GTAP-E: An Energy-Environmental 

Version of the GTAP Model 

Jean-Marc Burniaux* and Truong P. Truong**

GTAP Technical Paper No. 16 

Revised 

January 2002 

Jean-Marc Burniaux was on leave from the OECD as visiting Associate Professor with the Center for 

Global Trade Analysis, Purdue University, West Lafayette, Indiana when this paper was written. Truong P. 

Truong was visiting Associate Professor with the Center for Global Trade Analysis, Purdue University, 

West Lafayette, Indiana, on leave from the School of Economics, University of New South Wales, Sydney 

NSW 2052, Australia. This technical paper is a revised version of an earlier GTAP Technical Paper written 

by T.P. Truong (Truong, 1999). 

GTAP stands for the Global Trade Analysis Project which is administered by the Center for Global Trade

Analysis, Purdue University, West Lafayette, Indiana, USA 47907-1145. For more information about 

GTAP, please refer to our Worldwide Web site at: http://www.agecon.purdue.edu/gtap/, or send a request to 

conner@agecon.purdue.edu 
GTAP-E: An Energy-Environmental 

Version of the GTAP Model 

Jean-Marc Burniaux and Truong P. Truong ∗

GTAP Technical Paper No. 16 

Abstract

 Energy is an important commodity in many economic activities. Its usage affects the environment 

via CO2 emissions and the Greenhouse Effect. Modeling the energy-economy-environment-trade 

linkages is an important objective in applied economic policy analysis. Previously, however, the 

modeling of these linkages in GTAP has been incomplete. This is because energy substitution, a 

key factor in this chain of linkages, is absent from the standard model specification. This 

technical paper remedies this deficiency by incorporating energy substitution into the standard 

GTAP model. It begins by first reviewing some of the existing approaches to this problem in 

contemporary CGE models. It then suggests an approach for GTAP which incorporates some of 

these desirable features of energy substitution. The approach is implemented as an extended 

version of the GTAP model called GTAP-E. In addition, GTAP-E incorporates carbon emissions 

from the combustion of fossil fuels and this revised version of GTAP-E provides for a 

mechanism to trade these emissions internationally. The policy relevance of GTAP-E in the 

context of the existing debate about climate change is illustrated by some simulations of the 

implementation of the Kyoto Protocol. It is hoped that the proposed model will be used by 

individuals in the GTAP network who may not be themselves energy modelers, but who require a 

better representation of the energy-economy linkages than is currently offered in the standard 

GTAP model. 

∗

The authors are indebted to Tom Hertel for originally suggesting the topic of this study, and for his 

continued support and encouragement. Thanks are due also to Kevin Hanslow, and Mustafa Babiker for 

providing many helpful comments and suggestions on an earlier draft. Ken Pearson was quite indispensable 

in providing the technical advice for the illustrative experiments. Finally, note that this paper is a revised 

version of the GTAP Technical Paper No. 16 by Truong (see Truong, 1999). 
ii

Table of Contents 

1. Introduction .............................................................................................................................................. 1 

2. Review of existing approaches................................................................................................................. 1 

2.1 The CETM model - Rutherford et al. (1997)...................................................................................... 2 

2.1.1 The structure of CETM ............................................................................................................. 2 

2.1.2 The Linkage of ETA to MACRO .............................................................................................. 4 

2.1.3 Comments on the structure of CETM........................................................................................ 7 

2.2 The MEGABARE Model and the “Technology Bundle' Approach.................................................... 9 

2.2.1 Description of the technology bundle approach........................................................................ 9 

2.2.2 Comments on the technology bundle approach....................................................................... 11 

2.3 The OECD’S GREEN model ........................................................................................................... 12 

2.3.1 Dynamics in GREEN............................................................................................................... 13 

2.3.2 Inter-fuel substitution .............................................................................................................. 14 

2.3.3 Fuel-factor substitution............................................................................................................ 18 

2.3.4 Comments on the GREEN model............................................................................................ 19

2.4 The Babiker-Maskus-Rutherford (BMR) model............................................................................... 20 

2.5 Borges and Goulder (1984) model................................................................................................. 207 

3. Towards a GTAP model with energy substitution ............................................................................... 259

3.1 Top-down versus bottom-up approach ............................................................................................ 29 

3.2 The issue of energy-capital substitutability or complementarity ......................................................................30 

3.2.1 Importance of the issue ............................................................................................................................30 

3.2.2 Empirical estimates of )EK ......................................................................................................................31 

3.3 The structure of inter-fuel and fuel-factor substitution in GTAP-E ..................................................................32 

3.3.1 Production structure with energy substitution .........................................................................................32 

3.3.2 Consumption structure ........................................................................................................................38 

4. Illustrative scenarios............................................................................................................................... 40 

4.1 Alternative implementations of the Kyoto Protocol......................................................................... 41
iii

4.2 Macroeconomic results.................................................................................................................... 45 

5. Conclusion.............................................................................................................................................. 47 

References .............................................................................................................................................. 62 

Annexes

 Annex 1 : General equilibrium elasticities in GTAP-E and GTAP. 

 Annex 2 : Specifying country-specific carbon reductions with no emission trading in 

GTAP-E 

 Annex 3 : Specifying emission trading in GTAP-E 

Figures

Figure 1: Structure of CETM ....................................................................................................................... 3 

Figure 2: MACRO production nest.............................................................................................................. 4 

Figure 3: MACRO consumption nest........................................................................................................... 4 

Figure 4: ETA - MACRO linkage ................................................................................................................ 8 

Figure 5: Technology bundle approach........................................................................................................ 9 

Figure 6: Composition of the technology bundle for the electricity industry............................................ 10 

Figure 7: Composition of the technology bundle for the steel industry..................................................... 10 

Figure 8: The structure of production in GREEN...................................................................................... 18 

Figure 9: Energy and backstop technologies in GREEN ........................................................................... 19

Figure 10: The structure of household demand in GREEN ....................................................................... 20 

Figure 11: Substitution elasticity when total output is held constant. ....................................................... 22

Figure 12: Structure of production in the Babiker-Maskus-Rutherford (1997) model .............................. 23

Figure 13: Structure of final demand in the Babiker-Maskus-Rutherford (1997) model .......................... 24 

Figure 14: Structure of production in Borges and Goulder (1984) model................................................. 25 

Figure 15: Standard GTAP production structure ....................................................................................... 30 

Figure 16: GTAP–E production structure ................................................................................................ 304 

Figure 17: GTAP–E capital-energy composite structure ........................................................................... 34

Figure 18: GTAP-E government purchases ............................................................................................... 39 

Figure 19: GTAP-E household private purchases...................................................................................... 40 

Figure 20: Emission trading among Annex 1 countries ............................................................................. 43 

Figure 21: Worldwide emission trading..................................................................................................... 43 
iv

Figure 22: Welfare decomposition of implementing the Kyoto Protocol with no use of the 

flexibility mechanisms ............................................................................................................................... 47 

Figure 23: Welfare decomposition of implementing the Kyoto Protocol with trading among 

Annex 1 countries....................................................................................................................................... 47 

Figure 24 : Welfare decomposition of implementing the Kyoto Protocol with worldwide 

emission trading ......................................................................................................................................... 48 

Tables 

Table 17.1: List of Technologies in ETA..................................................................................................... 6 

Table 17.2: List of Important Equations in ETA ......................................................................................... 8 

Table 3 Summary Characteristics of CETM ............................................................................................. 11 

Table 4: Summary Characteristics of MEGABARE.................................................................................. 15

Table 5: Summary Characteristics of GREEN........................................................................................... 23 

Table 6: Summary Characteristics of BMR Model.................................................................................... 27 

Table 7: Summary Characteristics of Borges and Goulder Model ............................................................ 29 

Table 8: Estimates of the partial Hicks-Allen elasticities of substitution ()) and factor shares ()).......... 32 

Table 9: Energy substitution elasticities in GTAP-E and other models..................................................... 35 

Table 10: Elasticities of substitution between different factors of production.......................................... 36 

Table 11: The relationship between inner ()KE-inner) and outer ()KE-outer) elasticities of substitution 

for the cases of Japan and the US............................................................................................................... 37 

Table 12: Elasticities of substitution between domestic and foreign sources ()D).................................. 347 

Table 13: Elasticities of substitution between different regions ()M)........................................................ 36 

Table 14: Marginal costs of achieving the Kyoto targets with and without using the flexibility 

mechanisms. ............................................................................................................................................... 44 

Table 15: Macroeconomic impacts of implementing the Kyoto Protocol ................................................ 46 
1

GTAP-E: Incorporating Energy

Substitution into GTAP Model 

1. Introduction

Energy is an important commodity in many economic activities. Its usage affects the environment 

via CO2 emissions and the Greenhouse Effect. Modeling the energy-economy-environment-trade 

linkages is an important objective in applied economic policy analysis. Up to now, however, the 

modeling of these linkages in GTAP has been incomplete. This is because energy substitution, a 

key factor in this chain of linkages, is absent from the standard model specification. This paper 

remedies this deficiency by incorporating energy substitution into the standard GTAP model. It 

begins by first reviewing some of the existing approaches to this problem in contemporary CGE 

models. It then suggests an approach for GTAP which incorporates some of these desirable 

features of energy substitution. 

The approach is implemented as an extended version of the GTAP model called GTAP-E. 

In addition, GTAP-E incorporates carbon emissions from the combustion of fossil fuels 

as well as a mechanism to trade these emissions internationally. The policy relevance of 

GTAP-E in the context of the existing debate about climate change is illustrated by some 

illustrative simulations of the implementation of the Kyoto Protocol. This technical paper 

is a revised version of a earlier paper written by T.P. Truong (Truong, 1999). Compared 

with this version, the model used here is derived from the version 6.1 of the GTAP model 

based on 1997 data (version 5 of the GTAP data base). In addition to inter-fuel 

substitution, this model incorporates some further improvements, such as the computation 

of a Social Account Matrice (SAM) which provides a full account of the carbon tax 

revenues and expenditures and a more specific treatment of carbon emission trading. 

2. Review of Existing Approaches 

In this section, we review some of the existing approaches to incorporating energy substitution 

into AGE models. The purpose of this section is not to undertake an exhaustive review of the 

literature, but rather, to select some typical approaches and examine their important features for 

possible incorporation into the GTAP model. There are three main models to be considered in 

this section, and these are: (1) the CETM model by Rutherford et al. (1997), (2) the 

MEGABARE model by ABARE (1996), and (3) the OECD’s GREEN model by Burniaux et al.

(1992). Some other models are also considered in sub-section 2.4. 
2

2.1 The CETM Model - Rutherford et al. (1997) 

This model represents an attempt to bridge the gap between the (top down) economic models 

often used by economists, and the (bottom-up) process models used by engineers and 

environmentalists in studying the effect of energy policies on the environment. Recognizing that 

full integration of these two types of models is methodologically and computationally difficult, 

the authors of CETM attempted a ‘partial’ link. This means, firstly, the construction of a partial 

equilibrium ‘process model’ of the energy sector (ETA) (which is based on the MERGE model 

of Manne and Richels (1996)). The model is then linked to a general equilibrium model called 

MACRO. The process of linking the two sub-models is through the process of passing the energy 

price and quantity variables between the two sub-models and iteration until the ‘input reference 

quantities’ from ETA are close to the solutions of the MACRO model (Rutherford et al (1997, 

p6)). In light of the fact that the energy sector makes up only a small fraction (less than 5%) of 

the gross output of most economies, ‘convergence’ of the two sets of results from ETA and 

MACRO is considered most likely. This is because if energy is only a small part of the industry 

cost structure then the changes in the prices and quantities of energy demand within ETA will 

affect only marginally the overall results of industry costs and prices within MACRO. This 

means convergence of the two sets of results from ETA and MACRO can be achieved through an 

iteration process as described above, rather than by having to solve the optimization problems of 

the two sub-models simultaneously. 

2.1.1 The Structure of CETM 

The structure of CETM is described in Figure 1. Within this structure, the MACRO sub-model is 

a conventional computable general equilibrium (CGE) model, which has 5 internationally traded 

commodities and five industries: Y - Other manufactures and services, NFM = Non-ferrous 

metals, PPP = Pulp and paper, TRN = Transport industries, OTH = Other energy intensive 

sectors. The first industry is an aggregate of non-energy intensive industries, and the other four 

represent energy-intensive industries. Factors of production include: land, labor, capital, 

electricity, and non-electric energy. The latter two energy inputs are linked to ETA. 

There are nine regions in MACRO: USA, JAPAN, CANZ (Canada, Australia, New 

Zealand), OECDE (Other OECD), CHINA, INDIA, EFFSU (Eastern Europe and Former Soviet 

Union), MOPEC (Mexico and OPEC countries), and ROW (The rest of the world). With eleven 

ten-year time periods, this model begins the period of simulation from 1990 (benchmark year) 

and ends in 2100.

The structure of industry production in MACRO is as described in Figure 2. First, capital 

and labor are combined via a Cobb-Douglas production function1

. So are electric and non-electric 

energy inputs. The composite of non-energy material inputs, however, is combined using 

Leontief technology. The overall aggregation of composite primary factors, energy inputs, and 

non-energy materials is CES with an elasticity of substitution of 0.5. 

1

 Figure 3 in Rutherford et al (1997, p. 15) did not show land but the text (p. 9) mentioned land as one of the factors of 

production. 
3

Figure 1 Structure of CETM Source: Rutherford et al. (1997), Figure 1, p. 7.

ENERGY CONVERSION TECHNOLOGIES ETA MACRO SECTORS 

ENERGY RESERVES AND NATURAL RESOURCES LABOR, LAND 

ELECTRIC, NON-ELECTRIC ENERGY (E, N) ENERGY COSTS (EC) 

INTERMEDIATE AND FINAL DEMAND (D) 

INVESTMENT (I) 

CAPITAL (K) 
1

Figure 2 MACRO Production Nest 

Source: Rutherford et al. (1997), Figure 3, p. 15. 

Figure 3 MACRO Consumption Nest 

Source: Rutherford et al. (1997), Figure 2, p. 14. 

Consumption in MACRO is described as CES-nested aggregate of energy and nonenergy composite goods. Composite energy is a Cobb-Douglas aggregate of electric and nonelectric inputs, while composite non-energy is a Cobb-Douglas aggregate of the five industrial 

goods. Consumers substitute composite energy and non-energy inputs with an elasticity of 

substitution of )end = 0.5, which is chosen to approximate the own-price elasticity of demand for 

energy.

Crt

ELEC NONELEC

Y NFM PPP TRN OTH

σ=1 σ=1

σ=0.5

Yirt 

ELEC NONELEC

K L

σ=1 σ=0

σ=0.5

σ=1

Y NFM PPP TRN OTH
2

MACRO is linked to ETA, a partial equilibrium sub-model which describes in greater 

details the energy sub-sector. ETA specifies the supply functions of electric and non-electric 

energy. Electric energy is produced by a combination of hydro-electricity, natural gas, oil, coal, 

and two 'backstop' technologies: advanced high cost, and advanced low cost. Non-electric energy 

can be produced either from oil, gas, coal, or by non-conventional technologies (such as carbonfree backstop, renewables, synthetic fuels). The list of electric and non-electric technologies in 

ETA are given in Table 1. 

ETA includes the following internationally traded goods (g): 

1 OIL Crude oil 

2 COAL Coal 

3 GAS Natural gas 

4 CRT Carbon emission rights 

ETA is formulated as a non-linear mathematical program. The decision variables in ETA include the 

following: 

SURPLUS The non-linear programming maxim and defined as the sum of consumer and producer 

surplus 

ECr,t Energy cost (in region r and time period t) - trillion dollars 

ENr,t Composite energy demand 

Er,t Electric energy (total) 

Nr,t Non-electric energy (total) 

PEe,t,r Production of electric energy (by source e) - tkwh 

PNn,t,r Production of non-electric energy (by source n) - exaj 

GASNONt,r Gas consumed to meet non-electric demands 

OILNONt,r Oil consumed to meet non-electric demands 

RSCr,x,t Undiscovered resources (by type x)

RSVr,x,t Proven reserves 

RAr,x,t Reserve additions 

CLEVt,r Carbon emissions level – billion tons 

CRLXt,r Carbon limit relaxation – billion tons 

EXPRTg,t,r Exports (of goods g)

IMPRTg,t,r Imports 

To understand the internal workings of ETA, a list of some of the important equations in ETA is given in 

Table 2. 

