IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Log in (now much improved!) to save this paper

Zipf's Law for Cities: On a New Testing Procedure

Author Info

Listed author(s):
  • Sebastien TERRA

    ()

Abstract

In this paper, we provide a new framework to assess the validity of Zipf 's Law for cities. Zipf 's Law states that, within a country, the distribution of city sizes follows a Pareto distribution with a Pareto index equal to 1. We adopt a two-step approach where we formally test if the distribution of city sizes is a Pareto distribution and then we estimate the Pareto index. Through Monte Carlo experiments, we investigate the nite sample performances of this testing procedure and we compare the small-sample properties of a new estimator (the minimum variance unbiased estimator) to those of commonly used estimators. The minimum variance unbiased estimator turns out to be more efficient and unbiased. We use this two-step approach to examine empirically the validity of Zipf 's Law on a sample of 115 countries. Zipf 's Law is not rejected in most countries (62 out of 115, or 53.9%).

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: http://publi.cerdi.org/ed/2009/2009.20.pdf
Download Restriction: no

Paper provided by CERDI in its series Working Papers with number 200920.

as
in new window

Length: 28
Date of creation: 2009
Handle: RePEc:cdi:wpaper:1102
Contact details of provider: Postal:
65 Bd. F. Mitterrand, 63000 Clermont-Ferrand

Phone: (33-4) 73 17 74 00
Fax: (33-4) 73 17 74 28
Web page: http://cerdi.org/

More information through EDIRC

Keywords: Zipf 's Law; Pareto distribution; Monte Carlo study; Minimum variance unbiased estimator; Developing countries;

This paper has been announced in the following NEP Reports:

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as
in new window


  1. Xavier Gabaix & Rustam Ibragimov, 2011. "Rank - 1 / 2: A Simple Way to Improve the OLS Estimation of Tail Exponents," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(1), pages 24-39, January.
  2. Yannis M. Ioannides & Henry G. Overman & Esteban Rossi-Hansberg & Kurt Schmidheiny, 2008. "The effect of information and communication technologies on urban structure," Economic Policy, CEPR;CES;MSH, vol. 23, pages 201-242, 04.
  3. Esteban Rossi-Hansberg & Mark L. J. Wright, 2007. "Urban Structure and Growth," Review of Economic Studies, Oxford University Press, vol. 74(2), pages 597-624.
  4. Córdoba, Juan-Carlos, 2008. "On the distribution of city sizes," Journal of Urban Economics, Elsevier, vol. 63(1), pages 177-197, January.
  5. Gabaix, Xavier & Ioannides, Yannis M., 2004. "The evolution of city size distributions," Handbook of Regional and Urban Economics,in: J. V. Henderson & J. F. Thisse (ed.), Handbook of Regional and Urban Economics, edition 1, volume 4, chapter 53, pages 2341-2378 Elsevier.
  6. Kwok Tong Soo, 2007. "Zipf's Law and Urban Growth in Malaysia," Urban Studies, Urban Studies Journal Limited, vol. 44(1), pages 1-14, January.
  7. Jan Eeckhout, 2004. "Gibrat's Law for (All) Cities," American Economic Review, American Economic Association, vol. 94(5), pages 1429-1451, December.
  8. Alperovich, Gershon, 1988. "A new testing procedure of the rank size distribution," Journal of Urban Economics, Elsevier, vol. 23(2), pages 251-259, March.
  9. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521766555, September.
  10. Krugman, Paul, 1996. "Confronting the Mystery of Urban Hierarchy," Journal of the Japanese and International Economies, Elsevier, vol. 10(4), pages 399-418, December.
  11. Mansury, Yuri & Gulyas, Laszlo, 2007. "The emergence of Zipf's Law in a system of cities: An agent-based simulation approach," Journal of Economic Dynamics and Control, Elsevier, vol. 31(7), pages 2438-2460, July.
  12. Alperovich, Gershon, 1984. "The size distribution of cities: On the empirical validity of the rank-size rule," Journal of Urban Economics, Elsevier, vol. 16(2), pages 232-239, September.
  13. Julie Gallo & Coro Chasco, 2008. "Spatial analysis of urban growth in Spain, 1900–2001," Empirical Economics, Springer, vol. 34(1), pages 59-80, February.
  14. R. Quandt, 1966. "Old and new methods of estimation and the pareto distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 10(1), pages 55-82, December.
  15. M. Baxter, 1980. "Minimum variance unbiased estimation of the parameters of the Pareto distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 27(1), pages 133-138, December.
  16. Soo, Kwok Tong, 2005. "Zipf's Law for cities: a cross-country investigation," Regional Science and Urban Economics, Elsevier, vol. 35(3), pages 239-263, May.
  17. Duranton, Gilles, 2006. "Some foundations for Zipf's law: Product proliferation and local spillovers," Regional Science and Urban Economics, Elsevier, vol. 36(4), pages 542-563, July.
  18. Alberto F. Ades & Edward L. Glaeser, 1995. "Trade and Circuses: Explaining Urban Giants," The Quarterly Journal of Economics, Oxford University Press, vol. 110(1), pages 195-227.
  19. Jan Eeckhout, 2009. "Gibrat's Law for (All) Cities: Reply," American Economic Review, American Economic Association, vol. 99(4), pages 1676-1683, September.
  20. Moshe Levy, 2009. "Gibrat's Law for (All) Cities: Comment," American Economic Review, American Economic Association, vol. 99(4), pages 1672-1675, September.
  21. Pavel Cizek & Wolfgang Karl Härdle & Rafal Weron, 2005. "Statistical Tools for Finance and Insurance," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook0501.
  22. Rosen, Kenneth T. & Resnick, Mitchel, 1980. "The size distribution of cities: An examination of the Pareto law and primacy," Journal of Urban Economics, Elsevier, vol. 8(2), pages 165-186, September.
  23. Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, Oxford University Press, vol. 114(3), pages 739-767.
  24. Cameron, Trudy Ann, 1990. "One-stage structural models to explain city size," Journal of Urban Economics, Elsevier, vol. 27(3), pages 294-307, May.
  25. Xavier Gabaix, 1999. "Zipf's Law and the Growth of Cities," American Economic Review, American Economic Association, vol. 89(2), pages 129-132, May.
  26. Nitsch, Volker, 2005. "Zipf zipped," Journal of Urban Economics, Elsevier, vol. 57(1), pages 86-100, January.
  27. Gan, Li & Li, Dong & Song, Shunfeng, 2006. "Is the Zipf law spurious in explaining city-size distributions?," Economics Letters, Elsevier, vol. 92(2), pages 256-262, August.
Full references (including those not matched with items on IDEAS)

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

as
in new window


Cited by:

  1. P. Nijkamp & A. Reggiani, 2012. "Did Zipf Anticipate Socio-Economic Spatial Networks?," Working Papers wp816, Dipartimento Scienze Economiche, Universita' di Bologna.

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:cdi:wpaper:1102. 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: (Vincent Mazenod)

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.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.