# Network Effects and Characteristics of Cross-Industrial Tail Risk Spillover in China

Authors: Bohui Wen; Shangde Gou; Yuting Wei; Jing Hao
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

In recent years, the Chinese capital market has suffered several violent shocks, and the characteristics of systemic risk contagion across industries and markets have become increasingly important. It brings great potential danger to the stability of financial markets. Therefore, exploring the risk spillover among the real sectors has gradually attracted the attention of scholars. This paper examines the cross-industrial tail risk spillover network in the Chinese financial market. The characteristics and the dynamic contribution of each industry in the tail risk transmission chains are explored. We use the ∆CoES-ENGDFM-LVDN model based on monthly data from 2006 to 2020 to measure the tail risk of 28 industries in China and form a cross-industrial tail risk spillover network. The results show that different industries have different levels of spillover and importance in the network. Tail risk mainly spills over from the nonfinancial sector to the financial sector. The nonbank financial industry is the main recipient of tail risk spillover and is becoming progressively more important in the risk network. In addition, with the promotion of industrial structure, emerging industries such as communications, computers, and health care have begun to play more important roles in the tail risk spillover network in China. This paper not only enriches the research in the areas of tail risk spillover and systemic risk, but also has implications for regulators to maintain financial stability and prevent financial risks.


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## Body

## 1. Introduction

One of the important tasks of China’s financial stability goal is to control risk spillover between the nonfinancial sector and financial sector and prevent cross-industrial or cross-market risk contagion. When the business performance of companies is poor, its negative impact may spread rapidly through the industry connection to the whole market. The deterioration of market fundamentals will trigger the increasing linkage between financial market return and risk. The tail risk spillover among industries will also amplify economic volatility. The linkages among industries have significantly exacerbated risk spillover effects and increased the impact of the nonfinancial sector on the financial system, giving rise to new challenges for preventing systemic risks. The industry-level systemic risk indicators include systemic risk contribution and systemic risk exposure. The former refers to the impact of an individual industry under extreme circumstances (e.g., the industry suffers severe losses) on the economic system, while the latter refers to the impact of the economy under extreme circumstances (e.g., the economy falls into a severe recession) on an individual industry. We consider the former. At the same time, since economic and financial variables are usually characterized by “sharp peaks and thick tails,” the measurement of systemic risk should focus on the tail risks of industries and economies in extreme situations.Tail risk is used not only in characterizing the extreme risks, but also to reflect the accumulation of risk spillover levels in extreme cases. Therefore, what is each industry contributing to the systemic risk in the tail risk network? Does the financial sector play a crucial role in risk spillover? How do the intensity, transmission direction, and path of tail risk spillover among industries vary with business cycles? This paper aims to answer these questions.In recent years, research on the risk spillover among industries in the real sector has gradually attracted academic attention. Networks constructed with the mean and variance tend to underestimate the risk contagion level by ignoring tail risks in extreme cases. The drawbacks of failing to measure the incremental change in risk spillovers from normal to extreme states violate the purpose of Adrian and Brunnermeier [1] on improving the risk spillover measure. In addition, most of the networks constructed by existing studies, either based on causality detection or based on variance decomposition, are information or volatility spillover networks instead of risk spillover networks [2–6]. In addition, most of the existing studies [7, 8] focus on measuring the intensity scale of risk spillover, that is, the level of network association. Scare attention is given to the direction and path of risk transmission and other association structures [9–11]. There are very few studies [12, 13] that consider both the level and structure of association and assess the contribution of risk in the tail risk network.Academic research has agreed on the level of correlation in China’s economic and financial system with obvious cyclical characteristics. The probability of risk spillover in specific industries increases significantly, and the intensity of spillover varies with cyclical characteristics, showing obvious asymmetry in different cycles. Most of the existing studies often ignore the difference in tail risk spillover between the risk accumulation and the release stage [14–16]. To overcome these drawbacks, this paper studies the level and structure of the tail risk spillover network among industries in China, as well as the systemic contribution characteristics of each industry in the risk transmission network. We also aim to identify the core industries in the risk network and make forward-looking suggestions for regulation. Moreover, we identify the differences in the above characteristics in the risk accumulation or release stages.We introduce a periodic perspective to measure cross-industrial upside and downside tail risks and construct a tail risk spillover network with cyclical properties among China’s industries using ∆CoES-ENGDFM-LVDN models, which may be more effective in measuring the cross-industrial tail risk spillover network effects. Specifically, we analyse the key industries in the contagion chain during tail risk spillover and examine the intensity, direction, path, and center of tail risk spillover according to the risk network. Then, from a dynamic perspective, we further consider the trend of tail risk spillover in each industry. We compare the spillover effects both in the risk accumulation stage and release stage and analyze the spillover levels from normal to extreme states. From the time dimension, we longitudinally examine the evolutionary relationship of tail risk spillover among industries in the full sample and each subsample, comparing the differences in spillover effects within different sample periods for the same risk phase (upside risk accumulation or downside risk mitigation).First, we begin our test by constructing a risk network and analyzing cross-industrial risk spillover effects directly for tail risk. Compared to the networks constructed from the returns and variance [1, 17, 18], tail risk could reflect the incremental change in the level of risk spillover from normal to extreme states. It is possible to avoid the underestimation of the level of risk contagion caused by return and volatility [19, 20].Second, we use ∆CoES instead of ∆CoVaR, which contains both left-tailed and right-tailed information and is based on a long-term stress scenario. However, ∆CoES does not measure network effects, resulting in tail risk spillover being underestimated [21]. The General Dynamic Factor Model (GDFM) proves the consistency of the estimators when both the sample and time series dimensions are infinite, but it is calculated only for the fluctuation spillover relation. Elastic Net (EN) combines the advantages of LASSO regression and ridge regression. Therefore, this paper introduces ∆CoES into the GDFM with EN to construct and estimate the tail risk spillover network with periodicity among China’s industries, which can overcome the limitations of the abovementioned methods. It could also demonstrate the tail risk spillover across industries in the risk accumulation stage and release stage. The results indicate that there are an overall persistent nonlinear spillover effect and significant periodicity effect among industry tail risks in China. Cross-industrial tail risk spillover is more pronounced in the risk release stage. However, the total degree of spillover in the risk accumulation stage gradually grows and has exceeded the total degree in the release stage. This suggests that while the scope of cross-industrial tail risk spillover in China is gradually expanding, the downside risk has not been released sharply.Third, this paper considers the level of industry tail risk association, structure, and network contribution for both the full sample and the dynamic evolution of each stage. We explore the pattern of risk spillover from normal to extreme and test the tail risk spillover in key industries. It forms a useful complement to previous studies on cross-industrial risk spillover.This paper contributes to the following streams of literature:First, identification and measurement of tail risk. Traditional methods are divided into three categories based on real operating business data, directly generated based on complex network theory, and based on financial market data such as stock prices. Linear or nonlinear Granger causality detection [22, 23], generalized variance decomposition [2], LASSO regression [21, 24], and TENET networks [25] were mainly used. In recent years, the construction of correlation networks based on financial market data has gained the attention and recognition of scholars. The network constructed through high-frequency financial market data is not limited to a particular form, which can overcome the untimely assessment of cross-industrial risk spillover caused by the lag of low-frequency data and measure the global and integrated channel effects formed by cross-industrial tail risk spillover [2, 26, 27]. Barigozzi and Hallin [28] use the EN approach to deal with the high-dimensional time series estimation problem involved in the GDFM model and further test the volatility spillover effect among industries in the SP100 index jointly with the LVDN, providing a reference for the study.The second is the risk spillover characteristics among industries. Most of the existing studies focus on risk contagion within the financial sector, few papers analyze the tail risk diffusion relationship among nonfinancial sectors, and the empirical findings remain controversial [29, 30]. On the one hand, some studies focus on volatility spillover rather than tail risk spillover; on the other hand, the related literature focuses on tail risk to the downside and ignores the upside [31–33]. It neither captures the differences presented by tail risk spillover in the process of upside risk accumulation and downside risk mitigation nor the process of incremental changes in the level of risk spillover.Finally, the impact of periodic factors on tail risk spillover is examined. The degree of risk spillover among China’s financial institutions was at a relatively high level during the subprime mortgage crisis and the implementation of the new round of easing monetary policy in the United States. Some studies suggest that the level of systemic correlation of financial institutions in China has a distinctly periodic character. Some Chinese scholars measure the downside risks of 11 industries in China. The results clearly demonstrate that when the economic downwards pressure increases, facing greater policy uncertainty or implementing expansionary credit policies, there will be more significant risk contagion among industries. At the same time, the nonfinancial sector has strong explanatory power for systemic risk. However, the current research focusing on the impact of cyclical factors on tail risk spillover among industries in the nonfinancial sector still needs to be supplemented.The rest of this paper is organized as follows: Section2 presents the methodology, introduces the data, and gives the measurement results of relevant variables. Section 3 reports empirical results and further analysis. Section 4 provides recommendations for improving cross-industrial risk spillover regulation in China.


## 2. Methodology and Data

### 2.1. ∆CoES Method to Calculate Upside and Downside Tail Risk

Using ES as a risk metric and replacing conditional events withXi≤VaRpi, Adrian and Brunnermeier [1] present estimates for CoES that measure the tail effect of individual risk contribution. We improved on these and learned the method from Brownlees and Engle [34] to estimate CoES. As a result, we can capture not only the institutions’ systemic risk exposure and the institutions’ contribution to systemic risk at the same time, but also the long-term stress profiles. It can also use the risk-taking behavior and risk accumulation of institutions during the upside to predict risk mitigation in the downside, thus addressing the procyclicality of the contemporaneous risk metric. Empirical tests show that the upside ∆CoES (as in equation (1)) is appropriate as a forward-looking measure of tail risk, while the downside ∆CoES (as in equation (2)) can lead CoVaR and CoES.This paper extends the application of the ∆CoES model, which is no longer limited to the financial sector. Using the overall industry-wide market as a benchmark, measure the upside and downside ∆CoES values of tail risk for each industry. The specific calculation steps are as follows: the BEKK-MGARCH model is used to estimate the variance equation of log returns for each industry. The distribution of future one-month returns is simulated by the residual bootstrap method, where the forecast periodh = 22 denotes the actual number of trading days in a month, and S denotes the number of simulations. The larger the value of S is, the better the simulation effect is, so we take S = 105. Based on the information for period T and conditional on the arithmetic rate of return R for the next month (h = 22), the ΔCoESi|N values for each industry are obtained separately.(1)upsideΔCoESTi|N=ETRi,T+1:T+h|RN,T+1:T+h≤VaR95N−ETRi,T+1:T+h|RN,T+1:T+h≤VaR50N,(2)downsideΔCoESTi|N=ETRi,T+1:T+h|RN,T+1:T+h≤VaR50N−ETRi,T+1:T+h|RN,T+1:T+h≤VaR5N,where N denotes the number of industries; RT+1 : T + h ≥ VaR95 denotes the extreme state of the upside risk accumulation phase, and RT+1 : T + h ≥ VaR50 denotes the normal state of the upside accumulation phase; RT+1 : T + h ≤ VaR5 denotes the extreme state of the downside risk mitigation, and RT+1 : T + h ≤ VaR50 denotes the normal state of the downside risk mitigation.


