A quasi-experimental identification strategy that exploits a known deterministic or probabilistic treatment assignment rule based on a continuous running (assignment) variable and a cutoff (threshold). Under the maintained assumptions—continuity of potential outcome functions in the running variable at the cutoff, and absence of precise manipulation of the running variable—any discontinuous jump in the conditional expectation of the outcome at the cutoff can be interpreted as a local causal effect of treatment for units at the threshold.

Principle

If potential outcomes as functions of the running variable would be continuous at the cutoff in the absence of treatment, then a discontinuity (jump) in observed outcomes at the cutoff reflects the causal impact of the treatment for units infinitesimally close to the threshold; estimation relies on local comparisons and bandwidth choice.

Demonstration

Illustrative scenario: Eligibility for a scholarship is assigned when an exam score exceeds 70. Recognition: treatment probability jumps at score = 70. Action: estimate the jump in mean outcomes (e.g., subsequent grades) using data close to the cutoff with a chosen bandwidth and polynomial or local linear fit. Consequence: the estimated jump is a credible local average treatment effect at the threshold, not necessarily representative away from the cutoff.

Misapplication

Treating the RDD estimate as a global average effect for all eligible individuals, failing to test for manipulation of the running variable near the cutoff (e.g., bunching), or using overly large bandwidths or high‑order polynomials that induce bias rather than local identification.

Consequence

When assumptions hold, RDD yields credible causal identification without randomization but only locally at the cutoff; it is valuable when random assignment is infeasible but a threshold rule governs treatment, though policy extrapolation requires caution.

Reversal

Identification fails if units can precisely manipulate the running variable to alter treatment status, if other policies or discontinuities coincide at the same cutoff, or if the running variable is measured with substantial error near the threshold; in fuzzy designs where assignment probability changes less than from 0 to 1, interpretation shifts to a local average treatment effect for compliers.

Boundary

Clearly within: sharp RDD with deterministic assignment at a known cutoff and continuous potential outcomes. Boundary case: fuzzy RDD where the probability of treatment jumps but is not deterministic. Clearly outside: discontinuities in observed outcomes caused by other simultaneous interventions or measurement artifacts are not valid RDD identification.

Semantic Tension

Credible local identification (internal validity at the cutoff) versus generalizability to populations away from the cutoff; RDD versus randomized experiments in terms of the extent and locus of causal claims.

Synthesis

RDD converts institutional or rule‑based thresholds into locally credible causal contrasts: it trades global applicability for identification at the margin. Proper inference requires testing for manipulation, careful bandwidth selection, and explicit acknowledgment that estimated effects pertain to units near the cutoff.