Keywords

JEL Classification

1 Introduction

Japan is a country that faces multiple natural disasters and resulting economic effects. It is difficult to predict the occurrence of natural disasters and evaluate their impact. It is still hard to say when and where earthquakes will occur despite ongoing research on earthquake prediction. Events such as typhoons and heavy rains cause damage even though predicted routes are announced in advance. Moreover, there is further damage in the aftermath of these disasters. For instance, the accident at the Fukushima Daiichi Nuclear Power Plant, damage to the connecting bridge at Kansai International Airport, and the Hokkaido earthquake led to a power outage. The Great East Japan Earthquake in 2011 was particularly large, and the government created the Reconstruction Agency for the purpose of restoration and reconstruction. This propagated research on the recovery process from natural disasters (Tokunaga and Resosudarmo 2017). This study focuses on analyzing the regional economic impacts of unexpected natural disasters by undertaking CGE simulations of the damage to productive capacity as predicted through Monte Carlo experiments.

In this study, we use an inter-regional input–output table consisting of two regions: Fukuoka prefecture and other prefectures. Fukuoka prefecture (Fukuoka-ken) is located on Kyushu Island near the Korean peninsula. It faces the sea on three sides, bordering Saga, Oita, and Kumamoto prefectures and facing Yamaguchi prefecture across the Kanmon Straits. Fukuoka prefecture, similar to other areas, faced a big earthquake, in 2005 (Fukuoka Prefecture West Offshore Earthquake).

We proceeded by first developing a CGE (Computable General Equilibrium) model based on the inter-regional input–output table. Natural disasters are expected to affect production factors (sudden decrease in capital and labor) and logistics networks (purchase and use of intermediate goods). We analyze the impact on the regional economy when such capital, labor, and intermediate goods decrease by using Monte Carlo experiments to determine the size of the shock to be applied to the CGE model.Footnote 1

2 The Model

The model in this study is based on the CGE models of economics used in various literature, mainly in Hosoe et al. (2004), the Global Trade Analysis Project (GTAP) model (Hertel 1997), and an intermediate model (Rutherford 2010).Footnote 2 This study incorporated the features of the said three models to create a unique one.

Table 17.1 shows the inter-regional input–output table in Fukuoka prefecture as a variable for model development. Here, intermediate goods are written as XM and final demand is written as FD. With labor L and capital K, value-added goods V are produced. Intermediate goods, on the other hand, consist of those from both Fukuoka prefecture and other prefectures. These assume imperfect substitution using the CES (Constant Elasticity of Substitution) function.Footnote 3 Intermediate goods and value-added inputs are combined in constant proportions to produce domestic goods Z. Furthermore, the domestic goods Z and the import goods M are combined, and the final production goods (output) Y are produced. Domestic goods and import goods are imperfect substitutes (Fig. 17.1). Finally, production goods are divided into various final demand FD, intermediate goods XM, and export E.Footnote 4

Table 17.1 Structure of inter-regional input–output table in Fukuoka prefecture
Full size table
Fig. 17.1
figure 1

Structure of CGE model’s production technology

Full size image

We now describe the mathematical equations. First, it is assumed that labor and capital stocks are fixed and the price fluctuates in the supply–demand relationship between labor and capital. The stock will decrease if it is damaged by a natural disaster.Footnote 5

$$ {l}_{r,j}={L}_{r,j} \vspace*{-20pt}$$
(17.1)
$$ {k}_{r,j}={K}_{r,j} $$
(17.2)

where l and k are endogenous variables of labor and capital stock and L and K are exogenous variables, respectively. The subscript r (s) indicates the region and j (i) indicates the industry. Since regions and industries are indicated, there will be no movement of labor and capital between regions and between industries.

Value-added goods are compounded by combining labor and capital. By constructing the optimization problem using the CES function, the cost function is expressed as follows:

$$ {{pv}}_{r,j}={\left({\alpha}_{r,j}^{{VL}}\cdot {{pl}}_{r,j}^{\left(1-{\sigma}_j^V\right)}+{\alpha}_{r,j}^{{VK}}\cdot {{pk}}_{r,j}^{\left(1-{\sigma}_j^V\right)}\right)}^{\left(\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\left(1-{\sigma}_j^V\right)$}\right.\right)} $$
(17.3)

Here, pv is the price of value-added goods, pl is the labor price, and pk is the capital price. α is a share parameter and σ is an elasticity parameter. The price of the intermediate goods combined is also shown as follows:Footnote 6

$$ {{pxm}}_{r,i,j}={\left(\sum \limits_s{\alpha}_{r,s,i,j}^{{XM}}\cdot {{py}}_{s,i}^{\left(1-{\sigma}_j^X\right)}\right)}^{\left(\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\left(1-{\sigma}_j^X\right)$}\right.\right)} $$
(17.4)

