Major Issues in the Economic Modeling of Global Warming

Transcription

1 Major Issues in the Economic Modeling of Global Warming William D. Nordhaus Yale University October 2-3, 2008 Workshop on Assessing Economic Impacts of Greenhouse Gas Mitigation The National Academies Slides are available at Full study is William Nordhaus, A Question of Balance: Weighing the Options on Climate Change, Yale University Press, 2008, available in full at author s web page. 1

2 Outline of lecture 1. Recent science of global warming 2. Integrated assessment models 3. Policy scenarios for analysis 4. The question of climate impacts 5. Dilemmas of uncertainty 6. The economics of participation 7. Weitzman s critique 8. Thoughts on discounting 9. Economist s bottom line 2

3 CO 2 concentrations at Mauna Loa,

4 Instrumental record, Temperature anomaly ( = 0) GISS Hadley

5 IPCC AR4 Model Results: History and Projections DICE-2007 model 2-sigma range DICE model 5

6 II. Integrated Assessment (IA) Models What are IA models? - These are models that include the full range of cause and effect in climate change ( end to end modeling). Major goals of IA models: Project trends Assess costs and benefits of climate policies Assess uncertainties and research priorities Estimate the carbon price and efficient emissions reductions for different goals 6

7 Fossil fuel use generates CO2 emissions The emissions -climateimpactspolicy nexus Carbon cycle: redistributes around atmosphere, oceans, etc. Impacts on ecosystems, agriculture, diseases, skiing, golfing, Climate system: change in radiative warming, precip, ocean currents, sea level rise, Measures to control emissions (limits, taxes, subsidies, ) 7

8 Economic Theory Behind DICE Model 1. Basic theorem of markets as maximization (Samuelson, Negishi) Outcome of efficient competitive market (however complex but finite time) = Maximization of weighted utility function: n = i= 1 W θ [U (c )] i i i k,s,t for utility functions U; individuals i=1,...,n; locations k, uncertain states of world s, i time periods t; welfare weights θ. 2. This allows us (in principle) to calculate the outcome of a market system by a constrained non-linear maximization. 8

9 Key Equations of DICE-2007 model 9

10 Limitations of DICE Model DICE-2007 is global aggregate ; however, regional model has been developed with Z. Yang and is being updated. Major uncertainties about many modules (particularly future technological change and impacts) Issues of catastrophic and irreversible climate change and impacts Weitzman s concerns about fat tails Stern Review concerns on discounting Dyson s critique that we know little about the impacts Gates s critique that we have drastically underestimated the pace of technological change. 10

11 III. Policy Scenarios for Analysis 1. Baseline. No emissions controls. 2. Optimal policy. Emissions and carbon prices to maximize discounted economic welfare. 3. Limit to 2 C. Climatic constraints with global temperature increase limited to 2 C above Strengthened Kyoto Protocol. Modeled on US proposal with rich countries at same time and developing countries join after 1-3 decades. 11

12 Assumptions for Strengthened Kyoto Protocol Emissions reductions of high-income countries as in the 2008 Senate bill 80 percent reductions from baseline by 2050 Other countries join gradually: Russia, FSU, Latin America 2 decades later China and India 3 decades later Global participation rate: 45 percent by percent by percent by 2100 Global emissions fall from 9 GtC in 2005 to 6.4 GtC in

13 Temperature profiles 6 Temperature change (C) Optimal 2x CO2 2o C limit Baseline Strong Kyoto

14 Carbon prices for major scenarios Carbon price (2005 US$ per ton C) Optimal Baseline < 2 degrees C Strong Kyoto

15 DICE-2008 model results Difference from baseline run: Case Consumption Abatement Damages Abatement plus damages [Trillions of dollars, discounted, 2005 US international $] Base run Strong Kyoto Optimal degree limit

16 IV. The Question of Climate Impacts Estimating the impact of climate change on society is the most treacherous of all areas. First approximation of climate damages: - Relatively minor impacts on market economies of North for a century (+ 1 percent of output) - Likely to have very large impacts on unmanaged ecosystems a century out and more Example of sea-level rise 16

