Federico A. Bugni, Federico Crippa, Daniel Restrepo
arXiv 31 Aug 2026 · Econometrics
arXiv:2609.00350 · PDF · Extracted main text
We propose the first manipulation test designed for boundary discontinuity designs (BDDs) with general boundary shapes. A BDD is a multidimensional extension of the regression discontinuity design (RDD) in which treatment assignment is determined by whether the multidimensional running variable crosses a lower-dimensional boundary set. The test avoids multivariate density estimation and builds on the observation that, in the absence of manipulation, observations near the boundary should be approximately evenly split between treatment and control within arbitrary groups defined by their projections onto the boundary. We test this implication using a collection of binomial balance tests on observations near the boundary, with groups formed by k-means clustering. We establish the asymptotic validity of the test under suitable regularity conditions. We also evaluate finite-sample performance through Monte Carlo simulations and illustrate the test in three empirical applications.
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| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Maggi, F (2012) Sets of finite perimeter and geometric variational problems: an introduction to Geometric Measure Theory | 1.000 | 12 | 3 | 100% |
| 2 | Dai, T., S. Jiang, X. Liu, and A. Sun (2022) The effects of a hypertension diagnosis on health behaviors: A two-dimensional regression discontinuity analysis | 1.000 | 11 | 4 | 100% |
| 3 | Lee, D. S (2008) Randomized experiments from non-random selection in U.S. House elections | 1.000 | 11 | 3 | 100% |
| 4 | McCrary, J (2008) Manipulation of the Running Variable in the Regression Discontinuity Design: A Density Test | 1.000 | 9 | 3 | 100% |
| 5 | Bugni, F. A. and I. A. Canay (2021) Testing Continuity of a Density via g-order statistics in the Regression Discontinuity Design self | 1.000 | 7 | 3 | 100% |
| 6 | Hirsch, M. W (2012) Differential topology | 1.000 | 5 | 3 | 100% |
| 7 | Federer, H (1996) Geometric Measure Theory | 0.928 | 4 | 3 | 100% |
| 8 | Keele, L. J. and R. Titiunik (2015) Geographic Boundaries as Regression Discontinuities | 0.874 | 9 | 2 | 100% |
| 9 | Elacqua, G., D. Hincapié, and M. Martńez (2024) The Effects of School Accountability on Teachers in Public and Private Schools: Evidence from Chile | 0.874 | 8 | 2 | 100% |
| 10 | Kauffman, E. and R.-D. Reiss (1992) On Conditional Distributions of Nearest Neighbors | 0.811 | 4 | 2 | 100% |
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