Discovering Systemic Risks of China's Listed Banks by CoVaR Approach in the Digital Economy Era

: The world has entered the digital economy era. As a developing country, China's banking industry plays an important role in the financial industry, and its size ranks first in the world. Therefore, it is of great significance to study the systemic risks of China's banks in the digital economy era. We first compare the traditional indicator approach and the market-based approach theoretically, and Conditional Value at Risk (CoVaR) model, a market-based approach, is considered to be an efficient way to discover systemic risk in different perspectives. Based on static and dynamic models, we evaluate the contributions of sixteen China's listed banks to the systemic risk. Furthermore, we model bank exposures, extend the models by considering extreme circumstance, and incorporate the effects of Fintech and non-bank financial institutions. The results show the levels of systemic risks and the corresponding systemic importance rankings vary in different time periods. We find that the contributions of some small banks to systemic risk are even higher than some big banks during the sample period. Moreover, the big banks face less risks than most of the small banks when the banking system is in distress. We make suggestions for improving financial supervision and maintaining financial stability.


Introduction
The world has entered an era of digital economy. Tapscott originally proposed the concept of the digital economy [1][2]. With the development of science and technology, the understanding of the digital economy has become clearer. According to a G20 report, the digital economy is defined by the economic activities where the digitized information and knowledge are considered as critical production factors with the development of modern information network, which boosts the growth and optimizes the economic structure [3]. The International Monetary Fund (IMF) defines a broad form of digital economy by the digitalization in all sectors of the economy. The use of the Internet could be considered as an exact example of the digitalization, and the 21 st century is an era of the digital economy. During the period, a series of economic activities that incorporate data and the Internet grow quickly and change the society [4]. In the digital economy era, Fintech, a combination of finance and technology, emerges and is playing an increasingly important role. Furthermore, the traditional concept of financial supervision needs to be developed and updated in the digital economy era.
In the digital economy era, for the financial industry, Fintech brings opportunities as well as challenges, and the supervision of systemic risk should be developed further. Due to the significant externality and the strong contagion effect of systemic risk, there is a strong need to strengthen the financial supervision of systemically important financial institutions (SIFIs) and forestall systemic risk, especially in the post-crisis era. Since the outbreak of the international financial crisis in 2008, there has been a persistent reform of the global financial regulatory system. One important part of this reform is to improve the regulatory framework and fortify the supervision of SIFIs. The international financial crisis shows that big financial institutions contribute seriously to the systemic risk, which promotes the reform of financial supervision, aiming at preventing the risk of the "too big to fail" financial institutions. However, as Greene et al. pointed out, an institution smaller in size did not indicate that it was less risky. They took an example of the event of Long-Term Capital Management (LTCM). An institution with relatively small size, could affect financial stability [5].
In the digital economy era, with the booming development of Fintech, we could focus on the systemic risk that a big institution causes, and we should also consider the systemic risk that may be induced by a small institution. In the era of the digital economy, the development of the information technology accelerates the speed for customers to enjoy financial services, and they have access to more and more diversified and even customized financial products. However, the risk will not disappear in the digital economy era. Compared with big institutions with relatively strong supervision, small institutions may be more sensitive to the financial environment and take more risks in terms of financial innovations, making them more prone to accumulating risk. Moreover, the digital economy era enables the institution to transfer the risk to the financial system faster and more seriously with possibly a more inconspicuous manner than before. Therefore, the importance of assessing the systemic risks of all institutions, especially the small institutions, should be precisely measured and should not be overlooked.
The Chinese government has always been attaching great importance to systemic risk prevention and ensuring financial stability. In recent years, the understanding of the significance for the financial sector to better prevent systemic risk has reached a new height. As Chinese president Xi Jinping pointed out in the National Financial Work Conference in 2017, finance is the lifeblood of the real economy. Therefore, a new committee, namely the State Council Financial Stability and Development Committee (SCFSDC), was announced to be set up in the conference. Further, the role of the central bank in China (People's Bank of China, PBC) in macroprudential management and forestalling systemic risk should be strengthened [6]. In the report of the 19 th National Congress, improving the financial supervision system and guarding against systemic risk were set as tasks for economic reform [7]. In 2018, the PBC, the CBIRC (China Banking and Insurance Regulatory Commission), and the CSRC (China Securities Regulatory Commission) jointly released a guideline for improving the supervision of SIFIs. The aims of this guideline were to recognize SIFIs, enhance the financial regulatory system, and maintain financial stability [8]. In 2019, PBC established the Macroprudential Policy Bureau (MPB) to evaluate and identify SIFIs [9]. The PBC also paid more attention to the financial supervision in the digital era and launched the pilot of supervision on Fintech innovations, aiming at improving the professionalism, the unity, and the penetration of the financial supervision [10].
In this paper, we aim to measure the systemic risks of China's banks in the digital economy era. The reasons are as follows. First, China is a bank-based country, and the banking industry plays an important role in its financial system. In China's financial system, because of a high proportion of the banking industry, the systemic risk of the financial system is likely to be contributed most to by the banking industry [11]. In addition, according to the latest report of the Financial Stability Board (FSB), four Chinese banks (Bank of China (ZGYH), Industrial and Commercial Bank of China (GSYH), Agricultural Bank of China (NYYH), and China Construction Bank (JSYH)) are included in the list of global systemically important banks [12]. Moreover, as a developing country, China's banking industry has seen rapid growth in terms of scale. Furthermore, the total assets of the Chinese banking industry in 2018 were ranked first in the world [13,14]. Besides, we collect the data of China's top 25 banks and the top 10 banks in the world in 2018, according to the report released by "The Banker" [15] on 30 June 2019 (see Table 1 and Table 2). China's banks play an important role in the world, and China's "Big Four Banks" (GSYH, JSYH, NYYH, ZGYH) topped the list in both 2018 and 2019 [16]. The tier 1 capital of China's "Big Four Banks", three banks in the United States, a bank in the United Kingdom, and a bank in Japan account for 51.915%, 34.232%, 6.950%, and 6.903% of the total Tier 1 capital of the top 10 banks in the world. Additionally, there are currently a few studies that measure the systemic risk in developing economies according to Khiari and Ben Sassi [17]. Therefore, our research on developing countries could be interesting and enrich existing studies. Thus, it is of great significance to study the systemic risks of China's banks, not only for financial stability in China, but also for financial stability throughout the world, as the Chinese banking industry plays an more and more important role in the world.  1 The "Abbr" and "Bank" refer to the acronyms of a bank's Chinese pinyin names and the abbreviation of the full name of a bank in English; the "WR" and "CR" respectively represent the rank of a bank in the world and in China; the unit for the Tier 1 capital is one billion dollars; the "Type" refers to the ownership type of a bank, moreover, "A1", "A2", and "A3" respectively refer to state-owned commercial banks (SOE banks), joint-stock commercial banks (JOI banks), and city commercial banks (CCB banks). The "Bank" refers to the abbreviation of the full name of a bank in English; the "WR" represents the rank of a bank in the world; the unit for the Tier 1 capital is one billion dollars.
In this paper, the main research questions are as follows. How can we effectively measure the contribution of each bank to the systemic risk of the banking industry? Is the systemic risk changing over time? For China, do the systemically important banks change, and which bank contributes the most to the systemic risk? We first build a series of Conditional Value at Risk (CoVaR) models to measure the systemic risks in the Chinese banking industry with a static and dynamic model through overall analyses and year-by-year analyses. We further extend the study to analyze the contribution of a bank in extreme circumstance to the systemic risk, and modify the dynamic model by incorporating the roles of Fintech and non-bank financial institutions. Another type of systemic risk, namely bank exposure, is also studied. Furthermore, we compare the results of the traditional indicator approach and the market-based CoVaR models, and we provide possible reasons and make suggestions for improving financial supervision and maintaining financial stability.
