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On the best functions to describe city size distributions

Author

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  • González-Val, Rafael
  • Ramos, Arturo
  • Sanz-Gracia, Fernando

Abstract

This paper analyses in detail the features offered by a function which is practically new to Urban Economics, the q-exponential, in describing city size distributions. We highlight two contributions. First, we propose a new and simple procedure for estimating their parameters. Second, and more importantly, we explain the characteristics associated with two traditional graphic methods (Zipf plots and cumulative density functions) for discriminating between functions. We apply them to the lognormal and q-exponential, justifying them as the best functions for explaining the entire distribution, and that the relationship between them is of complementarity.

Suggested Citation

  • González-Val, Rafael & Ramos, Arturo & Sanz-Gracia, Fernando, 2010. "On the best functions to describe city size distributions," MPRA Paper 21921, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:21921
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    References listed on IDEAS

    as
    1. Jan Eeckhout, 2004. "Gibrat's Law for (All) Cities," American Economic Review, American Economic Association, vol. 94(5), pages 1429-1451, December.
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    3. 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.
    4. 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.
    5. Paul Cheshire & Stefano Magrini, 2006. "Population growth in European cities: Weather matters - but only nationally," Regional Studies, Taylor & Francis Journals, vol. 40(1), pages 23-37.
    6. Kristian Giesen & Jens Suedekum, 2012. "The size distribution across all “cities”: a unifying approach," Working Papers 2012/2, Institut d'Economia de Barcelona (IEB).
    7. William J. Reed, 2002. "On the Rank‐Size Distribution for Human Settlements," Journal of Regional Science, Wiley Blackwell, vol. 42(1), pages 1-17, February.
    8. Jan Eeckhout, 2009. "Gibrat's Law for (All) Cities: Reply," American Economic Review, American Economic Association, vol. 99(4), pages 1676-1683, September.
    9. 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.
    10. Rafael González-Val & Luis Lanaspa & Fernando Sanz, 2011. "Gibrat's Law for Cities Revisited," ERSA conference papers ersa10p199, European Regional Science Association.
    11. 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.
    12. 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.
    13. 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.
    14. Duncan Black & Vernon Henderson, 2003. "Urban evolution in the USA," Journal of Economic Geography, Oxford University Press, vol. 3(4), pages 343-372, October.
    15. Kristian Giesen & Jens Suedekum, 2012. "The Size Distribution across all "Cities": A Unifying Approach," CESifo Working Paper Series 3730, CESifo Group Munich.
    16. 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.
    17. Krugman, Paul, 1996. "Confronting the Mystery of Urban Hierarchy," Journal of the Japanese and International Economies, Elsevier, vol. 10(4), pages 399-418, December.
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    More about this item

    Keywords

    city size distribution; q-exponential; lognormal;
    All these keywords.

    JEL classification:

    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General

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