Abstract
The exact shape of the distribution of city size is subject to considerable scholarly debate, as competing theoretical models yield different implications. The alternative distributions being tested are typically the Pareto and the log-normal, whose finite sample upper tail behavior is very difficult to tell apart. Using data at different levels of aggregation (census blocks and cities) we show that the tail behavior of the distribution changes upon aggregation, and the final result depends crucially on the shape of the distribution of the number of elementary units associated with each aggregate element.
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Notes
- 1.
This point is particularly stressed in Rozenfeld et al. (2011), who propose a new methodology to define cities based on microdata and a clustering algorithm that identifies a city as the maximal connected cluster of populated sites. By applying this methodology to both US and UK data, the authors find that a Zipf’s law approximates well the distribution of 1,947 US cities with more than 12,000 inhabitants (1,007 cities with more than 5,000 inhabitants for the UK). An alternative approach entails the use of high-resolution night-light satellite image data (Bagan and Yamagata 2015; Zhou et al. 2015).
- 2.
- 3.
In the rest of the chapter the terms city and populated place are used interchangeably.
- 4.
We thank an anonymous referee for highlighting this important point.
- 5.
- 6.
Such a conclusion is partially tempered by results of the GI test, which finds a power-law tail limited to the top 655 observations in the sampled dataset.
- 7.
See Asmussen and Rojas-Nandayapa (2008) for some asymptotic results in the special case of log-normal random variables with dependence structure given by the Gaussian copula.
- 8.
For a discussion of the role of increasing and decreasing returns to scale in determining the size of cities, see Masahisa et al. (2001, p. 225).
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Bee, M., Riccaboni, M., Schiavo, S. (2019). Distribution of City Size: Gibrat, Pareto, Zipf. In: D'Acci, L. (eds) The Mathematics of Urban Morphology. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-12381-9_4
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