The effects of the 2008 financial crisis and the 2011 Great Earthquake

Fig 1 shows the losses in terms of the index of industrial production (IIP) in Japan after the 2008 Lehman Brothers bankruptcy and the 2011 Great Earthquake. The two negative shocks are reflected by an initial crash in production and a progressive recovery. We will attempt to reproduce these IIP dynamics using our model. Fig 2 displays 4 ratios of Japanese banks from 1990 to 2012: ROA in Fig 2(a), the equity to assets ratio in Fig 2(b), profit and loss (PnL) growth in Fig 2(c) and the provision for loan losses (PLL) to loans ratio in Fig 2(d). The evolution of these ratios indicates that during negative shocks (the Hanshin-Awaji earthquake, the Japanese banking crisis, the dot-com crisis, the 2008 financial crisis and the 2011 Great Earthquake), Japanese banks became less stable, exhibiting a lower solvency ratio (Fig 2(b)) and higher loan losses (Fig 2(d)). Moreover, their performance was much lower, as reflected by the decreases in ROA and PnL growth, Fig 2(a) and 2(c). Fig 3(a) depicts the 1-year dynamics of the PLL-to-loans ratio after the 2008 Lehman Brothers bankruptcy, and Fig 3(b) displays the same statistics in the aftermath of the 2011 Great Earthquake. Both figures show a positive effect on the PLL-to-loans ratio, which reflects higher expected NPL. This ratio increased by 9.4% on average following the 2008 economic disaster and only 1.2% following the 2011 natural disaster, which also exhibited a faster recovery.

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Fig 1. The dynamics of the IIP of Japan after two negative shocks.

Lehman Brothers bankruptcy in September 2008 and the 2011 Great Earthquake. The initial IIP is treated as the reference. Source: The Ministry of Economy, Trade and Industry.

https://doi.org/10.1371/journal.pone.0239293.g001

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Fig 2. Some risk and performance ratios for Japanese banks from 1990 to 2012.

Return on assets (ROA) in Fig 2(a), equity to assets ratio in Fig 2(b), profit and loss (PnL) growth in Fig 2(c) and provision for loan losses (PLL) to loans ratio in Fig 2(d). All negative shocks are characterized by a higher risk level for banks with lower performance. Source: Bank of Japan statistics.

https://doi.org/10.1371/journal.pone.0239293.g002

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Fig 3. The dynamics of the provision for loan losses to loans ratio.

The 2008 Lehman Brothers bankruptcy (a) and the 2011 Great Earthquake (b). The grey line represents the level of NPL before the negative shock. Source: Bank of Japan statistics.

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The data used in the credit-based ARIO model

Two networks are considered in the credit-based ARIO model: the production network of Japanese listed firms and their corresponding bank-firm network. Fig 4 is a schematic representation of the considered economy. In the following, we present the data and discuss the initialization of the intermediate goods flows and firms’ balance sheets.

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Fig 4. A schematic representation of the production network and the bank-firm network considered in the credit-based ARIO.

Links between firms in the production network are weighted by the amount of the daily trading flows of intermediate goods A_ij between firms i and j. Links between firms and banks are weighted by the daily amounts of loans L_ij,t and deposits D_ij,t between firm i and bank j.

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The Japanese production network consists of 1,247,521 firms and 5,488,484 distinct links representing customer-supplier trading for the year 2016. Data are collected by Tokyo Shoko Research (TSR), Inc., one of the leading credit research agencies in Japan, and are commercially available. TSR collects information about the 24 major suppliers and clients of each firm through questionnaires. However, the number of suppliers and customers of each firm is not limited to 24 because large firms are designated by many other firms as suppliers or customers. Each firm belongs to an industrial sector. We use the 190 basic sector classifications of the IO tables for Japan in 2016 obtained from the Ministry of Economy, Trade, and Industry. Analysis of the Japanese production network is discussed in several works, such as [25–30].

The other data set used here is the bank-firm network. It represents the lending-borrowing relationships between listed Japanese firms and banks and their annual financial statements. The data set is collected yearly by Nikkei Media Marketing, Inc. and is also commercially available. We use the 2016 bank-firm network and consider the subset of listed firms from the TSR production network. Accordingly, the production network considered in the remainder of this paper has 2,169 firms and 8,841 production trading links, while the considered bank-firm network has 165 banks (including 88 listed banks), 2,169 firms and 18,535 lending-deposit links. Although the number of listed firms is small compared to the total size of the production network, they represent 22% of the total net sales of Japanese firms. A recent analysis of this network is provided in [31].

