Research on the Coupling Coordination Characteristics of Affordable Housing Market and Urban Development

Abstract

Affordable housing development is an important livelihood project for promoting the harmonious development of the urban economy and society. However, the unclear spatial–temporal characteristics of the affordable housing market and urban development are not conducive to the promotion of regional urban sustainable development. Hence, it is of great significance to research the interaction characteristics between the affordable housing market and urban development to promote sustainable development. This study constructed an evaluation index system, coupling coordination model, and spatial econometric model of the affordable housing market and urban development to analyze the development level and spatial-temporal characteristics of coupling coordination between the two systems in 70 large- and medium-sized cities in China from 2010 to 2020. The results show the following: (1) From 2010 to 2020, the development levels of the affordable housing market and urban development rose with obvious regional differences. The development of the affordable housing market and urban development had the characteristics of spatial similarity and common development trends in the horizontal distribution and kernel density aggregation distribution. (2) The coupling coordinated development level of the affordable housing market and urban development in 70 large- and medium-sized cities in China from 2010 to 2020 was generally low, showing an increasing trend year by year, with significant regional differences. The coupling coordination level of the two systems in the eastern region was much higher than those in the central, western and northeastern regions. The spatial distribution characteristics showed a spreading trend from a high level in the east to a low level in the west. The coupling coordination development levels of the two systems had obvious positive spatial correlation characteristics. There were obvious differences in the coupling coordination development level of the two systems between the cities, which need to be comprehensively improved through interactions between the cities.

1. Introduction

With the rapid development of technology and society, the gap between the rich and poor, as an important factor affecting the sustainable development of society, will bring instability and disunity to cities [1]. The affordable housing market can solve the most basic housing demands for low-income groups, is an important part of promoting the healthy and stable development of cities, and has been valued by governments around the world [2]. Research on the coupling coordination relationship between the affordable housing market and urban development is conducive to a scientific understanding of their interactive relationship; it also provides a theoretical basis and data support for the rational planning of affordable housing market construction and promotion of urban sustainable development.

As a rapidly developing country with a large population base, China’s rapid economic and urban development will lead to an unbalanced urbanization process and urbanization level [3]. The rapid urbanization speed and rapid influx of many people into the city in a short period will cause the urbanization quality to fail to match the speed of the urbanization process and inevitably lead to problems, such as housing difficulties, traffic congestion, energy supply shortage, ecological environment destruction and serious social class differentiation [4]. While responding to the overall national plan and accelerating high-quality urban development, local governments should also make every effort to improve people’s well-being and fulfill the people’s concept of a city [5]. Research on the affordable housing market and urban sustainable development can provide an analysis method reference and planning suggestions for unbalanced regions and countries and has great scientific and practical significance.

The research on affordable housing is a worldwide research topic related to people’s livelihoods. Scholars from various countries have conducted a series of studies on this subject. The research results have also confirmed that different countries play a regulating role in the real estate market based on meeting people’s basic housing demands through the reasonable promotion of affordable housing [6,7,8]. In 1925, Ernest W. Burgess, an American sociologist, discussed potential American housing market laws and proposed the phenomenon of urban housing change in the selection and replacement of housing by different population classes via the concentric circle theoretical model, which has become an important theoretical basis for the design of today’s housing security system [9]. However, the criteria for the definition and evaluation of affordable housing have not been completely unified because of different national conditions. As for the scope of affordable housing in China, Guo summarized relevant international studies and, combined with China’s specific national conditions, analyzed the housing consumption income ratio, housing price income ratio, and other indicators of China’s guaranteed objects using statistical grouping and backward inference methods; they also set the household consumption expenditure ratio and household disposable income corresponding to affordable housing [10]. Wu et al. studied the definition mechanism of affordable housing in China and believed that the scope of affordable housing should be defined according to the affordable housing type and the evolution process of affordable housing in a more realistic way [11]. In addition, given the different types of urban housing markets, the relationship between affordable housing and commercial housing has also become an important research object. In 1983, Murry studied the crowding-out effect of public housing construction on private housing development in the United States and found that the public housing targeted by the government for the middle-income group only replaces part of the commercial housing developed by individual enterprises [12]. Snai et al. also studied the crowding-out effect of affordable housing and commercial housing developed by individual enterprises in 2005 and showed that each unit of government-subsidized housing could have an impact of 0.35~0.52 units on the increase in national housing quantity. The conjectures of no-crowding-out effect and complete-crowding-out effect proposed by previous scholars were further investigated, and the two conjectures were refuted [13].

Zhang et al. used a VAR model to research the crowding-out effect of affordable housing on commercial housing; the results show that every 1% increase in the construction volume of affordable housing would have a crowding-out effect of 0.254% on the sales volume of commercial housing, which corresponds with the conclusion of foreign scholars [14]. Zou et al. discussed how affordable housing affects commodity housing prices regarding land resource competition through a statistical analysis with panel data from 248 cities; the results show that, although affordable housing can effectively squeeze out the supply of commercial housing through competitive rationing of land resources, it cannot completely replace the demand for commercial housing. Therefore, it will eventually lead to the upside-down U-shaped result of a price rise in commercial housing [15]. Regarding the factors affecting the development of the affordable housing market, scholars have also carried out a lot of studies, showing that urbanization [16], per capita disposable income [17], urban population [18], land supply area [19], policy support [20] and other factors have different degrees of influence on the development of the affordable housing market.

Research on urban development has become a research focus worldwide, and many world institutions have also set up relevant research projects on urban development, providing a reference for global sustainable urban development and strategic policy formulation. As for the indicators of urban development, many relevant studies have been carried out by international organizations. UN-HABITAT established the Global Urban indicator project in 1988 to carry out research on five dimensions: social development and poverty elimination, economic development, environmental management, urban management and housing [21]. To further increase research progress, in 1997, UN-HABITAT further constructed the City Development Index (CDI), which is the most simple and effective comprehensive index to measure the level of urban development at present. This composite index can reflect the level of urban development by measuring the human and material capitals of urban residents [22]. In addition, there are the Global City Indicators [21], Healthy City Indicator system [23], Environmental Economy and Urban Sustainable Development Index (EESD), etc. [24,25]. Based on different evaluation indicator systems, different scholars have evaluated the development of cities regarding green, sustainable, smart, livable and other aspects [26]. With the introduction of spatial theory, the spatial evolution trend of urban development has been studied and explored by different scholars regarding its development mechanism [27]. Urban sustainable development involves the coordinated development of residents’ quality of life, transportation environment, housing market and other aspects [28].

There have been relatively few studies on the correlation between affordable housing and urban development. Tang studied the relationship between the development of new towns in big cities and housing security in the process of rapid urbanization; they also analyzed and predicted the internal relationship by analyzing the conceptual connotation to theoretical refining and case analysis, providing policy support for the development of affordable housing in new towns from a new perspective [29]. Regarding citizenization and domestic demand integration, Wang systematically discussed the reasonable supply of affordable housing in the city, the interaction between the government and citizens under the existing housing affordable approach, and the internal relationship between affordable housing and urban inclusiveness, and then conducted a scenario simulation of the system. The results show that the combination of affordable housing policies and population control policies can improve the quality of urban housing, which can promote urban inclusive growth more effectively, and provide theoretical support for a future housing structure and affordable housing policy that is balanced between people and places [30]. Wang et al. studied the coupling and coordination relationship between affordable housing, urbanization and commercial housing by using measurement methods based on national statistical data. The results show that China’s affordable housing had a relatively high coupling relationship with urbanization and commercial housing, and with the rapid advancement of affordable housing, its internal coordination degree also increased. Affordable housing, urbanization and commercial housing all have certain regional differences, and the special environment provided by local conditions should also be considered in the specific research process [16]. However, there have been few studies on the analysis of systems based on data, and further discussion of the research details is still needed. Furthermore, there is a lack of research on the spatio-temporal characteristics of the intrinsic connection between the affordable housing market and urban development. In addition, as two complex systems, the interaction between the affordable housing market and urban development systems still needs further exploration.

This study took 70 large- and medium-sized cities in China to carry out development-level assessment and spatio-temporal analysis of the coupling coordination degree and analyze the trend of coupling and coordination development of the two systems based on quantitative measurement results of historical data to provide a theoretical scientific basis and suggestions for further policy formulation of the regional affordable housing market and urban development planning of government departments.

2. Materials and Methods

In this section, the research framework, the evaluation method of affordable housing market and urban development, coupling coordination degree model, and the research scope and data sources selected in this study are introduced.

2.1. Research Framework

This study focused on exploring the coupling coordination characteristics between the affordable housing market and urban development, and its research framework was systematically constructed around theoretical foundations, subsystem development evaluation, coupling coordination analysis and spatio-temporal pattern exploration, as detailed below (Figure 1).

This study examined the coupling coordination between the affordable housing market and urban development via a research framework encompassing four core components. First, six key theories, including housing filter theory, welfare economics theory, and urban sustainable development theory, were used to support analyses of market dynamics, government intervention rationale, urban development objectives and spatial patterns. Second, it evaluated the two subsystems by scientifically and reasonably selecting indicators from the closely related dimensions, followed by quantifying their respective development levels. Third, it employed a coupling coordination model to measure the interaction intensity and healthy development and conducted spatio-temporal analysis by tracing the temporal coordination trends and using kernel density estimation and spatial autocorrelation analysis to identify spatial agglomeration. Finally, it synthesized spatio-temporal patterns, identified key influencing factors, and proposed targeted policies to enhance their coupling coordination and further achieve sustainable development of regional cities.

2.2. Research Scope and Data Sources

This study mainly considered the internal coupling and coordination mechanism between the urban development level and affordable housing market to promote sustainable development goals. In the high-level areas of urban development, the main contradiction between urban development and affordable housing market is more obvious. According to the economic strength, residential transaction volume, city size and regional radiation power of the city, the National Bureau of Statistics has divided the list of 70 cities in China, including municipalities directly under the central government, provincial capitals, capital cities of autonomous regions (excluding Lhasa), separately planned cities, and other provinces and cities with better development, and researched the relevant trends of urban development and housing demand through statistical data. Therefore, the analysis scope of this study was limited to 70 large- and medium-sized cities across the country.

At the same time, to scientifically and accurately reflect the differentiation characteristics and evolution trend of the development level of the system studied using different regional cities in China, this study also conducted further research and analysis according to the four regions of eastern, central, western and northeast, with reference to the four regional classification standards defined by the National Bureau of Statistics and the current statistical yearbook. The details of specific cities and regional divisions are shown in

Table 1. The urban research area and regional divisions.

Research Region	Eastern Region	Central Region	Western Region	Northeast Region
Research urban area	Beijing, Tianjin, Shijiazhuang, Shanghai, Nanjing, Hangzhou, Ningbo, Fuzhou, Xiamen, Jinan, Qingdao, Guangzhou, Shenzhen, Haikou, Tangshan, Qinhuangdao, Wuxi, Yangzhou, Xuzhou, Wenzhou, Jinhua, Quanzhou, Yantai, Jining, Huizhou, Zhanjiang, Shaoguan, Sanya	Taiyuan, Hefei, Nanchang, Zhengzhou, Wuhan, Changsha, Bengbu, Anqing, Jiujiang, Ganzhou, Luoyang, Pingdingshan, Yichang, Xiangyang, Yueyang, Changde	Hohhot, Nanning, Chongqing, Chengdu, Guiyang, Kunming, Xi’an, Lanzhou, Xining, Yinchuan, Urumqi, Baotou, Guilin, Beihai, Luzhou, Nanchong, Zunyi, Dali	Shenyang, Dalian, Changchun, Harbin, Dandong, Jinzhou, Jilin, Mudanjiang

.

