An application of the logistic curve to the modeling of CO 2 emission reduction

1. An application of the logistic curve to the modelingof CO2 emission reduction Kazushi Hatase Graduate School of Economics, Kobe University

2. 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 CO2 emission reduction pathways and costs of emission reduction when the two parameters are varied SEEPS Annual Meeting, Shiga University

3. Preceding studies and significance of this study • Energy-economy models with substitutable two (fossil & new) energies • Significance of this study • Diffusion of low CO2-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 CO2 emission reduction is examined. SEEPS Annual Meeting, Shiga University

4. Model of global economy (the Ramsey model) • Intertemporal utility maximization • Production function • Capital accumulation • Income accounts identity SEEPS Annual Meeting, Shiga University

5. 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: SEEPS Annual Meeting, Shiga University

6. 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 SEEPS Annual Meeting, Shiga University

7. 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） SEEPS Annual Meeting, Shiga University

8. Learning-by-doing in the computer program • Using a finite difference form (Anderson & Winne, 2004) • Substituting Wtby the cumulative installed capacity of new energy • Estimation of W0 (Gerlagh and van der Zwaan, 2004) SEEPS Annual Meeting, Shiga University

9. Combining the Ramsey model, logistic curve and learning-by-doing Ramsey model Learning by doing Logistic curve SEEPS Annual Meeting, Shiga University

10. Climate change model • Adopt a simple CO2 accumulation model (Grubb et al., 1995) • Anthropogenic CO2 emission • Natural CO2 emission (adopting DEMETER’s parameterization) SEEPS Annual Meeting, Shiga University

11. 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 CO2 emission reduction pathways and the costs of reduction • Model runs and parameter settings STC: Slow Technological Change FTC: Fast Technological Change LL: Low Learning HL: High Learning SEEPS Annual Meeting, Shiga University

12. Common parameters (mainly adopted from DEMETER model) SEEPS Annual Meeting, Shiga University

13. Calibration of the production function (based on MERGE model’s method) • Setting up the reference values of Y(t), K(t), E(t) • Differentiating and rearranging the production function to obtain α and β SEEPS Annual Meeting, Shiga University

14. Optimal CO2 emission pathways • Four emission pathways are not very different • Learning-by-doing has almost no effect in STC (slow technological change) SEEPS Annual Meeting, Shiga University

15. Optimal CO2 reduction pathways • FTC + HL supports deferring CO2 emission reduction • The other three paths are nearly the same in the early 21st century SEEPS Annual Meeting, Shiga University

16. 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 SEEPS Annual Meeting, Shiga University

17. Emission reduction by reducing energy input and by new energy (a) STC + LL (b) STC + HL (c) FTC + LL (d) FTC + HL SEEPS Annual Meeting, Shiga University

18. Loss of GWP through CO2 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 SEEPS Annual Meeting, Shiga University

19. 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 SEEPS Annual Meeting, Shiga University

20. 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 SEEPS Annual Meeting, Shiga University

21. Conclusions • Progress of new carbon free technology justifies deferring CO2 emission reduction only in the case of FTC (fast technological change) + HL (high learning). • Optimal CO2 reduction paths are relatively similar between the 4 model runs, while the optimal technology diffusion paths diverge. • Larger learning rate makes the starting point of technology diffusion earlier. • 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. • 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. SEEPS Annual Meeting, Shiga University