Warr 2nd Iiasa Titech Technical Meeting

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

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Warr 2nd Iiasa Titech Technical Meeting

  1. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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

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