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Further Analysis of the Zipf Law: Does the Rank-Size Rule Really Exist?

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Author Info
Fungisai Nota () (Department of Economics, Wartburg College)
Shunfeng Song () (Department of Economics, University of Nevada, Reno)

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Abstract

The widely-used Zipf law has two striking regularities: excellent fit and close-to-one exponent. When the exponent equals to one, the Zipf law collapses into the rank-size rule. This paper further analyzes the Zipf exponent. By changing the sample size, the truncation point, and the mix of cities in the sample, we found that the exponent is close to one only for some selected sub-samples. Using the values of estimated exponent from the rolling sample method, we obtained an elasticity of the exponent with respect to sample size.

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File URL: http://www.business.unr.edu/econ/wp/papers/UNRECONWP08005.pdf
File Format: application/pdf
File Function: First version, 2008
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Publisher Info
Paper provided by University of Nevada, Reno, Department of Economics & University of Nevada, Reno , Department of Resource Economics in its series Working Papers with number 08-005.

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Length: 11 pages
Date of creation: Sep 2008
Date of revision:
Handle: RePEc:unr:wpaper:08-005

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Related research
Keywords: Zipf law; Rank-size rule; Rolling sample method;

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Find related papers by JEL classification:
C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General
R1 - Urban, Rural, and Regional Economics - - General Regional Economics

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References listed on IDEAS
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  1. 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. [Downloadable!] (restricted)
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  2. 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. [Downloadable!] (restricted)
  3. Xavier Gabaix, 1999. "Zipf's Law and the Growth of Cities," American Economic Review, American Economic Association, vol. 89(2), pages 129-132, May. [Downloadable!] (restricted)
  4. 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)
  5. Nitsch, Volker, 2005. "Zipf zipped," Journal of Urban Economics, Elsevier, vol. 57(1), pages 86-100, January. [Downloadable!] (restricted)
  6. Gan, Li & Li, Dong & Song, Shunfeng, 2006. "Is the Zipf law spurious in explaining city-size distributions?," Economics Letters, Elsevier, vol. 92(2), pages 256-262, August. [Downloadable!] (restricted)
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