Epstein–Zin Utility in DICE: Is Risk Aversion Irrelevant to Climate Policy?

Climate change involves uncertain probabilities of catastrophic risks, and very longterm consequences of current actions. Climate economics, therefore, is centrally concerned with the treatment of risk and time. Yet conventional assumptions about utility and optimal economic growth create a perverse connection between risk aversion and time preference, such that more aversion to current risks implies less concern for future outcomes, and vice versa. The same conflation of risk aversion and time preference leads to the equity premium puzzle in finance. A promising response to the equity premium puzzle, the recursive utility of Epstein and Zin, allows separation of risk aversion and time preference—at the cost of considerable analytic complexity. We introduce an accessible implementation of Epstein–Zin utility into the DICE model of climate economics, creating a hybrid “EZ-DICE” model. Using Epstein–Zin parameters from the finance literature and climate uncertainty parameters from the science literature, we find that the optimal climate policy in EZ-DICE calls for rapid abatement of carbon emissions; it is similar to standard DICE results with the discount rate set to equal the risk-free rate of return. EZ-DICE solutions are sensitive to the intertemporal elasticity of substitution, but remarkably insensitive to risk aversion. Insensitivity to risk aversion may reflect the difficulty of modeling catastrophic risks within DICE. Implicit in DICE are strong assumptions about the cost of climate stabilization and the certainty and speed of success; under these assumptions, risk aversion would in fact be unimportant. A more realistic analysis will require a subtler treatment of catastrophic climate risk.     

Scientific Ambiguity and Climate Policy

Economic evaluation of climate policy traditionally treats uncertainty by appealing to expected utility theory. Yet our knowledge of the impacts of climate policy may not be of sufficient quality to be described by unique probabilistic beliefs. In such circumstances, it has been argued that the axioms of expected utility theory may not be the correct standard of rationality. By contrast, several axiomatic frameworks have recently been proposed that account for ambiguous knowledge. In this paper, we apply static and dynamic versions of a smooth ambiguity model to climate mitigation policy. We obtain a general result on the comparative statics of optimal abatement and ambiguity aversion, and then extend our analysis to a more realistic, dynamic setting, where we introduce scientific ambiguity into the well-known DICE model of the climate-economy system. For policy-relevant exogenous mitigation policies, we show that the value of emissions abatement increases as ambiguity aversion increases, and that this ‘ambiguity premium’ can in some plausible cases be very large. In these cases the effect of ambiguity aversion on welfare is comparable to that of other much studied welfare parameters. Thus ambiguity aversion may be an important neglected aspect of climate change economics, and seems likely to provide another argument for strong abatement policy.     

Optimal Policy under Uncertainty and Learning about Climate Change: A Stochastic Dominance Approach

Global climate change presents a classic problem of decision making under uncertainty with learning. We provide stochastic dominance theorems that provide new insights into when abatement and investment into low carbon technology should increase in risk. We show that R&D into low-carbon technologies and near-term abatement are in some sense opposites in terms of risk. Abatement provides insurance against the possibility of major catastrophes; R&D provides insurance against the possibility that climate change is marginally worse than average. We extend our results to the comparative statics of learning.     

Climate Policy Under Uncertain and Heterogeneous Climate Damages

We highlight that uncertainty about climate damages and the fact that damages will be distributed heterogeneously across the global population can jointly be an argument for substantially stricter climate policy even if uncertainty and heterogeneity in isolation are not. The reason is that a given climate risk borne by fewer people implies greater welfare losses. However, these losses turn out to be significant only if society is both risk and inequality averse and if climate damages are highly heterogeneous. We discuss how insurance and self-insurance of climate risk could theoretically mitigate this joint effect of uncertainty and heterogeneity and thus admit weaker climate policy. Insurance provides more efficient risk sharing and self-insurance allows strongly impacted individuals to compensate damages by increasing savings. We first use a simple analytical model to introduce the different concepts and then provide more realistic results from the integrated assessment model DICE.     