Currently, the systemic risk evaluation approaches for identify the systemic importance of the SIFIs, could be divided into two categories: the indicator approach and the market-based approach. The indicator approach is built based on judgment from experience, which assesses the systemic importance of a financial institution from different perspectives [18]. Based on the report of the Basel Committee on Banking Supervision (BCBS) [19,20], we illustrate the indicator system with Figure 1, which contains the main indicators used to access systemically important global and domestic banks. This system comprises four or five major categories of indicators, and each major category consists of several subindicators. When measuring the systemic importance of a bank, we first calculate each subindicator and derive the index of each major category with equal weight, and then we obtain the systemic importance index with equal weight. In comparison with the indicator approach, the market-based approach directly measures the contribution of a financial institution to the whole financial system based on daily or quarterly data derived from financial markets, and identifies the systemically important financial institutions via the quantitative results. This method can capture more characteristics of financial institutions based on the market data than the traditional indicator approach. We will discuss the difference of the results based on the indicator approach and the market-based CoVaR model in Section 3.3.
The core model in this paper, "CoVaR", is an abbreviation for "Conditional Value at Risk", which has been increasingly applied in the field of systemic risk and can be used for analyzing the systemic risk in different perspectives. The idea of CoVaR was first proposed by Adrian and Brunnermeier [21]. This model has experienced several years of development and was published in the 12 th issue of American Economic Review in 2016. The basic concept and methodology of the CoVaR were originally built based on Value at Risk (VaR), which measures the maximum loss of a financial institution at a certain confidence level. The prefix of CoVaR, namely "Co", shows that "VaR" is conditional. CoVaR is defined as the VaR of the financial system conditional on a financial institution, while ΔCoVaR refers to the difference between the CoVaR when the institution is in distress and the CoVaR when the institution is in a normal state, which captures the contribution of the institution to the systemic risk of the financial system [22].
The CoVaR model, a market-based approach, is chosen as the core model for the following reasons. First, the traditional supervision focuses on the individual risks of financial institutions using risk indicators, including VaR, but it does not consider the risk at a system-wide level, especially the spillover effect of an institution to the system. CoVaR can efficiently measure the contributions of the institution to the systemic risk. As Adrian and Brunnermeier [22] pointed out, there are two situations in the banking industry: (1) There are some large banks in the banking system, and these banks are highly interconnected. When they are in distress, the risks transfer to the other banks, and cause a system-wide effect in the industry. (2) There are some small banks, but they may cause a herd effect and possibly engender a crisis. The spillover effect of a bank on systemic risk can be modeled with CoVaR. Second, the CoVaR model can measure the contribution to the system when a financial institution is in distress and in a normal state. It can also evaluate the exposure of an institution when the system is in distress (i.e., when a crisis breaks out). Third, we apply the CoVaR model based on data from the financial markets and can capture the changes in systemic risk contributions dynamically.
As the CoVaR model is built based on data from financial markets, it has been applied in an increasing number of studies, domestically and internationally. Drakos and Kouretas measured the contribution of listed financial institutions to systemic risk based on the daily data of the United Kingdom (UK) and the United States (US) financial institutions from 2000 to 2012. Based on the data, the authors found that all financial institutions had increased their contributions to systemic risk in the wake of the global financial crisis. In addition, for UK, banks contributed the most to the systemic risk; for US, the financial institutions that contributed the most to the systemic risk were US domestic banks [23]. Deng measured the risk spillover effects of financial institutions by using the CoVaR model based on quarterly data. Deng's study suggested that during the sample period of 2010-2017, when the banking industry was in distress, the spillover effect on the whole financial market was stronger than those of the other types of the financial institutions. The study also measured the spillover effect when other financial industry is in distress. The results showed that the Chinese banking industry could withstand external shocks from other financial industries well, and the value of the risk spillover effect was not high [24]. Using the CoVaR model, Wang et al. used 14 banks as a sample. The research showed that the sizes of HXYH and XYYH were not large compared to the state-owned banks in China (in this paper, we denote the banks by the acronyms of the Chinese pinyin names for brevity). Meanwhile, the results showed that the risk spillover effects of these two banks on the Chinese banking system are even higher than those of the state-owned banks, including ZGYH and GSYH [25]. Verma et al. built a CoVaR model to analyze the Indian banking industry. Their study was based on the weekly frequency data of Indian banks, including state-owned banks and private banks, and they found that the state-owned banks were more stable in the times of crisis than private banks [26]. Girardi and Ergün analyzed the systemic risk contributions of 74 financial institutions during the sample period from 2000 to 2008 with a dynamic CoVaR model. They found that depository institutions contributed more to the systemic risk than other financial institutions. Moreover, they observed a positive and statistically significant effect of size on ΔCoVaR [27]. López-Espinosa et al. measured the systemic risk contributions of international large banks with the data spanning from 2001 to 2009, and the results showed that the average systemic risk contributions is higher in the crisis times than those in the pre-crisis times [28]. In addition, CoVaR can also be used in the related areas (e.g., the spillover effect in the debt market). Zheng et al. [29] found that since 2006, the liquidity risk indicators of big banks including ZGYH, JSYH, GSYH and JTYH had been relatively stable. The risk indicators of the joint-stock banks were highest, while the fluctuations of the risk indicators of the city commercial banks were also high. They used the CoVaR model to analyze the spillover effect of the liquidity risk of banks with the quarterly data of 14 banks derived from financial reports. The results showed that the joint-stock banks contributed the most to the risks of the whole banking system. The authors believed that for the joint-stock banks, their motivations to pursue profit are stronger than those of the other banks, and they are thus more active in the interbank market, thereby contributing more risk. Reboredo and Ugolini modeled the systemic risk of the European sovereign debt markets during the period of 2000-2012 with the CoVaR model. They found that there was a similar trend of the systemic risk across all debt markets [30]. Bernal et al. pointed out that ΔCoVaR is a useful method, which assesses the effect of the financial distress of a single financial institution. They applied the method in measuring the spillover effect of the bond market in a country to the Eurozone bond market [31].
We contribute to the existing studies in several perspectives. First, in this paper, based on the daily data derived from financial markets, we build a series of CoVaR models and calculate the CoVaR when the sample banks are in a normal state or in distress. On this basis, we derive their contributions to systemic risk, namely ΔCoVaR. Typically, the papers related to systemic risk measurement using CoVaR focus on an overall analysis of the banks during the sample period. We introduce a year-by-year analysis, which can capture the dynamic changes of systemic risks and the rankings of systemic importance. Second, for the first time, we jointly build static CoVaR, dynamic CoVaR, and Exposure CoVaR models for analyzing China's listed banks. The contributions can be subdivided into three parts: (1) Based on the daily data derived from the financial markets, the traditional static CoVaR model is constructed to measure the systemic risk contribution (ΔCoVaR) of the sample banks with the combination of a year-by-year analysis and an overall analysis. (2) Considering the "time-varying" characteristics of the returns of the banking system and banks, seven kinds of state variables are introduced to establish a dynamic CoVaR model. (3) On the basis of the dynamic CoVaR model, the role of the return series of the banking system and those of a bank in the model are reversed, and the Exposure CoVaR model is established to calculate the risk exposure of a single bank when the whole banking system is unstable. Third, we also consider the extreme circumstance that a bank faces by using a 1% quantile. This further enrich the analysis of China's banks' systemic risk contribution. Fourth, we take the effects of Fintech and non-bank financial institutions into considerations, and modify the base model. Fifth, we conduct the indicator approach, and analyze the results based on the indicator approach and the CoVaR models by introducing Spearman's rank correlation. The results of statistical tests enrich the existing studies. We provide possible explanations and suggestions for improving financial supervision and maintaining financial stability.
The rest of the paper is structured as follows. In Section 2, we present the market-based systemic risk estimation methodologies including the static, dynamic, and exposure CoVaR models, and make an introduction of the sample. In Section 3, we first model the contribution of each bank to the systemic risk with the static CoVaR model. Then, we introduce the state variables, and the estimation process becomes more dynamic with the dynamic CoVaR model. Furthermore, we extend the research with a series of models aiming at measuring the systemic risk contribution when a bank is in extreme circumstance, another type of the systemic risk (the bank exposure), and the contribution to systemic risk which considers the effects of Fintech and non-bank financial institutions. We also analyze the differences of the results based on the indicator approach and the CoVaR approach. Section 4 concludes the paper.

