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Boundary Discontinuity Designs: Theory and Practice

Author

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

Abstract

The boundary discontinuity (BD) design is a non-experimental method for identifying causal effects that exploits a thresholding rule based on a bivariate score and a boundary curve. This widely used method generalizes the univariate regression discontinuity design but introduces unique challenges arising from its multidimensional nature. We synthesize over 80 empirical papers that use the BD design, tracing the method's application from its formative stages to its implementation in modern research. We also overview ongoing theoretical and methodological research on identification, estimation, and inference for BD designs employing local polynomial regression, and offer recommendations for practice.

Suggested Citation

  • Matias D. Cattaneo & Rocio Titiunik & Ruiqi Rae Yu, 2025. "Boundary Discontinuity Designs: Theory and Practice," Papers 2511.06474, arXiv.org, revised Feb 2026.
    • Handle: RePEc:arx:papers:2511.06474
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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. Ou, Dongshu, 2010. "To leave or not to leave? A regression discontinuity analysis of the impact of failing the high school exit exam," Economics of Education Review, Elsevier, vol. 29(2), pages 171-186, April.
    3. Angela Zheng, 2022. "The Valuation of Local School Quality under School Choice," American Economic Journal: Economic Policy, American Economic Association, vol. 14(2), pages 509-537, May.
    4. Connan Snider & Jonathan W. Williams, 2015. "Barriers to Entry in the Airline Industry: A Multidimensional Regression-Discontinuity Analysis of AIR-21," The Review of Economics and Statistics, MIT Press, vol. 97(5), pages 1002-1022, December.
    5. Salti, Nisreen & Chaaban, Jad & Moussa, Wael & Irani, Alexandra & Al Mokdad, Rima & Jamaluddine, Zeina & Ghattas, Hala, 2022. "The impact of cash transfers on Syrian refugees in Lebanon: Evidence from a multidimensional regression discontinuity design," Journal of Development Economics, Elsevier, vol. 155(C).
    6. Henn, Soeren J., 2025. "Complements or Substitutes? How Institutional Arrangements Bind Traditional Authorities and the State in Africa – ERRATUM," American Political Science Review, Cambridge University Press, vol. 119(4), pages 2028-2028, November.
    7. Brent J. Evans, 2017. "SMART Money: Do Financial Incentives Encourage College Students to Study Science?," Education Finance and Policy, MIT Press, vol. 12(3), pages 342-368, Summer.
    8. Patrick Bayer & Fernando Ferreira & Robert McMillan, 2007. "A Unified Framework for Measuring Preferences for Schools and Neighborhoods," Journal of Political Economy, University of Chicago Press, vol. 115(4), pages 588-638, August.
    9. Sara Lowes & Eduardo Montero, 2021. "Concessions, Violence, and Indirect Rule: Evidence from the Congo Free State," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 136(4), pages 2047-2091.
    10. Esteban Méndez & Diana Van Patten, 2022. "Multinationals, Monopsony, and Local Development: Evidence From the United Fruit Company," Econometrica, Econometric Society, vol. 90(6), pages 2685-2721, November.
    11. Xiaohong Chen & Wayne Yuan Gao, 2025. "Semiparametric Learning of Integral Functionals on Submanifolds," Cowles Foundation Discussion Papers 2450, Cowles Foundation for Research in Economics, Yale University.
    12. Esteban Méndez-Chacón & Diana Van Patten, 2022. "Multinationals, Monopsony, and Local Development: Evidence from the United Fruit Company," Documentos de Trabajo 2203, Banco Central de Costa Rica.
    13. Giuntella, Osea & Mazzonna, Fabrizio, 2019. "Sunset time and the economic effects of social jetlag: evidence from US time zone borders," Journal of Health Economics, Elsevier, vol. 65(C), pages 210-226.
    14. Melissa Dell & Pablo Querubin, 2018. "Nation Building Through Foreign Intervention: Evidence from Discontinuities in Military Strategies," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 133(2), pages 701-764.
    15. Maxime Rischard & Zach Branson & Luke Miratrix & Luke Bornn, 2021. "Do School Districts Affect NYC House Prices? Identifying Border Differences Using a Bayesian Nonparametric Approach to Geographic Regression Discontinuity Designs," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(534), pages 619-631, April.
    16. Tiantian Dai & Shenyi Jiang & Xiangbo Liu & Ang Sun, 2022. "The effects of a hypertension diagnosis on health behaviors: A two‐dimensional regression discontinuity analysis," Health Economics, John Wiley & Sons, Ltd., vol. 31(4), pages 574-596, April.
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