Spatial Structure Evolution of Urban Agglomerations and Its Driving Factors in Mainland China: From the Monocentric to the Polycentric Dimension

Abstract

Urban agglomerations (UAs) have become the urbanized “growth poles”, especially against the background of increasing population flow to cities. The spatial structure of UAs has been deemed the essential factor affecting regional function and sustainable development. Although there have been many meaningful studies on spatial structure changes in China, a systematically comparative work of UAs is still absent. Under this context, this paper examines the changing process of spatial structure in 20 Chinese UAs from monocentric to polycentric during the years 1992–2012 by using the night-time light data—an alternative to census data—and explores the major driving forces underlying the evolution. Our empirical results suggest that there is an obvious polycentric tendency of UAs, the spatial distribution pattern of which is not apparent. Panel regression models reveal that the economic level, the population size, the foreign direct investment (FDI), the human capital, and the transport infrastructure play significant positive roles in shaping the polycentric changing process, while the growth of the government expenditure does the opposite. Moreover, transport infrastructure and FDI are positively associated with polycentric spatial structure in mature UAs; on the contrary, they are negatively associated with it in the emerging UAs. Our study results have important policy implications for rapid Chinese urbanization—the policy whereby “China’s future urbanization development model is to limit the agglomeration of large cities while focusing on developing small and medium-sized cities” may be more efficient in mature UAs.

1. Introduction

With the rapid reform of the social and economic paradigm and the progress of urbanization, there have been more collective and cooperative developments among cities since the post-industrial era. The urban spatial form has transformed from individual cities into mega-city regions or metropolises. These emerging new urban forms are called urban agglomerations (UAs) in China, characterized by a cluster of cities consisting of big cities, middle cities, and small cities [1,2]. China’s urbanization level has been 58.5% in 2017 and it is expected to reach 75% by 2050, which means that more population will flow into the city in the future. In this context, UAs have become the main body for the implementation of further urbanization and regional development [3,4,5]. The spatial structure of UAs plays an important role in urban function and regional growth, and its evolution affects the overall efficiency of UAs. During the urbanization process, an efficient and systematic analysis of this issue is of critical importance. Over the past 30 years, many large UAs, such as the Yangtze River Delta UA and the Pearl River Delta UA, have attempted to pursue a polycentric spatial structure to address the employment, traffic, and environmental problems associated with an excessive concentration of urban functions in a single city [6,7,8,9]. In recent years, the mushrooming policies of China’s new polycentric spatial planning—from national-level planning (such as the New-type Urbanization Planning, which tends to encourage the development of small and medium-sized cities and limits large cities) to regional spatial development policies (such as the Social Development and Spatial Development Strategic Plan of the Yangzi River Delta)—have been created and implemented, which clearly highlights the Chinese government’s tendency to regulate the spatial structure of UAs. Therefore, we were prompted to think about the following questions: (1) What is the evolutionary situation of the spatial structure of UAs in China’s urbanization process? (2) How do the main influencing factors affect the evolution rules? (3) Does the correlation between the above-mentioned driving forces and spatial structure evolution support the willingness of the Chinese government to regulate the structure of UAs? Exploring these issues will help to correctly grasp the future trend of China’s urbanization and accelerate the transformation of urban development and the organization of spatial structure.

The spatial structure of UAs has been observed and analyzed in various dimensions, and we here will focus only on the monocentric-polycentric development. At present, the polycentric spatial structure is prevailing among cities in Europe and the United States and in other developed areas [7,10,11]. In general, research on the measurement and evolution of a polycentric spatial structure is rich, particular in the European region. City planners and policy makers have put forward a series of policies and measures for polycentric urban region development, such as the ESDP (European Spatial Development Perspective) and the ESPON (European Spatial Planning Observation Network). Based on the spatial structure theory [12] and central place theory [13,14], recent years have witnessed an increasing number of studies on the exploration and practice of the changing rules of urban spatial structures in mainland China, the most populous urbanization body in the world. Particularly, more attention has been paid to polycentric UAs than polycentricity in China recently. This focus stems from the fact that the UAs are at the core of China’s new urbanization policies [15]. In the wake of the current analysis of the geographic scale of UAs, polycentric structure studies have been largely focused on the biggest ones, such as the Yangzi River Delta UA and the Pearl River Delta UA [16,17,18,19]. For example, Zhao et al. [18] used an analytical framework focusing on the changing levels of polycentric mega-city regions, the two most important mega-city regions in China. To determine the aspects of spatial structure characteristics, a large number of scholars used population-related data to simulate the evolution trend of polycentric UAs in a period. For instance, Wei et al. [19] combined Landsat imagery with historical census data to present an estimate of population density that revealed the spatial–temporal evolution of the Pearl River Delta area, which incorporates 28 cities. Additionally, the research of Yang et al. [20] utilized the spatial statistics tool—the standard deviational ellipse of directional distribution—to measure the spatial pattern of individual Chinese mega-regions, reflecting the current path of regional urbanization in China. A few studies have analyzed the polycentric development in 22 UAs of China, which expanded the research scope [21,22]. They also pointed out that there are differences in the features of polycentric spatial structure between the Eastern and Western regions. However, no explanations were given for the above differences. In addition, the research into the rules of polycentric spatial structural change in UAs has mainly focused on more developed large UAs [5,23] or underdeveloped Western UAs [24].

Despite the many insightful studies on the evolution of UAs’ spatial structures, there are still several shortcomings. Firstly, research on individual UAs has greatly limited the portability of the findings. Second, the use of demographic data to measure the spatial structure of UAs does not accurately reflect the spatial structure of UAs, nor does it allow for a diachronic comparative study of the spatial structure evolution. Regardless of whether the population data are the registration population, the floating population, or the resident population, there are defects such as an inconsistent statistical caliber and a discontinuous time series. Third, the discussion of the driving forces is insufficient. Research based on panel data lacks an in-depth discussion of the model endogeneity and the robustness of the results.

