Pareto or log-normal? A recursive-truncation approach to the distribution of (all) cities

Giorgio Fazio and Marco Modica

Working Papers from Business School - Economics, University of Glasgow

Abstract: 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.

Keywords: City size distribution; Pareto and Log-normal; Zipf's Law; Kolmogorov- Smirnov; Recursive analysis (search for similar items in EconPapers)
JEL-codes: C46 D30 R12 (search for similar items in EconPapers)
Date: 2012-07
New Economics Papers: this item is included in nep-ure
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Working Paper: Pareto or log-normal? A recursive-truncation approach to the distribution of (all) cities (2012)
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