An RDD study finds that students who just barely scored above a scholarship threshold (score ≥ 70) have significantly better 10-year earnings than students who just barely scored below it. A policy advisor argues this proves scholarships improve earnings for all students. The most important methodological objection is:
AThe running variable (test score) may have measurement error near the threshold
BRDD identifies a local average treatment effect at the margin, which may not generalize to students far from the threshold
CThe bandwidth used was probably too narrow, causing high variance in the estimate
DRDD cannot be used with continuous outcomes like earnings
The core limitation of RDD is that it identifies the treatment effect *only* for units near the cutoff — those on the margin of qualifying. Students who scored 70 vs. 69 are very similar to each other but may be very different from students who scored 50 or 90. The scholarship effect for marginal students need not equal the effect for strong students (who might have thrived without the scholarship) or very weak students (who might lack the preparation to benefit). Generalizing a local estimate to a population average requires strong additional assumptions that the design alone cannot support.
Question 2 Multiple Choice
A researcher runs the McCrary density test on their RDD and finds a sharp spike in the density of the running variable just above the cutoff. What is the most concerning interpretation of this finding?
AThe outcome variable has a nonlinear relationship with the running variable near the threshold
BThe bandwidth is too wide, including observations where the treatment effect varies
CAdministrators or applicants may have manipulated the running variable to place units just above the threshold
DThe cutoff was chosen after the data were collected, introducing researcher degrees of freedom
A density spike just above the cutoff — but not below — is the signature of manipulation: someone has been sorting units to land just above the qualifying threshold (e.g., administrators rounding up test scores for borderline scholarship applicants). When this happens, units just above and below the cutoff are no longer comparable — those above have been selected for above-cutoff placement, while those below have not. This violates the as-if-random assignment assumption that makes RDD credible. The density test is specifically designed to detect this threat, which is why it is a core validity diagnostic rather than a formality.
Question 3 True / False
In RDD, using a wider bandwidth usually produces more accurate treatment effect estimates because more observations reduce sampling noise.
TTrue
FFalse
Answer: False
Bandwidth involves a bias-variance tradeoff, not a monotonic improvement. Narrower bandwidths include only observations closest to the cutoff (where the as-if-random assumption is most credible) but use fewer data points, producing higher variance. Wider bandwidths add observations further from the cutoff, reducing variance but increasing bias — observations far from the threshold are weaker counterfactuals and require more extrapolation across the regression function. The optimal bandwidth minimizes mean squared error by balancing these two forces. Neither extreme is 'always better,' which is why the CCT bandwidth selector and sensitivity checks across bandwidths are standard practice.
Question 4 True / False
RDD requires only that potential outcomes vary smoothly across the threshold — it does not require the full ignorability assumption needed by standard observational regression.
TTrue
FFalse
Answer: True
This is RDD's key advantage over observational regression. Standard regression requires ignorability (no unobserved confounders), which is almost never fully credible. RDD requires only that the distribution of all other outcome-relevant variables changes smoothly at the cutoff — that there is no simultaneous jump in covariates at exactly the threshold. If this holds, any discontinuous jump in outcomes at the cutoff must be caused by the treatment, since everything else is varying smoothly. This is a weaker and more defensible assumption in many policy contexts, which is why RDD is considered a strong quasi-experimental design when implemented well.
Question 5 Short Answer
Why might finding a statistically significant 'effect' at placebo cutoffs undermine confidence in a genuine RDD result at the true cutoff?
Think about your answer, then reveal below.
Model answer: Placebo cutoff tests apply the RDD estimation at values of the running variable where no treatment discontinuity exists. Under a valid design, you should find no effect at these placebo values, because there is nothing at those points to cause a jump in outcomes. If effects appear at multiple placebo cutoffs, it suggests the outcome variable is inherently discontinuous or lumpy near those values — perhaps for unrelated reasons — and that the apparent 'effect' at the true cutoff may just reflect that underlying pattern rather than treatment. Strong RDD results should be accompanied by flat placebo distributions, which build the evidential case that the discontinuity at the true cutoff is genuinely caused by the treatment assignment rule.
Placebo tests belong to a broader class of validity diagnostics that build the 'no other explanation' argument for causal inference. Along with covariate continuity checks (verifying pre-determined baseline characteristics don't jump at the cutoff) and density tests (verifying no manipulation), they constitute the empirical argument that the design is identifying a causal effect rather than a coincidental pattern in noisy data. Running only the main estimate without validity diagnostics is considered inadequate practice in modern applied econometrics.