The production network is initially unweighted, and the bank-firm network has information about loans only (no information on deposits between individual firms and banks is available). Thus, based on the 2016 IO table for Japan and firms’ balance sheets, we calibrate the initial weights of the model as described in the model validation section. A schematic representation of the data structure is given in Fig 16 of Appendix A.

Assumptions and model description

We assume a closed credit-based economy, where agents are firms, banks, and final consumers. Several macroeconomic agent-based models (ABMs) assume, e.g., [33], that the absence of a foreign market makes the model simpler and better able to focus on the spread of negative shocks within the economy. To relax this assumption, we need to model the interactions with foreign economies via international trade. This would capture the effects of local negative shocks on net export activity.

The modelled economy has short-term dynamics (1 year). Thus, we assume that firms keep their commercial partners identified in the real data from before the negative shock and that banks keep their borrowing-lending links with their pre-shock clients. Therefore, firms and banks do not create new connections within 1 year of a shock based on the fact that it is difficult to obtain new trade contracts during economic contractions with a lower level of solvency; see [11]. Moreover, it is assumed in the short run that final consumers maintain the same level of demand for final goods, which is supported by the empirical findings in [32]. This strong assumption should be relaxed to extend the model for the mid- and longer-term impact.

Each firm produces a specific product defined by its industrial sector, i.e., firms from same industrial sectors produce the same intermediate goods. Firm i initially produces P_ini,i using intermediate goods A_ij from all its suppliers j. Customer i in the production network purchases a quantity of intermediate goods A_ij on day t from its suppliers j. Then, customer i pays each of its suppliers j the amount A_ij. Customer i pays its obligations to its suppliers out of its total deposits; see Eq 26. If deposits cannot cover production expenses, customer i seeks a short-term loan from its banks.

For simplicity and without loss of generality, we suppose that banks are only risk managers, as in [33]. Indeed, our model focuses only on the effects of loan supply and the possible impact of negative shocks on credit default. Thus, banks are homogeneous in their behaviour and are not asset-liability optimizers, i.e., they do not attempt to optimize their credit portfolios. In addition, because we focus only on the supply of loans, the credit market between firms and banks is the only modelled financial market in the economy. Thus, no interbank market is considered, and no central bank is represented in the model. Because of the latter assumption, our model cannot capture the contagion effects between banks, as in the case of a financial crisis (see [34]), which could lead it to underestimate or overestimate the indirect losses related to exogenous negative shocks. However, because we are studying the short-run dynamics post-economic shock on the production network, we could assume that the contagion effect between banks will be delayed in time. Consequently, the absence of an interbank market will not significantly change the conclusions in this framework. To study longer-term economic dynamics, this assumption should be relaxed in future development of the model.

Firm production after a negative shock

The production process is given as follows: demand for intermediate goods, production process, trading, and inventory dynamics.

Short-term bank lending

Each firm i may seek a loan from its banks depending on its demand and its current deposit level D_i,t. If deposits cannot cover its expenses, firm i seeks a total amount of short-term loans given by: (13)

The demanded loan is divided equally among all its banks from the bank-firm network, i.e., for simplicity, we assume that bank-firm relationships are homogeneous. All short-term loans have the same maturity T_s. We further assume that all banks apply the same interest rate given by: (14)

r is the market interest rate and is assumed to be constant, r = 1%. Following Eq 11, in the pre-shock situation, Y_i,t = P_ini,i, loans are supplied at a 0 interest rate. In an analysis of the short-term lending market, [35] confirms that the interest rate elasticity of loan demand is significant. Thus, we expect that the interest rate increases when demand for loans increases. In the credit-based ARIO model, when firms face greater damage and lower sales Y_i,t, their deposits decrease because of their lower profits. Thus, these firms increase their loan demand. Accordingly, based on Eq 13, when sales decrease, loan demand and the interest rate on short-term loans both increase. In addition, Eq 14 reflects that the banks in our model follow risk-based pricing for the interest rate, as discussed in [36]. In fact, the more strongly affected firms have lower production, generate less profit and have higher risk of default, which increases the interest rate pricing based on Eq 14.