17 Damage functions in different estimates 11% 10% RICE-1999 Climate damage/global output 9% 8% 7% 6% 5% 4% 3% 2% DICE-2007 IPCC estimate 1% 0% Mean temperature increase (oc) 17

18 V. Dilemmas of uncertainty Uncertainty and the potential for catastrophic impacts are a major concern in global warming science and policy today. Some major risks include: Reversal of North Atlantic deepwater circulation Melting of Greenland and West Antarctic ice sheets Abrupt climate change Ocean carbonization How can we model risk and uncertainty in IAMs? 18

19 Hysteresis Loops for Ice Sheets and Tipping Points 19 Frank Pattyn, GRANTISM: Model of Greenland and Antarctica, Computers & Geosciences, April 2006, Pages

20 Alternative Approaches to Uncertainty 1. Scenario analysis 2. Probabilistic scenario analysis 3. Decision theoretic/subjective probability approach 20

21 Alternative Approaches to Uncertainty 1. Scenario analysis: Example from IPCC/SRES: [Scenarios] are not forecasts, projections or predictions of what is to come. Nor are they preferred views of the future. Rather, they are plausible alternative futures: they provide reasonable and consistent answers to the what if? questions relevant to business (Nakicenovic et al.) 2. Probabilistic scenario analysis: Attach p s to the scenarios without careful attention to model design or development of p s. Example is using the dispersion of model results as estimate of parameter uncertainty in IPCC AR4, Science. 21

22 3. Decision-theoretic approach a. The approach we have used is to combine modeling, subjective probability theory, and Monte Carlo sampling. b. Begin with a structure like DICE model equations. Can represent schematically as follows: where (1) y t = H(z t ; θ) y t = the endogenous variables (output, emissions, etc.) z t = exogenous and non-stochastic variables (financial meltdown, land-based emissions, etc.) θ = [θ 1,, θ n ] = uncertain parameters (including functional forms) c. Then develop subjective probabilities for major parameters, f(θ). d. Often, use thin- or medium-tailed distributions for parameters (2) θ N (θ, σ) But this has been criticized by Weitzman and others (more below). 22

23 Uncertainty analysis in DICE model For DICE model, we examine 100 random runs, where these are baseline for 8 uncertain parameters. Then fit a response-surface model that estimates major outcomes as function of uncertain parameters These provide information about uncertainties for major variables. They also point to a paradox that risk premium on high climate outcomes may be negative. 23

24 Major uncertain variables Standard Variable Mean deviation Rate of growth of total factor productivity (% per year) Rate of decarbonization (% per year) Equilibrium temperature-sensitivity coefficient ( C per CO2 doubling) Damage parameter (intercept of damage equation) Price of backstop technology ($ per ton C removed at 100 % removal) 1, Asymptotic global population (millions) 8,600 1,892 Transfer coefficient in carbon cycle Total resources of fossil fuels (billions of tons of carbon) 6,000 1,200 24

25 Uncertainty for future temperature: DICE 2007 baseline 6 Mean Mean + 1 sigma Global temperature increase (oc) Mean - 1 sigma Most likely

26 Uncertainty for 2015 social cost of carbon Number of cases (of 10,000) 1, Current Kyoto Protocol Mean EU ETS Social cost of capital, 2015 ($ per ton C) N = for response surface representation of DICE

27 The macro risk question Should we be paying a large risk premium on high-climate scenarios? The idea is that we would we invest more than the certainty equivalent to prevent the high-climate outcome. Earlier studies generally assume yes. These approaches applied a risk-averse utility function to the damages. (This was the approach in Nordhaus-Boyer 2000 and Stern 2007.) This is a partial-equilibrium approach. The correct approach would be to apply risk aversion to consumption as in consumption capital asset pricing model. In this framework, a positive risk premium when highclimate outcome is positively correlated with high MU consumption (or negatively correlated with consumption). 27

