Minimum distance estimator for sharp regression discontinuity with multiple running variables

Abstract

In typical regression discontinuity, a running variable (or 'score') crosses a cutoff to determine a treatment. There are, however, many regression discontinuity cases where multiple scores have to cross all of their cutoffs to get treated. One approach to deal with these cases is one-dimensional localization using a single score on the subpopulation with all the other scores already crossing the cutoffs ("conditional one-dimensional localization approach, CON"), which is, however, inconsistent when partial effects are present which occur when some, but not all, scores cross their cutoffs. Another approach is multidimensional localization explicitly allowing for partial effects, which is, however, less efficient than CON due to more localizations than in CON. We propose a minimum distance estimator that is at least as efficient as CON, yet consistent even when partial effects are present. A simulation study demonstrates these characteristics of the minimum distance estimator. (C) 2017 Elsevier B.V. All rights reserved.