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Analyzing Regression-Discontinuity Designs with Multiple Assignment Variables: A Comparative Study of Four Estimation Methods (WP-10-02)

Vivian C. Wong, Peter M. Steiner, and Thomas D. Cook

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 multi-dimensional frontier using multiple assignment variables and cutoffs. This paper introduces the multivariate regression-discontinuity design (MRDD). For a MRDD with two assignment variables, we 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. The paper discusses four methods for estimating MRDD treatment effects—the frontier, centering, univariate, and instrumental variable approaches—and compares their relative performance in a Monte Carlo simulation study under different scenarios. We find that given correct model specifications, all four approaches estimate treatment effects without bias, but the instrumental variable approach has severe limitations in terms of more stringent required assumptions and reduced efficiency.

Vivian C. Wong, PhD Student, Institute for Policy Research, Northwestern University
Peter M. Steiner, Senior Research Associate, Institute for Policy Research, Northwestern University

Thomas D. Cook, Professor of Sociology, Psychology, Education and Social Policy, Institute for Policy Research, Northwestern University

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