A scholarship program sends eligibility letters to students scoring above 70. 80% of eligible students accept; 5% of ineligible students receive it through exceptions. A researcher uses fuzzy RDD. What exactly does the estimated effect measure?
AThe average treatment effect of scholarships on the full population of students
BThe effect of receiving the eligibility letter on scholarship take-up (the first stage)
CThe effect of the scholarship on outcomes for compliers near the cutoff — those whose treatment status changes based on eligibility
DThe raw difference in outcomes between students just above and just below the cutoff
Fuzzy RDD estimates the LATE — the Local Average Treatment Effect for 'compliers' near the cutoff: students who take the scholarship when eligible but would not have received it otherwise. It is not the ATE for all students (too broad), not the effect of receiving a letter (that's the first stage), and not the raw outcome gap (that's the reduced form before correcting for incomplete takeup). The IV logic restricts identification to compliers near the threshold.
Question 2 Multiple Choice
What is the fuzzy RDD estimator equal to?
AThe jump in outcomes at the cutoff divided by the jump in treatment probability at the cutoff
BThe jump in treatment probability divided by the jump in outcomes at the cutoff
CThe regression coefficient on treatment status in a local linear regression, with no adjustment
DThe average difference in outcomes between all treated and untreated units near the cutoff
The fuzzy RDD estimator is the reduced-form discontinuity (jump in outcomes) divided by the first-stage discontinuity (jump in treatment probability) — exactly the IV ratio estimator applied locally at the threshold. When the first-stage jump equals 1 (sharp RDD), the denominator is 1 and the estimator collapses to the outcome jump alone, as expected.
Question 3 True / False
In fuzzy RDD, crossing the threshold serves as an instrumental variable for actual treatment receipt.
TTrue
FFalse
Answer: True
True. The threshold-crossing indicator satisfies IV conditions locally: it is strongly correlated with treatment (relevance — it causes a discontinuous jump in treatment probability), and it only affects outcomes through its effect on treatment take-up (exclusion — units just above and below the cutoff are otherwise comparable). The LATE is estimated via the IV ratio, not directly from the outcome discontinuity alone.
Question 4 True / False
Fuzzy RDD cannot be used when some units below the threshold still receive treatment, because this violates the design's identifying assumptions.
TTrue
FFalse
Answer: False
False. Some below-threshold units receiving treatment is precisely what defines fuzzy (as opposed to sharp) RDD. The design accommodates imperfect compliance — the threshold need only cause a discontinuous jump in the probability of treatment, not a jump from 0 to 1. The IV framework handles partial compliance by using threshold-crossing as an instrument and focusing estimation on compliers.
Question 5 Short Answer
Why does fuzzy RDD estimate the LATE rather than the ATE, and what types of units does this LATE cover?
Think about your answer, then reveal below.
Model answer: Fuzzy RDD estimates the LATE because the instrument (threshold-crossing) only generates variation in treatment for 'compliers' near the cutoff — units whose treatment status changes based on which side they fall. Always-takers (who receive treatment regardless) and never-takers (who don't, regardless) are unaffected by the instrument, so their treatment effects cannot be identified. The LATE is further restricted to units near the cutoff because that's the only region where the local natural experiment is credible.
This is IV logic applied locally. Just as standard IV estimates LATE for compliers in the instrument's region of variation, fuzzy RDD estimates LATE for compliers in the neighborhood of the cutoff. Sharp RDD is the special case where all units near the cutoff are compliers (treatment jumps from 0 to 1), so LATE = ATE at the cutoff.