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Size Distributions for All Cities: Lognormal and q-exponential functions

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  • Rafael González-Val

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  • Arturo Ramos-Gutiérrez
  • Fernando Sanz-Gracia

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. The empirical evidence relies on the analysis of urban data of three countries (USA, Spain and Italy) over all of the 20th century.

Suggested Citation

  • Rafael González-Val & Arturo Ramos-Gutiérrez & Fernando Sanz-Gracia, 2011. "Size Distributions for All Cities: Lognormal and q-exponential functions," ERSA conference papers ersa11p554, European Regional Science Association.
  • Handle: RePEc:wiw:wiwrsa:ersa11p554
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    File URL: http://www-sre.wu.ac.at/ersa/ersaconfs/ersa11/e110830aFinal00554.pdf
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    References listed on IDEAS

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    1. Bosker, Maarten & Brakman, Steven & Garretsen, Harry & Schramm, Marc, 2008. "A century of shocks: The evolution of the German city size distribution 1925-1999," Regional Science and Urban Economics, Elsevier, vol. 38(4), pages 330-347, July.
    2. 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.
    3. Hsing, Yu, 1990. "A note on functional forms and the urban size distribution," Journal of Urban Economics, Elsevier, vol. 27(1), pages 73-79, January.
    4. 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.
    5. Kamecke, Ulrich, 1990. "Testing the rank size rule hypothesis with an efficient estimator," Journal of Urban Economics, Elsevier, vol. 27(2), pages 222-231, March.
    6. Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, Oxford University Press, vol. 114(3), pages 739-767.
    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. Guy Michaels & Ferdinand Rauch & Stephen J. Redding, 2012. "Urbanization and Structural Transformation," The Quarterly Journal of Economics, Oxford University Press, vol. 127(2), pages 535-586.
    9. Yannis M. Ioannides & Spyros Skouras, 2009. "Gibrat's Law for (All) Cities: A Rejoinder," Discussion Papers Series, Department of Economics, Tufts University 0740, Department of Economics, Tufts University.
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    Cited by:

    1. Valente J. Matlaba & Mark J. Holmes & Philip McCann & Jacques Poot, 2013. "A Century Of The Evolution Of The Urban System In Brazil," Review of Urban & Regional Development Studies, Wiley Blackwell, vol. 25(3), pages 129-151, November.

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