Local-Polynomial Estimation for Multivariate Regression Discontinuity Designs

Author:

Masayuki Sawada, Takuya Ishihara, Daisuke Kurisu, Yasumasa Matsuda

Keyword:

Economics, Econometrics, Econometrics (econ.EM), Applications (stat.AP), Methodology (stat.ME)

journal:

date:

2024-02-14 00:00:00

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 distance running variable is incompatible with the assumption for asymptotic validity. 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 (including its absence) of the treatment effect that is hidden in the original estimates.

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