The affordable housing market and urban development are the changing trends produced by the long-term effects of multiple factors, where the changing trends are cyclical. Hence, to more scientifically and accurately analyze the space–time change process and evolution trend of the research objectives, it was necessary to consider the availability of data and the dimensional unity of relevant variable indicators. In this study, a total of 11 years’ time-series data from 2010 to 2020 were selected as the research dataset.

The data selected in this study came from statistical data, including China Statistical Yearbook, China Urban Statistical Yearbook, China Urban Construction Statistical Yearbook from 2011 to 2021, and China Land and Resources Statistical Yearbook from 2010 to 2018. For some missing data, this study supplemented the data through provincial and city statistical yearbooks and government statistical bulletins. For the individual year data that were still missing after the collection, to ensure the scientific accuracy of data, the mean replacement and trend extrapolation methods were selected to complete the dataset according to the characteristics of different indicators. The missing data accounted for less than 1% of the total data volume. Based on the comparison of the actual situation, the supplementary data conformed to the actual trend and did not bias the results.

2.3. Research Methods

In this section, the related theories and methods used to analyze the coupling coordination of affordable housing market and urban development are introduced.

According to the research framework, this study collected 11 years of panel data from 70 large- and medium-sized cities for calculation. To better highlight the variations and objectivity of the data, this study compared fuzzy models and entropy weight methods. The entropy weight method, which is suitable for determining weights based on the variation patterns of a large amount of data, was selected to measure the development level. Subsequently, a coupling coordination model was constructed to measure the coupling coordination development status between systems. Furthermore, the spatio-temporal development characteristics were analyzed using spatial metrology methods and Arcgis 10.8.1 software.

2.3.1. Entropy Weight Model

Step 1:

Normalization of indicator values

To ensure the accuracy of the evaluation results in a scientific study, the original data indicators should be normalized to eliminate the influence of different indicators on the same unit of measurement [31]. The systems’ indicators can be divided into positive and negative indicators; therefore, they should be standardized using Formulas (1) and (2) before applying the entropy weight model:

$$x_{ti}^{\prime }={\displaystyle \frac{x_{ti}-\min (x_i)}{\max (x_i)-\min (x_i)}} (\mathrm{Positive} \mathrm{indicator})$$

(1)

$$x_{ti}^{\prime }={\displaystyle \frac{\max (x_i)-x_{ti}}{\max (x_i)-\min (x_i)}} (\mathrm{Negative} \mathrm{indicator})$$

(2)

where $x_{ti}^{\prime }$ represents the value of the standardized indicator and $x_{ti}$ represents the value of the original indicator. max(x_i) and min(x_i) represent the maximum and minimum values of the indicator, respectively.

Step 2:

Calculating indicator weights

Initially, the ratio for the indicator $Y_{ti}$ can be calculated using Formula (3) to illustrate the contribution of the $i$-th evaluation indicator in the $t$-th year:

$$Y_{ti}=X_{ti}^{\prime }/{\displaystyle {\sum }_{t=1}^m{X}_{ti}^{\prime }}$$

(3)

Thereafter, the indicator’s entropy should be calculated using Formula (4), which is based on the definition of information entropy [31]:

$$e_i=-{\displaystyle \frac{1}{\ln m}}{\displaystyle {\sum }_{t=1}^m{Y}_{ti}\times }\ln Y_{ti}(0\le e_i\le 1)$$

(4)

The deviation degree for indicator $i$ can then be calculated based on $e_i$ by using Formula (5):

$$d_i=1-e_i$$

(5)

From Formula (6), the weight of indicator $i$ can be computed. The weight of an indicator is greater when the deviation degree for the indicator becomes larger:

$$W_i=d_i/{\displaystyle {\sum }_{i=1}^n{d}_i}$$

(6)

where $m$ represents the number of years and $n$ represents the number of indicators.

2.3.2. Coupling Coordination Degree Model

According to Sun and Cui [32], Formula (7) can be used to calculate the multi-system coupling coordination degree (CCD):

$$C_n={\left[{\displaystyle \frac{\left({\mu }_1·{\mu }_2·\cdot \cdot \cdot ·{\mu }_n\right)}{{\left(\frac{{\mu }_1+{\mu }_2+\cdot \cdot \cdot +{\mu }_n}{n}\right)}^n}}\right]}^{{\displaystyle \frac{1}{n}}}$$

(7)

Formula (7) can be rearranged into Formula (8):

$$C_n=n{\left\{\left({\mu }_1·{\mu }_2·\cdot \cdot \cdot ·{\mu }_n\right)/{\left({\mu }_1+{\mu }_2+\cdot \cdot \cdot +{\mu }_n\right)}^n\right\}}^{1/n}$$

(8)

In this study, two systems are calculated using Formula (8); thus, when $n=2$, the formula yields the following:

$$C_2=2{\left\{\left({\mu }_1·{\mu }_2\right)/{\left({\mu }_1+{\mu }_2\right)}^2\right\}}^{1/2}$$

(9)

$$\left\{\begin{array}{c}{\mu }_1={\displaystyle {\sum }_{i=1}^n{a}_i·x_i}\\ {\mu }_2={\displaystyle {\sum }_{i=1}^n{b}_i·y_i}\end{array}\right.$$

(10)

$$T=\alpha ·{\mu }_1+\beta ·{\mu }_2$$

(11)

$$D={\left(C·T\right)}^{\theta }$$

(12)

where C is the coupling degree; D is the CCD; ${\mu }_1$ and ${\mu }_2$ represent the subsystem comprehensive development levels for affordable housing market and urban development, respectively; T represents the total level of affordable housing market and urban development; $a_i$ and $b_i$ represent the weights of the two different subsystems, respectively; $\alpha$ and $\beta$ represent the contributions of affordable housing market and urban development, respectively; $\theta$ is an undetermined parameter. Following previous studies, the value of $\theta$ was set to 0.5 [16,32,33,34].

The classification of the CCD between affordable housing market and urban development was established (

Table 2. The division of coupling coordination development phases and types.

Coupling Coordination Stage	Indicator Value	Coupling Coordination Classification
Low Level Stage $(0\le D<0.3)$	$0\le D<0.1$	Extreme maladjustment
	$0.1\le D<0.2$	Serious maladjustment
	$0.2\le D<0.3$	Moderate maladjustment
Antagonism Stage $(0.3\le D<0.5)$	$0.3\le D<0.4$	Low maladjustment
	$0.4\le D<0.5$	Marginal maladjustment
Running-in Stage $(0.5\le D<0.8)$	$0.5\le D<0.6$	Reluctant coordination
	$0.6\le D<0.7$	Initial coordination
	$0.7\le D<0.8$	Moderate coordination
High Level Stage $(0.8\le D\le 1)$	$0.8\le D<0.9$	Satisfactory coordination
	$0.9\le D\le 1$	Superior coordination

). The CCD values range from 0 to 1 [16,32]. The classification was divided into four stages and ten types.

2.3.3. Growth Distribution Dynamic Analysis

The growth distribution dynamic method was proposed by Quah, in which the kernel density estimates are widely used.

Kernel density is mainly used to estimate the probability density of random variables. It is one of the important non-parametric estimation methods that can reflect the dynamic evolution of a sample distribution [35,36,37]. The expressions are as follows:

$$f\left(x\right)={\displaystyle \frac{1}{Nh}}{\displaystyle \sum _{i=1}^{N}K}\left({\displaystyle \frac{x-x_i}{h}}\right)$$

(13)

$$f\left(x\right)={\displaystyle \frac{1}{\sqrt{2\pi }}}exp\left(-{\displaystyle \frac{x^2}{2}}\right)$$

(14)

where h is the window width, N is the observation number, and $K\left(·\right)$ is the kernel function. In this study, the Gaussian kernel was selected to estimate the dynamic evolution of the coupling coordination degree level in 70 Chinese cities.

2.3.4. Spatial Correlation Analysis Model

Step 1:

Construction of spatial weight matrix

The research object was the coupling and coordination relationship between the affordable housing market and the urban development system, and the influencing factors cover many aspects, such as the economic level and urban residents’ demand. Hence, to research the coupling and coordination spatial relationship scientifically, this study adopted the economic–geographical distance matrix. The expression is as follows:

$$w_{ij}=\left\{\begin{array}{cc}{d}_{ij}·e_{ij},\hfill & i\ne j\hfill \\ 0,\hfill & i = j\hfill \end{array}\right.$$

(15)

where d_ij is the geographical distance matrix and e_ij is the economic distance matrix.

Step 2:

Construction of spatial correlation analysis model

(1)

Global spatial autocorrelation analysis

In 1950, Moran, an Australian statistician, proposed a measure of spatial autocorrelation called the global Moran index ($Moran\prime s I$) to reflect the degree of spatial correlation between regions that are interrelated and interdependent. $Moran\prime s I$ can be calculated using Formulas (16) and (17):

$$Moran\prime s I={\displaystyle \frac{{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^n{w}_{ij}\left(x_i-\overline{x}\right)\left(x_j-\overline{x}\right)}}}{S^2{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^n{w}_{ij}}}}}$$

(16)

$$S^2={\displaystyle \frac{{\displaystyle \sum _{i=1}^n\left(x_i-\overline{x}\right)}}{n}}$$

(17)

where n is the number of regions, and w_ij represents the spatial weight between regions i and j, that is, the values of row i and column j in the spatial weight matrix determined by the spatial effect analysis.

(2)

Local spatial autocorrelation analysis

To analyze the spatial aggregation around a region, the local $Moran\prime s I$ can be introduced, where it can reflect the spatial effect of a region and its neighboring regions in the form of a scatter plot and be expressed as Formula (18):

$$Local Moran\prime s I_i=\left(x_i-\overline{x}\right){\displaystyle \sum _{i\ne j}^n{w}_{ij}\left(x_j-\overline{x}\right)}$$

(18)

where $Local Moran\prime s I_i$ represents the local $Moran\prime s I$ of region i; n is the number of regions; x_i and x_j represent the actual values of region i and the spatial autocorrelation analysis region, respectively, and represent the mean value of the actual observed value of each region; and w_ij represents the spatial weight between regions i and j. The values of row i and column j in the spatial weight matrix are determined by the spatial effect analysis.

The local spatial autocorrelation analysis can reflect the spatial effect between the selected regional variable and its spatial lag vector in the form of a four-quadrant scatter diagram. The division basis and implications of the four quadrants of the local Moran scatter diagram are shown in

Table 3. Division of the four quadrants of the Moran scatter diagram and the meanings.

