Nothing Special   »   [go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/ifs/cemmap/20-18.html
   My bibliography  Save this paper

Testing continuity of a density via g -order statistics in the regression discontinuity design

Author

Listed:
  • Federico A. Bugni

    (Institute for Fiscal Studies and Duke University)

  • Ivan A. Canay

    (Institute for Fiscal Studies and Northwestern University)

Abstract
In the regression discontinuity design (RDD), it is common practice to assess the credibility of the design by testing the continuity of the density of the running variable at the cut-off, e.g., McCrary (2008). In this paper we propose a new test for continuity of a density at a point based on the so-called g-order statistics, and study its properties under a novel asymptotic framework. The asymptotic framework is intended to approximate a small sample phenomenon: even though the total number n of observations may be large, the number of effective observations local to the cut-off is often small. Thus, while traditional asymptotics in RDD require a growing number of observations local to the cut-off as n ? 8, our framework allows for the number q of observations local to the cut-off to be fixed as n ? 8. The new test is easy to implement, asymptotically valid under weaker conditions than those used by competing methods, exhibits finite sample validity under stronger conditions than those needed for its asymptotic validity, and has favorable power properties against certain alternatives. In a simulation study, we find that the new test controls size remarkably well across designs. We finally apply our test to the design in Lee (2008), a well-known application of the RDD to study incumbency advantage.

Suggested Citation

  • Federico A. Bugni & Ivan A. Canay, 2018. "Testing continuity of a density via g -order statistics in the regression discontinuity design," CeMMAP working papers CWP20/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:20/18
    as

