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We model optimal policy when the probability of a tipping point, the welfare change due to a tipping point, and knowledge about a tipping point's trigger all depend on the policy path. Analytic results demonstrate how optimal policy depends on the ability to affect both the probability of a tipping point and also welfare in a post-threshold world. Simulations with a numerical climate-economy model show that possible tipping points in the climate system increase the optimal near-term carbon tax by up to 45% in base case speciffcations. The resulting policy paths lower peak warming by up to 0.5 C compared to a model without possible tipping points. Different types of tipping points have qualitatively different effects on policy, demonstrating the importance of explicitly modeling tipping points' effects on system dynamics. Aversion to ambiguity in the threshold's distribution can amplify or dampen the effect of tipping points on optimal policy, but in our numerical model, ambiguity aversionincreases the optimal carbon tax.

The paper introduces a new notion of risk aversion that is independent of the good under observation and its measure scale. The representational framework builds on a time consistent combination of additive separability on certain consumption paths and the von Neumann & Morgenstern (1944) assumptions. In the one-commodity special case, the new notion of risk aversion closely relates to a disentanglement of standard risk aversion and intertemporal substitutability.

We analyze the impact of damage uncertainty on optimal mitigation policies in the integrated assessment of climate change. Usually, these models analyzeuncertainty by averaging deterministic paths. In contrast, we build a consistentmodel deriving optimal policy rules under persistent uncertainty. For this purpose,we construct a close relative of the DICE model in a recursive dynamic programming framework. Our recursive approach allows us to disentangle effects of risk, risk aversion, and aversion to intertemporal substitution. We analyze different ways how damage uncertainty can affect the DICE equations. We compare the optimal policies to those resulting from the wide-spread ex-ante uncertainty approach averaging deterministic paths.

The paper analyzes the discount rate under uncertainty. The analysis complements the probabilistic characterization of uncertainty by a measure of confidence. Special cases of the model comprise discounting under smooth ambiguity aversion as well as discounting under a disentanglement of risk aversion from aversion to intertemporal substitution. The paper characterizes the general 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.

The tendency to foreshorten time units as we peer further into the future provides an explanation for hyperbolic discounting at an intergenerational time scale. We study implications of hyperbolic discounting for climate change policy, when the probability of a climate-induced catastrophe depends on the stock of greenhouse gasses. We provide a positive analysis by characterizing the set of Markov perfect equilibria (MPE) of the intergenerational game amongst a succession of policymakers. Each policymaker reflects her generation’s preferences, including its hyperbolic discounting. For a binary action game, we compare the MPE set to a “restricted commitment” benchmark. We compare the associated “constant equivalent discount rates” and the willingness to pay to control climate change with assumptions and recommendations in the Stern Review on Climate Change. “. . .My picture of the world is drawn in perspective. . . I apply my perspective not merely to space but also to time” —Ramsey.

We study the importance of anticipated learning - about both environmental damages and abatement costs - in determining the level and the method of controlling greenhouse gas emissions. We also compare active learning, passive learning, and parameter uncertainty without learning. Current beliefs about damages and abatement costs have an important effect on the optimal level of emissions, However, the optimal level of emissions is not sensitive either to the possibility of learning about damages. or to the type of learning (active or passive), Taxes dominate quotas, but by a small margin.