Local-Polynomial Estimation for Multivariate Regression Discontinuity Designs

Masayuki Sawada, Takuya Ishihara, Daisuke Kurisu and Yasumasa Matsuda

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Abstract: We introduce a multivariate local-linear estimator for multivariate regression discontinuity designs in which treatment is assigned by crossing a boundary in the space of running variables. The dominant approach uses the Euclidean distance from a boundary point as the scalar running variable; hence, multivariate designs are handled as uni-variate designs. However, the bandwidth selection with the distance running variable is suboptimal and inefficient for the underlying multivariate problem. We handle multivariate designs as multivariate. In this study, we develop a novel asymptotic normality for multivariate local-polynomial estimators. Our estimator is asymptotically valid and can capture heterogeneous treatment effects over the boundary. We demonstrate the effectiveness of our estimator through numerical simulations. Our empirical illustration of a Colombian scholarship study reveals a richer heterogeneity of the treatment effect that is hidden in the original estimates.

Date: 2024-02, Revised 2025-05
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