Regression Discontinuity Designs With Multiple Rating-Score Variables

In the absence of a randomized control trial, regression discontinuity (RD) designs can produce plausible estimates of the treatment effect on an outcome for individuals near a cutoff score. In the standard RD design, individuals with rating scores higher than some exogenously determined cutoff score are assigned to one treatment condition; those with rating scores below the cutoff score are assigned to an alternate treatment condition. Many education policies, however, assign treatment status on the basis of more than one rating-score dimension. We refer to this class of RD designs as "multiple rating score regression discontinuity" (MRSRD) designs. In this paper, we discuss five different approaches to estimating treatment effects using MRSRD designs (response surface RD; frontier RD; fuzzy frontier RD; distance-based RD; and binding-score RD). We discuss differences among them in terms of their estimands, applications, statistical power, and potential extensions for studying heterogeneity of treatment effects.