Journal of Applied Input-Output Analysis, Vol.1, No.2, 1993

Reducing CO2 Emissions and Long Run Growthof the Japanese Economy1
By

Masahiro Kuroda* and Kazushige Shimpo*

Abstract

We outline the intertemporal general equilibrium model of the Japanese economy. Ourmodel of the Japanese economy incorporates a submodel of consumer behavior and a sub
model of producer behavior in which separate models of production has been economet-

rically estimated for seventeen industries.

In our model of the Japanese economy, giventhat the economic production technology is characterized by constant returns to scale ineach industry and all markets are perfectly competitive, the prices are determined so as toclear each market in each period. Further our intertemporal model incorporates backward-

looking and forward-looking equations that determine time paths of capital stock, fullconsumption and price of investment goods.

Under the perfect foresight assumption theprices which are determined in each period are solved to obtain a complete intertemporalequilibrium along these intertemporal equations. We tried to depict the long-run economic
growth path of the Japanese economy during the period 1990-2100 as a basic scenario byusing our general equilibrium model.

In order to evaluate the stabilization policy of theCO2 emissions in terms of the introduction of the carbon taxes to the Japanese economy,
we tried to simulate the growth path of the economy by imposing the carbon taxes in thesystem as following two alternative scenarios:[Case I] Employ an endogenous carbon tax
to stabilize per capita CO2 emissions at the level of 1990, 2.14tC, from 1991. The carbon
tax is levied as a indirect tax on secondary energies proportional to their carbon contents.
The revenue from carbon tax is applied so as to hold government spending constant at its
base case level and allow government transfer to the rest of the world to adjust to keep thegovernment deficit constant. [Case II] Under the same stabilization program as case I, therate of capital income tax is reduced by 10%. The application of revenue from carbon tax
is the same as case I.

1.

Introduction

The possibility that carbon dioxide emissions from fossil fuel combustion might lead to global
warming through the greenhouse effect has emerged as a leading international environment
concern.

At the end of the year 1990, Japanese government proposed her action program inorder to stabilize the CO2 emissions in Japan, where their objective aims to stabilize the per-capita CO2 emissions in the year 2000 at the 1990 level.

Although it has continued to makean effort to achieve this target in the Japanese economy, we think that it is not so easy toguarantee the carrying out of the program at this stage. Moreover, according to our impression,
Manuscript received June 2, 1993. Revised October 28, 1993.

* Keio University

aThis paper is prepared for Energy Technology Systems Analysis Programme Conference to be held in theHarwell Training Center, Oxford on 7-11 June, 1993.

We would like to thank Dale W. Jorgenson, Harvard

University and Hirobumi Uzawa, Niigata University for helpful comments and discussion. Any remaining errors
are our own.

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Journal of Applied Input-Output Analysis. Vol.1, No.2, 1993

the action program itself was not necessarily based upon the careful discussion deciding what
the optimum target would be, what kinds of impacts on the economy would be expected, whatkinds of policy instrument would be preferable and so on. Finding answers to these questions
requires a robust analysis of observed relationships between economy and environment and an
accurate assessment of the various policy instruments. In this paper, we present a multi-sectoral
dynamic general equilibrium model, which is econometrically estimated by Japanese historical
data. By using our model we try to simulate the dynamic growth path of the Japanese economy

and propose alternative scenarios concerning the reduction of CO2 emissions. As one of thepolicies for fighting the greenhouse effect, a tax on the carbon content of fossil fuels, so called a"carbon" tax could be an effective way to reduce CO2 emissions. We would like to focus on an
introduction of carbon taxes to reduce CO2 emission and analyze the impacts of the introduction
on the growth path and resource allocation of the Japanese economy.

Our developed model, which is similar to the model basically proposed by Cass(1965) andKoopmans(1967) and empirically developed by Jorgenson-Wilcoxen (1992, 1993a, 1993b) in
the U.S. economy, has several appropriate features to simulate a long-term economic impacts
such as reducing policy of CO2 emissions.

First, it is a multi-sectoral model in which the

production sectors of our model are divided into seventeen industrial sectors. There are muchdifferences in the energy intensity among industrial sectors.

Impacts of the introduction of

the carbon tax would be expected to be different among sectors because of the differences ofthe energy intensity.

Second, in our model the rate of productivity growth and the bias oftechnical changes are endogenously determined consistently with the changes of the system of
relative prices. Introduction of carbon tax would be expected to change the system of relative
prices of the economy. It would be highly important that the model has to provide a tool toevaluate their impacts on the changes of the productivity. Third, one of our key features in ourmodel is the dynamic properties, by which we can depict the dynamic path of the intertemporal
optimum resource allocation of the economy. Finally, our model is not a so called computable

general equilibrium model (CGE), but an empirically estimated econometric model based upon
the historical data in Japan. In section 2, we will provide a brief summary of our model. We
try to depict the dynamic path of the Japanese economy during the period 1990-2100 as a basic

scenario under the assumption of the exogenous variables as shown in section 3.1. Comparing theresults of the alternative policy concerning carbon tax with the basic scenario, we try to evaluate

the impacts of the introduction of carbon tax reducing CO2 emissions on the Japanese economy
in section 3.2. Carbon tax assumes to be introduced as increasing the rate of indirect taxes ofsecondary energies such as coal, petroleum and gas products excluding electricity, proportioned
to the carbon contents of each energy.

2.

An Overview of the ModelIn this section, we will give a brief summary of our intertemporal general equilibrium model of

the Japanese economy. Our model incorporates a submodel of consumer behavior and a sub
model of producer behavior. Models of production were econometrically estimated for seventeen

industries, in which four energy conversion sectors and thirteen energy combustion sectors areincluded as shown in Table 1. Given the production technology characterized by constant returns to scale in each production sector and the assumption of the perfect competitiveness of
all of the market, prices of goods and services, and factor prices are simultaneously determinedso as to clear the market in every periods of time. In the market, each individual is assumed

to behave rationally with perfect foresight in the future in order to determine the time paths ofcapital accumulation and full consumption in a forward looking way. On the other hand, behav

ior of each individual is constraint with the factor endowment such as the past accumulation ofcapital stock and the exogenously given human capital stock in a backward looking way. The

Reducing C02 Emissions and Long Run Growth of the Japanese Economy

3

Table 1: The Classification of Industries

NumberDescription (Abbreviation)

Coal products (Coal)

1
2

Petroleum refining products (Petro.)

3

Electric power generating(Elec)4

Gas supply (Gas)

56Agriculture, forestry and fisheries (Agric.)
Mining (Mining)

7

Construction (Const.)

8

Foods and kindred products (Food)

9

Textile and apparel (Text.)

10Paper and allied product (Paper)

11

Chemical (Chemic.)

12

Stone and clay (Stone)

13

Iron and steel (Iron)

14

Metal and machinery (Machine)

15

Miscellaneous manufacturing (Mfg.)

16

Transportation and communication (Transp.)

17Services (Service)

results presented in this paper are based on simulations we conducted using this disaggregated,econometrically estimated intertemporal general equilibrium model of the Japanese economy.
Before explaining our results, we will confine ourselves to outlining a few of its key featuresand discussing how we extended our model to simulate the impact of the stabilization of CO2
emissions in this section.

2.1.

