On Economic Growth, Energy Consumption and Technological

ChangeJussieu 24 Avril 2006

Dr Benjamin Warr Professor Robert Ayres

Introduction to INSEAD

• Two fully connected campuses in Asia (Singapore) and Europe (France), 143 faculty members from 31 countries, 880 MBA participants, 55 executive MBAs, over 7000 executives and 64 PhD candidates. On both campuses, faculty conduct leading edge research projects with the support of 17 Centres of Excellence.

Sommaire

• Critique de l’approche «neo-classique » de la croissance économique

• Considération de la rôle d’énergie

• Estimation d’une « proxy » mesure de Technologie

• Développement d’une méthode pour estimer la croissance du Produit Intérieur Brut.

Problématique

• L’approche neo-classique économique

– Ignore l’environnement et des ressources naturelles

• Comme facteur de production• Comme bien collectif

– Considère la technologie comme exogène, continue et perpétuelle.

• Mais le progrès technologique est plutôt non linéaire (learning by doing) avec des limites

Une fonction de production

• Décrit les relations entre le « output » (PIB) et les « inputs », (les facteurs de production)

• Cobb-Douglas ont développe la forme le plus utilisé,

Y = A KL where + = 1• Y=PIB, A=technology multiplier, K=capital,

L=labour, et les élasticités de production

Quelques problèmes

• Les ressources naturelles exclus….• Constant returns to scale (rendement constant)• Le dérivative défini la productivité marginal de

chaque facteur en tant que constant, égal au « factor cost » =0.3 capital, =0.7 labour.

• Static substitution• Rendu dynamique avec multiplicateur

technologie (A), l’erreur d’une modèle OLS.• PAS de RETROACTION suites aux

changements dans le quantité et qualité du bilan énergétique.

PIB et les facteurs de production, K, L, B, US 1900-2000

0

5

10

15

20

25

2000199019801970196019501940193019201910

année

ind

ex (

1900

=1)

PIB (Y)

Capital (K)

Labour (L)

Ressources Naturelles (B)

PIB empirique et estimé, et l'erreur (le progres technologique)

0

5

10

15

20

25

2000199019801970196019501940193019201910

année

ind

ex (

1900

=1)

PIB empirique

PIB estimé (Cobb-Douglas)

Erreur (technological progress)

Observations

• Même avec inclusion des ressources naturelles (B) le PIB estimé est inférieur au valeur empirique si on utilise les « factor costs » pour définir les paramètres.

• Le progrès technologique (l’erreur) est responsable pour plus que 80% de la croissance.

• Si on utilise pour prévision on est obligé de faire l’hypothèse que la technologie va développer comme avant. La croissance économique est assuré malgré nos actions.

Industrial Metabolism(Ayres and Simonis 1994)

• New conceptualisation of society’s relation to and pressures on the environment.

• The economy is physically embedded into the environment.• The economy is an open-system with regards matter &

energy.• Matter and energy societal throughputs must => minimum

requirements = technological progress.• RESOURCE SCARCITY: Societies intervene with purpose

to gain better access to supplies of natural resources (through technology and resource substitutions .i.e. energy) – a supply-side problem.

• ASSIMILATIVE CAPACITY: Societies must restrict waste flows to the environment (output side).

The Salter Cycle, an engine for growth.

Lower Prices ofMaterials &

Energy

INCREASED REVENUESIncreased Demand for

Final Goods and Services

R&D Substitution ofKnowledge for Labour;

Capital; and Exergy

ProductImprovement

Substitution ofExergy for Labour

and Capital

ProcessImprovement

Lower Limits toCosts of

Production

Economies ofScale

Criteria for Environmental Accounting

• Environmental accounting must be:– Politically relevant – strength of the concept to

provide information for policy decision and public discourse.

– Feasibility often requires reduced complexity– Definition of scale and then system

boundaries– Accurate source information– Methods to estimate stocks & flows

Energie comme facteur de production – quel mesure faut il?• Pas tout l’énergie utilisé est utile dans

l’économie – conséquence du 2eme loi de Thermodynamique.