ETA solves for the aggregate shares of electric and non-electric energy. The solution is arrived at by

MACRO first passing on to ETA the following variables and their time paths: 

e r,t Reference path of electric energy demand (TKW) 

n r,t Reference path of non-electric energy demand (EJ) 

pvcenr,t Present value unit cost of energy sector inputs 

pvper,t Present value price of electric energy 

pvpnr,t Present value price of non-electric energy 
3

Table 1 List of Technologies in ETA 

No. Short Name Long Name Restrictions 

Electricity supply technologies (e): 

1 HYDRO Hydro electric 

2 GAS-R Existing gas-fired 

3 OIL-R Existing oil-fired 

4 COAL-R Existing coal-fired 

5 NUC-R Existing nuclear 

6 GAS-N New vintage gas-fired DLE(e)

7 COAL-N New vintage coal-fired DLE(e)

8 ADV-HC Advanced high-cost DLE(e), XLE(e)

9 ADV-LC Advanced low-cost XLE(e)

Non-electricity energy supply technologies (n): 

10 OIL-LC Low cost oil reserves X(n)

11 OIL-HC High cost oil reserves X(n)

12 GAS-LC Low cost gas reserves X(n)

13 GAS-HC High cost gas reserves X(n)

14 CLDU Coal for direct use DLN(n)

15 NE-BAK Non-electric backstop DLN(n), XLN(n)

16 RNEW Renewables XLN(n)

17 SYNF Synthetic fuels (coal shales) DLN(n), XLN(n)

Note: X(n) Fossil fuels 

DLE(e) Electricity technologies subject to decline limits, 

DLN(n) Non-electric technologies subject to decline limits 

XLE(e) Electricity technologies subject to expansion limits 

XLN(n) Non-electric technologies subject to expansion limits 

ETA then uses the ‘reference time path’ of energy demand to calculate other variables and 

parameters such as the ‘reference present value of energy demand’ en r,t (equation (1)), the 

distributive share parameter of electric energy evlst,r (equation (2)) which is then used to 

calculate the composite energy demand (in volume terms) ENr,t (equation (4)), and the total of 

consumers’ and producers’ surplus (equation (3)). Note that the total surplus is normally 

calculated as the area between the consumers’ (regional) energy demand curve and the marginal 

cost curve. However, it can also be calculated as the total area under each region’s energy 

demand curve, then subtracting the total cost of energy supply. The demand function is assumed 

to have a constant own-price elasticity of ) and the function is ‘calibrated to MACRO’ (i.e. using 

the ‘reference present value of energy demand’ en r,t as calculated from MACRO - see equation 

(3)). The total cost to produce energy is a linear combination of the direct costs to produce 

electric and non-electric energy, with an allowance for oil-gas price differential of OGPD = 

$1.25/GJ for all regions, an allowance for interregional trade transportation costs of $2/GJ for 

gas, $1/GJ for coal, $0.33/GJ for oil, and $10/tonne for carbon emission rights (see equation 

(21)).

ETA then optimizes the mix of electric and non-electric technologies by maximizing the 

value of the total surplus subject to all the technological and institutional constraints (as 

described in equations (7-21) of Table 2). These constraints include things like: (a) market 

clearing conditions (supply of fuels and energy sources must at least meet the demand, total 

imports must equal total exports, etc.) (equations (7-9,20)), (b) ‘side constraints’ which control 
4

the ‘availability’ of different technologies, through ‘expansion limits’ on new technologies, 

‘decline limits’ on old (and new) technologies, and ‘exhaustion limits’ on non-renewable 

resources, etc. (equations (10-17)). In addition, equation (18) determines the carbon emission 

level and equation (19) specifies the limits on carbon emission rights which are given 

exogenously for each region and time period. Equation (22) defines the inverse demand function 

for composite energy in ETA, which is linked to the reference level in MACRO as explained in 

the next section below. 

2.1.2 The Linkage of ETA to MACRO 

In MACRO, the demand for composite (electric and non-electric) energy is structured as a CES 

function. This means the demand level for composite energy ENj in sector j is related to the 

sector output Qj, the sector unit cost Cj, and the composite energy price PEN,j by the relation: 

σ

 ̧

 ̧

1

·

 ̈

 ̈

©

§

=

j

j

j j

PEN

C

EN kQ (i) 

where k is some constant and ) is the own-price elasticity of demand for composite energy. 

Let EN j

, C j, and PEN j be the ‘reference level’ for these variables, i.e. the level as 

determined in the MACRO module. The linkage of ETA to MACRO is then defined by the 

following equation: 

−σ

 ̧

 ̧

1

·

 ̈

 ̈

©

§

=

j

j

j

j

j j

C

C

PEN

PEN

EN EN (ii) 

which follows from the previous relation, and 

j a j

N

j

N

j

N

j

N

a

E

j

E

j

E

j

E

j

P

P t

P

P t

PEN

− −

 ̧

 ̧

 ̧

1

·

 ̈

 ̈

 ̈

©

§

+ +

 ̧

 ̧

 ̧

1

·

 ̈

 ̈

 ̈

©

§

+ +

=

1

1( ) μ 1( ) μ

 (iii) 

where: 

N

j

E

j

t ,t are ad-valorem tax rates on electric and non-electric energy demand in sector j.

N

j

E μ j

, μ are distribution margins on electric and non-electric energy (cost indices). 

N

j

E Pj

,P are the reference prices (user costs) of electric and non-electric energy. 

The last equation is based on the assumption that the structure of the electric and non-electric 

energy composition is Cobb-Douglas. 

If energy cost is only a small proportion of the overall sector cost, i.e.: 

1

( )

<<

∂ ∂

=

⋅

j

j j j

j

j j

C

PEN C PEN

C

PEN EN

,
5

then equation (b) can be approximated by: 

−σ

 ̧

 ̧

1

·

 ̈

 ̈

©

§

=

t

j

j j

PEN

PEN

EN EN (iv) 

or

σ

1 −

 ̧

 ̧

1

·

 ̈

 ̈

©

§

=

t

j

j j

EN

EN

PEN PEN (v) 

Equation (v) can be used to represent the inverse demand function for composite energy in ETA 

which will come out to be close to that modeled in MACRO. This is added to the list of 

equations for ETA (shown as equation (22) in Table 2). 

Table 2 List of Important Equations in ETA 

tr tr tr tr tr

en pvpe e pvpn n , , , ,

, = ⋅ + . ⋅ (1) 

r t

r t

r t r t

en

e

elvs pvpe

,

,

, , = ⋅ (2) 

tr tr

tr

tr

tr

tr pvcen EC

en

EN

SURPLUS en , ,

1

,

,

,

,

1

− ⋅

 ̧

 ̧

1

·

 ̈

 ̈

©

§

 ̧

1

·

 ̈

©

§

−

= ⋅

−

¦

σ

σ

σ

σ

 (3) 

tr

elvs

tr

elvs E tr N EN r t r t

,

1

, ,

, ,

⋅ =

−

(4) 

= ¦

e

E ,tr PEe ,, tr(5) 

synf t r rnew t r ne bak t r

tr t r t r cldu t r

PN PN PN

N OILNON GASNON PN

,, ,, ,,

, , , ,,

+ + + −

= + +

(6) 

gas tr r gas tr r gas n t r gas n t r

t r gas lc t r gas hc t r gas t r gas t r

ch PE ch PE

GASNON PN PN IMPRT EXPRT

,, ,, ,, ,,

, ,, ,, ,, ,,

− − − −

− −

− ⋅ − ⋅

= + + −

 (7) 

GASNONt,r N ,tr ≤ 5.0 ⋅ (7b) 

oil r htrt r oil tr r

t r oil lc t r oil hc t r oil t r oil t r

ch PE

OILNON PN PN IMPRT EXPRT

, , ,,

, ,, ,, ,, ,,

− −

− −

− ⋅

= + + −

 (8) 
6

Table 2 List of Important Equations in ETA 

coal n htrt r coal n t r cldu t r synf t r

coal t r coal t r coal t r coal r htrt r coal tr r

ch PE PN syntpe PE

PN EXPRT IMPRT ch PE

, , ,, ,, ,,

,, ,, ,, , , ,,

+ ⋅ + + 1( + ) ⋅

= − − ⋅

− −

− −

 (9) 

10

dle,ty ,1 r dle,ty,r r PE ≥ PE ⋅ decf +

(10) 

10

dln,tp ,1 r dln,tp,r r PE ≥ PE ⋅ decf +

(11) 

xln t r r n N tr PNx t r PN nxpf nshf, 1 ln, ,1

10

,, + ≥ +

⋅ + ⋅ (12) 

¦¦( ⋅ )+ ⋅ ≥ ( ) + +

xle xle

xle tp r rg RG E tr PExle t r PE f nshf, 1 , ,1

10

, ,

exp (13) 

, , 1 , , , , , , 1

5 5 + + = − ⋅ − ⋅ RSCr tx RSCr tx RAr tx RAr tx(14) 

5 ( ) 5 ( ) RSVr, ,tx +1 RSVr, ,tx RAr, ,tx PN tx ,, r RAr, ,tx +1 − PN ,tx + ,1 r = + ⋅ − + ⋅ (15) 

x r RSCr tx RAr tx

rdf

, , , ≥ , ,

⋅ (16) 

x r RSVr tx PN tx r

prv , , , ≥ ,,⋅ (17) 

( )

( ) oil t r oil t r oil r

gas t r gas t r gas r

n

n r n t r

e

t r e r te r

EXPRT IMPRT cecn

EXPRT IMPRT cecn

CLEV et cece PE nt cecn PN

,, ,, ,

,, ,, ,

, , ,, , ,,

, ,

− − ⋅

− − ⋅

= ¦ ⋅ + ¦ ⋅

 (18) 

t r crt t r crt t r t r CLEV , = EXPRT ,, − IMPRT ,, ≤ carlim ,

(19) 

( ) 0 ¦ ,, − ,, =

r

q t r q t r EXPRT IMPRT (20) 

¦

¦ ¦

+ ⋅

= ⋅ + ⋅ + ⋅

n

q q t r

r t r

n

n t r n r

e

t r te r e r

cstcexp EXPRT

EC PE ecst PN ncst ogpd GASNON

( )

( ) ( )

,,

, ,, , ,, , ,

 (21) 

σ

1 −

 ̧

 ̧

1

·

 ̈

 ̈

©

§

=

t

j

j j

EN

EN

PEN PEN (22)
7

2.1.3 Comments on the Structure of CETM

2.1.3.1 The Structure of Production and Inter-fuel and Fuel-factor Substitution. 

The structure of production in the MACRO module of the CETM model groups labor and capital 

together, and these factors are separated from the energy branch (see Figure 2). This means that 

energy-capital and energy-labor will have the same substitution elasticity and this implies a 

severe restriction (see the discussion on the issue of capital - energy substitutability or 

complementarity in section 3.2 below). 

On the other hand, the internal structure of the inter-fuel substitution in the MACRO 

module makes a useful distinction between electric and non-electric energy inputs. Although 

econometric evidence is scarce with respect to the substitution between electric and non-electric 

energy inputs, this distinction is useful at least from a theoretical viewpoint. This is because the 

choice of the electricity generation technologies may have an important impact on the 

environment (such as the emission of CO2), and hence the focus on electric energy consumption 

level may help focus attention on the choice of these technologies2.

Different forms of non-electric energy such as oil, gas, coal (direct use), synthetic fuels, 

renewable fuels or the non-electric backstop technologies, are treated as perfect substitutes in the 

ETA module (see equation (6) in Table 2). This assumption is perhaps rather restrictive 

especially from the end-user’s point of view. Natural gas, for example, is known to command a 

premium over coal because of its ease of handling. It may also come into conflict with other 

assumptions made in the model such as the fact that the market share for natural gas is limited 

(see equation (7)). Limited market share often implies some difficulty of substitution rather than 

limitation in supply. Finally, if these non-electric energy forms are perfectly substitutable, then 

their marginal costs (prices) must also be set equal to each other. These are strong assumptions. 

2.1.3.2 The ‘Small’ Influence of the Energy Sector in Linking ETA to MACRO 

Relying on the fact that the energy sector makes up less than 5% of the gross output of most 

economies, it is anticipated that any changes in the prices and quantities of energy demand within 

ETA will have only a small influence on the overall industry cost (and hence prices and demand 

within MACRO). This means that convergence of the results of ETA and MACRO can be 

achieved fairly rapidly. But this is likely to depend also on the assumptions regarding supply and 

demand elasticities. If the supply elasticity is much greater than the absolute value of the demand 

elasticity then convergence can be assured. However, if the converse is true, then even if energy 

is only a small proportion of the overall industry costs, it can still act as a constraint on 

consumption activities, and can give rise to significant fluctuations in energy prices and demand, 

and therefore, will not help for convergence (see Figure 4). Since ETA is a process model rather 

than a conventional econometric model, the concept of ‘supply elasticity’ cannot be clearly 

2

Furthermore, as Hogan (1989, p. 54) noted, the grouping of all energy forms together in an aggregate energy demand 

function may mask the historically important trend of ‘electrification’ in an energy economy (such as that observed in 

the US economy during the period from 1960 to 1982).
8

Figure 4 ETA - MACRO Linkage 

defined and tested. However, the general concept of supply responsiveness to price and demand 

changes may still be an important factor to consider when looking at the issue of convergence. 

2.1.3.3 ‘Dynamic Adjustment Constraint’ on Technologies could be Linked to Endogenous 

Factors within the MACRO economy.

Equations (10-13) represent the ‘dynamic adjustment constraints’ on new and existing 

technologies. They define the limits to which existing technologies can be retired (because of 

sunk capital costs) or new technologies to be introduced (because of the difficulty of market 

penetration). These constraints reflect economic as well as institutional factors within the current 

and future markets, and therefore, they could also be determined ‘endogenously’ within the 

model rather than being set exogenously. For example, the rate of market penetration for new 

technologies may be dependent on the differences in production costs between existing and new 

technologies. The rate of retirement for existing technology can also be specified as a function of 

the expected increase in future demand and supply and the cost of capital. In other words, the 

dynamic adjustment constraints could be linked to the investment decisions within the model, 

rather than being specified as exogenous. Since the absence of such a linkage is largely due to 

practical considerations, this is probably an area for further research. 

Table 3 Summary Characteristics of CETM 

Model Characteristics CETM 

Top-down versus bottom-up Bottom-up in CETM, top-down in MACRO 

Dynamic Simultaneous 

Inter-fuel substitution Yes 

Fuel-factor Substitution Yes 

Capital – Energy 

complementarity/substitutability 

Energy and capital are substitutes in the MACRO production 

structure, but can be complements within the energy sub-module 

CETM. 

ENERGY COSTS

ENERGY QUANTITY

DEMAND

(MACRO)

ENERGY QUANTITY

SUPPLY

(ETA) 

DEMAND

(MACRO)

SUPPLY

(ETA) 

ENERGY COSTS

ELASTIC SUPPLY INELASTIC SUPPLY
9

2.2 The MEGABARE Model and the “Technology Bundle' Approach 3

In building the MEGABARE model on top of the GTAP framework, the authors of that model 

made ‘a deliberate decision ...not to adopt the nested CES (constant elasticity of substitution) 

production function approach’ to energy substitution. This was because: 

It was believed that it was possible to improve on the nested CES approach in terms of both 

accuracy and transparency by introducing what has been termed the 'technology bundle' 

approach. Using this approach, a level of detail about different technologies is introduced 

into MEGABARE that is normally found only in so-called 'bottom up' models. An attempt 

is made to introduce the realism in modelling substitution options that is a feature of 'bottom 

up' models while retaining extensive interactions between the energy and other sectors of 

the economy that is a feature of 'top down' models. (MEGABARE, 1996: 4). 

2.2.1 Description of the Technology Bundle Approach 

The ‘technology bundle’ approach is described below in figures 5-7. First, the intermediate 

inputs into production are divided into technology bundle inputs – typically primary factors and 

primary energy inputs - and non-technology bundle inputs (Figure 5). The technologies for an 

industry (for example, coal-fired electricity, gas-fired electricity etc.) are Leontief (fixed inputoutput coefficient) combinations of technology bundle inputs. The technology bundle for an 

industry is a conventional ‘smooth production function’ (such as CRESH) combination of the 

output of each technology. Industry output is a Leontief combination of the technology bundle 

and the non-technology bundle inputs 

The technology bundle approach is used in the MEGABARE model to describe the input 

use of the electricity generation industry (Figure 6) and the steel industry, which represent 

typical examples of energy intensive industries. The approach, however, can also be used to 

describe other energy intensive industries. With the steel industry, the input structure differs 

slightly from the electricity industry: electricity and minerals are added to the input list, along 

with the primary factors and the primary energy inputs (Figure 7). 

