The regression discontinuity (RD) design is popular because it provides a design-based estimate of the incumbency advantage. However, the RD estimate is “local”: it only identifies the effect in hypothetical elections with a 50-50 tie between the Democratic and Republican candidates. There is significant uncertainty and disagreement over the incumbency effect in safer districts away from this threshold. Indeed, mirroring the competing arguments in the theoretical literature, a survey of political scientists reveals that roughly equal numbers of respondents predict the effect to be either larger, smaller, or the same in less competitive districts. We employ a new method based on a validated conditional independence assumption that allows us to estimate the effect of incumbency in districts in a window around the threshold as large as 15 percentage points — that is, 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 cases.