• Faut considérer la quantité plus qualité de l’énergie utilisé

• Faut quantifier le progrès technologique et l’effet sur la quantité et le façon qu’on utilise énergie.

Task efficiency: specify service & define the task

• The first objective of any technical study of energy use is to establish a standard of performance.

• What is the difference between a service and a task?– (service) keeping warm, (task) providing heat to a home– (service) structures in society, (task) making aluminium– (service) mobility, (task) moving a vehicle

• Services must consider non-technical trade-offs, tasks require only a physics perspective.

• This permits,a) Evaluation of the efficiency of present uses.b) Definition of goals towards which technical

innovation can strive.

Thermodynamics and « available work »

Necessary to define a Minimum Task Energy to allow consideration of :

• Interchanging devices or systems (mass transport vs. Cars)• Seeking technological innovations (aluminium for steel)

• The 1st Law (convervation of energy) is inadequate for considering minimimum task energy.

• The 2nd law (the entropy law) indicates that « in any process involving heat, there is an inexorable increase of entropy (disorder), meaning that not all the energy is available in useful form »

The 1st Law (conservation of energy) is inadequate for considering minimimum

task energy.• η = energy transfer (of desired kind) /

energy input

• Maximum value may be greater than 1.

• No explicit consideration of the quality of the energy and its ability to do useful work.

• Cannot be generalised to complex systems with work and heat outputs.

The 2nd law (the entropy law)

• indicates that « in any process involving heat, there is an inexorable increase of entropy (disorder), meaning that not all the energy is available in useful form »

• For any device or system the 2nd Law Efficiency ε is the ratio of the minimum exergy that could perform the task (Bmin), to the exergy actually consumed in doing the job (Bactual).

• Its maximum value is 1.• Maximising ε minimises exergy demand and

wastes generated for a given task.

Exergy and Exergy Balance

• Exergy is the useful part of the energy.• There are 4 components:

– Kinetic exergy of bulk motion– Potential gravitational or electro-magnetic field

differentials– Physical exergy from temperature and pressure

differentials– Chemical exergy arising from differences in

chemical composition

• We can ignore the first two for many industrial and economic applications.

Exergy or « Available Work »

• So, not all energy can be made available in useful form (consequence of 2nd Law).

• Available work is an energy measure that is actually consumed in a process.

• Work is the highest quality (lowest entropy) form of energy. It is often called exergy.

• Exergy = The maximum amount of work that a subsystem can do on it’s surroundings as it approaches thermodynamic equilibrium reversibly.

• Exergy is proportional to the future entropy production, but has units of energy.

• Exergy is gained or lost in physical processes.• Minimising exergy consumption is a measureable objective

to optimise energy consuming tasks.

Example: Chemical exergy

• Production of pure iron (Fe2) from iron oxide (Fe2O3)

• This requires exergy from burning coke (pure carbon)

• Carbon dioxide (CO2) is the waste product2Fe2O3 + 3C 4Fe + 3CO2

Correct mass balance – all atoms in ome out. Conversion of mass causes inevitable joint product CO2

• 0.75 moles of CO2 per Kg of Fe.

Iron production 1

1. 2Fe2O3 + 3C 4Fe + 3CO2

2. Making 4 moles of Fe requires generation of 3 moles of CO2

3. And 1505.6 Kj which comes from this oxidation of carbon

4. But 3 moles of C contain only 1230.9

5. We need 0.76 C extra.

Weight kJ/mole

exergy

Fe 56 376.4

Fe2O3 160 16.5

C 12 410.3

CO2 44 19.9

O2 32 4.4

Iron Production 2

2Fe2O3 + 3C 4Fe + 3CO2

Correct mass balance, incorrect exergy balance

2 Fe2O3 + 3.76 C + 0.76 O2 4 Fe + 3.76 CO2

(33.0) (1542.7) (3.0) (1505.6) (74.8)On the input side oxygen has been added to fulfill the balance of the

extra C required

1580 kJ in 1580 kJ out• This is for an ideal reversible transformation. No entropy

generated or exergy lost.• Hence 0.94 moles of waste CO2 are inevitable per mole

Fe produced (corresponds to 0.74kg CO2 per kg Fe)• This is the thermodynamic minimum.

