The Spatial Correlation Effect of Real-Estate Financial Risk in China: A Social Network Analysis

Abstract

In this paper, we draw on real-estate finance data from 31 provinces in China over the period between 2006 and 2018 in order to develop a comprehensive index of real-estate finance risk. Our principal innovation lies in our use of the social network analysis method to portray the spatial correlation characteristics of real-estate financial risk dynamically. We find that (1) the spatial correlation effect of real-estate financial risks in China is increasing and exhibits multiple superposition characteristics and spatial spillover effects; (2) current trends in real-estate financial risk suggest that the eastern region has a strong contagion potential, that the middle region is highly vulnerable, and that the level of risk in the northwest is high; (3) the spatial network of real-estate financial risks in China can be divided into four functional blocks, namely a strong net-spillover block, a weak net-spillover block, a broker block, and a main damaged block. There is significant gradient transmission between them. The network structure of real-estate financial risks poses serious challenges to the formulation and implementation of regulatory policies. However, it creates favorable conditions for the construction of cross-regional risk prevention mechanisms as well as a practical basis for preventing systemic risks in the new era. (4) Meanwhile, the formation of a spillover network of real-estate financial risks is driven by the high dependence of local fiscal resources on land finance, not by local GDP growth.

1. Introduction

Real estate is a pillar of Chinese economic development, and its unique industrial role affects all walks of life. The real-estate industry has the essential attribute of capital intensity. All aspects of the industrial value chain, such as land grants, housing development, housing construction, and consumption by home buyers, are highly dependent on substantial support from the financial industry. At the same time, financial institutions favor real estate as high-quality collateral. Therefore, the real-estate industry and the financial industry are deeply interconnected. Under a financial system dominated by indirect bank financing, a large amount of credit resources has been flowing into the Chinese real-estate industry for a long time. According to the People’s Bank of China, the balance of RMB real-estate loans reached CNY 49.58 trillion at the end of 2020, a year-on-year increase of 11.7% that accounts for 26.1% of the total increase in the volume of loans over the same period. The supply of bank credit has caused the development of the real-estate industry to gradually become detached from the needs of the Chinese economy. The real-estate industry exhibits self-evolution and self-loop characteristics that are typical of financialization, bubbles, and virtualization. Financial risk has thus accumulated. Abnormal fluctuations in the real-estate industry can easily cause risk accumulation, spillovers, and contagion, undermining financial stability and the healthy and sustainable development of the national economy. At this stage, real-estate financial risk has become a potential “gray rhinoceros” that could easily trigger a systemic financial crisis. (On December 4, 2020, Guo Shuqing, Secretary of the Party Committee of the People’s Bank of China and Chairman of the CBRC, published an article “Improving the Modern Financial Regulatory System” in the Financial Times. He clearly pointed out that real estate is the biggest “gray rhinoceros” in terms of financial risks in China at this stage).

In China, the real-estate market is not national, and its development varies greatly between regions. Moreover, current regulations in each region are mainly based on local risk levels, with less consideration of the spatial spillover effects of local real-estate financial risks. However, under the general policy of preventing housing speculation, the intensity of real-estate policies in different regions has converged, mostly on the basis of similar tightening policies. This tendency is a manifestation of a macro-level approach to regulation. The real-estate industry is associated with many sectors and plays an important role in promoting regional economic development. Therefore, a single restrictive policy may exert different effects in different regions.

In fact, real-estate financial risks in China exhibit significant spatial correlation (Wang and He, 2015; Ju et al., 2018; Li and Zhang, 2019 [1,2,3]). Therefore, studying China’s real-estate financial risks by drawing on data from a single region would reduce generalizability. If real-estate financial risks are to be addressed, it is necessary to understand and analyze their spatial variability and correlation. It is also necessary to grasp the characteristics of the spatial distribution of real-estate financial risks clearly as well as to ascertain the source, intensity, and direction of risk transmission. Thus, regulators can focus on monitoring the sources of risk spillover while formulating other regulatory policies according to the actual situation. In this way, they can develop scientific and effective city-specific policies. These propositions are reflected in a series of guiding policies in China. For example, the 2016 Government Work Report stated that the development of each region should be considered carefully and that real-estate inventories should be analyzed by reference to city-specific policies. The 14th Five-Year Plan also re-emphasized the differentiated control approach to city-specific policies.

Presently, the spatial attributes and the evolution paths of regional real-estate financial risks in China are poorly documented. The relevant mechanisms have not been clarified. Existing studies, both academic and practical, focus on fluctuations in house prices as well as on macro features, such as housing bubbles, cycles, and policies. These studies mostly focus on descriptions. They ignore the influence of spatial factors and do not adopt a global approach to the spatial properties, aggregation, and correlation of structural and endogenous regional real-estate financial risks.

Considering the foregoing, the present paper innovates by introducing the social network analysis method, which is based on the theory of risk spillovers. It explores the transmission of financial risks, which are caused by regional real-estate economic activities, and their spatial distribution from the perspective of dynamic association. The paper aims to identify the distribution, the mechanisms, and the evolution of spatial correlation of real-estate financial risks in 31 provinces in China. It also attempts to provide a realistic basis and a reference point for attempts to curb contagion and prevent systemic financial risks.

2. Literature Review

2.1. Research on the Spatial Correlation of Real-Estate Financial Risks

The existing literature focuses on the spatial correlation effects of real-estate financial risks from the perspective of property prices and bubbles. Geoffrey (1999) showed that house prices in the United Kingdom exhibit different spatial patterns, with spatial correlations arising cyclically over time, first in the southeast and then spreading across the rest of the country [4]. Oikarinen (2006) found that changes in Finnish house prices spread from the economic center of the country to the regions and then to their surrounding areas [5]. Jeffrey et al. (2016) studied house prices in the US. Their analysis showed that prices were spatially and geographically linked [6]. Roehner BM (1999) found that the same spatial correlation obtains in real-estate bubbles [7]. Nneji et al. (2015) constructed a mechanism transformation model and a bubble spillover model to measure the real-estate bubble and its spatial contagion effect in each region of the US. The empirical results showed that the spatial contagion of a real-estate bubble in the US exhibited the typical characteristics of multidimensionality and multidirectionality [8]. Conversely, Gomez et al. (2018) drew on data from 20 Organisation for Economic Co-operation and Development (OECD) countries [9]. They found that the U.S. house price bubble was contagious to all other OECD countries except Spain [9]. Nanda et al. (2016) used a global vector autoregressive (GVAR) model to examine house prices in six cities, including Tokyo and Seoul, and found that house price bubbles in different cities exhibited a correlation effect characterized by mutual contagion [10]. They also found that cross-country migration may be an important cause of bubble contagion [10].

