The stability of the financial system plays a crucial role in the sustainable economic development. Hence, to identify systemically important banks and firms, we take lending relationships with different loan terms and common asset relationships with different investment cycles into consideration to present a multilayer DebtRank model of the bank-firm system. In the light of simulation research, we can obtain the following results. First, the bank-firm system constructed displays a significant core-periphery structure, which exists in the actual financial system. Then, only very few banks and firms show systemically important characteristics, where “important” subjects hold very high net assets and profits, while "fragile" subjects possess negative net assets and serious losses. Furthermore, the bank-firm multilayer DebtRank model presents a great stability to a certain extent. Overall, the multilayer DebtRank model constructed in this paper has certain theoretical reference value for the supervisory authorities to extract the internal characteristics of systemically important banks and firms and identify them effectively.
The sustainable and healthy development of the economy cannot do without the stability of financial systems [
In the aspect of identifying systemically important financial institutions, scholars have given diversified measurement methods from different dimensions such as models and indexes. The CoVaR model is the current mainstream research method [
However, the modern financial system is more and more complex, and the relationship between banks and firms is more and more close, which makes the use of financial network methods to study the systemic importance of financial systems more and more urgent [
For the study of the systemic importance from the perspective of financial networks, in addition to the above network centrality indicators, the DebtRank centrality has also received attention. Considering that the calculation process of the feedback centrality has multiple feedback effects among network nodes, the DebtRank sets different impact states so that the nodes are not affected by the secondary impact, which can well identify the systemically important financial institutions. Battiston et al. [
The related research of the DebtRank model mainly focuses on the single risk exposure of financial systems, which is difficult to truly describe the complexity and diversity of the business associations between real financial market subjects. In view of this, considering the lending relationships with different loan terms and the common asset relationships with different investment cycles, the multilayer DebtRank model of the bank-firm system is constructed. Compared with the existing research, the contribution of this paper is to construct a multilayer DebtRank model to identify systemically important banks and firms from the complexity and the diversity of bank-firm business associations. In addition, we analyze the internal characteristics of systemically important banks and firms and verify the robustness of the model. This paper is beneficial to deeply mine the internal relationships between the complex association structure and the systemic importance of financial systems, which has certain theoretical reference value for the supervisory authorities to extract the internal characteristics of systemically important banks and firms and identify them effectively.
The remainder of this paper is organized as follows. Section
In the artificial financial system, we consider two types of subjects: banks and firms. The entire model is divided into three parts, namely, bank-firm balance sheet construction, bank-firm behavior evolution, and bank-firm systemic importance identification.
We assume that an individual bank’s assets include interbank short-term loans
Bank balance sheet construction.
Assets | Liabilities |
---|---|
Interbank short-term loans | Interbank short-term borrowings |
Interbank long-term loans | Interbank long-term borrowings |
Firm short-term loans | Short-term deposits |
Firm long-term loans | Long-term deposits |
Short-term investments | |
Long-term investments | Net assets |
Liquid assets |
The indicators mentioned above can be measured as follows:
We assume that an individual firm’s assets include production costs
Firm balance sheet construction.
Assets | Liabilities |
---|---|
Production costs | Sale revenues |
Short-term investments | Bank short-term loans |
Long-term investments | Bank long-term loans |
Liquid assets | Net assets |
The indicators mentioned above can be measured as follows:
For simplicity,
For the debt bank
The potential debt banks and debt firms borrow funds from the potential creditor banks based on the optimal partner selection mechanism. If they cannot obtain the sufficient liquidity from the first potential creditor bank, they contact other banks for the remaining funds until their total demand for liquidity is satisfied or all loanable funds are exhausted. As a potential creditor bank, the amount that can be used for fund lending is
At time
Suppose there are
Banks and firms randomly choose a certain proportion of risk assets for equal investments. For simplicity, the selected risky assets are recorded as
In this paper, the systemic importance of the bank-firm system refers to the impact of losses suffered by banks and firms on the whole bank-firm system through lending correlations and common asset correlations. Considering the lending relationships with different loan terms and the common asset relationships with different investment cycles, we use the multilayer pressure diffusion to evaluate the multilayer DebtRank of banks and firms and then identify the systematically important banks and firms.
Drawing on the experience of research conducted by Bardoscia et al. [
Considering that if there is a loop in the network, the pressure will circulate between nodes. In order to avoid the nodes participating in the pressure diffusion process repeatedly, drawing on the experiences of the research conducted by Battiston et al. [
At the initial time
In order to further describe the bank-firm pressure level in different network layers, we set the number of layers of the complex network as
At time
In addition,
Similarly, at time
In addition,
Assume that the pressure diffusion stops at
Based on the above analysis, the multilayer DebtRank of the impacted node
Drawing on the experiences of research led by Li et al. [
Benchmark parameters of the model.
