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The paper discusses optimal carbon taxation in an analytic quantitative integrated assessment model (IAM). The model links IAM components and parametric assumptions directly to their policy impacts. The paper discusses the distinct tax impact of carbon versus temperature dynamics and uses the see-through model to illustrate various aspects of IAM calibrations including the differentiation between consumption and investments goods. Novel to analytic IAMs are the explicit temperature dynamics, a general economy, energy sectors including capital, various degrees of substitutability across energy sources, an approximation of capital persistence, and objective functions that include CES preferences and population weighting. ACE opens the door to tractable forward-looking stochastic modeling and dynamic strategic interactions in complex IAMs, explored in accompanying work.

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.

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.

Over the last few decades, integrated assessment models (IAM) have provided insight into the relationship between climate change, economy, and climate policies. The limitations of these models in capturing uncertainty in climate parameters, heterogeneity in damages and policies, have given rise to skepticism about the relevance of these models for policy making. IAM community needs to respond to these critics and to the new challenges posed by developments in the policy arena. New climate targets emerging from the Paris Agreement and the uncertainty about the signatories’ commitment to Nationally Determined Contributions (NDCs) are prime examples of challenges that need to be addressed in the next generation of IAMs. Given these challenges, calculating the social cost of carbon requires a new framework. This can be done by computing marginal abatement cost in cost-effective settings which provides different results than those calculated using constrained cost-benefit analysis. Here we focus on the areas where IAMs can be deployed to asses uncertainty and risk management, learning, and regional heterogeneity in climate change impacts.

Global warming, alterations of ecosystems, and sunk investments all imply irreversible changes with uncertain future costs and benefits. The Arrow–Fisher–Hanemann–Henry quasi-option value and the Dixit–Pindyck option value both measure how irreversibility and uncertainty change the value of preserving an ecosystem or postponing an investment. This paper shows the precise relation between the two option values and explains that the quasi-option value captures the value of learning conditional on preservation, whereas the Dixit–Pindyck option value captures the net value of preservation under learning. We show how either of the two concepts alters the common net present value decision rule. We illustrate similarities, differences, and the decision rules in two instructive examples.

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 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.

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 prevailing literature discusses intergenerational trade-offs in climate change predominantly in terms of the Ramsey equation relying on the infinitely lived agent model. We discuss these trade-offs in a continuous time OLG framework and relate our results to the infinitely lived agent setting. We identify three shortcomings of the latter: First, underlying normative assumptions about social preferences cannot be deduced unambiguously. Second, the distribution among generations living at the same time cannot be captured. Third, the optimal solution may not be implementable in overlapping generations market economies.