an application of the logistic curve to the modeling of co 2 emission reduction
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An application of the logistic curve to the modeling of CO 2 emission reduction. Kazushi Hatase Graduate School of Economics, Kobe University. The model and simulations of this study. Model: RAMLOG. Global economy is viewed as a two-sector Ramsey model - PowerPoint PPT PresentationTRANSCRIPT
An application of the logistic curve to the modelingof CO2 emission reduction
Kazushi Hatase
Graduate School of Economics, Kobe University
2007/10/7 SEEPS Annual Meeting, Shiga University 2
The model and simulations of this study
Model: RAMLOG
Global economy is viewed as a two-sector Ramsey model
Energy sector of the model consists of two energy technologies: Fossil energy New carbon-free energy
Diffusion of new energy technology is modeled by combining the logistic curve and learning-by-doing
Simulations
Varying two parameters which determine technology diffusion
Investigating the change of optimal CO2 emission reduction pathways and costs of emission reduction when the two parameters are varied
2007/10/7 SEEPS Annual Meeting, Shiga University 3
Preceding studies and significance of this study
Energy-economy models with substitutable two (fossil & new) energies
Goulder & Schneider (1999)
DEMETER
(2002)
ENTICE-BR
(2006)This study
Technological change
R&DLearning-by-
doingR&D
Learning-by- doing
Elasticity between two energies (σ)
σ=0.9 σ=2, 3, 4 σ=1.6, 2.2, 8.7Determined by logistic curve
Significance of this study
Diffusion of low CO2-emitting energy is crucial in climate change mitigation. This study proposes a model of long-term technology diffusion.
Logistic curve provides more realistic projection of future technology diffusion than the use of fixed elasticity between fossil and new energies.
Influence of technology-related parameters on CO2 emission reduction is examined.
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Model of global economy (the Ramsey model)
1. Intertemporal utility maximization
2. Production function
3. Capital accumulation
4. Income accounts identity
0
max 1 logT
t
t t t tt
V L C L
1 11
1t t t t t tY K L E
1 1t t tK K I
, t t t t t t tY C I EC EC p E
t 0: labor inputs : pure time preference; exp t tL d t
: energy inputs , : parameterst t tE
: energy production coststEC
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Logistic curve
Energy inputs consist of two energy technologies
Share of the new energy grows following the logistic curve
Modifying the equation above into the inequality form:
Finite difference form is used in the computer program:
1tt t
dSaS S
dt
1tt t
dSaS S
dt
1 1t t t tS S aS S t
1 1 1
1 1t t t t t t t t tY K L S E S E
1 : fossil energy inputs : new energy inputs : share of new energyt t t t tS E S E S
: coefficienta
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Logistic curve (continued)
Coefficient determines the speed of diffusion in
It determines the “potential” speed of diffusion in
In the inequality form, diffusion trajectory can take any paths under the logistic curve
0%
20%
40%
60%
80%
100%
0 5 10 15 20 25 30 35 40
Shar
e of
new
ene
rgy
a 1t t tdS dt aS S
1t t tdS dt aS S
curve with small a
curve with large a
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Learning-by-doing
Price of fossil energy is constant
Price of new energy declines as experience increases
Data of experience index ( source: McDonald & Schrattenholzer, 2001 )
Technology Period Value of b
Nuclear (OECD) 1975 – 1993 0.09
GTCC ( OECD ) 1984 – 1994 0.60
Wind (OECD) 1981 – 1995 0.27
Photovoltaics (OECD) 1968 – 1998 0.32
Ethanol (Brazil) 1979 – 1995 0.32
,F t Fp p
, ,00
b
tN t N
Wp p
W
Fp
Np
: cumulative experience : experience indextW b
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Learning-by-doing in the computer program
Using a finite difference form (Anderson & Winne, 2004)
Substituting Wt by the cumulative installed capacity of new energy
Estimation of W0 (Gerlagh and van der Zwaan, 2004)
0 0 0N N
N
gW S E
g
min 1, 1 , ,
1
t tN t N t N t N
t
W Wp p b p p
W
1
1 10
1t
t t t N t tW S E S E
: new energy inputs : plant's depreciation rate of new energyt t NS E
: growth rate of new energyNg
2007/10/7 SEEPS Annual Meeting, Shiga University 9
Combining the Ramsey model, logistic curve and learning-by-doing
0
max 1 logT
t
t t t tt
L C L
Ramsey model
1 11
1t t t t t tY K L E
1t N t t F t tp p S p S
1tt t
dSaS S
dt , ,0
0
b
tN t N
Wp p
W
1 1 t t t t t t t tK K I Y C I p E
1
1 10
1t
t NW S E S E
Logistic curve Learning by doing
2007/10/7 SEEPS Annual Meeting, Shiga University 10
Climate change model
Adopt a simple CO2 accumulation model (Grubb et al., 1995)
Anthropogenic CO2 emission
Natural CO2 emission (adopting DEMETER’s parameterization)
1Anth Nat
t t t t tM M Emis Emis M
maxtM M
max2: CO accumulation stabilization target (500ppm) : removal rateM M :
1Antht F t tEmis S E : emission intensity of fossil energyF
Nat NattEmis Emis : 1.33 /NatEmis GtC yr
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Simulation scenarios
Simulation is lead to a time path of emissions that satisfies the stabilization target of 500ppm (cost-effectiveness simulation)
Investigating how Potential speed of technological change (coefficient a) Leaning rate (experience index:b)
affect CO2 emission reduction pathways and the costs of reduction
Run : coefficient of logistic curve b: experience index
(a) STC + LL 0.05 0.1
(b) STC + HL 0.05 0.5
