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A Nonparametric Estimation of the Local Zipf Exponent for all US Cities

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  • González-Val, Rafael

Abstract

In this short paper we apply the methodology proposed by Ioannides and Overman (2003) to estimate a local Zipf exponent using data for the entire twentieth century of the complete distribution of cities (incorporated places) without any size restrictions in the US. The results reject Zipf’s Law from a long term perspective, as the estimated values are close to zero. However, decade by decade we find evidence in favour of Zipf’s Law. We also see how periods in which the Zipf exponent grows with city size are interspersed with others in which the relationship between the exponent and city shares is negative.

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File URL: http://mpra.ub.uni-muenchen.de/32222/
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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 26720.

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Date of creation: 15 Nov 2010
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Handle: RePEc:pra:mprapa:26720

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Keywords: Zipf’s Law; Gibrat’s Law; urban growth;

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  1. Xavier Gabaix & Rustam Ibragimov, 2007. "Rank-1/2: A Simple Way to Improve the OLS Estimation of Tail Exponents," NBER Technical Working Papers 0342, National Bureau of Economic Research, Inc.
  2. Kwok Tong Soo, 2004. "Zipfs Law for Cities: A Cross Country Investigation," CEP Discussion Papers dp0641, Centre for Economic Performance, LSE.
  3. 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.
  4. Yannis Menelaos Ioannides & Henry G. Overman, 2003. "Zipf’s law for cities : an empirical examination," LSE Research Online Documents on Economics 583, London School of Economics and Political Science, LSE Library.
  5. Y Ioannides & Henry Overman, 2000. "Cross Sectional Evolution of the US City Size Distribution," CEP Discussion Papers dp0483, Centre for Economic Performance, LSE.
  6. Xavier Gabaix & Yannis M. Ioannides, 2003. "The Evolution of City Size Distributions," Discussion Papers Series, Department of Economics, Tufts University 0310, Department of Economics, Tufts University.
  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.
  8. Xavier Gabaix, 1999. "Zipf'S Law For Cities: An Explanation," The Quarterly Journal of Economics, MIT Press, vol. 114(3), pages 739-767, August.
  9. Duncan Black & Vernon Henderson, 2003. "Urban evolution in the USA," Journal of Economic Geography, Oxford University Press, vol. 3(4), pages 343-372, October.
  10. M. Goldstein & S. Morris & G. Yen, 2004. "Problems with fitting to the power-law distribution," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 41(2), pages 255-258, 09.
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Cited by:
  1. Peter G. Backus, 2012. "Gibrat’s law and legacy for non-profit organisations: a non-parametric analysis," Working Papers 2012/8, Institut d'Economia de Barcelona (IEB).

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