The size distribution of cities in China: Evolution of urban system and deviations from Zipf’s law

doi:10.1016/j.ecolind.2019.106003

Ecological Indicators

Volume 111, April 2020, 106003

https://doi.org/10.1016/j.ecolind.2019.106003 Get rights and content

Highlights

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This paper explores urban system in China and its deviations from Zipf's law.
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The size distributions of Chinese cities did not follow Zipf's law until recently.
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Both large and small cities were under-sized relative to the Zipf’s law.
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Excluding the top 10% large cities, the data fit the Zipf's law better.
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The deviations rises with government interferences and decreases with market forces.

Abstract

How are urban residents distributed and agglomerated across different-sized cities? This question can be addressed by studying urban system or Zipf’s law. Using Chinese data for the period of 1990–2017, this paper contributes to the literature by exploring the evolution of urban system, and more importantly deviations from Zipf's law. It is found that (1) The size distribution of Chinese cities, as expected, did not follow Zipf’s law until very recently. Both large cities and small towns were under-sized relative to the Zipf’s law, implying possible loss of agglomeration economies; (2) When the top 10% large cities are excluded, the Chinese data fit the Zipf's law better, demonstrating the adverse role of government interference in containing the growth of mega-cities; (3) By and large, the distribution has been moving closer or further away from Zipf’s law, corroborating with policy directions in the relevant five-year plans of the central government; and (4) Government interferences helped enlarge while market forces helped reduce the numerical deviations of individual cities from Zipf’s law. The last three analytical findings are the first in the literature since no previous studies have focused on the issue of why urban system in China does not follow Zipf’s law. In particular, no earlier efforts have been made to model numerical deviations from Zipf’s law, as attempted in this paper. The results appeal for removal of government interferences and furthering market-based reforms in order to reap economies of agglomeration.

Introduction

To policy makers, the business community and society in general, three issues are most fundamental regarding urbanization as a process of population agglomeration and migration. These three issues correspond to three different concepts and research topics in urban and regional economics. The first is urbanization rate: for a given national population, what is the proportion of urban residents? To address this issue, a number of studies published in the 1970s and 1980s focused on the determinants of urbanization rate, e.g. Pandey, 1977, Firebaugh, 1979, Mohan, 1984. For more references, see Hofmann and Wan (2013).

The second concept relates to urban system or urban hierarchy: for a given total urban population, how are they distributed across different-sized cities? That is, how many in the prime city – the largest city in a country? how many in the second largest, third largest, …, smallest cities or towns? This rank-size distribution issue is often addressed by examining Zipf’s law (Zipf 1949). Finally, the third most fundamental issue and topic is spatial distribution of cities: given the size distribution of cities in a country, where are they located? There is relatively much less research work in this area.

This paper focuses on the evolution of urban system in China by exploring the applicability of Zipf’s law. By definition, Zipf’s law states that the second largest city is half the size of the largest, the third largest city is one third the size of the largest, and so on. It is clear that when Zipf’s law is applicable, population in each and every city can be easily estimated or projected once the urbanization rate and national population are known. Thus, it is of both theoretical and practical significance to examine Zipf’s law, at least for regional and urban development strategy-setting and planning, especially for infrastructure investment and public resource allocation decisions.

When an urban system deviates from Zipf’s law, as is the case in China (see hypothesis 1 and relevant discussions below), two important research questions arise. First, are urban population more concentrated or less concentrated than what is depicted by Zipf’s law? As recent studies show, Zipf’s law represents the outcome of a natural process (see literature review below). In particular, Eeckhout, 2004, Rossi-Hansberg and Wright, 2007 demonstrated that factor mobility is an important condition underlying the Zipf’s law. Thus, conformity with Zipf’s law implies full mobility of labor and capital, entailing optimal allocation of resources. On the contrary, rejection of Zipf’s law may well mean non-optimal allocation of resources. It follows that deviations from Zipf’s law can inform us whether urban population is over- or under-agglomerated. Second, what are the major drivers of the deviations? Needless to say, analytically identifying these drivers is essential for minimizing the deviations in order to gain economies of agglomeration or reduce losses due to over- or under-agglomeration.

Urbanization in China is one of the two most significant global events in the 21st century (Stiglitz, 1999). Characterized by stringent migration restrictions and policy interventions at all levels of governments, it is not unexpected that the urbanization rate, urban system and spatial distribution of cities in China are distorted. In particular, the Chinese government has instituted the household registration system (the so-called Hukou) to block or contain rural–urban migration. Even today, migration to mega-cities is strictly controlled and discouraged. Thus, urban system in China is expected not to follow Zipf’s law. But given gradual market-oriented reforms in China, the system is expected to be converging to the Zipf’s law.