28 The macro risk question: theory Begin with a utility function, U(C). Examine the expected utility in year t (say 2100). This is E(U t ) = p i U[c t (θ i )]. In this, p i are the probabilities, θ i =[θ 1,, θ n ] to the uncertain parameters, and i are the uncertain states of the world (SOW). Under modern risk theory, we apply risk premia to SOWs where U [c(θ i )] is high (consumption is low). When do these high MU states occur? 28

29 Consumption and 2100 Temperature in DICE 2007 Per capita consumption, The red dots are 100 runs of DICE model with random draw of uncertain parameters Key result is that per capita consumption is positively correlated with temperature Temperature change,

30 Implications for Risk Premium Study suggests that the most important uncertainty in longrun is growth in productivity. High climate damages are associated with high growth rates of TFP. - So good economic news = bad climate news in baseline. - Think of the $2500 car. But this also means that the worst climate cases are ones in which the world is rich, which is a situation where we are more likely to be able to afford more costly climate abatement. But major point is that risk premium here is negative! 30

31 VI. The economics of participation: math What are the costs of non-participation? In DICE model, we can model this in closed form. Start with a reduced-form cost function: (1) C = Qλµ β where C = mitigation cost, Q = GDP, µ = emissions control rate, λ, β are parameters. The overall control rate is µ = µ P π, where P indicates participants, and π is participation rate. Substituting yields C(π) = Qλµ β π 1-β = C(1)π 1-β. Thus the cost penalty C(π)/C(1) is: (2) Cost penalty = π 1-β The key parameter is β, which is the convexity of the cost function. 31

32 Example on participation For example, if β = 3 and π = ½. Then for a given global emissions reduction, the cost penalty is: C(π)/C(1) = (0.5) 1-3 = (0.5) -2 = 4x 32

33 Model studies from IPCC AR4 Source: IPCC, AR4, Mitigation. 33

34 Source for estimates of β (elasticity of cost function) Source: IPCC, AR4, Mitigation, p

35 Marginal cost function 0.50 Reduction from baseline bottom up a1b top down a1b bottom up b2 top down b Marginal cost ($ per ton C) Source: From last slide

36 Using the IPCC as data for the cost function Least squares estimate of cost function from IPCC [Equation is MC = a*(%reduction)^(β-1) Approach β-1 SE(β-1) t(β-1) Bottom up: A1B Bottom up: B Top down: A1B Top down: B Conclusion is that the cost function is EXTREMELY convex. 36

37 Cost penalty Cost penalty function Bottom up Top down Participation rate Source: From last slide

38 10 Penalty of non-participation in Kyoto Protocol Cost (as fraction of 100% participation) Original design Current participation Source: Question of Balance 38

39 Estimates from DICE model runs 39

40 Conclusions This simple example shows the extreme importance of universal participation for mitigation: All countries All sectors All time periods This also shows why an approach like Kyoto, which really has only one tightly regulated sector (the EU EMS with circa 7 % of global CO2 emissions) is extremely inefficient. 40

41 VII. Weitzman s Dismal Theorem The catastrophe-insurance aspect of a fat-tailed unlimited-exposure situation can dominate the social-discounting aspect, the purerisk aspect, and the consumption-smoothing aspect. The burden of proof in climate-change CBA [cost-benefit analysis] is presumptively upon whoever calculates expected discounted utilities without considering that structural uncertainty might matter more than discounting or pure risk. Such a middle-of-thedistribution modeler should explain why the bad fat tail does not play a very significant perhaps even decisive role in climatechange CBA. [Forthcoming, Rev. Econ. and Stat.] Pretty nice challenge!!! 41

42 What is the definition of fat tails? Weitzman uses an unusual definition: That a particular moment generating function of a p.d.f. is infinite: α x E( M) = e f ( x) dx Weitzman defines fat tails as f(x) for which E(M) =, where α is the CRRA elasticity and f(x) is the p.d.f. [Serious conceptual problem that this def involves preferences.] Standard definition: thin-tailed distribution has a finite range (such as the uniform), medium-tailed distribution has exponentially declining tails (such as the normal or exponential) fat-tailed distribution has power-law tails (such as the Pareto). [Schuster, Classification of Probability Laws by Tail Behavior, Journal of the American Statistical Association, Vol. 79, No. 388, Dec., 1984, pp ] 42