Returning to China, Liang and Gao (2007) and Zhang and Wang (2013) found that regional real-estate price fluctuations in the country are not completely isolated. There was evidence of significant regional correlations [11,12]. Wang et al. (2008) found large differences in the interactions between house prices in five major regional markets in China. However, the fluctuations of house prices in each city exhibited stable characteristics, which are indicative of mutual constraints, in the long term [13]. Zhang and Jing (2017) found that the spatial spillover effect of real-estate prices in China was gradually aggregated in spillover circles [14]. Zhang and Wang (2020) constructed a spatial Dubin model to show that the spatial spillover effect of house prices is significant in the eastern and western regions of China but not in the middle region [15]. Wei et al. (2018) found that the real-estate bubble in China was spatiotemporally contagious. They drew on a geographic information system to verify their spatial econometric model. On the time dimension, contagion capacity was shown to be increasing. On the spatial dimension, contagion capacity appeared to decrease from the southeast coast to the northwestern interior [16]. Drawing on quarterly data on house prices from 42 large-sized and medium-sized cities in China, Liu and Lv (2018) found that bubble contagion generally radiates from east to west and outward from the center. Moreover, bubbles in proximate regions are more likely to be affected by contagion [17]. Zhang et al. (2018) measured bubbles on the basis of a sup-augmented Dickey–Fuller test (SADF) and a generalized sup-augmented Dickey–Fuller test (GSADF). The results show that bubbles in China spread from first-tier cities to second- and third-tier cities consecutively. Multiple bubble evolution and cascade diffusion were significant problems [18].

2.2. Spatial Correlation and the Application of the Social Network Analysis Method

In recent years, social network analysis has become increasingly useful as a tool for the standardized analysis of social structures. It sees its widest use in macro and micro interdisciplinary research in the social sciences. Chen et al. (2013) used a Chinese city network that consisted of 51 cities as an example. They applied social network analysis to reveal an information linkage network. This network exhibited a high-density aggregated distribution [19]. Drawing on Chen et al. (2013), Wang et al. (2016) further analyzed the characteristics of the Chinese urban information space and showed that its density decreases from east to west [20]. Li et al. (2014) used the social network analysis method to demonstrate that the spatial network of regional economic growth in China exhibited stability and multiple superpositions. They also showed that the spillover effect of regional economic growth had a gradient [21]. Liu et al. (2015) used a social network approach to capture the spatial correlation of energy consumption in different regions of China [22]. Lin and Kong (2016) used social network analysis to test for spatial network correlations in Chinese industrial structure upgrades [23]. Lu and Sun (2017) used one social network analysis method, the quadratic assignment procedure, to reconstruct the gravitational model. They noted that haze pollution in China is highly correlated and that the spatial network has asymmetric characteristics [24]. Wang et al. (2019) constructed a modified gravitational model and used social network analysis to show that there are obvious directional differences in the strength of intercity economic ties in the urban agglomerations of the Yangtze River Economic Zone. The spatial structure of the urban network had a distribution that was “sparse in the west and dense in the east” [25]. Using the social network analysis method, Lin and Li (2020) found that China’s exhibition industry is characterized by a certain spatial correlation. However, the degree of correlation was low, and there was room for improvement [26]. As far as the spatial correlation of financial risks is concerned, Wang and Cao (2017) introduced the social network analysis method as a means of exploring the spatial transmission of interprovincial financial risks in China. They analyzed contagion effects, transmission modes, and the degree of contagion of financial risks at the spatial level [27].

2.3. Research Gaps

Research on the spatial correlation of real-estate financial risks has focused on prices, the spatial spillovers that inhere in bubbles, and core indicators that may be used to evaluate the risks in question. However, few studies have explored the spatial correlation effects of real-estate financial risks directly. At the same time, most of the analyses adopt spatial econometric methods. However, they limit their use to proving the existence of a spatial correlation through individual inter-regional linkages. They do not explore spatial form properties, spatial correlation mechanisms, or the laws that govern the spatial evolution of the risks from a national perspective.

The application of the social network analysis method is a departure from the singularity of research objects that typifies conventional methods. It bridges the gap between theoretical constructs and empirical assumptions to a large extent, and it dissolves the boundary between the natural and the social sciences. The method aids the identification of nested associations between layers, which enables an examination of the structural features of the whole network. It also yields insights into the nature of the interactions between actors while also quantifying their relationships.

The application of social network analysis in the social sciences provides general ideas and methods. At the same time, the extant literature only draws on social network analysis to study the spatial associations of financial risk. There are still limitations in its use to investigate the specificities of real-estate financial risk. Accordingly, this paper applies social network analysis to the spatial correlation effects of real-estate financial risks to reveal their spatial distribution status, their mechanisms, and the laws of their evolution in China. It provides empirical evidence that may be used to suppress regional transmission and contagion as well as to prevent systemic financial risks. In addition, the literature mainly focuses on descriptive network data. There is a gap in the quantitative analysis of network structures and the factors that shape their development. This paper introduces the exponential family random graph models (ERGM) to fill this gap.

3. Real-Estate Financial Risk: Spatial Correlation Mechanism

3.1. Influence of Population Movement

The economic development of the regions of China is unbalanced. The economic advantages of developed regions attract larger populations, thereby increasing demand for real estate and prices. As a result, bubbles form in those regions. The high cost of purchasing property in the developed areas makes them unaffordable for some residents. Therefore, they buy property in the relatively less developed areas around the cities in question. This increases demand for real estate in less developed regions, which, in turn, increases prices. As this cycle is repeated, the real-estate bubble spreads to less developed regions. The foregoing describes a type of spatial linkage effect. At present, frequent defaults on home-purchase loans in developed areas cause financial institutions to sell the properties that serve as collateral as rapidly as possible in order to recoup their losses. These sales increase the supply of real estate, causing prices in the region to fall. Furthermore, the linkage effect is such that prices in the less developed regions also decrease. A decline in property prices causes a decrease in the value of collateral, which increases the risk for financial institutions in less developed regions. The spillover mechanism that is caused by population movements is shown in Figure 1.

3.2. Influence of the Cross-Regional Development of Real-Estate Enterprises

Real-estate companies, especially head companies, are generally not confined to a fixed area. They operate within larger geographic areas, relying on comprehensive cost-benefit analyses. Core regions exert an influence on peripheral ones through industrial transfer, the flow of capital and talent, etc. In industry-centered market economies, the large concentration of industries in a core region tends to cause escalating business costs and external diseconomies, increasing the incentive for enterprises to expand or move into the periphery. Moreover, changes in regional comparative advantages and national policies may cause many enterprises in the core regions to shift their activities to peripheral regions that offer lower costs and more favorable regulations. The spatial distribution of industries then reflects the phenomenon of industrial transfer from core areas to peripheral ones and from developed regions to less developed ones. Similarly, real-estate enterprises have an incentive to move from economically developed but industrially saturated core regions to peripheral regions that have stronger development potential.

In practice, most real-estate companies conduct development projects in different regions simultaneously in order to improve the efficiency of capital turnover. Very often, sales begin before the development project in a certain region is completed. The purpose of presales is to generate cash that is needed to initiate a new round of projects in other regions. If a project in one region runs into sales difficulties, the subsequent default of an enterprise may strain the capital chain sufficiently to trigger defaults in other regions. The spillover mechanism that arises because of the cross-regional development of real-estate enterprises is shown in Figure 2.

