Turns out RD designs may not be so hot in studying electoral effects:
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 thresholg 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.
The paper is here (PDF).
H/T Monkey Cage Blog.