Assessing interconnectedness and systemic importance of Chinese financial institutions

Summary

This study proposes a directed acyclic graph (DAG)-based framework for generalized variance decomposition for investigating the heterogeneous return spillovers in financial system and measuring the systemic importance of financial institutions among 34 listed Chinese financial institutions from 2011 to 2023. Findings indicate pronounced information spillovers among institutions within the same sector due to contemporaneous causal relationships. Both static and dynamic financial network analyses highlight the significance of the securities sector. Dynamic structural characteristics align with macroeconomic development and are sensitive to internal and external shocks. Systemic importance assessment reveals that market size alone doesn’t determine importance, with notable disparities between banking and non-banking sectors. State-owned and joint-stock commercial banks play a vital role in banking, while local government and private capital-controlled institutions are crucial in the securities sector. This research aids regulatory efforts in maintaining a balanced regulatory environment, ensuring market efficiency, and reducing operational costs.

Graphical abstract

Highlights

• •A DAG-SVAR GFEVD framework to study the connectedness structure of financial system
• •Spillover relationship between financial institutions in the same sector is closer
• •The securities sector plays an important role in the spillover structure
• •The operational attribute of financial institution affects the systemic importance

Financial risk management; Complex network; Economics; Causal inference; Social sciences; Business

Introduction

In the era of financial globalization and liberalization, global financial markets consistently exhibit a heightened level of interconnectedness.^1,2,3 The interactions between financial institutions are progressively strengthened and intricate. The emergence of risks within individual financial institutions has the potential to be transmitted and amplified through the intricate network of financial systems, ultimately culminating in a financial crisis that can impact a single country or reverberate globally. Following the 2008 global financial crisis, systemic financial risk has attracted high attention from academia and regulatory authorities.^4,5,6 There have been many influential works in this field, including contributions by French et al. (2010),⁷ Hanson et al. (2011),⁸ Gennaioli et al. (2012),⁹ Galati and Moessner (2013),¹⁰ and Laeven et al. (2016).¹¹ As research has advanced, the exploration of systemic financial risk has encompassed various dimensions, such as effective measures,^12,13,14 contagion spillovers,^{15,16,17,18,19,20,21} driving factors,^{22,23,24,25,26} and policy regulation.^27,28

As the modern financial system has evolving into an interconnected network, the examination of linkages and the contagion of risks among financial institutions, viewed through the lens of a financial network, has emerged as a central and highly relevant topic within the realm of financial risk research.^29,30,31 On the one hand, financial network can cover various types of financial institutions, effectively complementing the limitation of traditional banking models. On the other hand, it can mitigate the procyclical nature of financial indicators and illuminate diverse transmission channels of financial risks.^32,33 The identification of linkages and risk contagion among financial institutions from the perspective of financial networks holds significant theoretical and practical implications for preventing systemic financial risks, establishing effective financial supervision, asset pricing mechanisms, and risk management systems.^34,35

Allen and Gale (2000)³⁶ pioneered the integration of network models into the study of systemic financial risk. Since then, network models have found widespread application across various domains, including delineating financial system architecture, measuring risk levels, uncovering contagion pathways, and providing policy foundations. Existing literature has predominantly explored systemic financial risk using diverse network types, such as relationship or events networks, proximity networks, and association networks.³⁷ Billo et al. (2012)³⁸ employed principal-component analysis (PCA) and Granger causality test to scrutinize pairwise Granger causality relationships between institutions and construct corresponding pairwise association networks of financial institutions. Diebold and Yılmaz (2012, 2014)^15,16 developed a generalized variance decomposition framework to explore interconnections and contagion based on information spillover networks, effectively unifying different risk measurement methods within the same research framework. Härdle et al. (2016)³⁹ utilized the TENET model, grounded in a semi-parametric quantile regression framework, to estimate the network interconnectedness of financial institutions based on tail-driven spillover effects. Glasserman and Young (2016)⁴⁰ delved into information regarding large financial institutions and their connectedness, emphasizing that more centralized financial institutions may pose greater systemic threats, colloquially known as being “too central to fail”. Wang et al. (2018)⁴¹ investigated volatility connectedness in the Chinese banking system using the framework of Diebold and Yılmaz (2014),¹⁶ and pointed out that a bank might be “too big to fail”, but not necessarily “too interconnected to fail”. Caccioli et al. (2018)³² summarized the latest advances in network methods for modeling financial system risks, reporting recent discoveries in the empirical structures of interbank networks. Battiston and Martinez-Jaramillo (2018)⁴² provided an overview of the role of financial network models in stress testing and financial stability, and discussed their limitations and future developments. Gai and Kapadia (2019)⁴³ concentrated on the application of network models based on epidemiological methods in the financial system, revealing different contagion mechanisms observed during the global financial crisis. Jackson and Pernoud (2021)⁴⁴ made distinctions in systemic financial risk and discussed how various risks depend on interdependent networks. Elliott and Golub (2022)⁴⁵ delved into the key structural characteristics in the financial system determining network vulnerability, emphasizing the importance of phase transitions.

