Yves Caseau - Coupling Coarse Earth Model – February 2023 1/26
CCEM :
Coupling Coarse Earth Models
Yves Caseau
National Academy of Technologies of France (NATF)
March 2023
D
R
A
F
T
Latest update : March 24th, 2023

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Outline
1. Why : Global Warming Dynamic Games
2. M1 (first model): Energy Resource Model
3. M2: Energy Consumption Model
4. M3: Energy Transition Model
5. M4: GDP Model
6. M5: Ecological Redirection Model
7. Coupling these five models (M1 to M5 together: CCEM)
In Memoriam

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Global Warming Dynamic Games
l Global Warming Games : (Wikipedia Definition)
A global warming game, also known as a climate game or a climate change game, is a type of serious game.
As a serious game, it attempts to simulate and explore real life issues to educate players through an interactive experience
l Our CCEM model looks at the interaction
between five “coarse” models:
n Energy Production
n Energy Consumption
n Energy Transition (fossil fuel to clean)
n Economy (value from energy)
n Ecological Redirection : reaction of society
to the outcome predicted by IPCC
l My goal is to produce a « serious game »
using GTES
n You select a block (continent)
n You select a strategy
n GTES plays the role of the other players
n Multiple scenarios based on beliefs about
peak oil, energy transition and reserves.
William Nordhaus
(Wikipedia)
Production
Primary Energy
Consommation/
Savings / Renouncements /
Substitution
Economy
Value
Growth
Investments
Gaia : Earth Ecosystem
Oil Coal
« Clean »
Energy
EU
China
Rest of
World
China
Rest of
World
CO2 emission
Global Warming
Natural Disasters
Societal Pressure
Uses Energy dégradation
C
O
2
/
e
n
e
r
g
y
f
e
e
d
b
a
c
k
Nat.
Gas
US
US
EU

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Global Warming Dynamic Games: Preliminary Roadmap
l 2008-2009: GWDG v1
l 2020 – 2021 :
foundations (CLAIRE 4)
l 2022 : GWDG v2
l 2023 : CCEM
l 2024: GTES/Game
Two goals for CCEM (2023):
l clear/formal presentation
(feedbacks / criticisms)
l Meta-model that is wide
enough to « capture »:
n W. Nordhaus
n P. Diamondis (Singularity)
n JM Jancovici (Shift Project)
Warning !
GWDG (CCEM as a tractable and meaningful computational
model) feasibility is only a hypothesis at this point
Iteration of despair & insights … will converge or not J
« Coarse Model »: capture beliefs into a simple computational model

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CCEM : Addressing Five “Known Unknowns”
« How much energy will be available in the
future ? At which costs? »
« How much energy is needed and acceptable
for the economy at a given cost ?»
Example:
At which speed can we add clean
energy in the next 30 years ?
EIA
« How fast can we substitute one form of
primary energy to another ? »
« What will be the economical and societal
consequences from the IPCCs predicted
global warming ?»
« which GDP growth can be expected from
investment, technology, energy
and workforce ? »
Example:
- How much energy subvention
must/can governments afford ?
Energy
To
GDP
Example:
What is the possible speed of
transition fossile>green for industry ?
2050
Eco
transition
Plan
Example:
Impact of reduced energy availability
on economical output ?
GDP
2050
Example:
- which damage to productive
resources ?
- Which redirection caused by fear ?
Temp
to GDP
loss

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CCEM : Simulation Model
l Each model M1 to M5 represents a discrete one-year difference equation
n Inputs: some of the state variables (at year n – 1)
n Outputs: some of state variables (M1 to M5 partitioning)
n 10 to 30 lines of code (each)
2010
State of the
world
Energy
Sources
Zones World
Earth N = 40,90, … times
2050 / 2100 / …
State(i) = ƒ (state(i-1),*)
M1 M2 M3 M4 M5
Outcome = time-series
GDP
CO2
Energy