### 2.2. Cross-Industrial Tail Risk Spillover Network

The available dataset is usually panel data of industry returns with high-dimensional properties when studying interdependencies among industries. We construct the long-term variance decomposition network ∆CoES-ENGDFM-LVDN that can solve the problem of high-dimensional data incidentally well. Second, this approach can study the correlation between financial and real sectors from the perspective of tail risk spillover, addressing the problem that methods such as correlation coefficients of returns and principal component analysis do not measure the contribution or exposure of individual institutions to systemic risk. The drawback that ∆CoVaR, MES, and other methods cannot capture the network effect of tail risk spillover is avoided. In addition, the method effectively bridges the previous deficiency of demonstrating risk only from the network of financial institutions. It should be noted that the results in this paper are mainly based on the heterogeneity part ofΔCoESi|N, and we argue about its rationality in 3.2. The specific process is as follows: extending the study of Barigozzi and Hallin [28], a two-step dynamic factorial procedure was used. First, the GDFM was applied to extract the common and idiosyncratic components from the tail risk data. Then, the EN model and the LVDN model are applied to identify the size and structure of tail risk spillover among industries.Denote the two-factor process formed by N industries with tail risk dataΔCoESi|N (including upside and downside) as(3)ΔCoES=ΔCoESti|N:i∈N,t∈T=χit+ξit,i∈N,t∈T,where ∆CoES satisfies second-order stationary, zero mean, and finite variance. ∆CoES is absolutely continuous with respect to the Lebesgue measure on −π,π. The qth eigenvector in the spectral density matrix diverges, and the qth+1st eigenvector is bounded. Hallin and Liška [35] prove that the horizontal market shock when the actual data are applied to the GDFM is unique, i.e., q = 1. Thus, there are autoregressive processes AiLχit=ηit=η1t,...,ηNt’,t∈T and FiLξit=vit=v1t,...,vNt′,t∈T, where ηit and vitare n-dimensional white noise processes, and FiL is a one-sided stable VAR filter. Barigozzi and Hallin [28] extracted the idiosyncratic components ξit of ∆CoES in FiL and used EN for sparse processing ξit, always admitting a Wold decomposition, which, after adequate transformation, yields the vector moving average (VMA) representation ξit=DiLeit. Comparing the above equations, we can obtain(4)DiL=FiL−1Ri,where the full-rank matrix Ri makes shocks Rn−1vn=en orthonormal. Ri follows from a Cholesky decomposition of the covariance Cn−1 of the shocks [36], namely, Cn−1=RnRn′. The residual centrality of the partial correlation network (PCN) based on Cn is ranked, so that the most correlated nodes are hit first. Decomposing Ri based on (4) yields the LVDN on the industry tail risk spillover. wijh=100∑k=0h−1dk,ij2/∑l=1n∑k=0h−1dk,il2,i,j=1,…,n means the dependence from contemporaneous to lagged h periods in the LVDN network. Taking the tail risk of each industry as node V, the industry tail risk spillover network GV,W can be mapped.


### 2.3. Network-Associated Metrics

Network correlation indicators from Billio et al. [22] and Wanget al. [37] are borrowed to analyze the level and structure of the correlation of tail risk spillover across industries.


#### 2.3.1. Degree of Association

The degree of association includes the degree of exitδiTo and the degree of entry δiFrom, which measures the external spillover effect of an industry in the network as well as its own spillover shock and is calculated as follows:(5)δiTo=∑i=1,j≠iNwijh,δiFrom=∑j=1,j≠iNwijh,j=1,2,…,n.The out-degree portrays the sum of tail risk spillover caused by the tail risk spillover of an industry as a source. A higher degree of exit indicates that the industry is an active sender of tail risk spillover and the greater the tail risk spillover effect of the industry. The in-degree portrays the sum of tail risk spillover shocks to an industry as a recipient of tail risk spillover from other industries. A higher degree of entry means that the industry is more vulnerable to tail risk spillover from other industries. The total degree of association can be obtained by summing the out-degree and the in-degree, i.e.,δTot=1/N∑i=1NδiFrom=1/N∑i=1NδiTo.


#### 2.3.2. Network Density and Closeness

The network density (ND) ofN industries reflects the degree of connection between nodes in the network; the greater the density is, the closer the relationship between the nodes is. The ND indicator is expressed as(6)ND=1NN−1∑i=1N∑j≠iEi⟶j.Closeness (C) measures the average of the shortest distance between an industry node and all other reachable industry nodes in the network; the smaller the C value is, the shorter the distance between the industry and the reachable nodes is. It also means that the connection to the whole network is closer.(7)Cj=1N−1∑i≠jdj⟶i.


#### 2.3.3. Relative Influence

Relative influence (RI) measures the relative size of the net external spillover of tail risk in an industry. The value of RI ranges from [−1, 1], and the machine formula is(8)RIi=δiToi−δiFromiδiToi+δiFromi.If the RI of an industry is positive (or negative), it means that its impact on other industries is greater (or less) than the impact of other industries on it; that is, the intensity of tail risk spillover from that industry to other industries is greater (or less) than the intensity of spillover from other industries to it. The greater the RI is, the greater the external spillover effect of tail risk in that industry is.


### 2.4. Sample Selection and Data Description

In the selection of industry indicators, we select 28 primary industry1 indices as the sample. The CSI 300 Index is a comprehensive stock price index that reflects the performance of China’s stock market as a whole. Therefore, this paper calculates theΔCoESi|N of each industry index to the CSI 300 index to characterize the industry tail risk. The total sample range is December 2006–December 2020, the data frequency is monthly, and all data are from the Wind database. Considering the information available at each point in time and the calculation volume of the bootstrap method, this paper selects the last trading day data of each month and uses the sliding window algorithm to calculate the upside and downside ΔCoESi|N. The rolling window is set to 12 months. In addition, real-time monitoring of the intensity scale and path direction of tail risk spillover can measure the dynamics of the industry tail risk spillover relationship. We, therefore, combine the characteristics of China’s financial market and use the structural breakpoint identification technique to exclude the impact of abnormal stock market fluctuations in 2015. Using a rolling analysis method, we select two subintervals of the total sample range, October 2008–March 2015 and July 2016–December 2020, to construct a phased risk network.


## 2.1. ∆CoES Method to Calculate Upside and Downside Tail Risk

Using ES as a risk metric and replacing conditional events withXi≤VaRpi, Adrian and Brunnermeier [1] present estimates for CoES that measure the tail effect of individual risk contribution. We improved on these and learned the method from Brownlees and Engle [34] to estimate CoES. As a result, we can capture not only the institutions’ systemic risk exposure and the institutions’ contribution to systemic risk at the same time, but also the long-term stress profiles. It can also use the risk-taking behavior and risk accumulation of institutions during the upside to predict risk mitigation in the downside, thus addressing the procyclicality of the contemporaneous risk metric. Empirical tests show that the upside ∆CoES (as in equation (1)) is appropriate as a forward-looking measure of tail risk, while the downside ∆CoES (as in equation (2)) can lead CoVaR and CoES.This paper extends the application of the ∆CoES model, which is no longer limited to the financial sector. Using the overall industry-wide market as a benchmark, measure the upside and downside ∆CoES values of tail risk for each industry. The specific calculation steps are as follows: the BEKK-MGARCH model is used to estimate the variance equation of log returns for each industry. The distribution of future one-month returns is simulated by the residual bootstrap method, where the forecast periodh = 22 denotes the actual number of trading days in a month, and S denotes the number of simulations. The larger the value of S is, the better the simulation effect is, so we take S = 105. Based on the information for period T and conditional on the arithmetic rate of return R for the next month (h = 22), the ΔCoESi|N values for each industry are obtained separately.(1)upsideΔCoESTi|N=ETRi,T+1:T+h|RN,T+1:T+h≤VaR95N−ETRi,T+1:T+h|RN,T+1:T+h≤VaR50N,(2)downsideΔCoESTi|N=ETRi,T+1:T+h|RN,T+1:T+h≤VaR50N−ETRi,T+1:T+h|RN,T+1:T+h≤VaR5N,where N denotes the number of industries; RT+1 : T + h ≥ VaR95 denotes the extreme state of the upside risk accumulation phase, and RT+1 : T + h ≥ VaR50 denotes the normal state of the upside accumulation phase; RT+1 : T + h ≤ VaR5 denotes the extreme state of the downside risk mitigation, and RT+1 : T + h ≤ VaR50 denotes the normal state of the downside risk mitigation.