(c) FTC + LL 0.15 0.1
(d) FTC + HL 0.15 0.5
STC: Slow Technological Change FTC: Fast Technological Change
LL: Low Learning HL: High Learning
Model runs and parameter settings
a
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Common parameters (mainly adopted from DEMETER model)
Parameter Description Value
K(0) Capital in 2000 76.746 $trillion
Y(0) Gross output (GWP) in 2000 29.068 $trillion
E(0) Total energy input in 2000 6.628 GtC
δ Depreciation rate on capital 7%/year
γ Capital’s value share 0.31
σ Elasticity between K-L and E 0.40
S(0) Share of new energy in 2000 4.2%
pF Price of fossil energy 276.29 $/tC
pN (0) Price of new energy in 2000 1000 $/tC
pNmin
Lowest possible cost of new energy 250 $/tC
σN Plant’s depreciation rate of new energy 7%/year
gN Growth rate of new energy inputs 4.8%/year
M(0) Carbon accumulation in the atmosphere in 2000 786 GtC
μ Removal rate of CO2 from the atmosphere 0.6%/year
θF Emission intensity of fossil energy 1.0
EmisNat Natural CO2 emission in 2000 1.33 GtC/year
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Calibration of the production function (based on MERGE model’s method)
1. Setting up the reference values of Y(t), K(t), E(t)
2. Differentiating and rearranging the production function to obtain α and β
00REF
A t L tY t Y
L
00REF
A t L tK t K
L
1
0 10
t
REF
A t L tE t E EEI
L
1
1
0 REF
REF
p Y tt
E t
1 1
11
REF REF
REF
Y t t E tt
K t L t
: labor productivity : energy efficiency improvementA t EEI t
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Optimal CO2 emission pathways
Four emission pathways are not very different Learning-by-doing has almost no effect in STC (slow technological
change)
5
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20
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2100
2110
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Em
issi
on (G
tC) BaU case
STC + LL
STC + HL
FTC + LL
FTC + HL
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Optimal CO2 reduction pathways
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Red
uced
em
issi
on (G
tC)
STC + LL
STC + HL
FTC + LL
FTC + HL
FTC + HL supports deferring CO2 emission reduction
The other three paths are nearly the same in the early 21st century
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Optimal technology switch timing
Larger learning rate makes the starting point of diffusion earlier
STC (slow technological change) acts as a “friction” to technology switch, making the starting point of technology diffusion further earlier so as to achieve the emission reduction target
0%
10%
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80%
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Shar
e of
new
ene
rgy (
%) STC + LL
STC + HL
FTC + LL
FTC + HL
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Emission reduction by reducing energy input and by new energy
0
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Red
uced
em
issi
on (
GtC
)
0
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Red
uced
em
issi
on (
GtC
)
0
2
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2010
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Red
uced
em
issi
on (G
tC)
by reducing energy input
by new energy
0
2
4
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Red
uced
em
issi
on (
GtC
)
(a) STC + LL
(c) FTC + LL
(b) STC + HL
(d) FTC + HL
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Loss of GWP through CO2 emission reduction
0%
2%
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6%
8%
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00
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50
GW
P L
oss STC + LL
STC + HL
FTC + LL
FTC + HL
GWP loss largely depends on the learning rate
Pathways with the same learning rate are close or the same in the early and late period
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Technology switch and GWP loss under High Learning
0%
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80%
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Sha
re o
f ne
w e
nerg
y (%
)
0%
2%
4%
6%
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GW
P L
oss
STC + HL FTC + HL
Technology diffusion of STC starts early, but GWP loss in the early period is not so different from FTC (major difference occurs after 2060)
Starting technology switch from the early period does not make big difference of GWP loss before 2050
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Carbon tax levels
0
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Car
bon
tax
($/tC
)
STC + LL
STC + HL
FTC + LL
FTC + HL
Patterns are similar to those of GWP loss
Pathways of the same learning rate are the same in the early and late period
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Conclusions
1. Progress of new carbon free technology justifies deferring CO2 emission reduction only in the case of FTC (fast technological change) + HL (high learning).
2. Optimal CO2 reduction paths are relatively similar between the 4 model runs, while the optimal technology diffusion paths diverge.
3. Larger learning rate makes the starting point of technology diffusion earlier.
4. Slow technological change acts as a “friction” to technology switch,
making the starting point of technology diffusion further earlier so as to achieve the emission reduction target.
5. GWP loss largely depends on the learning rate. Pathways of GWP loss with the same learning rate are close or the same in the early and late period.