Pareto or log-normal? A recursive-truncation approach to the distribution of (all) cities
AbstractTraditionally, it is assumed that the population size of cities in a country follows a Pareto distribution. This assumption is typically supported by finding evidence of Zipf's Law. Recent studies question this finding, highlighting that, while the Pareto distribution may fit reasonably well when the data is truncated at the upper tail, i.e. for the largest cities of a country, the log-normal distribution may apply when all cities are considered. Moreover, conclusions may be sensitive to the choice of a particular truncation threshold, a yet overlooked issue in the literature. In this paper, then, we reassess the city size distribution in relation to its sensitivity to the choice of truncation point. In particular, we look at US Census data and apply a recursive-truncation approach to estimate Zipf's Law and a non-parametric alternative test where we consider each possible truncation point of the distribution of all cities. Results confirm the sensitivity of results to the truncation point. Moreover, repeating the analysis over simulated data confirms the difficulty of distinguishing a Pareto tail from the tail of a log-normal and, in turn, identifying the city size distribution as a false or a weak Pareto law.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Business School - Economics, University of Glasgow in its series Working Papers with number 2012_10.
Date of creation: Jul 2012
Date of revision:
City size distribution; Pareto and Log-normal; Zipf's Law; Kolmogorov- Smirnov; Recursive analysis;
Find related papers by JEL classification:
- C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
- D30 - Microeconomics - - Distribution - - - General
- 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:
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.:
- Krugman, Paul, 1996. "Confronting the Mystery of Urban Hierarchy," Journal of the Japanese and International Economies, Elsevier, vol. 10(4), pages 399-418, December.
- Giesen, Kristian & Zimmermann, Arndt & Suedekum, Jens, 2010. "The size distribution across all cities - Double Pareto lognormal strikes," Journal of Urban Economics, Elsevier, vol. 68(2), pages 129-137, September.
- Kwok Tong Soo, 2004.
"Zipf's law for cities: a cross country investigation,"
LSE Research Online Documents on Economics
19947, London School of Economics and Political Science, LSE Library.
- Soo, Kwok Tong, 2005. "Zipf's Law for cities: a cross-country investigation," Regional Science and Urban Economics, Elsevier, vol. 35(3), pages 239-263, May.
- Kwok Tong Soo, 2004. "Zipfs Law for Cities: A Cross Country Investigation," CEP Discussion Papers dp0641, Centre for Economic Performance, LSE.
- Marco Bee & Massimo Riccaboni & Stefano Schiavo, 2011. "Pareto versus lognormal: a maximum entropy test," Department of Economics Working Papers 1102, Department of Economics, University of Trento, Italia.
- Edward L. Glaeser & Giacomo A.M. Ponzetto & Kristina Tobio, 2011.
"Cities, Skills, and Regional Change,"
NBER Working Papers
16934, National Bureau of Economic Research, Inc.
- 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.
- 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.
- Xavier Gabaix, 1999. "Zipf'S Law For Cities: An Explanation," The Quarterly Journal of Economics, MIT Press, vol. 114(3), pages 739-767, August.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Jeanette Findlay).
If references are entirely missing, you can add them using this form.