## 2.2. Cross-Industrial Tail Risk Spillover Network

The available dataset is usually panel data of industry returns with high-dimensional properties when studying interdependencies among industries. We construct the long-term variance decomposition network ∆CoES-ENGDFM-LVDN that can solve the problem of high-dimensional data incidentally well. Second, this approach can study the correlation between financial and real sectors from the perspective of tail risk spillover, addressing the problem that methods such as correlation coefficients of returns and principal component analysis do not measure the contribution or exposure of individual institutions to systemic risk. The drawback that ∆CoVaR, MES, and other methods cannot capture the network effect of tail risk spillover is avoided. In addition, the method effectively bridges the previous deficiency of demonstrating risk only from the network of financial institutions. It should be noted that the results in this paper are mainly based on the heterogeneity part ofΔCoESi|N, and we argue about its rationality in 3.2. The specific process is as follows: extending the study of Barigozzi and Hallin [28], a two-step dynamic factorial procedure was used. First, the GDFM was applied to extract the common and idiosyncratic components from the tail risk data. Then, the EN model and the LVDN model are applied to identify the size and structure of tail risk spillover among industries.Denote the two-factor process formed by N industries with tail risk dataΔCoESi|N (including upside and downside) as(3)ΔCoES=ΔCoESti|N:i∈N,t∈T=χit+ξit,i∈N,t∈T,where ∆CoES satisfies second-order stationary, zero mean, and finite variance. ∆CoES is absolutely continuous with respect to the Lebesgue measure on −π,π. The qth eigenvector in the spectral density matrix diverges, and the qth+1st eigenvector is bounded. Hallin and Liška [35] prove that the horizontal market shock when the actual data are applied to the GDFM is unique, i.e., q = 1. Thus, there are autoregressive processes AiLχit=ηit=η1t,...,ηNt’,t∈T and FiLξit=vit=v1t,...,vNt′,t∈T, where ηit and vitare n-dimensional white noise processes, and FiL is a one-sided stable VAR filter. Barigozzi and Hallin [28] extracted the idiosyncratic components ξit of ∆CoES in FiL and used EN for sparse processing ξit, always admitting a Wold decomposition, which, after adequate transformation, yields the vector moving average (VMA) representation ξit=DiLeit. Comparing the above equations, we can obtain(4)DiL=FiL−1Ri,where the full-rank matrix Ri makes shocks Rn−1vn=en orthonormal. Ri follows from a Cholesky decomposition of the covariance Cn−1 of the shocks [36], namely, Cn−1=RnRn′. The residual centrality of the partial correlation network (PCN) based on Cn is ranked, so that the most correlated nodes are hit first. Decomposing Ri based on (4) yields the LVDN on the industry tail risk spillover. wijh=100∑k=0h−1dk,ij2/∑l=1n∑k=0h−1dk,il2,i,j=1,…,n means the dependence from contemporaneous to lagged h periods in the LVDN network. Taking the tail risk of each industry as node V, the industry tail risk spillover network GV,W can be mapped.


## 2.3. Network-Associated Metrics

Network correlation indicators from Billio et al. [22] and Wanget al. [37] are borrowed to analyze the level and structure of the correlation of tail risk spillover across industries.


### 2.3.1. Degree of Association

The degree of association includes the degree of exitδiTo and the degree of entry δiFrom, which measures the external spillover effect of an industry in the network as well as its own spillover shock and is calculated as follows:(5)δiTo=∑i=1,j≠iNwijh,δiFrom=∑j=1,j≠iNwijh,j=1,2,…,n.The out-degree portrays the sum of tail risk spillover caused by the tail risk spillover of an industry as a source. A higher degree of exit indicates that the industry is an active sender of tail risk spillover and the greater the tail risk spillover effect of the industry. The in-degree portrays the sum of tail risk spillover shocks to an industry as a recipient of tail risk spillover from other industries. A higher degree of entry means that the industry is more vulnerable to tail risk spillover from other industries. The total degree of association can be obtained by summing the out-degree and the in-degree, i.e.,δTot=1/N∑i=1NδiFrom=1/N∑i=1NδiTo.


### 2.3.2. Network Density and Closeness

The network density (ND) ofN industries reflects the degree of connection between nodes in the network; the greater the density is, the closer the relationship between the nodes is. The ND indicator is expressed as(6)ND=1NN−1∑i=1N∑j≠iEi⟶j.Closeness (C) measures the average of the shortest distance between an industry node and all other reachable industry nodes in the network; the smaller the C value is, the shorter the distance between the industry and the reachable nodes is. It also means that the connection to the whole network is closer.(7)Cj=1N−1∑i≠jdj⟶i.


### 2.3.3. Relative Influence

Relative influence (RI) measures the relative size of the net external spillover of tail risk in an industry. The value of RI ranges from [−1, 1], and the machine formula is(8)RIi=δiToi−δiFromiδiToi+δiFromi.If the RI of an industry is positive (or negative), it means that its impact on other industries is greater (or less) than the impact of other industries on it; that is, the intensity of tail risk spillover from that industry to other industries is greater (or less) than the intensity of spillover from other industries to it. The greater the RI is, the greater the external spillover effect of tail risk in that industry is.


## 2.3.1. Degree of Association

The degree of association includes the degree of exitδiTo and the degree of entry δiFrom, which measures the external spillover effect of an industry in the network as well as its own spillover shock and is calculated as follows:(5)δiTo=∑i=1,j≠iNwijh,δiFrom=∑j=1,j≠iNwijh,j=1,2,…,n.The out-degree portrays the sum of tail risk spillover caused by the tail risk spillover of an industry as a source. A higher degree of exit indicates that the industry is an active sender of tail risk spillover and the greater the tail risk spillover effect of the industry. The in-degree portrays the sum of tail risk spillover shocks to an industry as a recipient of tail risk spillover from other industries. A higher degree of entry means that the industry is more vulnerable to tail risk spillover from other industries. The total degree of association can be obtained by summing the out-degree and the in-degree, i.e.,δTot=1/N∑i=1NδiFrom=1/N∑i=1NδiTo.


## 2.3.2. Network Density and Closeness

The network density (ND) ofN industries reflects the degree of connection between nodes in the network; the greater the density is, the closer the relationship between the nodes is. The ND indicator is expressed as(6)ND=1NN−1∑i=1N∑j≠iEi⟶j.Closeness (C) measures the average of the shortest distance between an industry node and all other reachable industry nodes in the network; the smaller the C value is, the shorter the distance between the industry and the reachable nodes is. It also means that the connection to the whole network is closer.(7)Cj=1N−1∑i≠jdj⟶i.


## 2.3.3. Relative Influence

Relative influence (RI) measures the relative size of the net external spillover of tail risk in an industry. The value of RI ranges from [−1, 1], and the machine formula is(8)RIi=δiToi−δiFromiδiToi+δiFromi.If the RI of an industry is positive (or negative), it means that its impact on other industries is greater (or less) than the impact of other industries on it; that is, the intensity of tail risk spillover from that industry to other industries is greater (or less) than the intensity of spillover from other industries to it. The greater the RI is, the greater the external spillover effect of tail risk in that industry is.


## 2.4. Sample Selection and Data Description

In the selection of industry indicators, we select 28 primary industry1 indices as the sample. The CSI 300 Index is a comprehensive stock price index that reflects the performance of China’s stock market as a whole. Therefore, this paper calculates theΔCoESi|N of each industry index to the CSI 300 index to characterize the industry tail risk. The total sample range is December 2006–December 2020, the data frequency is monthly, and all data are from the Wind database. Considering the information available at each point in time and the calculation volume of the bootstrap method, this paper selects the last trading day data of each month and uses the sliding window algorithm to calculate the upside and downside ΔCoESi|N. The rolling window is set to 12 months. In addition, real-time monitoring of the intensity scale and path direction of tail risk spillover can measure the dynamics of the industry tail risk spillover relationship. We, therefore, combine the characteristics of China’s financial market and use the structural breakpoint identification technique to exclude the impact of abnormal stock market fluctuations in 2015. Using a rolling analysis method, we select two subintervals of the total sample range, October 2008–March 2015 and July 2016–December 2020, to construct a phased risk network.


## 3. Results and Discussion

### 3.1. ∆CoES Measurement Results for Tail Risk

In this paper, we use ∆CoES to measure the level of tail risk spillover in each industry in China. Figure1 gives the trend in the level of tail risk. There are two points that can be derived from the figure as follows. One is that the level of spillover during the accumulation of risk determines the level of spillover when the risk is mitigated. The upside ∆CoES is greater than the downside ∆CoES in most periods for each industry in the full sample interval. The reason is that the tail risk accumulates in the economic upward period and releases continuously in the economic downward period. Taking figure (a) as an example, the level of risk spillover from the mining industries increased more significantly during the adjustment period after the international financial crisis in 2008, the stock market volatility in 2015, and the intensification of international trade frictions and geopolitical conflicts in 2018 and 2019. Comparing Figures (a)-(f), we find that the level of tail spillover in each industry shows cyclical variation. The synergy of tail risks among industries suggests that the real sector, represented by mining and transportation, will also be hit as hard as the financial sector when a crisis occurs. However, it should be noted that the level of tail risk spillover also varies among industries. For example, the overall level of tail risk in the transportation sector began to increase significantly in October 2013, and the utilities upside tail risk had several significant increases in August 2009 and 2015 to 2016. Compared with other industries, the overall tail risk level of the financial sector is relatively stable, mainly concentrated in the range of 0.05–0.15.Figure 1
Temporal variation characteristics of the ∆CoES.
(a)(b)(c)(d)(e)(f)


### 3.2. Sparsity Testing

In the spectral domain, partial spectral coherence (PSC) is strictly related to the coefficients of a VAR representation [38]. In line with the long-run spirit of the LVDN definition, and since volatilities have strong persistence, we first consider the PSCs at frequency θ=0, thus looking at long-run conditional dependencies. Selected percentiles of the distributions of the absolute value of the PSC entries for upside ΔCoESTi|N and idiosyncratic components ξit and the distribution of the absolute value of their differences are shown in Table 1. Both PSCs have many small (in absolute value) entries, which is consistent with our sparsity assumptions. Figures 2(a)-2(c) show the distributions of the absolute value of the PSC entries for upside ΔCoESTi|N and ξit and the distribution of the absolute value of their differences in turn. Similarly, Table 2 shows the distributions of the absolute value of the PSC entries for downside ΔCoESTi|N and idiosyncratic components ξit and the distribution of the absolute value of their differences. The two PSCs are shown in Figures 2(d) and 2(e). The above results suggest that the stochastic component also contains important dependencies after removing market-wide shocks. After ENGDFM processing, the form of factor plus sparse VAR can reveal the network internal dependencies. Therefore, we justify the application of ∆CoES-ENGDFM-LVDN to study the tail risk spillover among industries in terms of model treatment.Table 1
The distributions of the absolute value of PSC for risk accumulation.
QuartilesThe absolute value of the PSC50%90%95%97.50%99%MaximumPSCΔCoESθ=00.1243620.2919090.3232020.3766260.4288840.566802PSCξnθ=00.1171530.2896200.3282380.3801610.4687510.643701PSCΔCoESθ=0−PSCξnθ=00.0432720.1449790.1707330.1999300.2286740.287758Figure 2
PSC in the process of risk accumulation and risk mitigation. (a) PSC of upsideΔCoESTi|N. (b) PSC of upside ξit. (c) Absolute value of upside difference. (d) PSC of downside ΔCoESTi|N. (e) PSC of upside ξit. (f) Absolute value of downside difference.
(a)(b)(c)(d)(e)(f)Table 2
The distributions of the absolute value of the PSC for risk mitigation.
QuartilesThe absolute value of the PSC50%90%95%97.50%99%MaximumPSCΔCoESθ=00.1256150.3134930.3654950.4357550.5002130.592619PSCξnθ=00.1180300.2938030.3764950.4362530.5038970.626567PSCΔCoESθ=0−PSCξnθ=00.0420040.1094300.1434210.1770840.2308840.324330Left and middle panels: weights in absolute values below the 90th percentile in gray, weights above the 90th percentile in red, and weights below the 10th percentile in blue. Right panel: weights below the 90th percentile in gray, between the 90th and 95th percentiles in blue, and above the 95th percentile in red.