43 Examples Easiest to understand for case of t distribution, which comes from sample properties of normal distribution. Picture of tails for N(0,1) and t(n) distributions: 0 log10(1-f) = 1 - cumulative frequency Normal t(20) t(5) t(1)

44 Analytical Background to DT Assume maximize expected utility with log-normal error and CRRA: (1) max E[ U( c)] 1 α (2) U( c) = c /(1 α ): CRRA, α > 0 (3) ln( c) = c + ε (4) ε N(0, s) Assumptions about random term, ε: Case 1. Normal known mean and variance. Leads to standard results and finite EU. Case 2. Unknown variance estimated from Bayesian learning or classical estimation unbounded EU for α >1. [Geweke, Jour. Econ. Let., 2001] 44

45 Weitzman s contribution Weitzman modifies to include policy variable, P, with an uncertain multiplier, µ: (1) max E[ U( c)] 1 α (2) U( c) = c /(1 α ): CRRA, α > 0 (3) ln( c) = c + ε + µ P (4) ε = 0; µ N( m, s) Assume that P = 0 is no policy (e.g., strict emissions limits), and P = 1 is business as usual, then this maps directly into the Geweke proposition. In Weitzman, the µ is the policy multiplier. He takes example of temperature sensitivity coefficient (TSC). Because of limited sampling, he argues for fat tails on TSC and therefore for unbounded E(U). 45

46 Simple Example for Weitzman s Dismal Theorem 1 α - Utility function: U ( c) - c, for >1. - Probability distribution (power law fat tails): f ( c) c - Conditional expected value: V ( c) = f ( c) U ( c) -c - Expected value in (lower) tail over (0,c): c E( c ) -c c= = 0 { k + 1 α dc - if k+2-α < 0 - c ( k+ 2 α ) if k+2-α > 0 α k k + 1 α - DT does not hold always; depends here on relationship between risk aversion ( α) and fatness of power tail ( k). 46

47 Reflections on the DT 1. Fat tails not sufficient for Dismal Theorem 2. DT depends upon the parameters of preference function 3. CRRA a problematic utility function because U(0) = - ; may lead to unacceptable conclusions (asteroids, colliders as examples) 4. The meta-analysis of TSC is not correct statistical practice (e.g., don t get %ile by averaging %iles). 5. In general, DT covers limited terrain, but important to consider when doing uncertainty analysis. 47

48 VIII. Thoughts on Discounting Standard approach is the Ramsey equation: r = ρ + αg Here, r = rate of return on investments, ρ = pure rate of time preference, α = rate of inequality aversion, and g = growth rate of per capita consumption Alternative approaches (approx. numbers in % per year): I. DICE approach: r = 5.5% and g = 2% are data. If ρ = 1.5% then α = 2. II. Stern approach: Strong ethical presumption that ρ 0 and α = 1. With g = 1.3%, implies r =1.4%, which is below market return. III. Recalibrated DICE: Take r = 5.5% and g = 2% as data. If ρ = 0 then α = Then compare I, II, and III. 48

49 Results of DICE, Stern zero discounting, and recalibrated zero discounting Conclusion: If time preference is zero but we recalibrate to ensure that interest and growth rate data are satisfied, then the nearterm trajectory is virtually identical across different rates of time preference. It is the interest rate difference that produces the different outcomes, not the time preference difference. 49

50 IX. What is the economist s bottom on global warming? The fundamental problem is the climate-change externality a global public good Economic participants (millions of firms, billions of people, trillions of decisions) need to face realistic carbon prices if their decisions about consumption, investment, and innovation are to be correct. 1. To be effective, we need a market price of carbon emissions that reflects the social costs. 2. Moreover, to be efficient, the price must be universal and harmonized in every sector and country. 50

51 Mankind in spite of itself is conducting a great geophysical experiment, unprecedented in human history. Roger Ravelle (1957) 51