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

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  • Fungisai Nota

    ()
    (Department of Resource Economics, University of Nevada, Reno)

  • Shunfeng Song

    ()
    (Department of Economics, University of Nevada, Reno)

Abstract

The widely-used Zipf’s law has two striking regularities. One is its excellent fit; the other is its close-to-one exponent. When the exponent equals to one, the Zipf’s 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. Small samples of large cities alone provide higher value of the exponent whereas small cities introduce high variance and lower the value of the exponent. Using the values of estimated exponent from the rolling sample method, we obtained an elasticity of the exponent with respect to sample size. We concluded that the rank-size rule is not an economic regularity but a statistical phenomenon.

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Bibliographic 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 07-006.

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Length: 20 pages
Date of creation: Nov 2007
Date of revision:
Handle: RePEc:unr:wpaper:07-006

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Keywords: Zipf's law; Rank-size rule; Rolling sample method;

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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. 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.
  3. 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.
  4. Nitsch, Volker, 2005. "Zipf zipped," Journal of Urban Economics, Elsevier, vol. 57(1), pages 86-100, January.
  5. Xavier Gabaix, 1999. "Zipf's Law and the Growth of Cities," American Economic Review, American Economic Association, vol. 89(2), pages 129-132, May.
  6. Xavier Gabaix, 1999. "Zipf'S Law For Cities: An Explanation," The Quarterly Journal of Economics, MIT Press, vol. 114(3), pages 739-767, August.
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Cited by:
  1. P. Nijkamp & A. Reggiani, 2012. "Did Zipf Anticipate Socio-Economic Spatial Networks?," Working Papers wp816, Dipartimento Scienze Economiche, Universita' di Bologna.

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