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

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Rafael, González-Val

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Abstract

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.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 11504.

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Date of creation: 10 Nov 2008
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Handle: RePEc:pra:mprapa:11504

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Related research
Keywords: Cities; Zipf’s Law; deviations; Pareto distribution; Multinomial logit;

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Find related papers by JEL classification:
C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Econometric and Statistical Methods; Specific Distributions
R00 - Urban, Rural, and Regional Economics - - General - - - General
R12 - Urban, Rural, and Regional Economics - - General Regional Economics - - - Size and Spatial Distributions of Regional Economic Activity; Interregional Trade (economic geography)

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  1. 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 619-27, October. [Downloadable!] (restricted)
  2. Duncan Black & Vernon Henderson, 2003. "Urban evolution in the USA," Journal of Economic Geography, Oxford University Press, vol. 3(4), pages 343-372, October.
  3. 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. [Downloadable!] (restricted)
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  4. Esteban Rossi-Hansberg & Mark L. J. Wright, 2003. "Urban structure and growth," Discussion Paper / Institute for Empirical Macroeconomics 141, Federal Reserve Bank of Minneapolis. [Downloadable!]
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  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. [Downloadable!] (restricted)
  6. 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. [Downloadable!] (restricted)
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  7. Edward L. Glaeser & Matthew E. Kahn, 2001. "Decentralized Employment and the Transformation of the American City," NBER Working Papers 8117, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  8. Krugman, Paul, 1991. "Increasing Returns and Economic Geography," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 483-99, June. [Downloadable!] (restricted)
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  9. 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. [Downloadable!]
  10. Xavier Gabaix, 1999. "Zipf'S Law For Cities: An Explanation," The Quarterly Journal of Economics, MIT Press, vol. 114(3), pages 739-767, August. [Downloadable!] (restricted)
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