AN INTEGRATED MODEL OF ENERGY USEAND CARBON EMISSIONS

YOUNGHO CHANG

DEPARTMENT OF ECONOMICS

NATIONAL UNIVERSITY OF SINGAPORE

INTERNATIONAL ENERGY WORKSHOP 2005

Pa-lu-lu Plaza, Kyoto, Japan

5 - 7 July 2005

2

AN INTEGRATRED MODEL OF ENERGY USE AND CARBON EMISSIONS

• PROLOGUE

• MOTIVATION

• MODEL STRUCTURE

• DATA

• SIMULATION RESULTS– BASELINE AND FIVE SCENARIOS

• FINAL REMARKS

3

PROLOGUE: DEBATE ON GLOBAL WARMINGAND THE KYOTO PROTOCOL

• ACCUMULATION OF CARBON DIOXIDE IN THE ATMOSPHERE– A MAIN CAUSE OF GLOBAL WARMING AND CLIMATE CHANGE

• MELTING ICE OF ANTARCTICA AND CORRESPONDING SEA LEVEL RISE

• HOWEVER, CAUSES AND EFFECTS ARE STILL CONTROVERSIAL

• THE KYOTO PROTOCOL IS NOW A BINDING AGREEMENT– HOWEVER, THE U.S. HAS WITHDRAWN FROM THE KYOTO PROTOCOL

– AUSTRALIA IS ANOTHER COUNTRY WHO HAS NOT RATIFIED• SIMPLY TOO COSTLY

– RUSSIA HAS RATIFIEDTHE KYOTO PROTOCOL• BENEFITS AND COSTS

• CLEAN DEVELOPMENT MECHANISM (CDM) IS EXTENSIVELY USED BETWEEN THE EU AND ASIA-PACIFIC COUNTRIES

4

MOTIVATION

• ECONOMICS OF CLIMATE CHANGE

• BOTTOM-UP APPROACH– MOSTLY ENGINEERING-BASED– SECTOR-SPECIFIC ENERGY DEMAND FUNCTIONS– NO FEEDBACK BETWEEN ECONOMIC GROWTH AND ENERGY DEMAND

