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

Author

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

Abstract

Boundary discontinuity designs are used to learn about causal treatment effects along a continuous assignment boundary that splits units into control and treatment groups according to a bivariate location score. We analyze location-based local polynomial treatment effect estimators that directly employ the bivariate score of each unit. We develop pointwise and uniform estimation and inference methods for the \textit{Boundary Average Treatment Effect Curve} (BATEC), as well as for two aggregated causal parameters: the \textit{Weighted Boundary Average Treatment Effect} (WBATE) and the \textit{Largest Boundary Average Treatment Effect} (LBATE). Our results cover both sharp and fuzzy (imperfect compliance) designs. We illustrate the methods with an empirical application, and provide companion general-purpose software. The supplemental appendix includes additional substantive theoretical results, methodological details, and simulation evidence.

Suggested Citation

  • 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 May 2026.
    • Handle: RePEc:arx:papers:2505.05670
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    Cited by:

    1. Erik Ortiz-Covarrubias, 2026. "Legacies of the Reformation: How Religious Identity Shapes Political Preferences in Germany," Working Papers wp2026_2604, CEMFI.
    2. Philipp Alexander Schwarz & Oliver Schacht & Sven Klaassen & Johannes Oberpriller & Martin Spindler, 2025. "Effect Identification and Unit Categorization in the Multi-Score Regression Discontinuity Design with Application to LED Manufacturing," Papers 2508.15692, arXiv.org, revised Oct 2025.
    3. Matias D. Cattaneo & Rocio Titiunik & Ruiqi Rae Yu, 2025. "Estimation and Inference in Boundary Discontinuity Designs: Distance-Based Methods," Papers 2510.26051, arXiv.org, revised May 2026.
    4. Artem Samiahulin, 2026. "Global Testing in Multivariate Regression Discontinuity Designs," Papers 2602.03819, arXiv.org.
    5. Li, Zikai, 2025. "Unrequited Love: Estimating the Electoral Effect of a Place-based Green Subsidy with a 2D Regression Discontinuity Design," SocArXiv s4nje_v1, Center for Open Science.
    6. Jiang, Weiwei & Zhu, Rong J.B., 2025. "Identification in two-score regression discontinuity designs with partial compliance," Economics Letters, Elsevier, vol. 257(C).

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