Static CoVaR model
The traditional static CoVaR model (hereinafter we also use "static model") is built based on the concept of VaR. According to Adrian and Brunnermeier [22], the VaR of bank i can be defined as follow. In other words, VaR is defined as the th quantile of the conditional probability distribution.
The CoVaR of the financial system represents the maximum loss it experiences when bank i faces events, namely . Recalling Equation (1), we can define the CoVaR as follow. Furthermore, if the bank is in distress, =5; if the bank is in a normal state, =50.
where i and bank refer to bank i and the whole banking system. The stock prices and stock index series are treated with natural logarithmic transformation. is a series of the returns of the stock prices of bank i.
is a series of the returns of the banking system index, and the index is constructed by the average of the stock prices of the sample banks weighted by their lagged market values.
In Equation (3), ΔCoVaR is defined by the difference between the two CoVaRs: the one under distress and the one in a normal state. ΔCoVaR reflects the contribution of a bank to systemic risk, and the more a bank contributes, the more important the bank is in the banking system. In other words, the ranking of a bank in terms of its ΔCoVaR can be considered as a ranking of systemic importance.
Based on [22], to estimate ΔCoVaR, we need to build a quantile regression model with two variables ( and ) and use a 5% quantile, as shown in Equation (4). , , and are used to denote the intercept, coefficient, and stochastic disturbance of the regression, respectively. Second, we predict with a of and let =5 and =50. Then, we derive the two CoVaRs in Equation (3) and calculate ΔCoVaR.
In this paper, for simplicity, we use the acronyms of the sample banks' Chinese pinyin names as their abbreviations. In addition, as CoVaR and ΔCoVaR are two important elements in the following models, we simply use "static CoVaR model" and "dynamic CoVaR model" in the following sections. Furthermore, when we discuss the results, we use "CoVaR" or "ΔCoVaR" to analyze the sample banks more precisely. In a year-by-year analysis, the data on the specific year are used for computation and we use all the data for measurement in the overall analysis. Because the CoVaR of a bank in distress and ΔCoVaR are small and not positive, we use their absolute values and magnify the values 1000 times in the following charts of all CoVaR models for better comparison and illustration. In addition, all results of CoVaRs and ΔCoVaRs are rounded to two decimal places.

