Supplementary electronic Appendix:
Introduction of EC-IAM
Environment Canada’s integrated assessment model (EC-IAM), which is based on the MERGE model
(Manne and Richels, 1995, and 2005), combines an economic activity based economy-energyemission sub-model with a climate science based climate sub-model into an integrated assessment
model system for climate policy analysis.
Economy-energy-emission Sub-model
Economy-energy-emission sub-model is the core model. It can run standalone or in combination with
climate sub-model. In the economy-energy-emission submodel, the “Negishi Method” is utilized to
approach the decentralized multi-region intertemporal equilibrium solution by transferring it into a
global social planning problem (Negishi, 1960). The objective function (NWEL) is a global utility
function, which is a sum of regional discounted utilities (U(Crt,Trt) weighted by Negishi weights
(NWTr )1.
𝑁𝑊𝐸𝐿 = ∑𝑟 ∑𝑡 𝑁𝑊𝑇𝑟 ∗ 𝑈𝐷𝐹𝑟𝑡 ∗ log⁡(𝑈(𝐶𝑟𝑡, 𝑇𝑟𝑡 ))
(1)
The Negishi welfare weight for region r is updated iteratively according to the weights of regional
monetary utility value in overall global value. UDFrt is the utility discount factor for region r at period
t. U(Crt, Trt) is represented by a constant elasticity of substitution (CES) function between
consumption (Crt) and passenger transportation (Trt).
The optimal solution involves the maximization of the above global utility function subject to a
number of constraints including regional budget, economic production, energy supply and passenger
transportation technologies and /or climate equations of constraints.
Economic activity in each region is represented by a top-down putty-clay macro production function
where price responsive inputs, such as labour, capital and energy are introduced through a nested CES
technology. Different regions are linked through international trade flows. This regional aggregate
production (Yrt) satisfies the competitive demand for regional consumption (Crt), investment (Irt),
transportation cost (TCrt), energy cost (ECrt), abatement costs (ACrt) (for non-CO2 GHG abatement)
and net exports (𝑁𝑇𝑋𝑌rt).
𝑌𝑟𝑡 = 𝐶𝑟𝑡 + 𝐼𝑟𝑡 + 𝐸𝐶𝑟𝑡 + 𝑇𝐶𝑟𝑡 + 𝐴𝐶𝑟𝑡 + 𝑁𝑇𝑋𝑌𝑟𝑡
(2)
For the macro production, all inputs (i.e., labour, capital, electric and non-electric energy) and outputs,
as well as consumption, passenger transportation and utility are vintaged as old and new. Old vintages
are determined by the amount of last period minus depreciation.
New vintage output is represented by an economy-wide nested CES production function of new
vintages of capital (KNrt), labour (LNrt), electric energy (ENrt) and non-electric energy (NNrt) as
follows:
1
For debate on the equity issue of Negishi weight, see Stanton, E.A. (2011).
𝜌 1
𝛽
1−𝛽
𝛼
1−𝛼 )𝜌
𝑌𝑁𝑟𝑡 = 𝐴𝑟𝑡 [𝜃𝑟𝑡 (𝐾𝑁𝑟𝑡
𝐿𝑁𝑟𝑡
+ (1 − 𝜃𝑟𝑡 )(𝐸𝑁𝑟𝑡 𝑁𝑁𝑟𝑡 ) ] ⁄𝜌
(3)
New vintage utility is represented by a CES utility function of new vintages of consumption and
passenger transportation as follows,
𝑈𝑁𝑟𝑡 = 𝐵𝑟𝑡 [𝜑𝑟𝑡 𝐶𝑁 𝛿 + (1 − 𝜑𝑟𝑡 )𝑇𝑁 𝛿 ]1/𝛿
(4)
There are limited goods that are tradable. These include macro goods, oil, gas and emission permits
wherever applicable. Heckscher-Ohlin paradigm is assumed to govern the international trade (i.e.,
tradable goods are homogeneous, rather than region-specific). For each tradable good i and each
projection period t, there is a balance-of-trade constraint (NTXirt) that, at a global level net exports or
imports for all regions must sum up to zero.
∑rNTXirt = 0
(5)
New vintaged capital is formed by investment of last period and new vintaged labour and labour supply is
exogenously determined.
Energy supply is represented both by bottom up electric and non-electric technologies (vintage as well
as non-vintage), while transportation supply is captured by bottom up vehicle modes. Major electric
technologies are vintaged. A list of available technologies is provided in Appendix table A. Electric
Energy and non-electric technologies compete to supply electric energy and non-electric energy
demand by the macro production. Vehicle modes or technologies compete to supply the demand for
transportation by regional consumers.
Exogenous Levelized costs and heat rate (if applicable) are assumed for those electricity technologies
including renewable and backstop technologies, non-electric technologies and passenger transportation
technologies. The choices of those technologies are determined endogenously by cost minimizing
actions of agents subject to various energy supply constraints and/or with the climate policies taken
into consideration.
The energy supply includes the following blocks of equations or constraints:
1) Hotelling equations describing the supply and evolution of exhaustible resources: oil, natural gas
and uranium. There are two major costs associated with exhaustible resources. One is the extraction
cost, that is, the cost of removing the fuel resources from the earth. Another is the resource
exploration or discovery cost: the cost of converting undiscovered resources into proved resources for
extraction. The extraction costs rise with the fraction of accumulated extraction over aggregate
endowment. The discovery costs rise with cumulative reserve additions as a fraction of undiscovered
resources. Extractions of resources are constrained by the proven reserves. Reserve additions are
constrained by undiscovered resources.
2) Accounting identities linking the energy submodel and the macroeconomic model, flow variables
with stock variables, and component variables to aggregate variables: Demands for electric energy and
non-electric energy in the economic submodel equals the sum of supplies of electric technologies and
non-electric technologies respectively in the energy submodel. Total energy cost in the economic
2
model equals the sum of supply costs of electricity associated with electric technologies and nonelectric energy associated with non-eclectic technologies. Energy supplies must be balanced with
energy consumptions.
3) Various energy constraints based on experts’ knowledge: (1) Expansion constraints and / or
contraction constraints are set up for those energy technologies subject to expansion limits and /or
decline limits. (2) Market share constraints are set up for some electric technologies such as coal
fired or gas fired technologies or intermittent electric technologies of wind and low cost solar, and
some non-electric technologies. (3) Capacity constraints are set up for some electric technologies such
as hydro, nuclear, and wind and some non-electric technologies, such as bio fuels and synthetic fuels.
Energy related GHG emissions are directly related to the use of energy such as coal, oil and gas in the
energy production or conversion, or in the macro production and passenger transportation. Non-energy
related GHG emissions and abatement costs are set exogenously.
Climate submodel
The climate submodel is a reduced aggregate description of the climate system from GHG emissions
to GHG concentration to radiative forcing and to temperature change over the preindustrial level in
1750 (IPCC, 2001; IPCC 2007; Manne and Richels, 2005).
The global emissions of each GHG gas is the sum of regional energy related emissions endogenously
determined by the demand and supply of energy and non-energy emissions (exogenous) less
abatement.2 This provides the link between the climate submodel and the macroeconomic submodel &
the energy submodel.
The total stock of GHG gases is determined by a distributed lag process to account for the inertia of
the climate system represented by the decay or lifetime of GHG gases and the accumulation of current
emissions.
Concentration of GHG gases in the atmosphere is determined by the total stock of GHG gases
proportionally.
In turn, the radiative forcing of GHG gases is determined by the concentration of GHG gases, namely,
following IPCC;