As network models have evolved, there has been a notable rise in the application of high-order networks and high-dimensional networks. High-order networks consider multiple relationships between nodes, providing a more complex but realistic portrayal of the financial system. Bargigli et al. (2015)⁴⁶ explored the multilayer network structure among Italian banks, illustrating that solely focusing on the entire interbank network or specific feature layers might not fully capture interconnections in the interbank market, leading to biased estimates of systemic risk. Bookstaber and Kenett (2016)⁴⁷ modeled the financial system through the lens of multilayer networks, explaining how the collapse of two hedge funds at Bear Stearns in 2007 affected the entire financial system. Aldasoro and Alves (2018)⁴⁸ used risk exposure data between large European banks to describe the main characteristics of the multilayer structure of the financial network, measuring and decomposing the systemic importance indices of different banks. Cao et al. (2021)⁴⁹ proposed a new measure of systemic risk by constructing a multilayer network that considers the responsibilities and cross-holdings among financial institutions, evaluating the systemic importance of financial institutions. Wang et al. (2021)⁵⁰ proposed multilayer information spillover networks, including return spillover layer, volatility spillover layer, and extreme risk spillover layer to investigate the information spillovers and connectedness of Chinese financial institutions. Chao et al. (2022)⁵¹ discussed the application of various technologies, including multilayer network methods, in regulatory technology, providing support and a developmental foundation for financial stability. Wang et al. (2023)⁵² introduced a multilayer network framework based on variance decomposition and block aggregation techniques, analyzing correlations and risk transmission pathways between global stock markets and foreign exchange markets. Ouyang et al. (2024)⁵³ measured the volatility connectedness of Chinese financial institutions in the frequency domain. High-dimensional networks primarily address the “curse of dimensionality” issue arising from high-dimensional, low-sample financial risk events. Hautsch et al. (2015)⁵⁴ used the LASSO quantile regression model to construct a tail risk network of the US financial system. Demirer et al. (2018)⁵⁵ analyzed a high-dimensional network of publicly traded subsets of 150 global banks from 2003 to 2014 using LASSO and elastic net, assessing changes in interbank connections during the financial crisis. Gross and Siklos (2020)⁵⁶ modeled a high-dimensional network of European credit default swap spreads using factor models and elastic net, assessing the joint transmission of banking and sovereign risks to the non-financial corporate sector.

Information filtering is a crucial step in financial network analysis. A complex financial network typically needs information filtering to eliminate redundant information. Common methods for information filtering include thresholding,^50,57,58 minimum spanning trees,^{59,60,61,62,63} and maximum filter graphs.^64,65,66 Another important approach to generating incomplete networks involves preprocessing the data based on causal relationships, cointegration, and other factors before network modeling. Kenett et al. (2010)⁶⁷ constructed an association network based on the partial correlation coefficients between stock returns, revealing the special status of the financial sector within the network. Billio et al. (2012)³⁸ modeled the financial system by considering Granger causality relationships between institutions, showing significant asymmetry between different financial sectors. Yang et al. (2014)⁶⁸ studied risk contagion between global stock markets based on cointegration relationships among stock markets. Sprites et al. (2001)⁶⁹ firstly introduced the DAG approach into a vector autoregressive (VAR) model and applied it in the field of social sciences. After that, it is found that DAG can effectively identify causal relationships of information spillovers between financial institutions, prompting an increasing number of scholars to incorporate this method into research in the fields of economics and finance.^70,71,72,73

This study utilizes market data from 34 Chinese financial institutions to investigate the structure of heterogeneous return spillover networks and subsequently assess the systemic importance of financial institutions. Acknowledging that market data are influenced by common market factors, posing challenges in full capturing the heterogeneity between financial institutions, we decompose the original data through a capital asset pricing model (CAPM) regression to get the heterogeneous return data. A DAG approach⁶⁹ is employed to extract the contemporaneous causal flow pattern between heterogeneous data sequences. This pattern is then incorporated as a structural matrix into the classical generalized variance decomposition framework^15,16 to extract the information spillover structure between financial institutions. Through an analysis of the from, to, and net indices of financial institutions, this paper explores the systemic importance of various financial sectors and institutions. Additionally, it delves into the impact of the operational attributes of financial institutions on their systemic importance.

Empirical research findings indicate that the financial network based on the DAG exhibits distinct clustering characteristics. Financial institutions within the same sector are more prone to showcasing spillover relationships. Static network analysis across the full-sample underscores the significance of the securities sector. Dynamic analysis of rolling samples reveals that the time-varying characteristics of heterogeneous return networks align with macroeconomic development and demonstrate a heightened sensitivity to internal and external shocks. The evaluation of systemically importance financial institutions goes beyond market size as the sole determining factor. An analysis of the systemic importance based on the operational nature of financial institutions reveals substantial differences between banking and non-banking financial entities. Specifically, state-owned commercial banks and joint-stock commercial banks emerge as highly significant in the banking sector, whereas in the securities sector, institutions controlled by local governments and private capital assume greater importance. These findings underscore the impact of various factors, such as scale, connectedness, and governance level, on the systemic importance of financial institutions.

This paper contributes in the following areas. First, we contribute to a growing literature on financial networks and financial institutions’ connectedness. This literature is mainly based on the seminal work of Diebold and Yılmaz (2012, 2014).^15,16 Based on the generalized impulse response functions (GIRF) and generalized forecast error variance decomposition (GFEVD), scholars extensively study multiple fields, such as financial institutions,⁵³ stock markets,^74,75 futures,⁷⁶ and foreign exchanges.⁵² Our research enriches the modeling of financial networks based on heterogeneous returns, especially in the context of China’s financial system. We also contribute to literature evaluating the systemic importance of financial institutions. The discussion of this literature mainly focuses on “too-big-to-fail”⁴¹ and “too-connectedness-to-fail”,⁴⁰ and our study further considers the broader individual characteristics of financial institutions. Second, in terms of methodology, we apply a DAG-Structural VAR (SVAR)⁷¹ GFEVD analysis framework based on the CAPM regression. Compared to the classic framework of Diebold and Yılmaz (2012, 2014),^15,16 the structural matrix derived from causal inference more accurately reflects the relationship between financial institutions, while avoiding potential model identifiability issues that can arise from excessive parameter estimation. Using the heterogeneous return can better highlight the connectedness between financial institutions due to some unobservable special factors. Thirdly, we examine the relationship between the evolution of financial networks based on heterogeneous returns and crisis events, and conduct a dynamic and fine-grained analysis of the systemic importance of financial institutions based on their dynamic information spillover capabilities, integrating departmental categories, and operational attributes. The results reveal the differences between banking and non-banking sectors, as well as the impact of operational attributes on the systemic importance of different types of financial institutions.