    Download full text from publisher

    File URL: https://www.ifs.org.uk/uploads/CWP201818.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Timothy B. Armstrong & Michal Kolesár, 2018. "Optimal Inference in a Class of Regression Models," Econometrica, Econometric Society, vol. 86(2), pages 655-683, March.
    2. Timothy B. Armstrong & Michal Kolesár, 2020. "Simple and honest confidence intervals in nonparametric regression," Quantitative Economics, Econometric Society, vol. 11(1), pages 1-39, January.
    3. 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.
    4. Bertanha, Marinho & Moreira, Marcelo J., 2020. "Impossible inference in econometrics: Theory and applications," Journal of Econometrics, Elsevier, vol. 218(2), pages 247-270.
    5. Matias D. Cattaneo & Michael Jansson & Xinwei Ma, 2020. "Simple Local Polynomial Density Estimators," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(531), pages 1449-1455, July.
    6. François Gerard & Miikka Rokkanen & Christoph Rothe, 2020. "Bounds on treatment effects in regression discontinuity designs with a manipulated running variable," Quantitative Economics, Econometric Society, vol. 11(3), pages 839-870, July.
    7. Emmanuel Saez, 2010. "Do Taxpayers Bunch at Kink Points?," American Economic Journal: Economic Policy, American Economic Association, vol. 2(3), pages 180-212, August.
    8. Shu Shen & Xiaohan Zhang, 2016. "Distributional Tests for Regression Discontinuity: Theory and Empirical Examples," The Review of Economics and Statistics, MIT Press, vol. 98(4), pages 685-700, October.
    9. Taisuke Otsu & Ke-Li Xu & Yukitoshi Matsushita, 2013. "Estimation and Inference of Discontinuity in Density," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(4), pages 507-524, October.
    10. Ivan A. Canay & Joseph P. Romano & Azeem M. Shaikh, 2017. "Randomization Tests Under an Approximate Symmetry Assumption," Econometrica, Econometric Society, vol. 85, pages 1013-1030, May.
    11. Brigham R. Frandsen, 2017. "Party Bias in Union Representation Elections: Testing for Manipulation in the Regression Discontinuity Design when the Running Variable is Discrete," Advances in Econometrics, in: Regression Discontinuity Designs, volume 38, pages 281-315, Emerald Group Publishing Limited.
    12. Gerard, François & Rothe, Christoph & Rokkanen, Miikka, 2016. "Bounds on Treatment Effects in Regression Discontinuity Designs under Manipulation of the Running Variable, with an Application," CEPR Discussion Papers 11668, C.E.P.R. Discussion Papers.
    13. Ivan A Canay & Vishal Kamat, 2018. "Approximate Permutation Tests and Induced Order Statistics in the Regression Discontinuity Design," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(3), pages 1577-1608.
    14. 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.
    15. Imbens, Guido W. & Lemieux, Thomas, 2008. "Regression discontinuity designs: A guide to practice," Journal of Econometrics, Elsevier, vol. 142(2), pages 615-635, February.
    16. 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.
    17. Gerard, Francois & Rokkanen, Miikka & Rothe, Christoph, 2015. "Identification and Inference in Regression Discontinuity Designs with a Manipulated Running Variable," IZA Discussion Papers 9604, Institute of Labor Economics (IZA).
    18. Kaufmann, E. & Reiss, R. -D., 1992. "On conditional distributions of nearest neighbors," Journal of Multivariate Analysis, Elsevier, vol. 42(1), pages 67-76, July.
    19. McCrary, Justin, 2008. "Manipulation of the running variable in the regression discontinuity design: A density test," Journal of Econometrics, Elsevier, vol. 142(2), pages 698-714, February.
    20. 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.
    21. 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.
    22. 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.
    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. Takuya Ishihara & Masayuki Sawada, 2020. "Manipulation-Robust Regression Discontinuity Designs," Papers 2009.07551, arXiv.org, revised Sep 2024.
    2. 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.
    3. Tiago Cavalcanti & Kamiar Mohaddes & Hongyu Nian & Haitao Yin, 2023. "Air pollution and firm-level human capital, knowledge and innovation," Working Papers EPRG2301, Energy Policy Research Group, Cambridge Judge Business School, University of Cambridge.
    4. Leopoldo Fergusson & Arturo Harker & Carlos Molina & Juan Camilo Yamín, 2023. "Political incentives and corruption evidence from ghost students," Documentos CEDE 20732, Universidad de los Andes, Facultad de Economía, CEDE.
    5. Shi, Xunpeng & Tian, Binbin & Yang, Longjian & Yu, Jian & Zhou, Siyang, 2023. "How do regulatory environmental policies perform? A case study of China's Top-10,000 enterprises energy-saving program," Renewable and Sustainable Energy Reviews, Elsevier, vol. 187(C).
    6. Koki Fusejima & Takuya Ishihara & Masayuki Sawada, 2022. "A unified diagnostic test for regression discontinuity designs," Papers 2205.04345, arXiv.org, revised Jul 2024.
    7. Matias D. Cattaneo & Rocío Titiunik, 2022. "Regression Discontinuity Designs," Annual Review of Economics, Annual Reviews, vol. 14(1), pages 821-851, August.
    8. 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.
    9. Babii, Andrii & Kumar, Rohit, 2023. "Isotonic regression discontinuity designs," Journal of Econometrics, Elsevier, vol. 234(2), pages 371-393.
    10. Hsu, Yu-Chin & Shiu, Ji-Liang & Wan, Yuanyuan, 2024. "Testing identification conditions of LATE in fuzzy regression discontinuity designs," Journal of Econometrics, Elsevier, vol. 241(1).
    11. Marinho Bertanha & Eunyi Chung, 2023. "Permutation Tests at Nonparametric Rates," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(544), pages 2833-2846, October.
    12. Yingying DONG & Ying-Ying LEE & Michael GOU, 2019. "Regression Discontinuity Designs with a Continuous Treatment," Discussion papers 19058, Research Institute of Economy, Trade and Industry (RIETI).
    13. Yan Zhu & Hongfeng Zhang & Xu He, 2023. "Impact of New and Old Driving Force Conversion on Air Quality: Empirical Analysis Based on RDD," Sustainability, MDPI, vol. 15(4), pages 1-12, February.
    14. Noelia Bernal & Javier Olivera & Marc Suhrcke, 2024. "The effects of social pensions on nutrition‐related health outcomes of the poor: Quasi‐experimental evidence from Peru," Health Economics, John Wiley & Sons, Ltd., vol. 33(5), pages 971-991, May.
    15. Blaise Melly & Rafael Lalive, 2020. "Estimation, Inference, and Interpretation in the Regression Discontinuity Design," Diskussionsschriften dp2016, Universitaet Bern, Departement Volkswirtschaft.
    16. Somdeep Chatterjee & Pushkar Maitra & Manhar Manchanda, 2024. "The Relevant Third: Threat of Coalition and Economic Development," Monash Economics Working Papers 2024-13, Monash University, Department of Economics.
    17. Lu, Jiaxuan, 2023. "The economics of China’s between-city height competition: A regression discontinuity approach," Regional Science and Urban Economics, Elsevier, vol. 100(C).
    18. Federico Crippa, 2024. "Manipulation Test for Multidimensional RDD," Papers 2402.10836, arXiv.org, revised Jun 2024.

