2nd IIASA-TITECH Technical Meeting27th –28th April 2003, Vienna

Center for the Management of Environmental Resources (CMER)INSEAD

Boulevard de ConstanceFontainebleau

77300http://benjamin.warr.free.fr

An introduction to a simple endogenous evolutionary model of macro-economic

growth called REXS

ObjectivesForesight with the wisdom of hindsightMost projection methods rely on exogenous

assumptions of “factor productivity” or “technological progress”.

• Avoid assumption of exogenous technology & factor productivity growth

• Identify productive role of natural resource consumption

• Bridge gap between “bottom-up” and “top-down” models

Overview

• A. What is current ‘common’ practice ?

• B. How does our model work ?– i. (Labour Quality & Services)– ii. (Capital Accumulation & Services)– iii. Technology and Energy (Exergy) Services

• C. What does our model predict ?A First Test

• The effects of a declining energy intensity of output, on future rates of technical efficiency and output growth.

Common practice( )( ) ( ) ( )γβα

tttttttt

tttttttt

RFLGKHAY

RFLGKHAQY

=

= ,,,,

Yt is output at time t, given by Q a function of,• Kt, Lt, Rt, inputs of capital, labour and natural resource

services.• β and γ are parameters• At is total factor productivity• Ht, Ft, Gt, coefficients of factor qualityOutput growth is a function of• increases in quantity of factors (k, l, r)• increases in factor quality (f, g, m) – UNDEFINED &

EXOGENOUS• technology factor productivity (a)- UNDEFINED & EXOGENOUS• (changes in resource allocation – i.e. sectoral activity)

( ) ( ) ( )( )rflgkhaAQ

QtY

+−−+++++

∂∂

=∂∂ γβγβ 11

How does our model work

either Cobb-Douglas or LINEX

• At the ‘total factor productivity’ is REMOVED• Rt natural resource services replaced by U• Ft technical efficiency of energy to work conversion

• (H – hedonic pricing and G - hourly compensation in later versions of the model)

• α, β, γ (or in LINEX a, b, c) are empirically estimated ‘constant’ parameters

( )tttt RLKQY = ,,,

( ) ( ) ( ) γβαγβαtttttttt ULKRFLKY ==

−+

+

−= 12expULab

KULaUYt

Labour supply feedback dynamics

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

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

Labour “hire and fire” parametersSimulated labour hire and fire rate, USA 1900-2000

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000year

rate

(sta

ndar

dise

d la

bour

uni

ts p

er y

ear

Labour Hire Rate

Labour Fire Rate

Labour – validation by empirical fitSimulated and empirical labour, USA 1900-2000

0

0,5

1

1,5

2

2,5

3

3,5

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000year

norm

alis

ed la

bour

(19

00=1

)empirical

simulated

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 depreciationSimulated investment and depreciation, USA 1900-2000

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990year

norm

alis

ed c

apita

l (19

00=1

)investment

depreciation

Capital – validation by empirical fitSimulated and empirical capital, USA 1900-2000

0

2

4

6

8

10

12

14

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990year

norm

alis

ed c

apita

l (19

00=1

)

empirical

simulated

A commonly used reference modeEnergy Intensity of Capital, USA 1900-2000.

8

10

12

14

16

18

20

22

24

26

28

20001990198019701960195019401930192019101900year

inde

xb/k - total primary exergy supply(energy carriers, metals, minerals and phytomass exergy)

e/k - total fuel exergy supply(energy carriers only)

Start of the Great Depression

End of World War II

The REXS alternativeSimulated and empirical primary exergy intensity of output,

USA 1900-2000

0

0.2

0.4

0.6

0.8

1

1.2

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990year

r/y (

1900

=1)

empirical

simulated

Primary exergy intensity (R/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

Technical efficiency feedback mechanism and exergy services supply dynamics

CREATE(alpha*Primary Exergy

Production Growth Rate Coal)*(1-(1/1+exp(beta*Technical

Efficiency Saturation Index Coal-1)))

