IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2402.08941.html
   My bibliography  Save this paper

Local-Polynomial Estimation for Multivariate Regression Discontinuity Designs

Author

Listed:
  • Masayuki Sawada
  • Takuya Ishihara
  • Daisuke Kurisu
  • Yasumasa Matsuda

Abstract

We introduce a multivariate local-linear estimator for multivariate regression discontinuity designs in which treatment is assigned by crossing a boundary in the space of running variables. The dominant approach uses the Euclidean distance from a boundary point as the scalar running variable; hence, multivariate designs are handled as uni-variate designs. However, the distance running variable is incompatible with the assumption for asymptotic validity. We handle multivariate designs as multivariate. In this study, we develop a novel asymptotic normality for multivariate local-polynomial estimators. Our estimator is asymptotically valid and can capture heterogeneous treatment effects over the boundary. We demonstrate the effectiveness of our estimator through numerical simulations. Our empirical illustration of a Colombian scholarship study reveals a richer heterogeneity (including its absence) of the treatment effect that is hidden in the original estimates.

Suggested Citation

  • Masayuki Sawada & Takuya Ishihara & Daisuke Kurisu & Yasumasa Matsuda, 2024. "Local-Polynomial Estimation for Multivariate Regression Discontinuity Designs," Papers 2402.08941, arXiv.org.
    • Handle: RePEc:arx:papers:2402.08941
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2402.08941
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Yoichi Arai & Hidehiko Ichimura, 2018. "Simultaneous selection of optimal bandwidths for the sharp regression discontinuity estimator," Quantitative Economics, Econometric Society, vol. 9(1), pages 441-482, March.
    2. Keele, Luke J. & Titiunik, Rocío, 2015. "Geographic Boundaries as Regression Discontinuities," Political Analysis, Cambridge University Press, vol. 23(1), pages 127-155, January.
    3. Sandra E. Black, 1999. "Do Better Schools Matter? Parental Valuation of Elementary Education," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(2), pages 577-599.
    4. Markus Frölich & Martin Huber, 2019. "Including Covariates in the Regression Discontinuity Design," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(4), pages 736-748, October.
    5. Sebastian Calonico & Matias D. Cattaneo & Max H. Farrell & Rocío Titiunik, 2019. "Regression Discontinuity Designs Using Covariates," The Review of Economics and Statistics, MIT Press, vol. 101(3), pages 442-451, July.
    6. 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.
    7. Koohyun Kwon & Soonwoo Kwon, 2020. "Adaptive Inference in Multivariate Nonparametric Regression Models Under Monotonicity," Papers 2011.14219, arXiv.org.
    8. Imbens, Guido W. & Lemieux, Thomas, 2008. "Regression discontinuity designs: A guide to practice," Journal of Econometrics, Elsevier, vol. 142(2), pages 615-635, February.
    9. Sebastian Calonico & Matias D. Cattaneo & Rocio Titiunik, 2014. "Robust data-driven inference in the regression-discontinuity design," Stata Journal, StataCorp LP, vol. 14(4), pages 909-946, December.
    10. 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.
    11. 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.
    12. Myung Hwan Seo & Yoichi Arai & Taisuke Otsu, 2021. "Regression Discontinuity Design with Potentially Many Covariates," Working Paper Series no142, Institute of Economic Research, Seoul National University.
    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. 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.
    15. 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.
    16. Matias D. Cattaneo & Nicolas Idrobo & Rocio Titiunik, 2023. "A Practical Introduction to Regression Discontinuity Designs: Extensions," Papers 2301.08958, arXiv.org, revised Mar 2024.
    17. Matsudaira, Jordan D., 2008. "Mandatory summer school and student achievement," Journal of Econometrics, Elsevier, vol. 142(2), pages 829-850, February.
    18. Gonzalo Vazquez-Bare & Matias Cattaneo & Rocio Titiunik, 2016. "rdlocrand: a Stata Package for Inference in Regression Discontinuity Designs under Local Randomizati," 2016 Stata Conference 25, Stata Users Group.
    19. Matias D. Cattaneo & Nicolas Idrobo & Rocio Titiunik, 2019. "A Practical Introduction to Regression Discontinuity Designs: Foundations," Papers 1911.09511, arXiv.org.
    20. Guido Imbens & Stefan Wager, 2019. "Optimized Regression Discontinuity Designs," The Review of Economics and Statistics, MIT Press, vol. 101(2), pages 264-278, May.
    21. Matias D. Cattaneo & Roc ́ıo Titiunik & Gonzalo Vazquez-Bare, 2016. "Inference in regression discontinuity designs under local randomization," Stata Journal, StataCorp LP, vol. 16(2), pages 331-367, June.
    Full references (including those not matched with items on IDEAS)

