Pareto or log-normal? A recursive-truncation approach to the distribution of (all) cities
Traditionally, 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.
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- 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 & 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Krugman, Paul, 1996. "Confronting the Mystery of Urban Hierarchy," Journal of the Japanese and International Economies, Elsevier, vol. 10(4), pages 399-418, December.
- 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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