System of National Accounts and Outline of the Model

The basic framework of our modeling is based upon the system of national accounts for theJapanese economy composed by Kuroda(1991) and Kuroda and Shimpo( 1992).This system ofnational accounts integrates production accounts for each industry, input-output table, income-expenditure accounts, and capital accounts. In production accounts, the value of output is equal
to the value of inputs for each industry which is expressed as the following identities for eachjth industry:

PojQj

=
rNj )ePNi Nj + PKj Kj + PLj(1)

where the quantity of output from jth industry is represented by Qj and the jth industry's
quantities of inputs of ith commodity, non-competitive imports, capital and labor are denotedby X^, Nj, Kj, and Lj. Similarly, we denote the net price of output excluding indirect tax levy

in jih industry by Poj, and the input prices of ith commodity, non-competitive imports, capital,and labor by PSi, /V,, Pk5i and P^j respectively. Input price, Ps{ is defined as composite price,5

jof domestic commodity price, Pa and imported commodity price,because the quantity

4

Journal of Applied Input-Output Analysis, Vol.1, No.2, 1993of each input is a composite of products domestically produced and competitively imported.
e denotes the exchange rate and tn3 denotes the rate of import tax for the non-competitive
imports which is exogenously given in our model. rjj stands for the rate of net indirect tax,
which is also exogenously given in our model, so that P\j represents the supply price of output
including net indirect tax levy in jth industry2. Interdependence of the production sectors
are depicted by the framework of the input-output tables. Our system of input-output tables
are divided between a use table and a make table. The use table describes the inter-industry
transactions of intermediate inputs and incorporates the production account identities among
output and all of inputs by industries. On the other hand, since we allow for joint production,
we have to describe the relationships between output by industry and output by commodity.
Then the make table gives us information for the amount of each commodity produced by eachindustry, so that our production accounts include the following identity for the value of output

produced by jth industry:

ctji,

(2)

where Xji denotes the output of ith commodity produced by jth industry. The make tablealso links output prices to commodity prices and determines the allocation of the output of eachindustry among commodities in our model of producer behavior.
Given the prices of non-competitive imports, capital, and labor services, our model of pro
ducer behavior determines output prices and input demands simultaneously to maximize profit
in each period as a function of prices of output and input. Factor demands for capital service

and labor service meet their supplies in each market, and the rental price of capital, Pk, andthe price of labor input, Pl will be determined so as to clear each market in each period:

A'5

=

£>,-,

(3)

j

Ls = J2Lij(4)

where A'5 denotes supply of capital service at period t, which is predetermined proportion
ally to capital stock, KSK at the beginning of the period. We assume that the amount of
capital service is proportional to the amount of capital stock which is accumulated by all past
investments and predetermined at the beginning of each period as discussed later. Ls denotes
labor supply which is determined by the submodel of consumer behavior.
The input-output tables also depict the deliveries of commodities to domestic final demands
and the rest of the world. In the input-output table, demand and supply identity holds for each

ith commodity:

ij+Ci + Ii+Gi).

(5)

The left hand side of this identity shows total domestic supply of iih commodity. We denotetotal output ofith commodity domestically produced by X{. EX{ is the exports ofith commodity

to the rest of the world. I Mi denotes competitive imports of ith commodity from the rest of
the world. We denote its price and the rate of tariff by PIMi and rIM. respectively, which are
2 Net indirect tax implies that indirect tax minuses subcidies.

Reducing CO2 Emissions and Long Run Growth of the Japanese Economy

5exogenously given in our model. On the other hand the right hand side of the identity shows

total domestic demand of iih commodity. It consists of intermediate demands, Xij, household

consumption demand, Ct, investment demand, /,-, and government demand, G,-. Assuming
imperfect substitution among domestic goods and imported goods in consumer behavior, theshares of imported goods within each demand item are determined exogenously as a function of
the relative prices, PCi / PiMt>
Aggregating these identities we can obtain the output-expenditure identity for the economy
as a whole:

Y = PCCC + PINVI + G + EX-IM,

(6)

where

IM = ^(1 + TIMt)ePIMtIMi«

Pec, and C denote the aggregate price and quantity of goods-service consumption. Pinv,

and / denote the acquisition price and the quantity of investment for the economy as a whole.
G, EX, and IM represent the nominal value of the government expenditure, export and importin the aggregate level.

expenditure.

From the viewpoint of expenditure account Y shows gross domestic

On the other hand, from the viewpoint of production account Y shows grossdomestic product which is the sum of value added over all industries:

i -E

(7)

Furthermore, from the viewpoint of income distribution, Y is gross domestic products andit is also satisfied with the following identity:

Y = YK + YL,(8)where Yk shows the income share should be paid to owners of capital in compensation forrental of capital. We refer this as pre-tax capital income. Yl shows the value should be paid toworkers in compensation for the supply of labor. We refer this as pre-tax labor income. They
are defined as follows, respectively:

These identities described above are linked with the income-expenditure account in which
income less tax payment is equal to the consumption expenditure plus saving:.
Denoting saving by 5 and tax payment, equivalently government tax revenue by T:

(9)

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Journal of Applied Input-Output Analysis, Vol.1, No.2, 1993

T

=
j

J

+tkYk + rLYL + TPPINVi_xKs,(10)

where rjt, tx, and rp denote the rates of capital income tax, labor income tax, and property
tax, respectively.

To explain the income-expenditure accounts in greater detail, we must present some iden
tities relating to the consumer behavior. We assume that a representative consumer owns theinitial physical capital stock or claim on it. We also assume that he is endowed with a fixedamount of disposable life-time at the beginning of the period. We refer this endowment as timeendowment or human capital. In our model the amount of human capital for each period is
exogenously given. The claim on physical capital stock and the exogenously given amount of
the human capital stock are assumed to make up his lifetime wealth, which is referred as full
wealth. We assume that the representative consumer optimally allocates the lifetime wealth,in other words, income earned by his lifetime wealth, to consumption and saving over time bymaximizing his intertemporal utility. Consumption defined here includes current consumptionof goods and services and leisure consumption, which is called full consumption.

Especiallyleisure consumption is corresponding to a consumption of time endowment of a human capital.
Human capital can be consumed by leisure or by supplying labor service to the market, so that
we can define the following identity for each period:

PLH = PLLEIS + PLLS,(11)

where H denotes the time endowment or human capital, and LEIS denotes the hours devoted
to leisure. Next we must define full consumption which is an aggregate of leisure consumption
and goods and service consumption. For full consumption, the following identity is required:

PFF = PCCC + PLLE1S,(12)

where Pp and F denote the price and quantity of full consumption. We assume that the
representative consumer has his preference for the allocation of the full consumption between

goods-service consumption and leisure consumption subject to the budget constraint(12). We
can derive demands for goods-service and leisure as a function of these prices and the wealthallocated to the current period. This determines the supply of worked hours to labor market,
i.e. labor supply from equation (11).
We return to the income-expenditure identity (9) again. The left hand side of this identity

shows the current disposable income which is generated by wealth allocated to the current
period. As a consequence this identity implicitly determines the saving in our model of consumer
behavior. Then, we can summarize the identities discussed above as the following identity
between saving and investment in the economy:S - PJNVI = AFA + AGB.

(13)This identity requires that the I-S balance in private sector be equal to the current accountsurplus minus the government budget deficit. We denote the current account surplus by AFA =EX - IM and the government budget deficit by AGB = G -T.

