Estimating the Causal Effect of Incumbency 

 Since the early seventies, political scientists have been interested in the causal effects of incumbency, i.e. the electoral gain to being the incumbent in a district, relative to not being the incumbent. Unfortunately, these two potential outcomes are never observed simultaneously. Even worse, the inferential problem is compounded by selection on unobservables. Estimates are vulnerable to hidden bias because there probably is a lot of unobserved stuff that’s correlated with both incumbency and electoral success (such as candidate quality, etc.) that you cannot condition on. To identify the incumbency advantage, estimates had to rely on rather strong assumptions. In a recent paper entitled " Randomized Experiments from Non-random Selection in U.S. House Elections ", economist  David Lee  took an innovative whack at this issue. He employs a regression discontinuity design (RDD) that tackles the hidden bias problem based on a fairly weak assumption. 
 


 Somewhat ironically, this technique is rather old. The earliest published example dates back to Thistlethwaite and Campbell (1960). They examine the effect of scholarships on career outcomes by comparing students just above and below a threshold for test scores that determines whether students were granted the award. The underlying idea is that in the close neighborhood of the threshold, assignment to treatment is as good as random. Accordingly, unlucky students that just missed the threshold are virtually identical to lucky ones who scored just above the cutoff value. This provides a suitable counterfactual for causal inference. Take a look at the explanatory graph for the situation of a  positive causal effect  and the situation of  no effect . 

 See the parallel to the incumbency problem? Basically, the RDD works in settings in which assignment to treatment changes discontinuously as a function of one or more underlying variables. Lee argues that this is exactly what happens in the case of (party) incumbency. In a two party system, you become the incumbent if you exceed the (sharp) threshold of 50 percent of vote share. Now assume that parties usually do not exert perfect control over their observed vote share (observed vote share = true vote share + error term with a continuous density). The closer the race, the more likely that random factors determine who ends up winning (just imagine the weather had been different on election day).  

 Incumbents that did barely win the previous election are thus virtually identical to non-incumbents that did barely lose. Lee shows that as long as the covariate that determines assignment to treatment includes a random component with a continuous density, treatment status close to the threshold is (in the limit) statistically randomized. The plausibility of this identification assumption is a function of the degree to which parties are able to sort around the threshold. And the cool thing is that you can even test whether this identifying assumption holds - at least for the observed confounders – by using common covariate balance tests.  

 There is no free lunch, of course. One potential limitation of the RDD is that it identifies the incumbency effect only for close elections. However, one could argue that when looking at the incumbency advantage, marginal districts are precisely the subpopulation of interest. It is only in close elections that the incumbency advantage is likely to make any difference. Another potential limitation is that the RDD identifies the effect of “party? incumbency, which is not directly comparable to earlier estimates of incumbency advantage that focused on “legislator? incumbency advantage. Party incumbency subsumes legislator incumbency, but also contains a seperate party effect and there is no chance to disentangle the two. So surley, the RDD design is no paneca. Yet, it can be used to draw causal inferences from observational data based on weaker assumptions that previously employed in this literature.  

 The Lee paper has led to a surge in the use of the RDD in political science. Incumbency effects have been re-estimated not only for US House elections, but also for other countries as diverse as  India ,  Great Britain , and  Germany . It has also been used to study split-party delegations in the  Senate . There may be other political settings in which the RDD framework can be fruitfully applied. Think about it - before economists do :-)