Aiming to help fill these gaps, we attempt to expand the existing literature by considering the following four aspects: (1) we select 20 UAs covering western, middle, and eastern China to describe the spatial structure evolution process; (2) out of the demographic data, we employ the DMSP/OLS (Defense Meteorological Satellite Program’s Operational Linescan System) night-time light data as an alternative to tackle the challenges of accurately describing spatial structure evolution; (3) then, we establish panel data models which control the endogeneity of individual UAs and reduce the multicollinearity between regression variables to analyze the underlying socioeconomic factors that form spatial structure changes. Additionally, we test the results for robustness by using lagging independent variables and alternative dependent variables; (4) furthermore, we discuss the performance of the above factors in different types of UAs. Our findings can be used as a reference for future urbanization planning in China. More specifically, the remainder of this paper is organized as follows: Section 2 describes the study area and data, after which the measurement of the spatial structure of UAs is presented from the monocentric–polycentric perspective in Section 3. The regression analysis based on the panel data model is presented in Section 4. In Section 5 and Section 6, the description of spatial structure features and the changing process for UAs as well as the corresponding influence factors are presented and discussed. In particular, different performances of these affecting factors in different types of UAs are presented. Our conclusions are summarized in Section 7.

2. Study Area and Data

2.1. Study Area

Our analysis started with 20 mainland Chinese UAs (Figure 1 and

Table 1. The scope and cities included in the UAs.

ID	Urban Agglomerations	Abbreviations	Core Cities	Number of Cities
1	Yangtze River Delta	YRD	Shanghai, Nanjing, Hangzhou	45
2	Pearl River Delta	PRD	Guangzhou, Shenzhen	14
3	Beijing-Tianjin-Hebei	BTH	Beijing, Tianjin	27
4	Middle Yangtze	MYZ	Wuhan, Changsha, Nanchang	61
5	Chengdu-Chongqing	CHC	Chengdu, Chongqing	29
6	Harbin-Changchun	HAC	Harbin, Changchun	30
7	Shandong Peninsula	SDP	Jinan, Qingdao	38
8	Central Plain	CPL	Zhengzhou	23
9	Guanzhong Plain	GZP	Xi’an	10
10	Central and Southern Liaoning	CSLN	Shenyang, Dalian	27
11	Western Taiwan Straits	WTS	Fuzhou, Xiamen	23
12	Jianghuai	JIH	Hefei	15
13	Northern Tianshan Mountains	NTSM	Urumqi	9
14	Hohhot-Baotou-Erdos-Yulin	HBEY	Hohhot	8
15	Lanzhou-Xining	LAX	Lanzhou	6
16	Central Shanxi	CSX	Taiyuan	14
17	Southern Guangxi	SGX	Nanning	9
18	Ningxia Yellow River	NXYR	Yinchuan	6
19	Central Guizhou	CGZ	Guiyang	10
20	Central Yunnan	CYN	Kunming	6

) identified by Fang [25], whose definitions have been fully affirmed by the NDRC (National Development and Reform Commission). The 20 selected UAs are of high importance to China’s territorial development strategies; they collectively account for 422 cities (63.94% of the total in China) at the prefectural level and above, including four municipalities, 191 prefecture-level cities, and 231 county-level cities [25]. The definition of these city-regions considers the essential features based on regional social, economic, and environmental attributes [15] as well as the spatial connections among cities [22]. Our selected UAs cover the main National Urban System Planning city regions, and most of these UAs correspond to the 21 urbanization regions in major function-oriented zoning planning. Moreover, the State Council recently approved the plans for several UAs in our study, including the latest plan for Guanzhong Plain UA, which was approved in February 2018. To ease comprehension for international readers, we use the conventional English translations and abbreviations for letter codes (e.g., the Yangtze River Delta—YRD). These translations and letter codes adopt international conventions and refer to those used by Fang [25] and Liu et al. [21]. The core cities in each UA are presented in Table 1; for example, Shanghai, Nanjing, and Hangzhou are the central cities of the Yangtze River Delta. We also provide the number of cities at the prefectural level and above that each UA contains. For example, there are 27 cities in the Beijing-Tianjin-Hebei UA, including Beijing, Tianjin, Shijiazhuang, Tangshan, etc. The detailed information is shown in Table 1.

2.2. Data Sources

The use of night-time light data has recently attracted increasing attention in the study of human activity and economic and urban growth [26,27,28,29,30,31,32,33]. Multiple studies have demonstrated the feasibility and suitability of using night-time light data as a proxy to assess dynamic urban expansion or spatial structure changes [34,35,36,37].

In general, the urban population scale is the most direct indicator for expressing the urbanization process and urban spatial evolution. Current research shows that the night-time light data can be an effective surrogate indicator of the urban population, especially in large-scale regions, such as at the provincial or inter-city level [34]. Therefore, we extracted the night-time light data as an alternative method for measuring the spatial structure. Compared to the application of the urban population as the direct indicator to reflect the spatial structure transformation of UAs in China, night-time light data offers three advantages: first, this dataset characterizes the actual population size and urban economic growth at the inter-city geographic scale against the background of the frequent population flow between big cities and surrounding medium and small cities or towns in China, while the China City Statistical Yearbook usually offers registered population data that takes migrants out of consideration. Second, the existing drawback of census data is that it is time-series discontinuous (the interval between two consecutive censuses is approximately 10 years), whereas night-time light data allows the acquisition of continuous and highly comparable long time-series information to solve this problem. In addition, this dataset with long time-series data is appropriate for describing the characteristics because the spatial structure evolution of UAs is a long-term process. It also provides the precondition to establish a panel data model to analyze the influencing factors.