One of the key features of our model is that the current account surplus and the government

budget deficit can be treated as exogenous variables. This means that the exchange rate can be
determined endogenously so as to satisfy the exogenously specified current account surplus, andsimultaneously the government expenditure can be determined endogenously so as to satisfy theexogenously specified government budget deficit. As described above saving is determined by

Reducing CO2 Emissions and Long Run Growth of the Japanese Economy

7equation (9) reflecting the intertemporal allocation of lifetime wealth, so that the amount of
capital formation can be determined so as to satisfy the I-S balance (13). While the identities
discussed above characterize the static equilibrium as the I-S balance in each period, the capital
accumulation also importantly characterizes an intertemporal feature as a dynamic path of theeconomy. In other words, the capital accounts incorporates a backward-looking accumulation
equation for capital stock, linking the current flow of capital services to all past capital formations
as an aspect:

K + I,(14)

where Kf£x stands for capital stock at the beginning of the next period, t-f 1 and 6 denotes
the rate of economic depreciation of capital. The capital accumulation behavior also includes
a forward-looking one such as asset pricing equations in which the acquisition price of new
investment goods, PiNVt1 is equal to the present value of future capital services, weighted by the
relative efficiency of capital goods, i.e. the rate of depreciation of capital in each future period.
Thus the capital service price in each period is given by:

Pk

=

- TK

t],

(15)

where r is the rates of return on capital in period t and 6 is the rate of depreciation, while{tk,tp} are the rates of tax on capital income and property income respectively. {PiNVt} arecurrent prices of aggregate investment goods which are equal to the present discounted valuesof the returns expected on an extra unit of capital under the assumption of perfect foresight.
This equation is forward-looking, so the current price of aggregate investment goods in every
period will depend on the whole paths of future rental prices and interest rates.

2.2.

Producer Behavior

We next present our submodel of producer behavior. Substitutability of energy for other factorsof production and among energies, and price induced endogenous productivity growth give an
important features of our submodel of producer behavior relating to the environmental policy.
We divide the Japanese industries into seventeen industries as shown in Table l.This is essential
for analyzing the impact of introducing the carbon tax since these industries differ in energy

intensity. Energy treated in our model is divided into two categories. The first one is primaryenergies including fossil fuels(coal, oil, and natural gas) and nuclear power. The primary ener

gies, excluding nuclear power, are principally supplied by domestic mining industry and the restof the world. However, the endowment of natural resources in Japan is so poor that Japan has
historically obliged to depend upon imported sources of primary fossil fuels almost noncompetitively. It is one of the key features of the Japanese economy when it comes to consider energy
and environment problem in Japan. On the other hand, a portion of electric power is also gen
erated by nuclear power and its ratio will be expected to increase in the future. Although theperspectives of the ratio of the nuclear power is highly important in our concerns, the ratio of
nuclear power generation in total electric power supply is treated as exogenous at this moment.
The second one is secondary energies including coal products, petroleum refining products,

electric power and gas which are physically converted from primary energies. We refer theseindustries as energy conversion industries. The other thirteen industries combust the secondary
energies supplied by energy conversion industries. We refer these industries as energy combustion
industries.

Our submodel of producer behavior is based on a two-stage allocation.

We assume that

economic production technology in each industry is characterized by constant returns to scale

8

Journal of Applied Input-Output Analysis, Vol.1, No.2, 1993

without externality. We can summarize the representation of this production technology interms of unit cost or price functions. The unit cost or output price from each industry is afunction of input prices and state of technology. The functions must be homogeneous of degreeone, non-decreasing and concave in the input prices. We assume that the energy input andthe material input are homothetically separable in the price functions. Pej, and Ej denote theaggregate input price and quantity of energy for jth industry respectively. Similarly, Pmj , and

Mj denote the aggregate input price and quantity of material for jth industry. The functions

gj(t) represent the state of technology for each industry and it is a function of time, t.
At the first stage, the value of output is allocated among four inputs, capital, labor, aggregate

energy and aggregate material in each industry under the assumption of perfectly competitivemarkets of commodities and factors of production. This implies that the value of output is equal
to the value of inputs:

PojQj = PkjKj + PljLj + PEjEj + PmjMj.

(16)

We define the value shares of inputs in the value of output, representing vkj, vlj, vej, andvMj by:
PkjKj

PljLj

PejEj

PMjMj

PojQj

PojQj

PojQj

PojQj

At the second stage, the value of energy and material inputs are allocated among corre

sponding commodities. This implies that the values of energy and material inputs are equal to
the sum of the values of corresponding commodities:

Pej Ej = P'EEj Xeej ,Pmj Mj = P'MMj Xmmj ,(18)

where Xeej and Xmmj denote the vectors of quantities of individual commodities, eachelement of these vectors correspond to the price vectors Peej and Pmmj , respectively. We
define the value shares of commodities and noncompetitive imports in the value of output, i>,-;and VMj by:
Psi Xij

Vij = To'PNj Xjvj

VNj = p n '19Further, we denote the vectors of value shares of individual commodities in output corre
sponding to the price and quantity bundles (PEej>XEej) and (Pmmj,Xmmj) as vEEj andvmmj, respectively.

We try to specify the production model of energy combustion industries in the following way.
For simplicity we define the vector of logarithms of input prices faced by the industries as:
In Pj = (In PK., In PL., In PEj, In PMj)'.

Similarly, we define the vector of value shares of inputs for jth industry as:

We assume that the jth energy combustion industry allocates the value of its output amongfour inputs, capital, labor, energy and material at the first stage in accord with the translog
price function:

In POj = ajpQ + In Pja^ + i In PjBjpp In Pj

4ln pjP3Tp9j(t) + ^PJTT9](t),(20)

Reducing C02 Emissions and Long Run Growth of the Japanese Economy

9

The scalars aJPQ, aJT, and /?^T, the vectors oPp, and /3JTp, and the matrices B*pp are jth industry's constant parameters that differ among industries, reflecting the differences in economic
technology. All parameters should be constrained to integrability conditions. These conditions
should be imposed on parameters, when they are estimated. Necessary conditions for producer
equilibrium and the Shephard's lemma are given by equalities between the value shares of each

input in the value of output and the elasticities of price of output with respect to price of that
input:

Vj = ctp + BjPP In Pj
The parameters Bpp and (3JTP give very important features to our model since these pa
rameters capture the price induced improvements in the efficiency of utilization of energy andother inputs. The parameters BJpp are share elasticities and they measure the substitutability
among inputs since they give the response of the value shares of energy and other inputs to pro

portional changes in the input prices. The parameters (33Tp are biases of productivity growth 3.
The specification of function, gj(t), plays an important role in long run simulations. Usually,
the state of technology was taken to be linear in time, gj(t) = t. This linear formulation allows
for an unlimited growth of productivity. Consequently, if an input has an input-saving bias ofproductivity growth, its value share will eventually become negative.

Moreover, it should be

noted that negative value share would be able to occur regardless to the integrability conditionsof other parameters.

Further, if productivity growth is unlimited, the existence of balanced

growth equilibrium requires the rates of productivity growth become the same for all industries
in the long run. Otherwise, the industry with the highest productivity growth rate would cometo dominate the economy in the long run. In our model we assume that productivity growth islimited and converged in the long-run in order to avert the above unwilling possibilities. The
functions gj(t) are given by;where the scalars fij are constant parameters that differ among industries. With our specifi

cation, each of the state of technology goes to unity in the limit, so that the value shares depend
only on the input prices in the limit. We can express the endogenous rate of productivity growthin the jth industry, say, — vt,-, by differentiating the price function with respect to time:- vr. = (4 + lnP/^p + PJTT9j(t)) g^t).

(23)

With this specification the rate of growth of productivity approaches zero for all industries
since the derivatives gj(t) go to zero in the limit, so that the level of productivity in each industry
goes to a constant. This specification yields long run behavior of the economy consistent withbalanced growth equilibrium.