Figure 5 Technology Bundle Approach 

Source: ABARE (1996), Figure 6, p. 22. 

3

ABARE (1996), The MEGABARE model: interim documentation, February.

Gross output by industry

Leontief

Commodity 1 .......... Commodity Technology bundle
10

Figure 6 Composition of the Technology Bundle for the Electricity Industry 

Source: ABARE (1996), Figure 9, p. 32. 

Figure 7 Composition of the Technology Bundle for the Steel Industry 

Source: ABARE (1996), Figure 10, p. 32. 

‘EAF and ‘BOF’ stand for ‘electric arc furnace’ and ‘basic oxygen furnace’ respectively. 

CRESH

Technology bundle

Technology 1 .................

Leontief Leontief

K Primary 

energy e

L Primary 

energy 1

Primary 

energy 1

... K L Primary 

energy e

...

Technology

EAF ............... BOF

Leontief Leontief

L

Primary 

Electricity K L energy 1

Primary 

energy e

... Minerals

CRES

Technology 

Electricity Minerals

K
11

2.2.2 Comments on the Technology Bundle Approach 

The technology bundle approach is interesting and innovative. It tries to introduce the concept of 

‘substitution’ between alternative ‘technologies’ to give a more realistic description of the nature 

and range of substitution occurring within the energy producing and energy-using industries, in 

contrast to the more traditional concept of substitution between alternative energy and nonenergy inputs. In doing so, the approach can claim the following advantages: 

1. it ‘ensures that the pattern of input use is consistent with known technologies’ which 

usually exhibit what may be described as ‘lumpy’ or indivisibility constraints on certain 

inputs such as capital or labor, 

2. it is highly transparent in the sense that it allows an assessment of how some policy 

change can lead to ‘relative changes in the use of different technologies’ rather than a 

mere observation of the derived changes in inputs use (ABARE, 1996: 35). 

3. the elasticity of substitution parameters in the technology bundle approach can be 

estimated “by reference to the results from 'bottom up' models” and therefore, can cover 

‘a wider range of data values that might occur in a simulation’ (ABARE, 1996: 36). 

While in theory, it is true that the technology bundle approach can provide a more realistic 

description of the constraints facing the energy producing and energy-using industries than a 

conventional econometric approach, in practice, however, it is not clear how some of these 

potential advantages can always be implemented. In MEGABARE, for example, inputs into the 

technology bundles are still being specified as Leontief with no explicit ‘indivisibility’ or lumpy 

constraints imposed4

. On point 3, it is not evident how the CRESH substitution parameter used in 

the MEGABARE model had been actually derived from some simulation experiment of a 

‘bottom-up’ nature. 

On a more important point, the technology bundle approach is not dissimilar to the 

conventional approach in econometrics where a nested production structure is used to describe 

complex substitution possibilities among the inputs5

. As Powell and Rimmer (1998) note: 

“Models in which output is produced according to a technology in which capital (K), labor (L) 

and energy (E) are substitutable run into the difficulty of how to allow parsimoniously for the 

higher likely substitutability between K and E than between L and E”. In fact, the issue of 

‘substitutability’ or ‘complementarity’ between K and E is a long-standing issue in the energy 

debate (see section 3.2 below). To handle this issue, most models allow for K and E to be 

separated from L. In the technology-bundle approach, although E and K are complements within 

a given technology structure, they are substitutes at the higher level, where technologies are 

substitutable for each other. Thus, given an energy price increase, although K cannot be used to 

replace E immediately in any given technology, a less energy-intensive but more capitalintensive technology can be put in place, to counter the energy price rise, thus fulfilling the 

4

The MEGABARE documentation (ABARE, 1996) does not refer to any of these indivisibility constraints but in a 

different documentation (Hanslow et al. (1994:28)), a reference is made to ‘capacity constraint’ in the context of the 

discussion of the pricing formula for a commodity which is used as input into a particular 'technology'. Here, it is stated 

that ‘capacity constrained technology earns above normal returns to capital’ which is to be represented by a ‘slack’ 

variable. 

5

See for example, Perroni and Rutherford (1995), Powell and Rimmer (1998). 
12

Table 4 Summary Characteristics of MEGABARE 

Model Characteristics MEGABARE 

Top-down versus bottom-up Bottom-up in technology bundle specification, top-down in the 

rest of the model structure 

Dynamic Recursive 

Inter-fuel substitution Indirectly through technology substitution 

Fuel-factor Substitution Indirectly through technology substitution 

Capital – Energy 

complementarity/substitutability 

Energy-capital are complements within a given technology, but 

can be substitutable through technology substitution. 

function of substitutability between K and E in the longer run. In this respect, the technology 

bundle approach is quite innovative and flexible.

2.3 The OECD’S GREEN Model6

GREEN is a global, dynamic AGE model which highlights the relationships between depletion of 

fossil fuels, energy production and use, and CO2 emissions. The main focus is on the energy 

sector and its linkage to the economy. 

There are three types of fossil fuels in the model - oil, natural gas, and coal - and one 

source of non-fossil energy - the electricity sector. Each of these can be replaced at some future 

date by "backstop" technologies. These are assumed to become available at an identical time 

period in all regions. Their prices are determined exogenously and identically across all regions7

.

This implies an infinite elasticity of supply. 

For each of the three fossil fuels, there are two alternative backstop technologies: one 

carbon-free (e.g. biomass) and one carbon-based (synthetic fuel derived from shale or coal, with 

higher carbon content than conventional technology). For electricity, the backstop technology is 

carbon-free (nuclear fusion, solar or wind power, but excluding hydro, or nuclear fission). 

There are eight energy-producing sectors in GREEN: Coal mining, Crude oil, Natural 

gas, Refined oil, Electricity-gas-water distribution, Carbon-based back-stop, Carbon-free backstop, Carbon-free electric back-stop. The three non-energy producing sectors are Agriculture, 

Energy-intensive industries, and Other industries and services. 

There are four consumption goods: Food beverages and tobacco, Fuel and power, 

Transport and communication, and Other goods and services. These are chosen to be different 

from the outputs of the production sectors to highlight the principal components of final demand 

6

Burniaux, J. M., Nicoletti, G., and J. Oliveira-Martins (1992), “GREEN: A Global Model for Quantifying the Costs 

of Policies to Curb CO2 Emissions”, OECD Economic Studies No. 19, Winter, 49-92; Lee, Hiro, Joaquim OliveiraMartins, and Dominique van der Mensbrugghe (1994), “The OECD GREEN Model: An Updated Overview”, OECD 

Development Centre Technical Paper No. 97. 

7

Their marginal costs, however, are not identical, and therefore, there is a return attributed to the fixed factor. 

Backstops are not traded. Their role is primarily to limit the rise in prices, and therefore in carbon taxes. 
13

for energy. Consumers are assumed to be deciding on the optimal allocation of their given 

disposable income on saving and the four consumption goods. The demands for these 

consumption goods are then translated into the demands for producer goods (and energy) via a 

‘transition’ or make matrix. 

There are twelve regions in the GREEN model: United States, Japan, EC, Other OECD, 

Central and Eastern Europe, The former Soviet Union, Energy-exporting LDCs, China, India, 

Dynamic Asian Economies (Hong Kong, Philippines, Singapore, South Korea, Taiwan and 

Thailand), Brazil, Rest of the World (RoW). 

Finally, there are five different types of primary factors: labor, sector-specific "old" 

capital, "new" capital, sector-specific fixed factors (for each fossil fuel type, and for the carbonfree backstop), and land in agriculture. 

2.3.1 Dynamics in GREEN 

One special feature of the GREEN model is in its dynamic treatment of the energy-capital 

complementarity / substitutability issue and also in the handling of the resource depletion issue. 

The dynamics in GREEN in fact come mainly from these two issues: depletion of exhaustible 

resources, and capital accumulation. 

In the resource depletion ‘sub-model’, the total (proven plus unproven) reserves are 

assumed to be determined exogenously. However, the rate at which 'unproven' reserves are 

converted into 'proven' reserves (rate of discovery or rate of conversion) is made sensitive to the 

prices of oil and gas. This affects the 'potential supply', which is defined by the rate at which 

proven reserves are extracted8

. Potential supply provides an upper bound on actual supply, and if 

actual demand falls short of potential supply, then the difference between potential and actual 

supply is added to the future reserves of the fossil fuels. The resource depletion sub-model is thus 

recursively dynamic (i.e. based on current and past prices only) rather than forward looking (i.e. 

based on some expected future prices). 

Capital accumulation in the GREEN model is influenced by the putty/semi-putty 

assumption on the nature of capital. New capital (capital invested in current period) is putty, i.e. 

it is highly substitutable for other factors (elasticity of substitution is 2). Sector-specific old 

capital (capital invested in previous periods), on the other hand, is semi-putty and much less 

substitutable for other factors (elasticity of substitution can be as low as 0.25). Sector-specific 

old capital is also much less mobile between sectors (implying small and sector-specific supply 

elasticities). This can result in equilibrium rental values of old and new capital being 

significantly different from each other, and the ratio of these rental values is used in GREEN to 

stimulate 'disinvestment' of old capital (see Burniaux et al. (1992: 57)). Once disinvested, old 

capital becomes available for use in new investment. At any point in time, the stock of capital 

will consist of old and new capital, and the rate of substitution between the stock of capital as a 

whole and other factors will therefore depend on the vintage structure of capital. Apart from this 

dynamic vintage structure, GREEN does not include any other explicit investment behavior by 

firms. The total aggregate level of investment is defined as a residual from the aggregate level of 

8

Though the extraction rate is assumed constant overtime, energy prices affect the potential supply of oil and gas 

through the price sensitive conversion rate (Burniaux etal. 1992, vand der Mensbrugghe, 1994). 
14

savings minus government sector balance and plus net capital inflows. Once the aggregate level 

of investment is determined, this is then distributed optimally to the various sectors in order to 

equate rates of return on new investment. 

2.3.2 Inter-fuel Substitution 

2.3.2.1 Inter-fuel Substitution in Production 

In estimating the inter-fuel elasticities of substitution, the general assumption is that energy and 

capital are weakly separable in production. This means that firms choose the cost-minimizing 

energy-mix given an energy-capital bundle. But this makes sense only if there are dual-fired or 

multi-energy technologies available, otherwise, inter-fuel substitution will involve the 

installation of new capital and therefore, the assumption of separability between energy and 

capital breaks down (Burniaux et al. (1992, p. 75)). Thus, in choosing to represent the potential 

for inter-fuel substitution, the GREEN model assumes that short run to medium run elasticities of 

substitution between alternative forms of energy are small, between 0.5 and 1.0 in the medium 

term, and only 0.25 in the short term. Long-run9

 elasticities of inter-fuel substitution, however, 

are set as high as 2.0. This latter value is said to be based on empirical estimates of elasticities 

based on samples which have multiple power-generating facilities (Burniaux et al., loc. cit.).

These inter-fuel substitution elasticities apply only to the non-energy producing sectors and the 

electricity generation sector. For the rest of the energy producing sectors (coal mining, crude oil, 

natural gas, refined oil), there is no inter-fuel substitution (see Burniaux et al. (1992, Table 3, p. 

76))

The structure of inter-fuel substitution in production in the 1992 version of the GREEN 

model is as shown in Figure 9. In a subsequent version

10, the structure is altered significantly to 

allow for three levels of nested substitution: (i) substitution between electricity and a 'nonelectric' composite fuel, (ii) substitution between coal and a 'non-coal' composite within the nonelectric branch, and finally, (iii) substitution between oil, gas, and refined fuels within the noncoal branch. All substitution elasticities are set within the range 0.25 < ) < 2, depending on 

whether it is short-run, medium-run, or long-run. 

2.3.2.2 Inter-fuel Substitution in Household Demand 

Given the energy intensity of each consumer good, household demand for aggregate energy is 

derived from its demand for the four categories of consumer goods (see Figure 10). Once the 

demand for aggregate energy is known, this demand is then allocated optimally between the 

different fuels with the same structure of inter-fuel substitution as in the case of producers’ 

demand for energy (Figure 9). 

9

 This long run is defined as the period over which new capital can be installed. 

10 See Lee et al. (1994, Figure 1b, p. 49) 
15

Figure 8 The Structure of Production in GREEN

Domestic

Gross output 

Leontief

Imported

Region 1 ... Region r

Labor

Capital-Fixed 

factor Composite

Energy

Leontief

Fixed 

factor

Capital
16

Figure 9 Energy and Backstop Technologies in GREEN 

.

(a) With elasticity of substitution (σ=0.25) for ‘old’ capital, and (σ=2) for ‘new’ capital, in all sectors except coal 

mining, crude oil, natural gas, and refined oil (see Burniaux et. al., 1992, Figure 1b, p. 56, and Table 3, p. 76). In 

Lee et al. (1994), there is some further nesting (all with 0.25<σ<2): between electric and non-electric’ composite, 

then between ‘coal’ and non-coal’ composite within the non-electric branch, and finally between oil, gas, and 

refined fuel in the non-coal branch 

(b) Elasticity of substitution between conventional and backstop technologies is (σ=10) for agriculture, refined oil, 

electricity, energy-intensive industries, and other industries, as well as for consumer goods and government 

demand, and in the production of investment goods and inventories. 

(c) Elasticity of substitution between domestic and imported fuels is (σ=4) for all fuels, except electricity (σ=0.3), and 

crude oil (σ=∞).

(d) Elasticity of substitution for fuels from different regions (world trade elasticities) is (σ=∞) for crude oil, (σ=5) for 

coal mining and natural gas, and (σ=3.0) for refined oil. 

(e) Same as for coal. 

(f) Same as for coal except with (σ=∞) for domestic-imported and inter-regional substitutions. 

(g) Same as for coal except there are no backstop fuels and world trade elasticities is (σ=3). 

(h) Same as for coal except there is only one carbon-free backstop option and world trade elasticities is (σ=0.5).

Energy

CES (a)

Coal

CES (b) 

Carbon-based 

backstop fuel

Conventional Carbon-free 

backstop fuel

CES (c)

Domestic Imported

Region 1 ... Region r

CES (d) 

Gas 

(e)

Crude oil 

(f)

Electricity 

(h)

Petroleum 

Products

 (g) 
17

Figure 10 The Structure of Household Demand in GREEN 

(a) Same as for transport & communication. 

(b) See Figure 9. 

Disposable income

 ELES

Leontief 

Other producer

goods

Energy (b)

CES 

Domestic Imported

Food and 

Beverages

Fuels & Saving 

power

Transport & 

communication

Other goods 

and services

...(a) ...(a) ...(a)
18

2.3.3 Fuel-factor Substitution

The GREEN model assumes that capital-labor and energy-labor have the same (positive) 

elasticities of substitution. This assumption accords with empirical econometric evidence which 

supports substantial short-run and long-run substitutability between labor and capital on the one 

hand, and also between labor and energy on the other hand. On the issue of energy-capital 

substitutability or complementarity, however, empirical estimates seem to be more of a problem. 

A widely held opinion in this area is that perhaps energy and capital are complements in the 

short-run, but substitutes in the long-run. To incorporate this feature into the model, the approach 

in GREEN is to utilize a ‘vintage capital’ structure. Thus, short run substitution between ‘old’ 

capital and energy can be low, while long-run substitution between ‘new’ capital and energy can 

be high. The net effect will then depend on the capital vintage structure. Over time, the short-run 

elasticities will converge to the long-run elasticities (see Figure 5 in Burniaux et al. (1992, p. 

66)). The gap between short- and long-run elasticities and the speed of the convergence depends 

on the dynamics of the capital stock adjustment process which in turn depends on assumptions 

made about depreciation rate and rate of new capital formation. The larger the net replacement 

rate, the smaller the gap between short- and long-run elasticities and the faster the convergence 

of the former to the latter. 

In GREEN, capital is combined with a fixed factor through a Leontief structure before 

being combined with energy through a CES structure. The role of the fixed factor is to limit the 

substitution away from/towards capital formation in the energy-producing sectors so as to avoid 

an unrealistic situation where, for example, following an increase in the relative price of energy, 

'too much' investment will occur in these sectors even in the short run. The role of the fixed 

factor in primary-energy producing sectors is thus to impose limits on the supply elasticities of 

these primary energies. These supply elasticities have a critical role to play, especially in energyenvironmental policy simulation studies. 

