Fuzzy difference-in-discontinuities when the confounding variation is sharp: evidence from grade retention policies

Matthew Larsen and Jon Valant

Applied Economics Letters, 2023, vol. 30, issue 15, 2009-2013

Abstract: This letter examines a fuzzy difference-in-discontinuity design where the primary policy of interest has imperfect compliance but confounding variation has perfect compliance. After proposing the estimator, we examine an application in education policy where test score cut-offs are used to determine grade assignment with imperfect compliance but performance labels with perfect compliance. We find that students who are not retained in 8th grade are more likely to graduate high school and attend college. Furthermore, after accounting for the effect of confounding performance labels, estimates are even more positive. Notably, we also find that our fuzzy difference-in-discontinuity estimates are quite noisy, suggesting that applications of the estimator may be limited to settings with many observations near the threshold. This estimator may be useful in education research and other settings where scores are used to both assign treatment and label individuals.

Date: 2023
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DOI: 10.1080/13504851.2022.2089339

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