M.H. Babiker r Energy Economics 23 2001 121᎐139 123
reduction in leakage. The rest of the paper is organized as follows. Section 2 outlines the key features of our dynamic general equilibrium model. Section 3
presents the numerical results, and Section 4 concludes.
2. The model
The modeling framework adopted in this analysis is the conventional Ramsey type growth model, in which along the baseline all real variables grow at a uniform
growth rate and the present values of all nominal variables decrease at a uniform discount rate. The first year in the model is year 2000 and the horizon extends
Ž .
through 2040 in time-intervals or periods each of 5 years length. The model is built on a comprehensive energy᎐economy dataset that accommodates a consistent
representation of energy markets in physical units as well as detailed accounts of Ž
regional production and bilateral trade flows for 1992 for details on the dataset, .
see Rutherford and Babiker, 1997 . Ž
. There are seven regions in the model: OECD as defined in 1990 OEC ; oil
Ž .
Ž .
Ž .
exporting countries OEX ; former Soviet Union FSU ; China and India CHI ; Ž
. the dynamic Asian economies DAS ; the dynamic economies of South America
Ž .
Ž .
DSM ; and the rest of the world ROW . There are seven commodities in the model: five energy goods and two non-energy goods. The energy goods identified in
Ž .
Ž .
Ž .
the model include coal COL , natural gas GAS , crude oil CRU , refined oil Ž
. Ž
. products OIL , and electricity ELE . This disaggregation is essential to distin-
guish energy goods by carbon intensity and by the degree of substitutability. The Ž
. two non-energy goods are an energy intensive tradable good EIS , and a non-
Ž . energy intensive good Y . The primary factors in the model include labor, physical
capital, and fossil-fuel resources. Fossil-fuel resources are sector-specific, but labor and physical capital are treated as perfectly mobile across sectors. The key features
and equations in the model formulation are outlined in the following.
2.1. Consumer beha
¨
ior In each region, r, the intertemporal utility function of the infinitely lived
representative consumer is the discounted sum of the utility of consumption over the horizon:
⬁
1y
t
1 C
r t
Ž . Ž .
U . s
1
Ý
r
ž
1 q 1 y
t
In this equation, is the discount rate, is the coefficient-of-relative-risk-aversion Ž
. CRRA that controls the intertemporal elasticity of substitution, and C
is a
r t
Ž .
constant-elasticity-of-substitution CES aggregate of energy and non-energy con- sumer goods in the model:
M.H. Babiker r Energy Economics 23 2001 121᎐139 124
E E
E
1r
t i t
i t
Ž . C s ␣
C q 
C 2
r t r
i r t r
i r t
igE ifE
Where the elasticity of substitution between the energy and the non-energy
E
Ž
E
. composites is given by s 1r 1 y , i indexes all goods, E indexes energy
t t
goods, s are the value shares, and where ␣ and  are the requirement
i r
r
coefficients in the CES function.
2
In the standard manner, the representative consumer maximizes the utility Ž .
function in Eq. 1 subject to a life-time budget constraint that the present value of consumption equals the present value of income:
Ž .
max U C s.t.
r r t
C
r t
c k
l
Ž .
t R
P C s P
K 0 q
P 1 q G0 L0 q
P R
Ý Ý Ý
Ý Ý
i r t i r t
r ,1
r r t
r F r t
F r t
i t
t F
t
num g
Ž . q
P BOPD q
TR y P G
3
Ý Ý
Ý Ý
t r t
r t i r t
i r t
t t
i t
In this expression P
c
, P
k
, P
l
, P
R
, P
g
, and P
num
are present-value price indices for household consumption, capital, labor, rents on fossil-fuel resources, government
consumption, and a numeraire index, respectively. K 0 is the initial capital stock, L
0 is the initial labor supply, R is the fossil-fuel resource supply, TR is the total revenue from taxes, BOPD are the baseline exogenous capital flows, G0 is the
exogenous growth rate in the labor-augmented technical change, and G is the
r t
Ž . government consumption bundle and has the same form as C in Eq. 2 .
r t
In this representation the household consumption is financed from labor income, the value of the initial capital stock, the rents realized from the ownership of the
fossil-fuel resources, the tax revenues, and some exogenous capital flows. Taxes apply to energy as well as non-energy demand, to production and incomes, and to
international trade. The exogenous capital flows represent the initial balance of payment deficits in the dataset and we project them to grow along the baseline at
the GNP growth rate. The government consumption is financed through lump sum levies and does not enter the representative consumer utility function, hence the
level of the government activity is fixed exogenously in our model.
2.2. Production acti
¨
ities The model includes two types of production functions: those of fossil fuels
Ž .