Results

Heterogeneous return decomposition

A heterogeneity decomposition is conducted on the return sequences of 34 financial institutions, utilizing Equation 1 as the foundation. The descriptive statistics for the heterogeneous yields of these 34 financial institutions are presented in Table S1.

Table S1 reveals substantial variations between the decomposed residual sequences. The fluctuation range has surpassed the daily limit, ranging from a minimum value of −0.1331 (GYZQ) to a maximum value of 0.1584 (XNZQ). Despite the mean of heterogeneity returns being close to 0 across different sequences, there is a notable difference in the standard deviation among sequences. Broadly, the standard deviation of banking financial institutions tends to be lower than that of non-banking financial institutions. The augmented Dickey-Fuller (ADF) test results suggest that the residual sequence after heterogeneity decomposition still maintains stationarity. Furthermore, outcomes from the normal distribution test reject the assumption of the sequence adhering to a normal distribution.

DAG structure

The optimal lag of the vector error correction model (VECM) is determined by combining the results of multiple criteria including Akaike’s information criterion (AIC), Bayesian information criterion (BIC), Hannan-Quinn criterion (HQ), and final prediction error (FPE). Subsequently, a VECM with a lag of 1 is estimated to summarize the contemporaneous causal flow patterns among 34 financial institutions. Utilizing the residual correlation matrix of VECM, the resulting DAG at the conventional 10% significance level is shown in Figure 1. This graph depicts how stock return information spreads among financial institutions. In Figure 1, there are a total of 140 connections between 34 nodes, with a network density of 0.25. The maximum in-degree is 13, the maximum out-degree is 9, and the average node degree is 8.235. Notably, the network exhibits significant modularity, with financial institutions in the same sector significantly clustered in causal flows. Securities financial institutions demonstrate the closest relationship, followed by banking financial institutions.

Figure 1.

Contemporaneous causal flow patterns among the returns

According to Swanson and Granger (1997),⁷⁷ the contemporaneous causal structure revealed through the DAG analysis of the correlation matrix provides a data-driven solution for organizing variables in a VAR model. This step is essential before undertaking GFEVD in an SVAR model. Utilizing the causal network illustrated in Figure 1, we construct the matrix representing innovations and their correlations, as depicted in the following matrix.

Static analysis of heterogeneous return spillover network

We begin by examining the static shock transmission structure among financial institutions through the full sample spillover index matrix. The forward prediction order of the structural VAR model is established at 10. The connectedness structure of the 34 listed financial institutions is shown in Table S2.

As shown in Table S2, the average total heterogeneous return spillover index among the 34 financial institutions amounts to only 33.05. This value is notably lower than the total spillover index calculated from the original return rate in earlier studies. This suggests that a substantial portion of the information spillover between financial institutions is influenced by market-wide factors. By removing these common factors, the analysis can concentrate on the distinctive characteristics of financial institutions, providing a more precise insight into the interrelationships within the financial system.

Moreover, we conduct a detailed analysis of Table S2 focusing on three aspects: from, to, and net indices. Different financial institutions exhibit significant variations in both the from index and the to index. These findings are consistent with Wang et al. (2021),⁵⁰ where institutions in different financial sectors play different roles in receiving and sending shocks on different transmission channels. However, for the majority of specific financial institutions, the discrepancy between these two indices is not substantial. Specifically, the distribution range of the from index spans from 1.88 to 53.01, while the distribution range of the to index extends from 1.11 to 67.33. As the sole trust financial institution in the sample, SGTA demonstrates a relatively high degree of independence within the financial system, evident in both its from and to indices attaining their minimum values. In contrast, GDYH holds the maximum values for both indices. In general, most securities financial institutions exhibit high values for both from and to indices, whereas the data for banking financial institutions tends to be relatively low. Insurance financial institutions are distributed in the middle.

To further clarify the correlation between different types of financial institutions, we summarized the spillover relationships among four types of financial institutions based on the classification of the 34 sample financial institutions. For a category i containing n financial institutions, the process begins by aggregating the spillover relationships of each individual financial institution with all others in category j. Subsequently, we compute the mean of these aggregated values to derive the spillover index from category i to category j. The spillover relationships among the four types of financial institutions are illustrated in Figure 2.

Figure 2.

Connectedness structure between different types of financial institutions based on static analysis

(A) Connectedness structure of from index. Directed edges reveal the direction of spillover between nodes. The thickness of the lines reflects the strength of the directed spillover relationship, with thicker lines indicating stronger connections.

(B) Connectedness structure of to index. Directed edges reveal the direction of spillover between nodes. The thickness of the lines reflects the strength of the directed spillover relationship, with thicker lines indicating stronger connections.