### 3.3. Association Level and Structure of Cross-Industrial Tail Risk Spillover in the Full Sample

Using China’s 28 primary industries as network nodes, the cross-industrial tail risk spillover network is formed based on the estimated results of ∆CoES-ENGDFM-LVDN (as shown in Figure3). Figures a and b represent the tail risk spillover relationships for each industry between the upside risk accumulation and downside risk release, respectively. We predict the outbreak of financial crisis and the realization of systemic risk release in the downside cycle through the risk-taking behavior and systemic risk accumulation process in various industries in the upside cycle. In theory, the upside risk spillover and right tail dependence are forward warning indicators of the downside and left tail dependence, where the size of the node indicates the size of the tail risk spillover shock to the industry, and the direction of the arrow between the nodes indicates the risk spillover path. The network indicators defined in the previous section are used to analyze the tail risk spillover among industries.Figure 3
Full sample of China’s cross-industrial tail risk spillover networks. (a) Upside risk accumulation process. (b) Downside risk mitigation process.
(a)(b)In the process of upside risk accumulation and downside risk mitigation, the network density index (ND) is 0.2248677 and 0.1891534, respectively. The total correlations are 36.17 and 49.41, respectively. This indicates that there is an overall persistent nonlinear spillover effect among industry tail risks in China with periodic variation characteristics. The total correlation of the upside risk accumulation process is smaller than that of the downside risk mitigation process, indicating that when the financial cycle is in the downside, the tail risks of the industry are more likely to hit other sectors along the risk network, showing more significant risk spillover effects. The reason for this is that when economic growth slows and investment and consumption are weak, the relative vulnerability of the industries tends to amplify the shock. A continued deterioration in economic conditions will also affect market stability and investor expectations, so risk contagion effects may differ significantly between economic ups and downs.Based on the out-degree and in-degree indicators, we can calculate the spillover effect of industry tail risk in periodh and analyze its role in the contagion chain. Table 3 collates the out-degree, in-degree, and RI indicators of tail risk spillover relationships for 28 primary industries, with columns (2)-(4) indicating the upside risk accumulation phase and columns (5)-(7) indicating the downside risk mitigation phase. In the upside risk accumulation process, the top 10 industry tail risks in descending order of out-degree are Textile and Apparel, Mining, Media, Agriculture, Food and Beverage, Utilities, Chemicals, Conglomerate, Transportation, and Leisure Services. They are active senders of risk spillover, and the spillover effect is relatively strong. The top 10 industry tail risks of in-degree are Electronics, Machinery Equipment, Communications, Banks, Commerce, Automobiles, Construction Materials, Nonferrous Metal, nonbank finance, and Electrical Equipment. They are the primary recipients of the infection and are relatively vulnerable to spillover. In the downside risk mitigation process, the top 10 industry tail risks of out degree in order are Food & Beverage, Communications, Transportation, Electronics, Mining, Health Care, Chemicals, Utilities, Textile & Apparel, and Media. The top 10 industry tail risks of in-degree are construction materials, conglomerate, machinery equipment, chemicals, household appliances, nonbank finance, steel, light-industry manufacturing, commerce, and health care. From the above analysis, it can be seen that the nonbank financial industry is reflected in the in-degree ranking, indicating that whether in the upside risk accumulation or downside risk mitigation process, it has played the role of the recipient of tail risk spillover. Thus, it also indicates that the tail risk spillover from China’s industry is reflected in the associated directions from the nonfinancial sector to the financial sector. Especially in the process of downside risk mitigation, more attention should be given to the ability of the nonbank financial sector to withstand tail risk spillover. We also found that the real estate industry ranked relatively low in both out-degree and in-degree values throughout the sample period, indicating that the process of analyzing tail risk spillover among industries cannot be prevented and resolved simply by the inherent impression of the industry.Table 3
Out-degree, in-degree, and RI indicator of cross-industrial.
Industry (1)Upside risk accumulation phaseDownside risk mitigation phaseOut-degree (2)In-degree (3)RI (4)Out-degree (5)In-degree (6)RI (7)Mining114.054517.45300.73457027261.650132.86520.304552808Transportation38.40217.39690.67698421466.723018.13110.572652353Leisure services26.13119.83830.45296279612.814731.8501−0.426183482Media86.653810.56190.78271205217.733139.2600−0.377710635Utilities54.207726.29840.34667310929.121847.6602−0.241442005Agriculture82.318136.67100.3836242148.276652.5921−0.728050706Chemicals53.596337.60670.17531879437.689763.0075−0.251425064Health care25.143523.45280.03479071544.577555.4160−0.108392045Commerce4.857552.3779−0.8302623910.187757.2267−0.697758936National defense22.476133.6635−0.1992782289.316053.7339−0.704488032Household appliances11.746928.1271−0.4107990170.000062.5923−1Construction materials17.842248.3596−0.46097538116.588868.1793−0.608607483Construction furnishings15.118023.3335−0.21365876515.787632.0357−0.339752798Real estate5.493435.4223−0.7314771595.613852.0842−0.805407466Nonferrous metal4.186747.8813−0.8391833762.228653.2019−0.919589396Machinery equipment0.000060.7620−10.000063.0327−1Automobiles2.840448.3764−0.889083270.000051.7961−1Electronics16.932362.2757−0.57245985366.650444.87510.195249517Electrical equipment0.000043.5438−10.000054.4843−1Textile and apparel232.43490.0000122.412046.8030−0.352394712Conglomerate47.907233.70100.1740780953.496464.7932−0.897600806Computer11.749543.3565−0.5735673073.180251.7017−0.884107511Light-industry manufacturing19.244837.9764−0.3273541977.299860.7444−0.785439464Communications24.070760.1110−0.428125115239.534849.78380.655854826Steel7.020842.3321−0.7154858178.973362.0339−0.747256616Banks3.819354.7705−0.8696257718.893351.3620−0.704812689Nonbank finance4.561843.9214−0.8118193522.302062.3088−0.928742563Food and beverage80.058043.29670.298012966682.50410.00001Total degree36.173849.4127Columns (4) and (7) of Table3 present the relative impact indicators for each industry, which measure the magnitude of the net spillover of tail risk in a given industry. During the upside risk accumulation process, the RI indicators of the top ten industries in terms of out-degree are all greater than zero, implying that they all have a positive net tail risk spillover. This can indicate that risks accumulate in several sectors during the upside and start to be mitigated during the downside. Taking into account the ranking by out-degree and the net spillover from the tail risk of the industry represented by RI, there are ten industries, Textile and Apparel, Media, Mining, Transportation, Leisure Services, Agriculture, Utilities, Food and Beverage, Chemicals, and Conglomerate, which become important sources of risk spillover in the process of risk accumulation during the sample period. In the downside risk mitigation process, combining out-degree values and the RI indicator reveals that Food and Beverage, Communications, Transportation, Mining, and Electronics are the main sources of net tail risk spillover. In addition, the number of net spillover industries has decreased during downside risk mitigation. The reason is that the abovementioned industries are important net spillover nodes and sources of risk, and their spillover is gradually mitigated in the process of downside risk mitigation.A smaller tightness (C) indicates that the node is more closely connected to the whole network. During the accumulation of upside risk, the top 10 industries in order of C from smallest to largest are Machinery Equipment, Communications, Electrical Equipment, nonbank finance, Food and Beverage, Banks, Computer, Automobiles, Electronics, and Nonferrous Metal. During the downside risk mitigation process, the top 10 industries in ascending order of size C are Automobiles, Light-industry Manufacturing, Computer, Household Appliances, Banks, Electrical Equipment, Nonferrous Metal, Mining, nonbank finance, and Machinery Equipment. As shown in the columns of Table4(2)-(3), certain industries, which are important sources of spillover, do not have high network tightness. In contrast, some risk sources that are not at the center of the risk network may have a stronger tail risk network propagation. It is worth noting that the industries with the same top rankings for closeness, out degree, in degree, and RI in the full sample interval are Machinery Equipment, Communications, Electrical Equipment, nonbank finance, Food and Beverage, Banks, Automobiles, and Nonferrous Metal. The eight industries mentioned above are at the center of the spillover association in the overall tail risk spillover network.Table 4
Closeness values of China’s industry.
Sample intervalFull sample intervalInterval 1Interval 2IndustryUpside (2)Downside (3)Upside (4)Downside (5)Upside (6)Downside (7)Food and beverage103756624260289189Communications97729278702305219Transportation145702625387291258Mining124171625378702260Electronics108702409327311240Health care110702623363323254Utilities113186464375319257Chemicals116182464756312261Construction furnishings118197622358334235Textile and apparel756187541298315226Media112702278371296251Leisure services729675435393281255Construction materials113174624379325235Commerce111193383372308255National defense115621381361702247Banks104166569357308227Agriculture115648541371703250Steel114182390360293239Light-industry manufacturing109154356229273217Real estate110176595358323239Computer107156409341336211Conglomerate729175486265300258Nonferrous metal108168516369264237Nonbank finance101173567308299182Automobiles107143567335216211Household appliances123158303702284248Electrical equipment100167381326675234Machinery equipment79173541366254243