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CCEM : From Beliefs to Simulation to Outcomes
Beliefs
• Energy assets
• Savings roadmap
• GDP Energy-
elasticity
• Global Warming
impacts
• Expected growth if
resources
Foundations
• CO2 -> temperature (IPCC)
• Assets x Energy -> GDP -> investments -> delta(assets)
• Production to Demand adjust through prices
What you
Give as
An input
Do not use
CCEM if you
disagree
Levers
• Energy Transition roadmap
• CO2 Tax
• Redistribution
Outcome
(make an excel
Example)
N
iterations
What you
Play with during
simulation
True value : revisit your beliefs from observing outcomes
GTES
Game-Theory
Evolutionary Simulation

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Ecological Redirection (M5)
M5 answers the question « What kinds of redirection should we
expect from the IPCCs global warming consequences ?»
Bruno Latour’s redirection concept tells that this is a non-
linear coupling.
There is no “point A to point B” trajectory, but reactions along
the way, based on the catastrophic events that will unfold
M5 is made of three components:
l A simple projection from IPCC to link CO2 output (from M2-M3) to
expected temperature rise (using RCP 4.5, 6 and 8.5)
l A random, discrete function that define “pain thresholds” as CO2 &
temperature rise
l A redirection model (very naïve) with three components
n Increase into energy redistribution (feedback to M2)
n Increase CO2 tax (versus planned trajectory)
n Economic crisis (feedback to M4)
è Production capability damaged by warming
(e.g. agriculture)
è Workforce disruption (from strikes to massive death tolls of
natural catastrophes and wars)
IPCC model extraction T = f(CO2)
CO2 concentration
« pains » : weather
catastrophes and
cost of living
« Redirection »
Energy
Redistribution &
cancel
acceleration
Economy
Damage
(loss of resource)
CO2 Tax
Acceleration
time
CO2(PPM)
Close Economy Branches
Température (C°)
catastrophe
catastrophe
Three drivers : fear (of future production loss), pain (less
revenue) and compassion (disaster happening elsewhere)

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Ecological Redirection Feedback
l M5 Model of « World Feedback to Earth »
3 Loops (one large aggregation)
CO2 ↗ T (C°) ↗
M2
Less energy
available
Loop 1: T to ”pain” to reaction
M4 Loss of
productive
resources Loop 2: T to ”destruction”
to economy loss
M4 M2
CO2
tax ↗
cancel
renunciation
↗
Re-
distribution
↗
Composite Pain
Loop 3: Economy contraction
to pain to reaction canicules
droughts
floods
fires
Compassion
WW misery
Fear
Future impact
Pain Job &
Property loss
Death
Displacements
Agriculture
Losses
Economy
Hits
Aggregated into “T to pain” abstraction

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Non-linear reaction
Deaths,
Displacements
Agriculture
Losses
Economy
Hits
Less available
energy
Compassion
WW misery
Fear
Future impact
Pain Job &
Property loss
Composite
Pain
Loss of Productive
Resources
CO2
tax ↗
cancel
renunciation
↗
Re-
distribution
↗
time
REACTION
Température
(C°)
catastrophe
catastrophe
Aggregated into “T to pain” abstraction

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CO2 ↗ T (C°) ↗
Ecological
Redirection
• More CO2 tax
• Redistribution
• Restrictions
(renunciation)
Composite Pain
canicules
droughts
floods
fires
Deaths,
Displacements
Agriculture
Losses
Economy
Hits
Loss of Productive
Resources
Less available
energy