In Figure 2A, the from index among four types of financial institutions is illustrated, highlighting significant relationships of three groups of financial institutions. In descending order of magnitude, they are “Security → Trust” (1.64), “Bank → Insurance” (1.25), and “Security → Insurance” (0.80). Conversely, Figure 2B depicts the to index relationships between financial sectors, revealing three distinct sets of notable spillover relationships. The most pronounced is “Insurance → Bank” (1.51), followed by “Trust → Security” (0.95), and the third is “Insurance → Security” (0.73). From the analysis, it is evident that the securities sector plays a pivotal role as both a recipient and a transmitter for other financial sectors. Simultaneously, the banking and insurance sectors, respectively, play crucial roles as transmitters and receivers. Additionally, the net effect between sectors is calculated, as shown in Table S3. The securities sector, being a sector where all three net spillover indices are positive, exerts the most substantial spillover effect on other financial sectors. Meanwhile, the insurance sector demonstrates a positive spillover effect beyond the securities sector. From a quantitative perspective, while the securities sector displays positive effects on the other three sectors, these effects are relatively moderate. Conversely, the impact of insurance sector on the banking sector is notably stronger compared to the effects on the other sector groups, suggesting a close interdependence between them.

Dynamic analysis of heterogeneous return spillover network

Expanding on the static analysis of the complete dataset, we employ the rolling window method to explore the dynamic properties of the heterogeneous return network among financial institutions. Here, we set the window length to 240 and the step size to 20. Generally, financial markets generate around 20 daily data in a month, resulting in approximately 240 data annually. Taking into account the data length and the specified settings, we obtained a total of 140 heterogeneous return spillover financial networks based on causal inference.

Figure 3 portrays the dynamic evolution of financial system connectedness based on heterogeneous returns. Simultaneously, to dissect the underlying reasons for these shifts, we have annotated significant financial events within the graph. These events encompass individual crises, short-term policies, and ongoing developments.

Figure 3.

Dynamic financial system connectedness based on heterogeneity return

Figure 3 delineates that since 2011, the connectedness of the financial system has been broadly categorized into three stages. The initial trend spans from 2011 to the end of 2016 and is characterized by a fluctuating upward trajectory in connectedness. Specifically, there are four periodic fluctuations in the connectivity of the financial system at this stage, each with different underlying significant causes. The first fluctuation period, from early 2011 to mid-2013, was influenced by the 2008 financial crisis and subsequent rescue policies. The degree of connectedness among financial institutions exhibited continuous enhancement, reaching its zenith around the outbreak of the European sovereign debt crisis in mid-2012, and then slowly declining. The second relatively short fluctuation period, from mid-2013 to mid-2014, was mainly affected by the domestic liquidity crisis in China. The tightening monetary policy of the People’s Bank of China (PBC), coupled with uncertain expectations for the Chinese economy, led to a contraction of credit market activity and a sharp increase in short-term interest rates, particularly interbank lending rates. This caused severe liquidity tensions in the market, with the degree of connectedness between financial institutions rising during this period and then quickly declining after the intervention of the PBC. The fluctuation cycle from mid-2014 to mid-2015 was mainly due to the stock market crash in China. The extremely unstable financial situation increased the connectedness between various institutions in the financial system. The last upward trend in this stage, spanning from mid-2015 to the end of 2016, can be attributed primarily to the more stringent financial regulatory policies implemented by the central government in response to the stock market crash.

The second trend spans from early 2017 to the end of 2019, during which the connectedness of the financial system exhibited a significant downward trend. Notably, in this trend, from early 2018 to mid-2019, the level of correlation between financial institutions displayed intermittent fluctuations. This primarily reflects the financial system’s response to events such as the Sino-US trade war and domestic bond defaults.

The third trend, starting at the end of 2019 and ending at the end of the sample period, witnesses a steeper and more significant increase in the connectedness of the financial system. Clearly, the crisis sentiment endured for a year and a half, stemming from the outbreak of the COVID-19 epidemic and the ensuing uncertainty in the global economy, finance, trade, geopolitics, and other dimensions it introduced. Although market sentiment has somewhat eased after the epidemic, various issues in the global economic recovery, along with the Federal Reserve’s interest rate hikes and the Russia-Ukraine war, have once again pushed up the level of linkage in the financial system.

The aforementioned analysis indicates that the interconnectedness of financial systems, as measured by heterogeneous returns, reflects the evolving dynamics of macroeconomic and capital markets. Similar conclusions can also be found in Ouyang et al. (2023),⁵³ which report that during financial pressures such as the 2015 Chinese stock market turbulence and the 2020 COVID-19 pandemic, the connectedness between financial institutions has sharply increased. However, the impact of short-term policies and individual crises that were examined, such as the implementation of the pilot circuit breaker mechanism in the stock market in early 2016 and the takeover of Baotou Commercial Bank by the PBC in 2019, does not appear to be very substantial. Regarding the circuit breaker mechanism, the overall linkage level showed a brief increase but quickly declined with the end of the policy trial. As for the crisis involving Baotou Commercial Bank, the event did not significantly affect the correlation structure between financial institutions after the central bank took relevant measures, likely due to its relatively low total market value and lower degree of correlation within the Chinese financial system.

Similar to the static analysis, we also obtained the correlation structure among the four financial sectors based on the average spillover table derived from 140 windows. The results are shown in Figure 4. The correlation structure of the two spillover indices in the rolling window sample aligns with the findings from the static analysis. The only difference is that the average information transmission intensity in the dynamic analysis is higher than that in the static analysis (average from index from 0.39 to 1.05, average to index from 0.35 to 0.86). The rolling window method shortens the length of sample data entering the model, allowing for better extraction of local anomalies within a longer time interval. This leads to a variation in the average spillover intensity. The symbol of the net spillover index under dynamic analysis has not changed. Compared to static analysis, the net information transmission ability of the securities sector is further strengthened (from 0.09 to 0.31), while the trust sector is further reduced (from −0.78 to −2.25). Meanwhile, the net spillover from the insurance sector to the banking sector has significantly decreased (from 0.26 to 0.14).