Dynamic CoVaR model
The dynamic CoVaR model (hereinafter we also use "dynamic model") is built based on the static CoVaR model. As Scaillet [32] pointed out, an appropriate model for measuring risk should consider the time-varying market conditions. By introducing a series of lagged state variables, and are considered as the functions of the state variables (namely ) and become time-varying. Namely, the two variables change with the state variables. Thus, the time-varying characteristics can be captured and the suffix "t" is added to and . According to [22], the calculation procedures can be summarized as follows.
First, we use quantile regression to analyze the relationship between the state variables and the bank stock returns (see Equation (5)). , , and respectively denote the intercept, coefficient, and stochastic disturbance. Let the quantile be 5% and 50%, we then derive the VaRs for a bank in distress and in a normal state, respectively.
Second, we introduce the state variables into Equation (4) and modify the equation (see Equation (6)). Hereinafter, since the denotations of the intercept and the other terms of the regression are similar to those in Equation (4) and (5), which are easy to understand, the introduction of the denotations is omitted for brevity. Following the similar procedure used in the static CoVaR model, we derive the CoVaRs that are in two states based on Equation (6): Third, ΔCoVaR is defined as the difference between two CoVaRs that contain the same parts including the terms of the intercept and state variables. Therefore, the calculation of ΔCoVaR can be further simplified as the product of the coefficient of regression and the difference between two VaRs.
As Adrian and Brunnermeier [21,22] suggested, the selection of state variables should be liquid and tractable. They should also accurately capture the time-varying characteristics of the returns in different states. On this basis, we consider both the data availability of the related indicators in China and the corresponding studies (see [33][34][35][36]). Then, the state variables system is constructed with variables from seven perspectives, as shown in Table 3.

Exposure CoVaR model
The Exposure CoVaR model (hereinafter we also use "exposure model") can be considered as an extension of the dynamic CoVaR model, but with a focus on the maximum loss (i.e., the risk exposure) of a bank when the whole banking system is in a state of financial instability. By changing the role of the banking system and the bank in the dynamic CoVaR model, we can measure the exposure that a bank faces when there is a system-wide risk in the banking industry.
First, using quantile regression, we estimate the parameters in Equation (7) and derive the VaRs in two states (the bank in distress or in a normal state) with the predicted value of the regression. Second, according to the estimation of Equation (8) and the concept of CoVaR, we derive the Exposure CoVaRs based on the two VaRs, and the Exposure ΔCoVaR is the product of the coefficient of regression and the difference between two VaRs:

Sample description
As the IMF [4]  banks had a sufficient quantity of data for the sample period. Therefore, they were chosen as the sample. Table 4 contains the fundamental information of the banks. According to the public-disclosed statistical data released by the CBIRC, by the end of the fourth quarter of 2018, the total assets of commercial banks in China reached 209.9638 trillion yuan. As seen in Table 4, the total assets of the sample banks reached 151.5277 trillion yuan, which comprised a large proportion (72.17%) of the banking industry. Therefore, this sample is very representative.  1 The "Abbr" refers to the acronyms of a bank's Chinese pinyin names; the "SE" refers to the stock exchange where a bank is listed, moreover, "SZ" and "SH" refer to the Shenzhen Stock Exchange and the Shanghai Stock Exchange, respectively. the "Type" refers to the ownership type of a bank, moreover, "A1", "A2", and "A3" respectively refer to state-owned commercial banks (SOE banks), joint-stock commercial banks (JOI banks), and city commercial banks (CCB banks); the "IPO Date" refers to the date of the initial public offering (IPO) of a bank; the unit for the total assets is 100 million Chinese yuan. Figure 2A shows the measurements of the CoVaR and ΔCoVaR of the listed banks in 2011. For a list of the banks corresponding to all abbreviations, see Table 4. From the perspective of CoVaR, when the bank is in distress (in other words, when the stock return of the bank lies in the 5% quantile), the loss of the banking system when NJYH is in distress, is highest, with the value of CoVaR reaching 25.15. The CoVaRs of XYYH, ZSYH, PAYH, and BJYH are also higher than those of the other banks, and both their values exceed 24. All the banks are CCB banks or JOI banks. In terms of SOE banks, the CoVaR of GSYH ranks 1 st , with a value of 23.88, and it ranks 6 th among the sample banks. In addition, the CoVaRs of the other SOE banks (including NYYH, JTYH, ZGYH, and JSYH) are, respectively, 23 37. We find that, there is only one SOE bank among the seven banks, while the other banks are JOI or CCB banks. Therefore, the results of CoVaR and ΔCoVaR show that the maximum loss of the financial system when each SOE bank is in distress is not higher than that of some JOI and CCB banks; moreover, the contribution of a SOE bank to systemic risk is not bigger than those of JOI and CCB banks.

Year-by-year analysis
According to Figure 2B, the industrial averages of the CoVaRs and ΔCoVaRs of the sample banks in 2012 are lower than those in 2011. The CoVaR of GDYH ranks 1 st (19.10). Further, the CoVaRs of ZXYH, JSYH, HXYH, MSYH, NJYH, XYYH, and JTYH rank in the top 50% in the industry. From the perspective of ΔCoVaR, GDYH also ranks 1 st (12.10). The ΔCoVaRs of JSYH, ZXYH, HXYH, GSYH, JTYH, and XYYH rank from 2 nd to 7 th . Therefore, the relative rankings  According to Figure 3B,   As shown in Figure 4A, in 2015, both the CoVaRs and ΔCoVaRs of the listed banks change greatly. There are 11 banks whose CoVaR is higher than 50, which occupies a proportion of 68.75% of the sample. BJYH ranks 1 st , with a CoVaR of 55. 39   As seen from Figure 5A, in 2017, the CoVaRs and ΔCoVaRs of all the banks decrease by a certain degree, except for the CoVaR of JTYH, which increased by 5.42%. Overall, if a sample bank is in distress, the VaR of the banking system decreases. From the perspective of the CoVaR rankings, NYYH, NJYH, GDYH, XYYH, and GSYH rank from 1 st to 5 th , indicating that the maximum loss of the banking industry is relatively high when the banks are in distress. According to the ΔCoVaR rankings, five banks rank from 1 st to 5 th , including three SOE banks (GSYH, NYYH, and JSYH) and two joint-stock banks (XYYH and GDYH). When these banks are in distress, their contributions to systemic risk are relatively high in the industry. For instance, XYYH ranks 1 st for CoVaR, and its CoVaR (11.12) is 2.07 times that of PFYH, which has the lowest CoVaR (5.37).
According to Figure 5B, overall, the CoVaRs and ΔCoVaRs of the sample banks increased in 2018. XYYH ranks the lowest for CoVaR and ΔCoVaR, while its indicators are higher than those in 2017, indicating an increase in risk. In terms of CoVaRs, four CCB banks, including ZXYH, PFYH, ZSYH, and MSYH, rank 1 st , 2 nd , 4 th , and 6 th ; two CCB banks, including NJYH and BJYH, rank 3 rd and 4 th . The five SOE banks, including JTYH, JSYH, NYYH, ZGYH, and GSYH, rank 7 th , 9 th , 10 th , 13 th , and 15 th . In terms of ΔCoVaRs, three SOE banks (JSYH, NYYH, and ZGYH) and four JOI banks (ZSYH, ZXYH, PAYH, and PFYH) are top seven banks. ZSYH, JSYH, NYYH, ZXYH, PAYH, ZGYH, and PFYH, respectively, rank from 1 st to 7 th .  Figure 6 shows the calculations of CoVaRs and ΔCoVaRs of the sample banks during the entire sample period. On the whole, JOI banks and CCB banks are in the top 50% of the sample banks in terms of CoVaRs. PFYH, a JOI bank, with a CoVaR exceeding 30, ranks 1 st in the listed banking industry. Among the CCB banks, NJYH ranks 1 st in the subindustry and ranks 2 nd in the banking industry. Both the CoVaRs of NBYH and BJYH exceed 28 and, respectively, rank 5 th and 8 th . Among the JOI banks, ZXYH and GDYH rank 12 th and 15 th , with CoVaRs of 27. 16  In terms of ΔCoVaRs, three SOE banks (GSYH, NYYH, and JSYH) and five JOI banks (ZSYH, HXYH, PFYH, XYYH, and MSYH) rank in the top 50% of the sample banks during the sample period. Three CCB banks (NBYH, NJYH, and BJYH) rank from 9 th to 11 th . Among the SOE banks, GSYH, NYYH, and JSYH rank 3 rd , 5 th , and 7 th ; their contributions to systemic risk are at middle or upper middle levels. The ΔCoVaR rankings of JTYH and ZGYH are only 13 and 15, indicating that their contributions to systemic risk are relatively low in the industry. Among the JOI banks, ZSYH and HXYH contribute the most to systemic risk and rank 1 st and 2 nd in the industry. Meanwhile, the JOI banks GDYH and ZXYH, respectively, rank 14 th and 16 th .

