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

Quaderni - Working Paper DSE N° 1008

26 Pages Posted: 31 May 2015

See all articles by Marco Modica

Marco Modica

Gran Sasso Science Institute (GSSI)

Aura Reggiani

University of Bologna - Department of Economics

Peter Nijkamp

VU University of Amsterdam - Department of Spatial Economics; Tinbergen Institute

Date Written: May 29, 2015

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.

Keywords: rank-size rule, Zipf’s law, (generalised) Gibrat’s Law, hierarchical structure, spatial interaction, city growth

JEL Classification: C46, D30, O40, R11

Suggested Citation

Modica, Marco and Reggiani, Aura and Nijkamp, Peter, A Comparative Analysis of Gibrat's and Zipf's Law on Urban Population (May 29, 2015). Quaderni - Working Paper DSE N° 1008, Available at SSRN: https://ssrn.com/abstract=2611960 or http://dx.doi.org/10.2139/ssrn.2611960

Marco Modica (Contact Author)

Gran Sasso Science Institute (GSSI) ( email )

viale Francesco Crispi, 7
L'Aquila, 67100
Italy

Aura Reggiani

University of Bologna - Department of Economics ( email )

Piazza Scaravilli, 2
Bologna, 40126
Italy

Peter Nijkamp

VU University of Amsterdam - Department of Spatial Economics ( email )

De Boelelaan 1105
1081HV Amsterdam
Netherlands
+31 20 4446091 (Phone)
+31 20 4445611 (Fax)

Tinbergen Institute

Gustav Mahlerplein 117
Amsterdam, 1082 MS
Netherlands

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