IDEAS home Printed from https://ideas.repec.org/p/ifs/cemmap/27-13.html
   My bibliography  Save this paper

Optimal bandwidth selection for differences of nonparametric estimators with an application to the sharp regression discontinuity design

Author

Listed:
  • Yoichi Arai

    (Institute for Fiscal Studies)

  • Hidehiko Ichimura

    (Institute for Fiscal Studies and University of Arizona, University of Tokyo)

Abstract

We consider the problem of choosing two bandwidths simultaneously for estimating the difference of two functions at given points. When the asymptotic approximation of the mean squared error (AMSE) criterion is used, we show that minimisation problem is not well-defined when the sign of the product of the second derivatives of the underlying functions at the estimated points is positive. To address this problem, we theoretically define and construct estimators of the asymptotically first-order optimal (AFO) bandwidths which are well-defined regardless of the sign. They are based on objective functions which incorporate a second-order bias term. Our approach is general enough to cover estimation problems related to densities and regression functions at interior and boundary points. We provide a detailed treatment of the sharp regression discontinuity design. This article is accompanied by a web appendix in which we present omitted discussions, an algorithm to implement the proposed method for the sharp RSS and proofs for the main results.

Suggested Citation

  • Yoichi Arai & Hidehiko Ichimura, 2013. "Optimal bandwidth selection for differences of nonparametric estimators with an application to the sharp regression discontinuity design," CeMMAP working papers CWP27/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:27/13
    as

    Download full text from publisher

    File URL: http://www.cemmap.ac.uk/wps/cwp271313.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Jens Ludwig & Douglas L. Miller, 2007. "Does Head Start Improve Children's Life Chances? Evidence from a Regression Discontinuity Design," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 122(1), pages 159-208.
    2. Yoichi Arai & Hidehiko Ichimura, 2013. "Optimal Bandwidth Selection for Differences of Nonparametric Estimators with an Application to the Sharp Regression Discontinuity Design," CIRJE F-Series CIRJE-F-889, CIRJE, Faculty of Economics, University of Tokyo.
    3. Guido Imbens & Karthik Kalyanaraman, 2012. "Optimal Bandwidth Choice for the Regression Discontinuity Estimator," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 79(3), pages 933-959.
    4. Lee, David S., 2008. "Randomized experiments from non-random selection in U.S. House elections," Journal of Econometrics, Elsevier, vol. 142(2), pages 675-697, February.
    5. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    6. Doug Miller & Jens Ludwig, 2005. "Does Head Start Improve Children?s Life Chances? Evidence from a Regression Discontinuity Design," Working Papers 534, University of California, Davis, Department of Economics.
    7. 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.
    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. Yoichi Arai & Hidehiko Ichimura, 2013. "Optimal Bandwidth Selection for Differences of Nonparametric Estimators with an Application to the Sharp Regression Discontinuity Design," CIRJE F-Series CIRJE-F-889, CIRJE, Faculty of Economics, University of Tokyo.
    2. 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.
    3. Jales, Hugo & Ma, Jun & Yu, Zhengfei, 2017. "Optimal bandwidth selection for local linear estimation of discontinuity in density," Economics Letters, Elsevier, vol. 153(C), pages 23-27.

    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. 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. Guido W. Imbens & Jeffrey M. Wooldridge, 2009. "Recent Developments in the Econometrics of Program Evaluation," Journal of Economic Literature, American Economic Association, vol. 47(1), pages 5-86, March.
    3. Porter, Jack & Yu, Ping, 2015. "Regression discontinuity designs with unknown discontinuity points: Testing and estimation," Journal of Econometrics, Elsevier, vol. 189(1), pages 132-147.
    4. 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.
    5. Guido Imbens & Stefan Wager, 2019. "Optimized Regression Discontinuity Designs," The Review of Economics and Statistics, MIT Press, vol. 101(2), pages 264-278, May.
    6. Dong, Yingying, 2010. "Jumpy or Kinky? Regression Discontinuity without the Discontinuity," MPRA Paper 25461, University Library of Munich, Germany.
    7. Feng, Li & Figlio, David & Sass, Tim, 2018. "School accountability and teacher mobility," Journal of Urban Economics, Elsevier, vol. 103(C), pages 1-17.
    8. 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.
    9. 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.
    10. Ari Hyytinen & Jaakko Meriläinen & Tuukka Saarimaa & Otto Toivanen & Janne Tukiainen, 2018. "When does regression discontinuity design work? Evidence from random election outcomes," Quantitative Economics, Econometric Society, vol. 9(2), pages 1019-1051, July.
    11. 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.
    12. 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.
    13. Benjamin M. Marx & Lesley J. Turner, 2015. "Borrowing Trouble? Student Loans, the Cost of Borrowing, and Implications for the Effectiveness of Need-Based Grant Aid," NBER Working Papers 20850, National Bureau of Economic Research, Inc.
    14. 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.
    15. Bartalotti Otávio, 2019. "Regression Discontinuity and Heteroskedasticity Robust Standard Errors: Evidence from a Fixed-Bandwidth Approximation," Journal of Econometric Methods, De Gruyter, vol. 8(1), pages 1-26, January.
    16. Xiao Huang & Zhaoguo Zhan, 2022. "Local Composite Quantile Regression for Regression Discontinuity," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(4), pages 1863-1875, October.
    17. Zhuan Pei & David S. Lee & David Card & Andrea Weber, 2022. "Local Polynomial Order in Regression Discontinuity Designs," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(3), pages 1259-1267, June.
    18. Frederik Wild & David Stadelmann, 2024. "Heterogeneous Effects of Women's Schooling on Fertility, Literacy and Work: Evidence from Burundi's Free Primary Education Policy," Journal of African Economies, Centre for the Study of African Economies, vol. 33(1), pages 67-91.
    19. Daniel Muller & Lionel Page, 2016. "Born leaders: political selection and the relative age effect in the US Congress," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 179(3), pages 809-829, June.
    20. 'Agoston Reguly, 2021. "Heterogeneous Treatment Effects in Regression Discontinuity Designs," Papers 2106.11640, arXiv.org, revised Oct 2021.

    More about this item

    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:ifs:cemmap:27/13. 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: Emma Hyman (email available below). General contact details of provider: https://edirc.repec.org/data/cmifsuk.html .

    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.