Figure 4.

Connectedness structure between different types of financial institutions based on dynamic analysis

(A) Connectedness structure of from index. Directed edges reveal the direction of spillover between nodes. The thickness of the lines reflects the strength of the directed spillover relationship, with thicker lines indicating stronger connections.

(B) Connectedness structure of to index. Directed edges reveal the direction of spillover between nodes. The thickness of the lines reflects the strength of the directed spillover relationship, with thicker lines indicating stronger connections.

System importance analysis

Measuring the financial shock transmission structure holds particular importance in evaluating systemically important financial institutions (SIFIs). In line with Diebold and Yılmaz (2014),¹⁶ we classify SIFIs as those having a positive net spillover to other institutions (index net > 0) and exerting a substantial impact on other institutions (index to is significant). Considering the time-varying nature of financial institutions, our emphasis lies in identifying SIFIs through a dynamic structural perspective built upon static structure analysis.

In analyzing the systemic importance of financial institutions based on their industry categories, Figure 5 presents the to index of the 34 financial institutions across 140 windows in the form of a boxplot. Clearly, there are notable disparities in the volatility of the importance level among financial institutions. The volatility range for institutions like SGTA, BJYH, ZHPA, and JSYH is below 25, while for HXYH, GDYH, SXZQ, and DBZQ, it exceeds 75. Notably, certain institutions such as PAYH, NBYH, PFYH, GSYH, XNZQ, and SGTA exhibit considerably lower median systemic importance, all below 20. Conversely, institutions like GDYH, CJZQ, GJZQ, XYZQ, and GDZQ have median systemic importance surpassing 50. Specifically, among the five state-owned banks, JSYH demonstrates a narrow range of fluctuations, while the other four experience relatively broader fluctuations. Additionally, JTYH and ZGYH exhibit high median levels, whereas the remaining three have comparatively lower medians. In summary, banking financial institutions generally tend to have lower median systemic importance, securities financial institutions exhibit higher levels, insurance financial institutions fall in the middle, and trust financial institutions have the lowest median importance levels.

Figure 5.

Systemic important index of financial institutions by sector

Note on colors: green = banking institutions, pink = security institutions, purple = insurance institutions, gray = trust institutions.

Considering the profound impact of operational characteristics and equity composition on the systemic importance of financial institutions, we refine the categorization of sample financial institutions based on these factors. In the case of banking financial institutions, they are stratified into three groups: state-owned banks, joint-stock commercial banks, and urban commercial banks. Meanwhile, for non-banking financial institutions such as securities, insurance, and trust, the classification is grounded in the predominant shareholder information, leading to categories such as large state-owned enterprise-controlled, local government-controlled, and private capital-controlled.

Figure 6 presents the to index of the 34 sample financial institutions across 140 windows in the form of a boxplot. The insights derived from Figure 6 are as follows: for banking financial institutions, the analysis based on heterogeneous return yields different conclusions from Wang (2018).⁴¹ The systemic importance of state-owned banks and joint-stock commercial banks is remarkably pronounced, while the urban banks are relatively low. Specifically, when eliminating the influence of market factors on stock returns and considering the causal structure between financial institutions, the heterogeneous returns of state-owned banks reflect the distinctive position of this particular industry group in both the real economy and the financial market. State-owned banks, characterized by substantial asset sizes and early access to national policies, establish connections with numerous financial institutions through interbank operations. This association is, to some extent, mirrored in the inferred causal structure driven by heterogeneous returns. Furthermore, the median ranking of systemic importance among the five state-owned banks aligns with their market value, suggesting a discernible correlation between the systemic importance and key financial indicators of financial institutions. For joint-stock commercial banks, given their status as integral components of large financial holding groups and extensive connections with various financial institutions, they also exhibit high systemic importance. Secondly, concerning non-banking financial institutions, those controlled by large central enterprises tend to display a relatively modest median systemic importance. Following closely are financial institutions controlled by local governments, while those under private enterprise control tend to have comparatively higher systemic importance.

Figure 6.

Systemic important index of financial institutions by attributes

Note on colors: pink = state-owned banks, green = joint-stock commercial banks, purple = urban commercial banks, blue = large state-owned enterprise controlled, purplish red = local government controlled, gray = private capital controlled.

Moreover, Figure 7 depicts the dynamic evolution of the systemic importance of financial institutions with distinct attributes over the sample period. In the realm of banking financial institutions, the trajectories of state-owned commercial banks and joint-stock commercial banks are basically consistent, exhibiting relatively similar mean levels of systemic importance. In contrast, urban commercial banks follow a distinct and notably lower pattern of importance. The non-bank financial institutions display a more consistent evolution between those controlled by local governments and those controlled by private capital. Conversely, financial institutions held by large state-owned enterprises diverge significantly from these two categories. The systemic importance of non-bank financial institutions under private capital ownership is consistently higher than that of their local government-held counterparts. This discrepancy can be attributed to several factors. Banking financial institutions are generally subject to similar levels of policy regulation. Lower-level banks, with relatively limited business coverage, exhibit a lower level of interbank correlation compared to higher-level banks engaged in more comprehensive and in-depth interbank activities. Consequently, urban commercial banks tend to have lower systemic importance. State-owned banks, adhering to higher prudential standards, exhibit average systemic importance levels closer to those of joint-stock commercial banks. In contrast, the governance structures and risk mitigation measures associated with financial institutions held by large state-owned enterprises contribute to a relatively minor systemic risk. On the other hand, non-bank financial institutions controlled by local governments and private capital may face challenges such as a narrower business focus, incomplete corporate governance, and potential moral hazards. Given the intricate business structures of non-bank financial institutions, localized risks have a tendency to escalate into systemic financial risks. Therefore, private capital-controlled non-banking financial institutions often exhibit higher systemic importance in comparison to banking financial institutions.

