IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1803.07951.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
  • Ivan A. Canay

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 an approximate sign test for continuity of a density at a point based on the so-called g-order statistics, and study its properties under two complementary asymptotic frameworks. In the first asymptotic framework, the number q of observations local to the cut-off is fixed as the sample size n diverges to infinity, while in the second framework q diverges to infinity slowly as n diverges to infinity. Under both of these frameworks, we show that the test we propose is asymptotically valid in the sense that it has limiting rejection probability under the null hypothesis not exceeding the nominal level. More importantly, the test is easy to implement, asymptotically valid under weaker conditions than those used by competing methods, and exhibits finite sample validity under stronger conditions than those needed for its asymptotic validity. In a simulation study, we find that the approximate sign test provides good control of the rejection probability under the null hypothesis while remaining competitive under the alternative hypothesis. 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," Papers 1803.07951, arXiv.org, revised Feb 2020.
  • Handle: RePEc:arx:papers:1803.07951
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1803.07951
    File Function: Latest version
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Kaufmann, E. & Reiss, R. -D., 1992. "On conditional distributions of nearest neighbors," Journal of Multivariate Analysis, Elsevier, vol. 42(1), pages 67-76, July.
    4. Gerard, Francois & Rokkanen, Miikka & Rothe, Christoph, 2016. "Bounds on Treatment Effects in Regression Discontinuity Designs under Manipulation of the Running Variable, with an Application to Unemployment Insurance in Brazil," CEPR Discussion Papers 11668, C.E.P.R. Discussion Papers.
    5. 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.
    6. Imbens, Guido W. & Lemieux, Thomas, 2008. "Regression discontinuity designs: A guide to practice," Journal of Econometrics, Elsevier, vol. 142(2), pages 615-635, February.
    7. 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.
    8. 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.
    9. Emmanuel Saez, 2010. "Do Taxpayers Bunch at Kink Points?," American Economic Journal: Economic Policy, American Economic Association, vol. 2(3), pages 180-212, August.
    10. 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.
    11. 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.
    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.
    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. 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).
    2. Blaise Melly & Rafael Lalive, 2020. "Estimation, Inference, and Interpretation in the Regression Discontinuity Design," Diskussionsschriften dp2016, Universitaet Bern, Departement Volkswirtschaft.

    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. Ivan A Canay & Vishal Kamat, 2018. "Approximate Permutation Tests and Induced Order Statistics in the Regression Discontinuity Design," Review of Economic Studies, Oxford University Press, vol. 85(3), pages 1577-1608.
    2. Blaise Melly & Rafael Lalive, 2020. "Estimation, Inference, and Interpretation in the Regression Discontinuity Design," Diskussionsschriften dp2016, Universitaet Bern, Departement Volkswirtschaft.
    3. Bertanha, Marinho & Moreira, Marcelo J., 2020. "Impossible inference in econometrics: Theory and applications," Journal of Econometrics, Elsevier, vol. 218(2), pages 247-270.
    4. Slotwinski, Michaela & Schmidheiny, Kurt, 2014. "Behavioral Responses to Local Tax Rates: Quasi-Experimental Evidence from a Foreigners Tax Scheme in Switzerland," VfS Annual Conference 2014 (Hamburg): Evidence-based Economic Policy 100292, Verein für Socialpolitik / German Economic Association.
    5. Sander Gerritsen & Dinand Webbink & Bas Weel, 2017. "Sorting Around the Discontinuity Threshold: The Case of a Neighbourhood Investment Programme," De Economist, Springer, vol. 165(1), pages 101-128, March.
    6. Schmidheiny, Kurt & Slotwinski, Michaela, 2018. "Tax-induced mobility: Evidence from a foreigners' tax scheme in Switzerland," Journal of Public Economics, Elsevier, vol. 167(C), pages 293-324.
    7. Dong, Yingying, 2010. "Jumpy or Kinky? Regression Discontinuity without the Discontinuity," MPRA Paper 25461, University Library of Munich, Germany.
    8. 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.
    9. Vergolini, Loris & Zanini, Nadir, 2015. "Away, but not too far from home. The effects of financial aid on university enrolment decisions," Economics of Education Review, Elsevier, vol. 49(C), pages 91-109.
    10. Volker Schöer & Debra Shepherd, 2013. "Compulsory tutorial programmes and performance in undergraduate microeconomics: A regression discontinuity design," Working Papers 27/2013, Stellenbosch University, Department of Economics.
    11. Prakash, Nishith & Rockmore, Marc & Uppal, Yogesh, 2019. "Do criminally accused politicians affect economic outcomes? Evidence from India," Journal of Development Economics, Elsevier, vol. 141(C).
    12. Perez-Reyna, David & Villamizar-Villegas, Mauricio, 2019. "Exchange rate effects of financial regulations," Journal of International Money and Finance, Elsevier, vol. 96(C), pages 228-245.
    13. 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.
    14. Joaquín Artés & Ignacio Jurado, 2018. "Government fragmentation and fiscal deficits: a regression discontinuity approach," Public Choice, Springer, vol. 175(3), pages 367-391, June.
    15. 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.
    16. Baum-Snow, Nathaniel & Ferreira, Fernando, 2015. "Causal Inference in Urban and Regional Economics," Handbook of Regional and Urban Economics, in: Gilles Duranton & J. V. Henderson & William C. Strange (ed.), Handbook of Regional and Urban Economics, edition 1, volume 5, chapter 0, pages 3-68, Elsevier.
    17. Catherine Hausman & David S. Rapson, 2018. "Regression Discontinuity in Time: Considerations for Empirical Applications," Annual Review of Resource Economics, Annual Reviews, vol. 10(1), pages 533-552, October.
    18. Abou-Chadi, Tarik & Krause, Werner, 2020. "The Causal Effect of Radical Right Success on Mainstream Parties’ Policy Positions: A Regression Discontinuity Approach," EconStor Open Access Articles, ZBW - Leibniz Information Centre for Economics, pages 829-847.
    19. Solé-Ollé, Albert & Viladecans-Marsal, Elisabet, 2013. "Do political parties matter for local land use policies?," Journal of Urban Economics, Elsevier, vol. 78(C), pages 42-56.
    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

    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

    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:1803.07951. See general information about how to correct material in RePEc.

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

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.