MetaZipf. A dynamic meta-analysis of city size distributions.

Clémentine Cottineau,Wei-Xing Zhou

doi:10.1371/journal.pone.0183919

Abstract

The results from urban scaling in recent years have held the promise of increased efficiency to the societies who could actively control the distribution of their cities’ size. However, little evidence exists as to the factors which influence the level of urban unevenness, as expressed by the slope of the rank-size distribution, partly because the diversity of results found in the literature follows the heterogeneity of analysis specifications. In this study, I set up a meta-analysis of Zipf’s law which accounts for technical as well as topical factors of variations of Zipf’s coefficient. I found 86 studies publishing at least one empirical estimation of this coefficient and recorded their metadata into an open database. I regressed the 1962 corresponding estimates with variables describing the study and the estimation process as well as socio-demographic variables describing the territory under enquiry. A dynamic meta-analysis was also performed to look for factors of evolution of city size unevenness. The results of the most interesting models are presented in the article, whereas all analyses can be reproduced on a dedicated online platform. The results show that on average, 40% of the variation of Zipf’s coefficients is due to the technical choices. The main other variables associated with distinct evolutions are linked to the urbanisation process rather than the process of economic development and population growth. Finally, no evidence was found to support the effectiveness of past planning actions in modifying this urban feature.

Highlights

The regularity in city size distribution has been known for more than a century [1]
The urban hierarchy measured by the rank-size rule would vary with systematic factors, and so policies could have some leverage on the inequality level of city sizes
This could be the effect of rebalancing policies, which would appear in the form of negative residuals over the course and just after such policies in country applying them

Summary

Introduction

The regularity in city size distribution has been known for more than a century [1]. Auerbach found that the multiplication of cities’ size (population) by their rank (by decreasing population) resulted in a constant quantity. The rank-size power law was made famous by G. Research on urban scaling laws has shown that some indicators of urban efficiency could be expressed as a power law of urban population [4, 5]. Total income and GDP generally tend to scale superlinearly, i.e. the aggregate output in a city i of population double to that of j is more than twice the output of j. Larger cities tend to be, on average, richer per capita.

Methods

Results

Discussion

Conclusion