Analyzing Regression-Discontinuity Designs With Multiple Assignment Variables: A Comparative Study Of Four Estimation Methods

In a traditional Regression-Discontinuity Design (RDD), units are assigned to treatment on the basis of a cutoff score and a continuous assignment variable. The treatment effect is measured at a single cutoff location along the assignment variable. A more flexible conceptualization of RDD, however, allows researchers to examine effects along a multidimensional frontier using multiple assignment variables and cutoffs. This paper introduces the Multivariate Regression-Discontinuity Design (MRDD). For a MRDD with two assignment variables, the authors show that the overall treatment effect at the cutoff frontier can be decomposed into a weighted average of two univariate RDD effects, and that the weights depend on the scaling of the assignment variables.