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Economics 331b
Integrated Assessment Modelsof Economics of Climate Change
Integrated Assessment (IA) Models of Climate Change
• What are IA model?– These are models that include the full range of
cause and effect in climate change (“end to end” modeling).
– They are necessarily interdisciplinary and involve natural and social sciences
• Major goals:– Project the impact of current trends and of policies
on important variables– Assess the costs and benefits of alternative policies– Assess uncertainties and priorities for scientific and
technology research
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Person or nation 1
Person or nation 2
Inefficient initial (no-policy) position
Bargaining region (Pareto improving)
Pareto Improvement from Climate Policy
Elements of building/using an IAM1. Economics
– Population– Inputs: energy, capital, land, …– Technology (total factor productivity)
2. Emissions of CO2 and other GHGs3. Carbon cycle, forcings, temperature, other
geophysical4. Impacts or damages5. Policies
– Emissions controls, taxes, regulations, subsidies– International strategies for global externalities
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Basic economic methodology of IA models
We will use a very simple IA model to illustrate – the Yale “DICE” model.
Last published version is 2007 in your assignmentAlso:
- Regional version (RICE-2010)- Experimental or beta DICE-2010 in Excel format
Lint will give overview of IAM in section this week.
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Simplified Equations of DICE Model (QoB, pp. 205-209) Objective Function
(1)
1
T max
tW U[c(t),L(t)]R(t) [maximize for control rate (μ) and savings rate (s)]
Economics (2) 1-U [c(t),L(t )] =L(t)[c(t) / (1- )] Utility function (3) 2
1 AT 2 AT(t)=Dam/ GDP =[1+ T (t)+ T (t) ] Damage function (4) 2
1(t) = (t) (t) Abatement cost (5) 1g gQ (t) = A(t) K(t) L(t) C(t) s(t)Q (t) Gross output (6) gnQ (t) = [1- (t)] [1- (t)] Q (t) Net output (7) g
IndE (t) = (t)[1- (t)] Q (t) Industrial emissions Geosciences (8) 11 1AT ATM (t) E(t) M (t - ) ... Atmospheric CO2 (9) 2 AT AT EXF(t) {log [M (t) / M (0)] } F (t) Radiative forcings (10) 11 AT ATT (t) T (t ) {F(t) ... Global mean temperature Key variables (in addition to standard from growth theory):
Eind = industrial CO2 emissions F = radiative forcings MAT = atmospheric concentrations CO2 Qg = output gross of damages and abatement Qn = output net of damages and abatement TAT = global mean surface temperature
Λ = abatement (mitigation) cost/ output μ = emissions control rate (fraction of uncontrolled) σ = uncontrolled emissions/ output ratio Ω = damages as fraction of output s = savings rate = I/ Q R = utility discount factor = (1+ρ)-t
Basic structure of IAMEconomic sectors (more or less elaborate):
Q = A F(K, L) = C + Iplus:
• Energy sector • Emissions• Abatement• Climate damages
Geophysical sectors:• Carbon cycle• Climate model• Impacts
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I. Economics: DICE/RICE model examplePopulation exogenous: use UN and IIASA
projections. - Should we have endogenous fertility?
Total factor productivity exogenous - Problem that technological change is endogenous,
particularly with large changes in energy pricesSavings rate optimized by country
- Use Solow-Ramsey model of optimal economic growth
Put all these together (for 12 regions j=US, EU, …)
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1gj j j j
j j j
Q (t) = A (t) K (t) L (t)
K (t)=s(t)Q (t) K (t)
Per capita GDP: history and projections
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1
10
100
1960 1980 2000 2020 2040 2060 2080 2100
Per c
apita
GDP
(200
0$ P
PP)
US WE OHI
Russia EE/FSU Japan
China India World
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Emissions trajectories:Start with data on Q, L, and E of CO2 for major
countriesEstimate population, productivity, emissions growth Project these by decade for futureThen aggregate up by twelve major regions (US, EU,
…)Constrain by global fossil fuel resources
This is probably the largest uncertainty over the long run.
Modeling Strategies (II): Emissions
CO2-GDP ratios: history
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.0
.1
.2
.3
.4
.5
.6
.7
80 82 84 86 88 90 92 94 96 98 00 02 04
ChinaRussiaUS
WorldWestern/Central Europe
CO
2-G
DP
ratio
(ton
s pe
r con
stan
t PP
P $
)
Decarbonization projections
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-
0.05
0.10
0.15
0.20
0.25
0.30
0.35
2005 2015 2025 2035 2045 2055 2065 2075 2085 2095 2105
CO2
emiss
ions
/GDP
US EU
Japan Russia
China India
Africa
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Climate modelIdea here to use “reduced form” or simplified models.As we have seen, large models have very fine
resolution and require supercomputers for solution and cannot be used in economic modeling.
We take two-layers (atmosphere, deep oceans) and decadal time steps.
Calibrated to ensemble of models in IPCC science reports.