Using the Leontief function to combine value-added goods and intermediate goods, the equation is as follows:

$$ {{pz}}_{r,j}=\sum \limits_i{\alpha}_{r,i,j}^{{ZM}}\cdot {{pxm}}_{r,i,j}+{\alpha}_{r,j}^{{ZV}}\cdot {{pv}}_{r,j} $$
(17.5)

The CES function is used to combine imported goods and domestic goods. The relative price is set to 1 in the absence of a special assumption for the prices of imported goods.

$$ {{pm}}_{r,j}=1 \vspace*{-20pt} $$
(17.6)
$$ {{py}}_{r,j}={\left({\alpha}_{r,j}^{{YZ}}\cdot {{pz}}_{r,j}^{\left(1-{\sigma}_j^Y\right)}+{\alpha}_{r,j}^{{YM}}\cdot {{pm}}_{r,j}^{\left(1-{\sigma}_j^Y\right)}\right)}^{\left(\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\left(1-{\sigma}_j^Y\right)$}\right.\right)} $$
(17.7)

The price p of the consumer goods is determined by adding the indirect tax GTAX, the subsidy GSUB, and the margin MARG to the production goods price py.

$$ {p}_{r,i}={{py}}_{r,i}\cdot \left(1+{{GTAX}}_{r,i}+{{GSUB}}_{r,i}+{{MARG}}_{r,i}\right) $$
(17.8)

We now introduce the demand function of goods. The difference between this and the previous model is that the nested demand function is summarized, which makes it possible to reduce the equations to be determined on the computer. For example, the demand function for labor and capital is as follows:

$$ {l}_{r,j}={y}_{r,j}\cdot {\left(\frac{{{py}}_{r,j}}{{{pz}}_{r,j}}\right)}^{\sigma_j^Y}\cdot {\left(\frac{{{pz}}_{r,j}}{{{pv}}_{r,j}}\right)}^{\sigma_j^Z}\cdot {\left(\frac{{{pv}}_{r,j}}{{{pl}}_{r,j}}\right)}^{\sigma_j^V}\cdot {\left(\frac{{{pl}}_{r,j}}{1}\right)}^{\sigma_j^L} $$
(17.9)
$$ {k}_{r,j}={y}_{r,j}\cdot {\left(\frac{{{py}}_{r,j}}{{{pz}}_{r,j}}\right)}^{\sigma_j^Y}\cdot {\left(\frac{{{pz}}_{r,j}}{{{pv}}_{r,j}}\right)}^{\sigma_j^Z}\cdot {\left(\frac{{{pv}}_{r,j}}{{{pk}}_{r,j}}\right)}^{\sigma_j^V} $$
(17.10)

Here, the nested structure of capital demand is as follows:

$$ {k}_{r,j}={v}_{r,j}\cdot {\left(\frac{{{pv}}_{r,j}}{{{pk}}_{r,j}}\right)}^{\sigma_j^V},\kern0.5em {v}_{r,j}={z}_{r,j}\cdot {\left(\frac{{{pz}}_{r,j}}{{{pv}}_{r,j}}\right)}^{\sigma_j^Z},\kern0.5em {z}_{r,j}={y}_{r,j}\cdot {\left(\frac{{{py}}_{r,j}}{{{pz}}_{r,j}}\right)}^{\sigma_j^Y} $$
(17.10′)

Also, there is further nesting within labor demand. Thus, the labor stock of each industry is composed of multiple types of labor, with imperfect substitution among labor types. However, the price of each labor (wage index) is assumed to be 1.Footnote 7

Labor price (average labor price index in each industry) pl and capital price pk are determined using this demand structure and Eqs. (17.1) and (17.2).

