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Deviations from Zipf’s Law for American Cities

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  • Rafael González-Val

Abstract

This paper presents a simple method for calculating deviations between actual city size and the size which would correspond to it with a Pareto exponent equal to one (Zipf’s law). The results show two differentiated behaviours: most cities (80.25 per cent) present a greater size than that which would fulfil Zipf’s law, while small cities (19.75 per cent) tend to be too small. The aim of the paper is to analyse the distribution element by element, using data about city characteristics from all American cities in 2000, and to explain the deviation between the size predicted by Zipf’s law and the actual size of each city. To do this, a multinomial logit model is used. The most important variables affecting the probability of a city presenting a negative or positive deviation are per capita income, human capital levels and the percentage of the population employed in some sectors.

Suggested Citation

  • Rafael González-Val, 2011. "Deviations from Zipf’s Law for American Cities," Urban Studies, Urban Studies Journal Limited, vol. 48(5), pages 1017-1035, April.
    • Handle: RePEc:sae:urbstu:v:48:y:2011:i:5:p:1017-1035
    DOI: 10.1177/0042098010371394
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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.
    2. Y. Malevergne & V. Pisarenko & D. Sornette, 2009. "Gibrat’s law for cities: uniformly most powerful unbiased test of the Pareto against the lognormal," Swiss Finance Institute Research Paper Series 09-40, Swiss Finance Institute.
    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. 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.
    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. Pines,David & Sadka,Efraim & Zilcha,Itzhak (ed.), 1998. "Topics in Public Economics," Cambridge Books, Cambridge University Press, number 9780521561365.
    7. Yoshihiko Nishiyama & Susumu Osada & Yasuhiro Sato, 2008. "OLS ESTIMATION AND THE t TEST REVISITED IN RANK‐SIZE RULE REGRESSION," Journal of Regional Science, Wiley Blackwell, vol. 48(4), pages 691-716, October.
    8. Shunfeng Song & Kevin Honglin Zhang, 2002. "Urbanisation and City Size Distribution in China," Urban Studies, Urban Studies Journal Limited, vol. 39(12), pages 2317-2327, November.
    9. Cheshire, Paul, 1999. "Trends in sizes and structures of urban areas," Handbook of Regional and Urban Economics, in: P. C. Cheshire & E. S. Mills (ed.), Handbook of Regional and Urban Economics, edition 1, volume 3, chapter 35, pages 1339-1373, Elsevier.
    10. Edward Ludwig Glaeser & Albert Saiz, 2003. "The rise of the skilled city," Working Papers 04-2, Federal Reserve Bank of Philadelphia.
    11. Krugman, Paul, 1991. "Increasing Returns and Economic Geography," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 483-499, June.
    12. Glaeser, Edward L. & Kahn, Matthew E., 2004. "Sprawl and urban growth," 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 56, pages 2481-2527, Elsevier.
    13. Alberto F. Ades & Edward L. Glaeser, 1995. "Trade and Circuses: Explaining Urban Giants," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 110(1), pages 195-227.
    14. Wheaton, William C & Shishido, Hisanobu, 1981. "Urban Concentration, Agglomeration Economies, and the Level of Economic Development," Economic Development and Cultural Change, University of Chicago Press, vol. 30(1), pages 17-30, October.
    15. 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.
    16. Garmestani, Ahjond S. & Allen, Craig R. & Gallagher, Colin M., 2008. "Power laws, discontinuities and regional city size distributions," Journal of Economic Behavior & Organization, Elsevier, vol. 68(1), pages 209-216, October.
    17. Benguigui, Lucien & Blumenfeld-Lieberthal, Efrat, 2007. "A dynamic model for city size distribution beyond Zipf's law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(2), pages 613-627.
    18. Jan Eeckhout, 2009. "Gibrat's Law for (All) Cities: Reply," American Economic Review, American Economic Association, vol. 99(4), pages 1676-1683, September.
    19. 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.
    20. Tabuchi, Takatoshi, 1998. "Urban Agglomeration and Dispersion: A Synthesis of Alonso and Krugman," Journal of Urban Economics, Elsevier, vol. 44(3), pages 333-351, November.
    21. Kwok Tong Soo, 2007. "Zipf's Law and Urban Growth in Malaysia," Urban Studies, Urban Studies Journal Limited, vol. 44(1), pages 1-14, January.
    22. P. C. Cheshire & E. S. Mills (ed.), 1999. "Handbook of Regional and Urban Economics," Handbook of Regional and Urban Economics, Elsevier, edition 1, volume 3, number 3.
    23. 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.
    24. 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, March.
    25. Rafael González‐Val, 2010. "The Evolution Of U.S. City Size Distribution From A Long‐Term Perspective (1900–2000)," Journal of Regional Science, Wiley Blackwell, vol. 50(5), pages 952-972, December.
    26. 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.
    27. Duncan Black & Vernon Henderson, 2003. "Urban evolution in the USA," Journal of Economic Geography, Oxford University Press, vol. 3(4), pages 343-372, October.
    28. 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.
    29. F. Semboloni, 2008. "Hierarchy, cities size distribution and Zipf's law," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 63(3), pages 295-301, June.
    30. Edward L Glaeser & Jesse M Shapiro, 2003. "Urban Growth in the 1990s: Is City Living Back?," Journal of Regional Science, Wiley Blackwell, vol. 43(1), pages 139-165, February.
    31. 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.
    32. 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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