Regression Discontinuity Design (RDD)

Lee (2008): election winners with a margin below 1% gain +8 pp re-election probability. The 50% threshold is a natural experiment. 4,000+ citations.

• **Education:** RDD at exam score cutoffs estimates the effect of admission to an elite university, tutoring, and support programs.
• **Social programs:** income thresholds for Medicaid and food stamps are natural RDD designs with hundreds of AER studies.
• **Tech:** A/B test with geographic cutoff (city >100k vs <=100k) -- fuzzy RDD design.

Sharp RDD

Lee (2008) used RDD to estimate the incumbency advantage: winners with a margin below 1% gain +8 percentage points in re-election probability. The 50% vote threshold is a perfect natural experiment. This design has been cited over 4,000 times.

Fuzzy RDD and Validity Checks

Angrist and Lavy (1999) applied Fuzzy RDD to estimate class-size effects: Maimonides' rule (max 40 students) is violated in roughly 40% of cases -- treatment is probabilistic, not deterministic. An IV approach using the threshold as instrument yielded an estimate of -5 test points per +10 students.

Key ideas

• **Sharp RDD:** D_i=1[X_i>=c]. Effect tau = right limit - left limit of E[Y|X=x] at c. Estimated via local linear regression.
• **Fuzzy RDD:** P(D=1|X) jumps at c. Implemented as IV with Z=1[X>=c] as instrument.
• **Validity:** McCrary test (density continuity of X) and covariate balance at c. Violations signal manipulation.