The parameters related to the productivity growth, aip, 0iTP and (33TT were estimated with ahistorical data set and these parameters reflect the knowledge about the state of technology inthe sample periods. We assume that the rate of productivity growth built up with the knowledge

accumulated during the sample periods will be decreased gradually to certain saturated level ofthe productivity in the future.
3Ifa bias of productivity growth is positive, productivity growth is input-using since the corresponding value
share increases with a change in the state of technology, alternatively the productivity decreases with the input
price. If a bias of productivity growth is negative, productivity growth is input-saving since the corresponding
value share decreases with a change in the state of technology, alternatively the productivity increases with the
input price. Finally, if a bias of productivity growth is zero, productivity growth is neutral since the corresponding
value share is independent of the state of technology, alternatively the productivity is independent of the input
price.

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Journal of Applied Input-Output Analysis, Vol.1, No.2, 1993

In our model the producer behavior in the energy conversion sectors are not perfectly sym
metric to the producer behavior for the energy combustion industries. In the energy conversion
industries, we assume that primary energy requirement for producing unit of secondary energy
is physically and chemically fixed, so we represent this feature in energy conversion industry pro

duction by means of fixed input coefficients. The fixed input coefficients are exogenous so that
we can simulate an effect of increase in the energy conversion efficiency on the long run growthof the Japanese economy. Input coefficients are defined as an amount of the ith commodity
required to produce unit of output for the jth industry;Xij

aii = oT1

Xtfj

aNi = W

We first divide an unit cost in energy conversion industries into two parts, an unit cost of
primary energy input, say, Cpej> and an unit cost of other inputs, say, Cj\

POj = Cpej+Cj(j = 1,2,3,4).

(24)

Since the primary energy sources are supplied by domestic mining industry and the rest of
the world, the unit cost of primary energy for coal products, petroleum refining, and gas supply
industries is defined as follows:

Cpej = a6j PS6 + aNj PNj(j = 1,2,4)(25)

The unit cost of other inputs is defined so as to satisfy the cost-revenue identity for eachindustry:

CjQj = PkjKj + PljLj + PejEj + PmjMj,(j = 1,2,4).

(26)

These industries allocate the value of output among capital, labor, energy and material inaccordance with the translog unit cost functions for these four inputs:

In POj = 4o + In Pj<Jp + \ In PjBpP In Pj, (j = 1,2,4).

(27)

Necessary conditions of producer equilibrium are given by the following equalities with respect to the value shares of four inputs in the value of output and the elasticities of output pricewith respect to price of that input adjusted by the unit cost Cj per output price:

Vj = it (^ + BJpP ln Pj) ' {j = 1? 2> 4)'(28)

while the value shares of primary energy in the value of output are given by:&,oj(j = 1,2,4).

(29)

For the electric power generation industry, the requirements for coal products, petroleum
refining products and gas are also treated as fixed input coefficients, so that the unit cost offuels is defined by:
4

CpEZ = 2^ a«3^5» + ^63^56 + 0>N^Pn3-

(30)

t=l

The unit cost of other inputs is made up from the cost of capital, labor and non-energy
material is given so as to satisfy cost-revenue identity by:

Reducing C02 Emissions and Long Run Growth of the Japanese Economy

C3Q3 = PksKs + PlsL3 + Pm3M3.

11

(31)

The electric power generating industry allocates the value of output among capital, labor,
and non-energy material in accordance with the translog unit cost function for these three
inputs. The value shares of these three inputs are derived by differentiating the translog unit
cost function with respect to the logarithms of input prices and adjusted by the unit cost Cj
per output price. Although the demands for primary energies and secondary energies producing
unit of electric power are exogenously specified, their value shares are endogenously determined
as functions of input and output prices.

We turn next to present the second stage of our model of producer behavior. At the second

stage the jih industry except electric power generating industry allocates the value of energy
input among four individual energies with the translog energy price function:

In PEj = 40 + In P'EEj 4 + 5ln Peej &ee ln pEEj,(32)

The scalars or^0, the vectors o?E and the matrices BEE denote constant parameters thatdiffer among industries. Especially, the parameters B^EE are share elasticities and they measure
the degree of substitutability among individual energies for each industry. Necessary conditions
for producer equilibrium and the Shephard's lemma are given by equalities between the value

shares of each individual energy in the value of aggregate energy and the elasticities of price of
aggregate energy input with respect to price of that energy:

veej = (o4 + &EE In PEEj ) vEj(33)

Similarly, the jth industry allocates the value of material input among the corresponding
commodities and noncompetitive imports with the Cobb-Douglas material price function:

lnPMi=laP'MM. + ^MM,

(34)

The vectors o^M are constant parameters that differ among industries and can be interpreted as the value shares of each commodity in the value of aggregate material input, so thatthe value shares of individual commodities are given by:

MP

(35)

The outputs produced by each industry are supplied with net indirect taxes, so that jth
industry's sales price is given by:

j

(36)

where tjj denote the rates of net indirect tax. We allow for joint production. We have seventeen
commodity price functions which take in form Cobb-Douglas:

In Pa =Y,m>ilnPli>(37)

where rriji are constant parameters and can be interpreted as the market share of jth industry
in the value of ith commodity. The commodity price functions link industry output prices
to commodity prices and determine the allocation of the output of each commodity amongindustries.
In summary, given all of the input prices, our model of producer behavior determines sev

enteen industry output prices, seventeen commodity prices, and value shares of seventeen com

modities, capital, labor, and noncompetitive imports by each industry. Our model of producer

12

Journal of Applied Input-Output Analysis, Vol.1, No.2, 1993

behavior is consistent with the production accounts, so that it determines the input shares depicted by the use matrix endogenously. Further, the commodity price functions convert theindustry output prices into commodity prices consistent with the make table.
2.3.

Consumer Behavior

Let us explain our submodel of consumer behavior. We represent consumer preferences by meansof an infinite lived representative consumer. The representative consumer owns the capital stockor the claim to the income streams created by its capital stock and is also endowed with thehuman capital, which is given exogenously by time endowment, that can be allocated to labor
supply and leisure consumption. We assume that the representative consumer can capitalize
its future income which can be earned from the supply of its physical and human capital withperfect foresight of all future prices and discount rates. We refer this capitalized income as full
wealth. Thus, the full wealth is the present value of future earnings from the supply of capitaland labor service and the imputed value of leisure time.

For the simplicity of manipulation, we divide our submodel of consumer behavior into threestages. The first stage is intertemporal. At the first stage a representative consumer optimally
allocates its full wealth over time according to its rate of time preference and intertemporalelasticity of substitution, subject to an intertemporal budget constraint. This determines fullconsumption and saving in each period. The full consumption, here, is defined as an aggregate ofgoods-service and leisure. The second and the third stages are atemporal. At the second stage
we assume that the representative consumer has preferences between goods-service and leisure.
In accordance with the preference, the consumer demands for leisure time and goods-service andsupply of labor service can be derived in each period. At the third stage, we also assume thatthe consumer has preferences among commodities. The consumer allocates the goods-service
consumption among seventeen commodities and noncompetitive imports with a function of theirprices and expenditure as a budget constraint.

At the first stage, the infinite lived representative consumer with perfect foresight of all future

prices and discount rates maximizes an additively separable intertemporal utility function:

Ut is an utilitarian atemporal utility function, where the utility per capita multiplied bynumber of population, Nti which is exogenous variable in our model, p is the rate of time
preference. The atemporal utility depends on the per capita full consumption, fracFtNt:(39)
where a denotes the intertemporal elasticity of substitution.

