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Transcript

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 1 Lectures I. Introduction to Integrated Assessment Models II. Applications to Uncertainty 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 Major Components of Models Behavioral and Scientific Equations Identities Value Judgments (markets, policies, ethics, etc.) Person or nation 1 Pareto Improvement from Climate Policy Bargaining region (Pareto improving) Inefficient initial (nopolicy) position Person or nation 25 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. Fossil fuel use generates CO2 emissions The emissions -climateimpactspolicy nexus Carbon cycle: redistributes around atmosphere, oceans, etc. Climate system: change in radiation warming, precip, ocean currents, etc.. Impacts on ecosystems, agriculture, diseases, skiing, golfing, … Measures to control emissions (limits, taxes, subsidies, …) 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 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 Outcome of efficient competitive market (however complex but finite time) = Maximization of weighted utility function: n W i [U i (c ki ,s ,t )] i 1 for utility functions U; individuals i=1,...,n; locations k, uncertain states of world s, i time periods t; welfare weights . 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: max W { ( t )} T max U[c(t ),L(t )]R(t ) t 1 subject to c(t ) H[ (t ),s(t ); initial conditions, parameters] (The H[...] functions are production functions, climate model, carbon cycle, abatement costs, damages, and so forth.) We solve using various mathematical optimization techniques. 1. GAMS solver (proprietary). This takes the problem and solves it using LP-type solvers 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 and often doesn’t (next lecture). 3. MATLAB and the like. Useful if you know it. 4. 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 Period 0 10 20 30 Discount rate (per year) 0.10 Output 100.00 148.02 219.11 324.34 Emissions control rate Constant 0.50 0.50 0.50 0.50 Efficient 0.50 0.50 0.50 0.50 Emissions Uncontrolled 10.00 14.80 21.91 32.43 Controlled Constant rate 5.00 7.40 10.96 16.22 Efficient 5.00 7.40 10.96 16.22 Total emissions over time: The target is to achieve 50 percent reductions Uncontrolled 79.15 Controlled Constant rate 39.57 Efficient 39.57 Abatement costs (=.1*miu^3*Q) Constant rate 1.25 1.85 2.74 4.05 Efficient 1.25 1.85 2.74 4.05 Net output Constant rate 98.75 146.17 216.37 320.29 Efficient 98.75 146.17 216.37 320.29 PV output Level 205.6241 Efficient 205.6241 THESE ARE CONTROL VARIABLES THIS WILL BE THE ENVIRONMENTAL CONSTRAINT THIS WILL BE THE OBJECTIVE FUNCTION TO BE MAXIMIZED 14 Setup Period 0 10 20 30 Discount rate (per year) 0.10 Output 100.00 148.02 219.11 324.34 Emissions control rate Constant 0.50 0.50 0.50 0.50 Efficient 0.50 0.50 0.50 0.50 Emissions Uncontrolled 10.00 14.80 21.91 32.43 Controlled Constant rate 5.00 7.40 10.96 16.22 Efficient 5.00 7.40 10.96 16.22 Total emissions over time: The target is to achieve 50 percent reductions Uncontrolled 79.15 Controlled Constant rate 39.57 Efficient 39.57 Abatement costs (=.1*miu^3*Q) Constant rate 1.25 1.85 2.74 4.05 Efficient 1.25 1.85 2.74 4.05 Net output Constant rate 98.75 146.17 216.37 320.29 Efficient 98.75 146.17 216.37 320.29 PV output Level 205.6241 Efficient 205.6241 THESE ARE CONTROL VARIABLES THIS WILL BE THE ENVIRONMENTAL CONSTRAINT Start with an initial feasible solution, which is equal reductions in all periods. THIS WILL BE THE OBJECTIVE FUNCTION TO BE MAXIMIZED 15 Number crunch…. Period 0 10 20 30 Discount rate (per year) 0.10 Output 100.00 148.02 219.11 324.34 Emissions control rate Constant 0.50 0.50 0.50 0.50 Efficient 0.50 0.50 0.50 0.50 Emissions Uncontrolled 10.00 14.80 21.91 32.43 Controlled Constant rate 5.00 7.40 10.96 16.22 Efficient 5.00 7.40 10.96 16.22 Total emissions over time: The target is to achieve 50 percent reductions Uncontrolled 79.15 Controlled Constant rate 39.57 Efficient 39.57 Abatement costs (=.1*miu^3*Q) Constant rate 1.25 1.85 2.74 4.05 Efficient 1.25 1.85 2.74 4.05 Net output Constant rate 98.75 146.17 216.37 320.29 Efficient 98.75 146.17 216.37 320.29 PV output Level 205.6241 Efficient 205.6241 Then THESE maximize PV output ARE CONTROL VARIABLES Subject to the constraint that: THIS WILL BE THE ENVIRONMENTAL CONSTRAINT the sum of emissions < target sum of emissions THIS WILL BE THE OBJECTIVE FUNCTION TO BE MAXIMIZED 