Using Regression Discontinuity to Uncover the Personal Incumbency Advantage Available to Purchase

We study the conditions under which a regression discontinuity (RD) design can be used to recover the personal incumbency advantage, a quantity that has long been of interest to political scientists. We offer an expanded interpretation of the RD design that allows us to back out unbiased estimates of this quantity by focusing on open seats — elections with no incumbent running. Our focus on open seats avoids including in the personal incumbency advantage estimate the spurious advantage that stems from incumbents’ higher than average quality — a result of electoral selection. A central result of our model is that the RD design double-counts the personal incumbency advantage because each of the two groups of districts compared in the RD estimand has an incumbent running for reelection at the time the outcome is measured. We provide a brief empirical illustration of our model that analyzes northern open-seat U.S. House elections between 1968 and 2008, and we also discuss how this setup can be used to study incumbent races, where the required assumptions are more complex. A version of our model in its full generality — and a discussion of the assumptions it requires — is presented in the Supplemental Appendix.