### 3.4. Dynamics of Cross-Industrial Tail Risk Spillover Correlation

The magnitude and direction of the association of cross-industrial tail risk spillover can change over time. The above examines the spillover of tail risk across industries in the network based on the full sample results but may miss important information changes, and regulators need to grasp the dynamic characteristics of the magnitude and path direction of correlation intensity across industries. This paper divides the sample interval into 2 different periods based on the characteristics of China’s economic and financial market operations, combined with structural breakpoint2 identification. The two periods are October 2008–March 2015 (interval I) and July 2016–December 2020 (interval II), excluding the effect of the abnormal stock market volatility phase in 2015. Figure4 gives the dynamic characteristics of the network correlation structure for the above two intervals.Figure 4
Cross-industrial tail risk spillover networks in China. (a) Upside risk accumulation process in interval I. (b) Downside risk mitigation process in interval I. (c) Upside risk accumulation process in interval II. (d) Downside risk mitigation process in interval II.
(a)(b)(c)(d)In the process of risk accumulation in the interval of period I, the top 10 industry tail risks in order of out-degree are mining, food and beverage, health care, construction materials, construction furnishings, textile and apparel, transportation, agriculture, real estate, and nonferrous metals. The top 10 in-degree are communications, steel, automobiles, electrical equipment, chemicals, commerce, leisure services, national defense, electronics, and light-industry manufacturing. Columns 2–4 of Table5 show the RI values, and the top ten industries, from largest to smallest, are mining, health care, food and beverage, construction materials, transportation, construction furnishings, textile and apparel agriculture, real estate, and nonbank finance. Closeness (C) ranking in order: communications, media, household appliances, light-industry manufacturing, national defense, electrical equipment, commerce, steel, electronics, and computer (as in column 4 of Table 4). In the process of risk mitigation, the top 10 industries ranked by tail risk out-degree ranking in order: chemicals, communications, transportation, household appliances, mining, leisure services, utilities, nonferrous metals, construction materials, and construction furnishings. The top 10 in-degree are steel, automobiles, computer, conglomerate, nonbank finance, electrical equipment, light-industry manufacturing, machinery equipment, food and beverage, and electronics. The RI ranking in order is chemicals, transportation, communications, mining, household appliances, leisure services, utilities, nonferrous metals, agriculture, and construction furnishings (as listed in columns 5–7 in Table 5). C is listed in ascending order as follows: light-industry Manufacturing, Food and Beverage, conglomerate, textile and apparel, nonbank finance, electrical equipment, electronics, automobiles, computer, and banks (as in column 5 of Table 4).Table 5
Tail risk spillover network indicators among subsamples.
Interval IInterval IIUpside risks accumulateDownside risks mitigatedUpside risks accumulateDownside risks mitigatedIndustry (1)Out-deg (2)In-deg (3)RI (4)Out-deg (5)In-deg (6)RI (7)Out-deg (8)In-deg (9)RI (10)Out-deg (11)In-deg (12)RI (13)Mining350.6113.230.9273102.7248.180.36141503.034.430.99491.9337.600.419Transportation67.2920.950.5252134.8812.850.82610.000090.95−1162.3355.240.492Leisure services7.8181.43−0.824965.1956.080.07512.4185.09−0.9459.8359.43−0.716Media0.000070.37−114.9463.59−0.61952.1192.19−0.95556.4965.41−0.073Utilities24.1869.45−0.483536.5066.63−0.29228.6879.91−0.80435.3868.41−0.318Agriculture48.8861.31−0.112825.5649.71−0.3209160.9125.460.72729.3754.61−0.301Chemicals3.6381.78−0.91501026.230.0000148.4183.70−0.267111.8156.620.328Health care329.5216.760.903216.5363.15−0.585121.4149.21−0.39426.1554.26−0.35Commerce0.000081.43−118.4468.55−0.576012.6678.91−0.72322.9057.74−0.432National defense0.000080.79−13.1567.64−0.9111209.0343.790.6546.4678.32−0.848Household appliances0.000072.04−1126.7367.120.30750.000085.76−113.2861.10−0.643Construction materials294.4651.610.701734.5171.76−0.350542.4172.63−0.26322.6880.22−0.559Construction furnishing99.8142.280.404928.3656.16−0.328919.0083.91−0.6316.9877.86−0.836Real estate40.8563.78−0.21913.8572.92−0.89974.5472.21−0.8822.6175.06−0.933Nonferrous metal29.4578.37−0.453735.4166.59−0.30560.000084.44−110.7677.92−0.757Machinery equipment16.5471.38−0.623710.5477.06−0.75930.000095.88−11225.467.210.988Automobiles24.8884.78−0.54632.6286.32−0.94110.000084.76−10.000071.23−1Electronics7.5480.62−0.82902.3073.74−0.939412.9883.63−0.73113.3871.42−0.684Electrical equipment3.6883.79−0.91590.000079.23−126.7775.16−0.4758.2365.99−0.778Textile and apparel70.2546.040.20826.6070.73−0.82929.1777.62−0.7890.000071.22−1Conglomerate25.8877.18−0.49770.000083.89−10.000075.02−160.0270.03−0.077Computer7.9172.02−0.80200.000085.70−12.2181.01−0.9475.4686.55−0.881Light-industry manufacturing0.000079.79−10.000077.53−110.8289.12−0.7842.8487.95−0.937Communications0.000086.83−1141.4564.110.37627.3585.62−0.8420.000083.65−1Steel0.000084.83−12.3088.86−0.94950.000081.39−12.6884.51−0.939Banks6.08463.12−0.82426.1470.94−0.840714.1383.39−0.712.2887.56−0.949Nonbank financials26.5765.29−0.42150.000081.18−12.4489.83−0.9470.000093.56−1Food and beverage333.8238.410.79360.000074.75−14.5389.97−0.9040.000088.61−1Total degree64.9965.8975.8968.90In the process of risk accumulation during the interval II period, the top 10 out-degree rankings of industry tail risk are mining, national defense, agriculture, chemicals, construction materials, electrical equipment, health care, construction furnishings, banks, and electronics. The top 10 in-degree rankings are machinery equipment, media, transportation, food and beverage, nonbank finance, light-industry manufacturing, household appliances, communication, leisure services, and automobiles. Columns 8–10 of Table5 show the magnitude of RI, with the top ten in descending order: mining, agriculture, national defense, construction materials, chemicals, health care, electrical equipment, construction furnishings, banks, and commerce. C ranking in order: automobiles, machinery equipment, nonferrous metals, light-industry manufacturing, leisure services, household appliances, food and beverages, transportation, steel, and media (as in column 6 of Table 4). In the process of risk mitigation, the top 10 industry tail risks in order of out-degree are machinery equipment, transportation, chemicals, mining, conglomerate, media, utilities, agriculture, health care, and commerce. The top 10 in order of in-degree are nonbank finance, food and beverage, light-industry manufacturing, banks, computers, steel, communications, construction materials, national defense, and nonferrous metals. The RI ranking in order is machinery equipment, transportation, mining, chemicals, media, conglomerate, agriculture, utilities, health care, and commerce (as listed in Table 5, columns 11–13). The C ranking in order is nonbank finance, food and beverage, computer, automobiles, light-industry manufacturing, communications, textile and apparel, banks, electrical equipment, and construction furnishings (as in column 7 of Table 4).To facilitate the analysis, we briefly present the above results in Table6. They show that the level of risk spillover in different industries differs from the average cross-industrial risk spillover in the overall market in different intervals. The cross-sectional dimension allows us to compare the differences in spillover effects between the upside risk accumulation and downside risk mitigation phases within the same sample interval and analyze the accumulation of risk spillover levels from normal to extreme states. The time dimension allows for a longitudinal analysis of the evolution of the industry tail risk spillover relationship across the intervals. It is possible to compare the evolution of risk spillover within the same risk phase (upside risk accumulation or downside risk mitigation) across sample intervals.Table 6
Subsample index ranking.
Interval 1 UpsideInterval 2 UpsideIn-degreeCommunications, steel, automobiles, electrical equipment, chemicalsMachinery equipment, media, transportation, food and beverage, nonbank financialsOut-degreeMining, food and beverage, health care, construction materials, construction furnishingsMining, national defense, agriculture, chemicals, construction materialsRIMining, health care, food and beverage, construction materials, transportationMining, agriculture, national defense, construction materials, chemicalsClosenessCommunications, media, household appliances, light-industry manufacturing, national defenseAutomobiles, machinery equipment, nonferrous metal, light-industry manufacturing, leisure servicesInterval 1 downsideInterval 2 downsideIn-degreeSteel, automobiles, computer, conglomerate, nonbank financialsNonbank financials, food & beverage, light-industry manufacturing, banks, computerOut-degreeChemicals, communications, transportation, household appliances, miningMachinery equipment, transportation, chemicals, mining, conglomerateRIChemicals, transportation, communications, Mining, household appliancesMachinery equipment, transportation, mining, chemicals, mediaClosenessLight-industry manufacturing, food and beverage, conglomerate, textile & apparel, nonbank financialsNonbank financials, food and beverage, computer, automobiles, light-industry manufacturingFirst, the differences in tail risk spillover effects among industries are compared. In interval I, the senders of risk spillover during the upside risk accumulation process include the tail risk of the real estate industry, and the receivers of risk spillover do not have banks or nonbank financial industries. Nonbank finance appears in the in-degree ranking as the receivers of tail risk spillover during the downside risk mitigation process. There are no estimates of tail risk in the real estate industry in either the full sample interval or the sample interval II out-degree ranking, indicating that the impact of tail risk in the real estate industry is large in the earlier period. The impact of tail risk accumulation within the real estate industry in China has gradually decreased in recent years with the regulation of this industry. The risk spillover senders and receivers in Interval II are more likely to reflect the tail risks of industries involving emerging sectors of strategic importance, such as communications, computers, and health care, indicating that the impact of strategic emerging industries on the economic and financial system is of increasing concern in the process of structural transformation and upgrading of China’s industries. In Interval II, in terms of closeness, tail risks in the nonbank financial industry are not at the center of the network during the upside risk accumulation phase but evolve into an important network center during the downside risk mitigation phase, playing an important role in the risk spillover contagion chain.Second, the evolution of the cross-industrial tail risk spillover is compared across different intervals. In the process of upside risk accumulation and downside risk mitigation, the network density indicators ND in sample intervals I and II are 0.2592593 and 0.2301587 and 0.1931217 and 0.207672, respectively. The total correlations are 64.99 and 65.89 and 75.89 and 68.90, respectively; thus, the nonlinear effects and cyclical changes of tail risk spillover among industries still exist. Regardless of the upside risk accumulation or downside risk mitigation process, the total correlation in interval II is greater than that in interval I. This indicates that the impact of tail risk spillover in China has been gradually expanding in the cross-industrial range in recent years from the vertical time dimension. In the interval I time period, the total correlation of the upside risk accumulation process is smaller than the total correlation of the downside risk mitigation process, while in the interval II time period, the result is the exact opposite. The total correlation of the upside risk accumulation process shifts to be larger than the total correlation of the downside risk mitigation process, indicating that the downside risk is not fully mitigated in the process of expanding the impact of tail risk spillover in recent years. In addition, in the downside and upside risk phases of the two sample subregions, the tail risks of industries such as mining, transportation, utilities, and agriculture in the nonfinancial sector are among the stable risk spillover senders. They provide basic services and production materials supply for other sectors while generating more obvious risk shocks to other industries. The tail risks of the communications, health care, computer, and other industries are gradually rising in the network. This conclusion forms a synthesis of established studies related to cross-industrial risk spillover and an extended validation of them. It is worth noting that although the nonbank financial industry is not in the ranking of risk spillover senders, the in-degree ranking of the industry has improved more significantly in recent years. During the downside risk mitigation phase of Interval II, it is not only the top-ranked tail risk spillover recipient, but also in the center of the network in terms of closeness, which again confirms the characteristics of tail risk spillover from the nonfinancial sector to the financial sector. Based on the fact that China’s nonbank financial industry is not the sender but the receiver of tail risk spillover, it is more important to pay attention to the increase in risk exposure of the nonbank financial sector and strengthen its ability to bear tail risk spillover. At the same time, it is also necessary to pay attention to the risk-sending effect presented by the Bank sector during the upside risk accumulation phase and the role it played in promoting risk accumulation.Finally, the evolution of risk spillover within the same risk stage in different sample intervals is compared. Based on the estimation results, it is found that the total correlation within interval II during the accumulation of upside risk is significantly larger than the total correlation in interval I. This indicates that the upside risks have accumulated faster in recent years, but thanks to effective regulation, the downside risk mitigation is gradually resolved and does not show an accelerating trend of mitigation. That being said, there is still a need to focus on the impact of upside risks.


