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

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

3 Some Critical Issues in Uncertainty in Climate Models 1.What are standard estimates of uncertainty? 2.What is the effect of uncertainty compared to a certainty equivalent? 3.What is the state-contingent approach? 4.What are the state-contingent policies? 5.What is the welfare loss from uncertainty? 6.What is the cost of not knowing the state of the world (i.e., acting before learning)? 7.What is the value of early knowledge? 8.What is the precautionary principle, and what are the pros and cons of using it? 9.[What are the implications of “fat tailed” uncertainty?] 10.How does uncertainty affect the discount rate?

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? I will give an overview and an example. 4

Hysteresis loops for Ice Sheets and the “Tipping Point” 5 Frank Pattyn, “GRANTISM: Model of Greenland and Antrarctica,” Computers & Geosciences, April 2006, Pages

General Principles Intertemporal choice. Discounted utility (DU) model, where U(c) is cardinal utility over alternative bundles. Uncertainty. Very similar model is choice under uncertainty. 6

General Principles Intertemporal choice. Discounted utility (DU) model, where U(c) is cardinal utility over alternative bundles. Uncertainty. Very similar model is choice under uncertainty. This is expected utility or EU or von Neumann-Morgenstern model:, where U is a cardinal utility, π is a “state of the world,” and f( ) is the probability distribution. In this approach, decision makers wish to maximize EU. (This is like Arrow-Debreu model.) With two SOW, have What is U function in EU model? It is the value of consumption or wealth in certain prospects. 7

With linear systems If the system is linear, then optimal policy is certainty- equivalent; e.g., uncertainty is irrelevant. Proof left to student. A simple example is the following. Show that the optimal P is invariant to σ(ε). Max E[U(Y)] = E( a + bY +c Y 2 ) = Expected value of U where Y = kP + ε Y = income; P = policy; ε = additive uncertainty; σ(ε) = standard deviation ε; a, b, k, σ are known parameters. This is Tinbergen-Theil certainty equivalent theorem. See Readings. 8

Monte Carlo Approach (Also Learn then Act) 1.Common approach: combines modeling, subjective probability theory, and Monte Carlo sampling. 2.Begin with a structure like DICE model equations. Can represent schematically as follows: (1)y t = H( z t ; θ ) where 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) 3. We then develop subjective probabilities for major parameters, f( θ). 9

10 Example of temperature distribution Implementation 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 what the uncertainties are for major variables.

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12 A Simple Example For our example, we will assume that there is one major uncertainty: The damage function is D=YθT 2, θ uncertain. Assume two states of the world, SOW1 and SOW2. SOW2 has a damage function that is ten times higher than SOW1, or θ 2 = 10 θ 2 But we are uncertain about the damages. –State of world 1 (SOW1) has p = 90% –Catastrophic case 2 (SOW2) has p = 10%

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ACT now and in future High damages High carbon tax Low carbon tax Low damages This example: Learn then act LEARN TODAY

Assume that we learn about SOW right away 15

What is wrong with this story? This is “learn then act.” That is, we learn the role of the dice, then we adopt the best policy for that role. But this assumes that we know the future! -If you know the future and decide (learn then act) -If you have to make your choice and then live with the future as it unfolds (act then learn) In many problems (such as climate change), you must decide NOW and learn about the state of the world LATER: “act then learn” 16

Decision Analysis In reality, we do not know future trajectory or SOW (“state of the world”). Suppose that through dedicated research, we will learn the exact answer in 30 years. It means that we must set policy now for both SOW; we can make state-contingent policies after 30 years. How will that affect our optimal policy? 17

LEARN 2045 ACT TODAY ? Low damages High damages Realistic world: Act then learn

Optimal policies with 30 years of ignorance 19

Optimal policies with late and early learning 20

Compare average early and late learning 21

Lessons 1.Use schema of state-dependence prices and outputs to analyze learning 2.Critical issue of when we learn for policy. 3.In the case here, delayed learning leads to higher average carbon price. -In this extreme case, difference is 10-20% -Generally less in most models and scenarios 4. Note that prices (policies) are close to each other after we learn. Here, no big effect on post-learning policy. 22

Aggregate costs and benefits 23 Value of learning: $4,710 billion in this catastrophic situation. Economists are earning their wages.

Per capita costs and benefits 24 Values not huge relative to income.

Precautionary principle 1.Act to minimize the damage in the worst case. 2.Generally, not a sensible strategy. Too risk averse. 3.However, if you never learn, it is a better strategy that EU strategy which doesn’t take into account that you do not know the SOW. 4.In catastrophic situation without learning, the precautionary principle may be a better rule than the EU rule. 25

Precautionary v. EU in catastrophic situation 26

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Macroeconomic risks and climate change What is relationship between risk and discounting? Some have argued that we should use a lower discount rate to reflect climate risks. What is the appropriate approach. (Best reading and highly recommended: Gollier, Pricing the Planet, Princeton U Press, 2012.) 28

29 The macro risk question: theory 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 modern risk analysis in the consumption capital asset pricing model. In this framework, want to pay a risk premium ↔ the high-climate outcome is positively correlated with high MU consumption (or negatively correlated with consumption).

30 Consumption and 2100 Temperature The red dots are 100 runs of DICE model with random draw of uncertain parameters The blue dots are 10,000 runs of response- surface model. Key result is that per capita consumption is positively correlated with temperature.

31 Implications for Risk Premium Study suggests that the most important uncertainty in long-run 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. Leads to higher discount rates (lower prices in state-contingent approach). This is an open issue. Whether should have positive or negative pricing on climate not settled.

Conclusions Uncertainty does not lead to major change in state- dependent policy unless there are major non-linearities or learning. When you have learning, the structure of decision making is very different; it can increase or decrease early investments. In cases where there are major catastrophic damages, value of early information is very high. Another important issue is whether should apply higher discounting to climate investments because of risks; open issue. Best investment is sometimes knowledge rather than mitigation … that is why we are at summer school! 32

Readings: See end of first lecture 33