The representative consumer allocates the full wealth over time and chooses the time path offull consumption and saving to maximize the intertemporal utility, subject to an intertemporalbudget constraint. This requires that the present value of future full consumption is no greaterthan full wealth. In our model, since the stream of time endowment is exogenously specified,under perfect foresight of all future prices and discount rates, the intertemporal budget constraint
is given as follows:

W = PINV0K0 + f; -20*2- > J2 -p^—*=° n i+r,»=o«=o n i+r,
»=o

(40)

Reducing C02 Emissions and Long Run Growth of the Japanese Economy

13

The equality gives the definition of full wealth, W. rt represents the discount rate which isequal to the nominal rate of return after tax on physical capital in period t. wt denotes the after

tax wage rate, defined as, wt = (I-t^Ph, where tu is the exogenously specified labor income

tax rate. PinvoKo shows the present value of income generated by initial holding of capitalstock or its claim, since Pjnvo is the present value of future capital service produced by Ko. Htis the time endowment exogenously specified in period t, so that the second in the right handside of this equality shows the present value of income earned by the supply of labor service
and the imputation of leisure time. The inequality gives the intertemporal budget constraint.

In equilibrium this is satisfied with equality.
The conditions for optimality, where the intertemporal utility, (38)is maximized subject tothe budget constraint, (40), can be given in the form of Euler equation with respect to adjoining
two periods of time, t and t + 1:
Nt

/^

(41)

We find that the current level of full consumption depends on the price, discount rate,

population, and full consumption itself in next period. This relation is kept consecutively on
all future level of full consumption.

Thus, the current level of full consumption incorporates

expectations about all future prices and discount rates, so that the Euler equation is forwardlooking.

Once each period's full consumption has been determined, we proceed to the second stageof our submodel of consumer behavior. In this stage, the representative consumer allocates theexpenditure of full consumption between the goods-service expenditure and the leisure in accor

dance with its preference. For convenience sake, we refer the expenditure of full consumption as

full expenditure, Mpt, defined as MFt = PFtEt- We assume that the full expenditure is allocatedby maximizing an indirect utility function(dropping time subscript):

Ucl{C,LEIS)}(42)

subject to the budget constraint:

MF > PccC + w LEIS.

(43)

The indirect utility function is specified in the form of translog imposing homotheticity thatmeans the allocation is independent of full expenditure.

- In ^ = a'CL In PCL + \ In P'clBcl In Pcl,

(44)

where Pql — (PcCiwY- The vector olql and matrix Bql are constant parameters. The
parameters olcl is normalized as a'CL i = 1, where i is an unit vector. The homotheticity
VC Li
assumption allows the price of full consumption to be expressed as, In Pp = — In -tt—, so thatthe quantity of full consumption can be expressed as, F =Using Roy's identity, we can obtain the vector of share equations:

vcc

VLEIS

MF

w

LEIS

(45)

MF

These share equations give us demands for goods-service and leisure, given their prices andfull expenditure:

14

Journal of Applied Input-Output Analysis, Vol.1, No.2, 1993

LEIS = vLEIS—.
w(46)

The difference between the leisure time and the time endowment determines the time forlabor market, i.e. the supply of labor service:

Ls = H- LEIS.

(47)

The final stage of our submodel of consumer behavior allocates the expenditure of goods-

service among seventeen commodities and noncompetitive imports. For the sake of convenience,

we denote the expenditure of goods-service as Mcc = PccC + w LEIS, the vector of prices ofseventeen commodities and noncompetitive imports as:

Pc = (PsuPst, »., Psit, Pnc)'>
and the vector of corresponding quantities as:

Cc = (Cfi,C2,...,Ci7,CrAr)/.
We assume that the expenditure is allocated by maximizing an indirect utility function:

Vcc(Pc, Mcc) = max UCc(Cc),(48)

subject to the budget constraint:

Mcc > P'cCc-(49)

The indirect utility function is specified in the form of Cobb-Douglas, so that the value shareof each commodity is independent of their prices and the total expenditure, Mqc-

Mcc

Pc.

(50)

The vector ace represents constant parameters and the value shares of commodities. With

Vcc

this specification, the price of goods-service consumption can be expressed as, Pec = — In ——,and its quantity as, C = Vcc- The demand for each commodity is given by:

Cc = «'ccPZ1Mcc.
2.4.

Mcc

(51)

Foreign Trade and Government

The two remaining components of the model are the foreign sector and government. Beginningwith the foreign sector, it has two components: imports and exports. We assume that the prices

and the income in the foreign market which are represented by P/m» and Y* are exogenous
variables for the Japanese economy.

Concerning imports, we assume that the each import is an imperfect substitute of domestic

product and the share of the imported goods in the total demand is the same for all purchasers
including intermediate uses and final demand uses. The imports have to be principally distin
guished by types of the domestic purchasers-intermediate users or end users. It is reasonable totreat the imports by different manners by types of purchasers, because the producers' demands

have to be characterized by production technology and the consumers' demands have to bereflected by preferences. It is, however fairly difficult to treat separately import behavior bytypes of users. We assume that share of imported goods is not different among users.

Reducing C02 Emissions and Long Run Growth of the Japanese Economy

15

We assume that the purchaser determines the value share of ith commodity supplied todomestic market between domestic product and import in accordance with the translog pricefunction:

In PSi = olDMi In PDMi + 5ln PuMi^DMi In Pdmu
where Pdmx = (Pa, (I + T/M*)e-P/Mt)'-(52)

The vectors aoMi and the matrices Bdmi areparameters which are estimated by commodities. The parameters Bdm\ are share elasticities
that represent the degree of substitution between domestic product and imports.

Differentiating the price functions with respect to prices, we can obtain the vector of shareequations:ajXi - EXj)

))

VDOMi

(

iMi)

TIMi)ePmiIMi

VlMi

L Pa(Xi(53)The share equations give us the quantities of imports, given the prices and the values of total

domestic supply:

IMi = -^

vJM2-pCi(Xi - EXi).

PlMi VDOMi(54)

On the other hand, the demands for Japanese goods in the rest of the world, i.e. exports arefunctions of the relative prices and income:
r

D_.

11 Pi

Y*^\

(55)

where oiEXii iPii and rjyi denotes constant parameters that differ among commodities. The
parameters Tjpi and rjyi are the price and income elasticities, respectively.
Finally, the foreign trade submodel is completed by the explanation of the current accounts
and the exchange rate. It is impossible to determine both the current account and the exchange

rate simultaneously without an elaborate model of the international trade. Here, in the simu
lations reported below, we take the current account balance to be exogenous and the exchange
rate to be endogenous.

Next we will explain briefly the treatment of government sector. We determined final demand
for government consumption from the income-expenditure identity for the government sector.
At first we can determine total tax revenue by applying exogenous tax rate to transactions in
producers and consumers. After treating the non-tax government revenue exogenously, we canobtain total government revenue. Next, we make an important assumption about the government
budget deficit; namely that it can be specified exogenously. We can finally determine government

expenditure by adding the deficit to total revenue and adjusting other government expendituresuch as interest paid and transfer.

In the base case scenario reported below, we take thegovernment budget to be exogenous and the government expenditure to be endogenous.

3.