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 !!! Period 0 10 20 30 Discount rate (per year) 0.10 Output 100.00 148.02 219.11 324.34 Emissions control rate Constant 0.50 0.50 0.50 0.50 Efficient 0.17 0.28 0.45 0.73 Emissions Uncontrolled 10.00 14.80 21.91 32.43 Controlled Constant rate 5.00 7.40 10.96 16.22 Efficient 8.25 10.63 11.97 8.73 Total emissions over time: The target is to achieve 50 percent reductions Uncontrolled 79.15 Controlled Constant rate 39.57 Efficient 39.57 Abatement costs (=.1*miu^3*Q) Constant rate 1.25 1.85 2.74 4.05 Efficient 0.05 0.33 2.05 12.67 Net output Constant rate 98.75 146.17 216.37 320.29 Efficient 99.95 147.69 217.06 311.67 PV output Level 205.6241 Efficient 207.0152 THESE ARE CONTROL VARIABLES Note that the emissions controls are generally “backloaded” because of the positive discounting THIS WILL BE of THE capital) ENVIRONMENTAL (productivity and CONSTRAINT because damages are in future. THIS WILL BE THE OBJECTIVE FUNCTION TO BE MAXIMIZED 18 Can also calculate the “shadow prices,” here the efficient carbon taxes 600 Marginal cost of Emissions Reductions ($) 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: 500 400 300 200 100 0 0 10 20 30 Period 19 Example of DICE model 20 Basic economic strategy 1. Begin with a Solow-style economic growth model 2. Add the geophysical equations: note these impose an externality 3. Then add an objective function to be optimized subject to constraints: 4. 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. 21 Macrogeoeconomics Basic economics behind IA models. Have standard optimal growth model + geophysics externalities: (1) max W L(t )U[c(t )]e t dt { c( t )} 0 subject to economic and climate constraints: (2) c(t ) f [K(t ), (t ),T(t ); parameters, exogenous variables ] (3) T(t ) h[E{Q(t ), (t ); parameters, exogenous variables ] Then optimize W over emissions and capital stock, subject to economic and geophysical constraints. 22 Objective Function (1) W T max U[c(t ),L(t )]R(t ) t 1 Economics (2) U [c(t),L(t)] = L(t)[c(t)1- / (1 - )] Utility function (3) Q g (t) = A(t) K(t) L(t)1 Gross output (4) D(t) = 1TAT (t) + 2TAT (t) 2 2 (5) C(t) = Q (t) 1(t)(t) (6) Qn (t) = (t)[1 - (t)]A(t) K(t) L(t)1 g Damage function Abatement cost Net output (7) EInd (t) = (t)[1 - (t)]Q (t) g Geosciences (8) M AT (t ) E(t ) 11 M AT (t - 1 ) ... (9) F(t) {log2 [ MAT (t) / MAT (0)]} FEX (t) Industrial emissions Atmospheric CO2 (10) TAT (t ) TAT (t 1 ) 1 { F(t ) ... Radiative forcings Global mean temperature Key variables (in addition to standard from growth theory): Eind = industrial CO2 emissions F = radiative forcings MAT = atmospheric concentrations CO2 Qg = output gross of damages and abatement Qn = output net of damages and abatement TAT = global mean surface temperature C = abatement (mitigation) cost μ = emissions control rate (fraction of uncontrolled) σ = emissions/output ratio D = damages as fraction of output R = utility discount factor = (1+ρ)-t 23 Slightly Simplified Equations of DICE-type Model Objective Function (1) W T max U[c(t ),L(t )]R(t ) t 1 Economics (2) U [c(t),L(t)] = L(t)[c(t)1- / (1 - )] (3) Q g (t) = A(t) K(t) L(t)1 (4) D(t) = 1TAT (t) + 2TAT (t)2 (5) C(t) = Q g (t) 1(t)(t)2 (6) Utility function Gross output Damage function Abatement cost Qn (t) = [( 1 D(T )][1 - C(t)]A(t) K(t) L(t)1 = [( 1 D(T )][1 - C(t)]Q (t) (7) EInd (t) = (t)[1 - (t)]Q g (t) g Geosciences (8) M AT (t) E(t) 11 M AT (t - 1 ) ... (9) F(t) {log2 [ MAT (t) / MAT (0)]} FEX (t) (10) TAT (t) TAT (t 1 ) 1 {F(t) ... Net output Industrial emissions Atmospheric CO2 Radiative forcings Global mean temperature 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) Sigma: MER (DC) Sigma: PPP (DC) US 3.5 3.5 Russia US 3 Russia China 3 China CO2/GDP 2.5 2 1.5 2 1.5 1 1 0.5 0.5 20 02 19 96 19 90 19 84 19 78 19 72 19 66 2000 1995 1990 1985 1980 1975 1970 1965 19 60 0 0 1960 CO2/GDP 2.5 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 Actual and predicted global temperature history .6 .4 .2 .0 -.2 -.4 -.6 1840 1880 1920 1960 2000 YEAR T_DICE T_Hadley T_GISS 29 Projected DICE and IPCC: two scenarios 5 4 3 2 1 0 1920 1960 2000 2040 2080 2120 YE A R T_A2_DICE T_A2_IPCC T_B1_DICE T_B1_IPCC 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, highincome 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: C = Qλμ (1) 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 (2) dC/dE = MC emissions reductions = Qλβμ-1[dμ/dE] = λβμ-1/σ Taking logs: (3) 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 60 50 40 30 20 10 0 0 5 10 15 20 25 30 35 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: t 0 c(t )e t ˆ t ce t 0 where c(t ) is the actual path and cˆ is the 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. 