The night-time light data are acquired through the Defense Meteorological Satellite Program’s Operational Linescan System (DMSP/OLS). We downloaded the DMSP/OLS night-time light data from the National Geophysical Data Center (NGDC) of the National Oceanic and Atmospheric Administration (NOAA). What is notable here is that the night-time light images include cloud-free coverage night-time light data, night-time light data with no further filtering, and night-time stable light data [38]. Considering that a large amount of data noise is contained in the first two types of data, including light data from moonlight, firelight, and other ephemeral events, we selected the night-time stable light data which has persistent light [39,40]. As DMSP/OLS data are acquired from different satellites, there is a relatively large difference between data collected by the same satellites each year and data obtained by variations of the satellites within a given year. In other words, the data lacks comparability, which may affect the accuracy of subsequent studies. Therefore, the data cannot be directly used to extract the features of a UA’s spatial structure [40]. Following the method proposed by Liu et al. [38] and Cao et al. [41], a series of calibrations was implemented to improve the continuity and comparability of the DMSP/OLS time series data. On one hand, the quadratic regression function method is employed to correct the original DMSP/OLS night-time light data, which is to ensure its continuity and consistency with time. On the other hand, we applied a correction based on the invariant region method to correct the DMSP/OLS night-time light data. We select areas with relatively stable changes in light values as the invariant region, and it is used as a reference for calibrating the light values in other regions. This could help to eliminate the false growth of light values caused by other non-population growth, such as the development of lighting technology. Figure 2 shows a comparison of the night-time light images from 2012 before and after correction. Compared to the traditional DMSP/OLS stable night-time light data, the strict intercalibration data quantifies the actual night light more accurately. Therefore, we employed corrected DMSP/OLS data to generate an estimation index of the spatial structures of UAs, which provided an alternative way to measure the spatial structure.

Our analysis also included the factors influencing the spatial structure evolution process of UAs. The socio-economic data were employed to study the driving factors of temporal and spatial variations of UAs. The socio-economic data, such as gross domestic product (GDP), urban population scale, the number of college students, road mileage, government expenditure and actual foreign investment, were collected from the China Statistical Yearbook for cities, the China Statistical Yearbook for provinces, and the China Statistical Yearbook for regional economies.

3. Defining and Measuring the Spatial Structure of the UAs from Polycentric/Monocentric Dimensions

The premise of analyzing the changing process of spatial structures was to reasonably identify the UAs’ spatial structure characteristics. The spatial structure mentioned above refers to the distribution of human economic activities, which reflects the state of aggregation or dispersion at the inter-city level [42]. This can be described from the dimensions of compact/sprawl, centralized/decentralized, and monocentric/polycentric [6,43,44]. The first two methods are global description indicators that lack a concentrated description of the most iconic internal characteristics of UAs. Consequently, we concentrated on the monocentric/polycentric profile because it efficiently reflects the extent of the population and other human economic activities, especially in bigger regions. Furthermore, there are various descriptions of monocentric/polycentric development in the literature, which can be roughly divided into two perspectives: the morphological perspective [10,45,46] and the functional perspective [8,47,48]. We focused on measuring the polycentric morphology. The reason for this was that on the geographical scale of UAs, the monocentric/polycentric spatial structure mainly refers to the distribution of a group of cities with different sizes and relatively independent administrative divisions, which further emphasizes its morphological concept. Therefore, this study identified the spatial structures of UAs from the monocentric/polycentric dimension with a morphological perspective during the years 1992–2012. What needs to be explained here is that 1992–2012 is the study period of the spatial structure evolution of UAs. This research period is an appropriate period to observe the UAs’ evolution with the consideration of data availability.

In accordance with the above definition of the spatial structure of UAs, we found that the existing studies mainly adopted the following methods to describe the spatial structure: the Zipf’s law exponent [49,50], the primacy ratio [51], and the Hirschman–Herfindahl Index (HHI) [42]. In view of the fact that the Zipf’s law exponent measures the overall degree of disparity in the size distribution of UAs, in this paper, it served as an indicator of the spatial structure. It provided a useful indication of the extent of monocentric/polycentric features in UAs. The specific calculation equation used was as follows:

$$\ln \left(\mathrm{Light}\right)=\mathsf{\gamma }-\mathsf{\theta }\ln \left(\mathrm{Rank}\right)$$

(1)

where Light is the value of the night-time light in the UAs, which is the sum of the light values of all cities in the UAs. Rank represents the rank of each city unit in the UAs, according to its night-time light value. The value of θ is a constant, indicating the level of the monocentric/polycentric spatial structure: the lower the value, the greater the probability of being polycentric. More specifically, we employed corrected DMSP/OLS data to extract the value of the night-time light of the cities by using a mask polygon of selected cities’ administrative boundaries at a resolution of 1 km. Then, each city in the UAs was sorted from large to small, on the basis of extracting the night-time light values. Additionally, the coefficient θ, named the spatial structure index, was obtained using Equation (1). A value of θ of more than one indicated a monocentric spatial structure with the central cities being predominant in UAs. In contrast, a value of less than one implied a tendency for the distribution of these cities to be balanced and suggested the presence of a polycentric spatial structure.

4. Regression Analysis

4.1. Model Settings

Although measuring the spatial structure of UAs is interesting in itself, there has been a tremendous surge in interest regarding the exploration of its underlying influencing factors to provide more meaningful implications. Scholars in the fields of economic geography, urban economics, and regional science have long been concerned about this issue. They mainly explained the impact of various social, economic, and geographical factors on the spatial structure evolution of UAs. Admittedly, there are many potential explanations for its changes, which include the degree of economic scale, trade costs, the share of manufacturing in the economy, the share of international trade, the density of infrastructure, urbanization policies, and so on [49,52,53]. The above influencing factors act on the spatial agglomeration and decentralization of social and economic activities at a specific geographical scale. The balance between the centripetal forces and the centrifugal forces of social and economic activities is ultimately manifested in the spatial structure evolution in the UAs. In this study, we summarized the main six influencing factors as the independent variables that cover the aspects of economy, geography, and policy (

Table 2. Descriptive statistics for regression variables.

