Misunderstandings About the Regression Discontinuity Design in the Study of Close Elections

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Abstract
Recently, the regression discontinuity (RD) design has become increasingly popular among social scientists. One prominent application is the study of close elections. We explicate several methodological misunderstandings widespread across disciplines by revisiting the controversy concerning the validity of RD design when applied to close elections. Although many researchers invoke the local or as-if-random assumption near the threshold, it is more stringent than the required continuity assumption. We show that this seemingly subtle point determines the appropriateness of various statistical methods and changes our understanding of how sorting invalidates the design. When multiple-testing problems are also addressed, we find that evidence for sorting in US House elections is substantially weaker and highly dependent on estimation methods. Finally, we caution that despite the temptation to improve the external validity, the extrapolation of RD estimates away from the threshold sacrifices the design's advantage in internal validity.

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