Based on this, the demand for intermediate goods and imported goods is shown as follows:

$$ {{xm}}_{r,s,i,j}={y}_{r,j}\cdot {\left(\frac{{{py}}_{r,j}}{{{pz}}_{r,j}}\right)}^{\sigma_j^Y}\cdot {\left(\frac{{{pz}}_{r,j}}{{{pxm}}_{r,i,j}}\right)}^{\sigma_j^Z}\cdot {\left(\frac{{{pxm}}_{r,i,j}}{{{py}}_{s,j}}\right)}^{\sigma_j^X} $$
(17.11)
$$ {m}_{r,j}={y}_{r,j}\cdot {\left(\frac{{{py}}_{r,j}}{{{pm}}_{r,j}}\right)}^{\sigma_j^Y} $$
(17.12)

The supply–demand relationship of goods is shown as follows:

$$ {y}_{r,i}=\sum \limits_s{{fd}}_{s,r,i}+\sum \limits_{s,j}{{xm}}_{s,r,i,j}+{e}_{r,i}+{{ADJ}}_{r,i} $$
(17.13)

The income (GDP) of each region is shown as the sum of labor, capital, and other added value as follows:

$$ \fontsize{8.9}{10.9}\selectfont{\begin{array}{l} {{inco}}_r=\sum \limits_j{{pl}}_{r,j}\cdot {l}_{r,j}+\sum \limits_j{{pk}}_{r,j}\cdot {k}_{r,j}+\sum \limits_j{{py}}_{r,j}\cdot {y}_{r,j}\cdot \left({{GTAX}}_{r,j}+{{GSUB}}_{r,j}+{{MARG}}_{r,j}\right) \end{array}} $$
(17.14)

Finally, the final demand and the demand for export goods are indicated by the following Cobb–Douglas function (P is the initial value of p).

$$ {{fd}}_{r,s,i}={P}_{s.i}\cdot {{inco}}_r/{p}_{s,i} \vspace*{-20pt} $$
(17.15)
$$ {e}_{r,i}={P}_{r.i}\cdot {{inco}}_r/{p}_{r,i} $$
(17.16)

3 Data and Simulation

The data uses the 2011 table of the inter-regional input–output table consisting of two regions—Fukuoka prefecture (fp) and other prefectures (op). The sector (number of industries) is 42 (Table 17.2). In this study, a model is constructed using all the information in the table. The sum of consumer spending outside a household economy (row), wages and salary, social insurance premiums (employers’ costs), other salaries and allowances, was used as labor stock. For capital stock, we used capital depreciation.Footnote 8 GTAX is the ratio of indirect tax except customs duty, GSUB is the ratio of subsidy, and MARG is the ratio of operating surplus. On the other hand, the final demand used the sum of consumer spending outside a household economy (column), private consumption, government consumption, government investment, private investment, and inventory. Although it is assumed that the supply and demand of data are well-balanced, there is an apparent error in editing the table which is offset by an adjustment term (ADJ of Eq (17.13)).

Table 17.2 Industrial classification
Full size table

Table 17.3 summarizes the actual transaction amounts shown in the Fukuoka prefecture inter-regional input–output table (2011 version). The economic scale of Fukuoka prefecture is 3.78% of the value-added in other prefectures (remaining 46 prefectures) and 3.68% of other prefectures in production. Although these figures are higher than the average size of a prefecture (2.13%), the structure is such that national economic effects are unlikely to be large unless Fukuoka prefecture achieves quite significant results in its economic policy.

Table 17.3 Actual transaction amount in the inter-regional input–output table in Fukuoka Prefecture (trillion yen)
Full size table

Table 17.4 shows elasticity parameters. The elasticity of substitution between labor types is the logarithm of the half-power of labor stock, which could result in relatively large numbers.Footnote 9 For other elasticity parameters, for labor and capital substitution and for domestic goods and imported goods substitution, the elasticity parameters present in the GTAP 8 database are used. The degree of interregional substitution for intermediate goods is assumed to be twice that for substitution between domestic goods and imported goods. The substitution between value-added goods and intermediate goods is 0. This is assuming the use of the Leontief function.

Table 17.4 Elasticity parameter
Full size table

We undertook four types of simulations in this study (Table 17.5). First, we assumed that natural disasters cause damage to specific sectors in Fukuoka prefecture. When the damage occurred, we gave a width to the size of the damage based on the premise that no damage will occur throughout Fukuoka prefecture unless it is a significant disaster. As a result, two types of probability distributions were used in the Monte Carlo experiment. Use random numbers based on the binomial distribution to set the damage that occurs for a specific sector. Here, we determined whether the damage would occur with a probability of 50%; and the magnitude is determined with uniform distribution. The width of the uniform distribution is different for production factors and intermediate goods. Among the production factors, labor stock is to be damaged up to 8% and damage to capital stock up to 40%. Regarding intermediate goods, damage to intermediate goods transactions in Fukuoka prefecture is up to 80%, and 40% for those outside. Damage to labor stock means that laborers will not be able to work due to the disaster. Since saving lives is a priority, heavy casualties are not expected. However, a substantial proportion of the capital stock is expected to become unproductive due to the destruction of properties. Although we set a relatively high number for the degree of damage, we thought that complete destruction was not a realistic possibility. Regarding intermediate goods transactions, we thought that the numbers should reflect a near extinction of these transactions because the infrastructure for logistics is expected to collapse. Therefore, the damage was set at 80%. In addition, because the disaster is assumed to be in the Fukuoka prefecture, the logistics infrastructure in other prefectures would not collapse. Therefore, we considered that the damage to intermediate goods flows within the Others region would be smaller than these flows with a Fukuoka prefecture origin or destination (Simulation 1).Footnote 10