Variables	Description	Obs	Mean	Std.Dev	Min	Max
Spatial structure (STRUC)	The extent of monocentric-polycentric structure	380	−0.095	0.328	−0.557	0.653
Transport infrastructure (INF)	Total road mileage in an UA divided by population	380	4.417	0.479	3.836	13.270
Foreign direction investment (FDI)	Share of the FDI in GDP	380	−5.924	1.048	−9.433	−4.236
Population size (POP)	The total population in an UA	380	7.776	1.059	5.077	9.388
Government expenditure (GOV)	Share of the government expenditure in GDP	380	−2.748	1.200	−5.696	0.034
Economic level (ECM)	Share of the non-agricultural industry production in GDP	380	−0.116	1.032	−0.225	−0.072
Human capital (CAP)	Share of the university students in the total population	380	5.666	1.028	0.378	6.930

). Following the research approach of Soo [49] and Liu and Wang [46], a regression model was established to examine how they would be related to the evolution of spatial structure in UAs.

Thus, our estimated equation is

$$\mathrm{STRUC}=\alpha +{\beta }_1\mathrm{POP}+{\beta }_2\mathrm{ECOM}+{\beta }_3\mathrm{FDI}+{\beta }_4\mathrm{INF}+{\beta }_5\mathrm{GOV}+{\beta }_6\mathrm{CAP}+\epsilon$$

(2)

where STURC is a variable describing the monocentric/polycentric extent, which is calculated as the spatial structure index θ of UAs, as defined above. The variables of POP (population size), ECOM (economic level), FDI (foreign direct investment), INF (transport infrastructure), GOV (government expenditure), and CAP (human capital) present a set of economic geography variables that influence the structural changes of UAs. Detailed definitions of the variables are given in Section 4.2. Parameter β is a set of coefficients of independent variables waiting for estimation. What needs to be explained here is that 1994–2012 is the study period of the driving factors on the evolution of UAs. Since the socio-economic the data used at the prefecture city level, such as gross domestic product (GDP), urban population scale and the number of college students, are unavailable from the statistical yearbook for the years 1992 and 1993, especially in western cities, we have to adjust the study period of the driving forces to 1994–2012. Although the research period for analyzing the driving factors is slightly shorter than the period of describing the evolution process (1992–2012), we believe that lacking two-year study data should not have a substantial impact on the outcome.

4.2. Variable Selection and Description

According to inductive research on previous literature and the characteristics of this study, we selected six factors that affect spatial structure evolution. In the regression model, the variables selected were given detailed definitions as follows.

STRUC represents the spatial structure of UAs, calculated from Equation (1). The detailed definitions were given in Section 3.

POP is the population size. The city size may have an effect on economic performance [54], which further influences the spatial structure [23]. In other words, the population scale plays a significant role in shaping a city’s size and then plays the role of determining the city’s size distribution in UAs. Consequently, it is pertinent to include it in the regression. We expressed the UA sizes as the year-end population size in order to examine the impact of the agglomerate population size on its spatial structure.

ECOM is the degree of economic development. Some studies have shown that the level of the economy can further change the spatial structure of UAs by influencing various socio-economic behaviors and their spatial distribution in the UAs [1,16,23,24], so we selected it as one of the major factors. This was measured by the ratio of the sum of second and third industrial outputs to GDP since the economic development of UAs mainly comes from non-agricultural economic activity. In addition, the nominal GDP was adjusted to the comparable real GDP by using the GDP deflator to counteract the effects of inflation.

FDI is the foreign direct investment, which reflects the external impact of foreign economies. It was measured as the FDI to GDP ratio. FDI mainly flows in individual cities of UAs based on investment preference which changes the original rank-size rule. This phenomenon could benefit the promotion of the monocentric or polycentric development of UAs. As FDI is believed to influence a city size [55], we focused on exploring its effect on the spatial structure of UAs.

INF represents the transport infrastructure. The transportation facilities affect transportation costs and then change the spatial form of the city by influencing the centripetal and centrifugal forces of economic agglomeration [56,57]. We express transport infrastructure as the per capita road mileage to reflect the level of transportation infrastructure construction in the UAs. According to previous literature, there are three main indicators that are used to measure the level of transportation infrastructure: railway mileage, inland waterway mileage, and grade highway mileage. Considering that railways have generally been shown to have a greater impact on urban form than highways (thanks to the anonymous reviewer for providing this inspiration), highways and railways have been separated as independent variables that are incorporated into the analytical framework. But the results showed that the INF (highways) variable cannot be estimated, which may indicate significant collinearity among the independent variables. Since our study area was at the scale of UAs, the use of only urban railways as an indicator of transportation infrastructure could have caused systematic errors. Therefore, this paper used the sum of per capita highways (including municipal highways and expressways in the region) and per capita railway mileage as a proxy for per capita road mileage.

GOV denotes the government expenditure, which was measured as the ratio of government expenditure to GDP to express the internal intervention from the Chinese government (the greater the share of government expenditure in the economy, the greater the apparent government interventional force). Government policy and economical means played crucial roles in shaping the evolution of regional development [46,58]. For instance, the multiplier effect brought by government expenditure preferences not only accelerated the growth of certain cities, but also aggravated the problem of size-inequality development [59], which further affects the rank-size system of UAs. In other words, government expenditure may have multiple effects on the spatial structure changes of UAs, so this variable needed to be included in the regression analysis.

CAP represents the human capital. There is a strong correlation between human capital externalities and urban growth, especially in developing countries [60]. For simplicity, following the method of Rauch [61] and Moretti [62], externalities on urban-region human capital were measured as the share of university students to the total population. A higher ratio was assumed to indicate a larger human capital externality.

Consistent with our specifications, all variables in the regression model were log-transformed to avoid heteroskedastic errors. Table 2 provides the detailed descriptive statistics of the variables selected in Equation (2).