4. Construction of the Spatial Correlation Network Model

4.1. Indicator of Real-Estate Financial Risk

In this paper, we consider three sub-indicators as measurements of real-estate financial risk: the debt ratio of real-estate enterprises, the share of real-estate investment in regional GDP over a year, and the ratio of annual domestic loans to real-estate enterprises to the annual loan balance of financial institutions. We use the entropy value method to assign weights to each indicator and weigh them to obtain a composite indicator that represents real-estate financial risk. The debt ratio of real-estate enterprises is mainly used to measure the financial risks that they bear. The ratio of domestic loans extended to real-estate enterprises to the loan balance of financial institutions captures the real-estate risks that are borne by domestic financial institutions and the concentration of financial risk in the real-estate industry. The ratio of real-estate investment in a region to its GDP measures the extent to which regional economic development depends on real-estate investment and captures the volume of economic resources that is taken up by real-estate investments. If the ratio is too high, this means that the real-estate investment market is overheating. Consequently, risks accumulate.

The reason for choosing these sub-indicators is threefold. First, they reflect reality, in that real-estate enterprises in China are generally highly indebted. Financial institutions provide significant financial support to the real-estate market. Financial institutions and real-estate enterprises typically bear a large proportion of the overall financial risk. Second, the dependence of economic development on real-estate investment is a macro indicator. Third, the comparability and accessibility of indicator selection and data collection were considered fully.

It must be acknowledged that we have not exhausted all risk factors and that it was not our purpose to do so. Considering all risk factors may complicate matters and detract from the focus of our study, which concerns current spatial correlations, contagion, and their causes, not the causes of real-estate financial risk per se. Therefore, identifying variables that capture changes in real-estate financial risk should suffice. For example, we do not take government action into account (at least not in the calculation of the indicators) because the Chinese government often uses noneconomic administrative instruments to regulate the property market. Those instruments are unpredictable, and their effects are almost impossible to quantify. However, real-estate investment and the financing of real-estate firms eventually come to reflect regulation. Therefore, our indicators are sufficient to cover these influences. At the end of the paper, we also discuss the indirect influence of the government (through land policy and regional integration policy) by using the ERGM model. Likewise, international lobbying affects the Chinese real-estate market, but this influence is ultimately reflected in changes to investment in the real-estate industry and its financing. Otherwise, lobbying would not occur. Of course, these effects are interesting, but they fall beyond the scope of the present paper.

4.2. Spatial Correlation Network: Matrix Construction

The key to analyzing spatial network characteristics lies in constructing a spatial correlation network matrix. Compared with the traditional vector autoregression (VAR) model, the gravitational model is not affected by the time lag of data and can reveal the spatial correlation characteristics of the research object more clearly. Therefore, we adopted an optimized and improved gravitational model to construct a spatial correlation network matrix for real-estate financial risk in the Chinese provinces. The gravitational model was originally developed by analogy to the law of gravity in physics. Its basic form is as follows:

$$R_{ij}=K\frac{M_i{M}_j}{d_{ij}}$$

(1)

where $R_{ij}$ is the correlation between region i and region j; K is a constant, similar to the gravitational constant in the law of gravity; $d_{ij}$ is the distance between region i and region j; $M_i$ and $M_j$ denote the quality of region i and region j, which is not a concept in physics. Isard (1965) [28] used the product of urban population, GDP level, and a certain weight, that is, $M_i=w_{i}po{p}_{i}GD{P}_i$, where pop stands for population size, and w is the weight, which is related to the problem under investigation. This approach is also followed in most current studies.

Haynes and Fotheringham (1984) developed the equation above into a general power function as follows [29]:

$$R_{ij}=K\frac{M_i^{\alpha }{M}_j^{\beta }}{d_{ij}^{\gamma }}.$$

(2)

Chen and Liu [30] proved the correctness of this formula by using fractal theory and pointed out that, according to allometric growth theory, $\alpha =\beta .$

Since the object of this paper is a real-estate financial risk network for China, the comprehensive index of real-estate financial risk, $npl$, was chosen as a weight for the calculation of M. In addition, we made two changes to the basic gravity formula.

(1) The first change concerns the gravitational constant K. Most authors set K = 1, which implies that the interaction is symmetric for region i and region j. However, in practice, the interaction is often asymmetric for each region [31]. To represent this asymmetry, we define $K_{ij}=\frac{np{l}_i}{np{l}_i+np{l}_j}=co{n}_{ij}$. This means that the asymmetry of the impact is captured by the contributions of region i and region j to real-estate financial risk in the two regions. This reflects the results of some empirical studies on real-estate bubbles, which show that there is a ripple effect whereby bubbles spread from a center (originally a large bubble area) to a periphery (originally a smaller bubble area) [4,17,32]. Therefore, it can be expected that areas in which real-estate financial risk is higher have a strong impact on small areas.

(2) The second change concerns the setting of the distance d. In the original gravitational model, d simply denoted geographical distance. However, spillovers and contagion in intercity real-estate bubbles do not depend entirely on geographical factors [8]. For example, population movement and economic development affect bubble propagation paths [17]. Therefore, this paper draws on the method of constructing weight matrices in spatial econometrics and introduces economic distance. The difference between the GDPs of two places is taken as a measure of the gap in economic development between them. In order to avoid the repeated analysis of population factors, we chose GDP per capita as an indicator. The ripple effect is such that diffusion from the center to the periphery is more likely to occur between regions with large economic development gaps than within geographical areas. For this reason, we treat the reciprocal of economic development as a measure of economic distance. Total distance is then equal to the product of economic and geographical distance.

Referring to the setting of Wang and Cao (2017) [27], we define $\alpha =\beta =\frac{1}{3} \mathrm{and} \gamma =2$. By incorporating the factors that affect provincial real-estate financial risk into the gravitational model, we refined it as shown in Equation (1).

$$R_{ij}=co{n}_{ij}\frac{\sqrt[3]{np{l}_{i}po{p}_{i}GD{P}_i}\sqrt[3]{np{l}_{i}po{p}_{j}GD{P}_j}}{{\left(\frac{di{s}_{ij}}{gd{p}_i-gd{p}_j}\right)}^2}$$

(3)

The variables in the formula are described in

Table 1. Variables and their measurement.

Variable	Content
$npl$	It is a comprehensive indicator representing the financial risk of real estate, weighted by three indicators: the debt ratio of real-estate enterprises, the proportion of annual real-estate investment in the GDP of the year, and the proportion of domestic loans of real-estate enterprises to new loans of financial institutions in the year.
$co{n}_{ij}$	$\mathrm{It}\mathrm{refers}\mathrm{to}\mathrm{the}\mathrm{contribution}\mathrm{of}\mathrm{province}i\mathrm{in}\mathrm{the}\mathrm{regional}\mathrm{financial}\mathrm{risk}\mathrm{correlation}\mathrm{between}\mathrm{provinces}i\mathrm{and}j\mathrm{and}\mathrm{is}\mathrm{calculated}\mathrm{as}co{n}_{ij}=np{l}_i/\left(np{l}_i+np{l}_j\right)$.
$pop$	It refers to the total population of each province.
$GDP$	The real gross domestic product in a region.
$gdp$	Real GDP per capita in a region.
$di{s}_{ij}$	It represents the distance between the capital cities of province i and province j.

