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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.

Suggested Citation

  • 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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    References listed on IDEAS

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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.
    2. 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.
    3. 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.
    4. 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.
    5. Imbens, Guido W. & Lemieux, Thomas, 2008. "Regression discontinuity designs: A guide to practice," Journal of Econometrics, Elsevier, vol. 142(2), pages 615-635, February.
    6. Alberto Abadie, 2005. "Semiparametric Difference-in-Differences Estimators," Review of Economic Studies, Oxford University Press, vol. 72(1), pages 1-19.
    7. 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.
    8. 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.
    9. 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.
    10. Hunt Allcott, 2015. "Site Selection Bias in Program Evaluation," The Quarterly Journal of Economics, Oxford University Press, vol. 130(3), pages 1117-1165.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
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    Cited by:

    1. Mauricio Villamizar-Villegas & Yasin Kursat Onder, 2020. "Uncovering Time-Specific Heterogeneity in Regression Discontinuity Designs," Borradores de Economia 1141, Banco de la Republica de Colombia.
    2. Martin Huber, 2019. "An introduction to flexible methods for policy evaluation," Papers 1910.00641, arXiv.org.

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