## 3.1. ∆CoES Measurement Results for Tail Risk

In this paper, we use ∆CoES to measure the level of tail risk spillover in each industry in China. Figure1 gives the trend in the level of tail risk. There are two points that can be derived from the figure as follows. One is that the level of spillover during the accumulation of risk determines the level of spillover when the risk is mitigated. The upside ∆CoES is greater than the downside ∆CoES in most periods for each industry in the full sample interval. The reason is that the tail risk accumulates in the economic upward period and releases continuously in the economic downward period. Taking figure (a) as an example, the level of risk spillover from the mining industries increased more significantly during the adjustment period after the international financial crisis in 2008, the stock market volatility in 2015, and the intensification of international trade frictions and geopolitical conflicts in 2018 and 2019. Comparing Figures (a)-(f), we find that the level of tail spillover in each industry shows cyclical variation. The synergy of tail risks among industries suggests that the real sector, represented by mining and transportation, will also be hit as hard as the financial sector when a crisis occurs. However, it should be noted that the level of tail risk spillover also varies among industries. For example, the overall level of tail risk in the transportation sector began to increase significantly in October 2013, and the utilities upside tail risk had several significant increases in August 2009 and 2015 to 2016. Compared with other industries, the overall tail risk level of the financial sector is relatively stable, mainly concentrated in the range of 0.05–0.15.Figure 1
Temporal variation characteristics of the ∆CoES.
(a)(b)(c)(d)(e)(f)


## 3.2. Sparsity Testing

In the spectral domain, partial spectral coherence (PSC) is strictly related to the coefficients of a VAR representation [38]. In line with the long-run spirit of the LVDN definition, and since volatilities have strong persistence, we first consider the PSCs at frequency θ=0, thus looking at long-run conditional dependencies. Selected percentiles of the distributions of the absolute value of the PSC entries for upside ΔCoESTi|N and idiosyncratic components ξit and the distribution of the absolute value of their differences are shown in Table 1. Both PSCs have many small (in absolute value) entries, which is consistent with our sparsity assumptions. Figures 2(a)-2(c) show the distributions of the absolute value of the PSC entries for upside ΔCoESTi|N and ξit and the distribution of the absolute value of their differences in turn. Similarly, Table 2 shows the distributions of the absolute value of the PSC entries for downside ΔCoESTi|N and idiosyncratic components ξit and the distribution of the absolute value of their differences. The two PSCs are shown in Figures 2(d) and 2(e). The above results suggest that the stochastic component also contains important dependencies after removing market-wide shocks. After ENGDFM processing, the form of factor plus sparse VAR can reveal the network internal dependencies. Therefore, we justify the application of ∆CoES-ENGDFM-LVDN to study the tail risk spillover among industries in terms of model treatment.Table 1
The distributions of the absolute value of PSC for risk accumulation.
QuartilesThe absolute value of the PSC50%90%95%97.50%99%MaximumPSCΔCoESθ=00.1243620.2919090.3232020.3766260.4288840.566802PSCξnθ=00.1171530.2896200.3282380.3801610.4687510.643701PSCΔCoESθ=0−PSCξnθ=00.0432720.1449790.1707330.1999300.2286740.287758Figure 2
PSC in the process of risk accumulation and risk mitigation. (a) PSC of upsideΔCoESTi|N. (b) PSC of upside ξit. (c) Absolute value of upside difference. (d) PSC of downside ΔCoESTi|N. (e) PSC of upside ξit. (f) Absolute value of downside difference.
(a)(b)(c)(d)(e)(f)Table 2
The distributions of the absolute value of the PSC for risk mitigation.
QuartilesThe absolute value of the PSC50%90%95%97.50%99%MaximumPSCΔCoESθ=00.1256150.3134930.3654950.4357550.5002130.592619PSCξnθ=00.1180300.2938030.3764950.4362530.5038970.626567PSCΔCoESθ=0−PSCξnθ=00.0420040.1094300.1434210.1770840.2308840.324330Left and middle panels: weights in absolute values below the 90th percentile in gray, weights above the 90th percentile in red, and weights below the 10th percentile in blue. Right panel: weights below the 90th percentile in gray, between the 90th and 95th percentiles in blue, and above the 95th percentile in red.


