Reconsidering Zipf’s law for regional development: The case of settlements and cities in Croatia

Abstract Zipf’s law is a striking regularity in the field of urban economics that states that the sizes of cities should follow the rank-size distribution. Rank-size distribution, or the rank-size rule, is a commonly observed statistical relationship between the population size and population rank of a nations’ cities. The goal of this paper is to test Zipf’s law as applied to data for settlements and cities in Croatia using the Census of Population Survey for the year 2011. The results of the analysis have shown that Zipf’s law for settlements in Croatia holds true for the majority of the settlement sizes. However, the rank-size distribution does not hold true for extremely small and extremely large settlement sizes. When city proper and urban agglomeration of 127 Croatian cities were examined, Zipf’s law was found to hold true only for urban agglomerations. The results of the study are discussed in terms of regional development.

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Investigation of urban regularities for Croatia in the period from 1857 to 2011

Ekonomski pregled ◽

10.32910/ep.71.4.1 ◽

2020 ◽

Vol 71 (4) ◽

pp. 307-330

Author(s):

Hrvoje Jošić ◽

Berislav Žmuk

Keyword(s):

Size Distribution ◽

Unit Root ◽

Urban Economics ◽

Unit Roots ◽

City Size ◽

Zipf’S Law ◽

Urban Hierarchy ◽

Zipf's Law ◽

Gibrat’S Law ◽

Gibrat's Law

Two main regularities in the field of urban economics are Zipf’s law and Gibrat’s law. Zipf’s law states that distribution of largest cities should obey the Pareto rank-size distribution while Gibrat’s law states that proportionate growth of cities is independent of its size. These two laws are interconnected and therefore are often considered together. The objective of this paper is the investigation of urban regularities for Croatia in the period from 1857 to 2011. In order to estimate and evaluate the structure of Croatian urban hierarchy, Pareto or Zipf’s coefficients are calculated. The results have shown that the coefficient values for the largest settlements in different years are close to one, indicating that the Croatian urban hierarchy system follows the rank-size distribution and therefore obeys Zipf's law. The independence of city growth regarding the city size is tested using penal unit roots. Results for Gibrat's law testing using panel unit root tests have shown that there is a presence of unit root in growth of settlements therefore leading to the acceptance of Gibrat’s law.

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The Evolution of the Urban Spatial Pattern in the Yangtze River Economic Belt: Based on Multi-Source Remote Sensing Data

Sustainability ◽

10.3390/su10082733 ◽

2018 ◽

Vol 10 (8) ◽

pp. 2733 ◽

Cited By ~ 8

Author(s):

Yang Li ◽

Hua Shao ◽

Nan Jiang ◽

Ge Shi ◽

Xin Cheng

Keyword(s):

Size Distribution ◽

Urban Areas ◽

Yangtze River ◽

Size Structure ◽

Urban Land ◽

Urban Agglomeration ◽

Spatial Distance ◽

The Yangtze River ◽

Urban Agglomerations ◽

Urban Size

The development of the Yangtze River Economic Belt (YREB) is an important national regional development strategy and a strategic engineering development system. In this study, the evolution of urban spatial patterns in the YREB from 1990 to 2010 was mapped using the nighttime stable light (NSL) data, multi-temporal urban land products, and multiple sources of geographic data by using the rank-size distribution and the Gini coefficient method. Through statistical results, we found that urban land takes on the feature of “high in the east and low in the west”. The study area included cities of different development stages and sizes. The nighttime light increased in most cities from 1992 to 2010, and the rate assumed an obvious growth tendency in the three urban agglomerations in the YREB. The results revealed that the urban size distribution of the YREB is relatively dispersed, the speed of urban development is unequal, and the trend of urban size structure shows a decentralized distribution pattern that has continuously strengthened from 1990 to 2010. Affected by factors such as geographical conditions, spatial distance, and development stage, the lower reaches of the Yangtze River have developed rapidly, the upper and middle reaches have developed large cities, and a contiguous development trend is not obvious. The evolution of urban agglomerations in the region presents a variety of spatial development characteristics. Jiangsu, Zhejiang, and Shanghai have entered a phase of urban continuation, forming a more mature interregional urban agglomeration, while the YREB inland urban agglomerations are in suburbanization and multi-centered urban areas. At this stage, the conditions for the formation of transregional urban agglomerations do not yet exist, and there are many uncertainties in the boundary and spatial structure of each urban agglomeration.

