Regression Discontinuity Design

Regression discontinuity design (RDD) is a clever method for figuring out cause and effect when a treatment is awarded based on a clear cutoff rule. The key insight is that people just above and just below the cutoff are essentially identical—the only difference is whether they received the treatment. By comparing these similar groups, researchers can estimate the true effect of scholarships, medical treatments, or policy changes. Students scoring 79 and 81 on an exam have nearly identical abilities, yet only the 81-scoring student gets the scholarship. This creates a natural experiment. Check this: The next time you see a rule with a strict cutoff, ask whether people just above and below are truly different.

How It Works

RDD exploits situations where treatment changes abruptly at a specific threshold. The first step is identifying the running variable—the continuous measure that determines treatment, like test scores, income levels, or election margins. Next, researchers focus on a narrow bandwidth around the cutoff, where individuals on both sides are nearly identical in all observable and unobservable characteristics except treatment status. Finally, they compare outcomes across this threshold to estimate the causal effect.

Real-World Applications

Education researchers use RDD to evaluate scholarship programs that award funding based on test score cutoffs. Students scoring 79.9 and 80.1 are virtually identical academically, but only one receives the scholarship. Similarly, in politics, researchers study incumbency advantage by comparing candidates who barely won versus barely lost elections—their underlying competitiveness is nearly identical. Healthcare studies examine treatment effects when drugs are prescribed based on clinical thresholds like blood pressure or cholesterol levels.

Why It's Powerful

The strength of RDD comes from its credibility. Unlike many observational methods, RDD's assumptions are transparent and testable. If people can't precisely manipulate their running variable (like test scores), the comparison at the cutoff is as good as random. However, the estimated effect applies specifically to people near the threshold—it may not generalize to those far above or below.

Practical Considerations

When using or interpreting RDD studies, pay attention to the bandwidth choice. Narrower bandwidths ensure more similar comparison groups but reduce sample size. Also check for manipulation—do people cluster just above the cutoff? If so, the comparison may be biased. Remember: RDD gives you the effect for marginal cases, not everyone.

Regression discontinuity design, introduced by Thistlewaite and Campbell in 1960, has become one of the most credible quasi-experimental methods in social science research. The method's validity rests on the continuity assumption: potential outcomes change smoothly at the cutoff in the absence of treatment. When this holds, the jump in observed outcomes at the threshold represents the causal effect.

• Imbens and Lemieux (2007): Provide a comprehensive practical guide covering bandwidth selection, bias correction, and implementation details that remain the standard reference for applied researchers [1].
• Lee and Lemieux (2010): Demonstrate how RDD provides causal estimates comparable to randomized experiments when the continuity assumption is plausible, with extensive discussion of validation tests [2].
• Angrist and Pischke (2009): Show RDD's equivalence to local randomization and emphasize its transparency compared to other observational methods [3].

RDD comes in two main variants. Sharp RDD occurs when treatment assignment changes deterministically at the cutoff (everyone above receives treatment, everyone below does not). Fuzzy RDD allows for imperfect compliance—probability of treatment jumps at the cutoff but doesn't reach 100%. Both variants rely on similar identification assumptions.

RDD has important constraints. First, the estimated effect is local to the cutoff—it applies to marginal cases, not the entire population. Students near a scholarship cutoff may respond differently than those far above or below. Second, RDD requires sufficient data near the threshold; sparse data leads to imprecise estimates. Third, manipulation of the running variable can invalidate the design—if students can retake tests or teachers "grade on a curve" at cutoffs, the groups may not be comparable. Fourth, optimal bandwidth selection remains debated—different methods can yield different estimates. Finally, RDD cannot estimate effects where no threshold exists or where thresholds are manipulated endogenously.