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Ecological Redirection (M5)
M5 Inputs: CO2 yearly output in the atmosphere
M5 Outputs: Four feedback signals to other models: energy
redistribution, CO2 tax, cancel, damages to economy
Fours steps
l Computes CO2 concentration in the atmosphere, based on the ability of the Earth to absorb part of it.
This should be updated to reflect that this ability will probably decline, by works as an approximation
(CO2 in atmosphere = CO2 Output - 16Gt absorbed by forests, soil, ocean, …)
l Use IPCC models to extract the expected temperature rise
(note : the IPCC hypothesis about CO2 emissions in time are irrelevant here because they are computed by M1 to M4).
l A “pain level” is derived from
n Weather : floods, agriculture losses, fires, heat waves, …
n Economic welfare: based on growth/recessions and cost of energy.
Note: for the time being, redistribution is only modeled as “energy cost redistribution” –
Another model M6 would be necessary to represent “economic redistribution / social justice / social unrest”
l Pain drives “random, discrete” reactions (cf. illustration : step-wise pain-to-reaction functions)
n Energy redistribution factor
n CO2 tax acceleration
n Cancel Acceleration (collective decision to ban some usages)
n Loss of productive capacities and Loss of productive workforce are also captured through cancellation
Pain level
reaction
MSc Strategy
and Design for
the
Anthropocene
Open Question: add a “capital destruction” feedback ? natural disaster repair
reduce investments.
Currently, this is captured in the M5->M4 productivity ratio

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GDP Model (M4, World Economy)
M4 represents the question:
« which GDP is produced from investment, technology, energy and workforce ? »
Description
Economy is seen as a set of productive assets that
require energy and human capital to operate
Economy growth require investments that are a share
of results
We use a crude exponential growth model
• Output is linked to energy (cf M2 + redistribution)
• Demography is factored through energy consumption
• Assets grow as a result of investment
• Energy transition investments are subtracted from total investments to
compute growth investments
• GW Crises are modeled two ways : a reduction of productive assets and as an
acceleration of « cancellation »
• The model computes the consumption without savings that drives the GDP and
the consumption with savings that drives CO2 emissions
Productive
Assets
GDP
(Results)
Investments
Energy
Supply (Es)
population
Tech
Innovation
Energy transition
Growth
Invest
Global Warming
Natural Disasters
Loss of resources (people, land, factories …)
Energy
Demand
Open question (cf. O. Vidal) : model the “metal intensity” of value creation,
either as a feedback loop for M4 or a constraint for transition (M3)

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GDP Model (M4)
M4 Inputs: energy consumptions with price levels, for each source and each block.
Energy redistribution ratio (k : proportionality factor)
Energy transition investments
M4 Outputs: GDP (worldwide) and investments level
l Economic result (R = GDP) depends on energy consumption
Rn = R n-1 x (1 + Icn-1 × r) x (Esn / Edn)k × (Fn / Fn-1)
1. The GDP depends on the current level of productive assets, grown from previous year growth investments (r = ROI)
2. The output is adjusted to the actual energy available (Es: supply vs Ed: demand, Negawatts included)
The exponent k represents the results of energy redistribution
è without redistribution, k is derived from M2 (energy-to-value distribution), with complete redistribution, k = 1 (simplifying
assumption !)
3. The productive assets are adjusted through ”global warming disasters” loss (Fn )
l Investments are computed from the GDP result and its variation using a linear regression:
I n = x% × In-1 × (Rn / R n-1) + y% × (Rn - R n-1)
l Energy transition investments Ien are produced by M3 model
Growth investments are produced with the difference:
Icn = In – Ien
A negative value is interpreted as a loss of productive capacity
l Carbon taxes are computed from energy consumption, but the model assumes that the value is recirculated into
the economy (energy investments) without loss Another option would be to reinject CO2 to
alleviate pains due to loss of economic activity
Feedback from model 5
(loss of productive force)
“redistribution” only applies
to energy in version 3

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Energy Resource Model (M1)
M1 captures the answer to the questions « How much fossil resources do we have ? At which costs? »
Four categories
l Oil
l Natural Gas
l Coal
l Others (“clean”: hydro/solar/wind/nuclear)
Each resource is defined through:
l For fossil energies, its inventory chart
(available Toe according to sell price)
l For clean energies, a growth potential curve
(max capacity in the future year, according to
manufacturing and resource constraints
l A “max capacity” (yearly output)
l A constraint about the speed at which this capacity
may evolve
Caracteristic chart: « Peak Oil »
time
Production
Inventory
GTep
GToe
Price : €/Toe
410$
Inventory chart (oil example)
242