Iron Production: Reality

• The 410.3 kJ/mole from source C is never used 100% efficiently

• Blast furnace average have efficiencies of 33%.• So, one mole of C one obtains only 135.4kJ• As a result need 12.42 moles of C instead of

3.76.2 Fe2O3 + 12.42 C + 9.42 O2 4 Fe + 12.42 CO2+ heat (33.0) (5095.9) (37.7) (1505.6) (247.2)

• B lost = 3413.8 kJ• 2/3 rd of waste produced is unecessary.

Types of Exergy Service

• Prime Movers ( electricity)

• Transport

• High Temperature Process Heat

• Mid and Low Temperature Process Heat

• Lighting

• Non-Fuel

Petroleum Products

Apparent Consumption

Gasoline

Diesel

Aviation Fuel

Furnace Oil Heavy Fuel Oil

Kerosene

Feedstock

Petroleum Coke

Bitumen/ Waxes

Process Heat

Process Heat

Transport

Space Heating

Non Fuel

LPG

Lighting

Transport

Allocated to gas flows

Electricity

Petroleum Exergy Flows

Coal, Petroleum, Gas: Exergy breakdown by use, US 1900-2000

Figure 8. Coal consumption: Exergy allocation among types of work, USA 1900-1998

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

2000199019801970196019501940193019201910

year

Fra

cti

on

(%

)

HEAT

ELECTRICITY

PRIME MOVERS

NON-FUEL

Figure 9. Petroleum and NGL consumption: Exergy allocation among types of work, USA 1900-1998

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

2000199019801970196019501940193019201910

year

Fra

cti

on

(%

)

HEAT

ELECTRICITY

PRIME MOVERS

NON-FUEL

LIGHT

Figure 10. Natural Gas consumption: Exergy allocation among types of work, USA 1900-1998

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

2000199019801970196019501940193019201910

year

Fra

cti

on

(%

)

HEAT

ELECTRICITY

PRIME MOVERS

NON-FUEL

Declining fraction to heat

Increasing fraction to electricity

Transport uses

Total Exergy Breakdown by Use, US 1900-2000

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

2000199019801970196019501940193019201910

year

Fra

ctio

n (

%)

HEAT

ELECTRICITY

PRIME MOVERS

NON-FUEL

LIGHT

Heat

Other Prime Movers

Electricity

Non-Fuel

Efficiency (%) Year Kerosene Incandescent Fluorescent Average Efficiency Efficiency (%) 1% 5% 15% Market Share (%) 1900 20% 80% 0% 1.400% 1950 5% 70% 25% 2.433% 1972 1% 65% 33% 2.737% 2000 1% 60% 39% 2.953%

0.00%

0.50%

1.00%

1.50%

2.00%

2.50%

3.00%

3.50%

20001990198019701960195019401930192019101900

year

effi

cien

cy

Lighting Efficiency

Bauxite Ore 3.9kg (4.1MJ)

Cokes 1900 = 20 MJ/kg 2000 = 10 MJ/kg

Electricity 1900 = 190 MJ/kg 2000 = 66 MJ/kg

Aluminium 1kg (32.8MJ)

Refining

Electrolysis

Casting

Coal, Oil, Gas 1900 = 82 MJ/kg

2000 = 28 MJ/kg

Simplified process view:

Aluminium

MJ/1000kg % of total Coal 4092 5%

Oil 10912 14% Gas 8281 11%

Electricity 56559 70% Total 79845 100.00%

Table 1. Breakdown of total fuel exergy inputs for the production of 1 ton of primary aluminium (source: IAI LCS 2000).

