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

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.

KEYWORDS:

• Difference-in-discontinuity
• retention
• educational attainment
• regression discontinuity

JEL CLASSIFICATION:

• I00
• I20
• C20
• C10

Disclosure statement

No potential conflict of interest was reported by the author(s).

Supplementary material

Supplemental data for this article can be accessed online at https://doi.org/10.1080/13504851.2022.2089339

Notes

¹ Policy details appear in a full-length manuscript in which we analyse Louisiana’s grade retention policies without incorporating a fuzzy diff-in-disc design (see Larsen and Valant, 2022).

² Grade assignment depends on both maths and English language arts (ELA) scores (see Larsen and Valant, 2022). However, this letter focuses on students for whom the ELA threshold is decisive. While results are qualitatively similar at the maths threshold, the ELA threshold has more students near the threshold and therefore smaller standard errors.

Additional information

Funding

This work was supported by the Laura and John Arnold Foundation.