Table 17.5 Monte Carlo experiment
Full size table

In the second simulation, we analyze the economic impact of damage to all sectors, not to specific sectors. Simulation 2 sets the uniform distribution which becomes the same as the damage of Simulation 1 on average.Footnote 11 For the next two simulations, the magnitude of the damage was generated in a nonuniform distribution as it is more likely that damage will be minimal. Here, a half-normal distribution showing the positive part of the normal distribution (Simulation 3) and a triangular distribution with a minimum value and a mode value of 0 (Simulation 4) is adopted. The standard deviation and the maximum value are set so that the average of the damage is the same as in Simulation 1.Footnote 12

When damage occurs as shown in Table 17.5, the labor stock L, the capital stock K and the intermediate goods XM of Fukuoka prefecture decrease according to the probability.Footnote 13 The model is then recalculated under the changed variable. According to the equation of the model, the reduction of labor and capital stock firstly affects Eq. (17.14). The reduction in the intermediate goods transaction firstly affects Eq. (17.13). It also affects other equations and a new equilibrium solution is calculated.

4 Result

4.1 Simulation Based on Database

Table 17.6 shows the CGE results of Monte Carlo experiments for all simulations. The maximum, minimum, average, and standard deviation of output, price, nominal income (nominal GDP), and real income (real GDP) are shown. These experiments were repeated 500 times each.

Table 17.6 Result of Monte Carlo–CGE experiments (simulation 1–4)
Full size table

In terms of output, the average damage result in Fukuoka prefecture is 0.889283 (i.e., a decrease of approximately 11% from a no-change output level of 1.000000) in Simulation 1, 0.889276 in Simulation 2, 0.889073 in Simulation 3, and 0.889244 in Simulation 4. On the other hand, in other prefectures and Japan (jp), the damage is less than 1% in all simulations. Along with this, the price has decreased slightly, but the average is around 1.3% at maximum. The average of nominal income in Fukuoka prefecture was 0.934199 in Simulation 1, 0.933750 in Simulation 2, 0.933932 in Simulation 3, and 0.933665 in Simulation 4. Real income is slightly higher than nominal income because prices are decreasing. As far as the average is seen, it is almost the same, consistent with the intention at the onset of the simulation.

However, the standard deviation is very different. The standard deviation of the output of Fukuoka prefecture is 0.010588 in Simulation 1, 0.004978 in Simulation 2, 0.006098 in Simulation 3, and 0.005797 in Simulation 4. The combination of the binomial distribution and the uniform distribution seems to distort the distribution of experimental results. This is because increase in the standard deviation is that for the non-damaged industry and while the various stocks do not change here, they do so for the damaged industry. The half normal and triangular distributions could also see larger standard deviations than the uniform distribution because the distribution is concentrated to the damage rate closer to zero. Generally, there are two points. First, even if a large natural disaster occurs in Fukuoka prefecture, the impact on the Japanese economy is not significant. Second, although the economy of Fukuoka prefecture suffers substantially, the situation of damage varies depending on how such damage occurs and its magnitude.

Table 17.7 shows the results of Monte Carlo experiments by industry, showing the output and prices in Fukuoka prefecture. The same trend was shown for each simulation except for the size of the result, so the result of Simulation 1 is displayed.Footnote 14

Table 17.7 Results of Monte Carlo–CGE experiments (output and price in Fukuoka Prefecture), simulation 1
Full size table

Like Table 17.6, it can be seen from this table that the change in output is greater than the change in price. According to the table, in seven industries (i004, i007, i013, s026, s036, s041, and s042), the average output damage exceeds 30% and in 13 industries (i004, i011, i012, i013, i014, i020, i021, s026, s028, s031, s036, s041, and s042), the standard deviation of output exceeds 5%. Also, in five industries (a001, a003, i012, s029, and s042), the standard deviation of price exceeds 1%.

Figure 17.2 shows the distribution of experimental results of real income in each simulation. In creating the distribution, we used weighted frequency distribution to make it smooth.Footnote 15 Although the distribution of damage occurrence in each simulation is different, the result is close to normal distribution because the real income is the sum of each industry. Since the standard deviation is different, the shape of the distribution is also different hence showing that the distribution of Simulation 1 is the widest.