Quadrant List	$\mathit{L}\mathit{o}\mathit{c}\mathit{a}\mathit{l} \mathit{M}\mathit{o}\mathit{r}\mathit{a}\mathit{n}\prime \mathit{s} {\mathit{I}}_{\mathit{i}}$	${\mathit{x}}_{\mathit{i}}-\overline{\mathit{x}}$	${\displaystyle \sum _{\mathit{i}\ne \mathit{j}}^{\mathit{n}}{\mathit{w}}_{\mathit{i}\mathit{j}}\left({\mathit{x}}_{\mathit{j}}-\overline{\mathit{x}}\right)}$	Implication
First quadrant (HH)	$>0$	$>0$	$>0$	Region i and adjacent regions are high-value regions
Second quadrant (LH)	$<0$	$<0$	$>0$	Region i is the low value region, and the adjacent region is the high value region
Third quadrant (LL)	$>0$	$<0$	$<0$	Region i and adjacent regions are low-value regions
Fourth quadrant (HL)	$<0$	$>0$	$<0$	Region i is the high value region, and the adjacent region is the low value region

.

Table 3 lists the specific distinctions and implications of the four quadrants of the local Moran index. In the quadrant code, H represents the high-value region, L represents the low-value region, the first letter represents the set region i, and the second letter represents other adjacent regions.

3. Results

In this section, the affordable housing market development level, the urban development level and the coupling coordination characteristics of the two systems are analyzed.

3.1. Affordable Housing Market Evaluation

3.1.1. Affordable Housing Market Evaluation System Construction

An affordable housing market is a complex system involving many subjects and influencing factors. Considering the special nature of affordable housing, which is mainly supplied to meet the basic housing needs of low-income groups in cities, it involves housing filtering theory and social welfare. Hence, more attention should be paid to the supply policy of government departments and the demands of urban residents. Based on the index system of the previous authoritative research literature combined with China’s housing security system, this study considered the relevant factors of urban development and constructed an affordable housing market evaluation index system based on the principle of index system construction. The research dimension layer and index layer of affordable housing market development level were set up, in which the research dimension level was evaluated using the supply and demand dimensions, and the index layer contained specific research indicators related to each research dimension. To verify the rationality of the index system construction, the references are listed in the last column of

Table 4. The affordable housing market evaluation index system.

Research Dimension	Index Layer	No.	Properties	References
Supply dimension	Housing affordable expenditure	A1	+	[16,38,39,40,41]
	Affordable housing land supply	A2	+	[39,40,42,43]
	Affordable housing supply	A3	+	[39,41,42,43]
Demand dimension	Per capita disposable income—low-income	A4	+	[26,38,39,40,41,42,43,44]
	Per capita disposable income—low- and middle- income	A5	+	[26,38,39,40,41,42,44]
	Per capita housing area of low-income households	A6	+	[40,41,42,43,45,46]
	Per capita housing area of low- and middle-income households	A7	+	[40,41,42,43,45,46]
	Engel coefficient	A8	−	[42,46,47,48]
	Housing income ratio of low- and middle-income households	A9	−	[26,44,45,46,47,48]

Positive (+) and negative (−) indices denote that the selected index has a positive or negative effect on the system development, respectively.

.

3.1.2. Affordable Housing Market Evaluation Results

Based on the research method, MATLAB R2023a was used to carry out the dimensionless data processing and weight calculations. The weights are shown in

Table 5. The affordable housing market evaluation index weights.

Research Dimension	Index Layer	Weight
Supply dimension	A1	0.259
	A2	0.281
	A3	0.213
Demand dimension	A4	0.072
	A5	0.071
	A6	0.037
	A7	0.035
	A8	0.024
	A9	0.008

.

For the supply dimension, the weights of the A2, A1 and A3 indicators account for the top three affordable housing market indicators, indicating that the supply dimension played a decisive role in the impact of the affordable housing market. This is in line with the idea that government support is fundamental to promote affordable housing market development. For the demand dimension, the weight of A9 is the smallest, at only 0.008, indicating that the housing income ratio of lower-middle-income families had a minimal impact on the affordable housing market compared with other indicators, followed by A8, which has a value of 0.024. Regarding the research dimensions, the weight ratio of the supply and demand dimension is about 3:1.

3.2. Urban Development Evaluation

3.2.1. Urban Development Evaluation System Construction

As a complex system carrying human survival, development and various activities, the urban economic, social, spatial environment and other indicators are constantly changing. Combining this with the theory of sustainable development, the economic and social sustainability involved in a city is related to the potential and direction of its future development. In addition, the residential and spatial dimensions, as key factors for a city to attract human resources and migrant populations, are also related to the basic housing demand. The construction of a reasonable index system can accurately and comprehensively evaluate the development level of urban research. By using the classical index system of research institutions from around the world, combined with the authoritative research literature and regulations as the basis for reference, this study constructed an urban development index system. The research dimension layer and the index layer of the urban development level were set up, in which the research dimension level contained four dimensions, namely, economic, social, residential and spatial, and the index layer contained specific research indicators related to each research dimension. To verify the rationality of the index system construction, the references are listed in the last column of

Table 6. The urban development evaluation index system.

Research Dimension	Index Layer	No.	Properties	References
Economic dimension	Gross Domestic Product (GDP)	U1	+	[49,50,51,52,53,54,55]
	Economic density	U2	+	[55,56,57]
	Financial dependence	U3	+	[53,56,57,58]
	The proportion of tertiary industry	U4	+	[51,52,54,55,56,59,60,61]
	Local general public finance budgets	U5	+	[49,51,52,54,56,58,59]
Social dimension	Number of health technicians per 1000 people	U6	+	[52,56,58,60,61]
	Number of primary and secondary schools per 1000 people	U7	+	[52,60,61]
	Number of buses per 1000 people	U8	+	[52,58,60,61]
	Urban registered unemployment rate	U9	−	[16,49,51,56,59]
Resident dimension	The number of permanent residents	U10	+	[49,50,52,53]
	Population density	U11	+	[49,53,54,58]
	Per capita GDP	U12	+	[49,50,51,53,54,57,59]
	Per capita GDP contains gold	U13	+	[51,53,54,57]
Spatial dimension	Green coverage rate	U14	+	[49,51,56,62]
	Per capita built-up area	U15	+	[49,56,60,62,63]
	Per capita road area	U16	+	[52,54,58,62]

Positive (+) and negative (−) indices denote that the selected index has a positive or negative effect on the system development, respectively.

.

3.2.2. Urban Development Evaluation Results

Based on the research method, MATLAB was used to carry out the dimensionless data processing and weight calculations. The weights are shown in

Table 7. The urban development evaluation index weights.

Research Dimension	Index Layer	Weight
Economic dimension	U1	0.107
	U2	0.208
	U3	0.045
	U4	0.028
	U5	0.133
Social dimension	U6	0.024
	U7	0.033
	U8	0.083
	U9	0.026
Resident dimension	U10	0.056
	U11	0.069
	U12	0.043
	U13	0.033
Spatial dimension	U14	0.004
	U15	0.055
	U16	0.053

.

In the economic dimension, the weights of the U4, U2 and U3 indicators account for the top three weights of the urban development evaluation indicators, indicating that the economic dimension indicators had a greater impact on the urban development level. In the spatial dimension, U14 accounts for the smallest index weight, at only 0.004, indicating that the change in the green coverage rate had a relatively small impact on the level of urban development, and the other indicators made no significant difference. Regarding the research dimensions, the economic dimension has the largest weight, the social and residential dimensions have the same weight, and the spatial dimension has the smallest weight.

3.3. Coupling Coordination Degree Evaluation Results

According to the coupling coordination degree model, this study measured the comprehensive development level, coupling degree and coupling coordination degree between the two systems according to the statistical data and development-level measurement results of 70 large- and medium-sized cities in China from 2010 to 2020.

3.3.1. Systematic Comprehensive Development Level

The calculation results of the comprehensive development level of the system are shown in

Table A1. The affordable housing market evaluation results.