Overall analysis
According to the year-by-year analysis and overall analysis, we find that the levels of risk measured by CoVaR and ΔCoVaR vary across different time periods due to the changes in domestic and international economic and financial situations. Particularly, the risk levels significantly increase during certain time periods. For instance, the "money shortage" happened in 2013, the "stock market crash" occurred in 2015, and Sino-US trade war broke out in 2018. Moreover, we find that the CoVaR and ΔCoVaR rankings of most listed banks changed dynamically.  1 In the figure, the CoVaR refers to the Conditional Value at Risk when a bank is in distress; ΔCoVaR refers to the difference between the CoVaRs when the bank is in distress and in a normal state.

Year-by-year analysis
In the above section, we measured the risks of sample banks by using CoVaR and ΔCoVaR and analyzed those risks using a year-by-year and overall analysis. In this section, we introduce state variables into the estimation of CoVaR and ΔCoVaR, and the two indicators become time-varying. For simplicity, we pay more attention to the dynamic changes of systemic risk contribution. Therefore, we analyze ΔCoVaR based on the mean and standard deviation (hereinafter we use "Std." in the figures, measured by the standard deviation of daily ΔCoVaR) in this section. According to Figure 7A, for 2011, there are seven banks that contribute the most to the systemic risk of the banking system based on the means of ΔCoVaR: three JOI banks, two SOE banks, and two CCB banks. These banks are HXYH, XYYH, ZSYH, GSYH, NJYH, NYYH, and BJYH. Among the banks, HXYH ranks 1 st , with a ΔCoVaR of 16.55, and that of the other six banks both exceed 15. In terms of the standard deviations of the ΔCoVaRs, the ΔCoVaR fluctuations of the three JOI banks (HXYH, XYYH, and ZSYH) are at the middle level in the industry, ranking 12 th , 10 th , and 15 th , respectively, thereby indicating that their importance to the systemic risk of the banking system is stable. GSYH, NJYH, and NYYH are at an upper-middle level and, respectively, rank 6 th , 7 th , and 8 th . This indicates that systemic importance rankings have a certain degree of fluctuation.
According to the systemic importance rankings based on the dynamic CoVaR model, For SOE banks, GSYH, NYYH, JSYH, JTYH, and ZGYH rank 4 th , 6 th , 8 th , 11 th , and 12 th in the industry. The top three JOI banks with the highest systemic importance are HXYH, XYYH, and ZSYH, ranking from 1 st to 3 rd , while the top two CCB banks are NJYH and BJYH.
As Figure 7B shows, in 2012, among the top seven banks with the highest ΔCoVaRs, six banks belong to the group that contributes that most to systemic risk, including HXYH, ZSYH, XYYH, GSYH, NJYH, and NYYH. Additionally, the ranking of BJYH in ΔCoVaR rises, and its contribution to systemic risk enters the top five. As seen in Figure 8B, for 2014, in terms of the measurement of ΔCoVaRs, the industrial mean of systemic risk contributions decreases slightly, while the fluctuation of ΔCoVaRs significantly increases, and the standard deviation grows from 3.84 to 6.55. The standard deviations of the ΔCoVaRs of JSYH, GDYH, ZGYH, NYYH, and JTYH achieve values of 8.80, 8.68, 8.49, 7.96, and 7.96, which are higher than or equal to 1.70 times that in 2013. The average ΔCoVaRs of HXYH, ZSYH, GSYH, XYYH, and BJYH, respectively, rank from 1 st to 5 th , indicating that their contributions to systemic risk are at high levels in the industry. In terms of JOI banks, GDYH, HXYH, and XYYH rank 2 nd , 7 th , and 8 th . For CCB banks, NJYH and NBYH rank 6 th and 10 th . It is worth noting that the levels of the means of all the banks increase significantly compared to levels in the previous year. JSYH achieves the highest average ΔCoVaRs, with a value of 32.28, which is equivalent to 2.45 times the mean in 2014. Additionally, the average ΔCoVaR of ZXYH is at a low level in the industry, with a value of 19.97, but exceeds the highest average ΔCoVaR of HXYH (14.72).
As shown in Figure Figure 10A shows that the fluctuations of the industrial ΔCoVaR continue to decrease, with a value of 2.37; the mean in 2017 is the lowest during the past seven years, and the average of the contributions of the sample banks to systemic risk significantly drops. According to the ranking of means, five JOI banks (HXYH, ZSYH, PAYH, XYYH, and PFYH), respectively, rank 1 st , 2 nd , 3 rd , 5 th , and 7 th . Three CCB banks (NBYH, BJYH, and NJYH) rank 6 th , 8 th , and 9 th . In terms of SOE banks, GSYH, JSYH, and NYYH, respectively, rank 4 th , 10 th , and 11 th .
According to Figure 1 In the figure, we calculate the daily ΔCoVaR (the difference between the Conditional Value at Risk (CoVaRs) when the bank is in distress and in a normal state) of each bank, and then derive the corresponding mean and standard deviation for each bank.

