Can Close Election Regression Discontinuity Designs Identify Effects of Winning Politician Characteristics?

Politician characteristic regression discontinuity (PCRD) designs leveraging close elections are widely used to isolate effects of an elected politician characteristic on downstream outcomes. Unlike standard regression discontinuity designs, treatment is defined by a predetermined characteristic that could affect a politician's victory margin. I prove that, by conditioning on politicians who win close elections, PCRD estimators identify the effect of the specific characteristic of interest and all compensating differentials—candidate-level characteristics that ensure elections remain close between candidates who differ in the characteristic of interest. Avoiding this asymptotic bias generally requires assuming either that the characteristic of interest does not affect candidate vote shares or that no compensating differential affects the outcome. Because theories of voting behavior suggest that neither strong assumption usually holds, I further analyze the implications for interpreting continuity tests and consider if and how covariate adjustment, bounding, and recharacterizing treatment can mitigate the posttreatment bias afflicting PCRD designs.