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Gibrat, Zipf, Fisher and Tippett: City Size and Growth Distributions Reconsidered

Christian Schluter and Mark Trede ()

No 2713, CQE Working Papers from Center for Quantitative Economics (CQE), University of Muenster

Abstract: This paper is about the city size and growth rate distributions as seen from the perspectives of Zipf's and Gibrat's law. We demonstrate that the Gibrat and Zipf views are theoretically incompatible in view of the Fisher-Tippett theorem, and show that the conflicting hypotheses about the size distribution are testable in a coherent encompassing estimating framework based on a single index. We then show that the two views can be reconciled in a slightly modified but internally consistent statistical model: we connect economic activity and agglomeration in a model of Gibrat-like random growth of sectors, whose random number is linked to Zipf-like city size. The resulting average growth rate is a random mean, and we derive its invariant distribution. Our empirical analysis is based on a recent administrative panel of sizes for all cities in Germany. We find strong evidence for the prediction of the growth model, as well as for a weak version of Zipf's law characterising the right tail of the size distribution.

Keywords: Zip's law; Gibrat's law; city size; urban growth (search for similar items in EconPapers)
JEL-codes: R11 R12 (search for similar items in EconPapers)
Pages: 29 pages
Date: 2013-09
New Economics Papers: this item is included in nep-geo and nep-ure
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