Regression discontinuity designs exploit sharp thresholds — a policy kicks in at a cutoff, and comparing outcomes just above and just below estimates the causal effect. When the data is clustered (students within schools, patients within hospitals), the standard practice is to use clustered standard errors.
Noack, Olma, and Rothe show this standard practice can be inconsistent or overly conservative. The clustered standard errors that practitioners routinely report — the ones that referees require, that textbooks recommend — can give the wrong answer or the right answer inflated beyond usefulness.
The problem is specific to RD designs. In ordinary regression, clustered standard errors have well-understood behavior. But RD designs use local estimation — observations near the cutoff, weighted by distance — and this locality interacts with the cluster structure in ways the standard formulas don't account for. When cluster sizes grow, the usual clustered variance estimator can fail to converge to the right quantity.
The fix is a nearest-neighbor variance estimator that accounts for the local structure of RD estimation. It works where the standard approach fails, and the empirical case studies confirm the discrepancy matters in practice — not just asymptotically but in real datasets that economists publish with.
The structural lesson: a statistical method that is correct in one setting (ordinary regression) can be incorrect when transplanted to another (RD) without adjusting for the new setting's structure. “Use clustered standard errors” is a rule that presupposes a particular relationship between clusters and estimation, and RD designs violate that presupposition.