.

The network matrix of the regional financial risks can be calculated according to Equation (1). We calculated the matrix by using the UCINET software. Since the network diagram that can be calculated directly with the original data matrix R is complicated, we dichotomize the social relationship network with the mean as a critical value. For example, if the mean is lower than the critical value of a row, province i has no influence on j; if it is higher than the critical value of a row, i has an influence on j. Accordingly, the network matrix was divided into 0-1-type squares. The resulting measured relationship diagrams are more useful for analytical purposes.

$$R={\left(R_{ij}\right)}_{31\times 31}$$

(4)

4.3. Network Topology: Characteristics

The centrality of a node is an important indicator in social network analysis. It indicates whether a node is at the center of a network. Node centrality can be further divided into degree centrality, closeness centrality, and betweenness centrality. The meanings of those terms are described in

Table 2. Comparison of three centralities.

	Definition	Features
Degree centrality	The number of other nodes directly connected to node i.	It focuses on the ability of a node to communicate on its own does not involve controlling other nodes. In the network of real-estate financial risk, the node may spill risk to others or take spillover from others. Either way, it deserves attention.
Closeness centrality	The inverse of the sum of the distances between node i and other nodes in the network, with larger values indicating a more central position.	It focuses on the value of a node in the network, indicating the extent to which a point is not controlled by other nodes. In this paper, the distance between nodes includes both geographical distance and the difference in the level of economic development. Closeness centrality refers to the similarity between two regions. Intuitively, it is riskier for a real-estate developer to exploit the market in an unfamiliar region than in a region with high similarity. Therefore, it is easier to form spillover relationships between two similar regions.
Betweenness centrality	It represents whether the shortest distance between nodes passes through the node or not, if they all pass through it means the point is important in the network.	It focuses on the ability of nodes to regulate and control other points. The node with the ability has the intermediary moderation effect, which can be recognized as the external influence of a core region. The regions around the core region will experience a real-estate market boom because of the flourishing real-estate market and active policies in the core region. As a result, the risks may be accumulated and spill over to other peripheral regions.

.

We employed the block model to analyze the transmission mechanism of regional real-estate financial risks in China. The essence of the block model is that the nodes in the network are categorized according to certain criteria, thus forming blocks. The blocks can be classified by calculating intra- and extra-block correlations. A block is called a “net-spillover block” if the nodes within it are not strongly correlated with each other but have an impact on other blocks and are less affected by them, which is indicative of one-way transmission. A block is called a “two-way spillover block” if it affects other blocks and if the nodes within it also interact with each other with roughly equal intensity. In this paper, this indicates a two-way spillover. If such a block exists, it should be of particular concern. A block is called a “broker block” if there are no strong correlations within it but it affects others and is also clearly affected by them. Such a state of affairs is similar to the transitioning of real-estate financial risk from one segment to another, with the block functioning as a transmission bridge of sorts. Finally, a block that is strongly interconnected but does not influence others and is not significantly influenced by them is called a “main damaged block”.

5. Analysis of the Spatial Correlation Network Characteristics of Real-Estate Financial Risks

5.1. Calculation of the Comprehensive Index of Real-Estate Financial Risk

According to the method that we proposed in the preceding section, the comprehensive index of real-estate financial risk is synthesized from three indicators: the debt ratio of real-estate enterprises, the ratio of annual domestic loans to real-estate enterprises to the annual balance of new loans issued by financial institutions, and the proportion of real-estate investment to regional GDP over a given year. The synthesis is achieved through the entropy weight method. In order to conserve space, we only report the data for 2006, 2010, 2014, and 2018 in Figure 3. The figure shows that the overall risk in Shanxi, Inner Mongolia, Shaanxi, Gansu, Qinghai, Ningxia, and Xinjiang was at a high level in 2018, relative to the national real-estate financial risk index (0.6212). Shanxi had the highest risk index, at 0.7720. Tianjin, Heilongjiang, Shanghai, Fujian, Chongqing, and Tibet faced a relatively low level of overall risk. In broad terms, the overall level of real-estate financial risk in the 31 provinces and cities followed an upward trend between 2006 and 2018.

5.2. Spatial Correlation Network: Diagram

The spatial correlation network diagram for provincial real-estate financial risks provides a visual representation of the spatial correlation status of risks. The spatial network matrix (a 0-1 matrix) of real-estate financial risk in China was measured by Equation (1). Based on the 0-1 matrix above, the spatial correlations of real-estate financial risk in 31 provinces were represented for each year in a directed network structure map. The map was processed through social network analysis software (UCINET). In light of the limited space, only the network structure maps for 2006, 2010, 2014, and 2018 are presented in Figure 4.

Data from the 2006 to 2018 period were selected for the empirical sample because that period covers various stages in the development of the Chinese real-estate market. The period can be broadly divided into three phases: extreme prosperity, risk exposure, and gradual stabilization. The first stage lasted from 2006 to 2010, a period of rapid development in the market. Although the market was affected by the financial crisis of 2008, an investment stimulus plan with four trillion RMB maintained the boom. In the second half of 2010, there was a relatively stable period as government regulation and control intensified. However, in the second phase, from 2013 to 2014, several REITs were affected by cash-out crises. As a result, real-estate financial risks were exposed in a concentrated manner. In the third phase, which began in 2016, the Chinese government adopted the basic principle that housing speculation should be eradicated. The Chinese real-estate industry entered a period of stability. Therefore, it is possible to observe changes in the real-estate financial risk network during these periods.

5.3. Analysis of Network Topology Characteristics

5.3.1. Network Density

We used the spatial network of real-estate financial risks in China to understand their overall distribution. The number of links in

Table 3. Overall network description.

Year	Links	Average Links	Density	Degree of Correlation
2006	184	5.935	0.1978	1.000
2007	186	6.000	0.2000	1.000
2008	197	6.355	0.2118	1.000
2009	206	6.645	0.2215	1.000
2010	214	6.903	0.2301	1.000
2011	218	7.032	0.2344	1.000
2012	228	7.355	0.2452	1.000
2013	226	7.290	0.2430	1.000
2014	221	7.129	0.2376	1.000
2015	218	7.032	0.2344	1.000
2016	214	6.903	0.2301	1.000
2017	211	6.806	0.2269	1.000
2018	212	6.839	0.2280	1.000

corresponds to the number “1” in the network matrix, and the average number of links is equal to the number of links divided by 31.

The degree of correlation, which is 1, indicates that the real-estate financial risks in the provincial domains can interact. There is no province or city in which the risks are completely unrelated to those in other provinces and cities. Therefore, there is some spatial correlation between risks in the provinces and domains of China. From 2006 to 2018, the number of links between two provincial regions rose from 184 to 212, indicating growth. The number of links gradually increased between 2006 and 2012, especially after the financial crisis of 2008. At that time, the growth rate increased. It decreased slightly from 2012 to 2017, and it tended to rise after 2018. This indicates that the number of linkages between real-estate financial risks in Chinese provinces evolves dynamically.

