Estimating Unknown Cut-points in Regression Discontinuity and Kink Designs

Regression discontinuity designs (RDD) and regression kink designs (RKD) are popular identification strategies across the social sciences. The relatively weak assumptions required for identifying a causal effect with RDD/RKDs make the designs attractive quasi-experimental methods for causal inference. One limitation of RDD/RKDs is that they rely on an exogenously given and previously known treatment rule. To overcome this limitation, economists (Porter & Yu 2015, Hansen 2017, Boehnke & Bonaldi 2019, and Tanu 2020) and computer scientists (Herlands et al. 2018) have begun to develop methods and tests that can find unknown discontinuities. However, these tests are either largely theoretically focused, computationally intensive, inconvenient to implement, or otherwise do not fit the specific needs of applied political scientists. Accordingly, this paper presents a novel, more flexible, and extremely easy to implement approach to estimate unknown cut-points in both RDDs and RKDs. It is the first method that can detect unknown thresholds in both RDDs and RKDs. I call this method the unknown cut-point regression discontinuity/kink design (UCRDD/UCRKD). It works by uniformly dividing an assignment variable into quantiles to create a distribution of “candidate” cut-points. Each candidate threshold is then tested in a RDD model (Imbens & Kalyanaraman 2012) to find the “best” cut-point, the cut-point that has the largest substantive effect and highest degree of statistical significance. Researchers can use UCRDD/UCRKD to find “tipping-points” in behavior; to determine obscured or non-public policy criteria; and as a diagnostic tool to determine if there are other significant thresholds in their traditional RDD/RKD. In the application section, I apply UCRKD to assess how to define the concept of a minority district and to estimate the treatment effect of minority districts on electoral support for minority candidates.