Against the above background, this paper focuses on the evolution of urban system and deviations from Zipf's law in China. More specifically, using Chinese data for the period of 1990–2017, we make several contributions to the literature. First, most studies on Zipf’s law are based on data from developed nations whereas we focus on China - the largest and most dynamic developing economy in the world. Second, we extend the literature on deviations from Zipf’s law. So far, only one study (González-Val 2011) modelled numerical deviations from Zipf’s law, using data from the United States. Third, we directly and explicitly model numerical deviations of individual cities as a function of market forces and government interferences. This has not appeared in the literature.

The remainder of this paper is organized as follows. Section 2 presents a short literature review and sets up research hypotheses. This is followed by fitting Zipf’s law to the Chinese data and examining the evolution of urban system in China in Section 3. Section 4 models the size deviations of individual cities from Zipf’s law. Section 5 concludes.

Section snippets

Literature review and research hypotheses

Auerbach (1913) appears to be the pioneer in studying the size distribution of cities. He investigated the urban system in the United States and Europe. Using $P_{R}$ to denote population in the R-th largest city where $R$ denotes city rank in terms of population such that $P_{1} \geq P_{2} \geq \dots {\geq P}_{N}$ , Auerbach (1913) found that the city population multiplied by its rank is approximately a constant (C): $P_{R} R = C$

In Eq. (1), C represents the population of the largest or primate city in a country. A simple re-arrangement of

Evolution of size distribution of cities in China and hypotheses testing

As part of the preliminary data analysis, Table 1 reports change in the total number and average size of Chinese cities from 1990 to 2017, where population refers to urban residents with Hukou. Clearly, the median city size expanded from 597,800 in 1990 to1125000 in 2017. The size of the largest city (i.e., Shanghai) grew from 7.835 million in 1990 to 14.55 million in 2017. And the number of cities with population larger than 1.0 million increased from 68 in 1990 to 152 in 2017.

Fig. 1 present

Deviations from Zipf’s law

This section aims at testing hypothesis 4. Having rejected the applicability of Zipf’s law in most years (see the preceding section), attention is now turned to the deviations from Zipf’s law, which will be estimated for individual cities and then regressed on potential drivers of market forces vs government interventions.

Discussion and conclusions

Zipf’s law describes an empirical regularity that is shown to be the outcome of a random or natural process (Gibrat, 1931, Gabaix, 1999 and Batty 2006). Consequently, government interventions are expected to enlarge, while market forces are expected to reduce, deviations from Zipf’s law. Unfortunately, there has been little research that focuses on size deviations from Zipf’s law for individual cities, with only a couple of exceptions.

China provides a good case to analyze such deviations due to

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^☆: An earlier version of this paper was presented at the Workshop on Urbanization and Infrastructure in Asia, held in Beijing 16–17 June 2016. The authors acknowledge the useful and constructive comments of Professor Huaqing Wu and other workshop participants. Financial support from the Natural Science Foundation of China (NSFC projects 71703088, 71833003, 71834005 and 71973014) and Shanghai Pujiang Program (project 17PJC045) is acknowledged. All errors and shortcomings are solely our responsibility.

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Original ArticlesThe size distribution of cities in China: Evolution of urban system and deviations from Zipf’s law☆

Highlights

Abstract

Introduction

Section snippets

Literature review and research hypotheses

Evolution of size distribution of cities in China and hypotheses testing

Deviations from Zipf’s law

Discussion and conclusions

Regl. Sci. Urban Econ.

J. Comparat. Econ.

J. Urban Econ.

J. Urban Econ.

Regl. Sci. Urban Econ.

Economic development and population concentration

Econ. Dev. Cult. Change

Are Chinese cities too small?

Rev. Econ. Stud.

Das Gesetz der Bevölkerungskonzentration

Petermanns Geogr. Mitt.

Gibrat's Law for (all) cities

Am. Econ. Rev.

China’s development policies and city size distribution: An analysis based on Zipf’s law

Urban Stud.

Structural determinants of urbanization in Asia and Latin America, 1950–1970

Am. Sociol. Rev.

Zipf's law for cities: an explanation

Q. J. Econ.

Original Articles
The size distribution of cities in China: Evolution of urban system and deviations from Zipf’s law☆