An application of the logistic curve to the modeling of CO 2 emission reduction Kazushi Hatase Graduate School of Economics, Kobe University

2007/10/7SEEPS Annual Meeting, Shiga University2 The model and simulations of this study Model: RAMLOG  Global economy is viewed as a two-sector Ramsey model  Energy sector of the model consists of two energy technologies:  Fossil energy  New carbon-free energy  Diffusion of new energy technology is modeled by combining the logistic curve and learning-by-doing Simulations  Varying two parameters which determine technology diffusion  Investigating the change of optimal CO 2 emission reduction pathways and costs of emission reduction when the two parameters are varied

2007/10/7SEEPS Annual Meeting, Shiga University3 Preceding studies and significance of this study  Energy-economy models with substitutable two (fossil & new) energies Goulder & Schneider (1999) DEMETER (2002) ENTICE-BR (2006) This study Technological change R&D Learning-by- doing R&D Learning-by- doing Elasticity between two energies (σ) σ=0.9σ=2, 3, 4σ=1.6, 2.2, 8.7 Determined by logistic curve  Significance of this study  Diffusion of low CO 2 -emitting energy is crucial in climate change mitigation. This study proposes a model of long-term technology diffusion.  Logistic curve provides more realistic projection of future technology diffusion than the use of fixed elasticity between fossil and new energies.  Influence of technology-related parameters on CO 2 emission reduction is examined.

2007/10/7SEEPS Annual Meeting, Shiga University4 Model of global economy (the Ramsey model) 1.Intertemporal utility maximization 2.Production function 3.Capital accumulation 4.Income accounts identity

2007/10/7SEEPS Annual Meeting, Shiga University5 Logistic curve  Energy inputs consist of two energy technologies  Share of the new energy grows following the logistic curve  Modifying the equation above into the inequality form:  Finite difference form is used in the computer program:

2007/10/7SEEPS Annual Meeting, Shiga University6 Logistic curve (continued)  Coefficient determines the speed of diffusion in  It determines the “potential” speed of diffusion in  In the inequality form, diffusion trajectory can take any paths under the logistic curve

2007/10/7SEEPS Annual Meeting, Shiga University7 Learning-by-doing  Price of fossil energy is constant  Price of new energy declines as experience increases  Data of experience index （ source: McDonald & Schrattenholzer, 2001 ） TechnologyPeriodValue of b Nuclear (OECD)1975 – GTCC （ OECD ） 1984 – Wind (OECD)1981 – Photovoltaics (OECD)1968 – Ethanol (Brazil)1979 –

2007/10/7SEEPS Annual Meeting, Shiga University8 Learning-by-doing in the computer program  Using a finite difference form (Anderson & Winne, 2004)  Substituting W t by the cumulative installed capacity of new energy  Estimation of W 0 (Gerlagh and van der Zwaan, 2004)

2007/10/7SEEPS Annual Meeting, Shiga University9 Combining the Ramsey model, logistic curve and learning-by-doing Ramsey model Logistic curve Learning by doing

2007/10/7SEEPS Annual Meeting, Shiga University10 Climate change model  Adopt a simple CO 2 accumulation model (Grubb et al., 1995)  Anthropogenic CO 2 emission  Natural CO 2 emission (adopting DEMETER’s parameterization)

2007/10/7SEEPS Annual Meeting, Shiga University11 Simulation scenarios  Simulation is lead to a time path of emissions that satisfies the stabilization target of 500ppm (cost-effectiveness simulation)  Investigating how  Potential speed of technological change (coefficient a)  Leaning rate (experience index:b) affect CO 2 emission reduction pathways and the costs of reduction Run: coefficient of logistic curveb: experience index (a) STC + LL (b) STC + HL (c) FTC + LL (d) FTC + HL STC: Slow Technological Change FTC: Fast Technological Change LL: Low Learning HL: High Learning  Model runs and parameter settings

2007/10/7SEEPS Annual Meeting, Shiga University12 Common parameters (mainly adopted from DEMETER model) ParameterDescriptionValue K(0)Capital in $trillion Y(0)Gross output (GWP) in $trillion E(0)Total energy input in GtC δDepreciation rate on capital7%/year γCapital’s value share0.31 σElasticity between K-L and E0.40 S(0)Share of new energy in % pFpF Price of fossil energy $/tC p N (0)Price of new energy in $/tC p N min Lowest possible cost of new energy250 $/tC σNσN Plant’s depreciation rate of new energy7%/year gNgN Growth rate of new energy inputs4.8%/year M(0)Carbon accumulation in the atmosphere in GtC μRemoval rate of CO2 from the atmosphere0.6%/year θFθF Emission intensity of fossil energy1.0 Emis Nat Natural CO2 emission in GtC/year

2007/10/7SEEPS Annual Meeting, Shiga University13 Calibration of the production function (based on MERGE model’s method) 1.Setting up the reference values of Y(t), K(t), E(t) 2.Differentiating and rearranging the production function to obtain α and β

2007/10/7SEEPS Annual Meeting, Shiga University14 Optimal CO 2 emission pathways  Four emission pathways are not very different  Learning-by-doing has almost no effect in STC (slow technological change)

2007/10/7SEEPS Annual Meeting, Shiga University15 Optimal CO 2 reduction pathways  FTC + HL supports deferring CO 2 emission reduction  The other three paths are nearly the same in the early 21 st century

2007/10/7SEEPS Annual Meeting, Shiga University16 Optimal technology switch timing  Larger learning rate makes the starting point of diffusion earlier  STC (slow technological change) acts as a “friction” to technology switch, making the starting point of technology diffusion further earlier so as to achieve the emission reduction target

2007/10/7SEEPS Annual Meeting, Shiga University17 Emission reduction by reducing energy input and by new energy (a) STC + LL (c) FTC + LL (b) STC + HL (d) FTC + HL

2007/10/7SEEPS Annual Meeting, Shiga University18 Loss of GWP through CO 2 emission reduction  GWP loss largely depends on the learning rate  Pathways with the same learning rate are close or the same in the early and late period

2007/10/7SEEPS Annual Meeting, Shiga University19 Technology switch and GWP loss under High Learning  Technology diffusion of STC starts early, but GWP loss in the early period is not so different from FTC (major difference occurs after 2060)  Starting technology switch from the early period does not make big difference of GWP loss before 2050

2007/10/7SEEPS Annual Meeting, Shiga University20 Carbon tax levels  Patterns are similar to those of GWP loss  Pathways of the same learning rate are the same in the early and late period

2007/10/7SEEPS Annual Meeting, Shiga University21 Conclusions 1.Progress of new carbon free technology justifies deferring CO 2 emission reduction only in the case of FTC (fast technological change) + HL (high learning). 2.Optimal CO 2 reduction paths are relatively similar between the 4 model runs, while the optimal technology diffusion paths diverge. 3.Larger learning rate makes the starting point of technology diffusion earlier. 4.Slow technological change acts as a “friction” to technology switch, making the starting point of technology diffusion further earlier so as to achieve the emission reduction target. 5.GWP loss largely depends on the learning rate. Pathways of GWP loss with the same learning rate are close or the same in the early and late period.