    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. Matias D. Cattaneo & Rocío Titiunik, 2022. "Regression Discontinuity Designs," Annual Review of Economics, Annual Reviews, vol. 14(1), pages 821-851, August.
    3. 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.
    4. 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.
    5. Yiqi Liu & Yuan Qi, 2023. "Using Forests in Multivariate Regression Discontinuity Designs," Papers 2303.11721, arXiv.org.
    6. Onda, Masayuki & Seyler, Edward, 2020. "English learners reclassification and academic achievement: Evidence from Minnesota," Economics of Education Review, Elsevier, vol. 79(C).
    7. Cappelletti, Giuseppe & Ponte Marques, Aurea & Varraso, Paolo & Budrys, Žymantas & Peeters, Jonas, 2019. "Impact of higher capital buffers on banks’ lending and risk-taking: evidence from the euro area experiments," Working Paper Series 2292, European Central Bank.
    8. Meier, Pascal Flurin & Flepp, Raphael & Meier, Philippe & Franck, Egon, 2022. "Outcome bias in self-evaluations: Quasi-experimental field evidence from Swiss driving license exams," Journal of Economic Behavior & Organization, Elsevier, vol. 201(C), pages 292-309.
    9. Crespo Cristian, 2020. "Beyond Manipulation: Administrative Sorting in Regression Discontinuity Designs," Journal of Causal Inference, De Gruyter, vol. 8(1), pages 164-181, January.
    10. 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.
    11. Cuong Viet Nguyen & Finn Tarp, 2023. "Cash Transfers and Labor Supply: New Evidence on Impacts and Mechanisms," DERG working paper series 23-18, University of Copenhagen. Department of Economics. Development Economics Research Group (DERG).
    12. Likai Chen & Georg Keilbar & Liangjun Su & Weining Wang, 2023. "Tests for Many Treatment Effects in Regression Discontinuity Panel Data Models," Papers 2312.01162, arXiv.org.
    13. 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).
    14. Yang He & Otávio Bartalotti, 2020. "Wild bootstrap for fuzzy regression discontinuity designs: obtaining robust bias-corrected confidence intervals [Using Maimonides’ rule to estimate the effect of class size on scholastic achievemen," The Econometrics Journal, Royal Economic Society, vol. 23(2), pages 211-231.
    15. Hérault, Nicolas & Vu, Ha & Wilkins, Roger, 2020. "The effect of job search requirements on welfare receipt," GLO Discussion Paper Series 646, Global Labor Organization (GLO).
    16. Pasquini, Ricardo A., 2021. "Effects of regulating the brokerage commission in the rental market: Evidence from Buenos Aires," Journal of Housing Economics, Elsevier, vol. 54(C).
    17. Angelo D'Andrea, 2019. "Mayor’s wage and Public procurement," BAFFI CAREFIN Working Papers 19125, BAFFI CAREFIN, Centre for Applied Research on International Markets Banking Finance and Regulation, Universita' Bocconi, Milano, Italy.
    18. Crespo Cristian, 2020. "Beyond Manipulation: Administrative Sorting in Regression Discontinuity Designs," Journal of Causal Inference, De Gruyter, vol. 8(1), pages 164-181, January.
    19. Matias D. Cattaneo & Luke Keele & Rocio Titiunik, 2021. "Covariate Adjustment in Regression Discontinuity Designs," Papers 2110.08410, arXiv.org, revised Aug 2022.
    20. Burgherr, David, 2022. "Behavioral Responses to a Pension Savings Mandate : Quasi-experimental Evidence from Swiss Tax Data," CAGE Online Working Paper Series 645, Competitive Advantage in the Global Economy (CAGE).

    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:2402.08941. 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.