No Manipulation
The behavioural condition that makes regression discontinuity credible: units cannot precisely control the running variable near the cutoff. If they could sort across the threshold (e.g. to obtain treatment), the groups just above and below would differ in unobservables and Continuity-at-Cutoff would fail. Lee’s insight is that as long as manipulation is imprecise — there is some random chance in the exact realized value — assignment near the cutoff is “as good as random.” It is partially testable: a McCrary density test checks for a discontinuity (bunching) in the density of the running variable at the cutoff, and covariates should be continuous (balanced) across it.
Relied on by
RDD (sharp and fuzzy); the empirical justification for treating the cutoff as locally experimental.