Assessing the external validity of election RD estimates : an investigation of the incumbency advantage

The electoral regression discontinuity (RD) design is popular because it provides an unbiased, design-based estimate of the incumbency advantage with few assumptions. However, as is well known, the RD estimate is "local": it only identifies the effect in hypothetical districts with an exactly 50-50 tie between the Democratic and Republican candidates, and does not speak to the size of the incumbency advantage away from this threshold. There is significant uncertainty over the effect of incumbency in districts away from this threshold. Indeed, in a survey of political scientists that we administered, roughly equal numbers of respondents predict the effect to be either larger, smaller, or the same in less competitive districts. In this paper, we follow the method proposed in Angrist and Rokkanen (2013), employing a validated Conditional Independence Assumption that, unlike in typical cases, generates directly testable implications in the context of the RD. This technique allows us to estimate the average effect of incumbency in districts in a window around the threshold as large as 15 percentage points -- i.e., elections in which the winning candidate secured as much as 57.5% of the two-party vote. We find that the incumbency advantage is no larger or smaller in these less competitive districts