Overall analysis
As seen from Figure 11, the dynamic ΔCoVaR shows that seven banks, including three SOE banks and four JOI banks, contribute the most to the systemic risk. These banks are HXYH, XYYH, JSYH, GSYH, ZSYH, NYYH, and GDYH. Among the banks, the mean of the ΔCoVaR of HXYH achieves 17.20, while that of the other banks exceeds 16.00. In terms of the fluctuations of the ΔCoVaRs, MSYH and ZXYH have a low level of ΔCoVaR standard deviations in the industry, with values of 14.81 and 13.00. However, JSYH, GDYH, ZGYH, NYYH, and XYYH are at the upper level in the means of their ΔCoVaRs, with a higher standard deviations than the other banks, reflecting the dynamic changes of their systemic importance. Figure 11. The overall results of the mean and standard deviations of ΔCoVaR 1 : (2011-2018). 1 In the figure, we calculate the daily ΔCoVaR (the difference between the Conditional Value at Risk (CoVaRs) when the bank is in distress and in a normal state) of each bank, and then derive the corresponding mean and standard deviation for each bank.

Comparison: static and dynamic model
In the above sections, we first assessed the systemic importance of the sample banks with a static CoVaR model, and then we introduced the state variables and conducted an analysis based on the dynamic CoVaR model. In the section, we make a comparison of the overall results derived from the static and dynamic CoVaR models during the entire sample period. Figure 12 shows the rankings of ΔCoVaRs measured by the dynamic and static CoVaR models. We find that among the SOE banks, for GSYH and NYYH, the rankings based on one model are not significantly different from those based on the other model. GSYH and NYYH, respectively, rank 4 th and 6 th according to the dynamic CoVaR model and rank 3 rd and 5 th according to the static CoVaR model. JTYH ranks 11 th with the dynamic model and 13 th with the static model. The systemic importance rankings of JSYH and ZGYH increase by 4 and 6 in the dynamic model compared to the static model, ranking 3 rd and 9 th . Among the CCB banks, there is not a significant change between the rankings based on the two models. The systemic importance rankings of both NBYH and BJYH improve by 1 to 10 and 12 in the dynamic model, whereas the ranking of NJYH improves by 2 to 8 in the dynamic model. Among the JOI banks, the dynamic model incorporates the effects of state variables. There is no change in the ranking of ZXYH, while the ranking of systemic importance for PAYH decreases; their contributions to systemic risk are thus at low levels. The change in ranking of HXYH is only 1. Moreover, based on the measurements of both the static and dynamic ΔCoVaR models, its systemic risk contribution is at a high level. Further, the systemic importance of PFYH and MSYH significantly decreases in the dynamic model, while that of ZSYH slightly decreases and is one of the top five highest in the banking industry. The systemic importance rankings of XYYH and GDYH significantly increase.
The static ΔCoVaR is derived from the traditional CoVaR model. As seen from the figure, seven banks (ZSYH, HXYH, GSYH, PFYH, NYYH, XYYH, and JSYH) contribute more than the other banks based on the static model, and six banks (HXYH, XYYH, JSYH, GSYH, ZSYH, and NYYH) are still considered to be banks with highest Δ CoVaRs using the dynamic model. Meanwhile, the dynamic ΔCoVaR contains more information as it incorporates a series of state variables and becomes time-varying. In other words, the accurate systemic risk evaluation should be based on a dynamic model, and the static model is considered as an approach to measure systemic risk and identify the systemically important banks quicker. 1 The left axis refers to the rankings based on the overall results derived from two models. 2 In the figure, ΔCoVaR refers to the difference between the Conditional Value at Risk (CoVaRs) when the bank is in distress and in a normal state.

Systemic risk contribution of a bank (extreme circumstance)
The systemic risk contribution of a bank is measured by a ΔCoVaR based on quantile regressions. Typically, a 5% quantile is used to define the state in which a bank is in distress (see [17]). In this section, we use a 1% quantile, and model the systemic risk contributions of a bank when it is in an extreme circumstance. Figure 13 shows the year-by-year measurements of Δ CoVaRs using the dynamic model. We find that the systemic risk contributions of all banks when they are in extreme circumstances are higher than those in the state of distress, which we calculate in Section 3.2. Additionally, it is clearly that the ΔCoVaRs of the sample banks in 2015 are higher than that in the other years. Besides, the ΔCoVaR of each bank in 2018 is less than that in 2015, but it is higher than that in the other years. The figure implies that when a bank faces a severe event (e.g., the stock market crash happened in 2015), it contributes more to the banking system. This can be considered as an "amplification effect", the extreme event happens (the stock market crash, in 2015; the trade war, in 2018), and amplifies the systemic risk contribution; therefore, the banks contribute more than in the peaceful times when no extreme event happens. This shows the necessities of assessing systemic risk contributions and discovering the SIFIs in China's banking system. Figure 14 clearly shows that the rankings of the banks in terms of ΔCoVaRs change dynamically over time. However, the rankings of HXYH and ZXYH are stable in every year.  According to Figure 15, for all the banks, the ΔCoVaRs in extreme circumstance increase by more than 10, except for ZXYH. Among the top eight banks in terms of ΔCoVaRs, there are four SOE banks including JTYH, NYYH, JSYH, and ZGYH (respectively rank 3 rd , 4 th , 5 th and 6 th ). Three JOI banks (HXYH, PFYH, and XYYH) rank 2 nd , 7 th , and 8 th . A CCB bank, namely NBYH, ranks 1 st . Figure 15. Measurements and rankings of dynamic ΔCoVaRs (overall analysis, extreme circumstance) 1 . 1 The left axis and right axis refers to the value and ranking of the dynamic ΔCoVaR (the difference between the Conditional Value at Risk (CoVaRs) when the bank is in distress and in a normal state) of each bank. Figure 16 shows the Exposure ΔCoVaRs (E-ΔCoVaRs) measurements and rankings during the entire sample period. The values of the E-ΔCoVaRs reflect the maximum loss of a bank when the banking system is in distress. As seen from the figure, among the SOE banks, JTYH, JSYH, NYYH, GSYH, and ZGYH, respectively, rank 11 th , 12 th , 14 th , 15 th , and 16 th . Therefore, the exposures of the SOE banks are at low levels in the banking industry. Among the CCB banks, NBYH and NJYH, respectively, rank 1 st and 5 th . Among JOI banks, ZXYH, PAYH, HXYH, and XYYH, respectively, rank 2 nd , 3 rd , 4 th , and 6 th . To summarize, when the banking system is in distress, the JOI banks and CCB banks except BJYH, are more affected than all the SOE banks. Therefore, the SOE banks show relatively good stability when the banking system is in distress. Figure 16. Measurements and rankings of Exposure ΔCoVaRs 1 (overall analysis, exposure model). 1 The left axis and right axis refers to the value and ranking of the Exposure ΔCoVaR (the difference between the Exposure Conditional Value at Risk (CoVaRs) when the banking system is in distress and in a normal state) of each bank during the entire sample period.

