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rd2d: Causal Inference in Boundary Discontinuity Designs

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

Abstract

Boundary discontinuity designs -- also known as Multi-Score Regression Discontinuity (RD) designs, with Geographic RD designs as a prominent example -- are often used in empirical research to learn about causal treatment effects along a continuous assignment boundary defined by a bivariate score. This article introduces the R package rd2d, which implements and extends the methodological results developed in Cattaneo, Titiunik and Yu (2025) for boundary discontinuity designs. The package employs local polynomial estimation and inference using either the bivariate score or a univariate distance-to-boundary metric. It features novel data-driven bandwidth selection procedures, and offers both pointwise and uniform estimation and inference along the assignment boundary. The numerical performance of the package is demonstrated through a simulation study.

Suggested Citation

  • Matias D. Cattaneo & Rocio Titiunik & Ruiqi Rae Yu, 2025. "rd2d: Causal Inference in Boundary Discontinuity Designs," Papers 2505.07989, arXiv.org, revised Jun 2025.
    • Handle: RePEc:arx:papers:2505.07989
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    References listed on IDEAS

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    1. Sebastian Calonico & Matias D. Cattaneo & Max H. Farrell, 2018. "On the Effect of Bias Estimation on Coverage Accuracy in Nonparametric Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 767-779, April.
    2. Keele, Luke J. & Titiunik, Rocío, 2015. "Geographic Boundaries as Regression Discontinuities," Political Analysis, Cambridge University Press, vol. 23(1), pages 127-155, January.
    3. Sebastian Calonico & Matias D. Cattaneo & Rocio Titiunik, 2014. "Robust Nonparametric Confidence Intervals for Regression‐Discontinuity Designs," Econometrica, Econometric Society, vol. 82, pages 2295-2326, November.
    4. Zeileis, Achim, 2004. "Econometric Computing with HC and HAC Covariance Matrix Estimators," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 11(i10).
    5. Papay, John P. & Willett, John B. & Murnane, Richard J., 2011. "Extending the regression-discontinuity approach to multiple assignment variables," Journal of Econometrics, Elsevier, vol. 161(2), pages 203-207, April.
    6. Hahn, Jinyong & Todd, Petra & Van der Klaauw, Wilbert, 2001. "Identification and Estimation of Treatment Effects with a Regression-Discontinuity Design," Econometrica, Econometric Society, vol. 69(1), pages 201-209, January.
    7. Jardim, Ekaterina & Long, Mark C. & Plotnick, Robert & Vigdor, Jacob & Wiles, Emma, 2024. "Local minimum wage laws, boundary discontinuity methods, and policy spillovers," Journal of Public Economics, Elsevier, vol. 234(C).
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