Figure 7.

Evolution of systemic importance of financial institutions with different attributes

Discussion

The increasing complexity of asset-liability chains within the financial system has prompted a need for insightful analysis of interconnectedness and risk contagion among financial institutions. This study focuses on 34 financial institutions listed on the A-share and H-share markets in mainland China. By leveraging market data, return data are subjected to heterogeneous decomposition, eliminating the influence of common market factors on financial system interconnectedness. The study employs the DAG method to infer causal relationships among financial institutions, incorporating it as a structural matrix in the GFEVD framework to extract the spillover matrix, revealing interconnectedness between financial institutions. Both static and dynamic perspectives of the full sample and rolling sample are employed to analyze the spillover network. Finally, we delve into the systemic importance of various financial sectors and financial institutions, exploring the impact of operational attributes on their systemic importance.

The empirical findings of this study lead to several key conclusions. Firstly, the heterogeneous return spillover network, constructed under the DAG approach, displays noticeable clustering tendencies, with financial institutions within the same sector exhibiting significant spillover relationships. Secondly, both static analysis of the full sample and dynamic analysis of the rolling sample emphasizes the pivotal role of the securities sector in the financial system. The influence of the insurance sector on the banking sector is also prominently observed. Thirdly, the dynamic analysis of the financial network reveals time-varying structural characteristics that align with macroeconomic development, displaying sensitivity to internal and external shocks. Fourthly, the evaluation of SIFIs indicate that market size is not the sole determinant of systemic importance. Further categorization by financial institution type and operational attributes reveals notable distinctions between banking and non-banking financial institutions. Specifically, state-owned commercial banks and joint-stock commercial banks hold higher importance in the banking sector, while in the securities sector, significance is attributed to securities institutions controlled by local governments and private capital.

Systematic financial risk is a crucial consideration in macroprudential management. Understanding the interconnections within financial systems and determining the systemic importance of financial institutions holds significant importance for preventing systemic financial risks. The insights gained from this research can aid regulatory agencies in maintaining a balanced regulatory environment, promoting the effective functioning of financial markets, and minimizing the operational costs of financial institutions.

Limitation of the study

The limitations of this study include the following aspects: first, due to the impact of the listing time of financial institutions, we have only studied some of them. Although the total market value of these samples is quite representative, further inclusion of more institutions can still yield more insightful conclusions. Second, our data only considers market data and further research can also combine financial statement data, such as interbank business information. Third, we do not model financial networks from the perspective of high-dimensional or high-order networks. This may result in the study not being able to comprehensively examine the attributes of financial institutions.

STAR★Methods

Key resources table

REAGENT or RESOURCE	SOURCE	IDENTIFIER
Deposited data
Market data, including the ticker, daily opening, highest, lowest and closing price of 34 financial institutions	CSMAR database	https://data.csmar.com/
Classification of 34 financial institutions	CSMAR database	https://data.csmar.com/
Detailed information of 34 financial institutions	CSMAR database; Tianyancha	https://data.csmar.com/; https://www.tianyancha.com/; Table S4
Market data, including the daily opening, highest, lowest and closing price of CSI300	CSMAR database	https://data.csmar.com/
Fama-French factors, include SMB, HML, RMW, and CMA	CSMAR database	https://data.csmar.com/
DR007	WIND database	https://www.wind.com.cn/portal/zh/Home/index.html
CAPM regression	Hale & Lopez (2019)78	https://doi.org/10.1016/j.jeconom.2019.04.027
DAG	Sprites et al. (2001)69	Causation, prediction, and search. MIT Press.
GFEVD	Diebold & Yılmaz (2012, 2014)15,16	https://doi.org/10.1016/j.ijforecast.2011.02.006; https://doi.org/10.1016/j.jeconom.2014.04.012
Data generated by this paper (Descriptive statistics of the heterogeneity returns of the 34 financial institutions)	This paper	Table S1
Data generated by this paper (Full-sample inter financial institution spillover structure based on decomposition return)	This paper	Table S2
Data generated by this paper (Net spillover relationships between four financial sectors)	This paper	Table S3
Data generated by this paper (Descriptive statistics of the returns of the 34 financial institutions)	This paper	Table S5
Data generated by this paper (Descriptive statistics of control variables)	This paper	Table S6
MATLAB 2021b	This paper	https://ww2.mathworks.cn/en/products/new_products/release2021b.html
RStudio 2023.09.1 + 494	This paper	https://dailies.rstudio.com/version/2023.09.1+494/
Tetrad 7.5.0	This paper	https://github.com/cmu-phil/tetrad

Resource availability

Lead contact

Further information and request for resources should be directed to and will be fulfilled by the lead contact, Benshuo Yang (yangbenshuo@gmail.com).

Materials availability

This study did not generate new unique materials.

Data and code availability

• •This paper analyzes existing, publicly available data which are listed in the key resources table.
• •Code for the analysis was written in MATLAB and R, which can be requested from the lead contact.
• •Any additional information required to reanalyze the data reported in this paper is available from the lead contact upon request.