4.3. Estimation Methods and Robustness Test

We used a panel regression model for our analysis based on the obtained data. In terms of the choice of estimation methods, we used the fixed effect model because the unobservable heterogeneity that prevails in socio-economic research affects independent variables. Since random effects are rare, especially in geographical areas where observation units are relatively large, fixed effects are more appropriate [63]. Specifically, the Hausman test results showed that the fixed effect model is superior to the random effect model (p = 0.02, rejecting the random effect model). Consequently, the former model was used for regression analysis, and the overall goodness of fit of the equation was high (the adjusted-R² value was greater than 0.9). We mainly focused on the regression results of the fixed effect model (FE) and the results of the random effect model (RE) are only given as a comparison group at the same time (

Table 3. Regression analysis of influencing factors on spatial structure evolution—Full sample.

Independent Variables	Zipf’s Law Exponent a
	Model 1	Model 2 b	Model 3
	FE	FE	RE
INF	−0.1619 *** (0.0608)	−0.1499 *** (0.0571)	−0.1759 ** (0.0590)
FDI	−0.0445 * (0.0259)	−0.0484 ** (0.0251)	−0.0426 * (0.0260)
POP	−0.0287 * (0.0152)	−0.0357** (0.0143)	−0.0279 ** (0.0153)
GOV	0.0450 *** (0.0149)	0.0437 *** (0.0149)	0.0422 *** (0.0150)
ECM	−0.0693 *** (0.0134)	−0.0614 *** (0.0136)	−0.0681 *** (0.0135)
CAP	−0.0350 ** (0.0119)	−0.0223 *** (0.0113)	−0.0339 *** (0.0119)
Adjusted R-squared	0.9723	0.9760	-
Prob (F)	0.0000	0.0000	-
Time fixed effects	Yes	Yes	-
Number of obs.	367	347	367

*** p < 0.01; ** p < 0.05; * p < 0.1. ^a The indicator used to describe the urban spatial structure is the Zipf’s law exponent. ^b One-period lag for all the independent variables.

).

It should be pointed out here that there are still intractable endogeneity problems in the regression model. The potential endogeneity among the independent variables may be the first problem to be solved. Considering that the economic development, city growth, and facility perfection may have delayed effects on the spatial structure changes of the UAs, we used all independent variables with one period lagged (Model 2 in Table 3) to address this potentially serious issue. This was done to better eliminate the impact of the possible endogeneity of independent variables on the empirical results. Of course, controlling the problems of endogeneity in the regressions did not just stop here. We used the night-time light data, which has strong exogeneity and solves the problem of estimated bias better, as the proxy variable of spatial structure.

In order to ensure the reliability of the estimation results, this study also carried out a robustness test on the results (

Table 4. Robustness check of the influencing factors on spatial structure evolution.

Independent Variables	Zipf’s Law Exponent			Primacy
	Model 1 a	Model 2 b		Model 3	Model 4 c	Model 5
	FE	FE		FE	FE	RE
INF	−0.1228 ** (0.0528)	−0.09017 * (0.0490)		−0.1286 ** (0.0500)	−0.1158 ** (0.0471)	−0.1382 *** (0.0488)
FDI	−0.0651 *** (0.0528)	−0.0791 *** (0.0224)		−0.0520 ** (0.0213)	−0.0561 *** (0.0207)	−0.0510 ** (0.0214)
POP	−0.0403 *** (0.0136)	−0.0495 *** (0.0126)		−0.0286 ** (0.0125)	−0.0314 *** (0.0118)	−0.0279 ** (0.0125)
GOV	0.0465 *** (0.0147)	0.0557 *** (0.0146)		0.0297 ** (0.0123)	0.0310 ** (0.0123)	0.0280 ** (0.0123)
ECM	−0.0598 *** (0.0147)	−0.0507 *** (0.0153)		−0.0275 ** (0.0111)	−0.0241 ** (0.0112)	−0.0268 ** (0.0111)
CAP	−0.0100 * (0.0109)	0.0006 (0.0105)		−0.0260 *** (0.0098)	−0.0147 * (0.0094)	−0.0253 *** (0.0098)
Adjusted R-squared	0.9795	0.9827		0.9766	0.9797	-
Prob(F)	0.0000	0.0000		0.0000	0.0000	-
Time fixed effects	Yes	Yes		Yes	Yes	-
Number of obs.	327	307		367	347	367

*** p < 0.01; ** p < 0.05; * p < 0.1. ^a Two-period lag for all the independent variables; ^b Three-period lag for all the independent variables; ^c One-period lag for all the independent variables.

). The selected lag period of the explanatory variables was the specific “one period lagged”; this selection may lead to questions about the reliability of the regression results obtained. Further, the measurement of spatial structure at the provincial or regional geographic scale depends entirely on the Zipf’s law exponent method of urban scale distribution, which may inevitably have deviations. Due to defects in the regression analysis process above, this study included the respective testing of the robustness of the results by changing the one-period lag of the explanatory variables to a two-period lag, three-period lag, and replacing the indicator of the spatial structure with the primacy ratio method. In addition, this study explored the major influencing factors for the spatial structure evolution of the UAs with different typologies; that is, the diversity performance of factors affecting the monocentric/polycentric changes. The samples were divided into mature groups and emerging groups for the regression (

Table 5. Regression analysis of influencing factors on spatial structure evolution—Different typologies of UAs.

Independent Variables	The Mature UAs			The Emerging UAs
	Model 1	Model 2 a		Model 3	Model 4 a
	FE	FE		FE	FE
INF	−0.2112 *** (0.0713)	−0.1972 *** (0.0664)		0.3173 ** (0.1238)	0.3115 ** (0.1203)
FDI	−0.0679 ** (0.0299)	−0.0668 ** (0.0289)		0.1916 *** (0.0542)	0.1497 ** (0.0541)
POP	−0.0040 (0.0181)	−0.0151 (0.0170)		−0.2092 *** (0.0280)	−0.1950 *** (0.0271)
GOV	0.0503 ** (0.0228)	0.0565 ** (0.0222)		0.0342 ** (0.0147)	0.0272 * (0.0152)
ECM	−0.0711 *** (0.0175)	−0.0642 *** (0.0171)		−0.0429 ** (0.0200)	−0.0386 ** (0.0224)
CAP	−0.0496 *** (0.0160)	−0.0381 ** (0.0154)		−0.0425 *** (0.0139)	−0.0245 * (0.0136)
Adjusted R-squared	0.9664	0.9709		0.9881	0.9893
Prob (F)	0.0000	0.0000		0.0000	0.0000
Time fixed effects	YES	YES		YES	YES
Number of obs.	237	224		130	123

*** p < 0.01; ** p < 0.05; * p < 0.1. ^a One-period lag for all the independent variables.

). Why and how the whole sample was divided into two sub-samples for study is explained in Section 5.1.