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Energy Resource Model (M1)
M1 Inputs: 4 inventories / capacities / “capacity evolution” constraints
M1 Outputs: a curve that describes (for each simulated year) the output for a given market price
This is the simplest (parametric) model : for each possible sell
price,
l Compute the new inventory:
n Available resources based on 3Y averaged price,
n minus last year consumption
l Determine new capacity goal, based on net demand of
previous year (modulo a dampening factor to avoid oscillation)
and operations capacity constraint (capacity growth factor is
capped)
l Output is a fraction (0 to 1) of max capacity, with price
sensitivity that is extracted from past history
GToe
Price : €/Toe
410$
Production = f(price)
242
Max capacity = min (c0 x In/I0,
cn-1 x min( maxGrowth,
expectedGrowth)
Local price elasticity
There are two key aspects which are missing (first attempts to add into M1 failed)
• Strategy of the resource owner to speculate on current price versus expected value (versus the naïve linear
output model)
• Time delay between decision to extract a new resource and actual operation is long (over 10 years) –
versus the current capacity model that looks 3 years back

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Energy Consumption Model (M2)
M2 captures the answer to the question
« How much energy is needed for the economy at a given cost ?»
The heart of this model is (for each source) a
histogram of value production:
l Decomposition of value product (Y axis)
l Over segments of energy usage (X axis)
l This (virtual) decomposition is the base for telling how
each actor will react to price increases
The net behavior is represented by four curves :
l Cancelation (% of activity that stops because price is too high) = f(p)
l Economic loss due to cancelation
l “Savings“ (energy efficiency) – reduction of consumption at iso-activity
n Savings are a “policy” (decision ahead of time that gets implemented) -> similar
to transition (M3) and defined as a function of time (f(t))
l Substitution towards another form of energy (using the matrix provided
by M3)
The last two options triggers associated investments
Energy redistribution policy is a factor that lowers the pain of cancellation
but reduces the economic efficiency
Energy consumption for a given price
decreases according to cancelation
(upper histogram), energy savings and
substitution (M3: one energy source to
another)
Share of the PNB that can be
produced at a given price
Evergy cost /
value produced
=> Max price
100%
Pmax1
Pmax10
Share Of
energy
S(Xi) = 100%
X1 X2
X10
Energy consumtion
savings
cancel
Substitution to« clean »
Price / time
100%
p0
100%
Cancel Rate
The loss of economic value due to
Energy-based cancellation follows
a convex law (lower value creation
activities stop first)

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Energy Consumption Model (M2)
M2 Inputs: For each block, population and consumption history per energy source,
M2 Outputs: Net demand for each energy source, for each geography block
This is also parametric model (based on price) :
l Iterate over energy resources (assumes a DAG order for substitution)
n Computes the net energy need
è Based on economy evolution (proportional [iso techno – improvement factored as “savings”])
è Based on population (1 + a(P/P0)) – a: share of energy consumption that is linked to pop growth
n Distributes over energy sources using substitution that has been realized in the past years
n Computes the resulting parametric (demand = f(price)) curves
è Factoring cancellation according to the price
è Savings “achieved so far” are also factored in
M1 and M2 “coupling” means to find the price that adjust supply and demand
Current instantiation of CCEM uses 4 blocks : US, China, Europe and RestOfWorld
Note: A big oversimplification in the current model is to use the same cancel/saving curves for each
source of energy (using a dumb ratio to account for different energy prices today)

