IDEAS home Printed from https://ideas.repec.org/a/wly/emetrp/v85y2017ip1013-1030.html
   My bibliography  Save this article

Randomization Tests Under an Approximate Symmetry Assumption

Author

Listed:
  • Ivan A. Canay
  • Joseph P. Romano
  • Azeem M. Shaikh

Abstract

This paper develops a theory of randomization tests under an approximate symmetry assumption. Randomization tests provide a general means of constructing tests that control size in finite samples whenever the distribution of the observed data exhibits symmetry under the null hypothesis. Here, by exhibits symmetry we mean that the distribution remains invariant under a group of transformations. In this paper, we provide conditions under which the same construction can be used to construct tests that asymptotically control the probability of a false rejection whenever the distribution of the observed data exhibits approximate symmetry in the sense that the limiting distribution of a function of the data exhibits symmetry under the null hypothesis. An important application of this idea is in settings where the data may be grouped into a fixed number of “clusters” with a large number of observations within each cluster. In such settings, we show that the distribution of the observed data satisfies our approximate symmetry requirement under weak assumptions. In particular, our results allow for the clusters to be heterogeneous and also have dependence not only within each cluster, but also across clusters. This approach enjoys several advantages over other approaches in these settings.

Suggested Citation

  • 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.
  • Handle: RePEc:wly:emetrp:v:85:y:2017:i::p:1013-1030
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/
    Download Restriction: no

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Uri Gneezy & John List & Jeffrey Livingston & Xiangdong Qin & Sally Sadoff & Yang Xu, 2017. "Measuring success in education: the role of effort on the test itself," Framed Field Experiments 00614, The Field Experiments Website.
    2. Ivan A. Canay & Vishal Kamat, 2015. "Approximate permutation tests and induced order statistics in the regression discontinuity design," CeMMAP working papers CWP27/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. 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.
    4. Timmermann, Allan & Zhu, Yinchu, 2019. "Comparing Forecasting Performance with Panel Data," CEPR Discussion Papers 13746, C.E.P.R. Discussion Papers.
    5. Ivan A. Canay & Andres Santos & Azeem M. Shaikh, 2018. "The wild bootstrap with a "small" number of "large" clusters," CeMMAP working papers CWP27/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. Juwon Seo, 2018. "Randomization Tests for Equality in Dependence Structure," Papers 1811.02105, arXiv.org.
    7. Jinyong Hahn & Ruoyao Shi, 2017. "Synthetic Control and Inference," Econometrics, MDPI, Open Access Journal, vol. 5(4), pages 1-12, November.
    8. Hansen, Bruce E. & Lee, Seojeong, 2019. "Asymptotic theory for clustered samples," Journal of Econometrics, Elsevier, vol. 210(2), pages 268-290.
    9. James G. MacKinnon & Matthew D. Webb, 2017. "Pitfalls When Estimating Treatment Effects Using Clustered Data," Working Paper 1387, Economics Department, Queen's University.
    10. Ferman, Bruno, 2019. "Inference in Differences-in-Differences: How Much Should We Trust in Independent Clusters?," MPRA Paper 93746, University Library of Munich, Germany.
    11. Andreas Hagemann, 2019. "Permutation inference with a finite number of heterogeneous clusters," Papers 1907.01049, arXiv.org.
    12. 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 Jun 2019.
    13. Michael P. Leung & Hyungsik Roger Moon, 2019. "Normal Approximation in Large Network Models," Papers 1904.11060, arXiv.org.

    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:wly:emetrp:v:85:y:2017:i::p:1013-1030. 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: (Wiley Content Delivery). General contact details of provider: http://edirc.repec.org/data/essssea.html .

    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.

    We have no references for this item. You can help adding them by using 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.