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A Dynamic Generalization of Zipf's Rank-Size Rule

Environment and Planning A Economy and Space ◽

10.1068/a141449 ◽

1982 ◽

Vol 14 (11) ◽

pp. 1449-1467 ◽

Cited By ~ 12

Author(s):

B Roehner ◽

K E Wiese

Keyword(s):

Stochastic Model ◽

Size Distribution ◽

Urban Growth ◽

Simple Form ◽

Deterministic Model ◽

City Size ◽

Zipf’S Law ◽

Zipf's Law ◽

City Size Distribution ◽

Zero Growth

A dynamic deterministic model of urban growth is proposed, which in its most simple form yields Zipf's law for city-size distribution, and in its general form may account for distributions that deviate strongly from Zipf's law. The qualitative consequences of the model are examined, and a corresponding stochastic model is introduced, which permits, in particular, the study of zero-growth situations.

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Growth and Firm Size Distribution

Journal of Electronic Commerce in Organizations ◽

10.4018/jeco.2016040105 ◽

2016 ◽

Vol 14 (2) ◽

pp. 61-73

Author(s):

Wei Zhang ◽

Yan-Chun Zhu ◽

Jian-Bo Wen ◽

Yi-Jie Zhuang

Keyword(s):

Size Distribution ◽

Firm Size ◽

Zipf’S Law ◽

Growth Path ◽

Firm Size Distribution ◽

Zipf's Law ◽

Gibrat’S Law ◽

Gibrat's Law ◽

Quantile Regression Method ◽

The Relationship

Studies on the firm's size distribution (FSD) can set a good foundation to know about the growth path and mechanism of e-commerce firms. The purpose of this paper is to understand features of the China's listed e-commerce firms by testing Gibrat's law and Zipf's law within the Internet sectors. From a macroscopic perspective, with the approach of OLS estimation, Zipf's coefficient of the FSD is calculated to test whether Zipf's law holds. From a microscopic perspective, the relationship between e-commerce firm size and growth is explored by quantile regression method. The results indicate that from 2005 to 2014, Zipf's law cannot be rejected, with the relationship changing over time, Gibrat's law holds partly. It implies that competition status among China's e-commerce firms becomes more stable.

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Rank-size Distribution of Cities and Municipalities in Bangladesh

Sustainability ◽

10.3390/su12114643 ◽

2020 ◽

Vol 12 (11) ◽

pp. 4643

Author(s):

Pankaj Bajracharya ◽

Salima Sultana

Keyword(s):

Size Distribution ◽

Urban Areas ◽

Urban Expansion ◽

Population Data ◽

Google Earth ◽

Zipf’S Law ◽

Zipf's Law ◽

Spatial Inequalities ◽

Planning Framework ◽

Shed Light

This paper examines and updates the rank-size distribution of cities and municipalities in Bangladesh between 1990 and 2019 based on two criteria: (1) built-up urban areas; and (2) population. The distribution of built-up urban areas and population are compared to provide a robust theoretical underpinning of Zipf’s law for future urban developmental planning framework. The data on built-up urban areas is extracted from land cover classification using Google Earth Engine and the population data is obtained from the decennial censuses. The comparison of the conformity to Zipf’s law indicated contradictory results. While a greater proportion of the population has been increasingly concentrated in the smaller and midsized cities over the last three decades, built-up urban areas, on the other hand, have been mostly clustered in two largest cities— Dhaka and Chittagong—accounting for 50 to nearly 60 percent of the total built-up urban areas. These results shed light on the magnitude of continued spatial inequalities in urban development amongst cities and municipalities in Bangladesh despite there being an overall increase of evenness in the distribution of population over time. These results imply an unsustainable rate of urban expansion in Bangladesh and reinforce the need for the exploration of policies and regulations targeted at guiding the rate and direction of evenness in urban expansion.

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