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Manipulation & RD Validity
Bunching at a pass mark: density test, covariate jump, biased RD and the donut fix.
Day 77: RD Validity: Density Tests & Covariate Balancedensity test z
6.2
214 vs 365 in adjacent bins
covariate jump
0.379
RD estimate
3.35
truth 3.00
observations used
3,663
Students just below a pass mark whose families are better resourced (positive covariate) get their scores pushed just above it. The histogram shows the bunching; the density z-statistic compares the two bins next to the cutoff; the covariate jumps; and the RD estimate (true effect 3) is biased upward. A donut that drops observations near the cutoff removes most of the bias.