A study uses U.S. Medicare eligibility (which begins at age 65) as an RD design to estimate the effect of health insurance on mortality. What is the most accurate characterization of the causal effect this design identifies?
AThe average causal effect of insurance for the entire U.S. adult population
BThe causal effect of insurance specifically for people near age 65 — not necessarily for 40- or 75-year-olds
CThe effect only for people who voluntarily enroll in Medicare, not for all eligibles
DAn unbiased estimate of the effect only if mortality trends are linear with age
RD estimates a local average treatment effect (LATE) at the threshold — here, the causal effect of insurance for near-65-year-olds. Whether this generalizes to other age groups depends on substantive reasoning about treatment effect heterogeneity, not on the design itself. Option A is wrong because RD is explicitly a local estimator. Option C confuses compliance issues in a fuzzy RD with the scope of inference. Option D misunderstands bandwidth and functional-form choices as validity conditions.
Question 2 Multiple Choice
Before relying on an RD estimate, a researcher checks whether baseline health measures (prior hospitalization rates, income) show discontinuities at the threshold. This check is designed to test:
AWhether the running variable is measured without error
BWhether the smoothness assumption holds — that no other determinants of the outcome also jump at the cutoff
CWhether the bandwidth around the threshold is large enough for statistical power
DWhether the effect is linear in the running variable
The identifying assumption in RD is that all determinants of the outcome vary smoothly at the threshold — any jump in the outcome at the cutoff is attributed to the treatment. If observable covariates also show discontinuities, it suggests confounding variables are themselves discontinuous at the cutoff, compromising the design's validity. This check directly tests the smoothness assumption, not measurement precision, bandwidth, or functional form.
Question 3 True / False
If people can precisely manipulate their value of the running variable to sort themselves just above or just below the cutoff, the RD design remains valid as long as an outcome discontinuity is still detectable.
TTrue
FFalse
Answer: False
Manipulation of the running variable directly violates the comparability of units near the threshold, which is the design's foundation. If people can sort themselves, those just above and just below the cutoff are no longer similar — they differ systematically by their ability or motivation to manipulate. A McCrary density test detects this by checking for a spike in the running variable's distribution at the cutoff. A detectable outcome discontinuity does not rescue the design if the groups being compared are already systematically different.
Question 4 True / False
In a regression discontinuity design, the identifying assumption is that all determinants of the outcome vary smoothly at the threshold, so any jump in the outcome at the cutoff is caused by the treatment.
TTrue
FFalse
Answer: True
This is the core identifying assumption of RD. Because everything except treatment assignment is assumed to change smoothly at the cutoff, a sharp discontinuity in the outcome can only be caused by the treatment itself. This is why RD extracts credible causal evidence from arbitrary administrative rules: the cutoff is unrelated to outcomes except through the treatment it triggers.
Question 5 Short Answer
Why is a 'fuzzy' RD design analyzed using instrumental variables methods rather than a simple comparison of means above and below the threshold?
Think about your answer, then reveal below.
Model answer: In a fuzzy RD, crossing the threshold changes the probability of treatment but does not deterministically assign it — some units above the cutoff don't take up treatment and some below do. The threshold acts as an instrument: it affects treatment probability (relevance) but affects outcomes only through treatment (exclusion restriction). IV methods recover the causal effect for 'compliers' — those whose treatment status changes because of the threshold — and scale the reduced-form jump in outcomes by the jump in treatment probability at the cutoff.
A simple comparison of means above and below would conflate compliers and non-compliers, biasing the estimate. IV correctly accounts for imperfect compliance by using the discontinuity in treatment probability as the identifying variation. This connects fuzzy RD directly to the IV framework: the threshold is the instrument, the treatment indicator is the endogenous variable, and the outcome is what you are estimating.