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Extrapolating Treatment Effects in Multi-Cutoff Regression Discontinuity Designs

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

Abstract

Abstract–In nonexperimental 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. Supplementary materials for this article are available online.

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  • Matias D. Cattaneo & Luke Keele & Rocío Titiunik & Gonzalo Vazquez-Bare, 2021. "Extrapolating Treatment Effects in Multi-Cutoff Regression Discontinuity Designs," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1941-1952, October.
    • Handle: RePEc:taf:jnlasa:v:116:y:2021:i:536:p:1941-1952
    DOI: 10.1080/01621459.2020.1751646
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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.
    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 Aug 2023.
    9. 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.
    10. Machado, Anaely & Terra, Rafael & Tannuri-Pianto, Maria, 2024. "Higher education responses to accountability," Economics of Education Review, Elsevier, vol. 98(C).
    11. 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).
    12. Francesco Ruggieri, 2023. "Dynamic Regression Discontinuity: A Within-Design Approach," Papers 2307.14203, arXiv.org.
    13. Masayuki Sawada & Takuya Ishihara & Daisuke Kurisu & Yasumasa Matsuda, 2024. "Local-Polynomial Estimation for Multivariate Regression Discontinuity Designs," Papers 2402.08941, arXiv.org.
    14. Jiafeng Chen, 2021. "Nonparametric Treatment Effect Identification in School Choice," Papers 2112.03872, arXiv.org, revised Oct 2023.
    15. 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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