• NOT EXPLICITLY CONSIDER THE SHADOW PRICE OF CARBON

• TOP-DOWN APPROACH– ECONOMIC MODEL– ADOPTS A FEEDBACK RELATIONSHIP OF EMISSION AND ITS DAMAGE

UPON AN ECONOMY– LACK OF DETAILS IN REPRESENTING END-USES OF ENERGY

• INSUFFICIENT REFLECTION OF THE IMPACT OF MORE EFFICIENT END-USE TECHNOLOGIES

5

TOP-DOWN APPROACH WITH BOTTOM-UP MODEL

• COMBINES THE ECONOMIC GROWTH MODEL WITH THE SECTOR-SPECIFIC ENERGY USE

– A TWO-SECTOR GROWTH MODEL – THE UZAWA-TYPE• ENERGY RESOURCES WITH CAPTIAL AND LABOR

• ENDOGENIZE ENERGY USE

• THE MODEL CONSISTS OF THREE PARTS– AN OPTIMAL GROWTH-DAMAGE FRAMEWORK

• FEEDBACK BETWEEN ECONOMIC ACTIVITY AND CLIMATE CHANGE

– A SIMPLIFIED VERSION OF GENERAL CIRCULATION MODELS• CARBON DYNAMICS

– A SECTOR-SPECIFIC ENERGY-TECHNOLOGY FRAMEWORK• ENDOGENOUS SUBSTITUTION

6

ECONOMY, ENERGY,AND ENVIRONMENT

• ECONOMY, ENERGY, AND ENVIRONMENT ARE INTERCONNECTED

• HOW ARE THEY CONNECTED?– ECONOMY-ENERGY

• THROUGH THE PRODUCTION FUNCTION UNDER A TWO-SECTOR GROWTH FRAMEWORK

– ENERGY IS A THIRD INPUT FOR PRODUCTION ALONG WITH EXISTING TWO PRODUCTION FACTORS, CAPITAL AND LABOR

– ENERGY-ENVIRONMENT• THROUGH A CARBON DYNAMICS

– LIFE CYCLE OF CARBON– WHEN ENERGY IS USED, IT EMITS CARBON DIOXIDE AMONG OTHERS,

AND CAUSES EVENTUAL ACCUMULATION OF CARBON IN THE ATMOSPHERE

– ECONOMY-ENVIRONMENT• THROUGH POSSIBLE DAMAGE FROM THE ACCUMULATED

CARBON IN THE ATMOSPHERE OR CARBON-ABATING ACTIVITY

7

TWO-SECTOR ENERGY MODEL

• MAXIMIZES THE DISCOUNTED SUM OF UTILITY FROM PER CAPITA CONSUMPTION SUBJECT TO

– CAPITAL STOCK

– RESOURCE STOCK

– CARBON STOCK

• THE OBJECTIVE FUNCTION

– u(c): THE UTILITY FROM PER CAPITA CONSUMPTION

– c(t): THE PER CAPITA CONSUMPTION : THE PURE RATE OF SOCIAL TIME PREFERENCE

– POPULATION GROWS EXOGENOUSLY

– MULTIPLYING POPULATION, L(t), BY THE UTILITY FROM PER CAPITA CONSUMPTION YIELDS THE TOTAL UTILITY

dtetcuW t

tc

0)()]([max

8

CAPITAL BALANCE EQUATION

• THE CAPITAL GOOD – IS PRODUCED IN THE FIRST SECTOR– IS PERFECTLY MALLEABLE– IS USED IN BOTH SECTORS– DEPRECIATES EXPONENTIALLY OVER TIME

• THE CAPITAL GOODS PRODUCING SECTOR – BEARS ALL RESOURCE COSTS

• EXTRACTION AND CONVERSION COSTS

• THE CAPITAL BALANCE EQUATION

•  

– K: THE TOTAL CAPITAL STOCK ij: THE UNIT RESOURCE COST FOR THE RESOURCES USED IN EACH SECTOR (Ri) : THE RATE OF DEPRECIATION OF THE CAPITAL STOCK

, where,

)()(

1

21121

resourcesjusesendiRKFK

RKKFKK

iji j

ij

i jijij

9

RESOURCE (ENERGY)

• AN ENERGY-TECHNOLOGY FRAMEWORK– REPRESENTS ENDOGENOUS SUBSTITUTIONS AMONG ENERGY RESOURCES

– REFLECTS HETEROGENEOUS DEMAND BETWEEN SECTORS AND SIMULTANEOUS EXTRACTION OF ENERGY RESOURCES ACROSS SECTORS

– PROVIDES ENERGY PROFILES FOR PRODUCTION PROCESS

– SETS INTO A CARBON DYNAMICS

• STRUCTURE– EXTRACTION COST (RESOURCE PRODUCTION COST)

– CONVERSION COST• COST TO MEET THE CRITERIA OF EACH END-USE

– STOCK CONSTRAINT• SET AVAILABILITY OF THE RESOURCE

• PROVIDE TRANSITION FROM ONE RESOURCE TO ANOTHER

• SCARCITY RENT: IMPLICIT PRICE

10

RESOURCE CONSTRAINTS

• THE UNIT RESOURCE COST– THE SUM OF EXTRACTION AND CONVERSION COSTS

 • ij = ej + zij, where i = end-uses, j = resources

• ib = zib(t), where b = backstop technology

 

ij: THE UNIT RESOURCE COST OF OIL, COAL, AND NATURAL GAS BY SECTOR i (END-USE)– zib: THE CONVERSION COST OF SOLAR ENERGY BY SECTOR i

• STOCK BALANCE EQUATION  

 

– Sp(0): THE INITIAL STOCK OF OIL– Sa(0): THE INITIAL STOCK OF COAL– Sg(0): THE INITIAL STOCK OF NATURAL GAS

)]()([)0()(

)]()([)0()(

)]()([)0()(

21

21

21

tGtGStS

tAtAStS

tPtPStS

tgg

taa

tpp

11

RESOURCE COST FUNCTION

• THE RESOURCE COST, ij,

– DEFINED AS THE SUM OF EXTRACTION COST AND CONVERSION COSTS

• ij = ej + zij. AND ib = zib

 

