An introduction to a simple endogenous evolutionary model of macro-economic growth called REXS (Resource Exergy Services)

1. 2nd IIASA-TITECH Technical Meeting
27th –28th April 2003, Vienna
Center for the Management of Environmental Resources (CMER)
INSEAD
Boulevard de Constance
Fontainebleau
77300
http://benjamin.warr.free.fr
An introduction to a simple endogenous
evolutionary model of macro-economic
growth called REXS

2. Objectives
Foresight with the wisdom of hindsight
Most 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

3. 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.

4. Common practice
Y t = Q ( A t , H t K t , G t L t , F t R t ),
Y t = A t (H t K ) (G t L t ) (F t R t )
α β γ
t
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 quality
Output 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)
∂Y  1 ∂Q 
 Q ∂A a + β (h + k ) + γ ( g + l ) + (1 − β − γ )( f + r )
=
∂t  


5. How does our model work
Yt = Q(K t , Lt , Rt ), either Cobb-Douglas or LINEX
Yt = (K t ) (Lt ) (Ft Rt ) = K tα Lβ U tγ
α β γ
t
   L + U   L 
Yt = U expa 2 − 
   + ab − 1

   K  U 
• 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

6. Labour supply feedback dynamics
Labour
Labour Hire Labour Fire
Rate Rate
<Time>
Fr actional Fr actional
Labour Hire Rate Labour Fire Rate
A A
Structural Shift Structural Shift
Time C Time D
Fr actional Fr actional
Labour Hire Rate Labour Fire Rate
B B
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

7. Labour “hire and fire” parameters
Simulated labour hire and fire rate, USA 1900-2000
0,45
Labour Hire Rate
0,4
Labour Fire Rate
rate (standardised labour units per year
0,35
0,3
0,25
0,2
0,15
0,1
0,05
0
1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000
year

8. Labour – validation by empirical fit
Simulated and empirical labour, USA 1900-2000
3,5
empirical
3 simulated
2,5
normalised labour (1900=1)
2
1,5
1
0,5
0
1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000
year

9. Capital accumulation feedback loop
<Gr oss
Output>
Capital
Inv e stme nt Depre ciation
Investment Inv e stme nt Depre ciation Depreciation
Fraction A Fraction Rate Rate A
Investment Depreciation
Fraction B Rate B
Structural Shift <Time> Structural Shift
Time A Time B
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

10. Capital investment and depreciation
Simulated investment and depreciation, USA 1900-2000
1.8
investment
1.6
depreciation
1.4
normalised capital (1900=1)
1.2
1
0.8
0.6
0.4
0.2
0
1900 1910 1920 1930 1940 1950 1960 1970 1980 1990
year

11. Capital – validation by empirical fit
Simulated and empirical capital, USA 1900-2000
14
empirical
12
simulated
normalised capital (1900=1)
10
8
6
4
2
0
1900 1910 1920 1930 1940 1950 1960 1970 1980 1990
year

12. A commonly used reference mode
Energy Intensity of Capital, USA 1900-2000.
28
Start of the Great Depression b/k - total primary exergy supply
26 (energy carriers, metals,
minerals and phytomass exergy)
24
e/k - total fuel exergy supply
(energy carriers only)
22
20
index
18
16
14
12
10
End of World War II
8
1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000
year

13. The REXS alternative
Simulated and empirical primary exergy intensity of output,
USA 1900-2000
1.2
1
0.8
r/y (1900=1)
0.6
0.4
0.2 empirical
simulated
0
1900 1910 1920 1930 1940 1950 1960 1970 1980 1990
year

14. Primary exergy intensity (R/GDP) of
output decay feedback mechanism.
<Gr oss Primary Exe rgy
Output> Inte nsity of Output
Rate of Decay
Fractional
Primary Exe rgy Decay Rate
Demand
Parameters
Product R&D Substitution of
• Rate of Decay = Fractional Improvement Knowledge for Labour;
Decay Rate*Primary Exergy Capital; and Exergy
Process
Intensity of Output Improvement
Substitution of
• Fractional Decay Rate=0.012 Lower Limits to
Exergy for Labour
and Capital
Costs of
INCREASED REVENUES Production
Increased Demand for
To the right: Final Goods and Services
Processes aggregated in Economies of
Scale
Lower Prices of
Materials &
the REXS dynamics Energy

