Regression Discontinuity Design MOC
Regression discontinuity (RD) identifies a causal effect where treatment switches at a known threshold of a continuous running (forcing) variable. The classic foundation is Continuity-at-Cutoff: potential-outcome expectations are continuous at the threshold, so the jump in outcomes there is causal. The behavioural justification is No-Manipulation — when units cannot precisely sort across the cutoff, assignment near it is “as good as random,” giving RD near-experimental internal validity at the price of a purely local estimand. A second, stronger foundation, Local-Randomization, treats a narrow window as a randomized experiment. Designs are sharp (deterministic treatment at the cutoff) or fuzzy (the cutoff shifts treatment probability → an IV problem yielding a LATE).
Papers
- LeeLemieux2010-RDDInEconomics — the JEL user’s guide: continuity, the as-good-as-random argument, sharp vs. fuzzy, local linear regression.
- ImbensLemieux2008-RDDGuideToPractice — practice guide: local linear estimation, cross-validated bandwidths, fuzzy RD as Wald/IV, and falsification diagnostics.
- CattaneoEtAl2020-RDDHandbook — modern synthesis: continuity-based vs. local-randomization frameworks, robust bias-corrected inference, MSE-optimal bandwidths, systematic falsification.
Key Concepts
Continuity-at-Cutoff · No-Manipulation (McCrary density test) · Local-Randomization · LATE (fuzzy RD) · Exclusion-Restriction · Monotonicity · Causal-Estimand · SUTVA
Debates & Contradictions
- Continuity vs. local randomization. Two non-nested foundations: continuity is weaker and nonparametric; local randomization is stronger but enables finite-sample (Fisherian) inference. CattaneoEtAl2020-RDDHandbook treats them as complementary.
- How to estimate and infer. The field moved from global polynomials to local linear regression (ImbensLemieux2008-RDDGuideToPractice) and then to robust bias-corrected inference with data-driven bandwidths (CattaneoEtAl2020-RDDHandbook).
- Local vs. external validity. RD’s credibility is bought with a cutoff-local estimand; extrapolating away from the threshold requires extra assumptions.
Next
Fuzzy RD is an instrumental-variables problem at the cutoff — see IV and LATE. The local-randomization framework connects to design-based inference in Foundations and Randomization.