DESTROYdelta+(Primary Exergy

Production Growth Rate Coal^gamma)*(1+Technical Efficiency Saturation Index

Coal^phi)Primary Exergy

Production GrowthRate Coal

TechnicalEfficiency Coal

Create RateCoal

Maximum FeasibleTechnical Efficiency

Coal Technical EfficiencySaturation Index

Coal

FractionalCreate Rate

Coal

+

-

Destroy Rate Coal

FractionalDestroy Rate

TechnicalEfficiency Growth

Rate Coal

Endogenised Creationand Turnover of

Technology

Technical efficiency – validation

0

0,02

0,04

0,06

0,08

0,1

0,12

0,14

0,16

0,18

25 695 1486 2660 4677 7113

cumulative primary exergy production (eJ)

tech

nic

al eff

icie

ncy

, f

empirical (U/R)"

bilogistic model

Source Data: Ayres, Ayres and Warr, 2003

REXS economic output module

CumulativeProductionMonetaryMonetary

Output

Gross Output

Labour Capital

Linexparameter a

Linexparameter b

ExergyServ ices

ICT Fraction ofCapital

LinexParameter c

ICT CapitalGrowth Rate

Output – validation of full modelSimulated and empirical GDP, USA 1900-2000

0

5

10

15

20

25

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000year

norm

alis

ed G

DP

(190

0=1)

simulated

empirical

The full (simple) model

Capital Investment-

Depreciation Rate

ICTCAPITAL

LABOUR

WORK

GDP

Primary ExergyIntensity of GDP

Decline Rate

ICT CapitalFraction

Total CapitalAccumulation

PrimaryExergy

ProductionExperience

OutputExperience

non-ICTCAPITAL

Primary ExergyConversionTechnicalEfficiency

Labour Hire andFire Rate

+

+

REXS 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. For further details concerning the REXS model consult the REXS documentation.

The “dematerialising” dynamics

Declining resourceintensity of output

Continuing historicaltrends of technicale fficiency growth

Useful worksupply

Economicoutput

cumulativeoutput

experience

cumulative exergyproductionexperience

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%

effic

ienc

y

The ‘business as usual’ case:

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

Projected GDP (USA) 2000-2050 Gross Output

200

150

100

50

0 1900 1938 1975 2013 2050 Year

historical data 50% 75% 95% 100%

Inde

x (1

900=

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.

The future for REXSTHE MEET-REXS ANALYTICAL COMPARATIVE FRAMEWORK ~ of Model Families and ModelMembers represented by alternative framework structures.

Model Family (MF) and Model Members (MM)ALTERNATIVE STRUCTURES

NATURAL RESOURCES Renewable and non-

renewable, Fuels, Metals, Non-

Metals, Biomass Limits to supplies

ENERGY & MATERIALS Quantity & Quality Sources and Uses

Substitutions Possibilities

Technology Interactions

CAPITAL Alternative definitions (knowledge capital)

Accumulation, Quantity &Quality, Depreciation, Capacity Utilisation

INDICATORS & POLICY

Mass, Exergy, Work, Intensity Measures, Productivity/Efficiency

Taxes-subsidies.

ECONOMY Neo-classical – Type I

Endogenous- Type II

Evolutionary- Type III(and variants)

WASTES Pollution & Emissions,,Recycling, Regulatory

Constraints Monitoring

WELFARE Output, discounting, positive and negative

externalilties costs & benefits, time preferences

IMPACTS Land-uses

Common Property Resources, Uncertainty

Global Warming

ECOSYSTEM Global & regional

biogeochemical cycles assimilation, capacity resilience, thresholds

feedbacks

TECHNOLOGY Exogenous-Endogenous

Resource Saving Emissions reducing

Experience Dynamics by Fuel, by Work

POPULATION Birth-death dynamics & Mortality, Morbidity

Migration Per capita measures Social Characteristics

LABOUR Supply function:

Participation level Unemployment, Skills supply,

Retirement age.

Scenario Controls FIXED STRUCTURES