According to Table 3, network density increased gradually, from 0.1978 in 2006 to 0.2452 in 2012. It declined from 0.2452 in 2012 to 0.2269 in 2017. Then, it rose again to 0.2280 in 2018, with a dynamic change in density and an overall upward trend. The increase in network density implies the real-estate financial risks across the 31 provinces are closely related. This tendency became particularly pronounced after 2008 when the linkages became denser at a more rapid rate. The implication is that risk in a given province is either affected by spillovers from other provinces or likely to affect risk profiles elsewhere in the country. In recent years, the government has attached considerable importance to integrated regional economic development and coordination. It has also strengthened inter-regional interaction and cooperation, which facilitates interprovincial capital flows, personnel flows, project cooperation, and business crossovers. Accordingly, the association between real-estate financial risks is becoming closer.

5.3.2. Network Centrality

Table 4. The degree centrality of the spatial correlation network of real-estate financial risks.

Code	Province	Indegree	Outdegree	Degree	Code	Province	Indegree	Outdegree	Degree
1	Shanghai	5	23	28	17	Sichuan	3	5	8
2	Jiangsu	4	23	27	18	Xizang	2	6	8
3	Beijing	0	24	24	19	Shaanxi	4	4	8
4	Zhejiang	3	17	20	20	Qinghai	3	5	8
5	Tianjin	18	1	19	21	Xinjiang	2	6	8
6	Shandong	11	4	15	22	Shanxi	4	3	7
7	Guangdong	2	12	14	23	Anhui	5	2	7
8	Fujian	3	9	12	24	Jiangxi	1	6	7
9	Henan	4	6	10	25	Hainan	1	6	7
10	Hubei	4	6	10	26	Ningxia	3	4	7
11	Gansu	5	5	10	27	Jilin	2	4	6
12	Yunnan	3	6	9	28	Guizhou	1	5	6
13	Heilongjiang	4	4	8	29	Hebei	2	3	5
14	Hunan	2	6	8	30	Inner Mongolia	2	3	5
15	Guangxi	2	6	8	31	Liaoning	2	3	5
16	Chongqing	5	3	8		Total	112	220	332

shows the degree centrality of the spatial association network of real-estate financial risks. The term “degree” indicates the number of provinces that are connected directly to the one under observation. In the directed network, the term “indegree” denotes the number of real-estate financial risk liSnks that are directed at a provincial node. “Outdegree” indicates the number of links that the node directs at other nodes. Degree centrality is equal to the sum of the indegree and outdegree indicators. We used all three measures to analyze the centrality of provincial real-estate financial risk.

Firstly, the degree indicator suggests that the provinces that have the largest centralities are Shanghai, Jiangsu, Beijing, Zhejiang, Tianjin, Shandong, and Guangdong. In other words, these regions occupy a more important position in the real-estate financial risk correlation network and are more closely associated with other regions. This also indicates that the most prominent provincial real-estate financial risks are concentrated in the developed eastern regions. According to the previous analysis, the current real-estate financial risks in these provinces are not the highest in the country. However, their risks are closely related to those of other provinces and thus more likely to result in contagion.

Secondly, the provinces that rank highest on the indegree indicator are Tianjin, Shandong, Shanghai, Anhui, Chongqing, and Gansu. They are followed by Jiangsu, Henan, Hubei, Shaanxi, Zhejiang, Fujian, Sichuan, and others, and by the central and western regions of Guangxi, Xizang, Xinjiang, Jiangxi, Hainan, Guizhou, and so on. The top provinces in the outdegree ranking are Beijing, Jiangsu, Shanghai, Zhejiang, Guangdong, and Fujian. The bottom ones are Chongqing, Shanxi, Hebei, Inner Mongolia, Liaoning, Anhui, and Tianjin. The most active provinces, in terms of incoming and outgoing linkages, are in the eastern part of China. However, the distribution is fragmented and does not follow a patchy pattern. In the spatial correlation network of real-estate financial risks, the eastern provinces are the most active regions, regardless of whether they are infected or contagious to other provinces. The central and the western regions are less active and are mainly characterized by risk contagion from other regions.

Table 5. The betweenness centrality of the nodes in the spatial correlation network of real-estate financial risks.

Code	Province	Betweenness	nBetweenness	Code	Province	Betweenness	nBetweenness
1	Guangdong	152.247	17.500	17	Hebei	5.741	0.660
2	Shanghai	139.512	16.036	18	Guangxi	5.509	0.633
3	Jiangxi	100.098	11.506	19	Shanxi	4.982	0.573
4	Beijing	76.644	8.810	20	Liaoning	4.565	0.525
5	Jiangsu	45.473	5.227	21	Hubei	4.186	0.481
6	Hunan	41.858	4.811	22	Inner Mongolia	2.084	0.240
7	Chongqing	34.379	3.952	23	Anhui	1.675	0.192
8	Yunnan	27.245	3.132	24	Sichuan	1.283	0.148
9	Tianjin	25.366	2.916	25	Hainan	1.269	0.146
10	Guizhou	24.385	2.803	26	Heilongjiang	0.583	0.067
11	Henan	23.621	2.715	27	Shaanxi	0.375	0.043
12	Zhejiang	20.886	2.401	28	Xizang	0	0
13	Shandong	19.824	2.279	29	Jilin	0	0
14	Gansu	18.417	2.117	30	Ningxia	0	0
15	Fujian	17.793	2.045	31	Xinjiang	0	0
16	Qinghai	6.000	0.690

reports the betweenness centrality of each provincial node in the spatial correlation network of provincial real-estate financial risks. In the table, the term “betweenness” denotes betweenness centrality, and “nBetweenness” denotes relative betweenness centrality. Both are indicators of the strength of provincial control over activities that create real-estate financial risks. In terms of betweenness, the leading provinces are Guangdong, Shanghai, Jiangxi, Beijing, Jiangsu, Hunan, and Chongqing. Except for Beijing, Shanghai, and Guangdong, the other four provinces are in the center of China, with higher levels of economic development and more pronounced risk dynamics. They have higher-risk contagion capacities than neighboring provinces.

In conclusion, these seven provinces exercise strong control over activities that are related to real-estate financial risk at the inter-provincial level and play the role of bridges that control the spatially related forms of risks and the flow of contagion. In addition, the Betweenness and nBetweenness indices for Tibet, Jilin, Ningxia, and Xinjiang are 0, which indicates that the provinces in question do not have any control over the network and cannot influence others. They are thus isolated. This result may be partially attributable to the relatively small scale of real-estate investment in these provinces and the low dependence of their economies on such investments. For example, according to the data published by the National Bureau of Statistics of China, real-estate investment in Tibet, Jilin, Ningxia, and Xinjiang provinces accounted for 6.60%, 7.80%, 12.10%, and 8.50% of GDP in 2018, respectively. Their respective rankings were 29th, 28th, 19th, and 26th out of 31 provinces, excluding Hong Kong, Macao, and Taiwan. This makes these provinces less prone to accumulations of risk and spillovers. At the same time, the four provinces are relatively remote, with Xinjiang, Tibet, and Ningxia in northwest China and Jilin in northeast China, far from the network centers of Beijing, Shanghai, and Guangzhou. According to Equation (1), this remoteness also makes these provinces less susceptible to the influence of network hubs.