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Energy Transition Model (M3)
M3 captures the answer to « How fast can we substitute one form of primary energy to another ? »
Substitution matrix
l Oil to Coal to Gas to Clean
l 6 flows (N x N-1 / 2)
l A substitution matrix as 6 coefficients (share of
energy consumption that should be transitioned),
depending on year (policy)
l The matrix takes into account the “source to vector”
possible paths (cf. illustration) – It should also factor
the constraints from natural resources such as steel.
Mobile storage
electricity Industry
transportation
Heat
Oll & Natural Gas
Coal
Clean Energy
CTL
Static storage &
distributed
gas
Batteries, hydrogen
Vectors
The substitution matrix describes which substitution is feasible &
desirable from an energy policy viewpoint (on the demand side)
l Irreversible
l When acted (a given year), generate the associated Investment
(same for savings)
Note: Models M1 / M2 focus on primary energy sources, M3 takes
the energy vectors (electricity, hydrogen, …) into account to define
which transitions are feasible
Substitution
Matrix
Changes
Energy
Source
Demand
New
Capacities
and
transfer
Reflects the
Energy
Transition
policy
Speed of
changed is
capped (max
from M1)
Energy demand
(M2) is balanced
between 4 sources

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Energy Transition Model (M3)
M3 Inputs: Initial transition matrix, actual output for each energy source, actual market price (source
dependent)
M3 Outputs: transfer of energy consumption (yearly, starting on the date the decision is made), energy
investments
This model has two purposes:
l For M2, to compute how much energy is consumed for a given price, using the current level of
substitution (called the “substitution matrix”)
l As a complement to M2, once the price is set and the energy consumption is known for a year
n For each source and each block,
n Once cancellation and savings have been applied,
n Computes the new level of substitution using the transition matrix (reflect the zone policy)
n The substitution matrix is adjusted (monotonous, always grow, and capped by maxGrowth parameter from M2)
n Level of investment is adjusted based simple “energy investment costs” (cost to produce 1MWh)
n M3 uses a parameter “technology efficiency” that reduces over the years the cost to transition
l This model M3 also computes the CO2 yearly emissions for each energy source

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GWDG Dynamic System (2008 view)
Production
Consumption
Economy
Gaia
inventory
capacity
revenue
Conso
CO2 tax
Societal
Pressure
CO2
emissions
Unknown Model
IPCC Forecasts
Temperature
Water rise
GDP/person
démography
+
+
-
-
price
cost
needs
Equivalent
Consumption
Invest E
GDP
M4
World
Economy
Investments
Growth Invest
M1
supply
M2
demand
M3
Energy
transition
M5
Ecological
Redirection
delay
delay
delay
redistribution
renouncement
+
+
4 instances
• Oil
• Gas
• Coal
• Clean
4 instances:
• US
• Europe
• China
• Rest of
World
savings
cancel
Tech
Progress
substitution
Rate of CO2
catastrophies
crises
GWDG v3
One Economy

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Conclusion
l On-going work (this slide deck should be kept synchronized with the code)
l First implementation (with CLAIRE) – to be translated to JavaScript for easier share
l A tool to explore beliefs (mental models) and their combined effects
WARMING/ ADAPTATION
CARBON-NEUTRAL
Finite World
Radical Change
Open World
Continuous Change
Temperature
rises
Technology changes the game
W. Nordhaus
Adjust to GW
moderate GDP effects
P. Diamandis
Abundance
JM Jancovici
Carbon Shift
P.Sevigne
Collapse