Banks have access to the financial statements of their clients, which is reflected by the leverage ratio calculated as in [33]: (15)

The leverage ratio is used as a proxy to evaluate the risk level of the firm when applying for funding. In our credit-based ARIO, we simulate three models. The first model assumes that banks prioritize economic recovery. In this case, banks are not concerned about the risk levels of firms and lend to them to reduce the indirect demand shortage effect of the negative shock. The second simulated model assumes that banks are risk averse and fund those firms below a limit set on the leverage ratio, λ_i,t ≤ λ. The third model requires third-party intervention; banks are risk averse, as in the second model, but when there is a loan shortage for risky firms, the government or an insurance company provides the necessary funding to avoid and indirect demand shortage effect from the negative shock. We do not discuss the mechanisms of the third-party intervention in this paper: its role is solely to fund risky firms to support economic recovery.

The recovery process of damaged firms

In the credit-based ARIO model, we assume that directly damaged firms recover by using a reconstruction loan that has a maturity T_c. First, we assume that all directly damaged firms in the aftermath of the negative shock secure reconstruction loans from their banks. Recall that the direct damage is modelled as a loss to the initial production capacity in the amount of δ_i,0. We suppose that the amount of the reconstruction loan is equal to the lost production capacity, which is given by: (16)

The recovery is modelled as a reduction in the magnitude of the damage over time, where: (17)

γ_i,t is the recovery factor and defined in our model based on the financial health of the directly damaged firms. Let be the remaining reconstruction loan of firm i on day t, i.e., the remaining loan after each period’s reimbursement, as discussed in the balance sheet dynamics section. The recovery factor is calculated as follows: (18)

Eq 18 reflects that the recovery of firm i is faster when it has more deposits (the recovery of production) and when the amount of the reconstruction loan decreases through regular daily payments to banks. This assumption is motivated by the fact that a firm becomes more financially robust when its deposits increase, which facilitates reconstruction in the event of a natural disaster or the resolution of financial resource constraints in the event of a financial crisis. The recovery factor γ_i,t is linearly rescaled into the interval [γ_min, γ_max] ∈ [0, 1]². The values of γ_min and γ_max are calibrated by simulation experiments, as discussed below, i.e., higher values of [γ_min, γ_max] imply a faster recovery.

The updating of firm balance sheets

After trading on day t, all firms update their balance sheets. First, firms calculate their gross profits given as a fraction of their realized sales: (19)

The gross profit represents the total sales after paying production expenses, such as technology or labour costs. α_i is the ratio of the gross profit to total sales for firm i. Then, for each period until maturity, firms make payments on all the loans accumulated post shock L_i,t − L_i,0. For example, suppose that firm i has N loans j ∈ 〚1, N〛: with interest rate and maturity T. We assume a linear constant amortization of the loans, which yields the following periodic payment: (20)

The periodic amount M_j is formed by interest and capital; M_j = I_j + κ_j, where . Accordingly, the stock of loans in the balance sheet of firm i is updated as follows: (21) where is an indicator function of whether the current loan is paid, i.e., if paid, the value is equal to 0, and 1 otherwise. If a firm cannot pay its loan over consecutive periods T^default, the loan is considered nonperforming until it can be repaid again. The firm continues its activity and accumulates additional wealth to recover and repay its unpaid loans. After paying the banks, each firm calculates its profit as follows: (22)

Accordingly, deposits are updated as follows: (23)

Finally, equity capital is updated by: (24)

The validation of the model inputs

Design of experiments and exploration of the parameter space.

Table 1 shows the ranges of the parameters in our model. n is the average number of days that inventory is held. The number of days for each firm is generated as a Poisson distribution of the average n instead of constant. This parameter also requires empirical support, if it is possible as future developments. We assume that firms cannot exceed 1 month (30 days) of inventory (goods could be perishable) and cannot take a substantial production risk by holding inventory for fewer than 10 days. The magnitude of the initial damage δ_i,0 can be small, 10% of initial production losses, or very large, 100% of initial production losses. Through simulation experiments, the values of γ_min, γ_max are chosen between 0.001 for a slow recovery and 0.055 for a fast recovery. For values less than 0.001, the economy may not recover. When values higher than 0.055, the economy will recover much faster than we observe in Fig 1. When banks are risk managers, they could be very risk averse, λ = 2%, or have a relaxed risk policy by allowing firms with 30% leverage to obtain loans. The maturity of short-term loans used to purchase intermediate goods varies between 1 and 2 months, while the reconstruction loans are longer term and can have a maturity extending to the end of the year after the shock. Throughout the following simulations, we assume that 10% of the firms are initially damaged.