Substitution between energy and the fixed factor-capital composite is set at zero for all 

energy-producing sectors, except electricity. For electricity and other non energy-producing 

sectors, it is set at zero for 'old' capital, and at a low value of 0.8 for new capital. Substitution 

between labor and capital-energy-fixed factor composite is also set at zero for all energyproducing sectors including electricity. For other sectors, it is set at a low value of 0.12 for old 

capital and a high value of 1.0 for new capital (Burniaux at al. (1992, Table 3, p. 76). 

According to Borges and Goulder (1984, p. 340), to ensure that the capital-energy 

complementarity condition can be achieved, it is ‘sufficient’ that the elasticity of substitution 

between K and E within the KE nest be given a ‘substantially smaller (even if positive)’ value as 

compared to the elasticity of substitution between the KE composite and labor (or other factors) 

in the ‘outer nest’. To be more precise, we can use the following formula established for the case 

of a nested CES structure by Keller (1980, p. 83): 

σ KE−outer = σ KE−inner −σ VA SKE +σ VA [ /] 

In this formula, SKE is the share of the KE-composite in the outer (value-added) nest, and 

σ KE−inner and σ KE−outer stand for the inner and outer substitution elasticities between K and E 

respectively. If σ KE−inner is less than ıVA, then the first term on the right hand side is negative. But 

whether σ KE−outer is negative (implying complementarity between K and E in the outer nest) 

depends on the size of SKE as well. If SKE is small, then this is likely even if ıVA is large. For 
19

example, using the upper limit values of 0.8 and 1.0 for σ KE−inner and ıVA respectively as used in 

the GREEN model for the case of new capital, this requires SKE < 0.2 for σ KE−outer < 0 

(complementarity between K and E in the outer nest). Using the lower limit values of 0.0 and 

0.12 respectively for σ KE−inner and ıVA for the case of old capital, this requires SKE < 1.0 for 

σ KE−outer < 0. The condition is always satisfied since SKE is always less than 1. Overall, thus, 

‘old’ capital and energy will always come out as complements in the value added nest of the 

GREEN model production structure. For ‘new’ capital, this will also be the case if the share of 

capital-energy-fixed factor component in the value-added nest is less than 20 percent. Note that 

all these discussions apply to the non energy-producing sectors only. For the energy-producing 

sectors (except electricity) there is no fuel-factor substitution. The electricity sector is 

characterized by an ‘inner’ substitution elasticity of σ KE−inner = 0.8 (for new capital only), and a 

zero ‘outer’ substitution elasticity of ıVA= 0 in the value-added nest. This implies ‘new capitalfixed factor bundle’ and ‘energy’ are always substitutes in the electricity sector. 

2.3.4 Comments on the GREEN Model

One innovative feature of the GREEN model is in the handling of the energy-capital 

complementarity / substitutability issue through the use of a dynamic capital vintage structure. 

Through this structure, the issue of long-run substitutability versus short-run complementary 

between capital and energy is handled quite flexibly (see the illustrative numerical calculations 

carried out in the previous section). This is a significant improvement over many other models 

which do not handle this issue explicitly. 

The specification of the capital vintage structure is an important first step. However, the 

next step can perhaps focus attention also on the issue of capital investment. Currently, the 

aggregate level of investment in the GREEN model is specified as a residual from the level of 

aggregate saving minus government sector balance plus net capital inflows. Once the aggregate 

level of investment is determined, the aggregate level of new investment is then distributed 

optimally among the sectors. Following from this, the ratio of the new- to old-capital rates of 

return is also determined, and this will then influence the rate of old-capital disinvestment (i.e. 

the rate at which old capital is transformed back into the pool of ‘new’ investment in the next 

period). All of this will affect the capital vintage structure. Throughout this process, energy 

prices play an important role, in influencing the rate of return on (old and new) capital, and hence 

on aggregate investment. However, this influence is still indirect via the aggregate return on 

capital. A more direct role for energy prices may be in influencing the capital vintage structure 

directly, for example, in bringing about a rate of investment which will ‘equalize’ the rates of 

return on ‘old’ and ‘new’ capital over the ‘long run’. This, however, implies a more ‘forward 

looking’ investor than is currently assumed for the GREEN model. 
20

Table 5 Summary Characteristics of GREEN 

Model Characteristics GREEN 

Top-down versus bottom-up Top-down with some bottom-up details in backstop technologies 

specifications. 

Dynamic Recursive 

Inter-fuel substitution Yes 

Fuel-factor Substitution Yes 

Capital – Energy 

complementarity/substitutability 

Given the vintage structure of production, capital and energy 

tend to be compliments in the short term and substitution over 

the longer term. 

2.4 The Babiker-Maskus-Rutherford (BMR) Model 

Babiker, Maskus, and Rutherford (1997) utilize a model for studying the economic impact of 

international trade and environmental policies on the world economy. The model includes a 

detailed structure of the inter-fuel and energy-factor substitution possibilities for the firm and for

the household sector (see Figures 12 and 13). 

The structure of production in the BMR model groups labor and capital together. This 

means that one cannot give to the energy-capital components a different elasticity of substitution 

as compared to the energy-labor or capital-labor components, and this is a severe restriction. On 

the other hand, the internal structure of the inter-fuel substitution in the BMR model does contain 

a rich structure, firstly with a distinction between electricity and non-electricity inputs, and then 

further disaggregation of the non-electric inputs into various types of fuels using a nested-CES 

structure (see Figure 12) with 5 levels: oil and natural gas at level 0 (bottom level); coal at level 

1; electricity, land, labor, and capital are at level 2; aggregate energy and aggregate primary 

factor is at level 3; intermediate input and the combined energy-primary factor is at level 4; and 

finally output is at level 5. 

To calculate the elasticity of substitution between any two inputs n and m at a particular 

level L in the nested-CES structure, we can refer to the formula derived by Keller (1980, p. 83): 

[ ]

1

,

1

, 1

1

,

1

, ,

− −

−

= +

−

= − ¦ n l − n l

L

l K

σ nm σ n K Sn K σ n l S S 

where K represents the lowest level in the nested-CES structure at which a component exists, 

associated with both the n and the m inputs (the lowest common level) and L is the highest level 

in the nested structure at which the elasticity ınm is calculated, and the cost share Sn,l is defined 

by: 

¦∈

=

i n

n l i S S ,

 
21

i.e. the sum of all the cost shares associated with the aggregate input n at level l, or, in other 

words, the cost share of the input component n.

Using this formula, and considering the production structure of Figure 12, we can conclude that: 

(1) energy-capital11 substitution elasticity ıEK (considered at the top level, i.e. holding output 

constant, L=5) is simply equal to 0.5/SEF where SEF is the cost share of aggregate energyprimary factors (land, labor, capital) in the production structure. Since this value is less than 

1.0, ıEK is greater than 0.5 - the CES substitution elasticity at level K=4.

(2) For inter-fuel substitution, electricity and non-electricity have an elasticity of substitution of: 

1/SE – 0.5*[1/SE -1/SEF] = 0.5/SEF + 0.5/SE

where SE is the cost share of aggregate energy in the production structure. Since SE is rather 

small, the elasticity of substitution between electricity and non-electricity can therefore be 

very large. For example, with SE = 0.05, SEF = 0.70, the overall, output- constant, elasticity 

of substitution between electricity and non-electricity is 10.71. 

(3) The elasticity of substitution between oil and gas is given by: 

1/SOG – 0.5*[1/SOG -1/SCOG] – 1*[1/SCOG -1/SE] – 0.5 [1/SE -1/SEF] = 

0.5/SOG – 0.5*/SCOG + [0.5/SEF + 0.5/SE]

where SOG or SCOG is the cost share of inputs (oil, gas) or inputs (coal, oil, gas) in the total 

production structure. Again, assuming that SOG = 0.010 and SCOG = 0.015, the overall 

elasticity of substitution between oil and gas is then 22 + 10.71 = 32.71. This is a very large 

figure. 

The large magnitude of these output-constant (upper level) elasticities of substitution as 

compared to the composite input-constant (lower-level) elasticities of substitution can be 

explained as follows. When a composite input (such as aggregate energy E) is held constant, 

there is only a limited opportunity for the various components (fuels) of this composite energy to 

be substituted for one another. When the level of output is held constant, however, there are also 

substitutions between different types of aggregate inputs (e.g. aggregate energy E for capital K,

or composite K-E for labor L, etc). This increases the range of substitution (or complementarity) 

between the lower-level inputs (fuels). Refer to Figure 11, for example, where it is assumed for 

simplicity that aggregate energy consists of only oil and gas. When the level of aggregate energy 

is held constant, an increase in the price of oil (relative to gas) will induce a substitution of gas 

for oil (movement from A to B). When the level of output is held constant, aggregate energy 

consumption may fall because aggregate energy price has increased relative to other factors: B 

may now move towards C. The total movement is now from A to C, which shows a larger 

reduction in oil consumption following an oil price increase, and therefore, it seems as though 

the degree of ‘substitutability’ between oil and gas is now much larger. Furthermore, as we go up 

the production structure, the share of the energy inputs will get smaller, and since the elasticity of 

11 Or energy-labor, or energy-land: since labor, land, and capital are grouped together, their substitution elasticity with 

respect to energy will be the same for all three primary factors. 
22

substitution is price elasticity ‘normalized’ by the cost share, it will get even larger as the cost 

share gets smaller. 

The purpose of these upper- or outer-level elasticity calculations is to show that the 

overall level of substitution between any two input components within a particular nest may be 

much larger than the magnitude of the substitution elasticities. This point is important to keep in 

mind when we compare different models which may have similar elasticities, but different nested 

structures.

Figure 11 Substitution Elasticity when Total Output is Held Constant. 

Gas

Composite energy input held constant

Oil

Output held constant

A•

• B

• C
23

Figure 12 Structure of Production in the Babiker-Maskus-Rutherford (1997) Model 

OUTPUT

Leontief 

Cobb-Douglas 

CES (σ=0.5)

Land

Non-energy intermediaries 

(plus crude inputs to refining)

Labor Capital

Cobb-Douglas 

Electricity

CES (σ=0.5)

Oil Natural Gas

Coal

Cobb-Douglas 
24

Table 6 Summary Characteristics of the BMR Model 

Model Characteristics BMR Model 

Top-down versus bottom-up Top-Down 

Dynamic Recursive 

Inter-fuel substitution Yes 

Fuel-factor Substitution Yes 

Capital – Energy complementarity/substitutability Energy is rather a compliment to capital (as is 

land and labor. 

2.5 Borges and Goulder (1984) Model 

Borges and Goulder (1984, p. 340) assume a much simpler structure for the inter-fuel 

and fuel-factor substitution possibilities. However, the model allows for labor to be separated 

from capital, and energy and capital are to be grouped together in one nest. This is consistent 

with the approach taken in the GREEN model. To allow for the possibility of significant 

complementarity between K and E, Borges and Goulder assumed a fixed-coefficient structure for 

the KE composite. Using the Keller formula as described in the previous section, the substitution 

elasticity between energy and capital at the top level would then be given by )EK = –1*[1/SEK – 

1], where SEK is the cost share of capital and energy inputs. Since SEK < 1, then )EK < 0, i.e. 

capital and energy are significant complements at the top level of the production structure. On 

Figure 13 Structure of Final Demand in the Babiker-Maskus-Rutherford (1997) Model 

CES (σ=0.5)

All non-energy goods 

Cobb-Douglas 

Cobb-Douglas

Oil Natural Gas Coal Electricity

Final Demand 
25

Figure 14 Structure of Production in Borges and Goulder (1984) Model 

the issue of inter-fuel substitution, Borges and Goulder assume a Cobb-Douglas structure, but 

recognize that perhaps with the petroleum product and gas sectors, a fixed coefficient technology 

would be more appropriate (see Figure 14). 

On the household consumption side, the utility structure allows for substitution between 

‘current consumption and future consumption’, as well as between ‘goods and services’ and 

leisure. The goods and services sector is Cobb-Douglas with three different types of energy 

commodities: electricity, gas and ‘gasoline and other fuels’. 

OUTPUT

Cobb-Douglas 

Cobb-Douglas

Leontief

Coal 

mining

Non-energy intermediaries 

including imports 

Cobb-Douglas

Electricity Crude & 

natural 

gas

Capital

Labor

Energy

Leontief

Petroleum 

refining

Gas

utilities
26

Table 7 Summary Characteristics of the Borges and Goulder Model

Model Characteristics Borges and Goulder Model 

Top-down versus bottom-up Top-Down 

Dynamic Simultaneous 

Inter-fuel substitution Yes 

Fuel-factor Substitution Yes 

Capital – Energy 

complementarity/substitutability 

Strict complementarity between capital and energy. 

3. Towards a GTAP Model with Energy Substitution 

In this section we discuss the issue of how to incorporate the important features of energy 

substitution as reviewed in the previous section into the GTAP model. Currently, in the standard 

GTAP model12, there is no inter-fuel, nor fuel-factor (energy - primary factor) substitution, even 

though recent version of the model allows for a non-zero constant elasticity of substitution 

between all intermediate inputs. This latter feature is an improvement over previous versions. 

However, it still does not go far enough to allow for an adequate treatment of the issue of energy 

substitution, hence a more substantial approach needs to be taken here. 

There are two important issues which must be addressed when considering extending the 

GTAP model to include energy substitution in its structure. The first relates to the question of a 

choice between a ‘top-down’ versus a ‘bottom-up’ approach. The second relates to the question 

about complementarity / substitutability between energy and capital inputs over time. 

3.1 Top-Down Versus Bottom-Up Approach 

In selecting an approach for incorporating energy-substitution into the GTAP model, there are 

generally two different approaches13. The ‘bottom-up’ (engineering) approach often starts with a 

detailed treatment of the energy-producing processes or technologies, and then asks the 

questions: given a particular level of demand for energy services (which may be defined in terms 

of the level of outputs of certain activities, such as travel, heating, air conditioning, lighting, or 

even steel making, etc.), what is the most efficient way of going about meeting these demands in 

terms of the energy technologies employed and the level of inputs. The top-down (economic) 

approach, on the other hand, starts with a detailed description of the macro (and international) 

economy and then derives from there the demand for energy inputs in terms of the demand for 

various sectors’ outputs through highly aggregate production or cost functions. 

The advantage of a bottom-up approach is in the detailed specification of the energy 

technologies, through which newly developed or future technologies can be incorporated into the 

12 As documented in Hertel, T.W. and M.E. Tsigas "Structure of GTAP", Chapter 2 in Hertel (1997). 

13 See, for example, Wilson and Swisher (1993).
27

analysis. This provides it with much more realism than in the econometrically-specified 

‘production function’ of the top-down approach. On the other hand, the latter can claim 

advantage in the fact that there is historical evidence in support of the assumed behavioral

response implied in the production function specification, whereas the bottom-up technology 

specifications may lack this behavioral content14. To utilize the advantages of both approaches, a 

top-down (macro-econometric or computable general equilibrium) model can be ‘linked’ to a 

bottom-up process model and the two models are solved simultaneously. However, there are 

many theoretical and computational difficulties associated with such a linkage. As a result, in 

some cases, a ‘partial link’ is pursued (such as the ETA-MACRO link in the CETM model 

discussed in section 2) or a ‘simulated’ approach to a process model is used (such as the 

specification of the energy-sector production possibilities in terms of ‘technology bundles’ in the 

MEGABARE model, see also section 2). While there are certain advantages associated with 

these ‘partial’ approaches, the price to pay for such an approach is in the added complexity in 

model specification, and also the additional data and parameter requirements. For example, in the 

MEGABARE model, there is the question of what parameters are to be used for the substitution 

between the ‘technology bundles’ to ensure some consistency with observed behavior based on 

historical data. As a result of these difficulties, and the desire to offer a widely-accessible energy 

model, these approaches are not pursued here. Instead, it is suggested that a simple ‘top-down’ 

approach be used, which can incorporate most of the important features of the existing top-down 

models in this area, such as the GREEN or BMR models. 

3.2 The Issue of Energy-Capital Substitutability or Complementarity 

Having settled on a top-down approach to represent energy-substitution, the next question to 

consider is: which particular structure should be used to represent the substitution possibilities 

between alternative fuels (inter-fuel substitution) and between the energy aggregate as a whole 

and other primary factors, such as labor and capital (fuel-factor substitution). In particular, the 

question of energy-capital complementarity or substitutability is a major issue in this literature. 