Exergy consumption per kg of Al produced

0

50

100

150

200

250

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000

year

MJ/

kgBauxite

Coke

Coal, oil and gas

Electricity

Figure 1. Exergy consumed per kg primary aluminium produced. *electricity consumption adapted from Energy Implications of the Changing World of Aluminium Metal Supply (JOM 2004).

Efficiencies and GDP/Exergy Input

0%

5%

10%

15%

20%

25%

30%

35%

40%

2000199019801970196019501940193019201910year

eff

icie

nc

y

Low Temperature Space Heating

Mechanical Work

Medium Temperature Industrial Heat

High Temperature Industrial Heat

Electric Power Generation &Distribution

Technical efficiency, US 1900-2000Fig u re 3. Tech n ica l effi cien cy le a rn in g cu rve m od el,

U SA 19 00- 200 0.

0

0 ,02

0 ,04

0 ,06

0 ,08

0,1

0 ,12

0 ,14

0 ,16

0 ,18

25 6 95 14 86 26 60 4 6 77 7 11 3

cu m ula tive p rim a ry e xe rg y p rod uction (e J )

tech

nic

al

effi

cie

ncy

, f

e m p i r i ca l (U / R )"

b i l o g i s ti c m o d e l

So u r ce D a ta : A y r e s , A y r e s a n d W a r r , 2 0 0 3

Useful Work/GDP Ratios, US 1900-2000

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

2000199019801970196019501940193019201910

year

rati

o

work (Ue) / GDP ratio

work (Ub) / GDP ratio

1st Oil Crisis - US

Peak Oil Production

How does our model work ?

Cobb-Douglas or LINEX

• At the ‘total factor productivity’ is REMOVED• Rt natural resource services replaced by Useful

Work, where U = F * R• Ft technical efficiency of energy to work

conversion

tttttttt

tttt

ULKRFLKY

RLKQY

,,,

tttttttt

tttt

ULKRFLKY

RLKQY

,,,

12expU

Lab

K

ULaUYt

REXS economic output module

CumulativeProductionMonetaryMonetary

Output

Gross Output

Labour Capital

Linexparameter a

Linexparameter b

ExergyServ ices

ICT Fraction ofCapital

LinexParameter c

ICT CapitalGrowth Rate

Labour supply feedback dynamics

Parameters for USA 1900-2000• Structural Shift Time C=1959, Structural Shift Time D=1920• F Labour Fire Rate A=0.108, F Labour Fire Rate B=0.120• F Labour Hire Rate A=0.124 F Labour Hire Rate B=0.135

LabourLabour Hire

RateLabour Fire

Rate

FractionalLabour Hire Rate

A

FractionalLabour Hire Rate

B

FractionalLabour Fire Rate

A

FractionalLabour Fire Rate

B

Structural ShiftTime C

<Time>

Structural ShiftTime D

Labour “hire and fire” parametersS im u la te d l a b o u r h ir e a n d fi re r a te , U S A 1 9 0 0 -2 0 0 0

0

0 ,0 5

0 , 1

0 ,1 5

0 , 2

0 ,2 5

0 , 3

0 ,3 5

0 , 4

0 ,4 5

1 9 0 0 1 9 1 0 1 9 2 0 1 9 3 0 1 9 4 0 1 9 5 0 1 9 6 0 1 9 7 0 1 9 8 0 1 9 9 0 2 0 0 0

y e a r

rate

(st

anda

rdis

ed la

bou

r un

its p

er y

ear)

L a b o u r H i re R a te

L a b o u r F ir e R a te

Labour – validation by empirical fitS im u la t e d a n d e m p ir i c a l la b o u r, U S A 1 9 0 0 -2 0 0 0

0

0 ,5

1

1 ,5

2

2 ,5

3

3 ,5

1 9 0 0 1 9 1 0 1 9 2 0 1 9 3 0 1 9 4 0 1 9 5 0 1 9 6 0 1 9 7 0 1 9 8 0 1 9 9 0 2 0 0 0

y e a r

norm

alis

ed

labo

ur (

1900

=1)

e m p i r i c a l

s im u la te d

Capital accumulation feedback loop

Parameters for USA 1900-2000• Investment Fraction A=0.081 Investment Fraction B=0.074

