Further Analysis of the Zipf's Law: Does the Rank-Size Rule Really Exist?
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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- 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.
- 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
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- Xavier Gabaix & Rustam Ibragimov, 2011.
"Rank - 1 / 2: A Simple Way to Improve the OLS Estimation of Tail Exponents,"
Journal of Business & Economic Statistics,
Taylor & Francis Journals, vol. 29(1), pages 24-39, January.
- 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.
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Elsevier, vol. 57(1), pages 86-100, January.
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- Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, Oxford University Press, vol. 114(3), pages 739-767.
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