Computing Carbon Dioxide Emissions

There are several origins of CO2 emissions, for example, fossil fuels, biomass, deforestation andso on. In our model of the Japanese economy we treat the CO2 emissions originated by fossil
fuels and assume that CO2 is emitted by combusting fossil fuels and secondary energy in electric16

Journal of Applied Input-Output Analysis, Vol.1, No.2, 1993

Table 2: Unit prices of Energies
Fossil Fuels

Secondary Energies

0.007635xl09yen/10at

0.00709 xl09yen/103t

Oil0.0048 xl09yen/103kl

Gas

0.00757x 109yen/1010kcal

0.0097xl09yen/103kl
0.00883 xl09yen/1010kcal

Coal

Table 3: Heat Contents and Emission Rate

Coal

Oil
Gas

Heat Content

Emission Rate

0.3664 x 10"3MTOE/103t
0.920 x 10-3MTOE/103kl
0.1 x 10-2MTOE/1010kcal

0.96MT-C/MTOE
0.804MT-C/MTOE
0.574MT-C/MTOE

power industry, energy combustion industries and household. We also assume that these sectors

use fossil fuels or secondary energy as fuel not as material but 66.517% of the petroleum input
by chemical industry is treated as naphtha4. We measure CO2 emissions in mega-tons of carbon
content(MT-C).
We compute CO2 emissions in the following way. In our model the equilibrium prices areindices normalized to unity at 1970, the corresponding equilibrium quantities are evaluated in1970 constant prices and the values are evaluated in 109 yen for each fossil fuel and secondary
energy. We first convert the value of fossil fuel and secondary energy inputs to physical unit

quantities, say, coal origin in 103t, oil origin in 103kl, and natural gas origin in 1010kcal, respec
tively. For this we prepare the unit prices at 1970 of each fossil fuel and secondary energy shownin Table 2.
We can obtain the fossil fuels and the secondary energies inputs by electric power industry,

energy combustion industries and household in terms of each physical unit by dividing the valueof these inputs with the above unit prices multiplied by the equilibrium prices.
Next, we calculate the heat contents of these figures.

Finally, the carbon emissions arecalculated from the heat contents. The average heat content per unit and the carbon emission
rate per heat content are shown in Table 3.

4.

Simulation Results

In order to solve the model, we have to provide values for all exogenous variables in all periods.
First, we try to depict a basic scenario of the Japanese economy during the period 1990-2100
under a set of default assumption about values of each exogenous variable, in which government

will not provide any policy reducing CO2 emissions. Second, we try to introduce carbon taxes
for secondary energies as an indirect tax in order to stabilize the CO2 emissions, where the rates
of carbon taxes are endogenously determined as optimal rates reducing CO2 emissions by thetargeting level. Scenarios depicted by the introduction of carbon taxes would be compared withthe basic scenario in order to evaluate the impacts of the carbon tax on the economy.
Default assumptions about values of exogenous variables are as follows:
POPULATION

Estimates by the Welfare Ministry(September 1992). Until the year 2013, the Japanese pop4 This ratio of naphtha input is calculated from table on value and quantity of selected goods in 1985 INPUTOUTPUT TABLES FOR JAPA^(government of Japan).

Reducing CO2 Emissions and Long Run Growth of the Japanese Economy

17

ulation will continue to increase by 0.13 billion people. After the year 2013, it is expected todecrease gradually and in the year 2050, it will be 0.11 billion people.
GOVERNMENT DEFICIT

The values of government surplus are set at their historical value from 1985 to 1990(in 1990, 12.6
trillion yen). The government surplus gradually increases to the year 2000, where the values
will be 2.83 trillion yen in the year 2000. After that government surplus gradually decline to
the year 2050 and after 2050 government expenditure is assumed to balance constantly withgovernment revenue.

CURRENT ACCOUNT

The values of current account surplus are set at their historical value from 1985 to 1990(in 1990,
10 trillion yen). After that current account surplus gradually decline to zero at the year 2050.
After the year 2050 current accounts are assumed to be maintained in balance.
PRICES FOR IMPORTED GOODS
Annual Average Growth Rates to the year 2050

Coal products
Petroleum Refining
Coal
Crude Oil

LNG

3.8%
4.7%
3.7%
4.7%
5.2%

Other import prices are constant in real term at the level of 1985.
WORLD TRADE

Annual average growth rates of real world trade is 1.4%(in nominal value, 4.4%).
4.1.

Base Case Scenario

Under the default assumptions for various exogenous variables, we can solve the model during

the period 1990-2100 as a basic scenario. Let us focus on the main variables and depict the
dynamic path of the Japanese economy in the future.

The annual growth rate of real GNP

will reach 3.3%, 3.8%, 1.0% and 0.3% during the period 1985-1990, 1990-2000, 2000-2030 and
2030-2050 respectively. At the same time period, consumer price will increase by 2.4, 0.9, 2.6,

and 2.8% annually. As shown in Figure 1 , CO2 emissions is expected to expand from the levelof 0.27 billion ton in terms of carbon in 1990 to that of 0.38 billion ton in 2000, 0.50 billion
ton in 2030 and 0.53 billion ton in 2050. It implies that per-capita CO2 emissions in termsof carbon will increase rapidly from 2.14 ton in 1990 to 3.01 ton in 2000. After the year 2011,per-capita emissions is expected to expand more rapidly due to the population decrease in Japanand reach 4.73 ton in 2050. While the growth rate of total emission of CO2 in the economy

will be 0.13% annually, that of per-capita emission will increase by 0.27% annually during theperiod 2030-2100.
4.2.

Impacts of the carbon tax

We try to evaluate the impacts of the introduction of the carbon tax on the economy. In our

simulations, as we mentioned previously, carbon tax will be imposed on prices of the secondary
energies excluding electricity such as coal, petroleum and gas products as an indirect tax, where

the tax rate would be proportional to the carbon contents of each energy sources.

Imposing

the carbon tax on the secondary energies, energy price increases will simultaneously reflect
upon all of commodity markets and factor markets such as labor and capital, so that resource
allocation in the economy will be changed and the growth path of the economy will be influenced
dynamically. Due to the differences of the parameters of price functions among industrial sectors,
impacts of the increases of the energy prices will make different substitution among inputs and18

Journal of Applied Input-Output Analysis, Vol.1, No.2, 1993

MT-C

550.0 n500.0 450.0 400.0 -350.0 -

300.0 250.0
1990

2000

2010

2020

2030

2040

2050

2060

2070

2080

2090

2100

Year

Figure 1: Trend of CO2 Emission in Japan: 1990 - 2100

Table 4: Rates of Carbon Tax and Its Revenue (Case I)
Year
1991
2000
2030
2050

2100

Rates of

Carbon Tax

Per Capita

GNP

Carbon Tax

per HC

Revenue/Revenue

1.6%
61.1%
78.9%
97.1%
99.4%

1730 yen

3702 yen

62749 yen

134437 yen

97997 yen

209822 yen

134492 yen

289214 yen

143769 yen

307737 yen

0.1%
3.8%
5.0%
6.2%
6.5%

non-homogeneous changes of the productivity among industries. Not only substitutions among
energies and among inputs, but also the structural changes of resource allocation might promote

the stabilization of the CO2 emissions.
Here, in introducing carbon tax to the economy in order to reduce CO2 emissions, we try tosimulate two alternative scenarios and compare them to the basic scenario of the economy as
follows:

Case I: Employ an endogenous carbon tax to stabilize per capita CO2 emissions at the levelof 1990, 2.14tC, after 1991. The carbon tax is levied as an indirect tax on secondary energies
proportional to their carbon contents. The revenue from carbon tax is applied so as to holdgovernment spending constant at its base case level and allow government transfer to the restof the world to adjust to keep the government deficit constant.
Case II: Under the same stabilization program of carbon tax as Case I, the rate of capital income

tax is simultaneously decreased by 10% in order to reduce the tax levy of the corporate sector.
The application of revenue from carbon tax is the same as Case I, where government spendingis held to be the same at its base case level and the increased amount of the government revenue

more than deducted amount of the capital tax will be transferred to the rest of the world.