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Table 1. The possible values of the main parameters of the proposed credit-based ARIO model.

https://doi.org/10.1371/journal.pone.0239293.t001

Although we have 7 main parameters, the model space is quite large. We use the approach called the design of experiments (DoE) introduced in [38]. The DoE uses Latin hypercube sampling, which was introduced by [39], and indicates how to vary the parameters in a complex simulation model to capture the best response of the system; see [24] for a recent application. For a simulation model with 7 parameters, we need at least 33 samples, as suggested in [24, 38]. To cover the maximum number of points in our model space, we simulate the model for 200 sample combinations of our set of parameters.

The validation of the model output

Based on the exploration of the parameter space, we have 200 combinations of the considered 7 parameters. Each combination is simulated 1000 times. All simulations are conducted using independent parallel computing on the K supercomputer to reduce the run time (The K computer is the first 10-petaflop supercomputer; it was developed by RIKEN and Fujitsu under a Japanese national project. The system includes 82,944 compute nodes connected by Tofu high-speed interconnects. For further details, see [40]).

Calibration of the credit-based ARIO and reproduction of the real IIP of Japan.

Let be the set of parameters used in the experiments s₁. After 1000 simulations with different random seeds for design s₁, we calculate its simulated VA and define its daily percentage of the initial VA as . To calibrate our model based on the explored parameter space, we look at minimizing the distance between the simulated and the real output by using the Japanese IIP. As a distance measure, we employ the generalized subtracted L-divergence (GSL-div) introduced by [41], which measures the degree of similarity between the temporal series produced by the model and the real temporal dynamics.

To compare the impact of indirect production losses on risk in the banking system, we assume that banks follow the same policy in 2008 and 2011. Thus, we calibrate, first, the parameters of the system based on the 2011 Great Earthquake. These results are reported in the last column of Table 1. Therefore, the calibration of the credit-based ARIO for the period after the Lehman brothers bankruptcy uses the same values for the leverage ratio λ and loan maturities T_s and T_c. Only the production parameters are sampled based on the DoE procedure, and the model is calibrated based on 200 simulation experiments, i.e., the same calibration procedure explained previously. The third column of Table 1 reports the parameter values that reproduce the short-term economic dynamics after the 2008 financial crisis.

The credit-based ARIO model is calibrated using the third lending policy model (see the previous section). Here, we assume that banks are risk managers and consider the leverage ratios of firms through the limit value λ. In addition, when firms cannot obtain loans, they receive exogenous funding at the required amount from a third party. The reason for this choice is explained in the next section.

Table 1 shows the calibrated parameters of the model obtained by minimizing the GSL-div measure. Then, based on these parameters, Fig 5 reproduces the dynamics of the Japanese economy after the 2008 Lehman Brothers bankruptcy (Fig 5(a)) and the 2011 Great Earthquake (Fig 5(b)). The main differences between the two crises are as follows: the inventory strategy of firms n, the magnitude of the initial damage δ_i,0, and the capacity of firms to recover γ_min, γ_max. During the 2008 financial crisis, the initial damage is much smaller; a natural disaster reaches its maximum damage after 40 days. Moreover, during financial crisis, firms are more risk averse. They are aware that a crisis exists, and they improve their strategy by holding inventory for longer. In contrast, a natural disaster, especially an earthquake, is a surprise, which is why firms employ a softer inventory policy. Finally, after a natural disaster, the recovery is much faster. In fact, the effect of the 2008 financial crisis is delayed: it has lower initial damage but a longer recovery time.

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Fig 5. Comparison between simulated and real value added of the Japanese economy.

The case of the 2008 Lehman Brothers bankruptcy (a) and the case of the 2011 Great Earthquake (b).

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Fig 6 compares the cumulative distribution functions (CDFs) of the generated NPL defined as the ratio of defaulted loans to current loans. The NPL rate increases more after the 2008 financial crisis than after the 2011 natural disaster. On average, after the natural disaster, the simulated NPL increased by 3.5%, against 13.5% post financial crisis. Based on the real data depicted in Fig 3, after the 2011 Great Earthquake, the ratio of PLL to total loans increased by 1.2% on average over 1 year. However, the ratio increased by 9.5% on average after the 2008 Lehman Brothers bankruptcy.

