Further Analysis of the Zipf's Law: Does the Rank-Size Rule Really Exist?
AbstractThe 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 InfoPaper 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.
Length: 20 pages
Date of creation: Nov 2007
Date of revision:
Zipf's law; Rank-size rule; Rolling sample method;
Other versions of this item:
- Fungisai Nota & Shunfeng Song, 2008. "Further Analysis of the Zipf Law: Does the Rank-Size Rule Really Exist?," Working Papers 08-005, University of Nevada, Reno, Department of Economics & University of Nevada, Reno , Department of Resource Economics.
- C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
- R11 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Regional Economic Activity: Growth, Development, Environmental Issues, and Changes
- R12 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Size and Spatial Distributions of Regional Economic Activity; Interregional Trade (economic geography)
This paper has been announced in the following NEP Reports:
- NEP-ALL-2007-12-01 (All new papers)
- NEP-GEO-2007-12-01 (Economic Geography)
- NEP-URE-2007-12-01 (Urban & Real Estate Economics)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
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- repec:dar:vpaper:34471 is not listed on IDEAS
- 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.
- Nitsch, Volker, 2004.
2004/16, Free University Berlin, School of Business & Economics.
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- 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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