Modified model: Incorporation of the effects of Fintech and non-bank financial institutions
In the section, we modify the dynamic model, and the effects of Fintech and non-bank financial institutions (NBFIs) are introduced as the state variables, which are measured by the returns of China Securities Index (CSI) Fintech stock index and the NBFI stock index. The two variables are selected for three reasons. First, Fintech, namely Finance Technology, is the trend of finance, which transforms the business model of traditional financial institutions and brings financial innovations in the digital economy era. Second, the non-bank financial institutions are considered by China's central bank to play a more and more important role in China's financial system [38]. Therefore, we should also take the potential effect of NBFIs into consideration. Third, they all meet the requirements of the selection principles of the state variables. As in the discussion section, we need to compare the year-by-year results; thus, the sample period should cover the entire period of each year. Moreover, the Fintech index has been released since July 2014, therefore the systemic risk is measured based on the data from 2015 to 2018. As seen from Figure 17, during the sample period of 2015-2018, among the top eight banks, JSYH, NYYH, GSYH, and ZGYH, four SOE banks, respectively rank 1 st , 2 nd , 3 rd , and 4 th . ZSYH, HXYH and XYYH, three JOI banks respectively rank from 5 th to 7 th . NBYH, a CCB bank, ranks 8 th . In this section, we conduct a systemic risk evaluation with the indicator approach, and the variable list is shown in Table 5. We take an example of the systemic risk evaluation in 2018. In Figure 18, from the perspective of the indicator approach, five SOE banks (GSYH, ZGYH, JSYH, NYYH, and JTYH) respectively rank from 1 st to 5 th . The systemic risks of six JOI banks (XYYH, ZSYH, PFYH, ZXYH, MSYH, and GDYH) are at middle levels. The systemic risks of two JOI banks and three CCB banks are at low levels.

No.
Indicators Definition 1 Size The total assets.

Interconnectedness
The intra-financial system assets and liabilities, including the lendings to banks and other financial institutions, the due from placements with banks and other financial institutions, the redemptory monetary capital for sale, the due to placements with banks and other financial institutions, the borrowings from banks and other financial institutions, and the financial assets sold for repurchase.

Substitutability
The loans and advances, the fee and commission income, and the deposits from customers.