Table 6. Closeness centrality of nodes in the spatial correlation network of real-estate financial risk.

Code	Province	inFarness	outFarness	inCloseness	outCloseness
1	Beijing	37	313	81.081	9.585
2	Tianjin	42	314	71.429	9.554
3	Hebei	57	304	52.632	9.868
4	Shanxi	60	304	50.000	9.868
5	Inner Mongolia	66	304	45.455	9.868
6	Liaoning	64	305	46.875	9.836
7	Jilin	900	245	3.333	12.245
8	Heilongjiang	900	243	3.333	12.346
9	Shanghai	33	294	90.909	10.204
10	Jiangsu	33	303	90.909	9.901
11	Zhejiang	41	299	73.171	10.033
12	Anhui	53	313	56.604	9.585
13	Fujian	72	295	41.667	10.169
14	Jiangxi	56	288	53.571	10.417
15	Shandong	47	301	63.830	9.967
16	Henan	50	303	60.000	9.901
17	Hubei	58	292	51.724	10.274
18	Hunan	59	287	50.847	10.453
19	Guangdong	62	287	48.387	10.453
20	Guangxi	86	289	34.884	10.381
21	Hainan	91	288	32.967	10.417
22	Chongqing	109	286	27.523	10.490
23	Sichuan	138	285	21.739	10.526
24	Guizhou	89	287	33.708	10.453
25	Yunnan	89	283	33.708	10.601
26	Xizang	930	258	3.226	11.628
27	Shaanxi	842	205	3.563	14.634
28	Gansu	840	198	3.571	15.152
29	Qinghai	842	198	3.563	15.152
30	Ningxia	930	177	3.226	16.949
31	Xinjiang	930	258	3.226	11.628

shows the closeness centrality of the spatial correlation network of real-estate financial risks. In the directed spatial network, “inCloseness” indicates the ease with which real-estate financial risk in the province is influenced passively by that of other provinces. The higher its value, the easier it is for risks from other provinces to reach the province under observation. The term “outCloseness” indicates how difficult it is for real-estate financial risk from a given province to affect risk in others. The larger its value, the easier it is for the province under observation to transmit risk. “InFarness” captures the sum of the distances between all spatial association relations that originate from a certain provincial domain and are received by other provincial domains. A smaller value indicates fewer spatial overflow relations. “OutFarness” indicates the sum of the distances of all the spatial overflow relations generated by a province that is affected by other provinces. A smaller value indicates less acceptance of spatial risk spillovers.

The provinces that rank highest for inCloseness are Shanghai, Jiangsu, Beijing, Zhejiang, Tianjin, Shandong, and Henan. The inFarness centrality values for these provinces are also smaller. They are likely to receive spatial spillovers. However, they emit fewer spillovers and are thus risk receiving. The provinces that are ranked highest for outCloseness are Ningxia, Gansu, Qinghai, Shaanxi, Heilongjiang, Jilin, Xizang, and Xinjiang. The outFarness of these provinces is also smaller. Real-estate financial risks in these provinces are more likely to reflect spatial spillover relationships and a low number of recipient relationships. It follows that the provinces are risk emitting. It is worth noting that Ningxia, Gansu, Qinghai, Shaanxi, Heilongjiang, Jilin, Xizang, and Xinjiang are mostly northwestern provinces. Their real-estate financial risks are higher than those of others, they are risk emitting, and the risks in question are highly contagious. Therefore, when attempting to prevent the financial risks that are associated with real estate, administrators should pay particular attention to avoiding contagion from these northwestern provinces. Measures should focus on capital flows, industrial orientation, and credit policy.

Table 7. Summary of centrality.

Centrality	Sub-Indicator	Province
Degree centrality	indegree	Tianjin, Shandong, Shanghai, Anhui, Chongqing, Gansu
	outdegree	Beijing, Jiangsu, Shanghai, Zhejiang, Guangdong, Fujian
Betweenness centrality	/	Guangdong, Shanghai, Jiangxi, Beijing, Jiangsu, Hunan, Chongqing
Closeness centrality	incloseness	Shanghai, Jiangsu, Beijing, Zhejiang, Tianjin, Shandong, Henan
	outcloseness	Ningxia, Gansu, Qinghai, Shaanxi, Heilongjiang, Jilin, Xizang, Xinjiang

combines the results from the three types of centrality calculations. It shows, intuitively, that financial risks in the developed eastern regions are very prominent in the provincial space. Although the eastern provinces do not have the highest levels of risk, they act as bridges and have a strong capacity to transfer risk. Most of the provinces in the northwest face high real-estate financial risks and also emit them.

5.4. Block Model Analysis

If maximum segmentation depth and the convergence criterion are set at 2 and 0.2, respectively, four real-estate financial risk blocks emerge (see

Table 8. Classification and spillover relationship of real-estate financial risk blocks.

Block	Province	Total Relations Received from Other Blocks	Total Relations Sent to Other Blocks	Block Role
Block 1	Beijing, Jiangsu, Shanghai, Zhejiang, Guangdong	14	99	Strong net spillover
Block 2	Fujian, Jiangxi, Hunan, Guangxi, Yunnan, Guizhou, Hainan, Xizang, Xinjiang	17	56	Weak net spillover
Block 3	Henan, Hubei, Sichuan, Qinghai, Jilin, Ningxia, Hebei, Inner Mongolia, Liaoning, Gansu, Heilongjiang, Shaanxi	38	52	Broker
Block 4	Shanxi, Chongqing, Anhui, Shandong, Tianjin	43	13	Primary loss

). Block 1 includes five developed provinces, namely Beijing, Jiangsu, Shanghai, Zhejiang, and Guangdong. Block 2 includes the following nine provinces: Fujian, Jiangxi, Hunan, Guangxi, Yunnan, Guizhou, Hainan, Xizang, and Xinjiang. Block 3 includes 12 provinces. The 12 are Henan, Hubei, Sichuan, Qinghai, Jilin, Ningxia, Hebei, Inner Mongolia, Liaoning, Gansu, Heilongjiang, and Shaanxi. Block 4 includes five provinces: Shanxi, Chongqing, Anhui, Shandong, and Tianjin.

Among the 332 associations in the entire spatial association network, the number of associations within the four blocks is 112, and the number of associations between them is 220. Therefore, linkages between provincial real-estate financial risk blocks in China are strong. The risks are highly contagious between regions. Table 8 shows that the number of the relationships that originate in Block 1 and Block 2 is higher than the number of received relationships. These two blocks belong to the net-spillover block. Block 1 has the strongest spillover capacity. It is thus a strong net-spillover block. Block 2 is a weak net-spillover block. Most of the members of the two blocks belong to economically developed regions, which also indicates that developed provinces can generate more extensive spatial spillovers. Block 3 mainly includes provinces with strong economic dynamics. For the most part, it receives risk spillovers from Block 1 and Block 2, and it is the origin of spillovers in Block 4. It thus functions as a bridge. Therefore, it is a broker block, that is, a communication intermediary for risk transmission between provinces. The number of relationships that Block 4 receives is significantly higher than that of the relationships that originate in it. The spatial spillover relationship of real-estate financial risks between provinces is weak, which is typical of the primary loss block. In short, most provinces in China export and receive real-estate financial risks with a strong spatial correlation of risks.

