MetaZipf. (Re)producing knowledge about city size distributions

TL;DR

This paper conducts a comprehensive meta-analysis of city size distributions related to Zipf's law, revealing that many variations in findings stem from definitional differences and challenging existing theories.

Contribution

It provides the largest open data collection and an interactive tool for exploring city size distribution studies, clarifying sources of variation in Zipf's law estimations.

Findings

Much variation is due to city definition choices

Some theories explaining Zipf's law are challenged by results

A reproducible meta-analysis clarifies inconsistencies in literature

Abstract

Zipf's law for cities is probably the most famous regularity in social sciences. So much that, a hundred years of publication later, its status is not clear: is it a law of social organisation? Is it an instrument of description of city size distributions? Is it an element of validation of geographical objects (cities and systems of cities in particular)? Empirical estimations of the rank-size parameters are very numerous and contradict each other. In this study, we present the results of a reproducible meta-analysis of the largest pool of papers regarding this issue, obtained from the collection of data made open and the construction of an online interactive application which allows the reader to explore this literature. We find that a large part of the variations observed in the measure of Zipf's coefficient is unnecessary as it comes from the choice of different technical specifications in the way cities are defined, whereas some of the current theories to explain the remaining share of variations are challenged by our results.