In this section, we look at this issue from a theoretical viewpoint and then go on to review some 

of the empirical estimates of the parameters for energy and capital substitution /complementarity 

in the literature. 

3.2.1 Importance of the Issue 

According to Vinals (1984), the issue of energy-capital complementarity or substitutability may 

turn out to be a crucial one in determining the direction of the adjustment of aggregate output 

following energy price changes: 

‘...the key parameter that determines whether output produced goes up or down after 

an energy price increase is the degree of complementarity/substitutability between 

energy and capital, measured by ıEK [the substitution elasticity between energy and 

capital]’ (Vinals, 1984: 237-238). 

14 As a result, there would be some difficulties in guessing what would be the future rates of penetration of new 

technologies into the market. 
28

In Vinals' simple one-sector model with no distortions, when the capital stock is given, and the 

wage level is flexible, energy-capital substitutability ‘is a sufficient condition for output 

produced to decline following an energy price increase. Alternatively, energy-capital 

complementarity is a necessary condition for output produced to rise following an energy price 

increase’. These results point out ‘how crucial it is for macroeconomic analysis to determine 

whether energy and capital are complements or substitutes’ (Vinals, 1984, p 238, italics original) 

3.2.2 Empirical Estimates of σEK

Despite the theoretical importance of the ıEK parameter, empirical estimates of this parameter 

must overcome many difficulties. Table 4 gives some indicative values of ıEK as estimated from 

various empirical studies. It can be seen from this Table that both the sign and magnitude of this 

parameter varies significantly between different studies.

The problem arises partly because energy-capital substitutability is a long-term 

adjustment process, and therefore, empirical estimates of ıEK must take into account the issue of 

how short-term energy usage can be dynamically adjusted to a ‘theoretically optimal’ level in the 

long run, based on the level of investment. Conversely, capital must also adjust to the expected 

level of energy prices in the long term. Hogan (1989) has shown that where a ‘correct’ 

specification of a dynamic capital-energy usage structure is specified, more meaningful and 

accurate estimates of the inter-fuel and energy-primary factor substitution elasticities can be 

achieved. The key to the problem of specification is that a model must be able to represent the 

flexibility (in energy usage) in the long run but also allow for rigidity or inflexibility in the short 

to medium term due to capital constraint: 

....responses to price changes take time. Although there is overwhelming evidence of 

great flexibility in the use of energy and other inputs, the most important changes in 

energy utilization depend upon changes in energy-using equipment. If this 

equipment changes slowly, then the full response to energy price changes will take 

many years to unfold... Initially, the price shocks have little effect on demand per 

unit of output; often the effects are so small as to suggest little response at all. But 

the new prices unleash forces that eventually produce dramatic changes in total 

energy demand...this demand response can be both a substantial break from trend 

and a confusing mixture of fuel substitutions. Analysis of this short-run record, in 

the search for insights into long-run possibilities, places great emphasis on the need 

for a description of the dynamics of energy demand adjustment15

.

Inflexibility in capital adjustment comes from technological factors (such as discrete or 

lumpy investments), as well as adjustment costs. To describe this ‘inflexibility’, one approach is 

to use a technology or process model. Alternatively, the long-term adjustment process of capital 

can also be specified directly in an economic model (such as in GREEN). However, it is not 

always easy to find empirical estimates for the parameters of these models, hence the uncertainty 

surrounding the extent of energy-capital substitutability or complementarity. 

15 Hogan (1989, p. 54) 
29

Table 8 Estimates of the Partial Hicks-Allen Elasticities of Substitution (ı) and Factor 

Shares (ı).

 US 

Berndt-Wood 

(1975)

US

Kulatilaka 

(1980)

US

Pindyck 

(1979)

Europe 

Pyndyck 

(1979)

Australia 

Truong 

(1985)

)KK -8.8 -2.75 -1.66 -0.98 -16.46 

)LL -1.5 -0.22 -1.19 -0.82 -1.388 

)EE -10.7 -2.70 -24.21 -13.16 -19.60 

)MM -0.39 -0.222 

)KL 1.01 0.69 1.41 0.69 1.02 

)KE -3.5 -1.09 1.77 0.60 -2.95 

)LE 0.68 0.61 0.05 1.13 1.77 

)KM 0.49 0.78 

)LM 0.61 0.42 

)EM 0.75 0.17 

L 0.289 0.76 0.478 0.526 0.263 

E 0.044 0.10 0.032 0.055 0.023 

K 0.046 0.14 0.488 0.409 0.044 

M 0.619 0.67 

K = Capital, L= Labor, E = Energy, M= Material. 

Source: Vinals (1984), Table 3, p. 242, and Truong (1985).

3.3 The Structure of Inter-fuel and Fuel-factor Substitution in GTAP-E 

3.3.1 Production Structure with Energy Substitution 

Based on the various structures of inter-fuel and fuel-factor substitutions adopted in other models 

as described in section 2, the following is suggested as a good option for GTAP-E. 

On the production side, energy16 must be taken out of the intermediate input ‘nest’ to be 

incorporated into the ‘value-added’ nest (see Figures 15 and 16). The incorporation of energy 

into the value-added nest is in two steps. First, following the structure in the CETM model as 

well as the Babiker-Maskus-Rutherford (1997) model, energy commodities are first separated 

into ‘electricity’ and ‘non-electricity’ groups. Some degree of substitution is allowed within the 

non-electricity group (ıNELY) as well as between the electricity and the non-electricity groups 

(ıENER). The values of these substitution elasticities are shown in Table 5. These are chosen to be 

in the middle range of the values adopted in other models. 

16 Primary energy (such as coal, gas, crude oil) can be used, not only as a source of energy input for various industrial 

and household activities (e.g. natural gas to provide the energy source for electricity production, coal as energy source 

for steel making), they can also be used as a ‘feedstock’. In this latter use, the chemical content of the energy input 

(such as natural gas) is simply ‘transformed’ to become part of the output commodity (such as fertilizer) rather than 

being ‘used up’ as an energy source. Similar examples are crude oil used as feedstock in the petroleum refinery 

industry, coke used as a feedstock in steel production, etc. 
30

Next, the energy composite is then combined with capital to produce an energy-capital 

composite17, which is in turn combined with other primary factors in a value-added-energy 

(VAE)

18 nest through a CES structure (See Figure 17). The substitution elasticity between capital 

and the energy composite (ıKE) is still assumed to be positive (indicating energy and capital are 

substitutes in the ‘inner nest’). However, provided the value of ıKE is set at a level lower than 

ıVAE, the overall substitution elasticity (as viewed from the ‘outer nest’) between capital and 

energy may still be negative (Borge and Goulder (1984, p. 340)). To be more precise, we can use 

the formula derived by Keller (1980, p. 83) which specifies the relationship between the ‘inner’ 

and ‘outer’ elasticity of substitution between K and E as follows: 

KE outer KE inner VAE SKE VAE SVAE σ = [σ −σ /] +σ / − −

 

where SKE is the cost share of the KE-composite in the outer (value-added) nest, and ıKE-inner and 

ıKE-outer indicate the inner and outer substitution elasticities between K and E respectively. 

Figure 15 Standard GTAP Production Structure 

17 The reason for a focus on the energy-capital composite was given in section 3.2. See also the discussion in section 

2.3.3 regarding the differences between energy-capital and energy-labor substitution. 

18 The term ‘value-added-energy’ is used to emphasize the fact that energy is now present in this nest. 

21 For details on the industry sector aggregation, see Table A1 of the Appendix. 

Output

Capital Foreign

σD

Value-added All other inputs 

(including energy inputs)

σ = 0

Land Labor

σVA

Domestic

σM

Region 1 Region ... r
31

Figure 16 GTAP–E Production Structure 

Figure 17 GTAP–E Capital-Energy Composite Structure 

Output

Capital-Energy

Composite

Foreign

σD

Value-added-Energy 

(Including energy inputs) 

All other inputs 

(Excluding energy inputs but 

including energy feedstock)

σ = 0

Lan Labor

σVAE

Domestic

Region 1 

σM

Natural 

Resource

s

Skille Uskilled

)LAB

... Region r 

σD

Capital-Energy Composite

Electric

Foreign

σD

Capital Energy Composite

σKE

σENER = 1.0

Domesti

c

σM

Non- Electric

Coal

σNELY =0.5

σM

Foreign

σD

Domestic

Region 1

...

...

Region 1

Region 

... Region r

...

σNCOL =1.0

Petroleum 

products

Oil

Non-Coal

Domestic Foreign

Region 1 Region 

Gas

σM
32

Table 9 Energy Substitution Elasticities in GTAP-E and Other Models SECTOR Capital-Energy (K-E) Inter-Fuel 

GTAP-E (e) 

SECTOR 

GTAP-E (a) GREEN (b) Rutherford (c) Electric vs 

Non-electric 

Coal vs other 

non-electric 

between non-coal, 

non-electric 

GREEN 

Coal 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Crude Oil 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Gas 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Petroleum, coal products 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Electricity 0.5 0.0 - 0.8 -(d)- 1.0 0.5 1.0 0.25 - 2.0 Ferrous metals 0.5 0.0 - 0.8 0.5 1.0 0.5 1.0 0.25 - 2.0 Chemical, rubber, plastic products 0.5 0.0 - 0.8 0.5 1.0 0.5 1.0 0.25 - 2.0 Other manufacturing; trade, transport 0.5 0.0 - 0.8 0.5 1.0 0.5 1.0 0.25 - 2.0 Agriculture, forestry, and fishery 0.0 0.0 - 0.8 0.5 1.0 0.5 1.0 0.25 - 2.0 Commercial/public services, dwellings 0.5 0.0 - 0.8 0.5 1.0 0.5 1.0 0.25 - 2.0 

For details on the sector aggregation, see Table A1 of the Appendix. aTo ensure capital and energy are complements in the short run, while substitutes in the long run, the elasticity of substitution between K and E aggregate must be set lower than the 

elasticity between K and other primary factors ()VAE). bIn the GREEN model, if the long-term elasticity between K and E is equal to 2.0 and the short run value set equal to 0.25, then the ‘intermediate’ term (approximately 5 years) 

elasticity - which depends on the vintage structure of the capital - will be about 0.8 (see Figure 5, Burniaux et al. (1992), p. 66). cIn Rutherford models, a value of 0.5 is set for substitution between energy composite and land-labor-capital composite in the non energy-producing industries (Babiker et al. (1997)), 

or between energy composite and labor-capital composite (Rutherford et al (1997), and Bohringer and Pahlke (1997)). dK-E substitution for the electricity industry is determined, not by an econometric parameter, but by the specification of alternative electricity-generation technologies in the ‘process 

model’. 

e This is based on the values of 1.0 chosen for the substitution between electric and non-electric, and between non-coal fossil fuels in (Babiker et al. (1997)), Rutherford et al. (1997). 

Bohringer and Pahlke (1997) however, chose a value of 2.0 for the substitution between non-coal fossil fuels. For substitution between coal and non-coal fossil fuels, Babiker et al.

(1997) chose a value of 0.5, whereas Bohringer and Pahlke (1997) chose a value of 0.25 if the non-coal aggregate includes electricity. 
33

In GTAP-E, the (inner) value of ıKE is assumed to be 0.5 for most industries21 (including 

electricity), and is set equal to 0.0 for coal, oil, gas, petroleum and coal products, and 

agriculture/forestry/fishery. This is based on the (low-to-middle) range of the values adopted by 

other models, such as the GREEN model, and the models used by Babiker et al. (1997), 

Rutherford et al. (1997), Bohringer and Pahlke (1997) (see Table 5). The value of ıVAE ranges 

from 0.2 to 1.45 and this seems to be slightly larger than the values adopted by other models (see 

Table 6), but these are the values currently used in the standard GTAP model. 

 Based on the values of SKE for some typical regions in the GTAP- 4E data base22, the 

‘outer’ values of ıKE are derived using the above formula and are shown in Table 7. From this 

Table, it can be seen that most industries (with the exception of ‘electricity’ in the USA, and 

‘electricity’, ‘ferrous metals’, and ‘chemical, rubber, plastic products’ in Japan) are characterized 

as having an overall complementarity relationship between energy and capital despite the fact 

that ıKE is still specified as non-negative within the energy-capital nest. 

Table 10 Elasticities of Substitution Between Different Factors of Production 

GREEN

Sector

GTAP-Ea

(VAE) L - KEFb E - KFc

Rutherfordd

Coal 0.2 0.0 0.0 1.0 

Crude Oil 0.2 0.0 0.0 1.0 

Gas 0.84 0.0 0.0 1.0 

Petroleum, coal products 1.26 0.0 0.0 1.0 

Electricity 1.26 0.0 0.0 - 0.8 1.0 

Ferrous metals 1.26 0.12 - 1.0 0.0 - 0.8 1.0 

Chemical, rubber, plastic products 1.26 0.12 - 1.0 0.0 - 0.8 1.0 

Other manufacturing; trade, transport 1.45 0.12 - 1.0 0.0 - 0.8 1.0 

Agriculture, forestry, and fishery 0.23 0.12 - 1.0 0.0 - 0.8 1.0 

Commercial/public services, dwellings 1.28 0.12 - 1.0 0.0 - 0.8 1.0 

a

 In GTAP-E: between land, natural resources, aggregate labor, and capital-energy composite. 

b

 Between labor (L), and energy-capital-fixed factor composite (EKF).

c

 Between energy (E) and capital-fixed factor composite (KF).

d

 Between land, labor, and capital (see Babiker et al. (1997)), or between labor and capital (Rutherford et

al (1997), and Bohringer and Pahlke (1997)).

22 See Malcolm and Truong (1999).
34

Table 11 The Relationship Between Inner ()KE-inner) and Outer )KE-outer) Elasticities of 

Substitution for the Cases of Japan and the US 

Sector Japan USA

KE-inner VAE SVAE SKE KE-outer SVAE SKE KE-outer

Coal 0.0 0.2 0.49 0.11 -1.50 0.67 0.16 -0.97 

Crude Oil 0.0 0.2 0.64 0.24 -0.52 0.69 0.34 -0.30 

Gas 0.0 0.84 0.97 0.95 -0.02 0.81 0.55 -0.49 

Petroleum, coal products 0.0 1.26 0.68 0.59 -0.28 0.91 0.88 -0.04 

Electricity 0.5 1.26 0.83 0.71 0.45 0.84 0.71 0.43

Ferrous metals 0.5 1.26 0.51 0.34 0.27 0.43 0.18 -1.35 

Chemical, rubber, plastic 

products 0.5 1.26 0.42 0.26 0.05 0.50 0.30 -0.05 

Other manufacturing; trade, 

transport 0.5 1.45 0.46 0.16 -2.65 0.51 0.18 -2.45 

Agriculture, forestry, and 

fishery 0.0 0.23 0.58 0.20 -0.77 0.46 0.26 -0.38 

Commercial/public 

services, dwellings 0.5 1.28 0.62 0.30 -0.58 0.63 0.23 -1.41 

Note: KE outer KE inner VAE SKE VAE SVAE σ = [σ −σ /] +σ / − −

, where SKE, σKE-inner are the cost share and substitution elasticity 

respectively for the capital-energy composite and SVAE, σVAE are the cost share and substitution elasticity respectively for the 

value-added-energy composite. 

 Finally, Tables 8 and 9 show the Armington elasticities for the substitution between 

domestic and imported good (ıD), and between imported goods from different regions (ıM). The 

values of ıD and ıM for GTAP-E are taken from the ‘standard’ GTAP model, and are seen to be 

lower than some of the values used in other models, such as those in Babiker et al. (1997). In 

studies which seek to simulate the trade effect of a ‘homogeneous energy commodity market’ 

(such as that for coal) in response to an energy-environmental shock (such as the imposition of a 

carbon tax), these Armington elasticities may play a crucial role. However, this issue is not 

considered in this paper.

