1. 1 Economics 331b Spring 2009 Integrated Assessment Models of Economics of Climate Change

2. 2 Slightly Simplified Equations of DICE-2007 Model: Revised Note: For complete listing, see Question of Balance, pp. 205-209.

3. 3

4. How do we solve IA models numerically? We take discrete version of model, simplified as follows. We solve using various mathematical optimization techniques. 1.GAMS solver (proprietary). This takes the problem and solves it using linear programming (LP) through successive steps. It is extremely reliable. 2.Use EXCEL solver. This is available with standard EXCEL and uses various numerical techniques. It is not 100% reliable for difficult or complex problems. 3.MATHLAB. Useful if you know it. 4.Genetic algorithms. Some like these. 4

5. Example: Minimize cost of emissions to limit the sum of emissions over time 5

6. 6 Start with an initial feasible solution, which is equal reductions in all periods. Setup

7. 7 Then maximize PV output Subject to the constraint that: the sum of emissions < target sum of emissions Number crunch….

8. This is the solver dialogue box Objective function 8 Control variables Constraints

9. If you have set it up right and have a good optimization program, then voilà !!! 9 Note that the emissions controls are generally “backloaded” because of the positive discounting (productivity of capital) and because damages are in future.

10. Can also calculate the “shadow prices,” here the efficient carbon taxes Remember that in a constrained optimization (Lagrangean), the multipliers have the interpretation of d[Objective Function]/dX. So, in this problem, interpretation is MC of emissions reduction. Optimization programs (particularly LP) will generate the shadow prices of carbon emissions in the optimal path. For example, in the problem we just did, we have the following shadow prices: 10 With a little work, you can show that the rate of growth of prices = interest rate for this case.

11. 11 Applications of IA Models Major applications of IA Models: 1.Project the impact of current trends and of policies on important variables. 2.Assess the costs and benefits of alternative policies 3.Determine efficient levels of policy variables (carbon taxes, emissions control rates, emissions, …) For these, I will illustrate using the DICE-2007 model: –Full analysis Question of Balance (see reading list). –There is a “beta” version using an Excel spreadsheet at http://www.econ.yale.edu/~nordhaus/homepage/DICE 2007.htm (both an *.xls and *.xlsx version)

12. 12 1. No controls ("baseline"). No emissions controls. 2. Optimal policy. Emissions and carbon prices set for economic optimum. 3. Climatic constraints with CO2 concentration constraints. Concentrations limited to 550 ppm 4. Climatic constraints with temperature constraints. Temperature limited to 2½ °C 5. Kyoto Protocol. Kyoto Protocol without the U.S. 6. Strengthened Kyoto Protocol. Roughly, the Obama/EU policy proposals. 7. Geoengineering. Implements a geoengineering option that offsets radiative forcing at low cost. Illustrative Policies for DICE-2007

13. Snapshot of DICE-Excel model 13 http://www.econ.yale.edu/~nordhaus/homepage/DICE2007.htm

14. Per capita GDP: history and projections 14

15. CO2-GDP ratios: history 15

16. IPCC AR4 Model Results: History and Projections 16 DICE-2007 model 2-sigma range DICE model

17. DICE-2007 model results 17

18. Concentrations profiles: DICE 2007 18

19. Temperature profiles 19

20. Policy outcomes variables Overall evaluation Two major policy variables are - emissions control rate - carbon tax 20

21. Economic evaluation We want to examine the economic efficiency of each of the scenarios. Some techniques: - PV of abatement, damages, and total - PV as percent of PV of total consumption - Consumption annuity equivalent: 21

22. Evaluation: PV trillions of 2000 $ 22

23. Evaluation: as percent of PV consumption 23

24. Evaluation: Consumption annuity per capita 24

25. Emissions control rate (industrial CO2), 2015 25

26. Carbon prices for major scenarios 26

27. Carbon prices for major scenarios 27

28. Carbon prices 2010 for major scenarios ($/tC) 28 190140305

29. What do carbon prices mean in practice? 29 Carbon tax, 2010 Increase, price of energy, US [$/tC]Gasoline All energy expenditures Kyoto: global average$20.2%0.3% "Optimal"353.3%5.4% Climate constrained504.8%7.7% "Ambitious"20019.0%30.7%

30. Impact on PCE expenditures of $50 C tax 30

31. Policy question The impact of efficient/climate target carbon taxes is relatively modest: –abatement/output circa 0.1 – 0.6 % of output –net impact -0.1 to +0.2 % of output Why is the debate so strident? Why are some people so opposed? 31