## 3.3. Association Level and Structure of Cross-Industrial Tail Risk Spillover in the Full Sample

Using China’s 28 primary industries as network nodes, the cross-industrial tail risk spillover network is formed based on the estimated results of ∆CoES-ENGDFM-LVDN (as shown in Figure3). Figures a and b represent the tail risk spillover relationships for each industry between the upside risk accumulation and downside risk release, respectively. We predict the outbreak of financial crisis and the realization of systemic risk release in the downside cycle through the risk-taking behavior and systemic risk accumulation process in various industries in the upside cycle. In theory, the upside risk spillover and right tail dependence are forward warning indicators of the downside and left tail dependence, where the size of the node indicates the size of the tail risk spillover shock to the industry, and the direction of the arrow between the nodes indicates the risk spillover path. The network indicators defined in the previous section are used to analyze the tail risk spillover among industries.Figure 3
Full sample of China’s cross-industrial tail risk spillover networks. (a) Upside risk accumulation process. (b) Downside risk mitigation process.
(a)(b)In the process of upside risk accumulation and downside risk mitigation, the network density index (ND) is 0.2248677 and 0.1891534, respectively. The total correlations are 36.17 and 49.41, respectively. This indicates that there is an overall persistent nonlinear spillover effect among industry tail risks in China with periodic variation characteristics. The total correlation of the upside risk accumulation process is smaller than that of the downside risk mitigation process, indicating that when the financial cycle is in the downside, the tail risks of the industry are more likely to hit other sectors along the risk network, showing more significant risk spillover effects. The reason for this is that when economic growth slows and investment and consumption are weak, the relative vulnerability of the industries tends to amplify the shock. A continued deterioration in economic conditions will also affect market stability and investor expectations, so risk contagion effects may differ significantly between economic ups and downs.Based on the out-degree and in-degree indicators, we can calculate the spillover effect of industry tail risk in periodh and analyze its role in the contagion chain. Table 3 collates the out-degree, in-degree, and RI indicators of tail risk spillover relationships for 28 primary industries, with columns (2)-(4) indicating the upside risk accumulation phase and columns (5)-(7) indicating the downside risk mitigation phase. In the upside risk accumulation process, the top 10 industry tail risks in descending order of out-degree are Textile and Apparel, Mining, Media, Agriculture, Food and Beverage, Utilities, Chemicals, Conglomerate, Transportation, and Leisure Services. They are active senders of risk spillover, and the spillover effect is relatively strong. The top 10 industry tail risks of in-degree are Electronics, Machinery Equipment, Communications, Banks, Commerce, Automobiles, Construction Materials, Nonferrous Metal, nonbank finance, and Electrical Equipment. They are the primary recipients of the infection and are relatively vulnerable to spillover. In the downside risk mitigation process, the top 10 industry tail risks of out degree in order are Food & Beverage, Communications, Transportation, Electronics, Mining, Health Care, Chemicals, Utilities, Textile & Apparel, and Media. The top 10 industry tail risks of in-degree are construction materials, conglomerate, machinery equipment, chemicals, household appliances, nonbank finance, steel, light-industry manufacturing, commerce, and health care. From the above analysis, it can be seen that the nonbank financial industry is reflected in the in-degree ranking, indicating that whether in the upside risk accumulation or downside risk mitigation process, it has played the role of the recipient of tail risk spillover. Thus, it also indicates that the tail risk spillover from China’s industry is reflected in the associated directions from the nonfinancial sector to the financial sector. Especially in the process of downside risk mitigation, more attention should be given to the ability of the nonbank financial sector to withstand tail risk spillover. We also found that the real estate industry ranked relatively low in both out-degree and in-degree values throughout the sample period, indicating that the process of analyzing tail risk spillover among industries cannot be prevented and resolved simply by the inherent impression of the industry.Table 3
Out-degree, in-degree, and RI indicator of cross-industrial.
Industry (1)Upside risk accumulation phaseDownside risk mitigation phaseOut-degree (2)In-degree (3)RI (4)Out-degree (5)In-degree (6)RI (7)Mining114.054517.45300.73457027261.650132.86520.304552808Transportation38.40217.39690.67698421466.723018.13110.572652353Leisure services26.13119.83830.45296279612.814731.8501−0.426183482Media86.653810.56190.78271205217.733139.2600−0.377710635Utilities54.207726.29840.34667310929.121847.6602−0.241442005Agriculture82.318136.67100.3836242148.276652.5921−0.728050706Chemicals53.596337.60670.17531879437.689763.0075−0.251425064Health care25.143523.45280.03479071544.577555.4160−0.108392045Commerce4.857552.3779−0.8302623910.187757.2267−0.697758936National defense22.476133.6635−0.1992782289.316053.7339−0.704488032Household appliances11.746928.1271−0.4107990170.000062.5923−1Construction materials17.842248.3596−0.46097538116.588868.1793−0.608607483Construction furnishings15.118023.3335−0.21365876515.787632.0357−0.339752798Real estate5.493435.4223−0.7314771595.613852.0842−0.805407466Nonferrous metal4.186747.8813−0.8391833762.228653.2019−0.919589396Machinery equipment0.000060.7620−10.000063.0327−1Automobiles2.840448.3764−0.889083270.000051.7961−1Electronics16.932362.2757−0.57245985366.650444.87510.195249517Electrical equipment0.000043.5438−10.000054.4843−1Textile and apparel232.43490.0000122.412046.8030−0.352394712Conglomerate47.907233.70100.1740780953.496464.7932−0.897600806Computer11.749543.3565−0.5735673073.180251.7017−0.884107511Light-industry manufacturing19.244837.9764−0.3273541977.299860.7444−0.785439464Communications24.070760.1110−0.428125115239.534849.78380.655854826Steel7.020842.3321−0.7154858178.973362.0339−0.747256616Banks3.819354.7705−0.8696257718.893351.3620−0.704812689Nonbank finance4.561843.9214−0.8118193522.302062.3088−0.928742563Food and beverage80.058043.29670.298012966682.50410.00001Total degree36.173849.4127Columns (4) and (7) of Table3 present the relative impact indicators for each industry, which measure the magnitude of the net spillover of tail risk in a given industry. During the upside risk accumulation process, the RI indicators of the top ten industries in terms of out-degree are all greater than zero, implying that they all have a positive net tail risk spillover. This can indicate that risks accumulate in several sectors during the upside and start to be mitigated during the downside. Taking into account the ranking by out-degree and the net spillover from the tail risk of the industry represented by RI, there are ten industries, Textile and Apparel, Media, Mining, Transportation, Leisure Services, Agriculture, Utilities, Food and Beverage, Chemicals, and Conglomerate, which become important sources of risk spillover in the process of risk accumulation during the sample period. In the downside risk mitigation process, combining out-degree values and the RI indicator reveals that Food and Beverage, Communications, Transportation, Mining, and Electronics are the main sources of net tail risk spillover. In addition, the number of net spillover industries has decreased during downside risk mitigation. The reason is that the abovementioned industries are important net spillover nodes and sources of risk, and their spillover is gradually mitigated in the process of downside risk mitigation.A smaller tightness (C) indicates that the node is more closely connected to the whole network. During the accumulation of upside risk, the top 10 industries in order of C from smallest to largest are Machinery Equipment, Communications, Electrical Equipment, nonbank finance, Food and Beverage, Banks, Computer, Automobiles, Electronics, and Nonferrous Metal. During the downside risk mitigation process, the top 10 industries in ascending order of size C are Automobiles, Light-industry Manufacturing, Computer, Household Appliances, Banks, Electrical Equipment, Nonferrous Metal, Mining, nonbank finance, and Machinery Equipment. As shown in the columns of Table4(2)-(3), certain industries, which are important sources of spillover, do not have high network tightness. In contrast, some risk sources that are not at the center of the risk network may have a stronger tail risk network propagation. It is worth noting that the industries with the same top rankings for closeness, out degree, in degree, and RI in the full sample interval are Machinery Equipment, Communications, Electrical Equipment, nonbank finance, Food and Beverage, Banks, Automobiles, and Nonferrous Metal. The eight industries mentioned above are at the center of the spillover association in the overall tail risk spillover network.Table 4
Closeness values of China’s industry.
Sample intervalFull sample intervalInterval 1Interval 2IndustryUpside (2)Downside (3)Upside (4)Downside (5)Upside (6)Downside (7)Food and beverage103756624260289189Communications97729278702305219Transportation145702625387291258Mining124171625378702260Electronics108702409327311240Health care110702623363323254Utilities113186464375319257Chemicals116182464756312261Construction furnishings118197622358334235Textile and apparel756187541298315226Media112702278371296251Leisure services729675435393281255Construction materials113174624379325235Commerce111193383372308255National defense115621381361702247Banks104166569357308227Agriculture115648541371703250Steel114182390360293239Light-industry manufacturing109154356229273217Real estate110176595358323239Computer107156409341336211Conglomerate729175486265300258Nonferrous metal108168516369264237Nonbank finance101173567308299182Automobiles107143567335216211Household appliances123158303702284248Electrical equipment100167381326675234Machinery equipment79173541366254243