City	2010	2011	2012	2013	2014	2015	2016	2017	2018	2019	2020
Beijing	0.231	0.264	0.254	0.251	0.230	0.247	0.374	0.327	0.299	0.324	0.314
Tianjin	0.246	0.349	0.335	0.196	0.209	0.118	0.247	0.181	0.286	0.295	0.273
Shijiazhuang	0.081	0.116	0.109	0.125	0.114	0.118	0.151	0.149	0.171	0.153	0.158
Hohhot	0.086	0.114	0.113	0.113	0.111	0.109	0.128	0.113	0.129	0.134	0.121
Taiyuan	0.070	0.103	0.105	0.093	0.089	0.096	0.104	0.097	0.104	0.122	0.121
Shenyang	0.085	0.088	0.105	0.122	0.121	0.105	0.119	0.112	0.123	0.133	0.129
Dalian	0.078	0.174	0.108	0.119	0.097	0.098	0.104	0.102	0.119	0.130	0.130
Changchun	0.117	0.118	0.143	0.097	0.118	0.095	0.104	0.116	0.132	0.145	0.150
Harbin	0.114	0.146	0.101	0.081	0.098	0.090	0.097	0.104	0.110	0.122	0.118
Shanghai	0.170	0.313	0.262	0.214	0.248	0.253	0.289	0.327	0.345	0.355	0.363
Nanjing	0.181	0.375	0.214	0.227	0.237	0.165	0.256	0.309	0.303	0.314	0.339
Hangzhou	0.140	0.158	0.268	0.270	0.215	0.164	0.261	0.226	0.271	0.319	0.323
Ningbo	0.322	0.155	0.372	0.317	0.240	0.172	0.233	0.200	0.305	0.320	0.319
Hefei	0.107	0.150	0.185	0.169	0.180	0.104	0.189	0.186	0.192	0.219	0.206
Fuzhou	0.087	0.111	0.105	0.111	0.121	0.130	0.135	0.139	0.163	0.165	0.166
Xiamen	0.099	0.124	0.113	0.109	0.111	0.116	0.134	0.144	0.154	0.160	0.156
Nanchang	0.076	0.093	0.089	0.210	0.113	0.108	0.142	0.134	0.156	0.176	0.179
Jinan	0.128	0.128	0.122	0.140	0.156	0.145	0.165	0.178	0.188	0.201	0.216
Qingdao	0.110	0.194	0.169	0.184	0.158	0.133	0.164	0.154	0.216	0.213	0.222
Zhengzhou	0.204	0.172	0.113	0.149	0.236	0.250	0.230	0.225	0.247	0.237	0.259
Wuhan	0.105	0.194	0.194	0.283	0.190	0.181	0.160	0.173	0.215	0.218	0.212
Changsha	0.136	0.142	0.200	0.179	0.202	0.160	0.213	0.175	0.241	0.239	0.248
Guangzhou	0.139	0.181	0.162	0.168	0.178	0.203	0.189	0.216	0.221	0.235	0.266
Shenzhen	0.117	0.161	0.151	0.154	0.158	0.182	0.303	0.407	0.272	0.286	0.292
Nanning	0.097	0.111	0.080	0.117	0.089	0.102	0.099	0.108	0.120	0.119	0.135
Haikou	0.061	0.069	0.079	0.072	0.077	0.080	0.091	0.103	0.097	0.101	0.099
Chongqing	0.392	0.610	0.518	0.344	0.302	0.292	0.269	0.232	0.380	0.400	0.414
Chengdu	0.125	0.292	0.159	0.210	0.252	0.212	0.171	0.227	0.275	0.271	0.270
Guiyang	0.123	0.118	0.099	0.114	0.105	0.118	0.100	0.117	0.149	0.150	0.141
Kunming	0.083	0.144	0.174	0.133	0.124	0.129	0.136	0.134	0.140	0.154	0.155
Xi’an	0.114	0.135	0.187	0.227	0.208	0.193	0.192	0.173	0.201	0.243	0.239
Lanzhou	0.075	0.088	0.081	0.085	0.093	0.125	0.115	0.108	0.139	0.138	0.152
Xining	0.042	0.070	0.066	0.079	0.073	0.113	0.117	0.107	0.115	0.112	0.115
Yinchuan	0.093	0.141	0.151	0.131	0.168	0.168	0.140	0.129	0.183	0.175	0.171
Urumqi	0.068	0.079	0.070	0.064	0.124	0.092	0.104	0.127	0.159	0.171	0.158
Tangshan	0.088	0.134	0.098	0.101	0.105	0.115	0.119	0.120	0.133	0.140	0.136
Qinhuangdao	0.073	0.122	0.091	0.182	0.099	0.103	0.126	0.126	0.138	0.145	0.147
Baotou	0.095	0.144	0.123	0.128	0.139	0.131	0.139	0.129	0.142	0.144	0.143
Dandong	0.033	0.059	0.052	0.059	0.063	0.069	0.073	0.076	0.082	0.090	0.090
Jinzhou	0.056	0.074	0.076	0.092	0.085	0.082	0.080	0.082	0.090	0.095	0.096
Jilin	0.070	0.085	0.102	0.090	0.090	0.093	0.085	0.087	0.092	0.092	0.094
Mudanjiang	0.050	0.055	0.067	0.067	0.072	0.082	0.097	0.092	0.094	0.096	0.100
Wuxi	0.236	0.283	0.253	0.194	0.215	0.158	0.180	0.181	0.250	0.267	0.259
Yangzhou	0.083	0.143	0.119	0.110	0.121	0.130	0.157	0.179	0.184	0.202	0.204
Xuzhou	0.099	0.096	0.255	0.108	0.172	0.099	0.172	0.151	0.203	0.220	0.246
Wenzhou	0.112	0.141	0.232	0.267	0.291	0.156	0.212	0.289	0.290	0.286	0.285
Jinhua	0.122	0.131	0.157	0.202	0.199	0.161	0.195	0.191	0.218	0.227	0.225
Bengbu	0.070	0.067	0.077	0.077	0.142	0.124	0.129	0.103	0.117	0.127	0.131
Anqing	0.060	0.104	0.087	0.112	0.115	0.102	0.108	0.134	0.134	0.138	0.133
Quanzhou	0.104	0.140	0.133	0.134	0.138	0.142	0.149	0.150	0.159	0.173	0.175
Jiujiang	0.071	0.100	0.159	0.185	0.178	0.135	0.133	0.125	0.147	0.166	0.167
Ganzhou	0.103	0.162	0.149	0.293	0.145	0.117	0.115	0.139	0.198	0.242	0.207
Yantai	0.086	0.104	0.109	0.119	0.125	0.122	0.126	0.138	0.167	0.142	0.145
Jining	0.076	0.110	0.101	0.088	0.099	0.105	0.131	0.143	0.151	0.126	0.122
Luoyang	0.076	0.143	0.101	0.111	0.116	0.137	0.134	0.120	0.143	0.155	0.164
Pingdingshan	0.096	0.080	0.110	0.079	0.096	0.086	0.106	0.122	0.126	0.122	0.115
Yichang	0.059	0.084	0.095	0.128	0.152	0.212	0.157	0.165	0.175	0.167	0.154
Xiangyang	0.058	0.069	0.078	0.098	0.153	0.137	0.135	0.130	0.140	0.151	0.151
Yueyang	0.085	0.117	0.124	0.121	0.129	0.123	0.141	0.147	0.141	0.154	0.149
Changde	0.074	0.118	0.107	0.129	0.130	0.148	0.140	0.136	0.149	0.151	0.163
Huizhou	0.081	0.101	0.099	0.079	0.101	0.094	0.105	0.122	0.115	0.127	0.138
Zhanjiang	0.043	0.067	0.063	0.062	0.070	0.073	0.079	0.082	0.085	0.090	0.097
Shaoguan	0.060	0.080	0.083	0.082	0.081	0.107	0.093	0.095	0.098	0.104	0.107
Guilin	0.058	0.091	0.085	0.103	0.187	0.170	0.112	0.096	0.154	0.172	0.197
Beihai	0.086	0.113	0.110	0.080	0.100	0.094	0.091	0.094	0.100	0.108	0.095
Sanya	0.060	0.072	0.074	0.080	0.086	0.099	0.097	0.095	0.112	0.123	0.108
Luzhou	0.063	0.075	0.081	0.096	0.117	0.107	0.079	0.105	0.123	0.124	0.124
Nanchong	0.061	0.101	0.064	0.063	0.137	0.094	0.098	0.105	0.122	0.132	0.128
Zunyi	0.083	0.088	0.088	0.121	0.113	0.142	0.166	0.157	0.172	0.155	0.149
Dali	0.058	0.076	0.075	0.077	0.093	0.094	0.113	0.110	0.115	0.122	0.123
Average	0.104	0.139	0.138	0.140	0.143	0.133	0.148	0.151	0.171	0.179	0.180

in Appendix A. The average of the comprehensive development of the 70 large- and medium-sized cities in China basically showed a steady upward trend, but it dropped slightly in 2020, which indicates that after 10 years of development, the comprehensive development level of the 70 large- and medium-sized cities in China tended to be flat, and the comprehensive development level will be stable in the next few years. According to the data of various cities, the comprehensive development level of Chinese cities had obvious differences in the ten-year study period. From 2010 to 2013, the comprehensive development level of Chongqing ranked at a high level in China and gradually decreased from 2012 to 2016. Chongqing began to lag behind other cities in 2013 and steadily rose from 2017. The high comprehensive development level of Chongqing was influenced by the early high level of its urban affordable housing market. Since 2010, except for some years, the comprehensive development levels of Shanghai, Shenzhen and Beijing maintained a trend of near-linear growth and have been ranked among the top three cities in China since 2014. Since 2013, Tianjin’s comprehensive development level has gradually lagged that of other cities, and the comprehensive development trend was unstable and, thus, cannot be further predicted based on the currently available data.

3.3.2. Coupling Degree

The calculation results of the coupling degree are shown in

Table A2. The urban development evaluation results.

City	2010	2011	2012	2013	2014	2015	2016	2017	2018	2019	2020
Beijing	0.301	0.320	0.337	0.364	0.374	0.401	0.427	0.446	0.465	0.485	0.461
Tianjin	0.197	0.215	0.234	0.260	0.285	0.291	0.312	0.312	0.313	0.303	0.285
Shijiazhuang	0.144	0.148	0.151	0.151	0.154	0.160	0.165	0.169	0.179	0.180	0.185
Hohhot	0.151	0.143	0.168	0.184	0.170	0.172	0.177	0.170	0.175	0.182	0.154
Taiyuan	0.141	0.153	0.161	0.165	0.170	0.175	0.180	0.187	0.185	0.195	0.175
Shenyang	0.150	0.160	0.169	0.179	0.180	0.181	0.175	0.185	0.192	0.197	0.193
Dalian	0.160	0.168	0.175	0.187	0.181	0.182	0.178	0.192	0.200	0.195	0.185
Changchun	0.140	0.147	0.152	0.158	0.161	0.169	0.170	0.175	0.184	0.183	0.182
Harbin	0.135	0.140	0.145	0.145	0.149	0.156	0.159	0.166	0.170	0.163	0.161
Shanghai	0.313	0.335	0.348	0.371	0.384	0.420	0.453	0.480	0.513	0.544	0.554
Nanjing	0.197	0.211	0.223	0.243	0.256	0.269	0.282	0.294	0.309	0.320	0.306
Hangzhou	0.174	0.184	0.193	0.204	0.214	0.227	0.241	0.259	0.272	0.282	0.267
Ningbo	0.143	0.153	0.158	0.172	0.175	0.184	0.195	0.221	0.226	0.240	0.231
Hefei	0.139	0.144	0.155	0.145	0.146	0.160	0.169	0.184	0.186	0.205	0.200
Fuzhou	0.140	0.140	0.147	0.156	0.155	0.165	0.173	0.184	0.188	0.200	0.199
Xiamen	0.236	0.253	0.264	0.275	0.278	0.289	0.295	0.311	0.315	0.325	0.265
Nanchang	0.123	0.129	0.142	0.158	0.151	0.163	0.167	0.162	0.173	0.181	0.177
Jinan	0.159	0.167	0.168	0.179	0.197	0.206	0.214	0.219	0.229	0.239	0.237
Qingdao	0.152	0.166	0.179	0.196	0.204	0.214	0.224	0.232	0.252	0.255	0.248
Zhengzhou	0.151	0.159	0.165	0.172	0.184	0.198	0.208	0.223	0.235	0.250	0.240
Wuhan	0.170	0.183	0.197	0.214	0.218	0.228	0.241	0.258	0.282	0.300	0.283
Changsha	0.150	0.156	0.159	0.169	0.186	0.202	0.214	0.227	0.239	0.249	0.255
Guangzhou	0.259	0.271	0.285	0.312	0.310	0.329	0.342	0.354	0.390	0.409	0.361
Shenzhen	0.320	0.282	0.377	0.404	0.430	0.468	0.504	0.550	0.566	0.602	0.627
Nanning	0.132	0.136	0.139	0.142	0.147	0.149	0.154	0.156	0.162	0.170	0.169
Haikou	0.152	0.169	0.177	0.166	0.161	0.167	0.178	0.194	0.194	0.194	0.161
Chongqing	0.173	0.198	0.214	0.221	0.228	0.242	0.250	0.268	0.275	0.296	0.292
Chengdu	0.147	0.156	0.174	0.186	0.199	0.203	0.212	0.234	0.248	0.261	0.259
Guiyang	0.131	0.128	0.137	0.139	0.152	0.151	0.154	0.172	0.167	0.173	0.152
Kunming	0.149	0.150	0.161	0.163	0.178	0.183	0.189	0.193	0.192	0.189	0.169
Xi’an	0.147	0.157	0.168	0.178	0.183	0.190	0.195	0.204	0.209	0.225	0.211
Lanzhou	0.121	0.125	0.139	0.137	0.134	0.149	0.155	0.162	0.170	0.161	0.146
Xining	0.090	0.094	0.111	0.097	0.109	0.135	0.130	0.126	0.131	0.143	0.144
Yinchuan	0.122	0.126	0.128	0.138	0.137	0.143	0.150	0.159	0.163	0.155	0.140
Urumqi	0.154	0.162	0.169	0.181	0.191	0.202	0.205	0.232	0.244	0.277	0.199
Tangshan	0.104	0.110	0.114	0.119	0.121	0.125	0.131	0.131	0.145	0.148	0.149
Qinhuangdao	0.098	0.100	0.101	0.104	0.107	0.113	0.116	0.122	0.129	0.133	0.132
Baotou	0.126	0.133	0.136	0.142	0.144	0.147	0.153	0.144	0.154	0.148	0.134
Dandong	0.077	0.077	0.082	0.092	0.094	0.091	0.105	0.106	0.098	0.106	0.101
Jinzhou	0.075	0.082	0.091	0.091	0.087	0.084	0.095	0.093	0.093	0.099	0.096
Jilin	0.084	0.088	0.091	0.097	0.107	0.107	0.103	0.109	0.112	0.114	0.119
Mudanjiang	0.079	0.082	0.081	0.085	0.090	0.086	0.087	0.099	0.092	0.102	0.102
Wuxi	0.162	0.178	0.189	0.207	0.203	0.211	0.219	0.230	0.245	0.251	0.239
Yangzhou	0.086	0.098	0.102	0.108	0.115	0.123	0.130	0.138	0.148	0.157	0.159
Xuzhou	0.101	0.108	0.115	0.123	0.128	0.134	0.139	0.143	0.150	0.154	0.160
Wenzhou	0.113	0.117	0.127	0.129	0.134	0.141	0.147	0.154	0.160	0.169	0.168
Jinhua	0.086	0.088	0.092	0.095	0.102	0.111	0.118	0.125	0.132	0.140	0.137
Bengbu	0.095	0.096	0.102	0.106	0.104	0.109	0.113	0.124	0.120	0.130	0.138
Anqing	0.089	0.090	0.090	0.099	0.095	0.094	0.099	0.099	0.106	0.107	0.115
Quanzhou	0.118	0.123	0.128	0.131	0.135	0.139	0.144	0.159	0.163	0.172	0.165
Jiujiang	0.100	0.099	0.088	0.091	0.093	0.098	0.096	0.105	0.103	0.109	0.114
Ganzhou	0.103	0.101	0.105	0.110	0.111	0.117	0.118	0.122	0.125	0.129	0.136
Yantai	0.103	0.110	0.116	0.121	0.127	0.130	0.138	0.147	0.165	0.165	0.166
Jining	0.090	0.099	0.108	0.116	0.117	0.118	0.122	0.128	0.134	0.139	0.148
Luoyang	0.104	0.108	0.110	0.111	0.114	0.116	0.118	0.125	0.120	0.130	0.136
Pingdingshan	0.087	0.089	0.096	0.099	0.101	0.103	0.105	0.114	0.112	0.120	0.116
Yichang	0.070	0.073	0.079	0.086	0.099	0.107	0.109	0.110	0.114	0.123	0.115
Xiangyang	0.066	0.069	0.072	0.080	0.080	0.094	0.103	0.108	0.110	0.119	0.115
Yueyang	0.079	0.077	0.080	0.081	0.083	0.100	0.099	0.111	0.105	0.112	0.123
Changde	0.069	0.071	0.077	0.080	0.078	0.091	0.090	0.095	0.105	0.110	0.107
Huizhou	0.116	0.118	0.123	0.127	0.139	0.141	0.150	0.154	0.161	0.165	0.144
Zhanjiang	0.100	0.100	0.103	0.101	0.092	0.102	0.098	0.104	0.105	0.109	0.123
Shaoguan	0.077	0.077	0.080	0.084	0.079	0.083	0.087	0.095	0.096	0.101	0.102
Guilin	0.084	0.087	0.085	0.091	0.089	0.090	0.088	0.108	0.105	0.112	0.109
Beihai	0.087	0.092	0.089	0.094	0.095	0.099	0.100	0.107	0.115	0.118	0.121
Sanya	0.140	0.148	0.156	0.163	0.171	0.182	0.180	0.183	0.207	0.216	0.163
Luzhou	0.068	0.071	0.075	0.084	0.082	0.082	0.068	0.093	0.099	0.107	0.117
Nanchong	0.064	0.067	0.070	0.078	0.077	0.081	0.086	0.093	0.098	0.102	0.106
Zunyi	0.100	0.100	0.099	0.103	0.095	0.096	0.101	0.109	0.106	0.111	0.115
Dali	0.140	0.135	0.139	0.135	0.133	0.138	0.143	0.152	0.149	0.153	0.165
Average	0.131	0.137	0.145	0.153	0.156	0.164	0.171	0.180	0.187	0.194	0.188

