A Regression Discontinuity Design for Studying Divided Government

The regression discontinuity design (RDD) is a valuable tool for identifying causal effects with observational data. However, applying the traditional electoral RDD to the study of divided government is challenging. Because assignment to treatment in this case is the result of elections to multiple institutions, there is no obvious single forcing variable. Here, we use simulations in which we apply shocks to real-world election results in order to generate two measures of the likelihood of divided government, both of which can be used for causal analysis. The first captures the electoral distance to divided government and can easily be utilized in conjunction with the standard sharp RDD toolkit. The second is a simulated probability of divided government. This measure does not easily fit into a sharp RDD framework, so we develop a probability restricted design (PRD) which relies upon the underlying logic of an RDD. This design incorporates common regression techniques but limits the sample to those observations for which assignment to treatment approaches “as-if random.” To illustrate both of our approaches, we reevaluate the link between divided government and the size of budget deficits.