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

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  • González-Val, Rafael

Abstract

In this short paper we apply the methodology proposed by Ioannides and Overman (2003) to estimate a local Zipf exponent using data for the entire twentieth century of the complete distribution of cities (incorporated places) without any size restrictions in the US. The results reject Zipf’s Law from a long term perspective, as the estimated values are close to zero. However, decade by decade we find evidence in favour of Zipf’s Law. We also see how periods in which the Zipf exponent grows with city size are interspersed with others in which the relationship between the exponent and city shares is negative.

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  • González-Val, Rafael, 2010. "A Nonparametric Estimation of the Local Zipf Exponent for all US Cities," MPRA Paper 26720, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:26720
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    References listed on IDEAS

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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.
    2. 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.
    3. Jan Eeckhout, 2004. "Gibrat's Law for (All) Cities," American Economic Review, American Economic Association, vol. 94(5), pages 1429-1451, December.
    4. Y. Malevergne & V. Pisarenko & D. Sornette, 2009. "Gibrat’s law for cities: uniformly most powerful unbiased test of the Pareto against the lognormal," Swiss Finance Institute Research Paper Series 09-40, Swiss Finance Institute.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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, October.
    10. Duncan Black & Vernon Henderson, 2003. "Urban evolution in the USA," Journal of Economic Geography, Oxford University Press, vol. 3(4), pages 343-372, October.
    11. 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.
    12. 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.
    13. Giesen, Kristian & Zimmermann, Arndt & Suedekum, Jens, 2010. "The size distribution across all cities - Double Pareto lognormal strikes," Journal of Urban Economics, Elsevier, vol. 68(2), pages 129-137, September.
    14. P. C. Cheshire & E. S. Mills (ed.), 1999. "Handbook of Regional and Urban Economics," Handbook of Regional and Urban Economics, Elsevier, edition 1, volume 3, number 3.
    15. Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(3), pages 739-767.
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    Cited by:

    1. 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.
    2. 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).
    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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