in Appendix A. The coupling degree measurement results of 70 large- and medium-sized cities show that the coupling degree between the affordable housing market and urban development in China during 2010–2020 was generally in a relatively high state, usually above 0.9. However, from 2010 to 2015, the national urban coupling degree values showed some differences within the range. Among them, the coupling degree levels of Chongqing, Ningbo, Shenzhen and Wenzhou were low, even as low as 0.860, which was largely because the concept of housing security had just been proposed during the “Twelfth Five-Year Plan” period, and the relevant policies and markets for affordable housing were not perfect. Different cities have different levels of development due to the different intensities of promoting the affordable housing market and the different development statuses of different cities. As the concept of housing security gradually gained popularity during the “13th Five-Year Plan” period from 2015 to 2020, the national urban coupling degree was basically in the range of 0.90 to 1.00, and the urban coupling degree was mostly concentrated within 0.95 to 1.00, indicating that the affordable housing market and urban development level have been significantly improved. Numerically, the development level of the two urban systems has a high coupling degree and a high correlation. A high level of coupling shows that the development level of the inter-city affordable housing market and the urban development level are in a state of mutual influence. When one party develops too fast, the coupling degree will decrease. The coupling degree value can only reflect the degree of mutual influence and cannot represent the development speed of the middle system. Returning to the level of specific system development for further analysis and taking Chongqing as an example, the coupling degree of Chongqing from 2010 to 2012 was at the lowest level in the country. Although the score of Chongqing’s affordable housing market was always in a relatively advanced state in the country, the urban development level of Chongqing from 2010 to 2012 was relatively low compared with the development level of its affordable housing market, and, thus, the coupling degree was low. However, since 2011, due to the gradual popularization of the housing security concept, the coupling degree has risen in a straight line and stabilized within 0.95–1.00, which also confirms that the attention and promotion of the affordable housing market in various cities led to the affordable housing market and urban development. However, in recent years, there are still some cities, such as Ganzhou, Wenzhou, Jinhua, Zunyi and Guilin, whose coupling degrees are at a low level in the country; this is because the coupling degree is directly related to the development level of the two systems, where the low coupling degree of these cities indicates that their urban development or affordable housing market level needs improvement. The higher the coupling degree result, the closer the correlation between the systems. However, whether there is a mutually promoting and coordinated development state between the systems still needs to be calculated based on the coupling coordination degree.

3.3.3. Coupling Coordination Degree

The coupling coordination results are shown in

Table A3. Comprehensive development evaluation results.

City	2010	2011	2012	2013	2014	2015	2016	2017	2018	2019	2020
Beijing	0.266	0.292	0.296	0.307	0.302	0.324	0.400	0.387	0.382	0.405	0.388
Tianjin	0.221	0.282	0.284	0.228	0.247	0.204	0.279	0.247	0.300	0.299	0.279
Shijiazhuang	0.112	0.132	0.130	0.138	0.134	0.139	0.158	0.159	0.175	0.166	0.171
Hohhot	0.119	0.129	0.141	0.148	0.141	0.140	0.153	0.141	0.152	0.158	0.137
Taiyuan	0.106	0.128	0.133	0.129	0.129	0.136	0.142	0.142	0.144	0.159	0.148
Shenyang	0.118	0.124	0.137	0.151	0.151	0.143	0.147	0.148	0.158	0.165	0.161
Dalian	0.119	0.171	0.142	0.153	0.139	0.140	0.141	0.147	0.160	0.162	0.157
Changchun	0.129	0.132	0.147	0.128	0.139	0.132	0.137	0.146	0.158	0.164	0.166
Harbin	0.124	0.143	0.123	0.113	0.123	0.123	0.128	0.135	0.140	0.142	0.140
Shanghai	0.241	0.324	0.305	0.292	0.316	0.337	0.371	0.403	0.429	0.449	0.458
Nanjing	0.189	0.293	0.218	0.235	0.247	0.217	0.269	0.301	0.306	0.317	0.322
Hangzhou	0.157	0.171	0.230	0.237	0.214	0.195	0.251	0.243	0.271	0.301	0.295
Ningbo	0.232	0.154	0.265	0.244	0.207	0.178	0.214	0.210	0.266	0.280	0.275
Hefei	0.123	0.147	0.170	0.157	0.163	0.132	0.179	0.185	0.189	0.212	0.203
Fuzhou	0.114	0.126	0.126	0.134	0.138	0.148	0.154	0.161	0.175	0.182	0.183
Xiamen	0.167	0.189	0.189	0.192	0.195	0.203	0.214	0.227	0.235	0.243	0.210
Nanchang	0.099	0.111	0.116	0.184	0.132	0.136	0.155	0.148	0.164	0.179	0.178
Jinan	0.143	0.147	0.145	0.159	0.177	0.175	0.189	0.198	0.209	0.220	0.226
Qingdao	0.131	0.180	0.174	0.190	0.181	0.174	0.194	0.193	0.234	0.234	0.235
Zhengzhou	0.177	0.165	0.139	0.161	0.210	0.224	0.219	0.224	0.241	0.244	0.249
Wuhan	0.137	0.189	0.196	0.249	0.204	0.205	0.201	0.215	0.249	0.259	0.247
Changsha	0.143	0.149	0.180	0.174	0.194	0.181	0.214	0.201	0.240	0.244	0.251
Guangzhou	0.199	0.226	0.223	0.240	0.244	0.266	0.266	0.285	0.306	0.322	0.313
Shenzhen	0.218	0.222	0.264	0.279	0.294	0.325	0.404	0.479	0.419	0.444	0.459
Nanning	0.114	0.123	0.109	0.129	0.118	0.126	0.127	0.132	0.141	0.145	0.152
Haikou	0.107	0.119	0.128	0.119	0.119	0.124	0.134	0.149	0.146	0.147	0.130
Chongqing	0.283	0.404	0.366	0.282	0.265	0.267	0.259	0.250	0.327	0.348	0.353
Chengdu	0.136	0.224	0.167	0.198	0.225	0.208	0.191	0.230	0.261	0.266	0.264
Guiyang	0.127	0.123	0.118	0.127	0.129	0.134	0.127	0.144	0.158	0.162	0.146
Kunming	0.116	0.147	0.168	0.148	0.151	0.156	0.162	0.163	0.166	0.171	0.162
Xi’an	0.131	0.146	0.177	0.203	0.195	0.192	0.193	0.188	0.205	0.234	0.225
Lanzhou	0.098	0.107	0.110	0.111	0.114	0.137	0.135	0.135	0.155	0.150	0.149
Xining	0.066	0.082	0.088	0.088	0.091	0.124	0.124	0.116	0.123	0.128	0.130
Yinchuan	0.108	0.134	0.140	0.135	0.152	0.155	0.145	0.144	0.173	0.165	0.155
Urumqi	0.111	0.121	0.120	0.122	0.158	0.147	0.154	0.180	0.201	0.224	0.178
Tangshan	0.096	0.122	0.106	0.110	0.113	0.120	0.125	0.126	0.139	0.144	0.143
Qinhuangdao	0.085	0.111	0.096	0.143	0.103	0.108	0.121	0.124	0.133	0.139	0.139
Baotou	0.111	0.138	0.129	0.135	0.141	0.139	0.146	0.136	0.148	0.146	0.139
Dandong	0.055	0.068	0.067	0.076	0.079	0.080	0.089	0.091	0.090	0.098	0.095
Jinzhou	0.066	0.078	0.083	0.091	0.086	0.083	0.087	0.088	0.091	0.097	0.096
Jilin	0.077	0.086	0.097	0.093	0.099	0.100	0.094	0.098	0.102	0.103	0.106
Mudanjiang	0.064	0.068	0.074	0.076	0.081	0.084	0.092	0.095	0.093	0.099	0.101
Wuxi	0.199	0.230	0.221	0.201	0.209	0.185	0.199	0.205	0.248	0.259	0.249
Yangzhou	0.085	0.120	0.111	0.109	0.118	0.127	0.143	0.159	0.166	0.179	0.181
Xuzhou	0.100	0.102	0.185	0.116	0.150	0.117	0.156	0.147	0.177	0.187	0.203
Wenzhou	0.113	0.129	0.180	0.198	0.213	0.148	0.179	0.222	0.225	0.228	0.227
Jinhua	0.104	0.110	0.124	0.148	0.150	0.136	0.157	0.158	0.175	0.183	0.181
Bengbu	0.082	0.081	0.090	0.092	0.123	0.116	0.121	0.113	0.118	0.129	0.134
Anqing	0.075	0.097	0.088	0.106	0.105	0.098	0.104	0.116	0.120	0.123	0.124
Quanzhou	0.111	0.131	0.131	0.133	0.137	0.140	0.146	0.154	0.161	0.173	0.170
Jiujiang	0.085	0.099	0.124	0.138	0.135	0.117	0.114	0.115	0.125	0.138	0.141
Ganzhou	0.103	0.131	0.127	0.202	0.128	0.117	0.117	0.131	0.161	0.185	0.171
Yantai	0.094	0.107	0.112	0.120	0.126	0.126	0.132	0.143	0.166	0.153	0.156
Jining	0.083	0.105	0.104	0.102	0.108	0.112	0.127	0.135	0.143	0.133	0.135
Luoyang	0.090	0.125	0.105	0.111	0.115	0.127	0.126	0.123	0.132	0.143	0.150
Pingdingshan	0.091	0.084	0.103	0.089	0.099	0.095	0.106	0.118	0.119	0.121	0.116
Yichang	0.065	0.079	0.087	0.107	0.126	0.159	0.133	0.138	0.144	0.145	0.135
Xiangyang	0.062	0.069	0.075	0.089	0.117	0.115	0.119	0.119	0.125	0.135	0.133
Yueyang	0.082	0.097	0.102	0.101	0.106	0.111	0.120	0.129	0.123	0.133	0.136
Changde	0.071	0.095	0.092	0.104	0.104	0.120	0.115	0.115	0.127	0.130	0.135
Huizhou	0.098	0.110	0.111	0.103	0.120	0.118	0.128	0.138	0.138	0.146	0.141
Zhanjiang	0.071	0.084	0.083	0.082	0.081	0.088	0.088	0.093	0.095	0.099	0.110
Shaoguan	0.069	0.078	0.081	0.083	0.080	0.095	0.090	0.095	0.097	0.102	0.104
Guilin	0.071	0.089	0.085	0.097	0.138	0.130	0.100	0.102	0.129	0.142	0.153
Beihai	0.087	0.102	0.100	0.087	0.097	0.096	0.095	0.100	0.107	0.113	0.108
Sanya	0.100	0.110	0.115	0.121	0.129	0.141	0.138	0.139	0.160	0.169	0.136
Luzhou	0.065	0.073	0.078	0.090	0.100	0.094	0.074	0.099	0.111	0.116	0.121
Nanchong	0.063	0.084	0.067	0.071	0.107	0.087	0.092	0.099	0.110	0.117	0.117
Zunyi	0.091	0.094	0.094	0.112	0.104	0.119	0.134	0.133	0.139	0.133	0.132
Dali	0.099	0.106	0.107	0.106	0.113	0.116	0.128	0.131	0.132	0.137	0.144
Average	0.283	0.404	0.366	0.307	0.316	0.337	0.404	0.479	0.429	0.449	0.459