Table 4 and 5 are summaries of results concerning the rate of carbon tax for coal products
and total amounts of carbon tax revenue in each case. According to the results in Table 4, therate of carbon tax for coal products has to be imposed by 1.6% in 1991, 61.1% in 2000 and

99.4% in 2100 in order to stabilize the per-capita CO2 emission at the level of that in 1990. It
implies that the amount of carbon tax per one ton carbon emission will increase from 1730 yen

in 1991 to 62,749 yen in 2000 and 97,997 yen in 2030 at the constant price of the year 1985.
These levy of carbon tax will reach from 0.1% of GNP in 1991, through 3.8% in 2000 and 5.0%

Reducing CO2 Emissions and Long Run Growth of the Japanese Economy

19

Table 5: Rates of Carbon Tax and Its Revenue (Case II)
Year

Rates of

Carbon Tax

Per Capita

GNP

Carbon Tax

per ltC

Revenue/Revenue

1991

16.4%

16048 yen

34578 yen

1.2%

2000

68806 yen

147355 yen

4.2%

120608 yen

258178 yen

2050

74.0%
103.0%
120.2%

158357 yen

339105 yen

2100

121.8%

166283 yen

356040 yen

6.0%
7.1%
7.3%

2030

o Case I

-35.0
1990

2000

2010

2020

2030

2040

• Case II

2050

2060

2070

2080

2090

2100

Year

Figure 2: Percentage Changes in Real GNP

in 2030. It might be interesting to compare the results in Case I with those in Case II. In Case
II capital accumulation is promoted rapidly as a result of the deduction of capital income tax

and CO2 emissions increased as compared to that in Case I. Consequently, carbon tax levy has
to be increased in order to stabilize the emission at the targeting level as shown in Table 5.

Focusing on the ratio of the tax burden to GNP, total government tax revenue reaches 22.3%
and 24.3% of GNP including 3.8% and 6.2% carbon tax in the year 2000 and 2050 respectively

in Case I, while those are 21.6% and 24.0% of GNP including 4.2% and 7.1% carbon tax in theyear 2000 and 2050 in Case II. Comparing these results of both cases with the basic scenario,

carbon tax due to the stabilization of CO2 emissions seems to increase tax burden of the publicby almost 3.0% in 2000 and 5.0% in 2050.
We will turn our focus to the dynamic changes of real GNP growth. Figure 2 presents thepercentage changes of real GNP in Case I and Case II from that in the base case. In Case I,

real GNP will decrease by 7.3%, 20.3%, 25.0% and 25.3% in the year 2000, 2030, 2050 and 2100
respectively, while in Case II, 7.0%, 17.4%, 22.7% and 23.3% decreases will be expected in thecorresponding period. In the year 2000, we have to reduce CO2 emissions from the per-capita
emission level, 3.01 tC to the targeting level, 2.14 tC. As shown in Table 4, we have to impose

additively the carbon tax which rate is 61.1% in order to achieve this target and it forces todecrease real GNP by 7.8%. While in Case II decreases of real GNP will be slightly smaller thanthat in Case I, due to the effect of the deduction of capital income tax, its rate of carbon tax isforced to increase more than 10% in comparison with that of Case I. Average annual growth rateof real GNP during the period 1991-2050 is 0.68% and 0.7% in Case I and II, while in the basescenario, it is 1.16%. It is reasonable that in Case I which all of the carbon tax revenue assume
to transfer to the rest of the world without any deduction of other tax levies, the impact on the

20

Journal of Applied Input-Output Analysis, Vol.1, No.2, 1993

economy would be expected to be relatively serious in comparison with that in Case II, which apart of the carbon tax revenue assumes to be restored to the deduction of capital income tax.
Introduction of the carbon tax are expected to have different impacts on industries, becauseof the differences of the energy intensity by industries. In Figure 3, we try to depict the impact

on the output prices by industry, which are shown by the percentage changes from the base case.
Prices of secondary energy products such as coal, petroleum and gas increases directly due to theimposition of the carbon tax, where the impacts in Case II are finally larger than those in Case I.
In the year 2030, output prices of secondary energies would be expected to increase by more than

220%, 200% and 130% for coal, petroleum and gas products respectively in Case II. Althoughcarbon tax is not directly imposed on electricity, price of electricity will increase by almost 90% incomparison with that of the base case as an indirect effect due to increases of material input prices

such as secondary energies and non-competitive energy imports. Output prices in the energy
combustion sectors would be expected to increase due to the indirect effects. Their increases,

however, will be within 50% because they would be mitigated by the structural changes of input
compositions in industries due to the possibility of the substitutions among inputs. According to
the estimated parameters on price functions by industry, complementarity between capital andenergy are dominant in twelve of the thirteen industries, while substitutability between energy
and labor, and energy and material are dominant in nine and eight of the thirteen industries

respectively. Thus, we can expect that increases of prices of secondary energies by carbon tax
levy force to save energies and simultaneously promote to save capital inputs instead of laborand material inputs. Finally such changes on inputs structure by industry would be expected tomitigate the impacts of the price increases due to the carbon tax levy. It is highly interesting that

although price increases of secondary energies in Case II are expected to be larger than those inCase I due to the higher carbon tax levy, rates of increase of output prices in energy combustion

sectors in Case II are relatively smaller than those in Case I. It implies that promoting thecapital accumulation by the deduction of capital income tax has a preferable impact on thestabilization of the price increases.

Figure 4 presents the percentage changes of output level by industry. It shows that output
level will decrease in all industries. Especially, in energy conversion sectors, where almost morethan 60% decreases in coal, petroleum and gas products are inevitable, their impacts are remarkable. On the other hand, decreases of the output level in electricity are relatively small
because of the promotion of the substitution from fuel energies to electricity. In energy com
bustion sectors carbon tax decreases the output level by 15-30%. Their impacts are completely

different by industries, where high energy intensive industries such as stone k clay, iron &; steel
and paper k. pulp are forced to have serious impacts relatively. It is highly important to see thatthe introduction of carbon tax has a completely different impact by industry. Furthermore, theintroduction of carbon tax will be expected to weaken the international price competitivenessby industry because of the increases of output prices. According to our results, exchange rate
will be depreciated slightly under the same assumption of the current accounts as that in thebase case. Because of the decreases of real GNP and the depreciation of yen value, real importwill decrease as shown in Figure 5.

Finally, we would like to focus on the impacts of the carbon tax on the input structuresand resource allocation among industries. Figure 6 presents changes in input coefficients in theyear 2030 after imposing carbon tax in Case I in comparison with those in the base case. In

our model we can endogenously determine the input coefficients in terms of material inputs andfactor inputs by using the price functions formulated by translog type, in which parameters of
the price function by industry are characterized by the technological properties in each industry.

In Figure 6 each cell in matrix represents the size of changes in input coefficients in Case I
in comparison with those of the base case, where white and black boxes stand for changes ofdecrease and increase respectively. For example, second column, which is designated by industry
number '6' in the top of the column, represents the changes of input coefficients in mining sector,

Reducing CO2 Emissions and Long Run Growth of the Japanese Economy□ Case I
50

100

*

1 Case II
150

200

Coal

Petro.
Elec.
Gas
Agric.
Minig
Const.

