Gibrat's Law for (All) Cities

Abstract

Two empirical regularities concerning the size distribution of cities have repeatedly been established: Zipf's law holds (the upper tail is Pareto), and city growth is proportionate. Census 2000 data are used covering the entire size distribution, not just the upper tail. The nontruncated distribution is shown to be lognormal, rather than Pareto. This provides a simple justification for the coexistence of proportionate growth and the resulting lognormal distribution. An equilibrium theory of local externalities that can explain the empirical size distribution of cities is proposed. The driving force is a random productivity process of local economies and the perfect mobility of workers.

Sequential city growth in the US: Does age matter?

“…Others, such as Ioannides and Overman (2003), focus their attention on the dynamics and conclude that Gibrat's law holds, while others, including Black and Henderson (2003), reject this hypothesis. Interestingly, Eeckhout (2004) demonstrates that while Gibrat's law explains city size distribution for the entire sample of US cities, Zipf's law holds for the upper tail of the distribution. Ioannides and Skouras (2012) estimate the switching point between the body and the upper tail of the distribution.…”

“…According to Eeckhout (2004) Here, we draw on data for US cities and metropolitan areas in order to analyze their pattern of growth and evolution after they enter the sample. To the best of our knowledge, this is the first paper to analyze the growth patterns of new-born cities (and metropolitan areas) within a country.…”

Workload Modeling for Computer Systems Performance Evaluation

“…A somewhat simpler procedure has been proposed by Eeckhout [196]. Its point of departure is the observation that fitting a straight line to the right end of an LLCD plot (or alternatively, to the left end of a Zipf size-rank plot) depends on the definition of the starting point, which separates the body from the tail.…”

“…Another possible model is provided by the lognormal distribution, which has been shown to fit various datasets from different fields of study [444,196,189]. Like the shifted and truncated Pareto distribution, this model has the additional benefits of potentially fitting the whole distribution, rather than just the tail, and of having finite moments.…”

“…For example, when studying the distribution of city sizes, Gabaix suggested a model leading to a heavy-tailed distribution [272], whereas Eeckhout proposed a model leading to a lognormal distribution [196]. In the context of modeling the world wide web, Barabási and Albert proposed the preferential attachment model including system growth [49], whereas Huberman and Adamic proposed a multiplicative model with different growth rates and system growth [352].…”