A 4-Stated DICE: Quantitatively Addressing Uncertainty Effects in Climate Change

We introduce a version of the DICE-2007 model designed for uncertainty analysis. DICE is a wide-spread deterministic integrated assessment model of climate change. Climate change, long-term economic development, and their interactions are highly uncertain. The quantitative analysis of optimal mitigation policy under uncertainty requires a recursive dynamic programming implementation of integrated assessment models. Such implementations are subject to the curse of dimensionality. Every increase in the dimension of the state space is paid for by a combination of (exponentially) increasing processor time, lower quality of the value or policy function approximations, and reductions of the uncertainty domain. The paper promotes a state-reduced, recursive dynamic programming implementation of the DICE-2007 model. We achieve the reduction by simplifying the carbon cycle and the temperature delay equations. We compare our model’s performance and that of the DICE model to the scientific AOGCM models emulated by MAGICC 6.0 and find that our simplified model performs equally well as the original DICE model. Our implementation solves the infinite planning horizon problem in an arbitrary time step. The paper is the first to carefully analyze the quality of the value function approximation using two different types of basis functions and systematically varying the dimension of the basis. We present the closed form, continuous time approximation to the exogenous (discretely and inductively defined) processes in DICE, and we present a numerically more efficient re-normalized Bellman equation that, in addition, can disentangle risk attitude from the propensity to smooth consumption over time.     

Why uncertainty matters: discounting under intertemporal risk aversion and ambiguity

Uncertainty has an almost negligible impact on project value in the standard economic model. I show that a comprehensive evaluation of uncertainty and uncertainty attitude changes this picture fundamentally. The illustration of this result relies on the discount rate, which is the crucial determinant in balancing immediate costs against future benefits, and the single most important determinant of optimal mitigation policies in the integrated assessment of climate change. First, the paper removes an implicit assumption of (intertemporal or intrinsic) risk neutrality from the standard economic model. Second, the paper introduces aversion to non-risk uncertainty (ambiguity). I show a close formal similarity between the model of intertemporal risk aversion, which is a reformulation of the widespread Epstein–Zin–Weil model, and a recent model of smooth ambiguity aversion. I merge the models, achieving a threefold disentanglement between risk aversion, ambiguity aversion, and the propensity to smooth consumption over time.     

Climate Policy,Learning, and Technology Adoption in Small Countries

A significant reduction in global greenhouse gas emissions requires international cooperation in emission abatement as well as individual countries’ investment in the adoption of abatement technology. The existing literature on climate policy pays insufficient attention to small countries, which account for a substantial proportion of global emission. In this study, we investigate how climate policy and learning about climate damage affect investment in abatement technology in small countries. We consider three alternative climate policy instruments: emission standards, harmonized taxes and auctioned permits. We say that learning is feasible if an international environmental agreement (IEA) is formed after the resolution of uncertainty about climate damage. We find that, either with learning and quadratic abatement costs or without learning, harmonized taxes outperform emission standards and auctioned permits in terms of investment efficiency. Without learning, a large cost of nonparticipation (that a country incurs) in the IEA can be beneficial to the country. Whether learning improves investment efficiency depends on the size of this nonparticipation cost.     

A Real Options Approach to Abatement Investments and Green Goodwill

In this paper we adopt the green goodwill argument as to why firms voluntarily invest in abatement capital. We investigate the effects on the abatement investment decision of changes in uncertainty about future green goodwill, competitor abatement investments, regulations, etc., using a real options framework. Our results indicate that increased uncertainty about consumers' willingness to pay for green products in the future discourage voluntary abatement investments. The model also suggests that voluntary abatement investments are promoted by an increased threat of regulation and competitor abatement investments. Furthermore, the benefit-cost ratio of the abatement investment project, at the point where it is optimal to invest, is independent of what regulatory regime (stringent or lenient) the firm operates in. We also conclude that despite the fact that voluntary abatement investment exists, there may still be room for environmental policy.     

Reconciling Economic Growth and Carbon Mitigation: Challenges and Policy Options in China

As the biggest carbon emitter in the world, China is facing tremendous pressure domestically and internationally. To promote the international efforts to tackle climate change, the Chinese government announced its 2020 carbon intensity target and is actively taking part in the international climate negotiations. In this paper, we review some of the climate burden-sharing proposals raised by Chinese scholars to shed some light on China's perspective on the post-Kyoto climate architecture. Then we summarize China's current pollution abatement policies and measures, and analyze some potential policy instruments for China to reconcile its future economic growth and carbon mitigation, as well as some practical design and enforcement issues to be considered for the near term.     

