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We analyze the policy implications of aversion to Knightian uncertainty (ambiguity) about the possibility of tipping points. We demonstrate two channels through which uncertainty aversion affects optimal policy in the general setting. The first channel relates to the policy's effect on the probability of tipping, and the second channel to its differential impact in the pre- and post-tipping regimes. We then extend a recursive dynamic model of climate policy and tipping points to include uncertainty aversion. Numerically, aversion to Knightian uncertainty in the face of an ambiguous tipping point increases the optimal tax on carbon dioxide emissions, but only by a small amount.

The present paper introduces a novel idea of what constitutes risk attitude, how we can represent it, and how we can compare risk attitude across agents with differing tastes. In contrast to the Arrow--Pratt measure, it links directly to preferences on the multidimensional consumption space and is independent of the way in which we measure consumption. The paper derives a corresponding preference representation and applied insights governing Epstein-Zin preferences and asset pricing models. In particular, it suggests why the popular long-run risk model finds estimates of the elasticity of intertemporal substitution constrasting sharply with the rest of macroeconomics.

We investigate the optimal policy response to the possibility of abrupt, irreversible shifts in system dynamics. The welfare cost of a tipping point emerges from the policymaker's response to altered system dynamics. Our policymaker also learns about a threshold's location by observing the system's response in each period. Simulations with a recursive, numerical climate-economy model show that tipping possibilities raise the optimal carbon tax more strongly over time. The resulting policy paths ultimately lower optimal peak warming by up to 0.5°C. Different types of posttipping shifts in dynamics generate qualitatively different optimal pretipping policy paths. (JEL D78, H23, Q54, Q58)

The uncertainty of future economic development affects the term structure of discount rates and, thus, the intertemporal weights that are to be used in cost benefit analysis. The U.K. and France have recently adopted a falling term structure to incorporate uncertainty and the U.S. is considering a similar step. A series of publications discusses the following concern: A seemingly analogous argument used to justify falling discount rates can also justify increasing discount rates. We show that increasing and decreasing discount rates mean different things, can coexist, are created by different channels through which risk affects evaluation, and have the same qualitative effect of making long-term payoffs more attractive.

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.

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 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 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.