Table 8 also reflects the spatial transmission mechanism that applies in provincial areas. Block 1 and Block 2 are the sources of real-estate financial risks. Their main role is connected to risk spillovers, and they are most active in the spatial correlation of real-estate financial risks. Block 3 is an intermediary, acting as a bridge and a hub, and has both spillover and risk-receiving functions. In particular, Block 3 contains northwestern provinces with high risk levels, such as Inner Mongolia, Shaanxi, Gansu, Qinghai, Ningxia, and Xinjiang, which is liable to lead to significant contagion. Finally, Block 4 is the primary loss block. For the most part, it receives risk and participates in top-down risk transmission.

5.5. Analysis of Network Structure: The ERGM Model

The analyses above identified the fundamental features of the spillover network of real-estate financial risk in China. However, the methods of those analyses only refer to indicators from traditional social networks, which cannot reveal structural characteristics fully. In addition, these indicators do not enable analyses of the influence that node attributes exercise on the network. Accordingly, we employed the ERGM to explore structural characteristics and influencing factors.

The ERGM is a network statistical model that integrates the effects of various factors on the formation of the network. This model compares an actual network with a randomly generated one. This comparison allows observation of the differential effects of various network-generation processes on the network structure. The basic equation of the ERGM model can be expressed as follows:

$$p\left(Y=y\right)=\left(\frac{1}{k}\right)\exp ({\displaystyle \sum }_A{\theta }_A{g}_A\left(y\right))$$

(5)

where $Y$ refers to all possible networks, and y is defined as a particular reality network. $P\left(Y=y\right)$ denotes the probability that a particular reality network will appear in all possible networks. $K$ is the variable that guarantees that the sum of the probabilities of each possible network is equal to 1. $A$ refers to the factors that influence the formation of a network, which can be divided into structural factors, node attributes, and external factors. $\theta$ is a parameter that captures the effect of various network structures on network formation, and $g_A\left(y\right)$ denotes the statistical data of the network structures that are included in the model.

The ERGM model can be estimated for a variety of network structures. Given its practical economic orientation, this paper focuses on two structures, the mutual relationship and the three-node balance relationship. The two structures are presented in Figure 5 and Figure 6.

Turning to the node attributes that pertain to the formation of a reality risk network, we introduce a new factor, the land element, which has not been considered before. The issue of land finance in China has been discussed extensively and widely. The high dependence of local governments on land concession revenue may also be an important factor that influences the formation of risk networks. Accordingly, the degree to which the government depends on land finance is measured by the ratio of local government land sales turnover to the general public budget revenue of that local government. The larger the ratio, the stronger the dependence of the local government in question on land finance. In addition, we treat the rate of GDP growth as another attribute of network nodes. Since the objects of the research are provinces in the same country, the macroenvironment, the policy environment, and the social environment are relatively similar. Therefore, the external covariates are not included in the model.

As for the data source, the data on GDP and general public budget expenditure in each province are from the National Bureau of Statistics of China. The data on land sales are from the China Land and Resources Statistical Yearbook. It should be noted that this yearbook was suspended in 2018. At present, data are only available up to 2017. Therefore, we do not examine the 2018 network.

We estimated the ERGM model by using the Markov chain Monte Carlo method. Given the limitations of the article,

Table 9. The result of ERGM.

Variables	Coefficients (Model 1)	Coefficients (Model 2)
Edges	−2.54 *** (0.25)	−2.44 *** (0.27)
Dland	0.94 *** (0.17)	1.21 *** (0.21)
GDP_growth	0.21 (1.06)	0.13 (1.17)
mutual	1.36 *** (0.25)
balance		0.05 *** (0.02)
AIC	−324.67	−302.02
BIC	−305.33	−282.68

Note: *** indicate significance at the level of 1%. Standard deviations are in parentheses.

only reports the 2017 estimates.

The coefficient of “mutual” in Model 1 is significantly positive. This suggests that real-estate financial risks in China have inter-regional spillover effects. Cross-regional investment by developers results in the simultaneous existence of loans in different regions. A depression in the real-estate market is likely to disrupt the cash flows of the developer. As a result, the financial risk of a developer who has engaged in cross-regional investment spreads across areas.

Model 2 estimates the network structure with a three-node balance relationship. The coefficient of “balance” is significantly positive. This suggests that there are spillovers across multiple regions in the real-estate financial risk network. This tendency may be related to the Chinese regional synergistic development strategy. The regional synergistic development strategy is a long-standing program, with projects such as the Yangtze River Delta, the Pearl River Delta, and the Beijing–Tianjin–Hebei integration. The strategy has accelerated the flow of resources such as capital, talent, and technology. This has certainly driven the real-estate market in each region, and it is not surprising that the attendant financial risks can be transmitted. Many empirical results provide supporting evidence. Degen and Kathrin (2017), for example, wrote that an inflow of immigrants of 1% of the local population causes an increase in house prices of approximately 3% [33]. Theoretically, integration policies make regional economic development more coordinated and facilitate the elimination of development gaps. However, in terms of actual implementation, the regional development gap in China is still widening and may have expanded after COVID-19 [34]. The gravity model that was developed in this paper shows that the widening of the economic development gap will lead to an intensification of regional interactions without any change in geographical distance. Therefore, regions that are subject to the same integrated development strategy, which are all geographically close, will see the mutual transmission of real-estate financial risks become more pronounced if the gap continues to widen.

The coefficient for the land finance dependence variable Dland is significantly positive. This suggests that strong land finance dependencies have facilitated the formation of a spillover network in China. This conclusion is also intuitive. Since the reform of the housing system and the introduction of the Land Management Law in 1998, local governments have been given the legal right to sell land. As a result, local governments in China have developed a land finance model that is based on three pillars: land acquisition, land sale, and tax collection. The land monopoly of local governments allows land to be sold at high prices. The government uses part of the revenue from land concessions to construct urban infrastructure, which causes land prices to increase [35]. This creates an incentive for local governments to drive land prices upward. At the same time, local governments mortgage their land reserves to acquire finance from banks and society or to construct local financing platforms so as to cover fiscal gaps. The stronger the pressure that economic growth exerts on local governments, the more they mortgage land [36]. This means that if the economic development of a region is lagging, its government is more dependent on land finance and the need to maintain land values. Consequently, housing becomes inordinately expensive [37]. At the same time, real-estate companies (and some non-real-estate companies) that acquire land can use it as collateral to secure loans from banks. Consequently, they develop real estate because of the high value of the land. Later, the real-estate companies recover the funds through presales and the like. These funds can be used by the companies to buy land in other regions and to develop more real estate. The constant repetition of this process creates a mutual influence between the regions. This phenomenon is consistent with the findings of Cao and Zhang (2021) [38]. They pointed out that the violence of the cyclical fluctuations that some provinces experience is related to their dependence on land finance. The gap in fiscal deficit pressures between provinces is therefore a key factor that drives spillovers in financial-cycle fluctuations.

