1. Explaining voter turnout: A review of aggregate-level research
2. In addition, a number of works have cited Lee (2008) as an exemplary application of the RD design, and many of them use the data set from the paper to illustrate the design or demonstrate particular techniques (e.g., Imbens and Lemieux 2008; McCrary 2008; Angrist and Pischke 2009; Imbens and Kalyanaraman 2009; and Lee and Lemieux, 2010). By contrast, Snyder (2005) in an unpublished working paper provides empirical evidence that bare winners and losers are not comparable. He examines congressional elections in which an incumbent is running for reelection.
3. One reasonable question that might arise in response to this characterization is whether the “fuzzy” RD (FRD) design should be applied to U. S. House elections instead of the “sharp” design used by Lee (see Imbens and Lemieux 2008 and Lee and Lemieux 2010 for reviews). In the FRD design, treatment assignment is not fully determined by whether a unit's score on the assignment variable is above the threshold. Rather, treatment assignment is a joint function of this exogenous component and a component that may be endogenous to the outcome of interest. The local average effect of treatment on compliers can be estimated by using the threshold as an instrument. The case of U. S. House elections is superficially similar in that there is substantial but not perfect sorting at the cut-point, indicating that the assignment variable is manipulable but at least some elections may be randomly decided. The obstacle to using the FRD design in this context is that the unmanipulated (random) component of the assignment variable cannot be observed separately from the systematic component and thus cannot be used as an instrument.
4. See Fig. 1 in online Appendix C for histograms of Democratic Margin t broken down by incumbent party. Following Lee (2008), we define Democratic Margin as the difference between the main Democratic candidate's vote total and that of her nearest opponent, as a percentage of all votes cast.
5. A randomized experiment comparing random and cutoff-based assignment.