Ž .
CRU, COL, OIL, and GAS and those of non-fossil fuels ELE, EIS, and Y . An index Y
denotes the level of production of good i in region r in period t. Except
i r t
for crude oil, which is modeled as a perfectly homogenous good, good i is produced
2
To economize on notation, we shall use the symbols ␣ ,  and throughout to denote these technology coefficients.
M.H. Babiker r Energy Economics 23 2001 121᎐139 125
as differentiated products for sale in the domestic and international markets. The shares of sales at home and abroad are determined by relative prices. A constant-
Ž .
elasticity-of-transformation CET function characterizes the allocation of output between domestic and export sales. Producers of the final good maximize profits
subject to the constraint:
w
x
1r
Ž . Y
s ␣ D q  X
4
i r t i r
i r t i r
i r t t r
Ž .
In this equation the transformation elasticity is given by s 1r 1 q . The production of the non-fossil fuel good, N, is associated with a nested CES
function based on non-energy intermediate inputs, Z, an energy component, E, and a primary factor composite, V. Given the prices of these components, the
producer of good N operates to minimize the production cost for a given level of output subject to the technology constraint:
E E
E
1r
t t
t
4 Ž .
Y s
min min ␣ Z
,  E q V
5
N r t j N r
j N r t N r
N r t N r
N r t
½ 5
j
In this function the non-energy intermediate inputs enter at the top nest in fixed proportions among themselves as well as in relation to the energy-primary-factor
aggregate. In the second nest, we account for the substitution between energy and
E
Ž
E
. primary factors through s 1r 1 y . In the third nest we characterize sepa-
t t
rately the substitution possibilities among the components of the primary factor composite and among the components of the energy composite. The primary factor
composite is represented by a Cobb᎐Douglas aggregate of labor and capital services:
␣
N r
1y ␣
N r
Ž . V
s L K
6
N r t N r t
N r t
In this equation labor is expressed in efficiency units and ␣ is the labor value share.
The aggregate energy good, E, is produced by the linear technology:
f b
Ž . E
s E q E
7
N r t N r t
N r t
According to this equation there are two sources for the aggregate energy good that are perfectly substitutable. There is a current low-cost fossil fuel source, f, and
there is a high-cost ‘backstop’ carbon free source that may be introduced in the future.
3
The fossil-fuel energy source is in turn associated with a nested CES
3
Different from the conventional treatment, here we differentiate the backstop technology by sector. This seems more appropriate than assuming a uniform technology, since it is more conceivable that the
Ž .
form of backstop for producing electricity e.g. from biomass may be quite different from the form suitable for producing chemical products. In our model, these technologies are calibrated according to
cost, market share, and the date of entry.
M.H. Babiker r Energy Economics 23 2001 121᎐139 126
function based on refined oil, gas, coal, and fossil-fuel based electricity:
o o
o
f
r 1y
N r N r
Ž . E
s ␣
O y G q  COL
ELE 8
½ 5
N r t N r
N r t N r
N r t N r t
In this expression electricity enters in a Cobb᎐Douglas form with oil, gas, and coal Ž
. at the top nest, with a value share defined by 1 y . At the second level the
o
Ž
o
. oil᎐gas composite substitutes with coal according s 1r 1 y . The oil᎐gas
composite, on the other hand, is assumed to have a simple Cobb᎐Douglas repre- sentation. Hence, in our model, carbon abatement may be achieved in three ways:
changing the fossil fuels mix, reducing the amount of energy per unit of output, and by investing in the carbon free source.
In contrast, the production of fossil fuel F is associated with a nested CES function based on a fuel-specific resource, labor, and intermediate inputs. Given
the prices of these inputs, mine managers minimize production costs subject to the technology constraint:
R
1r
R F r
R
F r
F r
4 Ž .
Y s ␣
R q 
min Z , L
9
Ž .
F r t F r
F r t F r
jF r t F r t
In this equation production is characterized by the presence of a resource in fixed-supply that substitutes with the rest of inputs at the top level nest according
R
Ž
R
. to the elasticity s 1r 1 y
. This substitution elasticity is controlled by the
F r F r
Ž . supply price elasticity for the particular fuel according to the formula
F r
1 y ␥
F r R
s
, with ␥ being the resource value share. At the second nest, the
F r F r
␥
F r
rest of the inputs enter in fixed proportions. On the other hand, since the refinery activity does not require a sector-specific resource, the production technology for
Ž . refined oil collapses to the fixed proportion part of Eq. 9 .