in Appendix A. The coupling coordination degree development trend is basically consistent with the comprehensive development level of cities. The average coupling coordination degree of 70 large- and medium-sized cities in China showed a steady rising trend from 2010 to 2020, but it dropped slightly in 2015 and 2020. This shows that, after 10 years of development, the change trend of the coupling coordination degree flattened out, and the coupling coordination degree will be stable in the next few years. Regarding the specific city data, Chongqing’s coupling coordination level ranked first in China from 2010 to 2012 because Chongqing’s affordable housing market had a high development level in early 2010, which had a certain promotion effect on urban development. In 2012, it began to decline, and since 2017, it has shown a rebound trend, but it has always maintained a top five position in China. Shanghai and Beijing have maintained a steady upward trend. The coupling coordination degree of Shenzhen showed a trend of nearly exponential growth in general and began to rank first in China in 2012. In addition, during 2010 to 2020, there was a phenomenon where the difference in coupling coordination degree gradually increased between domestic cities, and the difference between the highest and lowest coupling coordination degree increased from 0.269 in 2010 to 0.350 in 2020. This shows that the gap between the urban development level and the coupling and coordination degree of the affordable housing market between different cities also increased. Cities with higher coupling and coordination degrees can better reflect the mutual promotion between the affordable housing market and urban development, which can better guarantee people’s livelihoods in the process of urban development and meet people’s yearning for a better life.

To reflect the changing trend of the coupling coordination degrees of different cities, this study used the mean coupling coordination degree data of the eastern, central, western and northeastern regions, as well as the overall mean, from 2010 to 2020. The horizontal measurement results of the coupling coordination degree of the four regions and the overall mean are shown in Figure 2.

As can be seen from Figure 2, the mean distribution of coupling coordination degree in all regions was in a state of steady growth, and the coupling coordination degree in the eastern region was significantly higher than that in the other three regions. The coupling coordination degree of the northeastern region was obviously lower than that of the other three regions. The coupling coordination degrees of the central and western regions steadily increased within the range of the national total average. Regarding the development trend, the development rate of the coupling coordination degree in the eastern region was higher than that in the other three regions, and that in the northeast region was lower than that in the other three regions, which led to an increased gap in the coupling coordination degree between regions. Numerically, the average gap of the regional coupling coordination degree increased from 0.059 in 2010 to 0.104 in 2020. The main differences existed in the eastern and northeastern regions. Although the coupling degree in the northeastern region developed stably from 2010 to 2020 compared with the other regions due to the relatively low development level and relatively slow growth of the two systems, the coupling coordination degree between urban development and affordable housing market in the region also grew relatively slowly.

To study the development status of 70 large- and medium-sized cities in China’s four major regions from 2010 to 2020 in more detail, this study made a further detailed comparison of the coupling coordination degree of the two systems and their regional mean values in each city in the four major regions. The specific trend is shown in Figure 3.

Figure 3 shows that the coupling coordination development level and trend of different cities in the region were also different. Although the coupling coordination degree relationships between the affordable housing market and urban development in the eastern, western, central and northeastern regions increased, it is still notable that the development level in each region had a certain development space to ensure coordination between the urban development and the affordable housing market. In addition, to reduce regional differences and improve the overall mean of the coupling coordination degree, on the premise of ensuring the high momentum of development in the east, efforts should be made to promote coordinated urban and affordable housing market development in the western and northeastern regions and then improve the coupling coordination degree of the affordable housing market and urban development across the country.

3.4. Coupling Coordination Degree Spatial Characteristics

In this study, the spatial characteristics of the coupling coordination degree between the affordable housing market and urban development in 70 large- and medium-sized cities in China were analyzed with geographic information software, and the spatial development characteristics of the results were analyzed.

3.4.1. Spatial Distribution Analysis

ArcGIS 10.8.1 was adopted to visualize the coupling coordination degree of the affordable housing market and urban development in 70 large- and medium-sized cities in China in 2010, 2015 and 2020. To analyze the spatial distribution characteristics of the coupling coordination degree level, this study classified the coupling coordination degree level values of the system in 2010, 2015 and 2020 according to the coupling coordination classification in Table 2. The details are shown in Figure 4.

Figure 4 shows that the spatial distribution of the coupling coordination degree of 70 large- and medium-sized cities in China was radially distributed from east to west. The coupling coordination degree levels in 2010, 2015 and 2020 were significantly different. From 2010 to 2015, the number of cities with moderate maladjustment in China decreased and developed into low and marginal maladjustment cities. The coupling coordination level of the affordable housing market and urban development in Beijing, Shanghai, Guangzhou and Shenzhen developed well and reached the reluctant coordination level, while the development of the northeastern region was slower; eight cities showed no change in their coupling coordination level classifications. From 2015 to 2020, the coupling coordination level significantly improved nationwide, and 70 large- and medium-sized cities were at the low maladjustment level or above. In China, the cities with the highest coupling coordination development levels of the two systems in 2020 included Beijing, Shanghai and Shenzhen, which showed initial coordination levels, indicating that the affordable housing market and urban development system in these three cities had a good mutual promotion effect; Guangzhou, Chongqing, Chengdu, Tianjin, Nanjing, Ningbo, Hangzhou and Changsha reached the reluctant coordination level. Compared with the cities with faster urban development levels from 2010 to 2020, the more support given to the affordable housing market, the faster the improvement in the coupling coordination development level between the two systems. There is still a certain space for development in the northeastern and western regions.

3.4.2. Development Level Trend Analysis

To explore the horizontal trend of the coupling coordination degree, this study further drew a horizontal trend chart of the coupling coordination degree of each city in three dimensions using ArcGIS 10.8.1, where the X-axis denotes east, the Y-axis denotes north, and the Z-axis represents the horizontal development value of the coupling coordination degree (Figure 5).

Figure 5 shows that the coupling coordination degree of the affordable housing market and urban development nationwide had a trend of decreasing from southeast to northwest, in which the east–west trend was very obvious, and from 2010 to 2020, the coupling coordination level of high in the east and low in the west was obvious. In addition, the coupling coordination levels between the affordable housing market and urban development in some cities in the central and western regions were in a relatively well-developed state, and a slight inverted “U” curve can be seen on the east–west trend line. Regarding the north–south trend, the trend of high in the south and low in the north indicates that the difference in the level of coupling coordination between the north and south was not obvious, but the development level of each system was not equal. Although the difference value is inconspicuous, numerically, the coupling coordination level between the national affordable housing market and urban development has room to improve.

3.4.3. Kernel Density Regional Distribution Analysis

Based on the analysis of spatial characteristics in Section 3.4.1 and Section 3.4.2, the kernel density distribution of the coupling coordination degree could be further analyzed from the degree of distribution aggregation. ArcGIS 10.8.1 was used to draw a regional distribution map of the kernel density of the coupling coordination degree in China in 2010, 2015 and 2020 (Figure 6a, b and c, respectively).

