Integrated Assessment Models: Background (I) and Uncertainty (II)

1. Integrated Assessment Models:Background (I) and Uncertainty (II) William D. Nordhaus Yale University Summer School in Resource and Environmental Economics Venice International University June 30 – July 6, 2013

2. Lectures I. Introduction to Integrated Assessment Models II. Applications to Uncertainty

3. 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

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

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

6. 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.

7. The Need for IAMs • Many areas of the natural and social sciences involve complicated systems that link together multiple sectors. This is particularly true for environmental problems, which are intrinsically ones having strong roots in the natural sciences and require social and policy sciences to solve in an effective and efficient manner. • A good example, which will be the subject of this survey, is climate change science and policy, which involve at a minimum a wide variety of geophysical sciences such as atmospheric chemistry and climate sciences, ecology, economics, political science, game theory, and international law. • As understanding progresses in the different areas, it is increasingly necessary to link together the different areas to develop effective understanding and efficient policies. In this role, integrated assessment analysis and models play a key role. Integrated assessment models (IAMs) can be defined as approaches that integrate knowledge from two or more domains into a single framework.

8. 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

9. 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 • Why efficiency. Policy is set to some ultimate objective (economic or environmental) • How efficiency. Point to most effective policy instruments for reaching target. • Bargaining efficiency: What are Pareto-improving allocations of emissions reductions across players?

10. Economic Theory Behind Modeling 1. Basic theorem of “markets as maximization” (Samuelson, Negishi) Non-linear constrained optimization Fixed point 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.

11. 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 LP-type solvers 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 and often doesn’t (next lecture). • MATLAB and the like. Useful if you know it. • Genetic algorithms. Some like these.

12. Example using Excel-Solver The most transparent method of solving is using Excel. For any optimization, can use Solver (free for small problems) and Risk Solver Platform ($1000 for complicated problems. I will show some screenshots of a simple Excel example using DICE-like model.

13. Example: Minimize cost of emissions to attain a total emissions constraint

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

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

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

17. 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.

18. Can also calculate the “shadow prices,” here the efficient carbon taxes Remember that in a constrained optimization (Lagrangean), the multipliers have the interpretation of ∂[Objective Function]/∂X. So, in this problem, interpretation is MC of emissions reduction. Price = MC in efficiency. Optimization programs (particularly those based on 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:

19. Example of DICE model

20. 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: • So we have: • 1 + 3 = optimal growth model (Ramsey model) • 1 + 2 + 3 = integrated assessment model 5. Then estimate or calibrate the various components. 6. Then do various simulations and policy runs.

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

24. The next few slides are available for students but will not be reviewed in summer school. They are necessary components of IAMs and should be understood by modelers and users.For today, they go beyond the time-scope of our studies.We will pick up the lecture at the slide “Applications of IA Models”

25. Modeling Strategies (I): Emissions in DICE/RICE Emissions trajectories: Start with data base of major countries. 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

26. CO2-GDP: Three countries (PPP v. MER)

27. 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.* DICE uses two-layers (atmosphere, deep oceans) and 5-year time steps. Calibrated to ensemble of models in IPCC FAR science reports with updates. *http://www.aip.org/history/exhibits/climate/GCM.htm

28. .6 .4 .2 .0 -.2 -.4 -.6 1840 1880 1920 1960 2000 Y E A R T_DICE T _Hadley T _GISS Actual and predicted global temperature history

29. 5 4 3 2 1 0 1920 1960 2000 2040 2080 2120 Y E A R T_A2_DICE T_B1_DICE T_A2_IPCC T_B1_IPCC Projected DICE and IPCC: two scenarios

30. 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, …)

31. Summary of Impacts Estimates Early studies contained a major surprise: Modest impacts for gradual climate change, market impacts, high-income economies, next 50-100 years: - Impact about 0 (+ 2) percent of output. - Further studies confirmed this general result. BUT, outside of this narrow finding, potential for big problems: • many subtle thresholds • abrupt climate change (“inevitable surprises”) • ecological disruptions • stress to small, topical, developing countries • gradual coastal inundation of 1 – 10 meters over 1-5 centuries OVERALL: “…global mean losses could be 1-5% Gross Domestic Product (GDP) for 4 ºC of warming.” (IPCC, FAR, April 2007)

32. Estimated Damages from Tol survey, DICE model, and IPCC Estimate

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

34. 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.

35. Example from McKinsey Study

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

37. 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).

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

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

40. Lecture resumes here: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.

41. 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:

42. Some results from DICE-2013: Scenarios • Baseline • Optimal • Temperature-limited • Low discounting according to Stern Review. • Low time preference with calibrated interest rates. • Copenhagen Accord. IMPORTANT NOTE: The ability to do scenario comparisons is the major advantage of IAMs over other modeling.

43. Details on Scenarios • Baseline: No climate-change policies are adopted. The baseline can be interpreted as the status quo of inaction on climate policies. • Optimal: Climate-change policies maximize economic welfare, with full participation by all nations starting in 2015 and without climatic constraints. • Temperature-limited: The optimal policies are undertaken subject to a further constraint that global temperature does not exceed 2 °C above the 1900 average. • Low discounting according to Stern Review.The Stern Review advocated using very low discount rates for climate-change policy. This was implemented using a time discount rate of 0.1 percent per year and a consumption elasticity of 1. • Low time preference with calibrated interest rates. Because the Stern Review run leads to real interest rates that are below the assumed level, we adjust the parameters of the preference function to match the calibrated real interest rates. • Copenhagen Accord. In this scenario, high-income countries are assumed to implement deep emissions reductions over the next four decades, with developing countries following gradually.

49. Policies