Table 12 Elasticities of Substitution Between Domestic and Foreign Sources (σD)

Sector GTAP-E GREENb Rutherfordc

Low-High 

 Coal 2.80 4.0 2.0 

Crude Oil 10.0a ∞ ∞

Gas 2.80 4.0 2.0 

Petroleum, coal products 1.90 4.0 2.0 

Electricity 2.80 0.3 2.0 

Ferrous metals 2.80 2.0 4.0 – 8.0 

Chemical, rubber, plastic products 1.90 2.0 4.0 – 8.0 

Other manufacturing; trade, transport 2.59 2.0 4.0 – 8.0 

Agriculture, forestry, and fishery 2.47 3.0 4.0 – 8.0 

Commercial/public services, dwellings 1.91 2.0 4.0 – 8.0 

a This is higher than the standard value of 2.8 used in most GTAP applications. 

bBurniaux et al. (1992), p. 76. 

c Babiker et al. (1997), 
35
36

Table 13 Elasticities of Substitution Between Different Regions ()M)

Sector GTAP-E GREENb Rutherfordc

Low-High 

Coal 5.60 5.0 4.0 

Crude Oil 20.0a ∞ ∞

Gas 5.60 5.0 4.0 

Petroleum, coal products 3.80 3.0 4.0 

Electricity 5.60 0.5 4.0 

Ferrous metals 5.60 3.0 8.0 - 16.0 

Chemical, rubber, plastic products 3.80 3.0 8.0 - 16.0 

Other manufacturing; trade, transport 6.04 3.0 8.0 - 16.0 

Agriculture, forestry, and fishery 4.62 4.0 8.0 - 16.0 

Commercial/public services, dwellings 3.80 3.0 8.0 - 16.0 

a This is higher than the standard value of 5.6 used in most GTAP applications. 

bBurniaux et al. (1992), p. 76. 

c Babiker et al. (1997). 

3.3.2 Consumption Structure 

On the consumption side, the existing structure of GTAP assumes a separation of ‘private’ 

consumption from ‘government’ consumption (consumption by households of publicly provided 

goods) and private savings. Government consumption expenditure is then assumed to be CobbDouglas with respect to all commodities ()G = 1). In the GTAP-E model, energy commodities are 

separated from the non-energy commodities with a nested-CES structure as shown in Figure 18. 

If, however, the substitution elasticity )GEN given to the inner energy nest and )GENNE given to the 

outer nest are both equal to 1 (substitution elasticity )GNE in the non-energy nest is assumed to be 

equal to )G and is therefore also equal to 1), then the GTAP-E structure is equivalent to the 

original GTAP structure. In general, however, if )GEN ≠ )GENNE ≠ 1, then the GTAP-E structure 

allows for different substitution elasticities within the energy and non-energy sub-groups, as well 

as between the two groups. For the current version of GTAP-E, the following values are adopted: 

)GEN = 1, and )GENNE = 0.5. This structure is very similar to the structure of household demand 

given in Rutherford et al. (1997) (see Figure 3), and Bohringer and Pahlke (1997), except that in 

the model of Bohringer and Pahlke, a smaller value of 0.3 is used for substitution between energy 

and non-energy aggregates, and a higher value of 2 is used for substitution between fossil fuels 

(excluding coal). 
37

Figure 18 GTAP-E Government Purchases 

Household ‘private’ consumption (i.e. consumption of private goods) is assumed to be 

structured according to the constant-difference of elasticities (CDE) functional form in the 

existing GTAP model. If the energy commodities within the CDE structure have the same 

income and substitution parameters, then according to the theory of the CDE structure, these 

commodities can be aggregated into a single composite with the same parameters as that of the 

individual components. Currently, in fact, within the GTAP model, four of the five energy 

commodities (coal, oil, gas, and electricity) have similar parameters, which differ only from that 

of the ‘petroleum and coal products’. This implies we can aggregate the energy commodities into 

a composite which remains in the CDE structure and has the same (or the average of the) CDE 

parameter values characterizing the individual energy commodities. To allow for flexible 

substitution between the individual energy commodities, the energy composite is now specified 

as a CES sub-structure, with a substitution elasticity of )PEN = 1 (see Figure 19) which is similar 

to the value given to )GEN (see Figure 18). This is the same as the value adopted in Rutherford et

al. (1997) (see Figure 3) and consistent with the medium term value adopted in the GREEN 

model (see section 2.3.2). 

Demand for composite 

goods

Domestic Foreign

σGNE = 1

Energy composite Non-energy composite

σGENNE = 0.5 

Region r

σD

....

σGEN = 1

Coal

σM

.... .... .... .... ....

Region r
38

Figure 19 GTAP-E Household Private Purchases 

 To better characterize the behavior of GTAP-E in comparison with GTAP, it is worth 

calculating the overall general equilibrium elasticities in both models (see Annex 1). GE 

elasticities depend on the structure of the model, the value of the substitution parameters and the 

particular closure assumed. They also depend on the benchmark database. The elasticities in 

Annex 1 have been calculated by using the version 4 of the GTAP data base. Thus the elasticities 

reported in Annex 1 are primarily to illustrate the behavioral implications of introducing interfuel substitution. Since these elasticities are also dependent on the base data, they are different in

the current version of the model that is based on the version 5 of the GTAP data base. 

4 .Illustrative Scenario 

GTAP-E has been specifically designed to simulate policies in the context of Greenhouse 

Gas (GHG) mitigation. This is best illustrated by using GTAP-E (based on GTAP Version 5 Data 

Base) to simulate the Kyoto Protocol. By signing this Protocol in 1997, a number of 

industrialized countries – referred to hereafter as Annex 1 countries – committed themselves to 

reduce their GHGs emissions relative to their 1990 levels. Initially, the Protocol aimed at 

ambitious reductions: the total emissions of Annex 1 countries were planned to be brought down 

in 2012 by 5 per cent below their 1990 levels. The Protocol made provision for country specific 

targets. A number of so-called “flexibility mechanisms” were also provided in order to allow 

emission reductions to be reallocated among Annex 1 countries. The “Emission Trading” (ET) 

Household demand for 

Private Goods

Domestic Foreign

Energy composite

Å Non-energy commodities Æ

CDE

Region r

σD

....

σPEN = 1

Coal

σM

.... ....

Region r

Domestic Foreign

Region r

....

σM

Region r

σD
39

mechanism and the “Joint Implementation” (JI) mechanism aimed at reallocating the burden of 

the emission reductions among Annex 1 countries. In contrast, the “Clean Development 

mechanism” (CDM) would allow Annex 1 countries to fund emission reductions in non-Annex 1 

countries.

However, the initial impetus of the Protocol rapidly faded away. While subsequent COP 

(Conferences of Parties) meetings struggled with intricate methodological and implementation 

issues, emissions in most Annex 1 countries were growing well beyond the Kyoto targets. As 

time passed, the Kyoto objectives increasingly appeared out of range to some Annex 1 members -

- particularly the USA. In March 2001, the USA decided to withdraw from the Protocol. Though 

the remaining Annex 1 countries reiterated their commitment to implement the Protocol in Bonn, 

it is most likely that the US withdrawal will make the Protocol aggregate constraint nearly nonbinding at the level of the remaining Annex 1 countries23

.

The scenarios discussed in this section are primarily illustrative. Specific limitations include, 

firstly that they refer to the initial version of the Protocol, including the US. Secondly, they only 

consider emissions of carbon dioxide while the Protocol covers a basket of GHGs and includes 

net emissions from land use changes. Thirdly, the use of the flexibility mechanisms is 

approximated by assuming unrestricted emission trading leading to complete equalization of the 

marginal of costs of abatement among participating countries, an outcome that is most unlikely 

given the real-world limitations associated with flexibility mechanisms. Finally, the Protocol is 

simulated in a static framework that leaves aside all aspects related to the timing of its 

implementation. 

4.1 Alternative Implementations of the Kyoto Protocol 

Three scenarios are considered. The first one is the “no trade” case. Here, Annex 1 countries 

meet their commitments individually without relying on the use of the flexibility mechanisms. 

The applied emission constraints correspond to the reductions that Annex 1 countries are forecast 

to achieve in 2012 – i.e. the first commitment period of the Protocol – relative to their 

corresponding emission levels in an unconstrained baseline scenario. Since this information 

requires using a dynamic model with an explicit time dimension, it is not readily available in 

GTAP-E. The emission constraints used here are taken from the OECD GREEN model (OECD, 

1999, p. 29). In the second scenario, unrestricted emission trading among Annex 1 countries 

approximates the use of ET and JI mechanisms (“Annex 1 trade” case). The total emission 

constraint applied to Annex 1 countries in the second scenario is the same as in the first one, 

augmented by the amount of “hot air”24 from the Former Soviet Union. The third scenario 

assumes that carbon emissions are traded worldwide without any restriction (“world trade” case). 

The constraint applied to world emissions is the sum of the Annex 1 commitments and of the 

benchmark emission levels for the non-Annex1 countries. 

23 This is because the emission surplus originating from the economic recession in the Former Soviet Union – often 

referred to as “hot air” – suffices to compensate the reductions to be achieved in the remaining Annex 1 countries. 

24 If Emission Trading is used, the emission surplus in the Former Soviet Union can be, in principle, transferred to 

other Annex 1 Parties at no cost. In this scenario, the amount of “hot air” in the Former Soviet Union is assumed equal 

to 100 million tons of carbon or 13 percent of the 1997 emission levels of the EEFSU region. 
40

Table 10 reports the emission changes relative to the benchmark levels and the 

corresponding marginal abatement costs of meeting the emission limitations. In the no-trade case, 

emission reductions range from 20 to almost 40 percent. These relatively sharp reductions reflect 

the fast growth rates of emissions, as observed in many Annex 1 countries since 1990, the 

reference year of the Protocol. The GREEN model makes the assumptions that these rates will 

remain almost unchanged during the first decade of the 21st century. The marginal abatement 

costs corresponding to these reductions range from $126 in the US to $233 in Japan (where these 

are 1997 US dollars). These costs are in the range of estimates from other studies (see Weyant 

and Hill, 1999; OECD, 1999). Marginal costs are lower in the US than in other Annex 1 

countries – despite the higher reduction rate – because the US uses relatively more coal and taxes 

energy less heavily. In more carbon-efficient countries, such as Japan, the marginal abatement 

costs rise faster, other things being equal. 

The first column of Table 10 shows that while emissions are reduced in Annex 1 countries 

that are subject to binding constraints, they increase in the other countries, a phenomenon that 

used to be referred to as “carbon leakage”. The causes of carbon leakage are multiple and 

involve competitiveness effects as well as the reactions of the world energy markets25. In this 

scenario, the leakage rate – defined as the additional emissions in countries with no binding 

constraint relative to the emission reductions in countries with binding constraints – amounts to 7 

per cent including the EEFSU region and 4 percent, excluding EEFSU26

Allowing unrestricted trade among Annex 1 countries shifts the burden of the reduction away 

from oil products in the relatively carbon-efficient economies (USA, EU, JPN, and RoA1) 

towards coal in the Former Soviet Union. This induces a substantial reduction of the marginal 

abatement costs: from around $150 in the no-trade case to $78 in the “Annex 1 trade” case). 

These cost savings imply that the EEFSU region sells about 300 million tons of carbon per year 

to other Annex 1 Parties, the largest single share of which is purchased by the USA (see Figure 

20). This represents a transaction worth $24 billion per year.

The right-hand section of Table 10 shows the results from a hypothetical worldwide emission 

trading system. In this case, the largest reduction takes place in the CHIND region (China and 

India) while the Annex 1 countries account for less than half of the world reduction. The world 

marginal abatement cost does not exceed $30 per ton of carbon. At this price, around 650 million 

tons of carbon are traded each year, with China and India accounting for the largest sale share 

and the USA buying more than half of these emissions (see Figure 21). 

25 See Burniaux and Oliveira-Martins (2002) for an analytical assessment of these effects. 

26 Emission trading among Annex 1 counties implies that constraint of the EEFSU region becomes effective

as part of the Annex 1 total constraint while this constraint is not binding in the “no trade” scenario. As a 

result, Annex 1 emissions increase “ex post” relative to their levels in the “no trade” scenario by an amount 

equal to the “hot air” less the leakage that would occur in the EEFSU in the “not trade” case. In the same 

way, world emissions in the “world trade” case are higher than in the “no trade” case by an amount equal to 

the “hot air: less the total leakage generated in the EEFSU and in the non-Annex 2 regions in the “no trade” 

case. As for the non-Annex 1 regions, this might not be realistic as most analysts recognize that the Clean 

Development Mechanisms is not going to prevent carbon leakages. 
41

Figure 20 : Emission trading among Annex 1 

countries

-350

-250

-150

-50

50

150

250

350

Million tons of carbon

USA

EU

JPN

RoA1

positive figures are sales; negative figures are purchases

EEFSU

hot air

Figure 21 : Worldwide emission trading

-700

-500

-300

-100

100

300

500

700

Million tons of carbon

positive figures are sales; negative figures are purchases

USA

EU

JPN

RoA1

EEFSU

hot air

EEX

CHIND

RoW
42

Table 14 Marginal Costs of Achieving the Kyoto Targets with and Without Using the Flexibility Mechanisms

Kyoto with No Use of the Marginal 

Costs Kyoto with Emission Trading Kyoto with Worldwide Marginal Costs 

% Reduction of Emissions 

(1997 USD per Ton of Carbon) 

% Reduction of Emissions 

(1997 USD per Ton of Carbon) 

% Reduction of Emissions 

(1997 USD per Ton of Carbon) 

USA -36 126 -27 78 -13 30 EU -22 147 -14 78 -6 30 EEFSU 4 0 -27 76 -13 30 JPN -32 233 -15 78 -6 30 RoA1 -36 178 -21 78 -9 30 EEx 3 0 2 0 -7 30 CHIND -1 0 -1 0 -32 29 RoW 4 0 4 0 -9 30 Annex 1 -24 -22 -10 Non-Annex 1 2 1 -19 Leakage rate (incl. EEFSU) 7.1% na na Leakage rate (incl. EEFSU) 4.0% 3.7% na 

Note that the marginal costs are expressed in real terms (i.e. deflated by the GDP deflator of each country/region). Therefore, slightly different marginal costs in case of 

emission trading are consistent with a common trading price of nominal terms 
43

4.2 Macroeconomic Results 

 Table 11 reports the macroeconomic costs of implementing the Kyoto Protocol in terms 

of the percentage change in per capita utility of the representative household and the associated 

terms-of-trade changes. If the flexibility mechanisms are not used, the costs for the Annex 1 

Parties (measured in terms of utility of the representative regional household) ranges from 0.25 

per cent in the USA to 1.3 per cent in the RoA1 region. The higher cost in the RoA1 region is 

partly explained by the degradation of the terms-of-trade related to the fact that many countries 

belonging to this region are net energy exporters. In contrast, in the net energy-importing, Annex 

1 economies, the costs of imposing carbon restrictions are partly mitigated by terms-of-trade 

improvements associated with the reduction in international energy prices – particularly for oil. 

The EEFSU region loses 0.4 % of its welfare despite the fact that it has no carbon constraint to 

comply with; this loss is entirely explained by the fall of the energy exports value. Interestingly, 

some non-Annex 1 countries/regions might even lose more than the Annex 1 countries following 

the implementation of the Kyoto Protocol. This is clearly the case for the energy exporters (EEx). 

 Emission trading among Annex 1 countries (see the middle columns of Table 11) 

reduces the losses in all Annex 1 countries while generating substantial gains (+ 2.8 percent) in 

the EEFSU region. It also contributes to a reduction in the losses incurred by the non-Annex 1 

energy exporters as it shifts the burden of the reduction from oil towards coal and therefore 

implies a lower fall of the international oil price. A worldwide emission trading system would 

contribute to a reduction in the economic costs for the Annex 1 countries and energy exporters, 

while generating net gains in China, India and the EEFSU region. 

 Figures 22 to 23 summarize the real income changes (in terms of equivalent variation) 

implied by the three alternative implementations of the Kyoto Protocol and provide a 

decomposition of the real income variations into terms-of-trade and allocative27 effects. The most 

noticeable outcome is that substantial cost saving can be achieved by allowing emissions to be 

traded. Annex 1 trading would cut the aggregate world real income loss by a half ($110 billion 

(1997 USD) to $50 billion) and a worldwide trading system would further reduce the cost by 

another half (from $50 billion to less than $25 billion). It must also be noted that almost every 

party has a vested interest in some form of emission trading (with the noticeable exception of the 

RoW region) though the Former Soviet Union has an unambiguous interest in restricting trading 

to Annex 1 countries only. 

27 In Figures 22 to 24, allocative effects include pure losses from less efficient allocations of production and 

consumption as well as the real income benefits and losses from the sales and purchases of carbon emissions. 
44

Figure 22 : Welfare decomposition of implementing the Kyoto Protocol with no 

use of the flexibility mechanisms

-120

-100

-80

-60

-40

-20

0

20

40

USA EU EEFSU JPN RoA1 EEx CHIND RoW A1 N-A1 World

Terms of trade eff.

Allocative eff.

