A causal method for treatments assigned by a cutoff on a score, such as a scholarship for test scores above a threshold. Units just above and just below the cutoff are nearly identical, so a jump in the outcome right at the cutoff estimates the treatment's effect there.
Card 1 of 276. Answer: A causal method for treatments assigned by a cutoff on a score, such as a scholarship for test scores above a threshold. Units just above and just below the cutoff are nearly identical, so a jump in the outcome right at the cutoff estimates the treatment's effect there.
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Fit the relationship between the score and the outcome separately on each side of the cutoff, usually within a narrow bandwidth, and measure the gap where the two fits meet the threshold. In a sharp design everyone above the cutoff is treated; in a fuzzy design the cutoff only raises the chance of treatment, and the jump in treatment is used as an instrument. Donald Thistlethwaite and Donald Campbell introduced the design in 1960 to study the effect of merit awards on students.
Example: customers who spend $500 or more in a year get a loyalty tier. Fitting next-year spend against this year's spend, the line from the left predicts $520 at $500, and the line from the right starts at $560. The estimated effect of the tier, for customers near the cutoff, is $40.
Interview follow-ups: the estimate is local, so it may not hold for customers far from the cutoff; the design breaks if people can manipulate their score to land just above it, which a jump in the number of units at the cutoff reveals (McCrary's density test); and results should be checked across bandwidths.