44 45 46 47 1400 Atmospheric CO2 Concentration Atmospheric concentrations CO2 (ppm) 1200 1000 800 600 400 200 0 2000 Base Optimal Lim2t Stern SternCalib Copen 2020 2040 2060 2080 2100 2120 2140 2160 2180 2200 48 7 Atmospheric Temperature Global mean temperature (increase from 1900, °C ) Base 6 Optimal Lim2t Stern 5 SternCalib Copen 4 3 2 1 0 2000 2020 2040 2060 2080 2100 2120 2140 2160 2180 2200 49 Policies 50 120% Emissions control rate (% of baseline) Emissions Control Rate 100% 80% 60% Base Optimal 40% Lim2t Stern SternCalib 20% Copen 0% 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 51 300 Stern Carbon Price Price of carbon emissions ($ per ton of CO2) Lim2t 250 Optimal SternCalib Copen 200 Base 150 100 50 0 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 52 Overall economic impact 53 Three economic results from IAMs 1. Overall cost. An economically oriented climate-change policy would be relatively inexpensive and have a substantial impact on long-run climate change. 2. Measures of tightness. The best way to gauge the optimal “tightness” of climate change policies is the optimal carbon price or carbon tax. 3. Time path of optimal policies. Most optimal policies ramp up over time from modest C prices today to very very high ones in a few decades. 54 Three inconvenient truths from IAMs 4. An inconvenient scientific truth: Global warming is not a hoax. It will (almost surely) become an increasingly important and obvious feature of earth systems. 5. An inconvenient economic truth: To be efficient, firms and consumers must face a market price of carbon emissions that reflects the social costs. 6. An inconvenient political truth: To be effective, the price must be universal and harmonized in every sector and country. 55 Readings for lectures Lecture 1 on Integrated Assessment W. Nordhaus, 56 References General Background: The Stern Review, 2005. On RICE and DICE models: W.D. Nordhaus, A Question of Balance, Yale Press, 2008; W.D. Nordhaus, “Copenhagen Accord,” PNAS, 2010; W.D. Nordhaus and P. Sztorc, DICE-2013: A Users Manual. On IA models: W.D. Nordhaus, “Integrated Assessment Models…”Handbook of CGE Models, available at cowles.econ.yale.edu/P/cd/d18a/d1839.pdf; P. Kelly and C. Kolstad, “Integrated Assessment Models For Climate Change Control,” International Yearbook 1999-2000, available as pdf. On disaggregation: H. Theil, Linear Aggregation of Economic Relations; Grunfeld and Griliches, “Is Aggregation Necessarily Bad?” ReStat, 1960. On uncertainty: David Kelly and Charles Kolstad, Bayesian learning, growth, and pollution. Journal of Economic Dynamics and Control, 23(4):491-518, 1999; Pindyck, R. S. , Fat tails, thin tails, and climate change policy. Review of Environmental Economics and Policy 5(2): 258-274, 2008; Weitzman, M. L. On modeling and interpreting the economics of catastrophic climate change. Review of Economics and Statistics 91(1): 1-19, 2009; Weitzman, M. L. Fat-tailed uncertainty in the economics of catastrophic climate change. Review of Environmental Economics and Policy 5(2): 275-292, 2011. 57 References (cont) On uncertainty and discouting: Christian Gollier, Pricing the Planet, Princeton U Press, 2012; M. Weitzman, “On Modeling and Interpreting Catastrophic Events,” ReStat, Feb 2009; W. Nordhaus, “Economics of Tail Events,” REEP, 2011. On learning and decision theory: Basics: A. K. Dixit and R.S. Pindyck, Investments under Uncertainty, 1994, Princeton University Press; On learning and decision theory: Good applications: A.S. Manne and R.G. Richels, Buying Greenhouse Insurance: The Economic Costs of Carbon Dioxide Emission Limits. Cambridge, Mass., MIT Press, 1992; M. Webster, The Curious Role of ”Learning” in Climate Policy: Should We Wait for More Data? The Energy Journal, 2002. Data: US output data from bea.gov. CO2 emissions from CDIAC at http://cdiac.ornl.gov/trends/emis/overview_2008.html and IEA. CO2 concentrations at Mauna Loa from http://www.esrl.noaa.gov/gmd/ccgg/trends/ Mann reconstruction from http://www.ncdc.noaa.gov /paleo/pubs/mann2008/mann2008.html. Vostok ice core record from http://www.nature.com/nature/journal/v399/n6735/abs/399429a0.html. Global output data from Maddison and World Bank use PPP valuation. Global temperature estimates aveaged from Hadley, GISS, and NCDC. 58