Andrew Eggers, Olle Folke, Anthony Fowler, Jens Hainmueller, Andrew Hall, and Jim Snyder write:
Many papers use regression discontinuity (RD) designs that exploit “close” election outcomes in order to identify the effects of election results on various political and economic outcomes of interest. Several recent papers critique the use of RD designs based on close elections because of the potential for imbalance near the threshold that distinguishes winners from losers. In particular, for U.S. House elections during the post-war period, lagged variables such as incumbency status and previous vote share are significantly correlated with victory even in very close elections. This type of sorting naturally raises doubts about the key RD assumption that the assignment of treatment around the threshold is quasi-random. In this paper, we examine whether similar sorting occurs in other electoral settings, including the U.S. House in other time periods, statewide, state legislative, and mayoral races in the U.S., and national and/or local elections in a variety of other countries, including the U.K., Canada, Germany, France, Australia, India, and Brazil. No other case exhibits sorting. Evidently, the U.S. House during the post-war period is an anomaly.
In case you got lost somewhere during that paragraph, here it is again:
Across more than 40,000 closely contested elections in many different electoral settings, we find no systematic evidence of sorting around the electoral threshold. Conditional on being in a very close election, incumbents are no better at winning than challengers. . . . the sorting and imbalance that has been discovered in the U.S. House is most likely a statistical fluke . . . Recent concerns about the validity of electoral RD designs appear overblown, as we find no evidence that the underlying assumptions are categorically unsound.
Got it? It makes sense to me.