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Estimation and Inference in Boundary Discontinuity Designs: Distance-Based Methods

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  • Matias D. Cattaneo
  • Rocio Titiunik
  • Ruiqi Rae Yu

Abstract

We study the statistical properties of nonparametric distance-based (isotropic) local polynomial regression estimators of the boundary average treatment effect curve, a key causal functional parameter capturing heterogeneous treatment effects in boundary discontinuity designs. We present necessary and/or sufficient conditions for identification, estimation, and inference in large samples, both pointwise and uniformly along the boundary. Our theoretical results highlight the crucial role played by the ``regularity'' of the boundary (a one-dimensional manifold) over which identification, estimation, and inference are conducted. Our methods are illustrated with simulated data. Companion general-purpose software is provided.

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  • Matias D. Cattaneo & Rocio Titiunik & Ruiqi Rae Yu, 2025. "Estimation and Inference in Boundary Discontinuity Designs: Distance-Based Methods," Papers 2510.26051, arXiv.org.
    • Handle: RePEc:arx:papers:2510.26051
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    References listed on IDEAS

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    1. Victor Chernozhukov & Denis Chetverikov & Kengo Kato & Yuta Koike, 2019. "Improved Central Limit Theorem and bootstrap approximations in high dimensions," Papers 1912.10529, arXiv.org, revised May 2022.
    2. Matias D. Cattaneo & Rocio Titiunik & Ruiqi Rae Yu, 2025. "Estimation and Inference in Boundary Discontinuity Designs: Distance-Based Methods," Papers 2510.26051, arXiv.org.
    3. Matias D. Cattaneo & Rocio Titiunik & Ruiqi Rae Yu, 2025. "Estimation and Inference in Boundary Discontinuity Designs: Location-Based Methods," Papers 2505.05670, arXiv.org, revised Oct 2025.
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    Cited by:

    1. Xiaohong Chen & Zhenxiao Chen & Wayne Yuan Gao, 2025. "Inference on Welfare and Value Functionals under Optimal Treatment Assignment," Papers 2510.25607, arXiv.org.
    2. Matias D. Cattaneo & Rocio Titiunik & Ruiqi Rae Yu, 2025. "Estimation and Inference in Boundary Discontinuity Designs: Distance-Based Methods," Papers 2510.26051, arXiv.org.

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