Nothing Special   »   [go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/cwl/cwldpp/2044.html
   My bibliography  Save this paper

Simple and Honest Confidence Intervals in Nonparametric Regression

Author

Listed:
Abstract
We consider the problem of constructing honest confidence intervals (CIs) for a scalar parameter of interest, such as the regression discontinuity parameter, in nonparametric regression based on kernel or local polynomial estimators. To ensure that our CIs are honest, we derive and tabulate novel critical values that take into account the possible bias of the estimator upon which the CIs are based. We give sharp efficiency bounds of using different kernels, and derive the optimal bandwidth for constructing honest CIs. We show that using the bandwidth that minimizes the maximum mean-squared error results in CIs that are nearly efficient and that in this case, the critical value depends only on the rate of convergence. For the common case in which the rate of convergence is n^{-4/5}, the appropriate critical value for 95% CIs is 2.18, rather than the usual 1.96 critical value. We illustrate our results in an empirical application.

Suggested Citation

  • Timothy B. Armstrong & Michal Koles�r, 2016. "Simple and Honest Confidence Intervals in Nonparametric Regression," Cowles Foundation Discussion Papers 2044, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:2044
    as

    Download full text from publisher

    File URL: https://cowles.yale.edu/sites/default/files/d20/d2044.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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. 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.
    3. Jianqing Fan & Theo Gasser & Irène Gijbels & Michael Brockmann & Joachim Engel, 1997. "Local Polynomial Regression: Optimal Kernels and Asymptotic Minimax Efficiency," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(1), pages 79-99, March.
    4. 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.
    5. 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.
    6. Alberto Abadie & Guido W. Imbens & Fanyin Zheng, 2014. "Inference for Misspecified Models With Fixed Regressors," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(508), pages 1601-1614, December.
    7. Alberto Abadie & Guido W. Imbens, 2006. "Large Sample Properties of Matching Estimators for Average Treatment Effects," Econometrica, Econometric Society, vol. 74(1), pages 235-267, January.
    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. Hansen, Benjamin & Miller, Keaton & Weber, Caroline, 2020. "Federalism, partial prohibition, and cross-border sales: Evidence from recreational marijuana," Journal of Public Economics, Elsevier, vol. 187(C).
    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. 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.
    4. Nicholas Barton & Tessa Bold & Justin Sandefur, 2017. "Measuring Rents from Public Employment: Regression Discontinuity Evidence from Kenya - Working Paper 457," Working Papers 457, Center for Global Development.
    5. 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.
    6. 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.
    7. 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.
    8. Bold, Tessa & Barton, Nicholas & Sandefur, Justin, 2017. "Measuring Rents from Public Employment: Regression discontinuity evidence from Kenya," CEPR Discussion Papers 12105, C.E.P.R. Discussion Papers.
    9. Jin-young Choi & Myoung-jae Lee, 2017. "Regression discontinuity: review with extensions," Statistical Papers, Springer, vol. 58(4), pages 1217-1246, December.
    10. 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.
    11. 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.
    12. Louise Grogan & Fraser Summerfield, 2019. "Government Transfers, Work, and Wellbeing: Evidence from the Russian Old-Age Pension," Journal of Population Economics, Springer;European Society for Population Economics, vol. 32(4), pages 1247-1292, October.
    13. 'Agoston Reguly, 2021. "Heterogeneous Treatment Effects in Regression Discontinuity Designs," Papers 2106.11640, arXiv.org, revised Oct 2021.
    14. 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.
    15. Deng, Taotao & Hu, Yukun & Ma, Mulan, 2019. "Regional policy and tourism: A quasi-natural experiment," Annals of Tourism Research, Elsevier, vol. 74(C), pages 1-16.
    16. Tatiana Komarova & Denis Nekipelov, 2020. "Identification and Formal Privacy Guarantees," Papers 2006.14732, arXiv.org, revised May 2021.
    17. Harrison H. Li & Art B. Owen, 2022. "A general characterization of optimal tie-breaker designs," Papers 2202.12511, arXiv.org, revised Oct 2022.
    18. Anderson, Kathryn & Gong, Xue & Hong, Kai & Zhang, Xi, 2016. "Do selective high schools improve student achievement? Effects of exam schools in China," China Economic Review, Elsevier, vol. 40(C), pages 121-134.
    19. Wu, Jia & Wei, Xiangdong & Zhang, Hongliang & Zhou, Xiang, 2019. "Elite schools, magnet classes, and academic performances: Regression-discontinuity evidence from China," China Economic Review, Elsevier, vol. 55(C), pages 143-167.
    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.

    More about this item

    Keywords

    Nonparametric inference; relative efficiency;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

    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:cwl:cwldpp:2044. 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: Brittany Ladd (email available below). General contact details of provider: https://edirc.repec.org/data/cowleus.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.