Non-monotonic Selection Issues in Electoral Regression Discontinuity Designs

The Regression Discontinuity Design (RDD) has become a popular method for program evaluation in recent years. While it is compelling in its simplicity and requires little in terms of a priori assumptions, it is vulnerable to bias introduced by self-selection into treatment or control group. The purpose of this article is to discuss the issue of non-monotonic self-selection, by which similar numbers of individuals select into and out of treatment simultaneously. This kind of selection has not been discussed in detail so far in the literature, and can be hard to detect with the commonly used methods for data-driven RDD specification testing. The focus of this article lies on selection in the context of close elections, since those are popular natural experiments for RDD applications, and because in this context the issue of non-monotonic selection is rarely considered in practise. I will present a slightly modified approach to specification testing, designed to detect non-monotonic self selection and based on the density test by McCrary (2008). In order to demonstrate how RDDs can be affected by the issue, two existing RDD applications are analysed with respect to non-monotonic sorting. In the first, this article follows up and expands on the remarks made by Caughey & Sekhon (2011) about selection issues in the well known RDD application by D. Lee (2008). The second application is based on the Mexican mayoral election RDD by Dell (2015).