Modeling Strategies (III): Climate Models
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Actual and predicted global temperature history
-.6
-.4
-.2
.0
.2
.4
.6
1840 1880 1920 1960 2000YEAR
T_DICE2007 T_Hadley T_GISS
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T projections multi-model comparison
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100
Glob
al m
ean
tem
pera
ture
incr
ease
(from
190
0,
◦C)
RICE-201
EMF-22
A1B
A2
B1
B2
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Modeling Strategies (IV): Impacts• Central difficulty is evaluation of the impact of
climate change on society• Two major areas:
– market economy (agriculture, manufacturing, housing, …)
– non-market sectors • human (health, recreation, …)• non-human (ecosystems, fish, trees, …)
Summary from Tol Survey
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-3
-2
-1
0
1
2
3
4
5
6
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
Dam
ages
as p
erce
nt o
f out
put
Global mean temperature increase (°C)
Tol survey
Richard Tol, “The Economic Impact of Climate Change,” Journal of Economic Perspectives, Vol. 23, No. 2, Spring 2009
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Modeling Strategies (V): Abatement costs
These are the abatement cost functions we discussed in energy economics.– Some use econometric analysis of costs of reductions– Some use engineering/mathematical programming
estimates– DICE model generally uses “reduced form” estimates
of marginal costs of reduction as function of emissions reduction rate
– We will return to this later.Marginal cost of reductions
0 Reductions in energy use or CO2 emissions
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Outcome of efficientcompetitive market(however complex
but finite time)
Maximization of weighted utility function:
Economic Theory Behind Modeling
1for utility functions U; individuals i=1,...,n; locations k, uncertain states of world s,
time periods t; welfare weights
ni i i
k,s,ti
i .
W [U (c )]
=
1. Basic theorem of “markets as maximization” (Samuelson, Negishi)
2. This allows us (in principle) to calculate the outcome of a marketsystem by a constrained non-linear maximization.
How do we solve IA models?The structure of the models is the following:
We solve using various mathematical optimization techniques.
1. GAMS solver (proprietary). This takes the problem and solves it using linear programming (LP) through successive steps. It is extremely reliable.
2. Use EXCEL solver. This is available with standard EXCEL and uses various numerical techniques. It is not 100% reliable for difficult or complex problems.
3. MATHLAB. Useful if you know it.4. Genetic algorithms. Some like these.
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1
subject to initial conditions, parameters]
(The functions are production functions, climate model,carbon cycle, abatement costs, damages, and
T max
{ (t)} tmax W U[c(t),L(t)]R(t)
c(t) H[ (t),s(t);H[...]
so forth.)
Can also calculate the “shadow prices,” here the efficient carbon taxes
Remember that in a constrained optimization (Lagrangean), the multipliers have the interpretation of d[Objective Function]/dX.
So, in this problem, interpretation is MC of emissions reduction.
Optimization programs (particularly LP) will generate the shadow prices of carbon emissions in the optimal path.
For example, if we look at the DICE model, the carbon shadow price might be $30 per ton carbon ($7 per ton CO2)
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0
100
200
300
400
500
600
0 10 20 30M
argi
nal c
ost o
f Em
issio
ns R
educ
tions
($)
Period
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Applications of IA ModelsI will give an example that compares different
policies and scenarios.
1. No controls ("baseline"). No emissions controls.2. Optimal policy. Emissions and carbon prices set
for economic optimum.3. Various international agreements (Strong Kyoto ≈
Obama proposals and Copenhagen Accord)
For these, I will use latest modeling results (RICE-2010, Nordhaus, PNAS, 2010).
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Emissions Trajectories for RICE-2010
0
2
4
6
8
10
12
14
16
18
20
2005 2025 2045 2065 2085 2105
CO2
emiss
ions
(GtC
per
year
)Optimal
Baseline
Lim T<2
Copenhagen Accord
Source: Nordhaus, “Economics of Copenhagen Accord,” PNAS (US), 2010.
Concentrations profiles: RICE-2010
25
0
200
400
600
800
1,000
1,200
1,400
2005 2025 2045 2065 2085 2105 2125 2145 2165 2185 2205
Atm
osph
eric
conc
entra
tions
CO2
(ppm
) Optimal
Baseline
Lim T<2
Copenhagen Accord
Temperature profiles
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0.0
1.0
2.0
3.0
4.0
5.0
6.0
2005 2025 2045 2065 2085 2105 2125 2145 2165 2185 2205
Glob
al m
ean t
empe
ratu
re (d
egre
es C
)Optimal
Baseline
Lim T<2
Copenhagen Accord
IPCC AR4 Model Results: History and Projections
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RICE-2010model
Policy outcomes variablesOverall evaluationTwo major policy variables are
- emissions with controls- carbon tax
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Carbon prices for major scenarios
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0
100
200
300
400
500
600
700
800
900
1,000
2005 2025 2045 2065 2085 2105
Carb
on p
rice (
2005
$ pe
r ton
C)
Optimal
Lim T<2
Copenhagen Accord
Source: Nordhaus, “Economics of Copenhagen Accord,” PNAS (US), 2010.
0
50
100
150
200
250
2005 2015 2025 2035
Carb
on p
rice (
2005
$ pe
r ton
C)
Optimal
Lim T<2
Copenhagen Accord
Where are we today?
Actual equivalent global carbon price = $1 / tCO2