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Fig 6. The generated defaulted loans after negative shocks.

A comparison between the 2008 Lehman Brothers bankruptcy and the 2011 Great Earthquake cases. The figure compares the CDFs of the percentage of the additional NPL.

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Analysis of the effect of different bank lending models on economic recovery after negatives shocks

The three models described previously are compared below. The results are the outcomes of 1000 simulations with different random seeds. Simulations are performed using the parameters for the 2011 Great Earthquake shown in Table 1. The results are compared on the basis of VA losses, the generated NPL and the liquidity ratio (total loans over total deposits).

After a negative shock and due to supply shortages, wealth accumulation decreases, and firms need loans to produce and survive. Accordingly, when banks follow a risk-averse policy (model 2), some firms cannot continue production because they cannot purchase intermediate goods due to their high leverage. Then, the economy is damaged by a second, loan-related wave of the crisis and bottoms out 70 days after the initial negative shock; see Fig 7. In model 2, banks seek to minimize their risk. The liquidity ratio is successfully minimized, in contrast to model 1, where banks do not follow a risk-averse strategy; see Fig 8(a). However, Fig 8(b) shows that the NPL rate increases drastically in model 2. In fact, firms were initially in good financial condition, had low leverage and could secure loans. Then, when banks stop making loans because firms were highly leveraged, the overall economy is significantly damaged, and firms default on past loans, which then remain unpaid. Model 1 is also problematic despite the fact that NPL growth is not very high. Banks supply a high volume of loans compared to what they can earn as deposits because production decreases after the negative shock. This situation is too risky for banks because it places them in a liquidity disequilibrium, which affects their asset and liability management and could lead to a serious financial crisis. See [42, 43]; i.e., in the real world, the liquidity issue is closely related to the function of the central bank (we intentionally do not introduce a central bank in this model). Model 3, as shown in Figs 7 and 8, allows for the complete recovery of the economy, the maintenance of a low liquidity ratio (lower than that in model 2) and low NPL growth (lower than that in model 1). Accordingly, banks must collaborate with other institutions, such as insurance companies and governmental institutions, to fund firms during the first year after the shock to boost recovery and maintain a low level of financial risk. In all experiments hereafter, model 3 is used with the calibration given in Table 1.

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Fig 7. The value-added losses after a negative shock.

Three models are simulated based on the 2011 Great Earthquake parameters. Outcomes from models 1 and 3 are very similar, and we cannot distinguish between the two curves in the plot.

https://doi.org/10.1371/journal.pone.0239293.g007

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Fig 8. The simulated financial losses after a negative shock.

Three policies are analyzed based on the 2011 Great Earthquake parameters. (a) The evolution of the liquidity ratio for banks; (b) the generated non-performing loans.

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Economic losses when varying the initially damaged industrial sectors

We consider 8 sectors: chemical and petroleum manufacturing; machinery manufacturing; plastic, metal and ceramic product manufacturing; food manufacturing; construction; transport; wholesale trading and retail trading. We simulate the initial damage to the industrial sectors using the 2008 financial crisis parameters (see Table 1). The results present the impact of the initial damage to the entire economy as the average of 100 simulations with different random seeds.

Fig 9 indicates that the total economic losses differ based on which industrial sectors are initially damaged. Little damage is observed when the construction sector is initially hit by a negative shock, i.e., non-significant indirect losses and a rapid economic recovery. When a crisis initially hits food manufacturing or retail trading, the economic losses are also limited in size, i.e., a maximum of 12% of the initial VA is lost. However, significant losses are observed when the following sectors are initially damaged: chemical and petroleum manufacturing; machinery manufacturing; plastic, metal and ceramic product manufacturing; and wholesale trading. Finally, the largest impact is observed when the transport sector is initially damaged; the economy loses up to 30% of its production capacity over 1 year.

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Fig 9. The post-crisis losses in value added simulated using the 2008 financial crisis parameters.

Initially, damaged firms are chosen at random from one industrial sector. The 8 major industrial sectors in the production network of Japanese listed firms are considered.