• WHEN WE TAKE INTO ACCOUNT HETEROGENEOUS DEMAND, CONVERSION COST, AND EXTRACTION COST, WE HAVE A RESOURCE COST MATRIX, ij

(2x4)

– i : THE SECTORS (END-USES)• THE CAPITAL GOODS PRODUCING SECTOR

• THE CONSUMPTION GOODS PRODUCING SECTOR

– j : THE RESOURCES• OIL

• COAL

• NATURAL GAS

• SOLAR ENERGY (BACKSTOP TECHNOLOGY)

12

ENDOGENOUS SUBSTITUTION: THE CHEAPEST RESOURCE COST FIRST

• WHEN WE CONSIDER ENERGY BEHAVIOR IN THE INTERACTIONS BETWEEN ENERGY AND ECONOMY, THE LEAST COST RESOURCES ARE USED FIRST

– KEMP and LONG (1982) – LEWIS (1982) – CHAKRAVORTY and KRULCE (1994)

• THE CHEAPEST RESOURCE COST SHOULD MEAN THE PRICE OF THE RESOURCES AND THE MARGINAL DAMAGE COSTS

• ij = ij[ej(Sj(t)), zij],

ij : THE UNIT RESOURCE COST (END-USE i, RESOURCE j)– ej: THE EXTRACTION COST OF RESOURCE j– Sj(t): THE EXISTING STOCK OF THE RESOURCE j AT TIME t– zij: THE CONVERSION COST OF THE RESOURCE j FOR EACH END-USE i– ASSUME THAT (ij/Sj) 0, (2ij/Sj

2) 0, and (ij/zij) 0.

13

ENVIRONMENT

• CARBON DYNAMICS– AN AGGREGATE REPRESENTATION OF GENERAL CIRCULATION MODELS (GCMs)

– AN OPTIMAL GROWTH-DAMAGE FRAMEWORK

– CAPTURES FEEDBACKS FROM EMISSION CONTROLS THROUGH THE CARBON DYNAMICS TO THE ECONOMY

– DAMAGES ARE QUANTIFIED AS SOME FRACTIONS OF THE GLOBAL OUTPUT

• STRUCTURE– EMISSIONS

– ATMOSPHERIC CONCENTRATION OF CARBONS a.k.a. CARBON STOCK

– RADIATIVE FORCINGS

– TEMPERATURE CHANGES

– AN OUTPUT SCALING FACTOR

14

WORKINGS OF CARBON DYNAMICS

• WHEN ENERGY RESOURCE IS USED IN AN ECONOMY, IT PRODUCES– OUTPUTS (GOODS & SERVICES)– CARBON EMISSIONS WITH OTHER GREENHOUSE GASES

• A FRACTION OF THE EMISSIONS INCREASES – ATMOSPHERIC CONCENTRATION OF GHGs– RADIATIVE FORCINGS– EQUILIBRIUM TEMPERATURE

• EVENTUALLY IMPOSES A CERTAIN LEVEL OF DAMAGE TO THE ECONOMY DUE TO THE HIGHER TEMPERATURE

• A FEEDBACK RELATIONSHIP BETWEEN CLIMATE AND ECONOMIC VARIABLES IN A MACROECONOMIC STRUCTURE

– AN ECONOMIC MODEL• IMPACT OF TEMPERATURE RISE ON THE ECONOMY AS A WHOLE

– AN ENERGY MODEL– A CARBON CYCLE/TEMPERATURE MODEL

• FLOWS OF CARBON DIOXIDE EMISSIONS BY ECONOMIC ACTIVITIES AND TEMPERATURE CHANGE

15

DAMAGE FROM CLIMATE CHANGE

• POSSIBLE DAMAGE FROM CLIMATE CHANGE– VERY ELUSIVE– A MAJOR SOURCE OF CLIMATE CHANGE

• TEMPERATURE CHANGES DUE TO HIGHER CONCENTRATIONS OF GREENHOUSE GASES

– THE IMPACT OF CLIMATE CHANGE • CAN BE EXPRESS AS A FUNCTION OF THE CHANGE IN GLOBAL MEAN TEMPERATURE

FROM PRE-INDUSTRIAL TIMES, T(t).

