Transcript Slide 1

Integrated Assessment Models
of Economics of Climate Change
Economics 331b
1
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
Person or
nation 1
Pareto Improvement from
Climate Policy
Bargaining
region (Pareto
improving)
Inefficient
initial (nopolicy)
position
Person or nation 24
Elements of building/using an IAM
1. Economics
–
–
–
Population
Inputs: energy, capital, land, …
Technology (total factor productivity)
2. Emissions of CO2 and other GHGs
3. Carbon cycle, forcings, temperature, other geophysical
4. Impacts or damages
5. Policies
–
–
Emissions controls, taxes, regulations, subsidies
International strategies for global externalities
5
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 assignment
Also:
- 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) W 
T max
 U[c(t),L(t)] R(t) [maximize for control rate (μ) and savings rate (s)]
t 1
Economics
(2) U [c(t),L(t )] = L(t)[c(t) 1- / (1-  )]
Utility function
(3)  (t) = Dam / GDP = [1+ 1 TAT (t)+ 2 TAT (t) 2 ]
Damage function
(4) (t) = 1(t) (t) 2
Abatement cost
(5) Qg (t) = A(t) K(t)  L(t) 1  C(t)  s(t)Q g(t)
Gross output
(6) Qn (t) = [1- (t)] [1- (t)] Qg (t)
Net output
(7) EInd (t) =  (t)[1- (t)] Qg (t)
Geosciences
(8) MAT (t)  E(t)   11 MAT (t - 1)  ...
Industrial emissions
(9) F(t)   { log2 [ MAT (t) / MAT (0)] }  F EX (t)
Radiative forcings
Atmospheric CO2
Key variables
from growth
theory): Global mean temperature
(t)addition
 TAT (t to
 1standard
)   1 {F(t)
...
(10) TAT(in
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
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R = utility discount factor = (1+ρ)-t
Basic structure of IAM
Economic sectors (more or less elaborate):
Q = A F(K, L) = C + I
plus:
•
•
•
•
Energy sector
Emissions
Abatement
Climate damages
Geophysical sectors:
•
•
•
Carbon cycle
Climate model
Impacts
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I. Economics: DICE/RICE model example
Population 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 prices
Savings rate optimized by country
- Use Solow-Ramsey model of optimal economic growth
Put all these together (for 12 regions j=US, EU, …)
Q jg (t) = A j (t) K j (t) L j (t)1 
K j (t) = s(t)Q j (t)   K j (t)
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Per capita GDP: history and projections
Per capita GDP (2000$ PPP)
100
10
US
WE
OHI
Russia
EE/FSU
Japan
China
India
World
1
1960
1980
2000
2020
2040
2060
2080
2100
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Modeling Strategies (II): Emissions
Emissions trajectories:
Start with data on Q, L, and E of CO2 for major countries
Estimate population, productivity, emissions growth
Project these by decade for future
Then aggregate up by twelve major regions (US, EU, …)
Constrain by global fossil fuel resources
This is probably the largest uncertainty over the long run.
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CO2-GDP ratios: history
CO2-GDP ratio (tons per constant PPP $)
.7
.6
China
Russia
US
World
Western/Central Europe
.5
.4
.3
.2
.1
.0
80 82 84 86 88 90 92 94 96 98 00 02 04
12
Decarbonization projections
0.35
US
EU
Japan
Russia
China
India
0.30
CO2 emissions/GDP
0.25
0.20
Africa
0.15
0.10
0.05
2005 2015 2025 2035 2045 2055 2065 2075 2085 2095 2105
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Modeling Strategies (III): Climate Models
Climate model
Idea 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.
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Actual and predicted global temperature history
.6
.4
.2
.0
-.2
-.4
-.6
1840
1880
1920
1960
2000
YEAR
T_DICE2007
T_Hadley
T_GISS
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T projections multi-model comparison
5.0
4.5
RICE-201
EMF-22
Global mean temperature increase
(from 1900, ◦C)
4.0
A1B
3.5
A2
3.0
B1
2.5
B2
2.0
1.5
1.0
0.5
0.0
2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100
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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, …)
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Summary from Tol Survey
6
Tol survey
Damages as percent of output
5
4
3
2
1
0
-1
-2
-3
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Global mean temperature increase (°C)
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
Marginal cost of reductions
–
We will return to this later.
0
Reductions in energy
use or CO2 emissions
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Economic Theory Behind Modeling
1. Basic theorem of “markets as maximization” (Samuelson, Negishi)
Outcome of efficient
competitive market
(however complex
but finite time)
Maximization of weighted
utility function:
=
n
W   i [U i (c ki ,s ,t )]
i 1
for utility functions U; individuals i=1,...,n;
locations k, uncertain states of world s,
i
time periods t; welfare weights  .
2. This allows us (in principle) to calculate the outcome of a market
system by a constrained non-linear maximization.
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How do we solve IA models?
The structure of the models is the following:
max W 
{  ( t )}
T max
 U[c(t ),L(t )]R(t )
t 1
subject to
c(t )  H[ (t ),s(t ); initial conditions, parameters]
(The H[...] functions are production functions, climate model,
carbon cycle, abatement costs, damages, and so forth.)
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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Can also calculate the “shadow prices,”
here the efficient carbon taxes
600
Marginal cost of Emissions Reductions ($)
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)
500
400
300
200
100
0
0
10
20
30
Period
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Applications of IA Models
I 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
20
Optimal
CO2 emissions (GtC per year)
18
Baseline
16
Lim T<2
14
Copenhagen Accord
12
10
8
6
4
2
0
2005
2025
2045
2065
2085
Source: Nordhaus, “Economics of Copenhagen Accord,” PNAS (US), 2010.
2105
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Concentrations profiles: RICE-2010
Atmospheric concentrations CO2 (ppm)
1,400
Optimal
1,200
Baseline
Lim T<2
1,000
Copenhagen Accord
800
600
400
200
0
2005
2025
2045
2065
2085
2105
2125
2145
2165
2185
2205
25
Temperature profiles
6.0
Global mean temperature (degrees C)
Optimal
5.0
4.0
3.0
Baseline
Lim T<2
Copenhagen
Accord
2.0
1.0
0.0
2005 2025 2045 2065 2085 2105 2125 2145 2165 2185 2205
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IPCC AR4 Model Results: History and Projections
RICE-2010
model
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Policy outcomes variables
Overall evaluation
Two major policy variables are
- emissions with controls
- carbon tax
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Carbon prices for major scenarios
1,000
Optimal
900
Lim T<2
Carbon price (2005 $ per ton C)
800
Copenhagen Accord
700
600
500
400
300
200
100
0
2005
2025
2045
2065
2085
2105
Source: Nordhaus, “Economics of Copenhagen Accord,” PNAS (US), 2010.
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Where are we today?
250
Optimal
Lim T<2
Actual
equivalent
global carbon
price = $1 /
tCO2
Carbon price (2005 $ per ton C)
200
Copenhagen Accord
150
100
50
0
2005
2015
2025
2035