2.3. Supplies of final goods and foreign trade Except for crude oil, intermediate and final consumption goods are differenti-
ated following the standard Armington convention. Accordingly, for each type, the total supply of the good is a CES composite of a domestic variety and an imported
one. Given the domestic and the import prices, firms in the distribution sector maximize profits subject to the constraints:
D D
Z s ␣ ZD
q  ZM ,
i r t i r
i r t i r
i r t
D D
D
1r
C s ␣ CD
q  CM ,
i r t i r
i r t i r
i r t
and
D D
D
1r
Ž .
G s ␣ GD
q  GM .
10
i r t i r
i r t i r
i r t
M.H. Babiker r Energy Economics 23 2001 121᎐139 127
In these expressions the Armington elasticity between the domestic and the imported varieties is controlled by
D
. All goods are traded in world markets subject to export taxes, tariffs, and
transport costs. Crude oil is exported and imported as a perfectly homogenous good, whereas all other goods are characterized by product differentiation with
explicit representation of bilateral trade flows. Given the regional export prices, tariffs, and transport costs, firms operating in the import sector minimize costs by
allocating their import orders across the different trading partners subject to the constraint:
M M
1r
Ž .
M s
␣ X
11
Ý
i r t i sr
i sr t
s
In this equation X is the amount imported by region r from region s, and
M i sr t
controls the extent of the product differentiability among the trading partners. 2.4. Capital accumulation
The region aggregate investment is the sum of the sectoral investments in the region. Part of the investment in period t is assumed to mature in the same period
and the rest in period t q 1. The capital stock evolves according to the standard rule:
Ž .
Ž .
K s
1 y ␦ K q 1 y I q I ,
r ,tq1
r t r t
r ,tq1
Ž .
K s K
12
r ,1
r
In this expression, ␦ is the capital depreciation rate, is the investment own-period maturation rate, and K 0 is the initial capital stock.
2.5. Market clearance conditions Output for the domestic market in period t is either consumed or invested:
Ž .
D s ZD
q CD q GD
q Invest
13
i r t i r t
i r t i r t
i r t
The output for the export market in period t has to meet the regional demands: Ž
. X
s X
14
Ý
i r t i r st
s
The import supply in period t has to satisfy the domestic demands for the imported good:
Ž .
M s ZM
q CM q GM
15
i r t i r t
i r t i r t
M.H. Babiker r Energy Economics 23 2001 121᎐139 128
Finally, international markets have to clear for each good and in each period: Ž
. X
s M
16
Ý Ý
i r t i r t
r r
2.6. Emissions and carbon leakage CO emissions are generated in fixed proportions via the consumption of fossil
2
fuels by the industry and the final demand sectors. Accordingly, the carbon emissions in region r in period t are given by:
Ž .
Ž .
Emissions s CO Coeff
Z q C
q G 17
Ý
r t 2
F F r t
F r t F r t
F
Ž In which, CO Coeff is the carbon content expressed in the heat units b tonr
2
. exajoule . Under a subglobal abatement action, the carbon leakage rates in the
non-abating regions are defined as the deviations in their emissions from their baseline trajectories divided by the corresponding amount of abatement in the
colluding regions. The global leakage rate is then simply the sum of the regional leakage rates.
2.7. Balance of payments and capital flows The net balance of payment deficit in region r in period t is given by the
expression: Ž
. NBOBD s
PM X
y PX
X q
Oil m y Oil x P
crude
Ý Ý Ý Ý
r t i sr t
i sr t i r st
i r st r t
r t t
s s
i i
num
Ž .
y P BOPD
18
t r t
In this expression PM is the cif present-value price of imports, PX is the fob present-value price of exports, Oil m is crude oil imports, Oil x is crude oil exports,
and Pcrude is the international present-value price of crude oil. As before, P
num
is a present-value numeraire price and BOPD is the baseline balance of payment
Ž .
deficit. Along the baseline the last term in Eq. 18 represents the net capital inflows. It is critical, however, which price to use as a numeraire for denominating
the baseline balance of payment deficits. In principle the price of any homogenous commodity traded in the international market can serve the role of a numeraire.
Ž .
Unfortunately, the only homogenous good in our model crude oil has its price directly affected by the carbon abatement action. Hence we can’t use crude oil as a
numeraire and instead we decide to use the OECD labor price index. Numerically, the model is formulated and solved as Mixed Complementarity
Ž .
Ž Problem MCP using GAMSrMPSGE system described in Rutherford 1995,
. 1997 . In terms of size and complexity, the model proved to be quite challenging
since it requires the solution of a highly non-linear system of approximately 10 000 equations. The full code of the model is available from the author upon request.
M.H. Babiker r Energy Economics 23 2001 121᎐139 129
3. Results