Regarding the overall spatial evolution, the coupling coordination degree in the whole country shows a radial distribution centered on the Yangtze River Delta, which has a spatial distribution characteristic similar to the economic development level. The relatively high-density level covered the Beijing–Tianjin–Hebei region, the Yangtze River and the Central Plains urban agglomeration region. The concentration range of the medium density level covered the whole eastern coastal area and the central area of the Sichuan and Chongqing region.

From the evolution of the kernel density values, the coupling coordination degrees of cities in China increased year by year in 2010, 2015 and 2020. Combined with the analysis of the measurement data, the cities with a high coupling coordination degree between the affordable housing market and urban development in 70 large- and medium-sized cities in China were concentrated in the Pearl River Delta and megacities, such as Beijing, Shanghai, Guangzhou and Shenzhen, which had relatively weak changes in their overall kernel density distributions from 2010 to 2020 because of their relatively stable development. Combined with the data measurement, the distribution and development trends showed that the matching degree between the urban development level and the affordable housing market system of the 70 large- and medium-sized cities in China gradually improved. It is necessary to give full play to the advantages of regional characteristics to gradually narrow the development gap between regions.

3.4.4. Kernel Density Development Trend Analysis

To further analyze the coupling coordination level of the affordable housing market and urban development in 70 large- and medium-sized cities regarding numerical changes and aggregation, the kernel density estimation curves for 2010, 2015 and 2020 were described using STATA 17 software (Figure 7).

The kernel density development trend map reveals the evolution of urban coupling and coordination degree nationwide (Figure 7). The evolution of the coupled and coordinated development levels of the affordable housing market and urban development in 70 large- and medium-sized cities in China had the following characteristics.

Regarding the position: The center of the kernel density distribution curve of the coupling coordination degree from 2010 to 2020 shows a right-shifting trend, indicating that the coupling coordination level of the two systems increased as a whole during the period. Among the kernel density curves for 2010, 2015 and 2020, the right side of the curve for 2015 has a short tail, and the span of the coupling coordination degree level of the curve is the narrowest, indicating that, from 2010 to 2015, the coupling coordination degree of the two systems in most cities was improved to a certain extent, but the cities with a high coupling coordination level did not increase too much. With the development of cities from 2015 to 2020, the affordable housing market and urban development in many cities rapidly entered the stage of mutual influence, and the coupling coordination level also greatly improved. The curve shifted to the right by a large amount, and the density value of the right tail is also higher than that of 2010 and 2015, which shows that the difference in the coupling coordination levels between cities became large in 2020, where some cities rapidly promoted their affordable housing market, and, thus, the coupling coordination level reached a better state.

Regarding the peak value: From 2010 to 2020, the main peak value of the coupling coordination degree between the two systems shows a trend of first increasing and then decreasing. In 2015, the coupling coordination level shows a high aggregation phenomenon, which was higher than the main peak in 2010 and 2020, indicating that from 2010 to 2015, some cities with weak development of their affordable housing markets were continuously promoting the construction of affordable housing. The continuous improvement in the affordable housing market caught up with the urban development level. In the process of improvement, the interaction and coordination between the affordable housing market and urban development was continuously realized. In the 70 large- and medium-sized cities, more cities started to develop in a coordinated way, and a large range of aggregation phenomena of coupling coordination levels of the two systems emerged. From 2015 to 2020, the main peak value of the kernel density curve decreased. During this period, the coupling coordination levels of the two systems developed unevenly, which resulted in some cities with relatively slow development gathering near the main peak in 2020, and cities with relatively fast development gradually distributed in the right tail. In addition, compared with the main peak value of the kernel density curve in 2010, the density value of the main peak value in 2020 was higher than that in 2010, indicating that the coupling coordination level of the two systems increased significantly in the study interval. Overall, the coupling coordination level of the affordable housing market and urban development in the 70 large- and medium-sized cities in China needs to be improved.

Regarding the morphology: The kernel density curve of 70 large- and medium-sized cities in China from 2010 to 2020 shows a skewed distribution, mainly to the left, indicating that the overall low-level aggregation degree was high. In addition, observing the kernel density curves of the coupling coordination levels in 2010, 2015 and 2020, it is not all strictly unimodal. From 2010 to 2015, the strictly single-peak state changed to a multi-peak state, indicating that, in 2015, although the research objects were developing their system coupling and coordination level with high aggregation, some cities were still at a relatively high coupling coordination level, and, thus, other peaks appeared in the right tail. In contrast, in 2020, the variation interval of the coupling coordination level increased significantly. Compared with the kernel density estimation curves of the coupling coordination degrees in 2010 and 2015, the curve distribution in 2020 tended to diverge, the right tail of the distribution moved much farther than the left tail, and a slight peak bulge can be seen in the right tail. The overall kernel density distribution and trend of coupling coordination level show that the proportion of regions with an uncoordinated coupling coordination degree decreased nationwide, while the proportion of regions with a higher coupling coordination degree increased. This was because, during the 13th Five-Year Plan period, the housing security policy was gradually popularized, and the affordable housing policy was constantly implemented in various cities, which led to the affordable housing market and urban development level showing a consistent state overall, and the coupling coordination degree of the two systems was relatively coordinated in more areas.

4. Discussion

Through the spatial–temporal characteristic results of the coupling coordination between the affordable housing market and urban development in 70 large- and medium-sized cities in China, it was found that the coupling coordination development of these two systems from 2010 to 2020 had a certain spatial distribution and evolution trend. Considering the interaction between cities in the spatial distribution within the research scope, the correlation degree within the cities should be demonstrated and analyzed to facilitate further scientific exploration of the coupling coordination relationship between the affordable housing market and urban development in China.

4.1. Global Spatial Autocorrelation Analysis of Coupling Coordination Degree

In this study, Stata 17 software was used to conduct a global spatial autocorrelation analysis of the measurement results of the coupling coordination degree between the affordable housing market and urban development in 70 large- and medium-sized cities in China. The results are shown in

Table 8. Global spatial autocorrelation of the coupling coordination degree between the affordable housing market and urban development in China from 2010 to 2020.

Year	Moran’s I	Z Score	p Value
2010	0.397	6.945	0.000 ***
2011	0.420	7.379	0.000 ***
2012	0.409	7.159	0.000 ***
2013	0.414	7.191	0.000 ***
2014	0.434	7.544	0.000 ***
2015	0.399	7.030	0.000 ***
2016	0.467	8.216	0.000 ***
2017	0.443	7.865	0.000 ***
2018	0.453	7.904	0.000 ***
2019	0.446	7.785	0.000 ***
2020	0.412	7.235	0.000 ***

*** is significant at the 1% levels.

.

As can be seen from Table 8, the Moran’s I values of the coupling coordination degree between the national affordable housing market and urban development of the 70 large- and medium-sized cities in China from 2010 to 2020 are all greater than 0.395, and the test value is significant at the level of 1%, which indicates that the coupling coordination degree between the affordable housing market and urban development had a relatively strong spatial positive correlation from 2010 to 2020. The cities with similar levels of coupling coordination development between the two systems had certain agglomeration. In the spatial autocorrelation analysis of the coupling coordination degree between the affordable housing market and urban development from 2010 to 2020, the Moran’s I values for 2010, 2012 and 2015 were relatively low but still passed the test at the 1% level, indicating that although the overall spatial effect of the model fluctuated, the spatial positive correlation was obvious. From the overall trend, the third-order sliding average of the Moran’s I value from 2010 to 2020 basically shows a strict upward trend, indicating that the coupling coordination degree between the affordable housing market and urban development in the 70 large- and medium-sized cities in China shows an overall upward trend with an obvious coupling effect and significant spatial aggregation.

4.2. Local Spatial Autocorrelation Analysis of Coupling Coordination Degree

This study conducted a local spatial correlation analysis on the coupling coordination degree between the affordable housing market and urban development in 70 large- and medium-sized cities in China in 2010, 2015 and 2020, with the distribution results for the four quadrants of the scatter plot shown in

Table 9. Distribution of Moran scatter quadrants of coupling coordination degrees in 2010, 2015 and 2020.

Quadrants	2010	2015	2020
HH	Beijing, Tianjin, Hohhot, Shenyang, Dalian, Shanghai, Nanjing, Hangzhou, Ningbo, Hefei, Fuzhou, Xiamen, Jinan, Qingdao, Wuhan, Changsha, Guangzhou, Shenzhen, Wuxi, Wenzhou	Beijing, Tianjin, Shanghai, Nanjing, Hangzhou, Ningbo, Fuzhou, Xiamen, Jinan, Qingdao, Wuhan, Changsha, Guangzhou, Shenzhen, Wuxi, Yichang	Beijing, Tianjin, Shanghai, Nanjing, Hangzhou, Ningbo, Fuzhou, Xiamen, Nanchang, Jinan, Qingdao, Wuhan, Changsha, Guangzhou, Shenzhen, Urumqi, Wuxi, Yangzhou, Jinhua
LH	Nanchang, Haikou, Urumqi, Tangshan, Baotou, Yangzhou, Yantai, Yichang	Hohhot, Taiyuan, Dalian, Hefei, Nanchang, Haikou, Urumqi, Tangshan, Baotou, Yangzhou, Quanzhou, Yantai, Huizhou	Hohhot, Shenyang, Dalian, Haikou, Tangshan, Baotou, Yantai, Yichang, Xiangyang
LL	Shijiazhuang, Taiyuan, Lanzhou, Xining, Yinchuan, Qinhuangdao, Dandong, Jinzhou, Jilin, Mudanjiang, Xuzhou, Jinhua, Bengbu, Anqing, Jiujiang, Ganzhou, Jining, Luoyang, Pingdingshan, Xiangyang, Yueyang, Changde, Huizhou, Zhanjiang, Shaoguan, Guilin, Beihai, Sanya, Luzhou, Nanchong, Zunyi, Dali	Shijiazhuang, Shenyang, Changchun, Harbin, Nanning, Guiyang, Lanzhou, Xining, Qinhuangdao, Dandong, Jinzhou, Jilin, Mudanjiang, Xuzhou, Jinhua, Bengbu, Anqing, Jiujiang, Ganzhou, Jining, Luoyang, Pingdingshan, Xiangyang, Yueyang, Changde, Zhanjiang, Shaoguan, Guilin, Beihai, Sanya, Luzhou, Nanchong, Zunyi, Dali	Shijiazhuang, Taiyuan, Changchun, Harbin, Nanning, Guiyang, Kunming, Lanzhou, Xining, Yinchuan, Qinhuangdao, Dandong, Jinzhou, Jilin, Mudanjiang, Bengbu, Anqing, Quanzhou, Jiujiang, Ganzhou, Jining, Luoyang, Pingdingshan, Yueyang, Changde, Huizhou, Zhanjiang, Shaoguan, Guilin, Beihai, Sanya, Luzhou, Nanchong, Zunyi, Dali
HL	Changchun, Harbin, Zhengzhou, Nanning, Chongqing, Chengdu, Guiyang, Kunming, Xi’an, Quanzhou	Zhengzhou, Chongqing, Chengdu, Kunming, Xi’an, Yinchuan, Wenzhou	Hefei, Zhengzhou, Chongqing, Chengdu, Xi’an, Xuzhou, Wenzhou

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HH quadrant: Beijing, Tianjin, Shanghai, Nanjing, Hangzhou, Ningbo, Fuzhou, Xiamen, Jinan, Qingdao, Wuhan, Changsha, Guangzhou, Shenzhen and Wuxi were in this quadrant in 2010, 2015 and 2020. This quadrant mainly concentrated the core cities of the Beijing–Tianjin–Hebei region, Yangtze River Delta, Pearl River Delta and some provinces. Core cities in urban agglomerations were in this quadrant due to their close geographical and economic distance, high level of urban development and coupling coordination, and the role of mutual driving and promotion in urban agglomerations. In addition, Hohhot, Shenyang, Dalian, Hefei and Wenzhou were in this quadrant in 2010; Yichang in 2015; and Urumqi, Nanchang, Yangzhou and Jinhua in 2020, indicating that compared with these core cities of urban agglomeration, the coupling coordination development levels of these cities in certain years were more prominent than other cities in the country. For these cities in the HH quadrant, there was a mutual promotion effect with the surrounding cities. However, due to factors such as location differences and the non-obvious urban advantages of these cities, there was no prominent coupling coordination development level in other years, and there was still a certain gap compared with other well-developed cities, which could not be maintained in this quadrant for long.

