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Further Analysis of the Zipf Law: Does the Rank-Size Rule Really Exist?


  • Fungisai Nota

    () (Department of Economics, Wartburg College)

  • Shunfeng Song

    () (Department of Economics, University of Nevada, Reno)


The widely-used Zipf law has two striking regularities: excellent fit and close-to-one exponent. When the exponent equals to one, the Zipf law collapses into the rank-size rule. This paper further analyzes the Zipf exponent. By changing the sample size, the truncation point, and the mix of cities in the sample, we found that the exponent is close to one only for some selected sub-samples. Using the values of estimated exponent from the rolling sample method, we obtained an elasticity of the exponent with respect to sample size.

Suggested Citation

  • Fungisai Nota & Shunfeng Song, 2008. "Further Analysis of the Zipf Law: Does the Rank-Size Rule Really Exist?," Working Papers 08-005, University of Nevada, Reno, Department of Economics;University of Nevada, Reno , Department of Resource Economics.
  • Handle: RePEc:unr:wpaper:08-005

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    References listed on IDEAS

    1. Jan Eeckhout, 2004. "Gibrat's Law for (All) Cities," American Economic Review, American Economic Association, vol. 94(5), pages 1429-1451, December.
    2. 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.
    3. Shunfeng Song & Kevin Honglin Zhang, 2002. "Urbanisation and City Size Distribution in China," Urban Studies, Urban Studies Journal Limited, vol. 39(12), pages 2317-2327, November.
    4. Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, Oxford University Press, vol. 114(3), pages 739-767.
    5. Xavier Gabaix, 1999. "Zipf's Law and the Growth of Cities," American Economic Review, American Economic Association, vol. 89(2), pages 129-132, May.
    6. Nitsch, Volker, 2005. "Zipf zipped," Journal of Urban Economics, Elsevier, vol. 57(1), pages 86-100, 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. 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.
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    Cited by:

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

    More about this item


    Zipf law; Rank-size rule; Rolling sample method;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • R1 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics

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