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In terms of NPL, in Fig 10(a), industrial sectors can be placed into two categories. The first is industrial sectors with a limited impact on the banking system: construction, food manufacturing and retail trading (sectors with lower economic losses), i.e., when firms from these sectors are damaged initially, the banking system suffers fewer defaulted loans. The second category is industrial sectors with significant impacts on the banking system: all other sectors generate high NPL, as summarized in Table 2, i.e., column 2 shows the average NPL generated in this case. The exogenous funding needed by firms is calculated as a part of the initial VA generated by the economy, and the CDFs are displayed in Fig 10(b). When the construction sector is damaged, the economy requires the least exogenous funding (less than 0.1% of the initial VA) to recover. However, when firms from the chemical and petroleum industries are damaged initially by the effects of a financial crisis, the required amount of exogenous funding is the highest: 9.7% of the initial VA of the economy on average, and it could reach 18.6% of the initial VA of the economy.

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Fig 10. The post-crisis financial losses simulated using the 2008 financial crisis parameters.

Initially, damaged firms are chosen at random from one industrial sector. The 8 major industrial sectors in the production network of Japanese listed firms are considered. Graphs show the generated non-performing loans (a) and the necessary exogenous funding under policy 3 required for the economy to recover (b).

https://doi.org/10.1371/journal.pone.0239293.g010

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Table 2. Properties of the initially damaged sectors.

https://doi.org/10.1371/journal.pone.0239293.t002

Table 2 reports the properties of each industrial sector to explain their systemic risk. Sectors are classified in Table 2 in descending order with respect to their initial VA; see column 4 of the table. Columns 2 and 3 report the average of the generated NPL and the exogenous funding required, respectively. Columns 5, 6 and 7 report the average in-strength and out-strength (the sum of money in- and outflows, respectively) and the total unweighted degrees (the sum of all firm-firm links) in each sector. Then, the sector-based production network is considered, i.e., if a firm from sector A is connected to a firm from sector B, a link from sector A to sector B is considered. The sector-based production network is weighted based on the aggregate flow of intermediate goods from our production network of listed firms. Columns 8 and 9 report the clustering coefficient and the average nearest neighbour degrees K_nn. K_nn computes the average degrees of the neighbours of a node in the network. It is useful to know whether a node is connected to highly or less connected neighbours. of each sector in the sector-based production network to specify the centrality of each sector in the economy.

In terms of NPL growth after the crisis, the riskiest sectors are chemical and petroleum manufacturing (33.1%), plastic, metal and ceramic product manufacturing (29.5%), transport (25.1%), machinery manufacturing (20.4%), and wholesale trading (18.8%). The chemical and petroleum manufacturing sector has the highest initial VA. Although the two latter sectors have the lowest initial VA, their impact on the economy leads to a higher growth rate of defaulted loans than the construction sector, which generates only 0.1% of additional NPL despite an initial VA four times higher than that of the transport sector, i.e., 19,595 for the construction sector compared to 4,765 for the transport sector. The riskiest sectors in terms of defaulted loans have a central position in the production network. In fact, some of them supply large amounts of intermediate goods based on out-strength (chemical and petroleum manufacturing, wholesale trading, and plastic, metal and ceramic product manufacturing). Other risky sectors are connected with highly connected sectors (higher K_nn) and display high clustering coefficients, such as transport and plastic, metal and ceramic product manufacturing. Moreover, we can explain the largest losses to the economy by the initial damage to the transport sector resulting from its central position in the supply chain. With a clustering coefficient of 0.48, this sector forms triangles with other sectors, which accelerates the spillover of the crisis. In addition, K_nn = 38.9 implies that the transport sector has, on average, the neighbours with the highest degrees, which stimulates the contagion effect in the event of a crisis. However, as shown in Table 2, sectors such as construction and retail trading have a very low impact on the production network of Japanese listed firms. The construction sector has no customers in the production network. The retail trading sector has few customers in the production network, but its outflow of money (out-strength) is too low. Therefore, initial damage to the construction or retail trading sectors causes a small supply shortage effect. In terms of strength, machinery manufacturing and food manufacturing have similar properties. However, the former has a larger impact on the economy, which is explained by its higher number of partners, 1,628, compared to only 322 for food manufacturing (which has the fewest partners in the production network). Accordingly, by jointly considering the financial and network properties of industrial sectors, we can understand their systemic risk.

