27.1 Conceptual Framework
To truly appreciate the logic of RD designs, one must think like an experimentalist, but with observational data. RD transforms a deterministic rule (e.g., a policy cutoff) into an opportunity for quasi-random assignment. It is, in essence, a localized experiment conducted at the threshold of a continuous running variable.
At the heart of the RD framework is a deceptively simple idea: individuals just above and just below the cutoff are virtually identical in all respects, except for the treatment status induced by their position relative to the threshold. This intuition enables RD designs to estimate causal effects with high internal validity, even in the absence of random assignment.
RD’s strength lies in its focus on a narrow window around the cutoff, often called the bandwidth, where the assumption of exchangeability is most plausible. Within this narrow range, the assignment mechanism approximates a randomized experiment.
- Internal Validity: Extremely strong near the cutoff. The closer the observations are to the threshold, the more credible the assumption that they are otherwise comparable.
- External Validity: More limited. Estimates are local to the cutoff and may not generalize to units far from the threshold. This tradeoff between precision and generalizability is a defining characteristic of RD.
One of the most compelling validations of RD comes from empirical comparisons with randomized controlled trials (RCTs). Evidence from studies such as Chaplin et al. (2018) and Gleason, Resch, and Berk (2018) suggest that RD and RCTs often yield remarkably similar treatment effect estimates, underscoring RD’s credibility when its assumptions are met. While RD is not a substitute for randomization, it can come surprisingly close in practice.
RD is not an island; it shares conceptual and methodological links with several other causal inference frameworks. Understanding these connections helps clarify when RD is appropriate and how it complements alternative approaches.
- Randomized Experiment: RD can be seen as a local randomization design (treatment is “as-if” randomly assigned near the cutoff).
- Instrumental Variables: RD can be framed as a special case of a structural IV model (J. D. Angrist and Lavy 1999), where the running variable induces exogenous variation in treatment at the threshold.
- Matching Methods: RD resembles a highly targeted form of matching (matching units just above and below a single threshold) (J. J. Heckman, LaLonde, and Smith 1999).
- Interrupted Time Series (ITS): RD outperforms ITS when the running variable is finely measured and continuous. However, in settings with highly discrete or temporally aggregated data (e.g., quarterly revenues or annual crime rates), ITS may be more suitable. Still, when the data are dense or effectively continuous, RD offers a more precise and defensible design.