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This paper is a revised version of: https://ssrn.com/abstract=2667972. The Analytic Climate Economy (ACE) closes a gap between analytic climate change assessments and quantitative numeric integrated assessment models (IAMs) used in policy advising. Its closed-form solution links IAM components and parametric assumptions directly to their policy impacts. Its analytic nature overcomes Bellman's curse of dimensionality for a wide range of stochastic processes. ACE shows that uncertainty flips the main drivers of the carbon tax. Uncertainty also makes IAMs even more sensitive to the discount rate and its composition. Under a recent survey's median estimate for pure time preference, uncertainty almost triples the optimal tax.

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.

The integrated assessment literature frequently replicates uncertainty by averaging Monte Carlo runs of deterministic models. This Monte Carlo analysis is, in essence, an averaged sensitivity analyses. The approach resolves all uncertainty before the first time period, drawing parameters from a distribution before initiating a given model run. This paper analyzes how closely a Monte Carlo based derivation of optimal policies is to the truly optimal policy, in which the decision maker acknowledges the full set of possible future trajectories in every period. Our analysis uses a stochastic dynamic programming version of the widespread integrated assessment model DICE, and focuses on damage uncertainty. We show that the optimizing Monte Carlo approach is not only off in magnitude, but can even lead to a wrong sign of the uncertainty effect. Moreover, it can lead to contradictory policy advice, suggesting a more stringent climate policy in terms of the abatement rate and a less stringent one in terms of the expenditure on abatement.

Time and uncertainty constitute essential ingredients to many of the most challenging resource problems. With respect to the time dimension, agents are generally assumed to have a pure time preference as well as a preference for smoothing consumption over time. With respect to risk, agents are generally assumed to be Arrow-Pratt risk averse. The discounted expected utility model assumes that aversion to risk and aversion to intertemporal fluctuations coincide. This review discusses models and concepts that aim at disentangling time and risk attitude and briefly sketches a generalization of risk attitude to situations where uncertainty is not captured by unique probability measures. This paper reviews resource economic applications and relates the concepts to the debate on the social discount rate.

This paper is a revised version of: http://ssrn.com/abstract=2643293.The paper derives the optimal carbon tax in closed-form from an integrated assessment of climate change. The formula shows how carbon, temperature, and economic dynamics quantify the optimal mitigation effort. The model's descriptive power is comparable to numeric models used in policy advising. Uncertainty surrounding climate change remains large, and the paper derives closed-form expressions of welfare loss from shocks and epistemological uncertainty. These expressions interact (intrinsic) risk attitude, distributional moments, and the climatic shadow values, and they exhibit different sensitivities to time preference. Welfare gains from reducing uncertainty about temperature feedbacks are much higher than the gains from better measurements of carbon flows.

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.

The precise consequences of climate change remain uncertain. We incorporate damage uncertainty into a joint model of climate and the economy, an integrated assessment model. First, both the science and the integrated assessment community analyze uncertainty by means of sensitivity analysis and Monte-Carlo simulations. These methods have serious limitations in deriving a carbon tax or cap under uncertainty: they do not incorporate the interaction between stochastic climate impacts and economic policy. We derive the optimal climate policies accounting for the full interaction between uncertain damage realizations, optimal policy response, and climatic feedback. Second, state of the art integrated assessment relies on the standard economic model. Modern decision theory and its applications to finance show that this discounted expected utility model is incapable of simultaneously capturing adequate risk premia and a reasonable discount rate, leading to the equity premium and the risk-free rate puzzles. We follow the finance literature in disentangling risk aversion from the propensity to smooth consumption over time, which gives rise to a model reflecting correctly the risk-free discount rate and the risk premia. We find that optimal mitigation efforts are twice as high in the comprehensive risk model as compared to the entangled standard model.

The paper analyzes the discount rate under uncertainty. The analy- sis complements the probabilistic characterization of uncertainty by a measure of confidence. Special cases of the model comprise discounting under smooth am- biguity aversion as well as discounting under a disentanglement of risk aversion from aversion to intertemporal substitution. The paper characterizes the gen- eral class of preferences for which uncertainty implies a reduction of the discount rate. It also characterizes how the more comprehensive description of uncertainty changes the discount rate with respect to the standard model. The paper relates different results in the literature by switching between different risk measures. It presents a parametric extension of the Ramsey discounting formula that takes into account confidence into future growth estimates and a measure of aversion to the lack of confidence. If confidence decreases in the futurity of the growth forecast, the discount rates have a falling term structure even in the case of an iid growth process.

The paper incorporates qualitative differences of probabilistic beliefs into a rational (or normatively motivated) decision framework. Probabilistic beliefs can range from objective probabilities to pure guesstimates. The decision maker in the present model takes into account his confidence in beliefs when evaluating general uncertain situations. From an axiomatic point of view, the approach stays as close as possible to the widespread von Neumann-Morgenstern framework. The resulting representation uses only basic tools from risk analysis, but employs them recursively. The paper extends the concept of smooth ambiguity aversion to a more general notion of aversion to the subjectivity of belief. As a special case, the framework permits a threefold disentanglement of intertemporal substitutability, Arrow-Pratt risk aversion, and smooth ambiguity aversion. A decision maker’s preferences can nest a variety of widespread decision criteria, which are selected according to his confidence in the uncertainty assessment of a particular setting.

Uncertainty has an almost negligible impact on project value in the economicstandard model. I show that a comprehensive evaluation of uncertainty and uncertainty attitude changes this picture fundamentally. The analysis 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. The paper examines two shortcomings in the recent debate and the current models addressing climate change assessment. First, removing an implicit assumption of (intertemporal) risk neutrality reduces the growth effect in social discounting and significantly amplifies the importance of risk and correlation. Second, debate and models largely overlook the difference in attitude with respect to risk and with respect to non-risk uncertainty. The paper derives the resulting changes of the risk-free and the stochastic social discount rate and points out the importance of even thin tailed uncertainty for climate change evaluation. It discusses combinations ofuncertainty and correlation that reduce the social discount rate to pure preference. In a theoretical contribution, the paper extends the smooth ambiguity model by providing a threefold disentanglement between, risk aversion, ambiguity aversion, and the propensityto smooth consumption over time.