Tiebout--Weibull equilibrium: Reconciliation of Gibrat's and Zipf's laws for cities population

Anna Kazmierczak, Alexander Shapoval and Shlomo Weber

No 19038, CEPR Discussion Papers from C.E.P.R. Discussion Papers

Abstract: While the existing literature on city formation recognizes two empirical regularities: Zipf's law, which describes the rank distribution of cities, and Gibrat's law, which describes their growth in proportion to their actual size, the aim of this paper is to identify a mechanism which places these two very different laws into a single, unified framework. We consider a Tiebout model of jurisdiction formation and introduce a new equilibrium notion that divides the population into a large core, immune against group deviations, and a tiny fringe. We then endow our model with the Weibull probability density of individuals' locations and show that our equilibrium city distribution approximates Zipf's and Gibrat's laws. Moreover, our theoretical results are consistent with the U.S. Census data.

Keywords: Zipf's law; Gibrat's law (search for similar items in EconPapers)
JEL-codes: C71 D30 D50 H41 R12 (search for similar items in EconPapers)
Date: 2024-05
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