work it through, then check your reasoning against the full solution.