Research Frontiers in the Economics of Climate Change

Academic and policy debates over climate change risks and policies have stimulated economic research in a variety of fields. In this article I briefly discuss eight overlapping areas of current research in which further effort is particularly warranted. These areas include decision criteria for policy; risk assessment and adaptation; uncertainty and learning; abatement cost and the innovation and diffusion of technology; and the credibility of policies and international agreements. Further analysis in these areas not only will advance academic understanding but also will provide insights of considerable importance to policymakers.     

Optimal climate change mitigation under long-term growth uncertainty: Stochastic integrated assessment and analytic findings

Economic growth over the coming centuries is one of the major determinants of today׳s optimal greenhouse gas mitigation policy. At the same time, long-run economic growth is highly uncertain. This paper is the first to evaluate optimal mitigation policy under long-term growth uncertainty in a stochastic integrated assessment model of climate change. The sign and magnitude of the impact depend on preference characteristics and on how damages scale with production. We explain the different mechanisms driving optimal mitigation under certain growth, under uncertain technological progress in the discounted expected utility model, and under uncertain technological progress in a more comprehensive asset pricing model based on Epstein–Zin–Weil preferences. In the latter framework, the dominating uncertainty impact has the opposite sign of a deterministic growth impact; the sign switch results from an endogenous pessimism weighting. All of our numeric scenarios use a DICE based assessment model and find a higher optimal carbon tax than the deterministic DICE base case calibration.     

Providing global public goods under uncertainty

We study how uncertainty and risk aversion affect international agreements to supply global public goods. We consider a benchmark model with homogeneous countries and linear payoffs. When countries directly contribute to a public good, uncertainty tends to lower signatories' efforts but may increase participation. Despite risk aversion, uncertainty may improve welfare. In contrast, when countries try to reduce a global public bad, uncertainty tends to increase signatories' efforts and decrease participation. In that case, an ex-ante reduction of uncertainty may have a large positive multiplier effect on welfare.     

Intertemporal Emission Permits Trading Under Uncertainty and Irreversibility

This paper analyzes the effect of emission permit banking on clean technology investment and abatement under conditions where the stringency of the future cap is uncertain. We examine the problem of heterogeneous firms minimizing the cost of intertemporal emission control in the presence of stochastic future pollution standards and emission permits that are tradable across firms and through time. A firm can invest in clean capital (an improved pollution abatement technology) to reduce its abatement cost. We consider two possibilities: that investment is reversible or irreversible. Uncertainty is captured within a two period model: only the current period cap is known. We show that if banking is positive and marginal abatement costs are sufficiently convex, there will be more abatement and investment in clean technology under uncertainty than there would be under certainty and no banking. These results are at odds with the common belief that uncertainty on future environmental policy is a barrier to investment in clean capital. Moreover, under uncertainty and irreversibility, we find that there are cases where banking enables firms to invest more in clean capital.     

Pricing Monitoring Uncertainty in Climate Policy

This article assesses the environmental and economic efficiency of three different approaches to treat monitoring uncertainty in climate policy, namely prescribing uncertainty, setting minimum certainty thresholds and pricing uncertainty through a discount. Our model of the behavior of profit-maximizing agents demonstrates that under the simplest set of assumptions the regulator has no interest in reducing monitoring uncertainty. However, in the presence of information asymmetry, monitoring uncertainty may hamper the economic and environmental performance of climate policy due to adverse selection. In a mandatory policy, prescribing a reasonable level of uncertainty is preferable if the regulator has enough information to determine this level. For voluntary mechanisms, such as carbon offsets, allowing agents to set their own monitoring uncertainty below a maximum threshold or discounting carbon revenues in proportion to monitoring uncertainty are the best approaches for the regulator to mitigate the negative effects of information asymmetry. These conclusions are much more pronounced when agents do not accrue revenues from their mitigation action, other than carbon. Our analysis of monitoring uncertainty under information asymmetry, which results in heterogeneity in the agents’ benefits from abatement, generalizes the classical trade-off between production efficiency and information rents.     

Climate Policy Under Fat-Tailed Risk: An Application of Dice

Uncertainty plays a significant role in evaluating climate policy, and fat-tailed uncertainty may dominate policy advice. Should we make our utmost effort to prevent the arbitrarily large impacts of climate change under deep uncertainty? In order to answer to this question, we propose a new way of investigating the impact of (fat-tailed) uncertainty on optimal climate policy: the curvature of the optimal carbon tax against the uncertainty. We find that the optimal carbon tax increases as the uncertainty about climate sensitivity increases, but it does not accelerate as implied by Weitzman’s Dismal Theorem. We find the same result in a wide variety of sensitivity analyses. These results emphasize the importance of balancing the costs of climate change against its benefits, also under deep uncertainty.     