## 3.4. Dynamics of Cross-Industrial Tail Risk Spillover Correlation

The magnitude and direction of the association of cross-industrial tail risk spillover can change over time. The above examines the spillover of tail risk across industries in the network based on the full sample results but may miss important information changes, and regulators need to grasp the dynamic characteristics of the magnitude and path direction of correlation intensity across industries. This paper divides the sample interval into 2 different periods based on the characteristics of China’s economic and financial market operations, combined with structural breakpoint2 identification. The two periods are October 2008–March 2015 (interval I) and July 2016–December 2020 (interval II), excluding the effect of the abnormal stock market volatility phase in 2015. Figure4 gives the dynamic characteristics of the network correlation structure for the above two intervals.Figure 4
Cross-industrial tail risk spillover networks in China. (a) Upside risk accumulation process in interval I. (b) Downside risk mitigation process in interval I. (c) Upside risk accumulation process in interval II. (d) Downside risk mitigation process in interval II.
(a)(b)(c)(d)In the process of risk accumulation in the interval of period I, the top 10 industry tail risks in order of out-degree are mining, food and beverage, health care, construction materials, construction furnishings, textile and apparel, transportation, agriculture, real estate, and nonferrous metals. The top 10 in-degree are communications, steel, automobiles, electrical equipment, chemicals, commerce, leisure services, national defense, electronics, and light-industry manufacturing. Columns 2–4 of Table5 show the RI values, and the top ten industries, from largest to smallest, are mining, health care, food and beverage, construction materials, transportation, construction furnishings, textile and apparel agriculture, real estate, and nonbank finance. Closeness (C) ranking in order: communications, media, household appliances, light-industry manufacturing, national defense, electrical equipment, commerce, steel, electronics, and computer (as in column 4 of Table 4). In the process of risk mitigation, the top 10 industries ranked by tail risk out-degree ranking in order: chemicals, communications, transportation, household appliances, mining, leisure services, utilities, nonferrous metals, construction materials, and construction furnishings. The top 10 in-degree are steel, automobiles, computer, conglomerate, nonbank finance, electrical equipment, light-industry manufacturing, machinery equipment, food and beverage, and electronics. The RI ranking in order is chemicals, transportation, communications, mining, household appliances, leisure services, utilities, nonferrous metals, agriculture, and construction furnishings (as listed in columns 5–7 in Table 5). C is listed in ascending order as follows: light-industry Manufacturing, Food and Beverage, conglomerate, textile and apparel, nonbank finance, electrical equipment, electronics, automobiles, computer, and banks (as in column 5 of Table 4).Table 5
Tail risk spillover network indicators among subsamples.
Interval IInterval IIUpside risks accumulateDownside risks mitigatedUpside risks accumulateDownside risks mitigatedIndustry (1)Out-deg (2)In-deg (3)RI (4)Out-deg (5)In-deg (6)RI (7)Out-deg (8)In-deg (9)RI (10)Out-deg (11)In-deg (12)RI (13)Mining350.6113.230.9273102.7248.180.36141503.034.430.99491.9337.600.419Transportation67.2920.950.5252134.8812.850.82610.000090.95−1162.3355.240.492Leisure services7.8181.43−0.824965.1956.080.07512.4185.09−0.9459.8359.43−0.716Media0.000070.37−114.9463.59−0.61952.1192.19−0.95556.4965.41−0.073Utilities24.1869.45−0.483536.5066.63−0.29228.6879.91−0.80435.3868.41−0.318Agriculture48.8861.31−0.112825.5649.71−0.3209160.9125.460.72729.3754.61−0.301Chemicals3.6381.78−0.91501026.230.0000148.4183.70−0.267111.8156.620.328Health care329.5216.760.903216.5363.15−0.585121.4149.21−0.39426.1554.26−0.35Commerce0.000081.43−118.4468.55−0.576012.6678.91−0.72322.9057.74−0.432National defense0.000080.79−13.1567.64−0.9111209.0343.790.6546.4678.32−0.848Household appliances0.000072.04−1126.7367.120.30750.000085.76−113.2861.10−0.643Construction materials294.4651.610.701734.5171.76−0.350542.4172.63−0.26322.6880.22−0.559Construction furnishing99.8142.280.404928.3656.16−0.328919.0083.91−0.6316.9877.86−0.836Real estate40.8563.78−0.21913.8572.92−0.89974.5472.21−0.8822.6175.06−0.933Nonferrous metal29.4578.37−0.453735.4166.59−0.30560.000084.44−110.7677.92−0.757Machinery equipment16.5471.38−0.623710.5477.06−0.75930.000095.88−11225.467.210.988Automobiles24.8884.78−0.54632.6286.32−0.94110.000084.76−10.000071.23−1Electronics7.5480.62−0.82902.3073.74−0.939412.9883.63−0.73113.3871.42−0.684Electrical equipment3.6883.79−0.91590.000079.23−126.7775.16−0.4758.2365.99−0.778Textile and apparel70.2546.040.20826.6070.73−0.82929.1777.62−0.7890.000071.22−1Conglomerate25.8877.18−0.49770.000083.89−10.000075.02−160.0270.03−0.077Computer7.9172.02−0.80200.000085.70−12.2181.01−0.9475.4686.55−0.881Light-industry manufacturing0.000079.79−10.000077.53−110.8289.12−0.7842.8487.95−0.937Communications0.000086.83−1141.4564.110.37627.3585.62−0.8420.000083.65−1Steel0.000084.83−12.3088.86−0.94950.000081.39−12.6884.51−0.939Banks6.08463.12−0.82426.1470.94−0.840714.1383.39−0.712.2887.56−0.949Nonbank financials26.5765.29−0.42150.000081.18−12.4489.83−0.9470.000093.56−1Food and beverage333.8238.410.79360.000074.75−14.5389.97−0.9040.000088.61−1Total degree64.9965.8975.8968.90In the process of risk accumulation during the interval II period, the top 10 out-degree rankings of industry tail risk are mining, national defense, agriculture, chemicals, construction materials, electrical equipment, health care, construction furnishings, banks, and electronics. The top 10 in-degree rankings are machinery equipment, media, transportation, food and beverage, nonbank finance, light-industry manufacturing, household appliances, communication, leisure services, and automobiles. Columns 8–10 of Table5 show the magnitude of RI, with the top ten in descending order: mining, agriculture, national defense, construction materials, chemicals, health care, electrical equipment, construction furnishings, banks, and commerce. C ranking in order: automobiles, machinery equipment, nonferrous metals, light-industry manufacturing, leisure services, household appliances, food and beverages, transportation, steel, and media (as in column 6 of Table 4). In the process of risk mitigation, the top 10 industry tail risks in order of out-degree are machinery equipment, transportation, chemicals, mining, conglomerate, media, utilities, agriculture, health care, and commerce. The top 10 in order of in-degree are nonbank finance, food and beverage, light-industry manufacturing, banks, computers, steel, communications, construction materials, national defense, and nonferrous metals. The RI ranking in order is machinery equipment, transportation, mining, chemicals, media, conglomerate, agriculture, utilities, health care, and commerce (as listed in Table 5, columns 11–13). The C ranking in order is nonbank finance, food and beverage, computer, automobiles, light-industry manufacturing, communications, textile and apparel, banks, electrical equipment, and construction furnishings (as in column 7 of Table 4).To facilitate the analysis, we briefly present the above results in Table6. They show that the level of risk spillover in different industries differs from the average cross-industrial risk spillover in the overall market in different intervals. The cross-sectional dimension allows us to compare the differences in spillover effects between the upside risk accumulation and downside risk mitigation phases within the same sample interval and analyze the accumulation of risk spillover levels from normal to extreme states. The time dimension allows for a longitudinal analysis of the evolution of the industry tail risk spillover relationship across the intervals. It is possible to compare the evolution of risk spillover within the same risk phase (upside risk accumulation or downside risk mitigation) across sample intervals.Table 6
Subsample index ranking.
Interval 1 UpsideInterval 2 UpsideIn-degreeCommunications, steel, automobiles, electrical equipment, chemicalsMachinery equipment, media, transportation, food and beverage, nonbank financialsOut-degreeMining, food and beverage, health care, construction materials, construction furnishingsMining, national defense, agriculture, chemicals, construction materialsRIMining, health care, food and beverage, construction materials, transportationMining, agriculture, national defense, construction materials, chemicalsClosenessCommunications, media, household appliances, light-industry manufacturing, national defenseAutomobiles, machinery equipment, nonferrous metal, light-industry manufacturing, leisure servicesInterval 1 downsideInterval 2 downsideIn-degreeSteel, automobiles, computer, conglomerate, nonbank financialsNonbank financials, food & beverage, light-industry manufacturing, banks, computerOut-degreeChemicals, communications, transportation, household appliances, miningMachinery equipment, transportation, chemicals, mining, conglomerateRIChemicals, transportation, communications, Mining, household appliancesMachinery equipment, transportation, mining, chemicals, mediaClosenessLight-industry manufacturing, food and beverage, conglomerate, textile & apparel, nonbank financialsNonbank financials, food and beverage, computer, automobiles, light-industry manufacturingFirst, the differences in tail risk spillover effects among industries are compared. In interval I, the senders of risk spillover during the upside risk accumulation process include the tail risk of the real estate industry, and the receivers of risk spillover do not have banks or nonbank financial industries. Nonbank finance appears in the in-degree ranking as the receivers of tail risk spillover during the downside risk mitigation process. There are no estimates of tail risk in the real estate industry in either the full sample interval or the sample interval II out-degree ranking, indicating that the impact of tail risk in the real estate industry is large in the earlier period. The impact of tail risk accumulation within the real estate industry in China has gradually decreased in recent years with the regulation of this industry. The risk spillover senders and receivers in Interval II are more likely to reflect the tail risks of industries involving emerging sectors of strategic importance, such as communications, computers, and health care, indicating that the impact of strategic emerging industries on the economic and financial system is of increasing concern in the process of structural transformation and upgrading of China’s industries. In Interval II, in terms of closeness, tail risks in the nonbank financial industry are not at the center of the network during the upside risk accumulation phase but evolve into an important network center during the downside risk mitigation phase, playing an important role in the risk spillover contagion chain.Second, the evolution of the cross-industrial tail risk spillover is compared across different intervals. In the process of upside risk accumulation and downside risk mitigation, the network density indicators ND in sample intervals I and II are 0.2592593 and 0.2301587 and 0.1931217 and 0.207672, respectively. The total correlations are 64.99 and 65.89 and 75.89 and 68.90, respectively; thus, the nonlinear effects and cyclical changes of tail risk spillover among industries still exist. Regardless of the upside risk accumulation or downside risk mitigation process, the total correlation in interval II is greater than that in interval I. This indicates that the impact of tail risk spillover in China has been gradually expanding in the cross-industrial range in recent years from the vertical time dimension. In the interval I time period, the total correlation of the upside risk accumulation process is smaller than the total correlation of the downside risk mitigation process, while in the interval II time period, the result is the exact opposite. The total correlation of the upside risk accumulation process shifts to be larger than the total correlation of the downside risk mitigation process, indicating that the downside risk is not fully mitigated in the process of expanding the impact of tail risk spillover in recent years. In addition, in the downside and upside risk phases of the two sample subregions, the tail risks of industries such as mining, transportation, utilities, and agriculture in the nonfinancial sector are among the stable risk spillover senders. They provide basic services and production materials supply for other sectors while generating more obvious risk shocks to other industries. The tail risks of the communications, health care, computer, and other industries are gradually rising in the network. This conclusion forms a synthesis of established studies related to cross-industrial risk spillover and an extended validation of them. It is worth noting that although the nonbank financial industry is not in the ranking of risk spillover senders, the in-degree ranking of the industry has improved more significantly in recent years. During the downside risk mitigation phase of Interval II, it is not only the top-ranked tail risk spillover recipient, but also in the center of the network in terms of closeness, which again confirms the characteristics of tail risk spillover from the nonfinancial sector to the financial sector. Based on the fact that China’s nonbank financial industry is not the sender but the receiver of tail risk spillover, it is more important to pay attention to the increase in risk exposure of the nonbank financial sector and strengthen its ability to bear tail risk spillover. At the same time, it is also necessary to pay attention to the risk-sending effect presented by the Bank sector during the upside risk accumulation phase and the role it played in promoting risk accumulation.Finally, the evolution of risk spillover within the same risk stage in different sample intervals is compared. Based on the estimation results, it is found that the total correlation within interval II during the accumulation of upside risk is significantly larger than the total correlation in interval I. This indicates that the upside risks have accumulated faster in recent years, but thanks to effective regulation, the downside risk mitigation is gradually resolved and does not show an accelerating trend of mitigation. That being said, there is still a need to focus on the impact of upside risks.


## 4. Conclusion

This paper applies the ∆CoES-ENGDFM-LVDN method to construct a tail risk spillover network with periodic properties among China’s industries and investigates the level and structure of association of the tail risk spillover network, as well as the role of each industry in the risk contagion chain. We identify the characteristics and the dynamic contribution of each industry in the tail risk transmission chains. On the one hand, this paper analyzes tail risk in-degree, out-degree, RI, and closeness indicators based on cross-sectional dimensions for the full sample period and finds that there is variability in the level of tail risk spillover among industries. For example, the real estate industry, an important source of risk inherently perceived, has ranked relatively poorly in recent years in terms of out and in indicators. The risk spillover indicators in both sample subintervals show that the mining, transportation, utilities, and agriculture sectors in the nonfinancial sector are stable sources of risk. The nonbank financial industry is the recipient of tail risk spillover and gradually evolves into an important network center in the downside risk mitigation phase. This indicates that the tail risk spillover in China’s industries is reflected in the direction of correlation from the nonfinancial sector to the financial sector. On the other hand, the in-degree ranking of the nonbank financial industry has improved significantly in recent years. It becomes the most central industry in the tail risk network and is very closely linked to other industries. The reason for this is likely due to the rapid growth of China’s nonbank financial business, whose regulatory avoidance, high leverage, and maturity mismatch characteristics have led to increased vulnerability of the nonbank finance. In addition, the real estate industry had a large tail risk impact in the early period (interval I), but the output effect of tail risk in the real estate industry is gradually weakening as national regulations are gradually taking effect (interval II). At the same time, emerging industries in China, such as communications, health care, and computers, have been more represented among the senders and receivers of tail risk since 2016. This also indicates that emerging industries in China are increasingly worthy of attention.The network density and the total degree of correlation indicators show that there are a continuous nonlinear spillover effect and an obvious cyclical characteristic among China’s industry tail risk as a whole. The spillover effect of industry tail risk during the downside risk mitigation process is more pronounced, but the gradual growth of the total degree of the upside risk accumulation process has exceeded the total degree of the downside. This suggests that although the impact of cross-industrial tail risk spillover in China has gradually expanded, due to effective regulation, it has not been released sharply.Based on the above findings, this paper puts forward the following policy recommendations. First, the regulator should expand the scope of concern, not only focusing on the financial sector, but also paying attention to the tail risk spillover effect of the nonfinancial sector. Focus more on stable risk spillover sectors represented by mining, transportation, utilities, and agriculture. At the same time, it is important to avoid falling into the rigidity of thinking and not simply focusing on risk prevention in traditional high-risk spillover industries, such as the real estate industry. Depending on the role and status of different industries in the tail risk spillover process, different regulatory policies should be selected in a targeted manner. When establishing a risk warning system related to each industry in China, the different systematic contributions of each industry in the risk transmission chain should be taken into account comprehensively. A dynamic adjustment mechanism should be introduced to lay the foundation for a more reasonable prevention of tail risk spillover. Second, as the nonbank finance has long been in the position of the recipient of tail risk spillover, improving the ability of the nonbank finance to resist risks, reducing the vulnerability of the industry, and regulating its operation are the focus of risk prevention. Third, with the improvement of capital structure and industrial restructuring, the importance of emerging industries in the risk spillover network is gradually increasing, and more attention should be given to the risk contagion of such industry fluctuations for the overall industries and preventing tail risk transmission from the nonfinancial sector to the financial sector. [39].



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*Source: 2685862-2022-06-28.xml*