Jens Hainmueller refers to a paper by David Lee, “Randomized experiments from non-random selection in U.S. House elections.” In the paper, Lee uses a regression discontinuity analysis to compare election outcomes in districts that, two years earlier, were either barely won by Democrats or barely won by Republicans. The difference between these districts in the next election can be identified as the causal effect of the incumbent party–that is, the difference it makes, having a Democrat or a Republican running, in otherwise nearly-identical districts.

Lee’s analysis is fine, and he has a nice picture on page 33 of his paper showing his model and how his estimate compares to that of Gelman and King (1990). However, he is wrong to label what he is estimating as “the electoral advantage to incumbency.” He is more precise in Section 3.5 and Appendix B of his paper, when he refers to his estimate of “the incumbent party advantage.” The difference is, as Lee makes clear in his paper, that in a hypothetical world in which incumbency itself were worth nothing–in which a Democrat in an open seat would run as well as a Democrat who is an incumbent–you could still have a nonzero incumbent *party* advantage, if voters preferred to stick with the same party they had before. So I agree with the message of Lee, that both these things–the incumbent party advantage and the incumbency advantage–are interesting. As Gary and I discuss on page 1153 in our 1990 paper, yet another quantity of interest is the personal incumbency advantage, a quantity that has also been studied by Cox, Katz, Ansolabehere, and others.

On a related point, I think Lee is misleading when he says (on page 28) that “the regression discontinuity estimates cannot be recovered from a Gelman-King type analysis.” I mean, yes, we use a linear model on vote proportions, and he has a model of probabilities. But we do have an incumbent party effect–it is the coefficient of the incumbent party indicator P_2 in our model–so we did in fact estimate this (within the context of a linear model).

One other, more technical issue: there is a lot of information in the actual vote shares received by the candidates, which is why political scientists typically model these directly. Modeling vote shares gives you the efficiency to get separate estimates for each election year and thus study time trends. I understand the appeal of simply looking at winning and losing, but there is much to be learned by studying vote shares.

In summary, I like Lee’s paper, and it’s good to see connections between different social sciences. For the particular example of incumbency advantage, I’d have more trust in simple regression estimators, separating the effects of incumbent party (P_i) and incumbency (I_i) as discussed in our 1990 paper and in Lee’s Appendix B. Or, to go in new directions, using the Bayesian method of Gelman and Huang (2006, to appear). But it can’t hurt to have new methods, and for other problems where the linear model doesn’t work so well, I could see Lee’s method providing a real advance.