Food
Text.
Paper

Chemic.
Stone
Iron
Machine
Mfg.

Transp.
Service

Figure 3: Percentage Changes in Industry Output Prices

250%
I

21

22

Journal of Applied Input-Output Analysis, Vol.1, No.2, 1993

-70

-60

-50

□ Cane I-40

H Cue II
-30
-20

-10

Coal
Petro.
Elec.

Gas
Agric.
Minig

Const.
Food
Text

Paper

Chemic.
Stone
Iron
MachineMfe.
IVansp.
Service

Figure 4: Percentage Changes in Industry Output
a Case I
-70

-60

-50

-40

Case II
-30

-20

-10

Coal

Petro.
Elec.
Gas
Agric.

Minig
Const.

Food
Text.
Paper
Chemic.
Stone

Iron

Machine

Mfe.
Transp.
Service

Figure 5: Percentage Changes in Industry Import(Real)Reducing C02 Emissions and Long Run Growth of the Japanese Economy

23

where the intermediate inputs from sector 1, sector 2 and non-competitive import such as coal,petroleum and other non-competitive import energy materials decreases remarkably and they aresubstituted by the intermediate inputs such as electricity and services and labor inputs. Broadly
speaking, in almost all industries, input coefficients of energies such as coal, petroleum, electricity
and gas decrease remarkably with the reduces of the input from the non-competitive imported
intermediate commodity, while other material input coefficients are slightly increasing. On theother hand, in almost all industries, labor input shows substitutable relationships to the energy

inputs, while capital input is mostly complements.

It implies that changes of relative prices

between energy and non-energy materials and energy and labor force to substitute from energy

to others rapidly and input structure in each industry is obliged to move to labor and non-energy
material using and energy and capital saving. Moreover, these changes of relative prices promote

the structural changes of resource allocation among industries simultaneously. Figure 7 and 8

represent so called skyline maps in the base case and Case I, where resource allocation, especially,labor input allocation in this chart, among sectors is designated in the year 2030. Numbers of
the bottom line represent industry number shown in Table 1. Vertical axis measures the degreeof the self-sufficiency by industry. In the Figure, width of the square between the bottom line
and the 100% degree line of the self-sufficiency in each industry represents the labor contents
corresponding to the output which is enough to satisfy the domestic final demand. Width of thesquare more than the 100% degree of the self-sufficiency represents the labor contents containedin the export demand in each industry and finally the width shadowed by black represents thelabor contents contained in the import demand. In other words, we can see the size of the labor
contents in each industry and its allocation among industries in the year 2030, which containedin domestic demand, export and import respectively. Comparing the results in Figure 8 withthose in Figure 7, we can recognize that the introduction of carbon tax has sizable impacts on the

allocation of labor input among industries and the degree of self-sufficiency of the labor contents.
As we have mentioned above, the introduction of the carbon tax increased prices of energy andcapital service and price of labor input becomes relatively cheaper.

Thus, relatively cheaperlabor input will increase the contribution of the labor using industry such as construction andservice sectors to the economy, while the share of energy using and capital using industry suchas chemical and iron & steel will decrease gradually. Also, relatively cheaper labor input pricewill increase the degree of self-sufficiency in terms of labor contents in Japan in comparison withthe base case.

5.

Concluding Remarks

We would like to summarize our key results of our analysis and point out some comments forfurther research as our concluding remarks.
1. In order to stabilize per capita CO2 emissions in the year 2000 at the level of the year
1990 by imposing carbon tax, the rate of carbon tax, which is levied proportionally tothe carbon contents in the secondary energies such as coal, petroleum and gas, has to bearound 60-70% in the year 2000, 80-100% in 2030 in terms of rate of indirect tax of coalproducts.

2. Total amount of carbon tax is almost 3-4% of GNP in 2000 and 6-5% in 2030.
3. Real GNP is forced to decrease by around 7% in 2000 and 17-20% in 2030 in comparison
with that of the base case.

Annual rate of growth in real GNP slows down by almost

0.4-0.5%.
4. Impacts on real GNP are fairly different by the cases in which there are alternative policies
in terms of the usage of the carbon tax revenue. In Case I which all of the carbon tax

24

Journal of Applied Input-Output Analysis, Vol.1, No.2, 1993

5

6

8

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Figure 6: Changes in Input Coefficients in 2030:Case I

Reducing C02 Emissions and Long Run Growth of the Japanese Economy

Skyline Map in 1990 (Base Case)

200 r

5

7

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15

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Skyline Map in 2030 (Base Case)

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Figure 7: Sky Line Map in Labor Contents in 1990 and 2030:Base Case

25

26

Journal of Applied Input-Output Analysis, Vol.1, No.2, 1993

Skyline Map in 1990 (Case I)

200

150

Skyline Map in 2030 (Case I)

5

7

89

14

15

16

Figure 8: Sky Line Map in Labor Contents in 1990 and 2030:Case I

Reducing CO2 Emissions and Long Run Growth of the Japanese Economy

27

revenue are assumed to transfer to the rest of the world, decrease in real GNP would belarger than that in Case II which a part of the carbon tax revenue assumes to restore to

the deduction of capital income tax. It has to be noted, however, that although the GNP
growth might be maintained in Case II rather than in Case I, the rate of carbon tax inorder to stabilize the CO2 emissions would be higher in Case II rather than in Case I,
because CO2 emission increases gradually due to the recovery of the economic activity.
5. The introduction of carbon tax has sizable impacts not only on the economic growth in
the aggregate level, but also on the prices and quantities by industries. Prices of energies
and capital service increase relatively rather than those of labor service and materials.

Consequently, there occurs input substitutions from energy and capital uses to labor andmaterial uses and simultaneously changes of resource allocation in the economy, in which
resource will be reallocated from energy and capital using industries to labor and materialusing industries.

6. According to our results shown in Table 4 and 5, we have to impose the carbon tax at thelevel of 600 - 700 dollars per 1 ton carbon in order to stabilize per capita CO2 emission

in the year 2000 at the level of 1990. On the other hand, Jorgenson - Wilcoxon (1993)
showed that in the United States 17 dollars carbon tax levy per 1 ton carbon is enough tostabilize the emissions at the per capita level of 1990. Comparing two results carefully, we
can conclude that the main sources of difference between the two came from the differencesof the reducing level of CO2 emission in the year 2000. The Japanese economy will be
expected to continue fairly higher economic growth and to expand the emissions rapidly
rather than that in the United States. In our results we have to reduce CO2 emission in2000 by almost 40%, while in the U.S. 14.4% reduction is enough to stabilize. We try toestimate carbon tax levy per 1 ton carbon at the same level of the reduction of CO2 in
our model. The results are as follows:
J orgenson- Wilcoxen

Kuroda-Shimpo

PeriodSteady State (2050)

1993

1994

CO2 reduction(%)

14.4%

13.4%

18.6%

Carbon Tax/tC$ 16.96/tC$ 37.09/tC$ 52.59/tC

There are still some differences at the level of carbon tax even if we would try to adjust

the reducing level. It might come from the possibility of energy saving in technology interms of the substitutability among factors and the feasibility of technical progress, whichmostly depend upon the level of the energy efficiency at the present stage in each country.

Therefore, we can conclude that it is highly important to choose and adjust the policy
target of reducing CO2 emissions carefully at the stage of development of the economy
internationally in order to avert inequality of the burden of the economy stemmed fromthe differences of the targets.

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