Method details

Data sources

For this study, the dataset encompasses the daily opening, highest, lowest, and closing prices of financial institutions listed on the Shanghai Stock Exchange (SSE) and Shenzhen Stock Exchange (SZSE) in China. The data spans from January 4, 2011, to June 30, 2023. The choice of the starting point is anchored in the listing date of the Agricultural Bank of China (ABC), one of China’s five major state-owned banks, which underwent an initial public offering at the end of 2010. Consequently, January 2011 is chosen as the starting point for our sample.

The sample institutions selected for this study adheres to industry classification standards and established literature, employing the following criteria: first, all financial institutions must be listed on the SSE and the SZSE from 2011 to 2023. Then, institutions that do not meet the following criteria are excluded: (1) maintaining a financial classification during the period, (2) possessing an annual average observation value of no less than 200, (3) having stocks that never received special treatment. Following these criteria, a total of 34 listed financial institutions are selected. Detailed information on these stocks, including the ticker, full name, abbreviation name, classification, and attribute can be found in Table S4. The price sequences for these stocks are extracted from the CSMAR database, with the pre-reinstated treatment applied. The yields of these stocks are computed using the logarithmic growth rate method, and the results of their description statistical analysis are presented in Table S5.

Table S5 displays the minimum, maximum, mean, and standard deviation values for the 34 financial institutions. Additionally, an analysis of the distribution characteristics and stability of each sequence is conducted. Due to the implementation of the limit-up/limit-down system, the returns of each stock tent to fluctuate within the range of [-10%, 10%]. The average return of the 34 stocks suggests that, during the sample period, the average return of most financial institutions is positive. However, negative average returns are observed among non-banking financial institutions. The standard deviation of all sequence hovers around 0.02, with banking financial institutions generally exhibiting values below 0.02. Conversely, non-banking financial institutions tend to have standard deviations above 0.02. Interestingly, our analysis reveals that among the 34 sample stocks, those with higher average returns tend to exhibit smaller standard deviations. The Augmented Dickey-Fuller (ADF) test conducted on the sequences rejects the assumption of unit roots, indicating that all sequences are stationary. Furthermore, normal distribution tests using Kolmogorov-Smirnov (KS) statistics reject the hypothesis that the samples follow a normal distribution. Hence, these sequences do not conform to a normal distribution.

The price of stocks is influenced by various factors, including macroeconomic factors, company operations, and investor decision-making. To more accurately understand the relationship between sample financial institutions, an effective method is to decompose their returns and obtain heterogeneous components. Following the approach of Hale & Lopez (2019),⁷⁸ we utilize the return of the China Securities Index (CSI) 300 Index to control for market returns, considering that the selected samples come from two markets. The benchmark interest rate is represented by the 7-day repo rate for interbank deposit financial institutions using interest rate bonds as collateral (DR007). Additionally, Fama-French factors are employed to measure market risk levels, encompassing small minus large (SMB), high minus low (HML), robust minus weak (RMW), and conservative minus aggressive (CMA). The data for CSI300 and Fama-French factors data are sourced from the CSMAR database, while DR007 data are obtained from the Wind database. The sample range of these indicators aligns with the selected financial institutions. Descriptive statistical test results for each variable are presented in Table S6.

Heterogeneous return decomposition

The CAPM regression proposed by Hale & Lopez (2019)⁷⁸ is employed to decompose the yields of the sample financial institutions in the following manner:

$$r_{i,t}={\alpha }_i+{\beta }_{i,1}{r}_t^{CSI}+{\beta }_{i,2}{r}_t^{DR007}+{\beta }_{i,3}SM{B}_t+{\beta }_{i,4}HM{L}_t+{\beta }_{i,5}RM{W}_t+{\beta }_{i,6}CM{A}_t+{\epsilon }_{i,t}$$ (Equation 1)

where $r_t^{CSI}$ is the return of the CSI300, $r_t^{DR007}$ is the data of DR007, and the rest control variables are Fama-French factors. ${\beta }_i=\left[{\beta }_{i,1},{\beta }_{i,2},{\beta }_{i,3},{\beta }_{i,4},{\beta }_{i,5},{\beta }_{i,6}\right]$ measures the impact of the common factors on the return of stock i, and the residual value represents the heterogeneous part of stock i’s return. A rolling window is implemented to introduce time-varying characteristics to the coefficient ${\beta }_i$. As all variables in Equation 1 have the same frequency, we utilize the ordinary least squares (OLS) to estimate.

Directed acyclic graph

The DAG approach is a data-driven method employed for identifying causal relationships. It discerns contemporaneous causal relationships among variables by scrutinizing their correlation coefficients. A typical DAG is comprised of nodes and directed edges, where nodes denote distinct variables, and directed edges indicate the direction and dependency of contemporaneous causality between variables. Prior to conducting a DAG analysis, it is necessary to establish a VECM as depicted in Equation 2.

$$\Delta X_t=\alpha {\beta }^{\prime }{X}_{t-1}+\sum _{i=1}^{p-1}{\tau }_i{X}_{t-i}+{\epsilon }_t$$ (Equation 2)

where $X_t$ is a column vector with a dimension N at time t. $\Delta$ represents difference. $\alpha {\beta }^{\prime }$ represents the parameter matrix, where $\alpha$ is the parameter adjustment matrix and $\beta$ is the cointegration vector matrix. Generally, ${\beta }^{\prime }{X}_{t-1}$ is referred to as the error correction term, representing the long-term equilibrium relationship between variables. This step ensures accurate estimation of the correlation coefficients between variables.