5. Results

5.1. The Spatial Structure Measures

Using Equation (1) in Section 3, we calculated the spatial structure value (θ) of the UAs, the detailed description of which is given in the Appendix A (

Table A1. The spatial structure index of the UAs from 1992 to 2012.

UAs	1992	1997	2002	2007	2012	UAs	1992	1997	2002	2007	2012
YRD	0.9946	0.8300	0.7724	0.7462	0.7020	WTS	0.7092	0.6800	0.6685	0.6769	0.6715
PRD	0.6557	0.6665	0.6480	0.6082	0.5970	JIH	0.8582	0.7718	0.7188	0.6375	0.6374
BTH	1.1312	0.9425	0.9299	0.8775	0.8116	SGX	1.3133	1.1572	1.1454	0.9642	0.7977
MYZ	0.8438	0.8098	0.7662	0.7482	0.7350	NTSM	1.6828	1.4778	1.4142	1.3845	1.2499
CHC	1.4144	1.3353	1.2280	1.2378	1.2057	HBEY	0.8288	0.7282	0.7100	0.6858	0.6495
HAC	1.0587	1.0491	1.0348	0.9981	0.9647	NXYR	1.2117	0.8260	0.8086	0.7664	0.7209
CPL	0.8929	0.7843	0.7690	0.8217	0.8140	LAX	1.9140	1.7449	1.6266	1.5746	1.3953
GZP	1.4787	1.1231	1.0424	1.0167	0.9915	CSX	0.8224	0.7823	0.8151	0.7491	0.6981
SDP	0.6943	0.6025	0.6035	0.5891	0.5806	CGZ	1.7009	1.4879	1.2722	1.2147	1.2009
CSLN	0.6193	0.6078	0.5870	0.6005	0.5731	CYN	2.1319	1.8009	1.7103	1.7027	1.6685

). Since the formation of the spatial structure of a UA is a long-term process involving slow changes [42], our spatial structure data for the years 1992 to 2012 is presented at five-year increments to sufficiently reflect the variation. Figure 3 presents the time variance of the spatial structure index. We took an average of the spatial structure index by year, which is shown in Figure 3e, to clearly display the trend in one figure. Both figures show that the value of the spatial structure indicator decreased over the years, indicating an obvious polycentric trend. Figure 3a–d shows the specific changes in each UA. A slight difference from the overall trend is that the Central Plains (CPL) UA, the Central and Southern Liaoning (CSLN) UA and the West Taiwan straits (WTS) UA had monocentric trends in 2002–2007 (Figure 3c,d). It was also found that the polycentric development of the spatial structure at the city-region level in China has been rather unbalanced. The spatial structure indexes of CHC, NTSM, LAX, CGZ, and CYN were greater than 1 from 1992 to 2012, indicating that the monocentric feature is very prominent. The spatial structure indexes for BTH, YRD, HAC, SGX, and NXYR were greater than or equal to 1, with monocentric dominant in 1992, but they were all less than 1 in 2012. This shows a clear transition from monocentric development to polycentric development. The other UAs, PRD, MYZ, CPL, SDP, CSLN, WTS, JIH, HBEY and CSX, were always less than 1 in 1992–2012, indicating that they had distinct multi-center spatial structures.

Figure 4 shows the distribution of the spatial structure index using Zipf’s law indicator for 1992, 1997, 2002, 2007, and 2012. The indicator values in 1992 were significantly higher than in 2012, which indicates more polycentric development. Additionally, the specific distribution pattern was not observed. UAs in the same geographical area did not have similar spatial structures. For example, HBEY and LAX are in Western China, but their polycentric values were shown to be largely different. In contrast, the spatial structures of UAs located in different areas were shown to be similar. For instance, the spatial structure index of PRD was shown to be approximately equal to CSX, which belong to eastern China and middle China, respectively. In other words, there is no fixed geographical distribution rule for the polycentric evolution of UAs, which may imply that the spatial structure index may be incomparable among Eastern, Western, and Middle UAs in China. This finding will be useful for the further analysis of the driving forces behind the process of spatial structure change. In subsequent research on the influencing factors, we will divide our selected 20 UAs into mature UAs and emerging UAs in accordance with the studies by Fang et al. [64] and Fang [25] and respectively build two regression models with these two sub-samples (see Table 5).

5.2. Socio-Economic Factors Influencing the Evolution of Spatial Structure

As discussed previously, there are many potential explanations for the evolution process of spatial structure. We start by reporting the results of the estimation (Table 3). For regression models 1 through 3, we used the Zipf’s law exponent to describe the spatial structure, and Model 2 was used as the base model. Specifically, the economic level (ECM) and population size (POP) were negative and significant at the 1% and 5% levels, indicating that economic development and urban population growth promoted the polycentric trend of the UAs. Foreign direct investment (FDI) had a negative coefficient with the spatial structure evolution, indicating the promotion of polycentric formation by FDI. The negative coefficient of the human capital (CAP) was also in line with our expectations (Model 2), which is significant at the 1% level. This shows that the higher the percentage of college students in urban population, the greater the likelihood of the UA having a multi-center structure is. The coefficient of the transport infrastructure (INF) was negative and significant at the 1% level. This result shows that the construction of transportation infrastructure itself can improve urban development through promoting local employment [65], and then facilitate the balanced development of the region. Further, infrastructure improvement leads to more intensive connections among cities within a UA, which creates shorter inter-city economic distances and encourages the formation of a polycentric spatial structure [66]. In addition, government expenditure (GOV) has positive and significant effects on the spatial structure, indicating that the presence of a higher monocentric degree in a UA is associated with a higher ration of the government’s expenditure to the GDP. This shows that the government spends more on big cities or the core city, which makes them more attractive for more resource inflow.