Figure 23 : W elfare decom position of im plementing the Kyoto Protocol with 

trading am ong Annex 1 countries

-60

-50

-40

-30

-20

-10

0

10

20

30

USA EU EEFSU JPN RoA1 EEx CHIND RoW A1 N-A1 World

Terms of trade eff.

Allocative eff.

Table 15 Macroeconomic Impacts of Implementing the Kyoto Protocol: Percent change 

in welfare (in ) and terms of trade (tot) 

 Kyoto With No Use of the 

Flexibility Mechanisms 

Kyoto with Emission Trading 

Among Annex 1 Countries 

only 

Kyoto with Worldwide 

Emission Trading 

USA -0.25 0.96 -0.26 0.54 -0.16 0.18 

EU -0.48 0.33 -0.27 0.20 -0.06 0.12 

EEFSU -0.41 -0.87 2.75 0.92 0.66 0.05 

JPN -0.61 1.34 -0.27 0.66 -0.07 0.43 

RoA1 -1.30 -0.65 -0.86 -0.56 -0.42 -0.40 

EEx -1.00 -3.02 -0.73 -2.19 -0.53 -1.47 

CHIND 0.08 0.03 0.05 -0.01 0.44 -080 

RoW 0.16 0.26 0.13 0.22 0.10 0.32 
45

Figure 24 : Welfare decomposition of implementing the Kyoto Protocol with 

worldwide emission trading

-25

-20

-15

-10

-5

0

5

10

USA EU EEFSU JPN RoA1 EEx CHIND RoW A1 N-A1 World

Terms of trade eff.

Allocative eff.

5. Conclusion 

This technical paper has surveyed some existing CGE models which deal with the issue 

of energy substitution. Important features of these models are highlighted, and where 

possible, some of these important features have been adapted into the existing standard 

GTAP model. The result in the model, nick-named GTAP-E is then used to conduct some 

alternative scenarios involving implementation of the Kyoto Protocol. The main purpose 

of these experiments is to highlight the suitability of the GTAP-E model in analyzing the 

implications of alternative strategies to reduce GHG emissions. The introduction of the 

energy-environmental dimension in GTAP is only one step towards the elaboration of a 

GTAP framework that is suitable to analyze GHG issues. It is hoped that the current 

version of GTAP-E could be further extended in order to incorporate some other aspects, 

such as the complex relationship between land uses and GHG emissions.
46

! closure with exogenous trade balances 

exogenous 

 pop 

 psaveslack pfactwld 

 profitslack incomeslack endwslack 

 tradslack 

 ams atm atf ats atd 

 aosec aoreg avasec avareg 

 afcom afsec afreg afecom afesec afereg 

 aoall afall afeall 

 au dppriv dpgov dpsave 

 to tp tm tms tx txs 

 qo(ENDW_COMM,REG) 

 RCTAX 

 MARKCTAX 

 dcwfd(NEGYCOM3,PROD_COMM,REG) 

 dcwfd(COALS,COALS,REG) 

 dcwfd(OILS,OILEXS,REG) 

 dcwfd(GASS,GASEXS,REG) 

 dcwfd(OIL_PCS,OIL_PCEXS,REG) 

 dcwfi(NEGYCOM3,PROD_COMM,REG) 

 dcwfi(COALS,COALS,REG) 

 dcwfi(OILS,OILEXS,REG) 

 dcwfi(GASS,GASEXS,REG) 

 dcwfi(OIL_PCS,OIL_PCEXS,REG) 

 dcwpd(NEGYCOM3,REG) 

 dcwpi(NEGYCOM3,REG) 

 dcwgd(NEGYCOM3,REG) 

 dcwgi(NEGYCOM3,REG) 

 c_CTAXBAS(REG,NEGYCOM3B) 

! DTBAL exogenous for all regions except one, 

! and cgdslack exogenous for that one region (which can be any one). 

 dtbal("USA") 

 dtbal("EU") 

 dtbal("EEFSU") 

 dtbal("JPN") 

 dtbal("RoA1") 

 dtbal("EEx") 

 dtbal("CHIND") 

 cgdslack("RoW") ; 

Rest Endogenous ; 

swap gco2t("USA")=RCTAX("USA"); 

swap gco2t("EU")=RCTAX("EU"); 

swap gco2t("JPN")=RCTAX("JPN"); 

swap gco2t("RoA1")=RCTAX("RoA1"); 

Shock gco2t("USA") = -35.6; 

Shock gco2t("EU") = -22.4; 

Shock gco2t("JPN") = -31.8; 

Shock gco2t("RoA1") = -35.7; 
47

Annex 1 General Equilibrium Elasticities in GTAP-E and 

GTAP 

To compare GTAP-E with GTAP, the simplest and most effective way is to compare the overall 

general-equilibrium (GE) elasticities of the GTAP-E model with those of the GTAP model. The 

GE elasticities are a function of the structure of the model, the values of the substitution 

parameters assumed, the benchmark database and the particular closure assumed28. For a 

standard GE closure where all the prices and quantities of non-endowment commodities are 

allowed to be endogenously determined, the GE elasticities calculated for this closure will truly 

reflect the general equilibrium character of the demand elasticities29

.

First we look at the GE own-price elasticities. These elasticities measure the percentage 

change in the output of commodity i in region r (i.e. qo(i,r)) following a 1% change in its ownprice (pm(i,r)) induced by an appropriate perturbation in the output tax to(i,r). The change in the 

output level can come from two different causes: (i) changes in the general level of activity (we 

can refer to this as the “output (expansion or contraction) effect”), and (ii) changes due to the 

substitution of one input or commodity for another (the “substitution effect”30).

For the energy commodities, because of the additional (energy) input-substitution 

structure introduced into the GTAP-E model, we expect the negative “substitution effect” in this 

model to add to the negative “output effect” when the price of an energy commodity increases. 

This means the magnitude of the GE own-price elasticities for energy commodities in the GTAPE model is likely to be greater than those in the GTAP model. This is in fact confirmed in Table 

10: the changes in the GE elasticities for the energy commodities are all negative when we go 

from GTAP to GTAP-E, indicating that the magnitudes of the (negative) elasticities are all 

increasing. 

For the non-energy commodities, on the other hand, since both the GTAP and GTAP-E 

models have similar structures for these commodities, we will expect that there are insignificant 

changes in the GE own-price elasticities as we move from GTAP to GTAP-E. From Table 10, 

this is again confirmed: the small variations in the magnitudes of these elasticities for the nonenergy commodities arise only from the output (expansion/contraction) effects and which are 

seen to be small. Also, the variation can be in either direction. 

Tables 11 and 12 give the GE cross-price elasticities for the US and China for 

illustrative purposes. For both of these countries, we notice that all energy commodities are 

substitutes (cross-price elasticities being positive), with the exception of the pairs: COL and 

ELY, and OIL and P_C. These pairs of energy commodity are complements because COL is a 

significant input into ELY, and similarly OIL is a significant input into P_C. 

As we move from GTAP to GTAP-E, the magnitudes of the cross-price GE elasticities 

for the energy commodities become greater, as expected. This is in contrast to the case of the GE 

28 As the GE elasticities are a function of the particular closure assumed, in this section, we present the GE elasticities 

which are associated with the experiment considered in the next section. Changing this experiment and its closure will 

affect the GE elasticities. 

29 See Chapter 5 of Hertel (ed.) (1997). 

30 Here substitution can occur between different outputs (i.e. in final demand) as well as between different inputs

(intermediate demand).
48

cross-price elasticities for the non-energy commodities. In the latter case, since both GTAP and 

GTAP-E assume similar structures for these non-energy commodities, their corresponding GE 

cross-price elasticities as thus also similar31

.

Finally, between the energy and non-energy commodities, we notice a significant degree 

of complementarity (negative cross-price elasticities) between P_C and ELY on the one hand, 

and the non-energy commodities on the other hand. This reflects the importance of P_C and ELY 

as major energy inputs into the production of these non-energy commodities. 

31 The non-energy commodities are also observed to be all ‘substitutable’ for each other despite the fact that in the 

intermediate input sub-structure, zero substitution was assumed between these non-energy intermediate inputs. The 

‘substitution’ as reflected in the GE cross-price elasticities, however, reflects mainly the output (contraction/expansion) 

effects, which come from a re-allocation of resources resulting from a change of the relative prices among these 

commodities. 
49

Table A1-1 General-Equilibrium Own-Price Elasticities

GE Elasticities WITH Energy Substitution from GTAP-E Model (A): 

Sectors/ 

Commodities JPN CHN IND USA E_U FSU NEX NEM 

COL -3.75 -0.43 -0.07 -0.85 -1.19 -1.59 -1.22 -1.38

OIL -9.88 -3.02 -9.39 -3.33 -7.09 -5.27 -0.88 -7.39

GAS -1.69 -1.03 -0.72 -0.94 -1.46 -1.68 -1.27 -1.18

P_C -0.91 -0.83 -1.13 -0.97 -0.91 -1.28 -1.28 -1.05

ELY -0.84 -1.00 -0.79 -0.82 -1.15 -1.07 -1.21 -1.15

I_S -0.47 -0.86 -1.09 -0.78 -1.00 -2.83 -1.66 -1.78

CRP -0.50 -1.02 -1.15 -0.95 -0.96 -1.27 -1.40 -1.26

OMN -0.75 -1.66 -1.43 -0.89 -0.87 -1.34 -1.40 -1.46

AGR -0.40 -0.32 -0.24 -0.67 -0.59 -0.99 -0.55 -0.56

SER -0.25 -0.27 -0.30 -0.32 -0.31 -0.30 -0.37 -0.35

GE Elasticities WITHOUT Energy Substitution from GTAP Model (B): 

Sectors/ 

Commodities JPN CHN IND USA E_U FSU NEX NEM 

COL -3.71 -0.40 -0.02 -0.26 -0.69 -1.14 -0.81 -1.03

OIL -9.82 -2.16 -9.13 -1.92 -4.70 -3.58 -0.24 -6.05

GAS -1.20 -0.03 0.00 -0.27 -0.92 -1.13 -0.65 -0.47 

P_C -0.41 -0.32 -0.79 -0.40 -0.50 -0.85 -0.90 -0.54

ELY -0.22 -0.08 -0.03 -0.16 -0.34 -0.33 -0.48 -0.27

I_S -0.47 -0.85 -1.09 -0.78 -1.00 -2.82 -1.66 -1.78

CRP -0.50 -1.03 -1.16 -0.95 -0.96 -1.27 -1.40 -1.26

OMN -0.80 -1.59 -1.62 -0.93 -0.84 -1.41 -1.38 -1.48

AGR -0.40 -0.31 -0.24 -0.67 -0.59 -0.99 -0.54 -0.56

SER -0.25 -0.25 -0.29 -0.32 -0.29 -0.31 -0.37 -0.34

Change in Own-Price Elasticity from (B) to (A) 

Sectors/ 

Commodities 

JPN CHN IND USA E_U FSU NEX NEM 

COL -0.04 -0.03 -0.05 -0.59 -0.50 -0.45 -0.41 -0.35

OIL -0.06 -0.86 -0.26 -1.41 -2.39 -1.69 -0.64 -1.34

GAS -0.49 -1.00 -0.72 -0.67 -0.54 -0.55 -0.62 -0.71

P_C -0.50 -0.51 -0.34 -0.57 -0.41 -0.43 -0.38 -0.51

ELY -0.62 -0.92 -0.76 -0.66 -0.81 -0.74 -0.73 -0.88

I_S 0.00 -0.01 0.00 0.00 0.00 -0.01 0.00 0.00 

CRP 0.00 0.01 0.01 0.00 0.00 0.00 0.00 0.00 

OMN 0.05 -0.07 0.19 0.04 -0.03 0.07 -0.02 0.02 

AGR 0.00 -0.01 0.00 0.00 0.00 0.00 -0.01 0.00 

SER 0.00 -0.02 -0.01 0.00 -0.02 0.01 0.00 -0.01 
50

Table A1.2 General-Equilibrium Cross-Price Elasticities for the USA 

GE Cross-price Elasticities WITH Energy Substitution from GTAP-E Model (A): 

Sectors/ 

Commodities COL OIL GAS P_C ELY I_S CRP OMN AGR SER 

COL 0.06 0.00 0.03 -0.15 -0.01 -0.01 0.14 -0.03 0.03 

OIL 0.01 0.01 -0.21 0.05 0.01 0.01 0.52 0.02 0.06 

GAS 0.00 0.14 0.16 0.09 -0.01 0.04 0.47 -0.13 0.11

P_C 0.02 -0.51 0.03 0.13 -0.02 -0.13 -0.94 -0.03 0.14 

ELY -0.07 0.10 0.01 0.10 -0.01 -0.02 0.20 -0.12 0.09 

I_S -0.01 0.04 0.00 -0.04 -0.03 0.06 0.21 0.04 0.32 

CRP 0.00 0.02 0.00 -0.06 -0.01 0.01 0.90 0.03 0.36

OMN 0.00 0.02 0.00 -0.02 0.00 0.00 0.04 0.01 0.35 

AGR -0.01 0.03 -0.01 -0.02 -0.08 0.01 0.04 0.28 0.18 

SER 0.00 0.00 0.00 0.01 0.00 0.01 0.03 0.56 0.01 

Sectors/ GE Cross-price Elasticities WITHOUT Energy Substitution from GTAP Model (B): 

Commodities COL OIL GAS P_C ELY I_S CRP OMN AGR SER 

COL 0.02 0.00 0.00 -0.09 -0.01 -0.01 0.40 -0.05 0.13 

OIL 0.00 0.00 -0.11 -0.01 0.01 0.01 0.81 0.02 0.15

GAS 0.00 0.02 0.00 -0.06 -0.01 0.02 0.50 -0.11 0.19 

P_C 0.00 0.02 0.00 0.00 -0.01 -0.12 -0.29 -0.01 0.36 

ELY 0.00 0.01 0.00 0.00 -0.01 -0.03 0.19 -0.10 0.14 

I_S 0.00 0.03 0.00 -0.02 -0.03 0.06 0.21 0.04 0.33

CRP 0.00 0.02 0.00 -0.01 -0.01 0.02 1.00 0.03 0.36

OMN 0.00 0.02 0.00 -0.01 -0.01 0.00 0.04 0.01 0.37

AGR 0.00 0.02 0.00 -0.01 -0.02 0.01 0.03 0.26 0.19

SER 0.00 0.00 0.00 0.01 0.01 0.01 0.03 0.62 0.01 

Sectors/ Absolute difference:(A) - (B) 

Commodities COL OIL GAS P_C ELY I_S CRP OMN AGR SER 

COL 0.04 0.00 0.03 -0.06 0.00 0.00 -0.26 0.02 -0.10 

OIL 0.01 0.01 -0.10 0.06 0.00 0.00 -0.29 0.00 -0.09 

GAS 0.00 0.12 0.16 0.15 0.00 0.02 -0.03 -0.02 -0.08 

P_C 0.02 -0.53 0.03 0.13 -0.01 -0.01 -0.65 -0.02 -0.22 

ELY -0.07 0.09 0.01 0.10 0.00 0.01 0.01 -0.02 -0.05 

I_S -0.01 0.01 0.00 -0.02 0.00 0.00 0.00 0.00 -0.01 

CRP 0.00 0.00 0.00 -0.05 0.00 -0.01 -0.10 0.00 0.00 

OMN 0.00 0.00 0.00 -0.01 0.01 0.00 0.00 0.00 -0.02

AGR -0.01 0.01 -0.01 -0.01 -0.06 0.00 0.01 0.02 -0.01 

SER 0.00 0.00 0.00 0.00 -0.01 0.00 0.00 -0.06 0.00 
51

Table A1-3 General-Equilibrium Cross-Price Elasticities for China

Sectors/ GE Cross-price Elasticities WITH Energy Substitution from GTAP-E Model (A): 

Commodities COL OIL GAS P_C ELY I_S CRP OMN AGR SER 

COL 0.05 0.01 0.04 -0.01 0.02 0.04 1.19 0.06 0.01 

OIL 0.01 0.00 -0.11 0.04 0.03 0.03 1.97 0.06 0.05 

GAS 0.16 0.19 0.22 0.07 0.03 -0.30 0.60 0.01 0.02 

P_C 0.03 -0.50 0.01 0.14 -0.04 -0.20 -2.01 -0.11 0.00 

ELY -0.01 0.16 0.00 0.14 -0.06 -0.13 -0.30 -0.03 0.01 

I_S 0.01 0.06 0.00 -0.02 -0.03 0.14 2.12 0.21 -0.03 

CRP 0.01 0.03 0.00 -0.06 -0.04 0.09 2.61 0.05 0.06

OMN 0.01 0.07 0.00 -0.02 -0.01 0.03 0.07 0.09 0.05

AGR 0.00 0.01 0.00 -0.01 -0.01 0.03 0.01 0.76 0.12

SER 0.00 0.01 0.00 0.00 0.00 0.00 0.02 0.73 0.08 

Sectors/ GE cross-price elasticities WITHOUT energy substitution from GTAP model (B): 