In empirical research, the PC algorithm⁶⁹ is widely employed for generating DAGs. This algorithm initially identifies potential causal relationships among variables by examining the correlation and partial correlation coefficients among disturbance terms. It then establishes undirected edges connecting variables, forming an undirected complete graph. If the correlation coefficient between two variables is 0, the undirected edge between them is is eliminated. Subsequently, for a system with N variables, the PC algorithm calculates partial correlation coefficients from 1^st order to (N-2)^nd order. If the partial correlation coefficient between variables is 0, the corresponding undirected edge is removed. Finally, for the remained undirected edges, the Fisher’s Z-statistic is utilized to ascertain the dependency and directionality of contemporaneous causal relationships between variables. The calculation of Fisher’s z statistic is as follows:

$$z\left[\rho \left(i,j|k\right),N\right]=\frac{1}{2}\sqrt{N-\left|k\right|-3}\ln \left\{\left[\left|1+\rho \left(i,j\right)|k\right|\right]{\left[1-\rho \left(i,j\right)|k\right]}^{-1}\right\}$$ (Equation 3)

where N is the number of variables. $\rho \left(i,j|k\right)$ represents the partial correlation coefficient between variables i and j conditioned on the variable set k. $\left|k\right|$ represents the number of variables included in the variable set k. Let $r\left(i,j|k\right)$ be the sample partial correlation coefficient. If variables i, j, and k follow a normal distribution, then $z\left[\rho \left(i,j|k\right),N\right]-z\left[r\left(i,j|k\right),N\right]$ follows a standard normal distribution.

Spillover index approach

For a VAR model with N variables as:

$$X_t=\alpha +\sum _{i=1}^p{\mathrm{\Phi }}_i{X}_{t-i}+{\epsilon }_t$$ (Equation 4)

where $X_t$ is a column vector of stocks return with a dimension N at time t. ${\epsilon }_t\sim iid\left(0,\mathrm{\Sigma }\right)$, and $\mathrm{\Sigma }$ is the covariance matrix. However, the VAR model often presents challenges in directly interpreting parameter estimates due to the excessive number of estimated parameters and intricate interactions between variables. To overcome this issue, greater emphasis is typically placed on considering alternative representations, such as the moving average representations of these coefficients, or other variants like impulse responses or variance decompositions. Consequently, the original VAR model is transformed into the following vector moving average (VMA) model:

$$X_t=\sum _{i=0}^{\infty }{A}_i{\epsilon }_{t-i}$$ (Equation 5)

where $A_0$ is a unit matrix with dimension N∗N, $A_i={\mathrm{\Phi }}_1{A}_{i-1}+{\mathrm{\Phi }}_2{A}_{i-2}+\cdots +{\mathrm{\Phi }}_p{A}_{i-p}$ when $i>0$, and $A_i=0$ otherwise. Then, the fraction of the H-step forecast error variance of the variable $x_i$ explained by variable $x_j$ can be calculated as:

$${\theta }_{ij}^g\left(H\right)=\frac{{\sigma }_{jj}^{-1}\sum _{h=0}^{H-1}{\left(e_i^{\prime }{A}_h\mathrm{\Sigma }{e}_j\right)}^2}{\sum _{h=0}^{H-1}{e}_i^{\prime }{A}_h\mathrm{\Sigma }{A}_h^{\prime }{e}_j}$$ (Equation 6)

where $\mathrm{\Sigma }$ is the covariance matrix of residuals of model (4), ${\sigma }_{jj}$ is the j^th diagonal element of $\mathrm{\Sigma }$, and $e_i$ is a vector where only the i^th element is 1 and the other elements are 0. As in the VAR model, the sum of the variance decomposition result is not always equal to 1, we need to standardize each row as follows:

$${\tilde{\theta }}_{ij}^g\left(H\right)=\frac{{\theta }_{ij}^g\left(H\right)}{\sum _{j=1}^N{\theta }_{ij}^g\left(H\right)}$$ (Equation 7)

Then, we get the measure of the information spillover from variable j to variable i as ${\tilde{\theta }}_{ij}^g\left(H\right)$. On this basis, we can further calculate the total impact of all other variables on variable i ($S_{i\leftarrow }^g\left(H\right)$, ‘from’), the total effect of variable i on all other variables ($S_{i\to }^g\left(H\right)$, ‘to’), and the net effect of variable i on all other variables ($S_i^g\left(H\right)$, ‘net’) as:

$$S_{i\leftarrow }^g\left(H\right)=\frac{\sum _{j=1,i\ne j}^N{\tilde{\theta }}_{ij}^g\left(H\right)}{\sum _{j=1}^N{\tilde{\theta }}_{ij}^g\left(H\right)}\times 100$$ (Equation 8)

$$S_{i\to }^g\left(H\right)=\frac{\sum _{j=1,i\ne j}^N{\tilde{\theta }}_{ji}^g\left(H\right)}{\sum _{j=1}^N{\tilde{\theta }}_{ji}^g\left(H\right)}\times 100$$ (Equation 9)

$$S_i^g\left(H\right)=S_{i\to }^g\left(H\right)-S_{i\leftarrow }^g\left(H\right)$$ (Equation 10)

The total connectedness can be expressed as

$$S^g\left(H\right)=\frac{\sum _{i,j=1,i\ne j}^N{\tilde{\theta }}_{ij}^g\left(H\right)}{\sum _{i,j=1}^N{\tilde{\theta }}_{ij}^g\left(H\right)}\times 100$$ (Equation 11)

Published: July 8, 2024