Table 4 reports the results of the robustness check. As stated in Section 4.3, the selection of an appropriate lag period and measurement of spatial structure are always difficult and subjective processes, and no single selection method is appropriate for a large area such as China. Therefore, we performed the following double check on our findings. Firstly, we used both a two-period lag and a three-period lag for the explanatory variables (Model 1 and 2); secondly, we calculated the spatial structure indicator—the dependent variable—based on the urban primacy ratio method (Model 3 through 5). In fact, there are two main methods for measuring primacy: measuring the share of the largest city of the total size of a UA, and measuring the share of the top four largest cities in the total size of a UA. In accordance with Meijers (2010) [6], we used the second method. From the estimation results, we found that the INF, POP, FDI, ECM, and CAP had significantly negative effects on the spatial structure of UAs and GOV had a significant positive effect. The coefficients of them did not show substantial differences in direction or significance compared with the results from Table 3. Hence, in general, we found that the economic level, population size, foreign direct investment, transport infrastructure, and human capital promote polycentric evolution similarly, and government expenditure facilitates monocentric development.

5.3. Typology Differences of the Influencing Factors on Polycentric UAs

In order to study whether the factors of the spatial structure have different effects on UAs of different sizes at different developmental stages, the 20 UAs were divided into mature UAs and emerging ones. Following comprehensive review of the Chinese UAs [25,67], based on the definition of such UAs and the rankings of their compactness, we defined 13 of the total 20—including YRD, PRD, BTH, MYZ, CHC, HAC, CPL, CXC, SDP, CSLN, WTS, JIH, and NSTM UAs—as mature UAs, while the rest of them were considered to be emerging UAs. As shown in Table 5, our results highlight the following three important facts.

Firstly, ECM and CAP were shown to have negative coefficients that were highly significant, and the coefficient of GOV was significantly positive (Model 1 and 3). This suggests that they remain the key drivers for the spatial structure evolution of the UAs. However, the impact of POP was not significant in our results (Model 1 and 2). Secondly, the coefficient of INF was inconsistent between Model 1 and Model 3, which were significantly negative and significantly positive, respectively. Specifically, the improvement in transportation infrastructure promoted polycentric changes in the mature UAs but facilitated monocentric development in the emerging UAs. Finally, the coefficient of FDI was significantly negative in Model 1, which means that the mature UAs characterized by a higher degree of polycentric development are associated with a greater share of FDI in GDP. However, for the emerging UAs, we found positive and significant effects of FDI on the monocentric spatial structure.

6. Discussion

Based on calculating the spatial structure index of UAs and analyzing its changes in time, we found an obvious polycentric development of UAs. This tendency also exists in other countries such as Europe and the United States [7,10]. Unlike this general trend, there were monocentric trends in very few UAs. The main reason for this may be the adjustment of administrative divisions; i.e., the biggest core cities of these UAs continue to annex peripheral counties or county-level cities. For example, during this period, Beijiao, Liuyuankou and Shuidao towns in the CPL continued to be included in Kaifeng city. Additionally, Gulangyu and Kaiyuan districts merged into the administrative jurisdiction of Xiamen city which belongs to the WTS. This process is known as the “turning county-level units into a part of the metropolis or an upper-level area” policy. The sizes of the largest cities expanded with increased artificial disturbance, which was a significant cause of the single centralized of UAs in corresponding time periods.

The panel regression model was employed to further explore the major driving forces underlying the spatial structure evolution of the UAs. We found that population size and economic development were the key polycentric drivers for polycentric changes of the 20 UAs. These results are supported by those presented in Sun et al. [23] and Ma et al. [59]. However, the impact of POP was not significant for the mature UAs, which conflicts with the results from relevant research [24,49]. We believe the possible reason for this is that it is not very accurate to measure the UAs’ sizes by using the registered population dataset, especially for the mature UAs where the floating population accounts for a large proportion of the population. Although it may be more appropriate to use census data, we still used registered population data. The reason for this is that the census data from 1994 to 2012 is not available for all cities for each year, which may have resulted in a large amount of missing data and had negative effects on the accuracy of the model estimations.

We also found that FDI could contribute to polycentric UAs by promoting growth in the core city and peripheral areas as a result of the increasingly open urban development policy. This also suggests that the location of foreign investment has continually expanded from core cities to surrounding areas. Compared to the result of Sun et al. [23], who focused on 13 large-scale UAs, the negative coefficient was not highly significant. The inferred reason for this may be that the FDI absorption capacity of the emerging UAs (part of our samples) was relatively small, which made the role of FDI in facilitating a multi-center less prominent under the full sample conditions. However, for the emerging UAs, we found monocentric effects of FDI on the spatial structure, which is inconsistent with the existing findings [24]. This move towards a monocentric trend could be explained, to some extent, by the FDI distribution in the emerging UAs. To be specific, the central city with a higher administrative level and autonomy has been given greater rights to import and export than the peripheral cities [67], which has led the FDI to mainly flow into the core city, further accelerating the central city’s expansion. Moreover, since most of the emerging UAs are composed of large, medium, and small cities from the same province, this organization pattern is usually predominated by provincial capitals—there is only one core city. Therefore, this makes UAs a single-centered spatial structure on the whole.

