We propose a novel estimator for use in a fuzzy regression discontinuity setting. The estimator can be thought of as extrapolating the traditional fuzzy regression discontinuity estimate or as an observational study that adjusts for endogenous selection into treatment using information at the discontinuity. We show that it can be motivated as being the least complex model consistent with the data or as an estimator that is preferable to both a traditional regression discontinuity design and an observational study. We further show theoretically that no other estimators consistently generate better estimates than our proposed estimator. We then use this approach to examine the effects of early grade retention beyond the compliers around the retention cutoff. We show that the benefits of early grade retention policies are larger for students with lower baseline achievement and smaller for low-performing students who are exempt from retention. These findings imply that (1) the benefits of early grade retention policies are larger than have been estimated using traditional fuzzy regression discontinuity designs and (2) retaining additional students would have a limited effect on student outcomes.
regression discontinuity designs; grade retention policies
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