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Preliminary results
l These are the outcome associated to the previous “three sets of beliefs”
33,8
65 84
104
128
154 165
198 208 212214
389
533
606
684
758
833 816
917
874
807
732
14,5 14,6 14,8 15,2 15,6 16 16,3 16,5 16,6 16,816,8
25 34 39,6 42,6 45,5 48,8 45,2 50,2 45,8 39,9 33
0
100
200
300
400
500
600
700
800
900
1000
2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100
Energy-Rich Scenario
GDP (T$) Energy (EJ)
Temperature(C) CO2(Gt/y)
33,8
65
81
100
119 133 144 156 169 180
197
389,2
533
567
650
676 662
611
571
521
467
427
14,5 14,6 14,8 15,1 15,4 15,6 15,8 15,9 16 16 15,9
25 34 36,6 38,3 35,3 31,5 26,1 21,9 17,6 13,7 10,3
0
100
200
300
400
500
600
700
800
2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100
Exponential Technologies
Scenario
GDP (T$) Energy (EJ)
Temperature(C) CO2(Gt/y)
33,8
65 77
90 94 97 94 92 90 88 90
389,2
533 532
580
541
502
430
375
325
289
269
14,5 14,6 14,8 15 15,3 15,5 15,6 15,6 15,6 15,5
15,4
25 34 34,3 35,1 30,2 26,2 20,3 15,4 11 8 6,2
0
100
200
300
400
500
600
700
2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100
Stick to Paris Agreement
GDP (T$) Energy (EJ) Temperature(C) CO2(Gt/y)

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Median Belief Scenario (WIP)
l Key PKI for CCEM outcome + Kaya coefficients
33,8
65
84
106 119 124 130 136 146 154 160
389,2
533
605
697 706
671
636
600
567
538
516
14,5 14,6 14,8 15,2 15,5 15,9 16,2 16,4 16,4 16,5 16,5
25 34 39,5 43,2 42,3 38,7 35,2 31,3 27,5 24,3 21,6
0
100
200
300
400
500
600
700
800
2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100
Median Belief Scenario
GDP (T$) Energy (EJ) Temperature(C) CO2(Gt/y)
6,6 7,3 8,1 8,9 9 9,2 9,2 9,3 9,4 9,3 9,2
25
34 39,5 43,2 42,3 38,7 35,2 31,3 27,5 24,3 21,6
240 239
232,6
221
214
206,1
198
186,3
173,1
161,8
150,1
319
227,9
199,1
182,4
164,2
149,9
135,5
121,7
107,7
96,8
89,4
5,12 9,8 12,8 16 18,1 18,8 19,7 20,7 22,1 23,4 24,2
0
50
100
150
200
250
300
350
2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100
Kaya Identity
Pop (G) CO2(Gt/y)
gCO2/KWh e-intensity (Wh/$) / 10
GDP/p (k$)

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Similar Earth Models
Nordhaus: DICE Model ACCL (Banque de France)
MIT Integrated Global System
Modeling (IGSM) Framework
SOS Trades
The IGSM framework consists primarily
of two interacting components—the
Economic Projection and Policy Analysis
(EPPA) model and the MIT Earth System
model (MESM). The EPPA model
simulates the evolution of economic,
demographic, trade and technological
processes involved in activities that affect
the environment at multiple scales, from
regional to global.
SoSTrades is a web-based, multi-user,
interactive publication-quality graph
simulation platform. It allows users to
drop new modules without additional
coding, and provides embedded
advanced numerical capabilities for
simulation and multi-disciplinary
optimization. It also has built-in
collaborative capabilities to allow
different experts to work together.
The economic model we will explore here
is based on a model created by William
Nordhaus of Yale University, who is
considered by many to be the leading
authority on the economics of climate
change. His model is called DICE, for
Dynamic, Integrated Climate and
Economics model. It consists of many
different parts … we can carry out some
experiments with this model to explore the
consequences of different policy options
regarding the reduction of carbon
emissions.
A tool to build climate change scenarios to
forecast Gross Domestic Product (GDP),
modelling both GDP damage due to climate
change and the GDP impact of mitigating
measures. It adopts a supply-side, long-term
view, with 2060 and 2100 horizons. It is a global
projection tool (30 countries / regions), with
assumptions and results both at the world and
the country / regional level. Five different types
of energy inputs are taken into account
according to their CO2 emission factors., Total
Factor Productivity (TFP), which is a major source
of uncertainty on future growth and hence on
CO2 emissions, is endogenously determined,