Christian P. Traeger

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

We introduce a version of the DICE-2007 model designed for uncertaintyanalysis. DICE is a wide-spread deterministic integrated assessment model of climatechange. However, climate change, long-term economic development, and theirinteractions are highly uncertain. A thorough empirical analysis of the effects ofuncertainty requires a recursive dynamic programming implementation of integratedassessment models. Such implementations are subject to the curse of dimensionality.Every increase in the dimension of the state space is paid for by a combinationof (exponentially) increasing processor time, lower quality of the value function andcontrol rules approximations, and reductions of the uncertainty domain. The paperpromotes a four stated recursive dynamic programming implementation of the DICEmodel. Our implementation solves the infinite planning horizon problem for an arbitrarytime step. Moreover, we present a closed form continuous time approximationto the exogenous (discretely and inductively defined) processes in DICE and presenta Bellman equation for DICE that disentangles risk attitude from the propensity tosmooth consumption over time.

Discounting Under Uncertainty: Disentangling the Weitzman and the Gollier Effect

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.

Subjective Risk, Confidence, and Ambiguity

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.

Analytic Integrated Assessment and Uncertainty

This paper is a revised version of: http://ssrn.com/abstract=2643293. A revised version of this paper can be found at: http://ssrn.com/abstract=3307622. 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 models 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 Social Discount Rate Under Intertemporal Risk Aversion and Ambiguity

The social discount rate crucially determines optimal mitigation policies. This paper examines two shortcomings of the recent debate and the models on 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.

Discounting and confidence

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.

Risk and Aversion in Assessing Climate Policy

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.