Local Randomization and Beyond for Regression Discontinuity Designs
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Regression discontinuity designs (RDDs) are a common quasi-experiment in economics, education, medicine, and statistics. While the most popular methodologies for analyzing RDDs are local polynomial regression methods, a recent strand of literature has developed a local randomization perspective for RDDs. A benefit of the local randomization perspective is that it avoids modeling assumptions, and instead places assumptions on the assignment mechanism for units near the cutoff in an RDD. However, most works have only considered completely randomized assignment mechanisms characterized by permutations of the treatment indicator, which posit that propensity scores are equal for all units near the cutoff. In this work, we extend the local randomization framework to allow for any assignment mechanism, such as Bernoulli trials and block randomization, where propensity scores are allowed to differ. We also develop exact randomization tests for covariate balance to test whether a particular assignment mechanism holds within an RDD. These tests allow for multiple testing corrections and can be used to select the largest window around the cutoff where a particular assignment mechanism is most plausible. Then, an analysis using this assignment mechanism can be conducted within that window. We apply our methodology to a fuzzy RDD that assesses the effects of financial aid on college dropout rates in Italy. We find that alternative assumptions on the assignment mechanism, such as block randomization, can lead to more precise causal inferences than the completely randomized assignment mechanism assumption that is common in the literature.
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