 

D(t) : THE LOSS OF GLOBAL OUTPUT 1 : A PARAMETER REPRESENTING THE SCALE OF DAMAGE, OBTAINED BY

ESTIMATING SECTORAL DAMAGE COMPRISING THE BALANCE OF MARKET OUTPUT AS WELL AS NON-MARKET IMPACTS IN EACH COUNTRY (TAKING THE U.S. AS A REPRESENTATIVE CASE) AND BY APPLYING THEM TO DIFFERENT COUNTRIES

2 : AN EXPONENT REFLECTING NON-LINEARITY IN THE DAMAGE FUNCTION (TAKES ORDER OF 2)

2)()()(1

tTtQtD

16

COSTS OF REDUCING EMISSIONS

• COSTS OF REDUCING GREENHOUSE GAS EMISSIONS– PROLIFIC STUDIES ON THE CALCULATION– MUCH UNCERTAINTY AND ROOM FOR FURTHER ANALYSIS– TWO GOODS

• CARBON-BASED• NON-CARBON-BASED

• CARBON-BASED SECTOR– THE STANDARD ISO-ELASTIC DEMAND AND SUPPLY– APPROPRIATE APPROXIMATION PRODUCES AN EQUATION

• THE COST OF REDUCING CARBON EMISSIONS– ADOPT THE EQUATION ESTIMATED WITH DATA USING ORDINARY LEAST

SQUARES (NORDHAUS, 1991)– INVERSE TO DEMAND ELASTICITY– QUADRATIC IN THE FRACTIONAL REDUCTION– PROPOTIONAL TO THE TOTAL EXPENDITURE ON CARBON OUTPUT

17

TOTAL COSTS FUNCTION

TC(t) : THE TOTAL COSTS OF REDUCING CARBON DIOXIDE EMISSIONS

: THE FRACTIONAL REDUCTION IN GREENHOUSE GAS EMISSIONS– b1 : THE SCALE FACTOR

– b2 : REPRESENT NON-LINEARITY OF THE COST FUNCTION

– THE INITIAL REDUCTION IN THE CARBON DIOXIDE EMISSIONS IS RELATIVELY INEXPENSIVE

– FOR EXAMPLE, • IF THE FRACTIONAL REDUCTION IN GREENHOUSE GAS EMISSIONS IN THE

YEAR OF 1995 IS 12 % (0.12), THEN THE TOTAL COST OF REDUCING EMISSIONS IS 0.015 % OF THE GLOBAL OUTPUT

2

1)()()(b

tbtQtTC

18

DAMAGE AND TOTAL COSTS

• LINK DAMAGE AND TOTAL COSTS OF REDUCING TO GLOBAL OUTPUT– AN OUTPUT SCALING FACTOR, (t).

– A DEFINITION OF • THE RATIO OF GLOBAL OUTPUT LESS THE TOTAL COST OF REDUCING EMISSIONS TO

THE GLOBAL OUTPUT PLUS POSSIBLE DAMAGES FROM CLIMATE CHANGE

 • A NUMERATOR

– REFLECTS THE COST INCURRED TO THE ECONOMY FROM GHGs ABATEMENTS

• A DENOMINATOR– REPRESENTS A POTENTIAL OUTPUT UNDER NO DAMAGE FROM CLIMATE

CHANGE

])()()([

])()()([)(

2

2

1

1

tTtQtQ

tbtQtQt

b

19

OUTPUT SCALING FACTOR

• A FINAL FORM OF OUTPUT SCALING FACTOR

– b1 and b2 : PARAMETERS OF EMISSION REDUCTION COST FUNCTION

1 and 2 : PARAMETERS OF DAMAGE FUNCTION

• EXAMPLE– IF WE ASSUME A 3-DEGREE INCREASE IN AVERAGE TEMPERATURE AND 12%

REDUCTION IN EMISSIONS, • THE VALUE OF IS 0.987191.

