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Pareto or log-normal? A recursive-truncation approach to the distribution of (all) cities

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  • Giorgio Fazio
  • Marco Modica

Abstract

Traditionally, it is assumed that the population size of cities in a country follows a Pareto distribution. This assumption is typically supported by finding evidence of Zipf's Law. Recent studies question this finding, highlighting that, while the Pareto distribution may fit reasonably well when the data is truncated at the upper tail, i.e. for the largest cities of a country, the log-normal distribution may apply when all cities are considered. Moreover, conclusions may be sensitive to the choice of a particular truncation threshold, a yet overlooked issue in the literature. In this paper, then, we reassess the city size distribution in relation to its sensitivity to the choice of truncation point. In particular, we look at US Census data and apply a recursive-truncation approach to estimate Zipf's Law and a non-parametric alternative test where we consider each possible truncation point of the distribution of all cities. Results confirm the sensitivity of results to the truncation point. Moreover, repeating the analysis over simulated data confirms the difficulty of distinguishing a Pareto tail from the tail of a log-normal and, in turn, identifying the city size distribution as a false or a weak Pareto law.

Suggested Citation

  • Giorgio Fazio & Marco Modica, 2012. "Pareto or log-normal? A recursive-truncation approach to the distribution of (all) cities," Working Papers 2012_10, Business School - Economics, University of Glasgow.
  • Handle: RePEc:gla:glaewp:2012_10
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    References listed on IDEAS

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    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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    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. Marco Bee & Massimo Riccaboni & Stefano Schiavo, 2011. "Pareto versus lognormal: a maximum entropy test," Department of Economics Working Papers 1102, Department of Economics, University of Trento, Italia.
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    Cited by:

    1. M. Modica & A. Reggiani & P. Nijkamp, 2015. "A Comparative Analysis of Gibrat’s and Zipf’s Law on Urban Population," Working Papers wp1008, Dipartimento Scienze Economiche, Universita' di Bologna.
    2. Marco Modica, 2014. "Does the EU have homogeneous urban structure area? The role of agglomeration and the impact of shocks on urban structure," ERSA conference papers ersa14p229, European Regional Science Association.
    3. Ioannides, Yannis M. & Zhang, Junfu, 2017. "Walled cities in late imperial China," Journal of Urban Economics, Elsevier, vol. 97(C), pages 71-88.

    More about this item

    Keywords

    City size distribution; Pareto and Log-normal; Zipf's Law; Kolmogorov- Smirnov; Recursive analysis;

    JEL classification:

    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • D30 - Microeconomics - - Distribution - - - General
    • 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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