Evaluating the Economic Impacts of a Disaster:
A CGE Application to the Tokai Region of Japan
Hiroyuki SHIBUSAWA*Abstract
Natural disasters have a negative effect on people and the regional economy.
The central and regional governments have made natural disaster reduction a highpriority. In this paper, we develop a dynamic spatial CGE model for evaluating theeconomic impact of an earthquake on the Tokai region of Japan. Our model ischaracterized as a decentralized economy with utility-maximizing consumers andvalue-maximizing firms in a dynamic context. This model embodies both the spatial
interactions among regions and the dynamics of regional investments. A simulation
model is constructed of an inter-regional inter-sectoral economy in which Japan issubdivided into 47 regions. All the regions are connected by transportation networks.
The model is calibrated for the regional economy in Japan. By numerical simulation,
we examine the economic impacts of an earthquake on the Tokai region using ouranalytical scenarios.
1. Introduction
In this paper, we develop a dynamic spatial computable general equilibrium(DSCGE) model to evaluate the economic impacts of an earthquake on the Tokai
region of Japan. Our model is characterized as a decentralized economy withutility-maximizing consumers and value-maximizing firms in a dynamic context. Thismodel embodies both the spatial interactions among regions and the dynamics ofregional investments.
A numerical simulation model is developed of an inter-regional inter-sectoral
economy in which Japan is subdivided into 47 regions. All the regions are connectedby road, rail, sea, and air transportation networks. The model is calibrated for theregional economy in Japan. The dynamic impacts of an earthquake on the Tokai region
are analyzed by numerical simulation. In our analytical scenario, a reduction in thecapital stock is the primary physical damage caused by an earthquake.
CGE analysis is a major artery in economics, regional science, andengineering. It is also widely recognized as a policy evaluation method. There is a vast
literature reporting applications of static CGE models, but few studies have employed*Toyohashi University of Technology, 1-1 Tempaku Toyohashi, Aichi 441-8580, Japandynamic and spatial frameworks. Recent trials of dynamic and spatial CGE modeling
have been undertaken by Giesecke (2002,2003), McGregor, Swales and Yin (1995),and McKibbin and Wilcoxen (1992). These previous studies mostly rely on aquasi-dynamic framework, which is characterized by an evolutionary approach and asequential procedure. Economic impacts of disasters in a spatial context have been
analyzed by Okuyama, Chang (2004) and Shon, Kim, Hewings, Lee and Jang (2003).
Koike and Ueda (2005) examined the economic damage caused by a catastrophe inJapan by using a static spatial CGE model.
In this study, the CGE model is developed based on dynamic macroeconomic
theory with a multi-regional and multi-sectoral specification. The investment isendogenously determined by the behavior of value-maximizing firms, which facecapital adjustment costs. The dynamic impact of an earthquake in Japan is evaluatedby using the spatial CGE model. In this paper, we show a modified version of themodel which was developed by Shibusawa, Yamaguchi and Miyata (2009).
2. Basic Assumptions
The world is subdivided by region. Throughout the world there are generalindustries, transportation industries and households. The economy is endowed with theprimary factors of labor and capital. Labor is mobile across industries but not regions
and capital is immobile across industries and regions. Goods and factor prices aredetermined in perfectly competitive regional markets. Commodity trade between
regions in the country generates demand for transportation services and unittransportation costs are endogenous. Commodities are perfect substitutes, i.e., thetrades are determined by the trade coefficients. The interaction of commodities amongregions is enabled by road, rail, sea and air transportation networks. The modal share isalso given. The model is solved for rational expectation equilibrium under theassumptions of perfect competition and foresight. However, we assume that firms
place priority on the investment-savings balance. Then the level of investment isdetermined by the firm’s optimization behavior.
The model is finitely set up in discrete time. T  {1, 2, , t F } denotes aplanning period index and t F is the final planning period. The world is divided into ahome country and foreign country. These are subdivided by region. R denotes aregional index in the home country. There are three kinds of industries, i.e. general,transportation and distribution industries. The general industry involves domestic andforeign trade between regions. I denotes a sector index for the general industry. M
is a sector index of the transportation industry. All the regions interact with each othervia the transportation networks. A transportation network is defined by nodes and links.
A transport path connecting two regions is fixed and the transport link distance isexogenously given.
3. The Model
The model is based on dynamic macroeconomic theory with a multi-region
and multi-sector specification. Each region has production and household sectors.
Commodity trade flows are determined by the trade and modal share coefficients. We
characterize the problems related to the maximization of the production and household
sectors in this economy.
3.1 Production Sectors
Each sector of the general and transportation industries maximize their present
cash flow values in each period NC rjt and the asset value of their industrial capital in
the final period  rj () . The sector operates with constant returns to scale technology.
The sector chooses the optimal investment and labor employment strategies. Thebehavior of the production sector j  I  M in region r  R is given asmax{ K rjt , Lrjt , Xrjt , Z rjt }  NC  tTtr
jt rj ( K rj ,tF 1 ) ,t F 1subject to K rj ,t 1  (1   j ) K rjt  K rjt (Ζ rjt ) ,wherer
r
r
r
r r
Drr
Dr rr
NC rjt  p Orjt Y j ( K jt , L jt , X jt )  wt L jt   pit X ijt   pit Gi ( Z ijt ) .
iI  MiI  M

t  1/(1   )t 1 represents the discount factor and  is the positive discount rate.
Y jr () is a production function of capital K rjt , labor Lrjt , and a vector of intermediate

input X rjt  { X 1rjt , , X Ijtr } . The value added production function for labor and capital
has a Cobb-Douglas form, while the intensities of intermediate goods are fixed. The
asset value for the final period  rj () is a linear function of the capital stock for thefinal period. The capital stock K rjt is accumulated by an investment function K rjt ()with constant returns to scale. It is a function of a vector of intermediate inputs for theinvestment Z rjt  {Z1rjt , , Z Ijtr } , and a Leontief type technology is assumed.  j is thedepreciation rate. It is assumed that the cost function of intermediate goods forinvestment Gir () has increasing returns to scale. It can be interpreted that thefunction reflects both the costs of intermediate goods and the costs of adjusting theircapital inputs.

