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Gibrat, Zipf, Fisher and Tippett: City Size and Growth Distributions Reconsidered

Author

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  • Christian Schluter
  • Mark Trede

Abstract

This paper is about the city size and growth rate distributions as seen from the perspectives of Zipf's and Gibrat's law. We demonstrate that the Gibrat and Zipf views are theoretically incompatible in view of the Fisher-Tippett theorem, and show that the conflicting hypotheses about the size distribution are testable in a coherent encompassing estimating framework based on a single index. We then show that the two views can be reconciled in a slightly modified but internally consistent statistical model: we connect economic activity and agglomeration in a model of Gibrat-like random growth of sectors, whose random number is linked to Zipf-like city size. The resulting average growth rate is a random mean, and we derive its invariant distribution. Our empirical analysis is based on a recent administrative panel of sizes for all cities in Germany. We find strong evidence for the prediction of the growth model, as well as for a weak version of Zipf's law characterising the right tail of the size distribution.

Suggested Citation

  • Christian Schluter & Mark Trede, 2013. "Gibrat, Zipf, Fisher and Tippett: City Size and Growth Distributions Reconsidered," CQE Working Papers 2713, Center for Quantitative Economics (CQE), University of Muenster.
    • Handle: RePEc:cqe:wpaper:2713
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    File URL: https://www.wiwi.uni-muenster.de/cqe/sites/cqe/files/CQE_Paper/CQE_WP_27_2013.pdf
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    Citations

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    Cited by:

    1. Miguel Puente-Ajovín & Arturo Ramos, 2015. "On the parametric description of the French, German, Italian and Spanish city size distributions," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 54(2), pages 489-509, March.
    2. Massing, Till & Puente-Ajovín, Miguel & Ramos, Arturo, 2020. "On the parametric description of log-growth rates of cities’ sizes of four European countries and the USA," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    3. Puente-Ajovin, Miguel & Ramos, Arturo, 2015. "An improvement over the normal distribution for log-growth rates of city sizes: Empirical evidence for France, Germany, Italy and Spain," MPRA Paper 67471, University Library of Munich, Germany.
    4. Băncescu, Irina & Chivu, Luminiţa & Massing, Till & Preda, Vasile & Puente-Ajovín, Miguel & Ramos, Arturo, 2024. "On the parametric description of log-growth rates of Romanian city sizes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 643(C).
    5. Arturo Ramos, 2017. "Are the log-growth rates of city sizes distributed normally? Empirical evidence for the USA," Empirical Economics, Springer, vol. 53(3), pages 1109-1123, November.
    6. Ramos, Arturo, 2015. "Are the log-growth rates of city sizes normally distributed? Empirical evidence for the US," MPRA Paper 65584, University Library of Munich, Germany.
    7. Ramos, Arturo & Sanz-Gracia, Fernando, 2015. "US city size distribution revisited: Theory and empirical evidence," MPRA Paper 64051, University Library of Munich, Germany.

    More about this item

    Keywords

    Zip's law; Gibrat's law; city size; urban growth;
    All these keywords.

    JEL classification:

    • R11 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Regional Economic Activity: Growth, Development, Environmental Issues, and Changes
    • R12 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Size and Spatial Distributions of Regional Economic Activity; Interregional Trade (economic geography)

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