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A Nonparametric Estimation of the Local Zipf Exponent for all US Cities

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  • Rafael González-Val

    (Universitat de Barcelona and Institut d'Economia de Barcelona (IEB), Departamento de Economía Pública, Economía Política y Economía Española, Universitat de Barcelona, Facultat d'Economia i Empresa, Av. Diagonal 690, 08034 Barcelona, Spain)

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.

Suggested Citation

  • Rafael González-Val, 2012. "A Nonparametric Estimation of the Local Zipf Exponent for all US Cities," Environment and Planning B, , vol. 39(6), pages 1119-1130, December.
    • Handle: RePEc:sae:envirb:v:39:y:2012:i:6:p:1119-1130
    DOI: 10.1068/b37182
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    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.
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    10. Rafael González‐Val, 2010. "The Evolution Of U.S. City Size Distribution From A Long‐Term Perspective (1900–2000)," Journal of Regional Science, Wiley Blackwell, vol. 50(5), pages 952-972, December.
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    12. 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.
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    14. 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.
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    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).
    2. Rafael González-Val & Luis Lanaspa & Fernando Sanz-Gracia, 2014. "New Evidence on Gibrat’s Law for Cities," Urban Studies, Urban Studies Journal Limited, vol. 51(1), pages 93-115, January.
    3. 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).
    4. Chengri Ding & Zhi Li, 2019. "Size and urban growth of Chinese cities during the era of transformation toward a market economy," Environment and Planning B, , vol. 46(1), pages 27-46, January.
    5. 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.

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    More about this item

    Keywords

    Zipf's law; Gibrat's law; urban growth;
    All these keywords.

    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

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