Matias D. Cattaneo, Rocio Titiunik, Ruiqi Rae Yu
arXiv 8 May 2025 · Econometrics
arXiv:2505.05670 · PDF · Extracted main text
Boundary Discontinuity Designs are used to learn about treatment effects along a continuous boundary that splits units into control and treatment groups according to a bivariate score variable. These research designs are also called Multi-Score Regression Discontinuity Designs, a leading special case being Geographic Regression Discontinuity Designs. We study the statistical properties of commonly used local polynomial treatment effects estimators along the continuous treatment assignment boundary. We consider two distinct approaches: one based explicitly on the bivariate score variable for each unit, and the other based on their univariate distance to the boundary. For each approach, we present pointwise and uniform estimation and inference methods for the treatment effect function over the assignment boundary. Notably, we show that methods based on univariate distance to the boundary exhibit an irreducible large misspecification bias when the assignment boundary has kinks or other irregularities, making the distance-based approach unsuitable for empirical work in those settings. In contrast, methods based on the bivariate score variable do not suffer from that drawback. We illustrate our methods with an empirical application. Companion general-purpose software is provided.
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| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Matias D. Cattaneo and Ruiqi (Rae) Yu (2025) Strong approximations for empirical processes indexed by lipschitz functions self | 1.000 | 6 | 4 | 100% |
| 2 | Aad W. van der Vaart and Jon A. Wellner (1996) Weak Convergence and Empirical Processes | 0.874 | 8 | 2 | 100% |
| 3 | Victor Chernozhukov, Denis Chetverikov, and Kengo Kato Gaussian approximation of suprema of empirical processes | 0.644 | 4 | 1 | 100% |
| 4 | Richard M Dudley (2014) Uniform central limit theorems, volume 142 | 0.644 | 2 | 2 | 100% |
| 5 | Matias D. Cattaneo, Rajita Chandak, Michael Jansson, and Xinwei Ma (2024) Boundary adaptive local polynomial conditional density estimators self | 0.511 | 2 | 1 | 100% |
| 6 | Victor Chernozhukov, Denis Chetverikov, and Kengo Kato Anti-concentration and honest, adaptive confidence bands | 0.511 | 2 | 1 | 100% |
| 7 | Evarist Giné and Richard Nickl (2016) Mathematical Foundations of Infinite-dimensional Statistical Models | 0.405 | 1 | 1 | 100% |
| 8 | Victor Chernozhuokov, Denis Chetverikov, Kengo Kato, and Yuta Koike (2022) Improved central limit theorem and bootstrap approximations in high dimensions | 0.405 | 1 | 1 | 100% |
| 9 | Herbert Federer (2014) Geometric measure theory | 0.405 | 1 | 1 | 100% |
| 10 | G.B. Folland (2002) Advanced Calculus | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 11 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | rd2d: Causal Inference in Boundary Discontinuity Designs | 1.000 | 11 | 5 |
| 2 | Local-Polynomial Estimation for Multivariate Regression Discontinuity Designs | 1.000 | 5 | 3 |
| 3 | A Practical Introduction to Regression Discontinuity Designs: Extensions | 0.511 | 2 | 1 |
| 4 | A Guide to Regression Discontinuity Designs in Medical Applications | 0.405 | 1 | 1 |