Parameter | Description | Value |
---|---|---|
Maturity of interbank short-term loans | 1 | |
Maturity of bank-firm short-term loans | 1 | |
Maturity of bank short-term investments | 1 | |
Maturity of short-term deposits | 1 | |
Maturity of firm short-term investments | 1 | |
Ratio of interbank short-term loans | 0.5 | |
Ratio of bank short-term investments | 0.5 | |
Short-term volatility of deposits | 0.3 | |
Labor wage for producing products | 2 | |
Risk-free interest rate | 0.025 | |
Sensitivity of the short-term lending rate | 0.1 | |
Firm comprehensive technical level | 1.2 | |
Stock common risk factor variance | 0.06 | |
Selection ratio of risk assets | 0.01 | |
Default amplification factor | 0.1 | |
Maturity of interbank long-term loans | 10 | |
Maturity of bank-firm long-term loans | 10 | |
Maturity of bank long-term investments | 10 | |
Maturity of long-term deposits | 10 | |
Maturity of firm long-term investments | 10 | |
Ratio of bank-firm short-term loans | 0.5 | |
Ratio of firm short-term investments | 0.5 | |
Long-term volatility of deposits | 0.5 | |
Product price per unit output | (0.5, 2.5) | |
Deposit reserve ratio | 0.2 | |
Sensitivity of the long-term lending rate | 0.2 | |
Firm capital output elasticity coefficient | 0.8 | |
Stock idiosyncratic risk factor variance | 0.03 | |
Selection ratio of creditor banks | 0.3 |
The ban-firm system constructed in this paper contains four network layers, including the short-term common asset network, the short-term lending network, the long-term common asset network, and the long-term lending network. The lending network describes the lending relationship between banks and firms, and the common asset network represents the common holding relationship of external assets between banks and firms. Figure
Complex network at
The node degree is a simple and important concept to describe the characteristics of bank-firm network structures. The larger the node degree, the more active the node in the bank-firm network. Drawing on the experience of research conducted by Boccaletti et al. [
Node degree distributions of bank-firm networks at different times. (a)
It can be seen from Figure
In addition, Figure
Complementary cumulative distribution function of assets at different times. (a)
The above research shows that the bank-firm system constructed in this paper shows the core-periphery structure, and most banks are active at the core of the network, while a few banks and firms are relatively less active at the periphery of the network. It is also very important to identify the systemically important banks and firms. Based on this, we use the multilayer DebtRank to analyze the problem. In order to explore whether there are differences in the systemic importance between banks and firms at different times during the operation of the ban-firm system, Figure
Bank-firm multilayer DebtRank at different times. (a)
Figure
The aforementioned research results show that only very small numbers of banks and firms show the systemic importance in the bank-firm system while the internal characteristics of systemically important banks and firms need to be further explored. Based on this, considering that the financial situations and the operation conditions of banks and firms may have significant impacts on the systemic importance of the bank-firm system [
In the actual operation process of the bank-firm system, due to the differences in asset scales and operation conditions between banks and firms, there may be large differences in the net assets between banks and firms. Whether this will affect the systemic importance of banks and firms remains to be further studied. Based on this, Figure
The distribution of the net assets and their multilayer DebtRank.
It can be seen from Figure
Banks and firms in good operating conditions may gradually evolve into systemically important banks and firms through the accumulation of profits while poorly managed banks and firms may gradually become systemically vulnerable banks and firms due to frequent losses. Whether this will affect the systemic importance of banks and firms remains to be further studied. Based on this, Figure
The distribution of the profits and their multilayer DebtRank.
It can be seen from Figure
In order to ensure the robustness of the simulation results, it is necessary to further verify the robustness of the bank-firm multilayer DebtRank. Considering that the parameter
Bank-firm multilayer DebtRank with different
It can be seen from Figure
The multilayer DebtRank is beneficial to deeply mine the internal relationships between the complex association structure and the systemic importance of financial systems. Considering the lending relationships with different loan terms and the common asset relationships with different investment cycles, the multilayer DebtRank model of the bank-firm system is constructed. The entire model is divided into three parts, namely, bank-firm balance sheet construction, bank-firm behavior evolution, and bank-firm systemic importance identification. This paper focuses on the identification of systemically important banks and firms, the internal characteristics of systemically important banks and firms, and the robustness test of the model.
The simulation results are as follows. Firstly, the bank-firm system constructed shows a significant core-periphery structure at different times, which means that most banks in the whole bank-firm system are highly active, while a few banks and all firms have relatively low activities. Secondly, we find that the distributions of total assets of the bank-firm system are lognormal distributions with Pareto tails, which suggests that most of the banks and firms have large-scale assets, while only a few banks and all firms possess a small amount of wealth. Thirdly, we discover that only very small numbers of banks and firms display the systemic importance in the bank-firm system, where “important” subjects hold very high net assets and profits, while “fragile” subjects possess negative net assets and serious losses. This suggests that we should pay more attention to the systemically important banks and firms that are “too connected to fail.” Finally, we verify that the overall systemic importance of the bank-firm system keeps a very good stability at different times.
It is urgent for the government departments to better understand the number and scale distribution of the current Chinese banks and firms, balance the development mode of related business, reasonably optimize the loan mechanism, and establish a multidirectional risk monitoring system. This study reveals the microbasis of complex business associations between banks and firms, which has certain theoretical reference value for the regulatory authorities to extract the internal characteristics of systemically important banks and firms and prevent financial systemic risks.
The authors declare no conflicts of interest.
Qianting Ma and Kun Yang contributed equally to this work. They are cofirst authors.
The authors are grateful to the financial support from the Postgraduate Research and Practice Innovation Program of Jiangsu Province (KYCX20_0165) and the Scientific Research Foundation of the Graduate School of Southeast University (YBPY1971).