Fig. 17.2
figure 2

Distribution of experimental results of real income in each simulation

Full size image

4.2 Comparison with Past Disasters

The Fukuoka Prefecture West Offshore Earthquake occurred in March 2005. Although this earthquake was relatively large, the damage was not so compared to the other one that introduced later. According to “Fukuoka Prefecture Main Natural Disaster Damage Statistics (after 1954)” in Fukuoka prefecture,Footnote 16 the damage amount was 31,497 billion yen. Other examples of large earthquakes include the Great Hanshin-Awaji Earthquake in January 1995, the Niigata Chuetsu Earthquake in October 2004, the Great East Japan Earthquake in March 2011, and the Kumamoto Earthquake in April 2016. According to the policy director of the Cabinet Office on “Assessing the impact of the 2016 Kumamoto earthquake”,Footnote 17 the estimated damage of these large earthquakes are 9.6–9.9 trillion yen (Hanshin-Awaji Earthquake) and 1.7–3 trillion yen (Niigata Chuetsu Earthquake), 16.9 trillion yen (Cabinet Office for Disaster Prevention) and 16–25 trillion yen (Cabinet Office for Analysis) (East Japan Earthquake), 2.4–4.6 trillion yen (Kumamoto Earthquake).

From here, we analyze the Kumamoto earthquake that occurred in Kumamoto and Oita prefectures, which are adjacent to the Fukuoka prefecture. According to “Assessing the impact of the 2016 Kumamoto earthquake,” the damage amount of Kumamoto prefecture is about 1.8–3.8 trillion yen while that of Oita prefecture is about 0.5–0.8 trillion yen. The total for both prefectures is estimated to be 2.4–4.6 trillion yen. This is the amount of loss of capital, and with respect to the capital stock of both prefectures, the estimated loss was about 63 trillion yen (34 trillion yen for Kumamoto prefecture and 28 trillion yen for Oita prefecture). If the damage amount is divided by the capital stock, the damage rate of the Kumamoto earthquake will be 3.8–7.3% (5.3–10.0% for Kumamoto prefecture, 1.8–2.9% for Oita prefecture). In addition, the impact on GDP is estimated to be about 90–127 billion yen (Kumamoto prefecture is 81–113 billion yen, Oita prefecture is 10–14 billion yen), and against each prefecture’s GDP (gross prefecture product) 55,645.6 billion yen and 43,782.32 billion yen,Footnote 18 the damage rate was 1.0–1.3% (1.5–2.0% for Kumamoto prefecture and 0.2–0.3% for Oita prefecture). In this way, when a large earthquake occurs, it can be seen that even if the stock has a relatively large impact, the flow has little impact.

Comparing this with the results in Table 17.6, the average real income was 0.946149 (about 5.4% loss) in Simulation 1. Although not introduced in the table, the average damage rate of capital was 10% in any simulation (one-half of the width of the uniform distribution is the average). This is realistic as the largest estimate of damage to capital stock in the Kumamoto earthquake is 10%. However, the average loss of real income in this study is over 5% versus 2% which is the largest estimate GDP loss in the Kumamoto earthquake. Even within the distribution of Fig. 17.2, damage within 2% (0.980) is negligible as it seems exaggerated. This study assumes that besides the loss of capital stock, there is a further loss on both labor stock and intermediate goods due to damage to logistics networks. As it is forecasting in advance, it seems better to make some pessimistic predictions.

5 Concluding Remarks

In this study, the adverse effects of natural disasters on the economy that cannot be easily measured are analyzed in advance through Monte Carlo experiments using CGE models aided by the inter-regional input–output table for Fukuoka prefecture and Other prefectures region. In the Monte Carlo experiment, random numbers from binomial distributions were generated as the possibility of damage occurrence, and degree of damage; random numbers with uniform distribution, half-normal distribution, and triangular distribution were generated.

It goes without saying that the larger the scale of the damage, the greater the negative impact on the economy. However, if there are regional and industrial variations in the occurrence of damage, the standard deviation of the impact on the economy will be larger. In this study, the damage scale was set relatively large. The negative impact on the Fukuoka economy was significant, but the impact on the Japanese economy was minimal. Also, compared with the actual damage of the Kumamoto earthquake, it can be said that the assumption of the damage in this study is significant.

Since it is not easy to prevent natural disasters in advance, it is necessary to exert efforts to minimize the damage. However, since unexpected damage may still occur, the response, in this case, is in need of examination.