LH quadrant: There were a few cities in this quadrant, among which Haikou, Tangshan, Baotou and Yantai were in this quadrant in 2010, 2015 and 2020. Most of these cities were driven by the radiation effects of the core cities of large urban agglomerations; the coupling coordination levels of these cities were relatively low, but the coupling coordination levels of the surrounding regions were relatively high. In addition, there were also cities with relatively remote locations and no obvious regional advantages, such as Haikou, whose coupling coordination level between the affordable housing market and urban development was relatively low, while the surrounding cities had a relatively high level, and, thus, it belonged to the LH quadrant. In 2010, 2015, and 2020, Hohhot, Dalian, Nanchang, Urumqi, Yangzhou, and Yichang moved between the LH and HH quadrants, indicating that the coupling coordination levels of these cities’ affordable housing markets and urban development fluctuated between high and low levels. This also indicates that the two quadrants were closely connected. In addition, Taiyuan and Huizhou in 2015 and Xiangyang in 2020 were also in this quadrant; these cities underwent quadrant changes due to the improvement in the coupling coordination levels of surrounding cities. Although these cities were also driven by the core cities of urban agglomerations, the level of radiation effects was not large, which meant they were in this quadrant in the later stage of the analysis period. This shows that China’s large urban agglomerations are still radiating further and the driving effect is spreading further, and the coupling coordination development process of the two systems in these cities will still be the main theme in the next period.

LL quadrant: Most cities were in this quadrant, indicating that among the 70 large- and medium-sized cities in China, there were still many cities with a relatively low coupling coordination level between the affordable housing market and urban development. Among them, Shijiazhuang, Lanzhou, Xining, Qinhuangdao, Dandong, Jinzhou, Jilin, Mudanjiang, Bengbu, Anqing, Jiujiang, Ganzhou, Jining, Luoyang, Pingdingshan, Yueyang, Changde, Zhanjiang, Shaoguan, Guilin, Beihai, Sanya, Luzhou, Nanzhong, Zunyi and Dali were in this quadrant for a long time. Most of these cities are far from the core urban agglomerations, resulting in the low-radiation driving effect of the core cities and low coupling coordination level between themselves and surrounding regions. At the same time, Taiyuan, Huizhou, Jinhua, Xiangyang and other cities that were not in this quadrant were all concentrated in the LH quadrant, indicating that at different times, the coupling and coordinated development levels of the two systems around these cities were in a state of fluctuation, and the coupling and coordinated development level within the scope of China changed in turn, which is why the quadrants changed. Meanwhile, when Huizhou, Jinhua and Xiangyang were not in this quadrant, they were all concentrated in the LH quadrant, indicating that, during different research periods, the coupling coordination development levels of the two systems around these cities fluctuated, which led to the quadrant changes.

In addition, Changchun, Harbin, Nanning and Guiyang were all in the HL quadrant in 2010 and in the LL quadrant in 2015 and 2020, which indicates that in the process of urban development, the coupling coordination level of the affordable housing market and urban development improved slowly due to factors such as urban resource constraints, remote locations and population loss. Yinchuan was in the HL quadrant in 2015 and in the LL quadrant in 2010 and 2020, indicating that the coupling coordination level of the affordable housing market and urban development in its region first rose and then fell, which may have been due to the promotion of relevant policies. Xuzhou was in the LL quadrant in 2010 and 2015 but in the HL quadrant in 2020, indicating that the coupling coordination level of Xuzhou between the two systems had improved by 2020 and had reached a high level relative to the development level in China. Shenyang, Kunming and Quanzhou were in the LL quadrant in 2015, 2020 and 2020, respectively, indicating that the coupling coordination level of the affordable housing market and urban development of these three cities in 2010 was still at a high level; however, due to the local location development restrictions and local policies, in the later research period, the coupling coordination level of these three cities dropped to a low level.

HL quadrant: The number of cities in this quadrant was the lowest, among which Zhengzhou, Chongqing, Chengdu and Xi’an were in this quadrant for a long time. Most of these cities are large non-urban agglomeration cities with relatively high urban development levels, high population aggregation degrees, and relatively early development of their affordable housing markets. However, the limited location and weak regional economic environments of these cities led to a weak radiation driving effect on the surrounding cities; therefore, the coupling coordination level of the city was high, but the surrounding region was low. At the same time, Kunming was in this quadrant in 2010 and 2015 and in the LL quadrant in 2020, indicating that in 2020, due to different development policies and economic progress, Kunming’s coupling coordination level between the two systems developed relatively slowly from the HL to LL quadrants. Wenzhou was in the HH quadrant in 2010 and in the HL quadrant in 2015 and 2020, indicating that in 2010, the coupling coordination level of the affordable housing market and urban development in Wenzhou and surrounding regional cities were at a relatively high level. Later, due to different development policies and economic progress, the coupling coordination levels of the two systems in Wenzhou and the surrounding cities were significantly different, resulting in the transformation from the HH to HL quadrants, where the urban development situation of these cities was similar to that of those cities that had been in this quadrant for a long time. In addition, Changchun, Harbin, Nanning, Guiyang and Quanzhou were in this quadrant in 2010; Yinchuan was in this quadrant in 2015; Hefei and Xuzhou were in this quadrant in 2020; and most of the other research years were in the LL quadrant, which may have been caused by regional radiation and policies over a short period that stimulated the coupling coordination degree of the region. After the policy stimulus, the coupling coordination level gradually recovered to the general level.

In general, the coupling coordination degree of the affordable housing market and urban development had an obvious spatial effect and strong spatial agglomeration. Due to the existence of polarization and spatial spillover effects, the number of cities in the four quadrants did not change much. Since most cities are in the LL quadrant at present, the coupling coordination degree between the affordable housing market and urban development in each city needs to be improved.

To better present the local spatial correlation of the 70 large- and medium-sized cities, the spatio-temporal characteristics of local Moran’s I are further demonstrated by drawing Lisa cluster maps from 2010 to 2015 and 2020 (Figure 8).

Figure 8 shows that most cities in the HH quadrant belonged to the relatively economically developed eastern coastal areas with relatively complete policy systems, as well as some central cities of regional developed urban agglomerations.

The affordable housing market follows the housing filtering theory and welfare economics theory. Under the background of its coordinated development trend with urban development, corresponding affordable housing systems should be designated according to the conditions of different cities. Furthermore, the construction of urban agglomeration systems would achieve spatial agglomeration, resource coordination and functional integration, which can further ensure that developed cities drive the surrounding cities to rationally allocate the scale of the floating population, guarantee housing demands are met and promote coordinated development within urban agglomerations. Furthermore, it can address the issue of unbalanced regional development and promote the realization of sustainable regional development.

5. Conclusions

This study measured the coupling coordination level of the affordable housing markets and urban development levels in 70 large- and medium-sized cities in China from 2010 to 2020 and analyzed the spatial and temporal development trends and characteristics using spatial theory and econometric analysis methods.

From the analysis of the measurement results, the overall levels of the affordable housing markets and comprehensive urban development levels in 70 large- and medium-sized cities in China were relatively low, but they showed a trend of increasing year by year, and there were regional differences. The eastern region has obvious development advantages, while the northeastern region is relatively limited. From 2010 to 2020, the coupling degree of the two systems was in a high coupling state, indicating that the correlation between the affordable housing market system and urban development system was high. From the analysis of the coupling coordination degree, the 70 large- and medium-sized cities in China showed an overall upward trend from 2010 to 2020, and the regional differences were similar to the comprehensive development level. Regarding the spatial distribution, the coupling coordination levels of the affordable housing market and urban development were better in the Beijing–Tianjin–Hebei, Yangtze River Delta, Pearl River Delta and Sichuan–Chongqing regions. From 2010 to 2020, the overall distribution trend differed greatly from east to west, the coupling coordinated level of the two systems in the eastern region was significantly higher than that in the western region, and the difference between the north and south was slight. Regarding the kernel density distribution, the two cores of the Yangtze River Delta and Beijing–Tianjin–Hebei were radiating to the surrounding areas in China, and the Sichuan–Chongqing region was radiating to the surrounding areas in a moderate horizontal way. The coupling coordination level kernel density of the two systems in the Yangtze River Delta region was always at the highest level. According to the analysis of the development trend of kernel density, the coupling coordination levels of the two systems in the 70 large- and medium-sized cities in China from 2010 to 2020 show a trend of first gathering and then diverging. According to the spatio-temporal distribution results of the coupling coordination characteristics between the two systems, the coupling coordination degree between the affordable housing market and urban development in the cities with better economic development levels improved relatively quickly during 2010 to 2020, which shows that cities with better economic development have advantages in promoting urban development and affordable housing market development and the coordinated development of the two systems.

In addition, according to the economic–geographical distance matrix of 70 large- and medium-sized cities in China, there was a strong spatial positive correlation of the coupling coordination level between the affordable housing market and urban development from 2010 to 2020. Specific to the local spatial correlation analysis of cities, among the 70 large- and medium-sized cities in China, the number of cities in the high-level coupling coordination spatial agglomeration was still a minority, which consisted mainly of large cities with better economic development, and most cities were still in the coupling coordination low-level spatial agglomeration state. The coupling coordination level between the affordable housing market and urban development in China still needs improvement. Furthermore, according to the spatial characteristics and development trends, combined with the characteristics of cities or urban agglomerations, the coordinated development between the affordable housing market and urban development can be better realized to enhance the urban resilience and promote regional sustainable development.

However, although this study investigated the spatio-temporal characteristics of the coupling coordination relationship between affordable housing and urban development in 70 large- and medium-sized cities from 2010 to 2020, the data after 2020 were not analyzed due to the change in policy direction. Moreover, in-depth research on the spatio-temporal interaction mechanism was not carried out in this study.

In future research, how to discover the spatial interaction mechanism between affordable housing and urban development among cities and transform the obvious spatial effect between cities into development advantages will be the top priority to promote the sustainable development of cities in the next step. Furthermore, conducting simulation experiments and predicting the interaction relationships between systems through system dynamics are also future research directions.