– THE PROJECTED GLOBAL OUTPUT IS 1.28% LESS THAN WHAT IT WOULD BE OTHERWISE

])(1[

])(1[)(

2

1

2

1

tT

btb

t

20

WORKINGS OF OUTPUT SCALING FACTOR

DAMAGE

YES NO

COSTS YES << 1 < 1

NO < 1 1

21

DATA

• ECONOMIC- AND CLIMATE-RELATED DATA– NORDHAUS (2000)

– IPCC REPORT (1990)

• TECHNOLOGY- AND ENERGY-RELATED DATA– CHAKRAVORTY, ROUMASSET AND TSE (1997)

• PARAMETERS ON TWO-SECTOR PRODUCTION FUNCTION– UZAWA (1961)

– SOLOW (1961)

– SHENG CHENG HU (1978)

– EISMONT (1994)

22

SIMULATION RESULTS WITH GAMS

• SIMULATION PERIODS – 1965-2355 (400 YEARS)

• SIMULATION SCENARIOS– BASELINE– TECHNOLOGY RELATED

• COSTS OF CONVERTING SOLAR ENERGY INTO ELECTRICTY• DECREASE AT 5%; 10%; 30%; 50% PER DECADE

– POLICY-RELATED• CARBON EMISSIONS LEVEL IS STABILZED AT 10 BILLION TONS OF CARBON PER YEAR

• ENERGY USE PATTERN BY SECTOR AND CARBON EMISSIONS

• GLOBAL MEAN SURFACE TEMPERATURE CHANGE

• CARBON TAXES– THE SHADOW PRICE OF CARBON

• IMPACT OF DIFFERENT SCENARIOS ON DISCOUNTED CONSUMPTION

23

ENERGY USE PATTERN BY SECTOR

Baseline 5% 10% 30% 50% Emission at 10Year Cap S Con S Cap S Con S Cap S Con S Cap S Con S Cap S Con S Cap S Con S1965 oil gas oil gas oil gas oil gas oil gas oil gas1975 oil gas oil gas oil gas oil gas oil gas oil gas1985 oil gas oil gas oil gas oil gas oil gas oil gas1995 oil gas/oil oil gas/oil oil gas/oil oil gas/oil oil gas/oil oil gas/oil2005 oil oil oil oil oil oil oil oil oil oil oil oil2015 oil oil/coal oil oil/coal oil oil/coal oil oil/coal oil solar oil oil/coal2025 coal coal coal coal coal coal coal solar solar solar coal coal2035 coal coal coal coal coal coal coal solar solar solar coal coal2045 coal coal coal coal coal coal coal solar solar solar coal coal2055 coal coal coal coal coal coal solar solar solar solar coal coal2065 coal coal coal coal coal coal solar solar solar solar coal coal2075 coal coal coal coal coal coal solar solar solar solar coal coal2085 coal coal coal coal coal coal solar solar solar solar coal coal2095 coal coal coal coal coal coal solar solar solar solar coal coal2105 coal coal coal coal coal coal solar solar solar solar coal coal2115 coal coal coal coal coal coal solar solar solar solar coal coal2125 coal coal coal coal coal solar solar solar solar solar coal coal2135 coal coal coal coal coal solar solar solar solar solar coal coal2145 coal coal coal coal coal solar solar solar solar solar coal coal2155 coal coal coal coal coal solar solar solar solar solar coal coal2165 coal coal coal coal coal solar solar solar solar solar coal coal2175 coal coal coal coal solar solar solar solar solar solar coal coal2185 coal coal coal coal solar solar solar solar solar solar coal coal2195 coal coal coal coal solar solar solar solar solar solar coal coal2205 coal coal coal coal solar solar solar solar solar solar coal coal2215 coal coal coal coal solar solar solar solar solar solar coal coal2225 coal coal coal coal solar solar solar solar solar solar coal coal2235 coal coal coal coal solar solar solar solar solar solar coal coal2245 coal coal coal coal solar solar solar solar solar solar coal coal2255 coal coal coal solar solar solar solar solar solar solar coal coal2265 coal coal solar solar solar solar solar solar solar solar coal coal2275 coal coal solar solar solar solar solar solar solar solar coal coal2285 coal coal solar solar solar solar solar solar solar solar coal coal2295 coal coal solar solar solar solar solar solar solar solar coal coal2305 coal coal solar solar solar solar solar solar solar solar coal coal2315 coal coal solar solar solar solar solar solar solar solar coal coal2325 coal coal solar solar solar solar solar solar solar solar coal coal2335 coal coal solar solar solar solar solar solar solar solar coal coal2345 coal coal solar solar solar solar solar solar solar solar coal coal