The high demand for government revenue from land sales has created a liberal environment for real-estate developers. They can operate with high leverage, creating a channel of risk contagion. Some local governments focus only on their immediate interests, allowing risks to accumulate and spread. Eventually, a general risk spillover network forms.

The results of the model diagnostics are shown in Figure 7 and Figure 8. The fit results for each variable are generally as expected. The above conclusions also hold for networks in other years, and the estimated results are omitted here.

6. Conclusions and Implications

6.1. Conclusions

Firstly, the degree of correlation in the spatial correlation network of real-estate financial risks is always 1, indicating that those risks always exert a spatial correlation effect in Chinese provinces. The correlation network density increased between 2006 and 2018. This indicates that contagion spreads more easily between provinces, that is, that the risk in any given province is affected by the risk in other provinces or will affect risk elsewhere.

Secondly, real-estate financial risks in the eastern region have a strong contagion potential. Vulnerability to risk infection is high in the middle region and in the northwest. Real-estate financial risks in Beijing, Jiangsu, Shanghai, Zhejiang, Guangdong, and Fujian, which are located in the developed eastern region, are very prominent in the provincial space. Although the risk levels in these provinces are not the highest, they are highly contagious and strongly correlated to risk in other provinces. Provinces such as Ningxia, Gansu, Qinghai, Shaanxi, Xinjiang, Heilongjiang, Jilin, and Xizang, which are mostly located in the northwest, face specific and higher real-estate financial risks than other provinces. The provinces in question are risk emitting. The middle region, where economic development is more dynamic, plays the role of a risk contagion broker. Its risk level can easily be amplified in the course of regional transmission.

Thirdly, the provincial real-estate financial risk spatial network can be divided into four functional blocks. Each block exhibits obvious gradient transmission characteristics and is typified by the corresponding mechanisms. Block 1 is a strong net-spillover block. It includes five provinces: Beijing, Jiangsu, Shanghai, Zhejiang, and Guangdong. Block 2 is a weak net-spillover block. It includes nine provinces: Fujian, Jiangxi, Hunan, Guangxi, Yunnan, Guizhou Hainan, Xizang, and Xinjiang. Block 3 is the broker block. It comprises 12 provinces: Henan, Hubei, Sichuan, Qinghai, Jilin, Ningxia, Hebei, Inner Mongolia, Liaoning, Gansu, Heilongjiang, and Shaanxi. Block 4 is the primary loss block and includes five provinces, namely Shanxi, Chongqing, Anhui, Shandong, and Tianjin. Block 1 and Block 2 are the sources of real-estate financial risks in China. Block 3 is the intermediary block, acting as a bridge and a hub. For the most part, Block 4 receives risk and is involved in top-down risk transmission.

Fourthly, as far as network structure is concerned, the estimation results from the ERGM model show that the inter-regional spillover of real-estate financial risks has a significant effect in China. There are also interactive spillovers between multiple regions. Meanwhile, strong dependence on land finance promotes the formation of the real-estate financial risk spillover network. The local GDP growth rate has no significant effect on its formation.

6.2. Implications

The first implication of our results is that regulation-and-control policies should reflect local conditions and city-specific policies. They should incorporate a combination of macro control and localized regional adjustments to curb the spread of financial risks in real estate. Real estate and finance are not on the opposite sides of the economy. They should play their respective roles in driving and supporting the real economy. Moreover, the stability of the real-estate market is related to sustainable development and structural transformation on the national level. Therefore, regulation and control in the real-estate market are also subject to higher requirements. Under the general policy of eliminating speculation in housing that is in place in China, regulation-and-control policies should be attuned to the specificities of particular provinces. There should be a policy for every city, and perhaps even a policy for every district. Regional differences in risk spillovers should be limited through measures directed at land finance, talent flow, real estate, infrastructure, and guidance for residents, which can shape expectations. For example, in provinces that exhibit active movements in the real-estate financial risk correlation network, the local government should be decisive and act in a timely manner. In other regions, the local government should consider the state of economic development carefully, focus on abnormal fluctuations, and take flexible and precise measures to prevent the transmission of real-estate financial risks from the eastern regions.

The second implication of the study is that it is necessary to accelerate the planning and construction of a cross-regional trading system for construction land and to institute supplementary arable land quotas at the national level. In the spatial correlation network of real-estate financial risk, the central cities, which are relatively developed economically, are the main sources of spillovers. The increasing degree of regional integration in these areas has triggered new risk transmission mechanisms. The establishment of a nationwide trading mechanism for construction land and supplemental arable land will facilitate access to construction space in the central cities of the regional economies. This will largely alleviate the problem of rising housing prices in central cities that receive large flows of internal migrants, which is caused by shortages of land resources and an imbalance between supply and demand.

The third implication has to do with the need to improve the manner in which real-estate financial risks are prevented and monitored at the regional level. First, technical regulatory mechanisms should be used to create a monitoring system that integrates the national level and the regional level. Such a system can respond effectively to trends and changes in the real-estate market in real time. It can also implement regulations in areas with abnormal price fluctuations accurately and rapidly. Second, efficient communication and feedback mechanisms should be established. Governments at all levels should uphold the concept of a community of destiny. Specifically, each local government should be committed to eliminating market segmentation and administrative barriers and to setting up an efficient and smooth channel for exchanging and sharing dynamic information, statistical data, and policy-relevant information about the real-estate market. Third, financial institutions should establish a reasonable mechanism for implementing credit policy. This mechanism would ensure that bank credit can be extended in a manner that avoids the escalation of house prices and speculation in the housing market, resulting in stable real-estate prices. Fourth, the analysis of risk spillovers and contagion between regions can be incorporated into an early warning system. For example, provinces in the broker block can be taken as key monitoring subjects that provide indications of risk status. The intensity of future real-estate financial risk spillovers and the possible contagion paths can be anticipated by monitoring these regions. In this way, the spread of risks can be arrested in a timely manner, effectively preventing the formation and accumulation of systemic threats.

6.3. Future Research Directions

This paper discussed some of the factors that may contribute to contagion in real-estate financial risk. Although the impact of specific policies was not analyzed in detail due to limitations of space, it cannot be ignored. The Chinese government emphasizes the need for city-based regulation in the real-estate industry—each region should formulate its own policies that reflect local conditions. This complicates policy factors and causes them to become unpredictable. Local and dynamic research methods may be needed.

We believe that the differential financial risk spillover effects that are caused by the regulatory policies of various regions can be studied further in the future. Research on that issue will help regions to coordinate and optimize their policies, thus preventing spillovers. In the future, a complete theoretical framework can be formulated in order to discuss this spillover mechanism. For example, a two-region model based on the study by Iacoviello (2005) [39] can be extended to create a dynamic stochastic general equilibrium framework and to explore the combined effects of factors such as credit policies and population mobility.