In these sectors, there are two kinds of prices in each region. One is theand the other is the purchaser’s price p Dr
in region r . If a
producer’s price p Or
jt
jt
commodity j is tradable between regions o and d , then the producer’s price inand the purchaser’s price is represented by p Dd
region o is represented by p Oo
jt
jOr
( j  I ) . In the transportation sector, p jt ( j  M ) means the unit price of thetransportation services in region r . wtr is the wage rate.
After having paid wages to households, the sector has to decide how todistribute profit and finance investment. In this model, the net investment is financed
by new bonds. Let B rjt be the number of bonds in period t and rjtr be the interestrate. The bonds are traded in each region. The initial number of bonds is normalized byB rj1  K rj1 . In this case, the profit dividend is calculated asrrrr
r rr rDzzrr
 rjt  p Orjt Y j ( K jt , L jt , X jt )  r jt B jt  wt L jt   pi X ij  p Bjt  j K jt .
iI IO

If the net investment is financed by issuing new bonds, it holds thatrrpBjt
B rjt   pitDr Gir ( Z ijtr )  pBjt
 j K rjt ,iI  M

where B rjt is the number of new bonds issued by sector j in region r for periodr
t . pBjt
is the price of the new bond. Therefore the outstanding bond is given byrB j ,t 1  B rjt  B rjt with B rj1  B jr1 . It is assumed that the price of the new bond is givenrby pBjt
 q rjt where q rjt is the costate variable of the current-value Hamiltonian
function H rjt  NC rjt  q rjt [K rjt ( Z rjt )   j K rjt ] .
In this model, we assume that tradable goods are perfect substitute. The profitof the distribution sector is given by ( j  M )roror
OoTororor
Oror
 Djt
 p Drwhere pTorjt    jmt F jt    ( p jt  p jmt )  jmt F jtjmt   jmt pmt D jmt .
oR mMoR mMThe commodity flow Fjtor is calculates asFjtor   orj (  X rjit  C rj )iI  M

where  is the given trade coefficient.  orjmt is the given modal share. pTor
jmt is theortransportation cost of mode m from region o to region r . Dmt is the distance
between origin and destination along with a path. The path is exogenously given by theshortest path rule.  mjt is a given unit transportation services of mode m for goods
i . From the zero profit condition, the purchaser’s price is given byorjOoTorororp Drjt    ( p j  p jm )  jm F j .
oR mM

3.2 Household Sector
A representative household maximizes the utility level subject to income
constraints. The full income consists of wages and interest on bond holdings. The
behavior of a household in region r  R is given as  U (C ) ,rmaxr
C tTsubject totrtr
wtr   ritr Aitr  dtr  FAtr   pitDr Citr   pBitAitr  0 .
iI  MiI  MiI  MU r () is a Cobb-Douglas utility function for period t and it is a function ofconsumptions Ctr  {C1rt , , CItr } . Aitr is the number of bond holdings per household.
Aitr represents new bonds issued for industrial investments. The household canreceive the interest income but must pay to obtain a new bond. FAtr is the income
transfer that provides a balance against a surplus or deficit in foreign and regional
trades. dtr is the profit dividend that is given as dtr   iI  M  itr / N tr since the utility
function is not identical among regions. If the production function is of the constantreturns to scale, then the profit of the firm becomes zero.
In this model, we assume that the level of investment is determined by afirm’s optimization behavior. Firms place priority on the investment-savings balance.
Therefore, the level of household savings is adjusted to coincide with the level ofinvestment. In this case, the new bonds and the bond holdings per household are
calculated asAitr  Bitr / N itr (i  I  M ) and Air,t 1  (Aitr  Aitr ) N tr / N tr1 (i  I  M ) .
3.3 Equilibrium Conditions
To obtain an equilibrium solution, the following market clearing conditions
should be satisfied in each region (r  R ) .
(1) Goods and Services Markets
General Goods

Y jr ( K rjt , Lrjt , X rjt )   X rjit  C rjt N tr   T jrd   T jor  E rjt  M rjt (i  I )iI  Md RoRrjt

where E is a given export from region r and M rjt is a given import to region r .
Transportation Servicesroror(m  M )
Ymr ( K mtr , Lrmt , X rmt )    imt
imor Dimt
FimtiI I oR(2) LaborN tr   LritiI  M

Nrtis the total labor force (population ) in each region and it is exogenously given.

(3) CapitalAitr N tr  Bitr (i  I I  M )Aitr N tr  Bitr  K itr with Air1 N1r  Bir1  Kir1 (i  I  M )A1ri is the initial number of bond holdings of a household.
(The simulation results will be shown in the meeting.)
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