Warr 2nd Iiasa Titech Technical Meeting
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Transcript of Warr 2nd Iiasa Titech Technical Meeting
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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
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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
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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.
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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REXS economic output module
CumulativeProductionMonetaryMonetary
Output
Gross Output
Labour Capital
Linexparameter a
Linexparameter b
ExergyServ ices
ICT Fraction ofCapital
LinexParameter c
ICT CapitalGrowth Rate
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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
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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
+
+
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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.
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The “dematerialising” dynamics
Declining resourceintensity of output
Continuing historicaltrends of technicale fficiency growth
Useful worksupply
Economicoutput
cumulativeoutput
experience
cumulative exergyproductionexperience
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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.
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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 ?
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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.
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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