Radiative forcing of CO2 is proportional to the logarithm of CO2 concentration.

Radiative forcing of CH4 or N2O is proportional to the square root of CH4 or N2O
concentration.

Radiative forcing of F-gas is proportional to the F-gas concentration.

Total radiative forcing of GHG gases is the sum of radiative forcing of various GHG gases.
2
For non-energy GHG emission and their abatement cost-potential, EC-IAM is based on the estimates provided by
the Energy Modeling Form Study 21.
3
In the end, the eventual equilibrium temperature is proportional to the aggregate radiative forcing. The
actual temperature increase from pre-industrial levels is determined by a lagged response to the
equilibrium temperature.
As in MERGE (Manne and Richels 1995, and 2005), there are a number of energy and technology
supply constraints some of which are based on expert knowledge and some are driven by resource
constraints. In addition, accounting identities linking supply and demand, flow variables and stock
variables, and component variables and aggregate variables must be met.
GHG emissions are tightly linked to economic and energy activities. Energy-related GHG emissions
are directly related to the use of energy such as coal, oil and natural gas in energy production or
conversion, or in macro production. Non-energy related GHG emissions and abatement potentials are
set exogenously using information from various sources such as the US EPA (2006) and those
obtained from Energy Modeling Forum Study 21.
Climate submodel
The climate submodel is a reduced form climate system model that links GHG emissions from the
economy-energy-emission submodel to GHG concentration, to radiative forcing and finally to
temperature change over the preindustrial level in 1750 (IPCC, 2001; IPCC 2007; Manne and Richels,
2005). The global emissions level of each GHG gas is the sum of regional emissions less abatement.
The total stock of GHG gases is determined by a distributed lag process to account for the inertia of
the climate system represented by the decay or lifetime of GHG gases and the accumulation of current
emissions. Concentration of GHG gases in the atmosphere is determined by the total stock of GHG
gases proportionally. Following IPCC guidelines, the radiative forcing of GHG gases is determined by
the concentration of GHG gases as follows:


Radiative forcing of CO2 is proportional to the logarithm of CO2 concentration.
Radiative forcing of CH4 or N2O is proportional to the square root of CH4 or N2O
concentration.
 Radiative forcing of F-gas is proportional to the F-gas concentration.
 Total radiative forcing of GHG gases is the sum of radiative forcing of various GHG gases.
In the end, the eventual equilibrium temperature is proportional to the aggregate radiative forcing. The
actual temperature increase from pre-industrial levels is determined by a lagged response to the
equilibrium temperature.
Currently, there are 11 regions in the model (Table A) The technology assumptions are presented in
Table B. The GDP growth rate and technology cost change parameters used in model calibration are
presented in Tables C and D.
4
Table A: Regions in the model
Region
code
OECD
EMRE
ROW
Definition
Group
Australia and New Zealand
Canada
I
I
Greater European Union
I
Japan
United States
Brazil
China
India
Middle income Rest of World (include Indonesia, South Korea,
Thailand, Malaysia, other high-income Asia, Low-income Eastern
Europe, Turkey, Mexico, Argentina, Chile, Uruguay, Other highincome ROW, South Africa)
Russia
I
I
II
II
II
Low income and oil exporting Rest of World ( include HighIncome oil-exporting countries, Mid- and Low-income oilexporting countries, Other low-income Latin America, Other
Former Soviet Union, Other low-income Latin America, Other
Middle East/North Africa, Other Sub-Saharan Africa)
5
II
III
III
Table B : Various technologies of the model
Electric Technology
Vintaged
Hydro-electric power
No
Nuclear power
Yes
Coal-fired electric power without CCS
Yes
Oil-fired electric power without CCS
Yes
Gas-fired electric power without CCS
Yes
Coal-fired electric power with CCS,
Yes
Gas-fired electric power with CCS,
Wind generated electric power
Yes
Yes
Solar generated electric power
Biomass fired electric power
Yes
Yes
Other renewable generation (geothermal , waste, and other renewable
generation)
No
Liquid fuel supply technologies
Refined oil
Biomass-based liquids
Coal-based synthetic liquids
Non-electric energy Technologies
Coal for end use
Gas for end use
Liquid for end use
Backstop fuel for end use
Passenger transportation Technologies
Internal combustion engine vehicle
Compressed natural gas vehicle
Plug-in hybrid electric vehicle
Full electric vehicle
Backstop (e.g. H2) vehicle
6
Table C: Expected Annual Average Economic Growth in
Starting decade 2011-2020
Region
GDP Grow Rate
Brazil
3.5%
Canada
2.4%
India
7.1%
Russia
3.5%
United States
2.8%
Europe
2.0%
Japan
1.4%
Australia, New Zealand
3.0%
China
6.6%
Middle income countries
3.2%
Low income and oil exporting countries
4.6%
Table D: Average cost change from 2010 to 2050 (%)
Technologies
OECD EMRE ROW
Coal-fired electric power without CCS
-14
-14
-14
Gas-fired electric power without CCS
-10
-10
-10
Oil-fired electric power without CCS
-10
-10
-10
Coal-fired electric power with CCS
-33
-42
-49
Nuclear power (generation II and III)
-3
-7
-10
Nuclear power (generation IV)
-33
-33
-33
Solar generated electric power (back stop)
-47
-54
-54
Solar generated electric power (intermittent)
-34
-36
-38
Wind generated electric power
-52
-54
-43
Biomass fired electric power
-39
-41
-32
References
EPA (2006), Global Mitigation of Non-CO2 Greenhouse Gases,
http://www.epa.gov/nonco2/econ-inv/international.html
7
IPCC (2001), IPCC Third Assessment Report: Climate Change
http://www.ipcc.ch/publications_and_data/publications_and_data_reports.shtml#1.
2001
(TAR),
IPCC (2007), IPCC Fourth Assessment Report: Climate Change
http://www.ipcc.ch/publications_and_data/publications_and_data_reports.shtml#1.
2007
(AR4),
Manne, A. and R. Richels (2005), “Merge: An Integrated Assessment Model for Global Climate
Change”, In Richard Loudon, Jean-Philippe Waaub, and George Zaccour (eds), Energy and
Environment, pages 175-189. Springer US.
Manne, A., Mendelson, R., and R. Richels (1995), “MERGE: A Model for Evaluating Regional and
Global Effects of GHG Reduction Policies”, Energy Policy, 23(1), 17-34.
Negishi, T. (1960), “Welfare Economics and Existence of Equilibrium for a Competitive Economy”,
Metroeconomics 12, 92-97.
8