Estimating Global Incumbency Effects Using an Instrumental Variable

In this paper, we propose a method that enables researchers to estimate the treatment effect averaged over an entire population using an instrumental variable (IV) in a setting where a running variable fully determines the treatment. We apply our method to the estimation of the incumbency effect in elections. We exploit that incumbency is wholly determined by a candidate's vote margins and show that it is possible to identify three latent groups: compliers, always-takers, and never-takers. Our approach allows us to estimate the incumbency effect for the compliers and the other latent groups. In addition, we show that it is possible to test for the IV exclusion restriction using the always- and never-takers. Our results also suggest that the exclusion restriction can be violated even when the IV is random