    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. Ivan A Canay & Vishal Kamat, 2018. "Approximate Permutation Tests and Induced Order Statistics in the Regression Discontinuity Design," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(3), pages 1577-1608.
    4. Hsu, Yu-Chin & Shiu, Ji-Liang & Wan, Yuanyuan, 2024. "Testing identification conditions of LATE in fuzzy regression discontinuity designs," Journal of Econometrics, Elsevier, vol. 241(1).
    5. 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.
    6. 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.
    7. Ivan A. Canay & Vishal Kamat, 2017. "Approximate permutation tests and induced order statistics in the regression discontinuity design," CeMMAP working papers 21/17, Institute for Fiscal Studies.
    8. 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.
    9. Takuya Ishihara & Masayuki Sawada, 2020. "Manipulation-Robust Regression Discontinuity Designs," Papers 2009.07551, arXiv.org, revised Sep 2024.
    10. Bertanha, Marinho & Moreira, Marcelo J., 2020. "Impossible inference in econometrics: Theory and applications," Journal of Econometrics, Elsevier, vol. 218(2), pages 247-270.
    11. Ivan A. Canay & Vishal Kamat, 2016. "Approximate permutation tests and induced order statistics in the regression discontinuity design," CeMMAP working papers 33/16, Institute for Fiscal Studies.
    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. Babii, Andrii & Kumar, Rohit, 2023. "Isotonic regression discontinuity designs," Journal of Econometrics, Elsevier, vol. 234(2), pages 371-393.
    14. Crespo Cristian, 2020. "Beyond Manipulation: Administrative Sorting in Regression Discontinuity Designs," Journal of Causal Inference, De Gruyter, vol. 8(1), pages 164-181, January.
    15. Filippo Belloc & Gabriel Burdin & Fabio Landini, 2023. "Advanced Technologies and Worker Voice," Economica, London School of Economics and Political Science, vol. 90(357), pages 1-38, January.
    16. Onda, Masayuki & Seyler, Edward, 2020. "English learners reclassification and academic achievement: Evidence from Minnesota," Economics of Education Review, Elsevier, vol. 79(C).
    17. Koki Fusejima & Takuya Ishihara & Masayuki Sawada, 2022. "A unified diagnostic test for regression discontinuity designs," Papers 2205.04345, arXiv.org, revised Jul 2024.
    18. 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.
    19. Guido Imbens & Stefan Wager, 2019. "Optimized Regression Discontinuity Designs," The Review of Economics and Statistics, MIT Press, vol. 101(2), pages 264-278, May.
    20. Adam C. Sales & Ben B. Hansen, 2020. "Limitless Regression Discontinuity," Journal of Educational and Behavioral Statistics, , vol. 45(2), pages 143-174, April.

    More about this item

    Keywords

    Regression discontinuity design; g-ordered statistics; sign tests; continuity; density;
    All these keywords.

    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:ifs:cemmap:20/18. 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.