A Comparative Analysis of Gibrat’s and Zipf’s Law on Urban Population

Modica, Marco ; Reggiani, Aura ; Nijkamp, Peter (2015) A Comparative Analysis of Gibrat’s and Zipf’s Law on Urban Population. Bologna: Dipartimento di Scienze economiche DSE, p. 26. DOI 10.6092/unibo/amsacta/4270. In: Quaderni - Working Paper DSE (1008). ISSN 2282-6483.
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Abstract

The regional economics and geography literature on urban population size has in recent years shown interesting conceptual and methodological contributions on the validity of Gibrat’s Law and Zipf’s Law. Despite distinct modeling features, they express similar fundamental characteristics in an equilibrium situation. Zipf’s law is formalized in a static form, while its associated dynamic process is articulated by Gibrat’s Law. Thus, it is likely that both Zipf’s Law and Gibrat’s Law share a common root. Unfortunately, empirical investigations on the direct relationship between Gibrat’s Law and Zipf’s Law are rather rare and not conclusive. The present paper aims to answer the question whether (a generalisation of) Gibrat’s Law allows us to infer Zipf’s Law, and vice versa? In our conceptual and applied framework, particular attention will be paid to the role of the mean and the variance of city population as key indicators for assessing the (non-) validity of the generalised Gibrat’s Law. Our empirical experiments are based on a comparative analysis between the dynamics of the urban population of four countries with entirely mutually contrasting spatial-economic and geographic characteristics: Botswana, Germany, Hungary and Luxembourg. We arrive at the following results: if (i) the mean is independent of city size (first necessary condition of Gibrat’s law) and (ii) the coefficient of the rank-size rule/Zipf’s Law is different from one, then the variance is dependent on city size.

Abstract
Document type
Monograph (Working Paper)
Creators
CreatorsAffiliationORCID
Modica, Marco
Reggiani, Aura
Nijkamp, Peter
Keywords
rank-size rule, Zipf’s law, (generalised) Gibrat’s Law, hierarchical structure, spatial interaction, city growth
Subjects
ISSN
2282-6483
DOI
Deposit date
03 Jun 2015 07:37
Last modified
21 Oct 2015 09:59
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