IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1808.04416.html
   My bibliography  Save this paper

Extrapolating Treatment Effects in Multi-Cutoff Regression Discontinuity Designs

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1808.04416
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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. 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.
    3. Imbens, Guido W. & Lemieux, Thomas, 2008. "Regression discontinuity designs: A guide to practice," Journal of Econometrics, Elsevier, vol. 142(2), pages 615-635, February.
    4. Alberto Abadie, 2005. "Semiparametric Difference-in-Differences Estimators," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(1), pages 1-19.
    5. 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.
    6. 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.
    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.
    8. 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.
    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.
    12. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Cappelletti, Giuseppe & Ponte Marques, Aurea & Varraso, Paolo, 2024. "Impact of higher capital buffers on banks’ lending and risk-taking in the short- and medium-term: Evidence from the euro area experiments," Journal of Financial Stability, Elsevier, vol. 72(C).
    2. Galindo-Silva, Hector, 2021. "Political openness and armed conflict: Evidence from local councils in Colombia," European Journal of Political Economy, Elsevier, vol. 67(C).
    3. Cingano, Federico & Palomba, Filippo & Pinotti, Paolo & Rettore, Enrico, 2022. "Making Subsidies Work: Rules vs. Discretion," IZA Discussion Papers 15172, Institute of Labor Economics (IZA).
    4. Martin Huber, 2019. "An introduction to flexible methods for policy evaluation," Papers 1910.00641, arXiv.org.
    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," The Review of Financial Studies, Society for Financial Studies, vol. 35(12), pages 5438-5482.
    6. Machado, Anaely & Terra, Rafael & Tannuri-Pianto, Maria, 2024. "Higher education responses to accountability," Economics of Education Review, Elsevier, vol. 98(C).
    7. 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.
    8. 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).
    9. Dor Leventer & Daniel Nevo, 2024. "Correcting invalid regression discontinuity designs with multiple time period data," Papers 2408.05847, arXiv.org.
    10. Francesco Ruggieri, 2023. "Dynamic Regression Discontinuity: A Within-Design Approach," Papers 2307.14203, arXiv.org.
    11. Yiwei Sun, 2023. "Extrapolating Away from the Cutoff in Regression Discontinuity Designs," Papers 2311.18136, arXiv.org.
    12. Masayuki Sawada & Takuya Ishihara & Daisuke Kurisu & Yasumasa Matsuda, 2024. "Local-Polynomial Estimation for Multivariate Regression Discontinuity Designs," Papers 2402.08941, arXiv.org.
    13. Jiafeng Chen, 2021. "Nonparametric Treatment Effect Identification in School Choice," Papers 2112.03872, arXiv.org, revised Oct 2023.
    14. 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).
    15. Kohei Yata, 2021. "Optimal Decision Rules Under Partial Identification," Papers 2111.04926, arXiv.org, revised Aug 2023.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Blaise Melly & Rafael Lalive, 2020. "Estimation, Inference, and Interpretation in the Regression Discontinuity Design," Diskussionsschriften dp2016, Universitaet Bern, Departement Volkswirtschaft.
    2. Jin-young Choi & Myoung-jae Lee, 2017. "Regression discontinuity: review with extensions," Statistical Papers, Springer, vol. 58(4), pages 1217-1246, December.
    3. Matias D. Cattaneo & Rocío Titiunik, 2022. "Regression Discontinuity Designs," Annual Review of Economics, Annual Reviews, vol. 14(1), pages 821-851, August.
    4. Sebastian Calonico & Matias D Cattaneo & Max H Farrell, 2020. "Optimal bandwidth choice for robust bias-corrected inference in regression discontinuity designs," The Econometrics Journal, Royal Economic Society, vol. 23(2), pages 192-210.
    5. Vanessa Cirulli & Giuliano Resce & Marco Ventura, 2024. "Co-payment exemption and healthcare consumption: quasi-experimental evidence from Italy," Empirical Economics, Springer, vol. 67(1), pages 355-380, July.
    6. Huber, Martin, 2019. "An introduction to flexible methods for policy evaluation," FSES Working Papers 504, Faculty of Economics and Social Sciences, University of Freiburg/Fribourg Switzerland.
    7. Yoichi Arai & Yu‐Chin Hsu & Toru Kitagawa & Ismael Mourifié & Yuanyuan Wan, 2022. "Testing identifying assumptions in fuzzy regression discontinuity designs," Quantitative Economics, Econometric Society, vol. 13(1), pages 1-28, January.
    8. Masayuki Sawada & Takuya Ishihara & Daisuke Kurisu & Yasumasa Matsuda, 2024. "Local-Polynomial Estimation for Multivariate Regression Discontinuity Designs," Papers 2402.08941, arXiv.org.
    9. Sebastian Galiani & Patrick J. McEwan & Brian Quistorff, 2017. "External and Internal Validity of a Geographic Quasi-Experiment Embedded in a Cluster-Randomized Experiment," Advances in Econometrics, in: Regression Discontinuity Designs, volume 38, pages 195-236, Emerald Group Publishing Limited.
    10. Atı̇la Abdulkadı̇roğlu & Joshua D. Angrist & Yusuke Narita & Parag Pathak, 2022. "Breaking Ties: Regression Discontinuity Design Meets Market Design," Econometrica, Econometric Society, vol. 90(1), pages 117-151, January.
    11. Gurgand, Marc & Lorenceau, Adrien & Mélonio, Thomas, 2023. "Student loans: Credit constraints and higher education in South Africa," Journal of Development Economics, Elsevier, vol. 161(C).
    12. Crespo Cristian, 2020. "Beyond Manipulation: Administrative Sorting in Regression Discontinuity Designs," Journal of Causal Inference, De Gruyter, vol. 8(1), pages 164-181, January.
    13. Mauricio Villamizar‐Villegas & Freddy A. Pinzon‐Puerto & Maria Alejandra Ruiz‐Sanchez, 2022. "A comprehensive history of regression discontinuity designs: An empirical survey of the last 60 years," Journal of Economic Surveys, Wiley Blackwell, vol. 36(4), pages 1130-1178, September.
    14. Hong Kai, 2017. "School Bond Referendum, Capital Expenditure, and Student Achievement," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 17(4), pages 1-26, October.
    15. Susan Athey & Guido W. Imbens, 2017. "The State of Applied Econometrics: Causality and Policy Evaluation," Journal of Economic Perspectives, American Economic Association, vol. 31(2), pages 3-32, Spring.
    16. Kettlewell, Nathan & Siminski, Peter, 2020. "Optimal Model Selection in RDD and Related Settings Using Placebo Zones," IZA Discussion Papers 13639, Institute of Labor Economics (IZA).
    17. Yang He & Otávio Bartalotti, 2020. "Wild bootstrap for fuzzy regression discontinuity designs: obtaining robust bias-corrected confidence intervals," The Econometrics Journal, Royal Economic Society, vol. 23(2), pages 211-231.
    18. Dor Leventer & Daniel Nevo, 2024. "Correcting invalid regression discontinuity designs with multiple time period data," Papers 2408.05847, arXiv.org.
    19. Bertanha, Marinho, 2020. "Regression discontinuity design with many thresholds," Journal of Econometrics, Elsevier, vol. 218(1), pages 216-241.
    20. Crespo Cristian, 2020. "Beyond Manipulation: Administrative Sorting in Regression Discontinuity Designs," Journal of Causal Inference, De Gruyter, vol. 8(1), pages 164-181, January.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1808.04416. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.