Integrated Assessment Models of Economics of Climate Change

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

2. Integrated Assessment (IA) Models of Climate Change • What are IA model? • These are models that include the full range of cause and effect in climate change (“end to end” modeling). • They are necessarily interdisciplinary and involve natural and social sciences • Major goals: • Project the impact of current trends and of policies on important variables • Assess the costs and benefits of alternative policies • Assess uncertainties and priorities for scientific and project/engineering research

3. Major Components of Models Identities Behavioral and Scientific Equations Value Judgments (markets, policies, ethics, etc.)

4. Pareto Improvement from Climate Policy Person or nation 1 Bargaining region (Pareto improving) Inefficient initial (no-policy) position Person or nation 2

5. Elements of IA Models. To be complete, the model needs to incorporate the following elements: - human activities generating emissions - carbon cycle - climate system - biological and physical impacts - socioeconomic impacts - policy levers to affect emissions or other parts of cycle.

6. Representative Scenarios for Models “Baseline” or uncontrolled path: - Set emissions at zero control or zero “tax” level. - Business as usual Alternative strategies: - “Optimal” where maximize objective function - Stabilize emissions, concentrations, or climate - Kyoto Protocol limitations

7. There are many kinds of IA models, useful for different purposes Policy evaluation models - Models that emphasize projecting the impacts of different assumptions and policies on the major systems; - often extend to non-economic variables Policy optimization models - Models that emphasize optimizing a few key control variables (such as taxes or control rates) with an eye to balancing costs and benefits or maximizing efficiency; - often limited to monetized variables

8. Some important objectives of policy • When efficiency. Timing of emissions reductions that minimizes discounted costs. • Where efficiency. Locate emissions reductions in regions where reductions are cheapest (in policy discussion later). • Why efficiency. Policy is set to some ultimate objective (economic or environmental) • How efficiency. Point to most effective policy instruments for reaching target (later). • Coasean bargains: What are Pareto-improving allocations of emissions reductions?

9. Basic economic strategy • Begin with a Solow-style economic growth model • Add the geophysical equations: note these impose an externality • Then add an objective function to be optimized subject to constraints: • 1 + 3 = optimal growth model [Friday] • 1 + 2 + 3 = integrated assessment model 4. Then estimate or calibrate the various components. 5. Then do various simulations and policy runs.

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

11. Modeling Strategies (I): Emissions Emissions trajectories: Start with data base of 70 major countries representing 97 % of output and emissions 1960-2004. Major issue of whether to use PPP or MER (next slide) Estimate productivity growth Estimate CO2 emissions-output ratios Project these by decade for next two centuries Then aggregate up by twelve major regions (US, EU, …) Constrain by global fossil fuel resources This is probably the largest uncertainty over the long run: σ(Q) ≈ .01 T, or + factor 2.5 in 100 yrs, +7 in 200 yrs

12. Modeling Strategies (II): Climate Models Climate model Idea here to use “reduced form” or simplified models. For example, large models have very fine resolution and require supercomputers for solution.* We take two-layers (atmosphere, deep oceans) and decadal time steps. Calibrated to ensemble of models in IPCC TAR and FAR science reports. *http://www.aip.org/history/exhibits/climate/GCM.htm

13. Modeling Strategies (III): Impacts • Central difficulty is evaluation of the impact of climate change on society • Two major areas: • market economy (agriculture, manufacturing, housing, …) • non-market sectors • human (health, recreation, …) • non-human (ecosystems, fish, trees, …)

14. Modeling Strategies (IV): Abatement costs IA models use different strategies to model abatement: • Some use econometric analysis of costs of reductions • Some use engineering/mathematical programming estimates (McKinsey) • DICE model generally uses “reduced form” estimates of marginal costs of reduction as function of emissions reduction rate

15. Derivation of mitigation cost function Start with a reduced-form cost function: (1) C = Qλμ where C = mitigation cost, Q = GDP, μ = emissions control rate, λ,  are parameters. Take the derivative w.r.t. emissions and substitute σ = E0 /Q • dC/dE = MC emissions reductions = Qλβμ-1[dμ/dE] =λβμ-1/σ Taking logs: • ln(MC) = constant + time trend + ( β-1) ln(μ) We can estimate this function from microeconomic/engineering studies of the cost of abatement.

16. Example from McKinsey Study

17. Reduced form equation: C=.0657*miu^1.66*Q

18. Further discussion However, there has been a great deal of controversy about the McKinsey study. The idea of “negative cost” emissions reduction raises major conceptual and policy issues. For the DICE model, we have generally relied on more micro and engineering studies. The next set of slides shows estimates based on the IPCC Fourth Assessment Report survey of mitigation costs. The bottom line is that the exponent is much higher (between 2.5 and 3). This has important implications that we will see later.

19. Note that the MC is much more convex than McKinsey: much more diminishing returns Source: IPCC, AR4, Mitigation.

20. Source for estimates of  (elasticity of cost function) Source: IPCC, AR4, Mitigation, p. 77.

21. Using the IPCC as data for the cost function Conclusion is that the cost function is EXTREMELY convex.

22. Alternative abatement cost functions: From IPCC Parameterized as C/Q = aμ2.8 , with backstop price(2005) = $1100/tC

23. Alternative abatement cost functions: IPCC and MK Parameterized as C/Q = aμ2.8 , with backstop price(2005) = $1100/tC

24. How do we solve IA models? The structure of the models is the following: We solve using various mathematical optimization techniques. • GAMS solver (proprietary). This takes the problem and solves it using linear programming (LP) through successive steps. It is extremely reliable. • Use EXCEL solver. This is available with standard EXCEL and uses various numerical techniques. It is not 100% reliable for difficult or complex problems. • MATHLAB. Useful if you know it. • Genetic algorithms. Some like these.

25. Economic Theory Behind Modeling 1. Basic theorem of “markets as maximization” (Samuelson, Negishi) Maximization of weighted utility function: Outcome of efficient competitive market (however complex but finite time) = 2. This allows us (in principle) to calculate the outcome of a market system by a constrained non-linear maximization.

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

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

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

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

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

31. 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: With a little work, you can show that the rate of growth of prices = interest rate for this case.

32. Applications of IA Models How can we use IA models to evaluate alternative approaches to climate-change policy? I will illustrate analyzing the economic and climatic implications of several prominent policies. For these, I use the recently developed DICE-2007 model.

33. 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. In the spirit of the Stern Review: Dual discounting case. 7. Geoengineering. Implements a geoengineering option that offsets radiative forcing at low cost. Illustrative Policies for DICE-2007