Advanced Search
MyIDEAS: Login to save this article or follow this journal



Author Info

  • Yoshihiko Nishiyama
  • Susumu Osada
  • Yasuhiro Sato


The rank-size rule and Zipf's law for city sizes have been traditionally examined by means of OLS estimation and the "t" test. This paper studies the accurate and approximate properties of the OLS estimator and obtains the distribution of the "t" statistic under the assumption of Zipf's law (i.e., Pareto distribution). Indeed, we show that the "t" statistic explodes asymptotically even under the null, indicating that a mechanical application of the "t" test yields a serious type I error. To overcome this problem, critical regions of the "t" test are constructed to test the Zipf's law. Using these corrected critical regions, we can conclude that our results are in favor of the Zipf's law for many more countries than in the previous researches such as Rosen and Resnick (1980) or Soo (2005). By using the same database as that used in Soo (2005), we demonstrate that the Zipf law is rejected for only one of 24 countries under our test whereas it is rejected for 23 of 24 countries under the usual "t" test. We also propose a more efficient estimation procedure and provide empirical applications of the theory for some countries. Copyright (c) 2008, Wiley Periodicals, Inc.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL:
File Function: link to full text
Download Restriction: Access to full text is restricted to subscribers.

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Bibliographic Info

Article provided by Wiley Blackwell in its journal Journal of Regional Science.

Volume (Year): 48 (2008)
Issue (Month): 4 ()
Pages: 691-716

as in new window
Handle: RePEc:bla:jregsc:v:48:y:2008:i:4:p:691-716

Contact details of provider:
Web page:

Order Information:

Related research



No references listed on IDEAS
You can help add them by filling out this form.


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

Cited by:
  1. Wen-Tai Hsu & Tomoya Mori & Tony E. Smith, 2014. "Spatial Patterns and Size Distributions of Cities," KIER Working Papers 882, Kyoto University, Institute of Economic Research.
  2. González-Val, Rafael, 2010. "A Nonparametric Estimation of the Local Zipf Exponent for all US Cities," MPRA Paper 26720, University Library of Munich, Germany.
  3. Rafael GONZÀLEZ-VAL, 2012. "Zipf’S Law: Main Issues In Empirical Work," Region et Developpement, Region et Developpement, LEAD, Universite du Sud - Toulon Var, vol. 36, pages 147-164.
  4. Harry P. Bowen & Haris Munandar & Jean-Marie Viaene, 2010. "On the Extent of Economic Integration: A Comparison of EU Countries and US States," Tinbergen Institute Discussion Papers 10-009/2, Tinbergen Institute, revised 04 Jul 2011.
  5. Francisco Goerlich, 2013. "A simple and efficient test for the Pareto law," Empirical Economics, Springer, vol. 45(3), pages 1367-1381, December.
  6. Sueli Moro & Reginaldo J. Santos, 2013. "The characteristics and evolution of the Brazilian spatial urban system: empirical evidences for the long-run, 1970-2010," Textos para Discussão Cedeplar-UFMG 474, Cedeplar, Universidade Federal de Minas Gerais.
  7. L. Benguigui & E. Blumenfeld-Lieberthal, 2011. "The end of a paradigm: is Zipf’s law universal?," Journal of Geographical Systems, Springer, vol. 13(1), pages 87-100, March.
  8. Tomoya Mori & Tony E. Smith, 2009. "A Reconsideration of the NAS Rule from an Industrial Agglomeration Perspective," KIER Working Papers 669, Kyoto University, Institute of Economic Research.


This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.


Access and download statistics


When requesting a correction, please mention this item's handle: RePEc:bla:jregsc:v:48:y:2008:i:4:p:691-716. 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-Blackwell Digital Licensing) or (Christopher F. Baum).

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 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.