A researcher uses sharp RDD to study a job training program assigned to workers who score below 50 on a skills test. She finds a significant positive jump in earnings at the cutoff. Her colleague claims this proves the training is effective for all low-skilled workers. What is wrong with this conclusion?
ANothing — RDD identifies the average treatment effect across the full sample
BThe estimate only applies to workers right at the threshold score of 50, not to all low-skilled workers; extrapolating to the full population is not supported by the design
CThe conclusion is wrong because RDD requires a regression, and regressions cannot prove causality
DThe finding is invalid unless the skills test has a normal distribution
Sharp RDD identifies a Local Average Treatment Effect (LATE) — the causal effect for individuals right at the cutoff. Workers scoring 20 or 80 may respond to the training very differently from those at 50. The design's credibility comes from local randomization near the threshold, but that local randomization only supports local inference. This is a fundamental limitation of RDD: it is highly credible for the threshold population but silent about treatment effects elsewhere in the running variable distribution.
Question 2 Multiple Choice
In a sharp RDD evaluation of a scholarship program (cutoff: exam score 75), what is the purpose of the McCrary density test?
ATo verify that the outcome variable (e.g., graduation rates) is continuously distributed near the cutoff
BTo detect whether students are manipulating their exam scores to land just above 75, which would invalidate the local randomization assumption
CTo select the optimal bandwidth for the local linear regression
DTo test whether the scholarship causes a discontinuous jump in earnings
The McCrary density test checks for a suspicious spike in the density of the running variable just above the cutoff. If students can manipulate their scores to land just above 75 (by re-taking the exam, getting extra tutoring, or having grades rounded up), then students just above 75 are systematically different from those just below — the local randomization argument fails. Students who successfully manipulate their score are likely higher-ability, more motivated, or better-resourced, creating selection bias. An RDD where manipulation is present cannot be trusted even if a discontinuity in outcomes is observed.
Question 3 True / False
Sharp RDD identifies the average treatment effect for the entire population of treated individuals.
TTrue
FFalse
Answer: False
Sharp RDD identifies a Local Average Treatment Effect (LATE) — the causal effect specifically for units right at the threshold, where the local randomization argument is valid. Units far from the cutoff are not comparable across the treatment boundary; their assignment is not quasi-random. This is why 'sharp' (deterministic assignment) RDD is highly credible for the threshold population but provides no direct evidence about treatment effects for the broader population. Extrapolating beyond the local neighborhood requires untestable assumptions about effect homogeneity.
Question 4 True / False
If observable pre-determined covariates (age, gender, baseline test scores) show a discontinuous jump at the RDD cutoff, this is evidence that the identification assumption may be violated.
TTrue
FFalse
Answer: True
This placebo test is one of the most important validity checks in RDD. The identifying assumption is that potential outcomes — and everything that determines them — vary smoothly through the cutoff. Pre-determined covariates that couldn't have been affected by treatment should show no discontinuity. If they jump at the cutoff, it suggests that units just above and just below are systematically different in ways beyond treatment assignment — exactly the selection problem RDD is supposed to eliminate. If observable characteristics show a jump, unobservable ones likely do too.
Question 5 Short Answer
Why does sharp RDD only estimate a local average treatment effect at the cutoff, rather than the average treatment effect for the full population? Why does this limitation matter?
Think about your answer, then reveal below.
Model answer: Sharp RDD's identification relies on the continuity of potential outcomes at the cutoff — in the absence of treatment, the outcome would vary smoothly through the threshold. This assumption is plausible only locally: units right at the cutoff are near-identical in observable and unobservable characteristics, making assignment essentially random. Units far from the cutoff differ systematically (a student scoring 60 is genuinely different from one scoring 90), so comparing their outcomes would confound treatment with pre-existing differences. The limitation matters because the threshold population may not be representative — a job training program might work well for workers right at the skill cutoff but have no effect for workers far below or far above it.
The LATE limitation is inherent to the design's strength: its credibility comes from local quasi-randomization, and that local randomization only permits local inference. This is the fundamental tension in causal identification — more credible designs often purchase their credibility by narrowing the scope of valid inference. RDD is among the most credible observational designs precisely because it doesn't extrapolate; the researcher who correctly respects this limitation is doing good science.