Commodities COL OIL GAS P_C ELY I_S CRP OMN AGR SER 

COL 0.01 0.00 0.00 0.00 0.03 0.05 1.10 0.04 0.00 

OIL 0.00 0.00 -0.05 0.00 0.04 0.04 2.68 0.09 0.06 

GAS 0.01 0.04 0.00 -0.01 0.02 -0.40 0.85 0.03 0.08 

P_C 0.00 0.04 0.00 -0.01 -0.01 -0.18 0.40 0.03 0.08 

ELY 0.00 0.04 0.00 0.00 -0.07 -0.13 0.39 0.05 0.06

I_S 0.00 0.05 0.00 -0.01 -0.01 0.15 2.26 0.21 -0.04 

CRP 0.01 0.05 0.00 0.00 0.00 0.08 2.71 0.05 0.05 

OMN 0.01 0.05 0.00 -0.01 -0.01 0.05 0.09 0.10 0.05

AGR 0.00 0.03 0.00 0.01 0.01 0.02 0.00 0.98 0.13 

SER 0.00 0.01 0.00 0.01 0.01 -0.02 0.00 0.89 0.09 

Sectors/ Absolute difference:(A) - (B) 

Commodities COL OIL GAS P_C ELY I_S CRP OMN AGR SER 

COL 0.04 0.01 0.04 -0.01 -0.01 -0.01 0.09 0.02 0.01 

OIL 0.01 0.00 -0.06 0.04 -0.01 -0.01 -0.71 -0.03 -0.01 

GAS 0.15 0.15 0.22 0.08 0.01 0.10 -0.25 -0.02 -0.06 

P_C 0.03 -0.54 0.01 0.15 -0.03 -0.02 -2.41 -0.14 -0.08 

ELY -0.01 0.12 0.00 0.14 0.01 0.00 -0.69 -0.08 -0.05 

I_S 0.01 0.01 0.00 -0.01 -0.02 -0.01 -0.14 0.00 0.01 

CRP 0.00 -0.02 0.00 -0.06 -0.04 0.01 -0.10 0.00 0.01 

OMN 0.00 0.02 0.00 -0.01 0.00 -0.02 -0.02 -0.01 0.00 

AGR 0.00 -0.02 0.00 -0.02 -0.02 0.01 0.01 -0.22 -0.01 

SER 0.00 0.00 0.00 -0.01 -0.01 0.02 0.02 -0.16 -0.01 
52

Annex 2 Specifying Country-specific Carbon Reductions 

with no Emission Trading in GTAP-E. 

The following box shows the closure and shocks used to simulate the “no-trade” case. 

This scenario assumes no change of the trade account: thus the variable DTBAL (a linear 

variable expressed in changes) is exogenous and equal to zero in all countries/regions except one. 

Accordingly, the slack variable cgdslack is made endogenous (while it is exogenous in the 

standard closure). Thus investment is calculated as a residue in order to guarantee no change of 

the trade account. The quantitative restrictions applied to carbon emissions are introduced by 

making the real carbon tax RCTAX (i.e. the nominal carbon tax deflated by the GDP deflator) 

endogenous and the emission growth rates gco2t exogenous and equal to the Kyoto commitments 

(expressed as a percentage reduction relative to the corresponding emission levels in 2010 in a 

scenario with no constraints). Alternatively, one might impose an exogenous real or nominal 

carbon tax (RCTAX or NCTAX) and leave the emission growth rates to be determined 

endogenously. 

 An accompanying program calculates the Social Account Matrices (SAMs). The Table 

A2-1 below shows the SAM of the US after the emission constraint has been applied. The best 

way to interpret the income flows associated to the restriction is to assume that the restriction is 

imposed through a domestic market of emission rights. The row CAG shows the revenues that 

are perceived by some kind of centralized Carbon Agency from selling emission permits. The 

total proceeds of these sales amounts to 124 billion 1997 USD, two thirds of which originate 

from sales to the electricity sector (42 billion 1997 USD) and to the other industries and services 

(40 billion 1997 USD). Thus, in the electricity sector, purchases of emission permits would 

amount up to 15 per cent of all electricity sales. The total proceeds from domestic permit sales 

are then refunded to the Regional Household (see the entry of 124 billion 1997 USD paid by of 

the RHH). 
53

Box A.2.1 Closure and Shocks for No Trading Scenario 

! closure with exogenous trade balances 

exogenous 

 pop 

 psaveslack pfactwld 

 profitslack incomeslack endwslack 

 tradslack 

 ams atm atf ats atd 

 aosec aoreg avasec avareg 

 afcom afsec afreg afecom afesec afereg 

 aoall afall afeall 

 au dppriv dpgov dpsave 

 to tp tm tms tx txs 

 qo(ENDW_COMM,REG)

 RCTAX 

 MARKCTAX 

 dcwfd(NEGYCOM3,PROD_COMM,REG) 

 dcwfd(COALS,COALS,REG) 

 dcwfd(OILS,OILEXS,REG) 

 dcwfd(GASS,GASEXS,REG) 

 dcwfd(OIL_PCS,OIL_PCEXS,REG) 

 dcwfi(NEGYCOM3,PROD_COMM,REG) 

 dcwfi(COALS,COALS,REG) 

 dcwfi(OILS,OILEXS,REG) 

 dcwfi(GASS,GASEXS,REG) 

 dcwfi(OIL_PCS,OIL_PCEXS,REG) 

! dcwpd(NEGYCOM3,REG) 

 dcwpi(NEGYCOM3,REG) 

 dcwgd(NEGYCOM3,REG) 

 dcwgi(NEGYCOM3,REG) 

 c_CTAXBAS(REG,NEGYCOM3B) 

 DTBAL exogenous for all regions except one, 

! and cgdslack exogenous for that one region (which can be any one). 

 dtbal("USA") 

 dtbal("EU") 

 dtbal("EEFSU") 

 dtbal("JPN") 

 dtbal("RoA1") 

 dtbal("EEx") 

 dtbal("CHIND") 

 cgdslack("RoW") ; 

Rest Endogenous ; 

swap gco2t("USA")=RCTAX("USA"); 

swap gco2t("EU")=RCTAX("EU"); 

swap gco2t("JPN")=RCTAX("JPN"); 

swap gco2t("RoA1")=RCTAX("RoA1"); 

Shock gco2t("USA") = -35.6; 

Shock gco2t("EU") = -22.4; 

Shock gco2t("JPN") = -31.8; 

Shock gco2t("RoA1") = -35.7;
54
55

Annex 3 Specifying Emission Trading in GTAP-E. 

 Setting up an emission trading system requires to identify a global emission constraint 

for the group of countries/regions involved in trading and to allocate emission quotas among 

these countries/regions, the sum of which is equal to the global constraint. The global constraint 

in GTAP-E is imposed by making exogenous the variable gmarkco2t (see the box below), while 

the corresponding marginal abatement cost for the trading area (i.e. corresponding to the 

common price at which permits are traded) is specified as an endogenous variable (see 

MARKCTAX in the box below). The quotas allocated to each trading partners are specified by 

making the corresponding variables gco2q exogenous (note that these variables are endogenous 

and automatically equal to gco2t in the “no trade” scenario) and by “shocking” these variables 

along with a given quota allocation. It is to the user to verify that the sum of the quotas in terms 

of emission levels corresponds to the total constraint imposed to the exogenous variable 

gmarkco2t (in the example below, the weighted sum of the quotas growth rates specified for the 

Annex 1 countries/regions must be equal to the exogenous reduction of the Annex 1 emissions by 

22.13 % imposed to the variable gmarkco2t). Failure to specify a consistent quota allocation will 

result into trading flows imbalances. 

 The closure below implies that the sum of the trade account and the net carbon flows (i.e. 

the proceeds of emission sales and the expenditures of emissions purchases) is set exogenous and 

equal to zero. In other words, if a country buys emission rights, it has to compensate for it by 

exporting more goods and services such as to satisfy to the assumption of a constant net capital 

flow with the rest of the world (i.e. the net investment-saving balance remains unchanged as will 

be illustrated later on). Alternative closure rules might, of course, be used. 

 The Table A3-1 shows the SAM for the US in the “Annex 1 trade” case. The total 

revenue perceived by the Carbon Agency (CAG) is lower than in the “no trade” case (76 billion 

of 1997 USD compared with 124 billion of 1997 USD). The explanation is twofold. First, 

extending emission trading to Annex 1 countries lowers the price of permits (from 126 1997 

USD to 78 1997 USD per ton of carbon). Second, assuming that the Carbon Agency plays a 

centralized role in articulating the domestic and the international permit market, it has now to pay 

for buying permits to the Former Soviet Union (see the negative entry of 11 billion 1997 USD of 

the CAG row to the ROW column). The Table A3-2 reports the international flows including 

those related to permit trading. It shows that the total amount of permit sales by the EEFSU 

region amounts to 24 billion of 1997 USD, 11 billions of it are sales to the USA (see the row 

CTRAD). Given the closure rule, the net capital flows in each country/region (ISBAL) remains 

constant and equal to their benchmark values so that any flow associated to permit trading has to 

be balanced by a compensatory change of the trade account (BALPW). For instance, permit sales 

in the EEFSU region make possible a deficit of the trade account by 41 billion of 1997 USD. 
56

To summarize, specifying a permit-trading scheme involving a sub-group of countries/reg

requires the following steps: 

o The countries/regions that are involved in trading are specified in the base data 

(basedata.har) by setting the corresponding values of the D_MARK coefficients (dum

variable for participation to permit trading, header EMTR) equal to unity. 

o The corresponding RCTAX variables are set endogenous in the closure. 

o The country/region specific quotas have to be specified. This is done by making

corresponding gco2q variables exogenous in the closure and by specifying the growth of t

quotas in the SHOCK file. 

o The aggregate emission growth for the trading area (gmarkco2t) is set exogenous 

“shocked” accordingly while the equilibrium permit price for the area (i.e. the price at w

permits are exchanged: MARKCTAX) becomes endogenous (see the corresponding SW

statement below). 

Note that all values of the D_MARK coefficients should be equal to zero unless a permit-tra

scheme is specified. 
57

Box A.3.1 Closure and Shocks for Emissions Trading Among Annex 1 Countries

! basic closure 

exogenous 

 pop 

 psaveslack pfactwld 

 profitslack incomeslack endwslack 

 tradslack 

 ams atm atf ats atd 

 aosec aoreg avasec avareg 

 afcom afsec afreg afecom afesec afereg 

 aoall afall afeall 

 au dppriv dpgov dpsave 

 to tp tm tms tx txs 

 qo(ENDW_COMM,REG) 

 RCTAX("EEx") 

 RCTAX("CHIND") 

 RCTAX("RoW") 

 MARKCTAX 

 dcwfd(NEGYCOM3,PROD_COMM,REG) 

 dcwfd(COALS,COALS,REG) 

 dcwfd(OILS,OILEXS,REG) 

 dcwfd(GASS,GASEXS,REG) 

 dcwfd(OIL_PCS,OIL_PCEXS,REG) 

 dcwfi(NEGYCOM3,PROD_COMM,REG) 

 dcwfi(COALS,COALS,REG) 

 dcwfi(OILS,OILEXS,REG) 

 dcwfi(GASS,GASEXS,REG) 

 dcwfi(OIL_PCS,OIL_PCEXS,REG) 

 dcwpd(NEGYCOM3,REG) 

 dcwpi(NEGYCOM3,REG) 

 dcwgd(NEGYCOM3,REG) 

 dcwgi(NEGYCOM3,REG) 

 c_CTAXBAS(REG,NEGYCOM3B) 

! DTBALCTRA (incl. permit trading) exogenous for all regions except one, 

! and SAVESLACK exogenous for that one region (which can be any one). 

 dtbalctra("USA") 

 dtbalctra("EU") 

 dtbalctra("EEFSU") 

 dtbalctra("JPN") 

 dtbalctra("RoA1") 

 dtbalctra("EEx") 

 dtbalctra("CHIND") 

 cgdslack("RoW") 

 gco2q("USA") gco2q("EU") gco2q("EEFSU") gco2q("JPN") gco2q("RoA1") ; 

Rest Endogenous ; 

swap gmarkco2t=MARKCTAX; 

Shock gco2q("USA") = -35.6; 

Shock gco2q("EU") = -22.4; 

Shock gco2q("JPN") = -31.8; 

Shock gco2q("RoA1") = -35.7; 

Shock gco2q("EEFSU") = 12.869; 

Shock gmarkco2t = -22.132; 
58

Table A3-2 International Flows in the “Annex 1 Trade” Scenario (billion of 1976 USD)  1 USA 2 EU 3 EEFSU 4 JPN 5 RoA1 6 EEx 7 CHIND 8 RoW Total 

1 BALPW -140 99 -41 92 52 -4 25 -83 0 2 CTRAD -11 -6 124 -4 -3 0 0 0 0 3 ISBAL 150 -93 17 -88 -49 4 -25 83 0 Total 0 0 0 0 0 0 0 0 0 
59

Annex 4 Specifying Emission Trading in GTAP-E 

Table A4-2 Sectoral Disaggregation 

No. New Code Region 

Description 

Comprising GTAP V5 Countries/Regions 

1 Agriculture Primary Agric., 

Forestry and 

Fishing 

paddy rice; wheat cereal grains n.e.c; vegetables, fruit, nuts; oil seeds; sugar

cane, sugar beet; plant-based fibers; crops n.e.c.; bovine cattle, sheep and 

goats; animal products n.e.c.; rat milk; wool, silk-worm cocoons; forestry; 

fishing 

2 Coal Coal Mining coal 

3 Oil Crude Oil oil 

4 Gas Natural Gas 

Extraction 

gas; gas manufacture, distribution 

5 Oil_Pcts Refined Oil 

Products 

petroleum, coal products 

6 Electricity Electricity electricity 

7 En_Int_Ind Energy Intensive 

Industries 

minerals n.e.c.; chemical, rubber, plastic prod; mineral products n.e.c.; 

ferrous metals; metals n.e.c. 

8 Oth_Ind_Se

r

Other Industry & 

Services 

bovine cattle, sheep and goad; meat products; vegetable oils and fats; dairy 

products; processed rice; sugar; food products n.e.c.; beverages and tobacco 

products; textiles; wearing apparel; leather products; wood products; paper 

products, publishing; metal products; motor vehicles and parts; transport 

equipment n.e.c.; electronic equipment; machinery and equipment n.e.c.; 

manufactures n.e.c.; water; construction; trade; transport n.e.c.; water 

transport; air transport; communication; financial services n.e.c.; insurance; 

business services n.e.c.; recreational and other services; public admin. And 

defense, edu; ownership of dwellings 

Table A4-1 Regional Disaggregation 

No. New Code Region Description Comprising GTAP V5 Countries/Regions 

1 USA United States United States 

2 EU European Union Austria; Belgium; Denmark; Finland; France; Germany; United Kingdom; 

Greece; Ireland; Italy; Luxembourg; Netherlands; Portugal; Spain; Sweden 

3 EEFSU Eastern Europe and 

FSU

Hungary; Poland; Rest of Central European Assoc: Former Soviet Union 

4 JPN Japan Japan 

5 RoA1 Oth. Annex 1 Countries Australia; New Zealand; Canada; Switzerland; Rest of EFTA 

6 EEx Net Energy Exporters Indonesia; Malaysia; Viet Nam; Mexico; Colombia; Venezuela; Rest of 

Andean Pact; Argentina; Rest of Middle East; Rest of North Africa; Rest of 

Southern Africa; Rest of Sub-Saharan Africa; Rest of World 

7 CHIND China and India China; India 

8 RoW Rest of the World Hong Kong; Korea, Republic of; Taiwan; Philippine; Singapore; Thailand; 

Bangladesh; Sri Lanka; Rest of South Asia; Central America and Caribbean; 

Peru; Brazil; Chile; Uruguay; Rest of South America; Turkey; Morocco; 

Botswana; Rest of SACU; Malawi; Mozambique; Tanzania, United Republic 

of; Zambia; Zimbabwe; Uganda 
60

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