• Depreciation Rate A=0.059 Depreciation Rate B=0.106

• Structural Shift Time A=1970 Structural Shift Time B=1930

CapitalInvestment Depreciation

InvestmentFraction

<Time>

DepreciationRate

<GrossOutput>

InvestmentFraction A

InvestmentFraction B

DepreciationRate A

DepreciationRate B

Structural ShiftTime A

Structural ShiftTime B

Capital investment and depreciationS im u l a t e d i n v e s tm e n t a n d d e p re c ia t io n , U S A 1 9 0 0 -2 0 0 0

0

0 .2

0 .4

0 .6

0 .8

1

1 .2

1 .4

1 .6

1 .8

1 9 0 0 1 9 1 0 1 9 2 0 1 9 3 0 1 9 4 0 1 9 5 0 1 9 6 0 1 9 7 0 1 9 8 0 1 9 9 0

y e a r

norm

alis

ed c

apita

l (19

00=

1)

i n v e s t m e n t

d e p r e c ia t io n

Capital – validation by empirical fitS im u l a te d a n d e m p i r i c a l c a p i ta l, U S A 1 9 0 0 -2 0 0 0

0

2

4

6

8

1 0

1 2

1 4

1 9 0 0 1 9 1 0 1 9 2 0 1 9 3 0 1 9 4 0 1 9 5 0 1 9 6 0 1 9 7 0 1 9 8 0 1 9 9 0

y e a r

norm

alis

ed c

apita

l (19

00=

1)

e m p i r i c a l

s im u la te d

Output – validation of full model, US 1900-2000

0

2

4

6

8

10

12

14

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990

year

no

rma

lise

d c

ap

ita

l (1

90

0=

1)

empirical

simulated

LINEX fits for GDP, Japan and US 1900-2000.Empirical and estimated GDP (using LINEX),

US and Japan 1900-2000

0

1000

2000

3000

4000

5000

6000

7000

8000

1900 1920 1940 1960 1980

year

GD

P (

tho

usa

nd

bil

lio

n 1

992$

)

empirical GDP, Japan

predicted GDP, Japan

empirical GDP, US

predicted GDP, US

Estimates of GDP, France 1960-2000

0

0.5

1

1.5

2

2.5

3

3.5

4

1963 1968 1973 1978 1983 1988 1993

ou

tpu

t (1

960=

1)Y

LINEX

Time Dependent CD

Time Average CD

A commonly used reference modeE n e rg y In t e n s i ty o f C a p i ta l, U S A 1 9 0 0 - 2 0 0 0 .

8

1 0

1 2

1 4

1 6

1 8

2 0

2 2

2 4

2 6

2 8

2 0 0 01 9 9 01 9 8 01 9 7 01 9 6 01 9 5 01 9 4 01 9 3 01 9 2 01 9 1 01 9 0 0

y e a r

inde

x

b /k - t o ta l p r i m a r y e x e rg y s u p p l y(e n e rg y c a r r i e rs , m e ta l s , m in e ra l s a n d p h y to m a s s e x e rg y )

e /k - t o ta l fu e l e x e rg y s u p p ly(e n e rg y c a r r i e rs o n ly )

S t a r t o f t h e G re a t D e p r e s s io n

E n d o f W o rld W a r II

The REXS alternativeS im u l a t e d a n d e m p ir i c a l p r im a r y e x e r g y i n te n s it y o f o u tp u t,

U S A 1 9 0 0 - 2 0 0 0

0

0 .2

0 .4

0 .6

0 .8

1

1 .2

1 9 0 0 1 9 1 0 1 9 2 0 1 9 3 0 1 9 4 0 1 9 5 0 1 9 6 0 1 9 7 0 1 9 8 0 1 9 9 0

y e a r

r/y

(190

0=1)

e m p ir ic a l

s im u la t e d

Average rate of decline 1.2% per annum

Declining resourceintensity of output

Continuing historicaltrends of technicale fficiency growth

Useful worksupply

Economicoutput

cumulativeoutput

experience

cumulative exergyproductionexperience

The “dematerialising” dynamics

Primary exergy intensity (B/GDP) of output decay feedback mechanism.

