The Regression Discontinuity Design (Handbook Chapter)
Causal Question / Estimand
The local treatment effect at the cutoff, presented under two distinct identification frameworks that imply subtly different estimands and inference.
Identification Strategy
Organizes RD around two frameworks. (1) Continuity-based: assume Continuity-at-Cutoff and estimate with local polynomial (typically local linear) regression in a neighbourhood, with robust bias-corrected inference and data-driven (MSE-optimal) bandwidth selection — the modern fix for the bias of undersmoothed local regression. (2) Local-Randomization: assume treatment is as-if-random within a window, enabling Fisherian randomization inference and large- sample analysis within that window, with explicit window selection. Emphasizes falsification/validation throughout.
Key Assumptions
Continuity framework: Continuity-at-Cutoff, No-Manipulation. Local-randomization framework: Local-Randomization within a window. Both: SUTVA; fuzzy designs add the IV assumptions (Exclusion-Restriction, Monotonicity).
Threats to Validity
Manipulation/sorting at the cutoff; bandwidth/window choice; coverage distortions from naive local-regression inference (hence robust bias correction). Recommends a battery of falsification methods: density (McCrary) tests, covariate-balance tests at the cutoff, placebo cutoffs, and sensitivity to bandwidth/window.
Setting / Data
n/a — methodological handbook chapter; uses an empirical illustration to demonstrate both frameworks.
Key Claims
- The continuity-based and local-randomization frameworks are complementary lenses; the latter is natural with discrete running variables or very narrow windows.
- Inference should use robust bias-corrected confidence intervals with MSE-optimal bandwidths, not ad hoc polynomial fits.
- Systematic falsification (density, covariates, placebo cutoffs) is integral to a credible RD study.
Connections
- Modernizes the practice of ImbensLemieux2008-RDDGuideToPractice and LeeLemieux2010-RDDInEconomics (robust inference; the local-randomization framework formalizes Lee’s “as-good-as-random” intuition).
- Local-randomization framework links RD to Randomization and design-based inference (Foundations). See also RDD
Citation
Cattaneo, M. D., Titiunik, R., & Vazquez-Bare, G. (2020). The Regression Discontinuity Design. In Handbook of Research Methods in Political Science and International Relations (Ch. 44, pp. 835–857). Sage Publications.