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

Author

Listed:
  • Matias D. Cattaneo

    (Rae)

  • Rocio Titiunik

    (Rae)

  • 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.

Suggested Citation

  • Matias D. Cattaneo & Rocio Titiunik & Ruiqi & 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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    File URL: http://arxiv.org/pdf/2510.26051
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