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Uneven landscapes and the city size distribution

Author

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  • Sanghoon Lee

    (University of British Columbia)

  • Qiang Li

    (Shanghai University of Finance and Economics)

Abstract

This paper proposes a new explanation for Zipf’s law often observed in the top tail of city size distribution. We show that Zipf’s law can emerge if city size can be expressed as a product of multiple random factors. Each of the factors need not generate Zipf’s law by itself. The key implication is that we cannot reject a model simply because the model does not generate Zipf’s law. A single model, typically representing only one factor, may not generate Zipf’s law, but if we have many such models together as in reality, Zipf’s law may emerge.

Suggested Citation

  • Sanghoon Lee & Qiang Li, 2010. "Uneven landscapes and the city size distribution," Working Papers 2010/41, Institut d'Economia de Barcelona (IEB).
    • Handle: RePEc:ieb:wpaper:doc2010-41
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    1. Henderson, J V, 1974. "The Sizes and Types of Cities," American Economic Review, American Economic Association, vol. 64(4), pages 640-656, September.
    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. Hernán D. Rozenfeld & Diego Rybski & Xavier Gabaix & Hernán A. Makse, 2011. "The Area and Population of Cities: New Insights from a Different Perspective on Cities," American Economic Review, American Economic Association, vol. 101(5), pages 2205-2225, August.
    5. Esteban Rossi-Hansberg & Mark L. J. Wright, 2007. "Urban Structure and Growth," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(2), pages 597-624.
    6. Kristian Behrens & Gilles Duranton & Frédéric Robert-Nicoud, 2014. "Productive Cities: Sorting, Selection, and Agglomeration," Journal of Political Economy, University of Chicago Press, vol. 122(3), pages 507-553.
    7. 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.
    8. Thomas J. Holmes & Sanghoon Lee, 2010. "Cities as Six-by-Six-Mile Squares: Zipf's Law?," NBER Chapters, in: Agglomeration Economics, pages 105-131, National Bureau of Economic Research, Inc.
    9. Krugman, Paul, 1991. "Increasing Returns and Economic Geography," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 483-499, June.
    10. Morris A. Davis & Francois Ortalo-Magne, 2011. "Household Expenditures, Wages, Rents," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 14(2), pages 248-261, April.
    11. Edward L. Glaeser & Giacomo A. M. Ponzetto & Kristina Tobio, 2014. "Cities, Skills and Regional Change," Regional Studies, Taylor & Francis Journals, vol. 48(1), pages 7-43, January.
    12. Duranton, Gilles, 2006. "Some foundations for Zipf's law: Product proliferation and local spillovers," Regional Science and Urban Economics, Elsevier, vol. 36(4), pages 542-563, July.
    13. 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.
    14. 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.
    15. 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.
    16. Harris Dobkins, Linda & Ioannides, Yannis M., 2001. "Spatial interactions among U.S. cities: 1900-1990," Regional Science and Urban Economics, Elsevier, vol. 31(6), pages 701-731, November.
    17. Rappaport, Jordan & Sachs, Jeffrey D, 2003. "The United States as a Coastal Nation," Journal of Economic Growth, Springer, vol. 8(1), pages 5-46, March.
    18. Roback, Jennifer, 1982. "Wages, Rents, and the Quality of Life," Journal of Political Economy, University of Chicago Press, vol. 90(6), pages 1257-1278, December.
    19. 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.
    20. Nikolaos Kourogenis & Nikitas Pittis, 2011. "Mixing Conditions, Central Limit Theorems, and Invariance Principles: A Survey of the Literature with Some New Results on Heteroscedastic Sequences," Econometric Reviews, Taylor & Francis Journals, vol. 30(1), pages 88-108.
    21. Ioannides, Yannis & Skouras, Spyros, 2013. "US city size distribution: Robustly Pareto, but only in the tail," Journal of Urban Economics, Elsevier, vol. 73(1), pages 18-29.
    22. Edward L. Glaeser & Joshua D. Gottlieb, 2009. "The Wealth of Cities: Agglomeration Economies and Spatial Equilibrium in the United States," Journal of Economic Literature, American Economic Association, vol. 47(4), pages 983-1028, December.
    23. Wen‐Tai Hsu, 2012. "Central Place Theory and City Size Distribution," Economic Journal, Royal Economic Society, vol. 122(563), pages 903-932, September.
    24. Duncan Black & Vernon Henderson, 2003. "Urban evolution in the USA," Journal of Economic Geography, Oxford University Press, vol. 3(4), pages 343-372, October.
    25. Moshe Levy, 2009. "Gibrat's Law for (All) Cities: Comment," American Economic Review, American Economic Association, vol. 99(4), pages 1672-1675, September.
    26. 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.
    27. Donald R. Davis & David E. Weinstein, 2002. "Bones, Bombs, and Break Points: The Geography of Economic Activity," American Economic Review, American Economic Association, vol. 92(5), pages 1269-1289, December.
    28. Krugman, Paul, 1996. "Confronting the Mystery of Urban Hierarchy," Journal of the Japanese and International Economies, Elsevier, vol. 10(4), pages 399-418, December.
    29. Rappaport, Jordan, 2008. "Consumption amenities and city population density," Regional Science and Urban Economics, Elsevier, vol. 38(6), pages 533-552, November.
    30. 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.
    31. J. V. Henderson & J. F. Thisse (ed.), 2004. "Handbook of Regional and Urban Economics," Handbook of Regional and Urban Economics, Elsevier, edition 1, volume 4, number 4.
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    8. Duranton, Gilles & Puga, Diego, 2014. "The Growth of Cities," Handbook of Economic Growth, in: Philippe Aghion & Steven Durlauf (ed.), Handbook of Economic Growth, edition 1, volume 2, chapter 5, pages 781-853, Elsevier.
    9. Arshad, Sidra & Hu, Shougeng & Ashraf, Badar Nadeem, 2019. "Zipf’s law, the coherence of the urban system and city size distribution: Evidence from Pakistan," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 87-103.
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    16. Kristian Behrens & Gilles Duranton & Frédéric Robert-Nicoud, 2014. "Productive Cities: Sorting, Selection, and Agglomeration," Journal of Political Economy, University of Chicago Press, vol. 122(3), pages 507-553.
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    More about this item

    Keywords

    City size distribution; Zipf’s law; rank-size rule; log-normal distribution;
    All these keywords.

    JEL classification:

    • D39 - Microeconomics - - Distribution - - - Other
    • 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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