Complexity
The derivative financial assets and the financial assets that are trading or available for sale. However, according to the measurements of the ΔCoVaRs based on the data from financial markets, the large SOE banks do not always have the highest contributions to systemic risk, which is consistent with the conclusions drawn by [39,40]. Furthermore, some JOI banks and even some CCB banks contribute more to the systemic risk of China's banking industry than the SOE banks, whose sizes are larger than those of the JOI and CCB banks.
We then calculate the Spearman's rank correlations between the size rankings and a series of systemic risk indicator rankings. In Table 6 and Table 7, "R" is the abbreviation of "Ranking". "Test statistic" refers to the statistic of the test whose null hypothesis is the size rankings and the rankings of a systemic risk indicator are independent. If a test statistic is less than the given significance level (5%), the correlation between the two rankings are statistically significant with a 95% level of confidence. The "Proportion" refers to the proportion of the number of the significant correlations to the number of all the correlations. We find that the correlation between the bank size rankings and the systemic importance rankings derived from the indicator approach are significant at the 5% level. This is because bank size is an important element of the systemic risk indicator measured by the indicator approach, and the other elements are likely to be affected by the bank size. For instance, the deposit and loan of a big bank are usually higher than that of a small bank. In other words, the bank size directly and indirectly affects the systemic risk indicator using the indicator approach.
If the bank size directly determines the systemic importance of a bank, we expect all the correlations in the following tables to be significant. Besides, we are curious about whether the correlations are positive or not. The results based on the market-based approach imply that for China, the bank size is only negatively correlated with the bank exposures, and the correlation is significant at the 5% level. When the banking system is in distress, the maximum loss of a big bank is smaller than that of a small bank, indicating that the big banks are more stable.
Furthermore, we observe a significant positive correlation between the size rankings and the rankings of the static ΔCoVaRs, only in 2017 and 2018. All the correlations between the size rankings and the rankings based on dynamic ΔCoVaRs derived from three dynamic models (a model with a 5% quantile, a model which considers a bank in extreme circumstance and use a 1% quantile, a model which incorporates the effects of Fintech and non-bank financial institutions) are insignificant at the 5% level. Additionally, the correlations are positive in some years and negative in the other years.
The possible reasons are follows. First, in the era of the digital economy, beyond the existing branches, the popularization of the Internet as well as the development of information technologies especially Fintech make it possible for small banks to compete with big banks on the Internet and provide services for customers in China and possibly in other countries. However, the small banks may not have sufficient experiences and measures to forestall the risks arising from Internet banking activities as the big banks do. Therefore, when a small bank is in distress, it could contribute more to the systemic risk than big banks. Second, for the same reason, when the crisis of a small bank occurs, people may believe that the bank is too small to handle the risk. Therefore, these customers may become too "rational" to trust the bank. They may believe that the bank will run out of money when the crisis event occurs, and their wise choice is to draw money from the small bank as soon as possible. The Internet enables people to draw money faster than before, which may accelerate the bank run and increase the systemic risk in the digital economy era. Third, in the era, customers choose diverse online banking services (i.e., financial products) simply by clicking the mouse. Meanwhile, the banking services may not be transparent enough for customers, and some products may be highly risky. In this way, a small bank can increase the systemic risk.
In addition, according to Acharya and Yorulmazer, regulatory institutions have recognized a phenomenon of "too big to fail" in the financial system, which arouses the interests of researchers and regulators to study the effect of big banks on systemic risk. However, in reality, there may be a situation of "too many to fail" as well, which should be also noticed. They point out that, a small bank may invest in the same direction as a big bank, thus increasing the correlation of investments between banks. Moreover, many small banks have incentives to do so. In this way, the risks at the individual bank level may turn into system-wide risks. In this case, small banks may also induce the systemic risk [41]. Varotto and Zhao propose another way in which a small bank may cause systemic risk: the small bank may occupy a considerable proportion of the banking industry of a certain region [42]. This situation is similar to that of the CCB banks studied in this paper. When people learn that local small banks have gone bankrupt, people may worry that other local banks will also go bankrupt. The bankruptcy of local small banks may be even perceived to herald a national bank crisis or trigger a chain reaction in the banking system. Therefore, we believe that the reform and development of financial supervision should keep pace with the times and be improved by market-based systemic risk estimation methodologies.
Currently, increasingly more empirical studies concentrate on systemic risk and suggest the significance of the effect of small banks on systemic risk. Manguzvane and Muteba [43] applied CoVaR methodology to model the systemic risk of the banking industry in South Africa. The results showed that since the global financial crisis, there had been a huge fluctuation in the ΔCoVaRs of the sample banks. For the means of ΔCoVaR during the sample period, First Rand was the bank with the highest ΔCoVaR, indicating that it is the bank with the most systemic importance to the banking industry in North Africa. Besides, the systemic risk of the African bank's contribution is the smallest, with a value of ΔCoVaR close to zero. Clearly, the contributions of different banks to systemic risk vary, and supervision should thus be differentiated. Additionally, the authors also find that a small bank in North Africa, namely Capitec, can affect systemic risk as big banks do. Moreover, they observe a noticeable increase of the contribution of Capitec to the systemic risk in the crisis times. Therefore, on the basis of microprudential supervision, which focuses on the individual risk of a financial institution, regulatory institutions should also consider the influence of small banks on systemic risk and adopt the concept of macroprudential supervision. Another study [44] measured systemic risk by the value of ΔCoVaR and found that CCB banks contributed more than SOE banks. The authors thought that, this may be because both SOE banks and CCB banks are backed by government credit, but state credit is higher than that of the local government. Therefore, the market will generate expectations that the state will bail out SOE banks (because they are backed by state credit), making them unlikely to trigger a run after a crisis or affect the stability of the entire banking system. However, JOI banks are not backed by state credit and are not as widely distributed as CCB banks and SOE banks. Therefore, JOI banks contribute more to systemic risk than SOE banks, so size is not the only factor that affects systemic risk contributions. Our research could provide empirical evidence to enrich existing studies from another perspective. The results based on the Exposure CoVaR model indicate that during the sample period, when the banking system is in distress, all the JOI banks and most of the CCB banks are more affected than all the SOE banks, which are less affected. In other words, when the banking industry is in distress, the SOE banks are more stable in the banking industry.

Discussion
In this paper, we first note that China is a bank-based country and that it is of great significance to study the systemic risks of Chinese banks in the digital economy era. In this paper, based on the static, dynamic, and modified CoVaR models, we quantitatively measure the systemic risk of 16 China's listed commercial banks during the period of 2011-2018. Our findings and suggestions are as follows.
First, the market-based CoVaR approach, which is a useful complement for the indicator approach, could provide more information for strengthening financial supervision than the traditional indicator approach. The indicator system as well as the statistical tests clearly shows that the systemically important banks identified by the indicator approach are always big banks. However, we can conclude that for China, the systemic importance of a bank could not be simplified as the bank size rankings. Besides, the bank size rankings are not always positive and sometimes even negatively correlated with the rankings of systemic risk indicators (i.e., rankings of systemic importance) in the digital economy era. The conclusion still holds true when we assume that a bank is in extreme circumstance or considers the effects of Fintech and non-bank financial institutions.
Second, the systemic risk changes over time. Based on the CoVaR models, we measure the systemic risk of 16 listed banks from 2011 to 2018, year by year, and integrate an overall analysis of the sample banks during the entire sample period. It is found that the levels of systemic risk vary across different time periods with the changes in domestic and international economic and financial situations. In the era of the digital economy, information transfers faster than before and customers can enjoy the benefits in the era, while we also need to know that the risk could also transfer faster. The periodical assessment of the systemic risk in the digital economy era could provide on timely early warning for regulators to avoid the accumulation of the risk and the occurrence of a crisis.
Third, based on both the static CoVaR model and the dynamic CoVaR models which introduce the state variables, the systemic importance rankings of banks change over time. Therefore, we suggest that the financial supervision of SIFIs requires dynamic evaluation, and the dynamic model is an enhanced model of the traditional static model, which contains more information and is time-varying, and it should be further developed for financial supervision. Furthermore, for China, the year-by-year analyses show that systemically important banks change over time, especially the bank which contributes the most to systemic risk. Interestingly, some SOE banks (big banks) are systemically important, and these banks are also identified by the indicator approach due to their huge sizes. However, the results based on the market data indicate that some SOE banks are not always systemically important, and some JOI and CCB banks (small banks) are identified as the systemically important banks. The base and extended models support the following view, which coincides with the point that we propose in the introduction section: small banks could also contribute to systemic risk and cause a systemic effect in the digital economy era. We contribute to the existing studies with empirical evidence and theoretical analysis.
Overall, we suggest that in the digital economy era, the measurement of systemic risk and the identification of systemically important banks should be based on more and more market-based approaches, including the CoVaR model. Besides, with the development of Fintech and non-bank financial institutions, we should develop more models that incorporate the effects of these financial activities. In addition, the financial supervision, especially the reform of the macroprudential framework, should deeply consider the systemic risk contributions of not only big banks but also small banks, which may be not as large as the SOE banks in China but remain systemically important to the banking system. Differential supervision should be further developed to maintain financial stability not only in China but also around the world.