24

CARBON EMISSIONS

Emissions (CO2 equivalent)

0

5

10

15

20

25

30

35

40

45

YEAR

Bil

lio

n t

on

of

Ca

rbo

n

Baseline

5%

10%

30%

50%

25

GLOBAL MEAN SURFACE TEMPERATURE CHANGE

Global Mean Temperature Change

0

1

2

3

4

5

6

7

YEAR

C D

eg

rees

Baseline

5%

10%

30%

50%

Stabilization

26

CARBON TAXESCarbon Tax

0.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

80.00

1965 1975 1985 1995 2005 2015 2025 2035 2045 2055 2065 2075 2085 2095 2105 2115 2125 2135 2145 2155 2165 2175 2185

YEAR

US

$ p

er

To

n o

f C

arb

on

Baseline

10%

30%

50%

27

CARBON EMISSIONS: BASELINE AND STABILIZATION

Emissions (CO2 equivalent): Baseline vs Stabiliazation

0

5

10

15

20

25

30

35

40

YEAR

Billio

n t

on

of

Carb

on

Baseline

Stabilization

28

GLOBAL MEAN SURFACE TEMPERATURE CHANGE:BASELINE AND STABILIZATION

Global Mean Temperature Change: Baseline vs Stabilization

0

1

2

3

4

5

6

7

YEAR

C D

eg

rees

Baseline

Stabilization

29

CARBON TAXES: BASELINE, 50% AND STABILIZATION

Carbon Tax: Baseline vs Stabilization

0.00

100.00

200.00

300.00

400.00

500.00

600.00

700.00

YEAR

US

$ p

er

To

n o

f C

arb

on

50%

Stabilization

Baseline

30

CARBON EMISSIONS:BASELINE, DICE AND OTHER MODELS

Carbon Emissions

0

10

20

30

40

50

60

YEAR

Bil

lio

n t

on

of

Ca

rbo

n

Baseline

DICE

CHAR'Y

50%

31

GLOBAL MEAN SURFACE TEMPERATURE CHANGE:BASELINE, DICE, IPCC AND OTHER MODELS

Global Mean Temperature Change

0

1

2

3

4

5

6

7

YEAR

C D

eg

rees Baseline

DICE

IPCC

50%

E at 10

32

CARBON TAXES:BASELINE VS DICE

Carbon Tax: Baseline vs DICE

0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

1965 1975 1985 1995 2005 2015 2025 2035 2045 2055 2065 2075 2085 2095 2105 2115 2125 2135 2145 2155 2165 2175 2185

YEAR

US

$ p

er

To

n o

f C

arb

on

Baseline

DICE

33

IMPACT OF PROGRAM ON DISCOUNTED CONSUMPTION

Impact of Program on Discounted Value of Consumption

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

5% 10% 30% 50% E at 10

SCENARIOS

Pe

rcen

t

34

FINAL REMARKS

• SWITCHING TO NON-CARBON EMITTING FUELS WOULD BE A SOLUTION FOR MITIGATING ATMOSPHERIC ACCUMULATION OF CARBON

– HOWEVER, COSTS NEEDED FOR REALIZNG SUCH TECHNOLOGIES ARE NOT VERIFIED

• POLICIES LIKE STABILIZING CARBON EMISSION AT A CERTAIN LEVEL ARE NOT EFFECTIVE IN MITIGATING TEMEPARTURE RISE AND COSTLY.

• THE DIFFERENCE BETWEEN A CLIMATE-CHANGE AND A NO-CLIMATE-CHANGE SCENARIO WOULD BE THINNER THAN THE PENCIL NEEDED TO DRAW THE CURVES.

– THOMAS SCHELLING (1983)