Parameters• Rate of Decay = Fractional

Decay Rate*Primary Exergy Intensity of Output

• Fractional Decay Rate=0.012

Primary ExergyIntensity of Output

Rate of Decay

FractionalDecay RatePrimary Exergy

Demand

<GrossOutput>

Lower Prices ofMaterials &

Energy

INCREASED REVENUESIncreased Demand for

Final Goods and Services

R&D Substitution ofKnowledge for Labour;

Capital; and Exergy

ProductImprovement

Substitution ofExergy for Labour

and Capital

ProcessImprovement

Lower Limits toCosts of

Production

Economies ofScale

To the right: Processes aggregated inthe REXS dynamics

Projections of future outputAltering the future rates of the energy intensity of output

•The average decay rate of the exergy intensity of output (R/GDP) for the period 1900-1998 is 1.2%

•The simulations involved increasing or decreasing this parameter from 1998 onwards, while keeping the values of all other parameters fixed.

•The following illustrations provide a summary of the results.

Varying rates of dematerialisation

Primary Exergy Intensity of Output Decline Rate 0

-0.5

-1

-1.5

-2 1900 1938 1975 2013 2050

Year

(%)

historical trend 50% 75% 95% 100%

The constant rate of exergy intensity decline was altered to vary between –0.55 and –1.65 % p.a.

Effects on ‘efficiency’ improvements

Technical Efficiency of Primary Exergy Conversion 0.4

0.3

0.2

0.1

0 1900 1938 1975 2013 2050

Year

historical data 50% 75% 95% 100%

effi

cien

cy

The ‘business as usual’ case:

If technical efficiency does not increase in pace with ‘de-materialisation’

The rate of growth slows.

GDP forecasts “dematerialisation scenarios” ,US 2000-2050

Gross Output 200

150

100

50

0 1900 1938 1975 2013 2050

Year

historical data 50% 75% 95% 100%

Ind

ex (

1900

=1)

The sensitivity of future projections of GDP were assessed, the red line indicates the ‘business as usual’ for a fractional decay rate of energy intensity of output –1.2 % per annum and technical efficiency at 1% p.a.

0

20

40

60

80

100

120

1950 1975 2000 2025 2050

year

GD

P (1

900=

1)1.2% per annum

1.3% per annum

1.4% per annum

1.5% per annum

empirical

Historical and forecast GDP for alternative rates of decline of the energy intensity of

output, US 1900-2000

Forecast GDP growth rates for three alternative technology scenarios (US 2050).

Alternative Technology Scenarios

Low Mid High

Growth rate f GDP f GDP f GDP

Minimum 0.16% -2.97% 0.43% -1.89% 1.11% 1.94%

Average 0.40% -1.29% 0.72% 0.38% 1.18% 2.20%

Maximum 0.62% 0.92% 0.89% 1.75% 1.23% 2.63%

Note the feedback between f growth and GDP growth

Historical and forecast technical efficiency of energy conversion, for 3 alternative rates of technical

efficiency growth, US 1950-2000.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

1950 1975 2000 2025 2050

year

tech

nica

l effi

cien

cy (f

)

low

mid

high

empirical

Historical and forecast GDP, for 3 alternative rates of technical efficiency growth, US 1950-

2050

0

10

20

30

40

50

60

70

1950 1975 2000 2025 2050

year

GD

P (1

900=

1)

low

mid

high

empirical

Conclusions

• Travail utile comme facteur de production• Application du 2° loi pour « proxy » de progrès

technologique• Fonction LINEX et représentation Systèmes

Dynamique permettant– Estimation historique– « substitution dynamique » suite aux progrès– Feedback entre progrès technologique et le quantité

et qualité des sources énergétique et l’efficacité d’utilisation