15. Technical efficiency feedback mechanism
and exergy services supply dynamics
Endogenised Creation
and Turnover of
Technology
CREATE
Maximum Feasible
-
(alpha*Primary Exergy
Technical Efficiency
Fractional
Create Rate Coal Technical Efficiency Production Growth Rate
Saturation Index
Coal
Coal Coal)*(1-(1/1+exp(beta*Technical
Efficiency Saturation Index
Coal-1)))
Create Rate
Coal
Technical
Efficiency Coal
DESTROY
+
delta+(Primary Exergy
Technical
Efficiency Growth
Fractional
Destroy Rate
Production Growth Rate
Rate Coal
Destroy Rate Coal Coal^gamma)*(1+Technical
Primary Exergy Efficiency Saturation Index
Production Growth
Rate Coal Coal^phi)

16. Technical efficiency – validation
0,18
0,16
0,14
technical efficiency, f
0,12
0,1
0,08
0,06
empirical (U/R)"
0,04
bilogistic model
0,02
0
25 695 1486 2660 4677 7113
cumulative primary exergy production (eJ)
Source Data: Ayres, Ayres and Warr, 2003

17. REXS economic output module
Exe rgy
Labour Capital
Serv ice s
Linex
parameter a ICT Fraction of
Gross Output
Capital
Linex
parameter b
ICT Capital
Growth Rate
Linex
Parameter c
Cumulativ e
Production
Monetary
Monetary
Output

18. Output – validation of full model
Simulated and empirical GDP, USA 1900-2000
25
simulated
empirical
20
normalised GDP (1900=1)
15
10
5
0
1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000
year

19. The full (simple) model
Capital
Investment- Total Capital non-ICT
Depreciation Accumulation CAPITAL
Rate
Output
Experience
+
ICT Capital ICT
Fraction CAPITAL
Labour Hire and
LABOUR GDP
Fire Rate
Primary Primary Exergy
Primary Exergy
Exergy Conversion
Intensity of GDP WORK
Production + Technical
Decline Rate
Experience Efficiency

20. REXS Projections of future output
Altering 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.

21. The “dematerialising” dynamics
Declining resource
inte nsity of output
cumulative
output
experience
Continuing historical
Economic tre nds of te chnical
output e fficie ncy growth
cumulative exergy
pr oduction
experience
Use ful wor k
supply

22. Varying rates of dematerialisation
Primary Exergy Intensity of Output Decline Rate
The constant 0
rate of exergy historical trend
50% 75% 95% 100%
intensity
decline was -0.5
altered to vary
between –0.55
and –1.65 % (%) -1
p.a.
-1.5
-2
1900 1938 1975 2013 2050
Year

23. Effects on ‘efficiency’ improvements
The ‘business Technical Efficiency of Primary Exergy Conversion
0.4
as usual’ case: historical data
50% 75% 95% 100%
If technical
efficiency does 0.3
not increase in
pace with ‘de-
efficiency
materialisation’ 0.2
growth slows ?
0.1
0
1900 1938 1975 2013 2050
Year

24. Projected GDP (USA) 2000-2050
Gross Output
200
The sensitivity of historical data
50% 75% 95% 100%
future projections
of GDP were
150
assessed, the red
line indicates the
Index (1900=1)
‘business as usual’
for a fractional 100
decay rate of
energy intensity of
output –1.2 % per
annum and 50
technical efficiency
at 1% p.a.
0
1900 1938 1975 2013 2050
Year

25. The future for REXS
THE MEET-REXS ANALYTICAL COMPARATIVE FRAMEWORK ~ of Model Families and Model
Members represented by alternative framework structures.
POPULATION LABOUR W ELFARE INDICATORS &
Birth-death dynamics Supply function: Output, discounting, POLICY
& Mortality, Morbidity Participation level positive and negative Mass, Exergy, Work,
Migration Unemployment, externalilties Intensity Measures,
Per capita measures Skills supply, costs & benefits, Productivity/Efficiency
Social Characteristics Retirement age. time preferences Taxes-subsidies.
NATURAL RESOURCES CAPITAL ECONOMY IMPACTS
Renewable and non- Alternative definitions Neo-classical – Type I Land-uses
renewable, (knowledge capital) Common Property
Fuels, Metals, Non- Endogenous- Type II
Accumulation, Quantity & Resources,
Metals, Biomass Quality, Depreciation, Evolutionary- Type III Uncertainty
Limits to supplies Capacity Utilisation (and variants) Global Warming
ENERGY & MATERIALS TECHNOLOGY WASTES ECOSYSTEM
Quantity & Quality Exogenous-Endogenous Pollution & Emissions,, Global & regional
Sources and Uses Resource Saving Recycling, Regulatory biogeochemical cycles
Substitutions Emissions reducing Constraints assimilation, capacity
Possibilities Experience Dynamics Monitoring resilience, thresholds
Technology Interactions by Fuel, by Work feedbacks
Model Family (MF) and Model Members (MM) Scenario Controls
ALTERNATIVE STRUCTURES FIXED STRUCTURES