Energy technology diffusion and CO2 emission reduction: An application of the Ramsey model with...

Energy technology diffusion and CO2 emission reduction: Anapplication of the Ramsey model with logistic process

Kazushi Hatase

Graduate School of Economics, Kobe University

November 22, 2008 2

Effect of economic inertia: motivation for this study

An explanation of economic inertia by Grubb (1997) Most capital stock in the energy sector has a lifetime of 30-40 years,

and once capital stock is built, it is not easy to replace

In addition, there are complex interdependent systems in energy infrastructures, and thus the energy sector cannot easily respond to the requirement of a technology change to help CO2 emissions reduction

⇒ The above raises questions about the optimal CO2 reduction pathways calculated by general equilibrium models

Objective of this study Expressing economic inertia in the energy sector by using a logistic

curve

Investigating the change of optimal CO2 emission reduction pathways when major parameters are varied

International Symposium on New Development in Environmental Economics, Sophia University

November 22, 2008 3

Ha-Duong, Grubb and Hourcade (1997), Nature, 390: 270 – 273

This is virtually the sole study which explicitly investigates the effect of economic inertia in the energy sector

Using a cost-minimization model, expressing CO2 abatement cost as:

whereCa, Cb: constant

Eref: reference CO2 emission (business as usual case)

d: decline rate of costε(t): emission reduction rate defined as:

‘Adjustment costs’ expressed by reflects economic inertia in the energy sector


22

0

11

ref

a b tref

dε t E tAbetementCost C ε t C

dt E t d

2 1 : CO emission with abatementrefE t E t ε t E t

2

b

dε tC

dt

November 22, 2008 4

Policy implications of Ha-Duong, Grubb and Hourcade (1997)

When the stabilization target is 550 ppm, deferring CO2 abatement does not affect abatement cost so much

When the stabilization target is 450 ppm, the cost of deferral rises sharply as the inertia of the system is increased


November 22, 2008 5

Model of this study

Model 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

Significance of the model of this study The model considers economic inertia and endogenous technological

change, both of which are important for policy decision-making

Use of logistic curve gives more realistic projections for policy studies compared to the use of CES production function with fixing elasticity between fossil and new energies


November 22, 2008 6

Model of global economy (the Ramsey model)

1. Intertemporal utility maximization

2. Production function

　　 3. Capital accumulation

4. Income accounts identity

　　

1

0 0

max log 1tT

t t t vt v

L C L

1 111

t 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


November 22, 2008 7

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

dS aS Sdt

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


November 22, 2008 8

Logistic curve (continued)

Coefficient determines the speed of diffusion in

It determines the ‘potential speed’ of diffusion in

Coefficient a can be interpreted as a parameter determining the degree of economic inertia: the smaller a is, the larger the economic inertia and the slower the technological change

0%

20%

40%

60%

80%

100%

0 5 10 15 20 25 30 35 40

Sha

re o

f new

ene

rgy

a 1t t tdS dt aS S

1t t tdS dt aS S

curve with small : high inertiaa

curve with large : low inertiaa


November 22, 2008 9

Energy price and learning-by-doing

Price of fossil energy increases as a result of fossil energy extraction

　　

Price of new energy declines as experience increases

Data of experience index （ source: McDonald & Schrattenholzer, 2001 ）

Technology Period Value of bNuclear (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

, ,00

b

tN t N

Wp pW

Np

: cumulative experience : experience indextW b


, , ,F t F tp q Markup 4

, 1 2 maxt

F tCumC

qCumC

1 2 163.29 $/tC: transportation/distribution costs, taxes =113 $/tC, 700 $/tCMarkup max: cumulative extraction 6000 : maximum possible extractiontCumC CumC GtC

November 22, 2008 10

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 Eg

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



Combining the Ramsey model, logistic curve and learning-by-doing

1

0 0

max log 1tT

t t t vt v

L C L

Ramsey model

1 111

t 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 pW

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



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



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 ChangeLL: Low Learning HL: High Learning

Model runs and parameter settings

a



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(0) Price of fossil energy in 2000 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/yearInternational Symposium on New Development in Environmental Economics, Sophia University


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

10 1

0

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



Optimal CO2 emission pathways

Four emission pathways are not very different Learning-by-doing has virtually no effect in STC (slow technological

change)

5

10

15

20

2000

2010

2020

2030

2040

2050

2060

2070

2080

2090

2100

2110

2120

2130

2140

2150

Em

issi

on (G

tC) BaU case

STC + LLSTC + HLFTC + LLFTC + HL



Optimal CO2 reduction pathways

0

2

4

6

8

10

12

14

2000

2010

2020

2030

2040

2050

2060

2070

2080

2090

2100

2110

2120

2130

2140

2150

Red

uced

em

issi

on (G

tC)

STC + LLSTC + HLFTC + LLFTC + HL

FTC + HL supports deferring CO2 emission reduction

The other three paths are nearly the same in the early 21st century



Optimal technology switch timing

HL (high learning) makes the starting point of technology switch earlier

STC (slow technological change = high economic inertia), like high learning, favors making a technology change sooner rather than later

0%

10%

20%

30%

40%

50%

60%

70%

80%

2000

2010

2020

2030

2040

2050

2060

2070

2080

2090

2100

2110

2120

2130

2140

2150

Sha

re o

f new

ene

rgy (%

) STC + LLSTC + HLFTC + LLFTC + HL



Loss of GWP through CO2 emission reduction

0%

2%

4%

6%

8%

2000

2010

2020

2030

2040

2050

2060

2070

2080

2090

2100

2110

2120

2130

2140

2150

GW

P L

oss STC + LL

STC + HLFTC + LLFTC + HL

Loss of GWP primarily depends on the learning rate Pathways of GWP loss with the same learning rate are nearly the

same in both the earlier and later periods



Technology switch and GWP loss under High Learning

0%

10%

20%

30%

40%

50%

60%

70%

80%

2000

2010

2020

2030

2040

2050

2060

2070

2080

2090

2100

Sha

re o

f ne

w e

nerg

y (%

)

0%

2%

4%

6%

2000

2010

2020

2030

2040

2050

2060

2070

2080

2090

2100

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



Other discussions

High economic inertia, like high learning, makes the starting point of technology switch earlier

⇒ This conclusion is quite obvious and the qualitative insight that the model provides is not really telling us much.

⇒ From the policy perspective, we need empirical evidence and quantitative analyses on the effect of economic inertia, i.e., to what extent economic inertia makes technology switch earlier.

Ha-Duong et al. (1997) shows that the cost of deferring abatement rises sharply when the stabilization target is 450 ppm, while in this study economic inertia does not make abatement cost so different before 2050

⇒ We need to model economic inertia in other ways (i.e. not using logistic curve but other expressions) to check the difference between the studies.

This study applies learning-by-doing model for expressing endogenous technological change.

⇒ Combining R&D model (Romer, 1990) and learning-by-doing model might be an idea to improve the model.


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Energy technology diffusion and CO2 emission reduction: An application of the Ramsey model with...

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