Similarly, the effects of transport infrastructure on the spatial structure evolution were different: polycentric changes in mature UAs and monocentric changes in emerging UAs. This implies that for the mature UAs, more convenient traffic helps element agglomeration in core cities [55], and surrounding smaller cities enjoy the effect of agglomeration economies in central cities by “borrowing scale” [67], which provides the small and medium-sized cities with opportunities to expand, further leading to a more balanced development of the urban scale in the region. For the emerging UAs, transportation improvement has contributed more to resource flow into large cities to a greater extent, instead of stimulating local development, showing that the labor and other resources of the surrounding smaller cities have been “sucked away” by the central cities. This places the smaller cities at a relatively unfavorable position in terms of regional competition, further widening the development gap between them. In summary, the explanation for the phenomenon of the monocentric/polycentric trend is that the role of transportation development is more presented as a “spillover effect” in the mature UAs, while it appears as a “siphon effect” in the emerging UAs.

The role of human capital was to promote polycentric development, whether in the full sample or in the subsample. In contrast to the results that showed no significant association between the urban human capital and the spatial structure [21], we found a highly significant coefficient. This difference may stem from different research units. This also means that it could be more reasonable to use a ratio of college students to the total population to express human capital on a larger geographic scale, such as the provincial scale or inter-city scale.

Different from the influence of the above factors, government expenditure always promoted a single center. Compared with the surrounding cities, the central city, which has the tendency to be centralized and monocentric, is given priority for development. That is, government expenditure has intensified regional inequality to some extent instead of addressing inter-city imbalances. This finding does not agree with the result that the greater the share of government interference in the economy (represented by government expenditure to GDP) is, the greater the probability is that tax revenue redistribution by the government will mitigate regional inequalities [23,49]. This may be related to the inappropriate administrative interventions by the Chinese government, and it also shows that the policy of increasing government investment to promote regional integration should be carefully examined.

7. Conclusions

This paper revealed the dynamic changing laws of 20 UAs’ spatial structures in mainland China from 1992 to 2012 by using a spatial structure index calculated by the DMSP/OLS night-time light data from the monocentric/polycentric perspective. Additionally, scientific clues for the city size distribution at the UA spatial scale were provided through an assessment of the major influencing factors underlying the spatial structure evolution of UAs based on panel data analysis. This study demonstrated that the spatial structure has had a distinct polycentric development trend at the UA geographic scale. Population, economic development, transport infrastructure, foreign direct investment, and human capital factors have played significant roles in shaping this path, while the growth of government expenditure has done the opposite. Moreover, there were clear differences among the effects of these factors on the evolution of the UAs. The improvements in transportation infrastructure and foreign investment promoted polycentric changes in mature UAs; on the contrary, their impact on the emerging UAs was monocentric.

The above conclusions provide a clear spatial orientation of cities’ organization mode under the geographical scale of UAs regarding the following policy: “China’s future urbanization development model is to limit the agglomeration of large cities while focusing on developing small and medium-sized cities”. Against the background of obvious polycentric trends, differentiated regional policies should be adopted according to the situation. For mature UAs with higher development levels, it is necessary to control the sprawl of large cities and to encourage migrant transfer to secondary-sized cities, so as to improve their urban size and the human capital level. The improvement of the transportation infrastructure and the government institution could be another useful way to speed up the development of integration within UAs, thus facilitating the formation of a polycentric spatial structure. Compared with the mature UAs, the distribution of the production elements was not as concentrated in the emerging UAs, and the radiation effect of the core cities to the peripheral cities has not fully worked [24]. Instead of intervening in the development of small and medium-sized cities directly through excessive government measures, we should implement a centralized development strategy to promote the radiation effect of the core cities, which will further play a role in this agglomeration economy.

Our study is important, but it is only the first step towards adequately understanding the processes of the spatial structure evolution of UAs. It should be enriched in following studies. First, we measured the spatial structure of monocentric/polycentric development in morphological terms, and future examinations from the other perspective may or may not come to similar conclusions. The polycentric change was a way to evaluate the development of urban agglomerations from the morphological perspective. Its description of urban spatial structure focused on the characteristics of the urban form and the driving forces focused on the socio-economic factors. Other than this, urban compact/sprawl may be another perspective to assess the urban growth. For instance, Stathakis and Tsilimigkas [68] adequately compared the compactness of European cities and Tsilimigkas, et al. [69] made a comparative analysis of the land use patterns of medium-sized Hellenic cities in order to shed light on issues concerning the urban development mode and the urban sprawl. Urban compactness could help us to assess urban development in terms of population distribution, building density, traffic accessibility, and industrial functions. Based on the point of land use patterns which contains more information on urban spatial structure, we would better capture more influencing factors on spatial structure evolution; for instance, the recent growth of tourism generated a significant increase of building land demand and further contributed to sprawl [70]. Although the compactness shares the same connotation with the polycentricity, this would stil merit further study. Second, we discussed the basic influencing factors on spatial structure changes, but an analysis concentrating on centralized employment or traffic contact may help to reveal the underlying mechanisms more explicitly. It should be acknowledged that city growth greater than a given scale would bring congestion, excessive commuting and environmental pollution, which may further encourage the sub-center to alleviate the diseconomy of scale. Limited by the availability of current data, these factors have not been included in the analysis. In the future, the method of field survey may help us to obtain commuter time data and better analyze the microscopic mechanism of polycentric evolution. Third, although it is difficult to include urban spatial planning into the analytical framework of this study, it must be pointed out that the change in spatial planning has a significant effect on the changes of urban spatial structure. As mentioned in Section 6, the implementation of the policy of “turning county-level units into a part of the metropolis or an upper-level area” has led to an obvious monocentric trend in the relevant UAs. This change is different from the general tendency and occurs in those years that coincide with the implementation of spatial planning. Similarly, the impact of spatial planning on urban spatial structure has been confirmed in foreign urban case studies. For example, the loose planning system has been considered as the principal driving factor for the particularly spatial characteristics that emerged in Hellenic cities [69]. Finally, our analysis provided an overview of the spatial structure evolution across Chinese UAs. An in-depth case study could examine how the evolution pattern was shaped in order to develop the strategies of urban sustainability in specific locations.