Economic losses when varying the initial damaged geographic locations

Here, we simulate a natural disaster with the properties of the 2011 Great Earthquake. The aim is to identify the most vulnerable Japanese prefectures. First, the economic effect on VA losses is depicted in Fig 11. Most headquarters are located in Tokyo prefecture, and our data consider headquarters locations and not branch locations. To avoid having effects driven by the size of each prefecture (the total number of firms), we consider the same number of initially damaged firms per prefecture, i.e., 4% of the total number of firms in the supply chain.

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Fig 11. The post-disaster value-added losses simulated using the 2011 Great Earthquake parameters.

Initially, damaged firms are chosen at random from one industrial sector. The 8 major industrial sectors in the production network of Japanese listed firms are considered.

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As expected, when Tokyo prefecture is directly damaged, the economy faces the highest losses. When Aichi or Hyogo prefectures are initially damaged, a smaller effect on the economy is observed. Fig 12 depicts the financial effects of the simulated natural disaster across Japanese prefectures. In terms of generated NPL (see Fig 12(a)), the effect of initial damage in Aichi and Hyogo prefectures is the lowest, i.e., 3.2% and 2.3%, respectively. This finding is confirmed in Fig 12(b), where the economy requires a small amount of additional exogenous funding to recover when these latter prefectures are initially damaged, i.e., 1.4% and 1.5% for Aichi and Hyogo prefectures, respectively. Although initial damage to Tokyo causes the highest production losses, Fig 12(a) and 12(b) show that damage to Osaka prefecture causes the greatest financial losses.

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Fig 12. The simulated post-disaster financial losses simulated using the 2011 Great Earthquake parameters.

Initially, damaged firms are chosen at random from one industrial sector. The 8 major industrial sectors in the production network of Japanese listed firms are considered. Graphs show the simulated non-performing loans (a) and the exogenous funding under policy 3 required for the economy to recover (b).

https://doi.org/10.1371/journal.pone.0239293.g012

To analyse this difference among prefectures, Fig 13 shows the business structure of each prefecture, i.e., the weights of the top 5 industrial sectors in each prefecture. Transportation equipment manufacturing is the dominant industrial sector in Aichi prefecture, as shown in Fig 13(c); Toyota’s headquarters is in Aichi prefecture. This sector causes little damage to the production network because it has only 25 customers, i.e., limited risk of supply shortages post disaster based on our previous analysis. Approximately 35% of firms in Hyogo prefecture are in the food manufacturing and food and beverage services, as shown in Fig 13(d), which are not sectors at high risk of supply shortages (low number of customers in the production network of listed firms). Tokyo and Osaka prefectures have similar business structures (see Fig 13(a) and 13(b)), with a higher weight of chemical and petroleum manufacturing in Osaka prefecture. In terms of VA, Tokyo prefecture contributes 10 times more than Osaka, which explains why we observe the greatest impact on economic losses when Tokyo is initially damaged. Fig 14 represents the CDF of the ratio α_i included in the credit-based ARIO model to calculate the profit of firm i after selling its intermediate goods. We recall that this ratio is calculated based on the real PL statements of Japanese listed firms (gross profits divided by total sales); see the explanations in the model section. Fig 14 shows that, on average, firms in Tokyo prefecture generate more profit from their sales than do firms in Osaka prefecture. This implies that firms in Osaka prefecture have lower profitability and that their deposits grow more slowly than the deposits of firms in Tokyo prefecture. Consequently, based on our model, firms in Osaka prefecture will demand more loans, which explains the higher NPL rate and the higher need for exogenous funding there. Thus, although Tokyo and Osaka have similar business structures in terms of industrial sectors, the difference in the financial efficiency of firms explains the higher financial damages faced by the economy when firms from Osaka prefecture are initially damaged.

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Fig 13. The business structure of the considered Japanese prefectures.

Tokyo prefecture (Fig 13(a)), Osaka prefecture (Fig 13(b)), Aichi prefecture (Fig 13(c)), and Hyogo prefecture (Fig 13(d)).

https://doi.org/10.1371/journal.pone.0239293.g013

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Fig 14. Comparison between the CDFs of the gross profit to sales ratio α_i.

The case of firms in Tokyo and Osaka prefectures.

https://doi.org/10.1371/journal.pone.0239293.g014