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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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    1. 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.
    2. Marinho Bertanha & Guido W. Imbens, 2020. "External Validity in Fuzzy Regression Discontinuity Designs," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(3), pages 593-612, July.
    3. 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.
    4. Imbens, Guido W. & Lemieux, Thomas, 2008. "Regression discontinuity designs: A guide to practice," Journal of Econometrics, Elsevier, vol. 142(2), pages 615-635, February.
    5. 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.
    6. Keele, Luke J. & Titiunik, Rocío, 2015. "Geographic Boundaries as Regression Discontinuities," Political Analysis, Cambridge University Press, vol. 23(1), pages 127-155, January.
    7. Alberto Abadie, 2005. "Semiparametric Difference-in-Differences Estimators," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(1), pages 1-19.
    8. 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.
    9. 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.
    10. 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.
    11. David S. Lee & Thomas Lemieux, 2010. "Regression Discontinuity Designs in Economics," Journal of Economic Literature, American Economic Association, vol. 48(2), pages 281-355, June.
    12. 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.
    13. Sebastian Calonico & Matias D. Cattaneo & Max H. Farrell & Roc ́ıo Titiunik, 2017. "rdrobust: Software for regression-discontinuity designs," Stata Journal, StataCorp LP, vol. 17(2), pages 372-404, June.
    14. 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.
    15. 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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    Cited by:

    1. Martin Huber, 2019. "An introduction to flexible methods for policy evaluation," Papers 1910.00641, arXiv.org.
    2. Yi Zhang & Eli Ben-Michael & Kosuke Imai, 2022. "Safe Policy Learning under Regression Discontinuity Designs with Multiple Cutoffs," Papers 2208.13323, arXiv.org, revised Jul 2023.
    3. Galindo-Silva, Hector, 2021. "Political openness and armed conflict: Evidence from local councils in Colombia," European Journal of Political Economy, Elsevier, vol. 67(C).
    4. Cingano, Federico & Palomba, Filippo & Pinotti, Paolo & Rettore, Enrico, 2022. "Making Subsidies Work: Rules vs. Discretion," IZA Discussion Papers 15172, Institute of Labor Economics (IZA).
    5. 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," Review of Financial Studies, Society for Financial Studies, vol. 35(12), pages 5438-5482.
    6. Francesco Ruggieri, 2023. "Dynamic Regression Discontinuity: A Within-Design Approach," Papers 2307.14203, arXiv.org.
    7. Masayuki Sawada & Takuya Ishihara & Daisuke Kurisu & Yasumasa Matsuda, 2024. "Local-Polynomial Estimation for Multivariate Regression Discontinuity Designs," Papers 2402.08941, arXiv.org.
    8. Kohei Yata, 2021. "Optimal Decision Rules Under Partial Identification," Papers 2111.04926, arXiv.org, revised Aug 2023.
    9. Yiwei Sun, 2023. "Extrapolating Away from the Cutoff in Regression Discontinuity Designs," Papers 2311.18136, arXiv.org.
    10. 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).
    11. Jiafeng Chen, 2021. "Nonparametric Treatment Effect Identification in School Choice," Papers 2112.03872, arXiv.org, revised Oct 2023.

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