IDEAS home Printed from https://ideas.repec.org/p/ifs/cemmap/21-17.html
   My bibliography  Save this paper

Approximate permutation tests and induced order statistics in the regression discontinuity design

Author

Listed:
  • Ivan A. Canay

    (Institute for Fiscal Studies and Northwestern University)

  • Vishal Kamat

    (Institute for Fiscal Studies and Toulouse School of Economics)

Abstract

In the regression discontinuity design (RDD), it is common practice to asses the credibility of the design by testing whether the means of baseline covariates do not change at the cutoff (or threshold) of the running variable. This practice is partly motivated by the stronger im-plication derived by Lee (2008), who showed that under certain conditions the distribution of baseline covariates in the RDD must be continuous at the cutoff. We propose a permutation test based on the so-called induced ordered statistics for the null hypothesis of continuity of the distribution of baseline covariates at the cutoff; and introduce a novel asymptotic framework to analyze its properties. 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 cutoff is often small. Thus, while traditional asymptotics in RDD require a growing number of observations local to the cutoff as n ? 8, our framework keeps the number q of observations local to the cutoff ?xed as n ? 8. The new test is easy to implement, asymptotically valid under weak conditions, exhibits ?nite sample validity under stronger conditions than those needed for its asymptotic validity, and has favorable power properties relative to tests based on means. In a simulation study, we ?nd that the new test controls size remarkably well across designs. We then use our test to evaluate the plausibility of the design in Lee (2008), a well-known application of the RDD to study incumbency advantage.

Suggested Citation

  • Ivan A. Canay & Vishal Kamat, 2017. "Approximate permutation tests and induced order statistics in the regression discontinuity design," CeMMAP working papers CWP21/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:21/17
    as

    Download full text from publisher

    File URL: https://www.ifs.org.uk/uploads/cemmap/wps/CWP211717.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Frandsen, Brigham R. & Frölich, Markus & Melly, Blaise, 2012. "Quantile treatment effects in the regression discontinuity design," Journal of Econometrics, Elsevier, vol. 168(2), pages 382-395.
    2. Miguel Urquiola & Eric Verhoogen, 2009. "Class-Size Caps, Sorting, and the Regression-Discontinuity Design," American Economic Review, American Economic Association, vol. 99(1), pages 179-215, March.
    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. Federico A. Bugni & Ivan A. Canay & Azeem M. Shaikh, 2018. "Inference Under Covariate-Adaptive Randomization," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(524), pages 1784-1796, October.
    5. Douglas Almond & Joseph J. Doyle & Amanda E. Kowalski & Heidi Williams, 2010. "Estimating Marginal Returns to Medical Care: Evidence from At-risk Newborns," The Quarterly Journal of Economics, Oxford University Press, vol. 125(2), pages 591-634.
    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. 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.
    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. 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.
    10. 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.
    11. David Card & Carlos Dobkin & Nicole Maestas, 2008. "The Impact of Nearly Universal Insurance Coverage on Health Care Utilization: Evidence from Medicare," American Economic Review, American Economic Association, vol. 98(5), pages 2242-2258, December.
    12. Melissa Dell, 2010. "The Persistent Effects of Peru's Mining Mita," Econometrica, Econometric Society, vol. 78(6), pages 1863-1903, November.
    13. Guido Imbens & Karthik Kalyanaraman, 2012. "Optimal Bandwidth Choice for the Regression Discontinuity Estimator," Review of Economic Studies, Oxford University Press, vol. 79(3), pages 933-959.
    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. Miriam Bruhn & David McKenzie, 2009. "In Pursuit of Balance: Randomization in Practice in Development Field Experiments," American Economic Journal: Applied Economics, American Economic Association, vol. 1(4), pages 200-232, October.
    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. 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.
    19. Peter Ganong & Simon Jäger, 2018. "A Permutation Test for the Regression Kink Design," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 494-504, April.
    20. 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.
    21. Seth D. Zimmerman, 2014. "The Returns to College Admission for Academically Marginal Students," Journal of Labor Economics, University of Chicago Press, vol. 32(4), pages 711-754.
    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. 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.
    2. 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.
    3. Ivan A. Canay & Vishal Kamat, 2015. "Approximate permutation tests and induced order statistics in the regression discontinuity design," CeMMAP working papers 27/15, Institute for Fiscal Studies.
    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. Blaise Melly & Rafael Lalive, 2020. "Estimation, Inference, and Interpretation in the Regression Discontinuity Design," Diskussionsschriften dp2016, Universitaet Bern, Departement Volkswirtschaft.
    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. Bugni, Federico A. & Canay, Ivan A., 2021. "Testing continuity of a density via g-order statistics in the regression discontinuity design," Journal of Econometrics, Elsevier, vol. 221(1), pages 138-159.
    8. Jin-young Choi & Myoung-jae Lee, 2017. "Regression discontinuity: review with extensions," Statistical Papers, Springer, vol. 58(4), pages 1217-1246, December.
    9. Matias D. Cattaneo & Rocío Titiunik, 2022. "Regression Discontinuity Designs," Annual Review of Economics, Annual Reviews, vol. 14(1), pages 821-851, August.
    10. 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).
    11. Montoya, Ana Maria & Noton, Carlos & Solis, Alex, 2018. "The Returns to College Choice: Loans, Scholarships and Labor Outcomes," Working Paper Series 2018:12, Uppsala University, Department of Economics.
    12. Bertanha, Marinho & Moreira, Marcelo J., 2020. "Impossible inference in econometrics: Theory and applications," Journal of Econometrics, Elsevier, vol. 218(2), pages 247-270.
    13. 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.
    14. Xu, Ke-Li, 2017. "Regression discontinuity with categorical outcomes," Journal of Econometrics, Elsevier, vol. 201(1), pages 1-18.
    15. Dong, Yingying, 2010. "Jumpy or Kinky? Regression Discontinuity without the Discontinuity," MPRA Paper 25461, University Library of Munich, Germany.
    16. Christelis, Dimitris & Georgarakos, Dimitris & Sanz-de-Galdeano, Anna, 2020. "The impact of health insurance on stockholding: A regression discontinuity approach," Journal of Health Economics, Elsevier, vol. 69(C).
    17. Christina Korting & Carl Lieberman & Jordan Matsudaira & Zhuan Pei & Yi Shen, 2023. "Visual Inference and Graphical Representation in Regression Discontinuity Designs," The Quarterly Journal of Economics, Oxford University Press, vol. 138(3), pages 1977-2019.
    18. Joaquín Artés & Ignacio Jurado, 2018. "Government fragmentation and fiscal deficits: a regression discontinuity approach," Public Choice, Springer, vol. 175(3), pages 367-391, June.
    19. Crespo Cristian, 2020. "Beyond Manipulation: Administrative Sorting in Regression Discontinuity Designs," Journal of Causal Inference, De Gruyter, vol. 8(1), pages 164-181, January.
    20. Babii, Andrii & Kumar, Rohit, 2023. "Isotonic regression discontinuity designs," Journal of Econometrics, Elsevier, vol. 234(2), pages 371-393.

    More about this item

    Keywords

    Regression discontinuity design; permutation tests; randomization tests; induced ordered statistics; rank tests.;
    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

    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:21/17. 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.