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Deviations from Zipf’s Law for American cities: an empirical examination


  • Rafael, González-Val


This work presents a simple method for calculating deviations regarding city size and the size which would correspond to it with a Pareto exponent equal to one unit (Zipf’s Law). Recent works show that when considering the entire sample without size restrictions, the estimated Pareto exponent tends to be much lower than one. Our aim is to analyse the distribution element by element, taking data from all American cities in 2000, and explain the deviation of the size predicted by Zipf’s Law and the real size of each city, using variables for each city of per capita income, distribution of employment among sectors, individuals by level of education, etc.; explicative variables which attempt to capture the influence of local externalities. To do this a Multinomial Logit Model is used.

Suggested Citation

  • Rafael, González-Val, 2008. "Deviations from Zipf’s Law for American cities: an empirical examination," MPRA Paper 11504, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:11504

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    References listed on IDEAS

    1. Esteban Rossi-Hansberg & Mark L. J. Wright, 2007. "Urban Structure and Growth," Review of Economic Studies, Oxford University Press, vol. 74(2), pages 597-624.
    2. Jan Eeckhout, 2004. "Gibrat's Law for (All) Cities," American Economic Review, American Economic Association, vol. 94(5), pages 1429-1451, December.
    3. Gilles Duranton, 2007. "Urban Evolutions: The Fast, the Slow, and the Still," American Economic Review, American Economic Association, vol. 97(1), pages 197-221, March.
    4. 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.
    5. 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.
    6. Duncan Black & Vernon Henderson, 2003. "Urban evolution in the USA," Journal of Economic Geography, Oxford University Press, vol. 3(4), pages 343-372, October.
    7. Krugman, Paul, 1991. "Increasing Returns and Economic Geography," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 483-499, June.
    8. Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, Oxford University Press, vol. 114(3), pages 739-767.
    9. Small, Kenneth A & Hsiao, Cheng, 1985. "Multinomial Logit Specification Tests," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(3), pages 619-627, October.
    10. Edward L. Glaeser & Joseph Gyourko & Raven E. Saks, 2006. "Urban growth and housing supply," Journal of Economic Geography, Oxford University Press, vol. 6(1), pages 71-89, January.
    11. Edward L. Glaeser & Matthew E. Kahn, 2001. "Decentralized Employment and the Transformation of the American City," Harvard Institute of Economic Research Working Papers 1912, Harvard - Institute of Economic Research.
    12. 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.
    13. J. Scott Long & Jeremy Freese, 2006. "Regression Models for Categorical Dependent Variables using Stata, 2nd Edition," Stata Press books, StataCorp LP, edition 2, number long2, December.
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    Cited by:

    1. Tarsha EASON & Ahjond S. GARMESTANI, 2012. "Cross-Scale Dynamics Of A Regional Urban System Through Time," Region et Developpement, Region et Developpement, LEAD, Universite du Sud - Toulon Var, vol. 36, pages 55-77.

    More about this item


    Cities; Zipf’s Law; deviations; Pareto distribution; Multinomial logit;

    JEL classification:

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