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Extrapolating Treatment Effects in Multi-Cutoff Regression Discontinuity Designs

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  • Matias D. Cattaneo
  • Luke Keele
  • Rocio Titiunik
  • Gonzalo Vazquez-Bare

Abstract

In non-experimental settings, the Regression Discontinuity (RD) design is one of the most credible identification strategies for program evaluation and causal inference. However, RD treatment effect estimands are necessarily local, making statistical methods for the extrapolation of these effects a key area for development. We introduce a new method for extrapolation of RD effects that relies on the presence of multiple cutoffs, and is therefore design-based. Our approach employs an easy-to-interpret identifying assumption that mimics the idea of "common trends" in difference-in-differences designs. We illustrate our methods with data on a subsidized loan program on post-education attendance in Colombia, and offer new evidence on program effects for students with test scores away from the cutoff that determined program eligibility.

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  • Matias D. Cattaneo & Luke Keele & Rocio Titiunik & Gonzalo Vazquez-Bare, 2018. "Extrapolating Treatment Effects in Multi-Cutoff Regression Discontinuity Designs," Papers 1808.04416, arXiv.org, revised Apr 2020.
    • Handle: RePEc:arx:papers:1808.04416
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    1. Keele, Luke J. & Titiunik, Rocío, 2015. "Geographic Boundaries as Regression Discontinuities," Political Analysis, Cambridge University Press, vol. 23(1), pages 127-155, January.
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    6. Sebastian Calonico & Matias D. Cattaneo & Max H. Farrell & Roc ́ıo Titiunik, 2017. "rdrobust: Software for regression-discontinuity designs," Stata Journal, StataCorp LLC, vol. 17(2), pages 372-404, June.
    7. Hunt Allcott, 2015. "Site Selection Bias in Program Evaluation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 130(3), pages 1117-1165.
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    9. 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.
    10. Burt S. Barnow & Matias D. Cattaneo & Rocío Titiunik & Gonzalo Vazquez‐Bare, 2017. "Comparing Inference Approaches for RD Designs: A Reexamination of the Effect of Head Start on Child Mortality," Journal of Policy Analysis and Management, John Wiley & Sons, Ltd., vol. 36(3), pages 643-681, June.
    11. Joshua D. Angrist & Miikka Rokkanen, 2015. "Wanna Get Away? Regression Discontinuity Estimation of Exam School Effects Away From the Cutoff," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1331-1344, December.
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    13. Rebecca A. Maynard & Kenneth A. Couch & Coady Wing & Thomas D. Cook, 2013. "Strengthening The Regression Discontinuity Design Using Additional Design Elements: A Within‐Study Comparison," Journal of Policy Analysis and Management, John Wiley & Sons, Ltd., vol. 32(4), pages 853-877, September.
    14. Melguizo, Tatiana & Sanchez, Fabio & Velasco, Tatiana, 2016. "Credit for Low-Income Students and Access to and Academic Performance in Higher Education in Colombia: A Regression Discontinuity Approach," World Development, Elsevier, vol. 80(C), pages 61-77.
    15. Yingying Dong & Arthur Lewbel, 2015. "Identifying the Effect of Changing the Policy Threshold in Regression Discontinuity Models," The Review of Economics and Statistics, MIT Press, vol. 97(5), pages 1081-1092, December.
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    2. Cingano, Federico & Palomba, Filippo & Pinotti, Paolo & Rettore, Enrico, 2022. "Making Subsidies Work: Rules vs. Discretion," IZA Discussion Papers 15172, Institute of Labor Economics (IZA).
    3. Martin Huber, 2019. "An introduction to flexible methods for policy evaluation," Papers 1910.00641, arXiv.org.
    4. Yi Zhang & Eli Ben-Michael & Kosuke Imai, 2022. "Safe Policy Learning under Regression Discontinuity Designs with Multiple Cutoffs," Papers 2208.13323, arXiv.org, revised Sep 2024.
    5. Galindo-Silva, Hector, 2021. "Political openness and armed conflict: Evidence from local councils in Colombia," European Journal of Political Economy, Elsevier, vol. 67(C).
    6. Dor Leventer & Daniel Nevo, 2024. "Correcting invalid regression discontinuity designs with multiple time period data," Papers 2408.05847, arXiv.org, revised Feb 2025.
    7. Yiwei Sun, 2023. "Extrapolating Away from the Cutoff in Regression Discontinuity Designs," Papers 2311.18136, arXiv.org.
    8. Kohei Yata, 2021. "Optimal Decision Rules Under Partial Identification," Papers 2111.04926, arXiv.org, revised Mar 2025.
    9. Michael Coury & Toru Kitagawa & Allison Shertzer & Matthew Turner, 2022. "The Value of Piped Water and Sewers: Evidence from 19th Century Chicago," NBER Working Papers 29718, National Bureau of Economic Research, Inc.
    10. Bo Becker & Marcus M Opp & Farzad Saidi, 2022. "Regulatory Forbearance in the U.S. Insurance Industry: The Effects of Removing Capital Requirements for an Asset Class," The Review of Financial Studies, Society for Financial Studies, vol. 35(12), pages 5438-5482.
    11. Machado, Anaely & Terra, Rafael & Tannuri-Pianto, Maria, 2024. "Higher education responses to accountability," Economics of Education Review, Elsevier, vol. 98(C).
    12. Cingano, Federico & Palomba, Filippo & Pinotti, Paolo & Rettore, Enrico, 2023. "Granting more bang for the buck: The heterogeneous effects of firm subsidies," Labour Economics, Elsevier, vol. 83(C).
    13. Francesco Ruggieri, 2023. "Dynamic Regression Discontinuity: An Event-Study Approach," Papers 2307.14203, arXiv.org, revised Mar 2025.
    14. Masayuki Sawada & Takuya Ishihara & Daisuke Kurisu & Yasumasa Matsuda, 2024. "Local-Polynomial Estimation for Multivariate Regression Discontinuity Designs," Papers 2402.08941, arXiv.org.
    15. Yuta Okamoto & Yuuki Ozaki, 2024. "On Extrapolation of Treatment Effects in Multiple-Cutoff Regression Discontinuity Designs," Papers 2412.04265, arXiv.org.
    16. Jiafeng Chen, 2021. "Nonparametric Treatment Effect Identification in School Choice," Papers 2112.03872, arXiv.org, revised Oct 2023.
    17. Ayertey, Winfred & Sharifi, Ayyoob & Yoshida, Yuichiro, 2024. "The impact of increase in block pricing on electricity demand responsiveness: Evidence from Ghana," Energy, Elsevier, vol. 288(C).

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