IDEAS home Printed from https://ideas.repec.org/a/pio/envirb/v39y2012i6p1119-1130.html
   My bibliography  Save this article

A nonparametric estimation of the local Zipf exponent for all US cities

Author

Listed:
  • Rafael González-Val

Abstract

The methodology proposed by Ioannides and Overman (2003 Regional Science and Urban Economics 33 127–137) is applied to estimate a local Zipf exponent using data for the entire 20th century of the complete distribution of cities (incorporated places) without any size restrictions in the US. First, kernel regressions are run using the Nadaraya–Watson estimator, excluding some atypical observations (5.66% of the sample). The results reject Zipf’s law from a long-term perspective, but the evidence supports Gibrat’s law. In the short term, decade by decade, the evidence in favour of Zipf’s law is stronger. Second, to consider the whole sample the LOcally WEighted Scatter plot Smoothing (LOWESS) algorithm is applied. From a long-term perspective the evidence supporting Zipf’s law increases, but the evidence supporting Gibrat’s law is weaker, as small cities exhibit higher variance than the other cities. Finally, the estimated values by decade are again closer to Zipf’s law. Keywords: Zipf’s law, Gibrat’s law, urban growth

Suggested Citation

  • Rafael González-Val, 2012. "A nonparametric estimation of the local Zipf exponent for all US cities," Environment and Planning B: Planning and Design, Pion Ltd, London, vol. 39(6), pages 1119-1130, November.
  • Handle: RePEc:pio:envirb:v:39:y:2012:i:6:p:1119-1130
    as

    Download full text from publisher

    File URL: http://www.envplan.com/abstract.cgi?id=b37182
    File Function: abstract
    Download Restriction: Fulltext access restricted to subscribers, see http://www.envplan.co.uk/B.html for details

    File URL: http://www.envplan.com/epb/fulltext/b39/b37182.pdf
    File Function: main text
    Download Restriction: Fulltext access restricted to subscribers, see http://www.envplan.co.uk/B.html for details

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Overman, Henry G. & Ioannides, Yannis M., 2001. "Cross-Sectional Evolution of the U.S. City Size Distribution," Journal of Urban Economics, Elsevier, vol. 49(3), pages 543-566, May.
    2. Ioannides, Yannis M. & Overman, Henry G., 2003. "Zipf's law for cities: an empirical examination," Regional Science and Urban Economics, Elsevier, vol. 33(2), pages 127-137, March.
    3. 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.
    4. Yoshihiko Nishiyama & Susumu Osada & Yasuhiro Sato, 2008. "OLS ESTIMATION AND THE "t" TEST REVISITED IN RANK-SIZE RULE REGRESSION," Journal of Regional Science, Wiley Blackwell, vol. 48(4), pages 691-716.
    5. Duncan Black & Vernon Henderson, 2003. "Urban evolution in the USA," Journal of Economic Geography, Oxford University Press, vol. 3(4), pages 343-372, October.
    6. Cheshire, Paul, 1999. "Trends in sizes and structures of urban areas," Handbook of Regional and Urban Economics,in: P. C. Cheshire & E. S. Mills (ed.), Handbook of Regional and Urban Economics, edition 1, volume 3, chapter 35, pages 1339-1373 Elsevier.
    7. M. Goldstein & S. Morris & G. Yen, 2004. "Problems with fitting to the power-law distribution," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 41(2), pages 255-258, September.
    8. Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, Oxford University Press, vol. 114(3), pages 739-767.
    9. 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.
    10. 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.
    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. Peter G. Backus, 2012. "Gibrat’s law and legacy for non-profit organisations: a non-parametric analysis," Working Papers 2012/8, Institut d'Economia de Barcelona (IEB).

    More about this item

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - 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:pio:envirb:v:39:y:2012:i:6:p:1119-1130. 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: (Neil Hammond). General contact details of provider: http://www.pion.co.uk .

    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.