IMPROVING ENVIRONMENTAL POLICY: ARE MARKETS THE SOLUTION?

While market approaches are clearly valuable for improving U.S. environmental policy, they cannot solve all of the problems, and not necessarily the most difficult ones. They can ensure that a given total abatement is achieved at minimum cost. But, if pollution damages depend on how abatement effort is allocated among polluters, this is not necessarily the most desirable outcome. One also needs to be sure that the potential gains from trade implicit in market solutions will actually be realized within some given time; the empirical evidence here is not necessarily promising. Rather than how aggregate abatement should be distributed among polluters, the chief difficulty often lies in determining how much overall abatement is required. A key factor that economists tend to overlook is the difficulty of ascertaining just how benefits vary with abatement effort. Uncertainty and risk aversion in connection with the marginal benefit curve may explain regulatory actions that are otherwise hard to justify.     

Precautionary Principle and Robustness for a Stock Pollutant with Multiplicative Risk

The interest shown by policy makers and economists in the precautionary principle indicates the importance of model uncertainty in global warming policy. I show that through robust control, policy makers can implement the precautionary principle to regulate a stock pollutant, and I analyze its effect on expected steady state pollution taxes, stocks and welfare. The paper is broadly comprised of a theoretical part and an application to global warming policy. I find that: (1) an increase in either uncertainty about the model or risk about abatement cost increases expected steady state pollution taxes; (2) a robust policy is preferred for any level of model uncertainty and this preference increases for either higher model uncertainty or higher multiplicative risk and (3) the effect on expected steady state pollution taxes and stock of introducing model uncertainty is relatively small for high levels of model uncertainty. These results advocate using robust policies for a stock pollutant in the presence of model uncertainty.      

Property rights and liability for deforestation under REDD+: Implications for ‘permanence’ in policy design

Reducing Emissions from Deforestation and forest Degradation (REDD+) is critical in efforts to mitigate the effects of anthropogenic climate change. Despite uncertainty about the exact form of a future, international REDD+ system, REDD+ carbon property rights would need to be created and allocated with liability assigned for the potential loss of climate benefits in the event of carbon reversal from deforestation. This commentary explores the links between forest property rights and liability, to different REDD+ policy options and their implications for permanence. Should national governments retain liability for permanence then project-level activities that have individually-assigned REDD+ carbon rights may have a higher risk of carbon reversal than policies where rights are assigned to the state. Knowledge of pre-existing forest rights is necessary for some policies implemented with government-assigned REDD+ rights in order to compensate for potential income losses from policy implementation.     

Climate Policy,Uncertainty, and the Role of Technological Innovation

We study how uncertainty about climate change severity affects the relative benefits of early abatement and a portfolio of research and development (R&D) in lowering future abatement costs. Optimal early abatement depends on the curvature of the marginal benefit and marginal abatement cost (MAC) functions and how the uncertain parameter affects marginal benefits. R&D in a particular technology depends on whether uncertainty increases early abatement; whether investment lowers marginal costs for that technology; whether R&D lowers the slope of that technology's MAC function; and the shape of that technology's MAC function. We illustrate, focusing on the role of backstop technologies.     

Dynamic general equilibrium model with uncertainty: Uncertainty regarding the future path of the economy

This paper develops a new method for incorporating uncertainty within a computable general equilibrium (CGE) model. The method involves incorporating uncertainty into the model by formulating different states of the world or paths that the economy may take. The risk then is that on one or more of the paths, there may be an external demand shock, for example, an exogenous shock in tourism demand. The multi-sector forward-looking CGE model with risk shows the impact of uncertainty on the economy and how households and industry respond to the presence of uncertainty. The results show that, where there is an asymmetric shock, the possibility of a future tourism demand shock creates a welfare loss. The welfare gains along the non-shocked path are a result of household's risk aversion and their substituting resources away from the shocked path. The difference in the monetary values of the welfare on the different paths can be interpreted as the ‘price’ of the risk. It is the price households would pay to remove the possibility of the tourism shock. Therefore, this research was able to quantify the monetary value of the risk. This method can be used in scenario modelling for other adverse contingent events, such as the uncertainty of climate change impacts, and agriculture production risks.