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Open Access Publications from the University of California

Scholarly Works (13 results)

  • Article
CUDARE Working Papers (2013)
We introduce a version of the DICE-2007 model designed for uncertaintyanalysis. DICE is a wide-spread deterministic integrated assessment model of climatechange. Climate change, long-term economic development, and their interactionsare highly uncertain. The quantitative analysis of optimal mitigation policy underuncertainty 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 combination of(exponentially) increasing processor time, lower quality of the value or policy functionapproximations, and reductions of the uncertainty domain. The paper promotes astate reduced, recursive dynamic programming implementation of the DICE-2007model. We achieve the reduction by simplifying the carbon cycle and the temperaturedelay equations. We compare our model’s performance and that of the DICE model tothe scientific AOGCM models emulated by MAGICC 6.0 and find that our simplifiedmodel performs equally well as the original DICE model. Our implementation solvesthe infinite planning horizon problem in an arbitrary time step. The paper is thefirst to carefully analyze the quality of the value function approximation using twodifferent types of basis functions and systematically varying the dimension of thebasis. We present the closed form, continuous time approximation to the exogenous(discretely and inductively defined) processes in DICE, and we present a numericallymore efficient re-normalized Bellman equation that, in addition, can disentangle riskattitude from the propensity to smooth consumption over time.
    Cover page: A 4-stated DICE: quantitatively addressing uncertainty effects in climate change
    • Article
    CUDARE Working Papers (2012)
    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.
      Cover page: A 4-stated DICE: quantitatively addressing uncertainty effects in climate change
      • Article
      CUDARE Working Papers (2013)
      Global warming, alterations of ecosystems, and sunk investmentsall imply irreversible changes with uncertain future costs and benefits. Twoconcepts measure how this combination of uncertainty and irreversibilitychanges the value of preserving an ecosystem or postponing an investment.First, the environmental and resource economics literature developed theArrow-Fisher-Hanemann-Henry quasi-option value. Second, the real optionsliterature developed the Dixit-Pindyck option value. This paper clarifiesthe precise differences between the two approaches in a simple two periodmodel. We explain that the quasi-option value captures the value of learningconditional on preservation, while the Dixit-Pindyck option value capturesthe net value of preservation under learning. We show how either of the twoconcepts alters the common net present value decision rule. We illustratesimilarities, differences, and the decision rules in two instructive examples.
        Cover page: What's the Option?
        • Article
        CUDARE Working Papers (2011)

        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.

          Cover page: Interemporal Risk Aversion - or - Wouldn't it be Nice to Tell Whether Robinson Crusoe is Risk
          • Article
          CUDARE Working Papers (2011)

          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.

            Cover page: Discounting and confidence
            • Article
            CUDARE Working Papers (2011)

            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.

              Cover page: Subjective Risk, Confidence, and Ambiguity
              • Article
              CUDARE Working Papers (2012)
              Uncertainty has an almost negligible impact on project value in the standardeconomic model. I show that a comprehensive evaluation of uncertainty and uncertainty attitude changes this picture fundamentally. The illustration of this result relies on the discount rate, which is the crucial determinant in balancing immediate costs againstfuture benefits, and the single most important determinant of optimal mitigation policies in the integrated assessment of climate change. First, the paper removes an implicit assumption of (intertemporal or intrinsic) risk neutrality from the standard economic model. Second, the paper introduces aversion to non-risk uncertainty (ambiguity). Ishow a close formal similarity between the model of intertemporal risk aversion, which is a reformulation of the widespread Epstein-Zin-Weil model, and a recent model of smooth ambiguity aversion. I merge the models, achieving a threefold disentanglement between, risk aversion, ambiguity aversion, and the propensity to smooth consumptionover time.
                Cover page: Why uncertainty matters - discounting under intertemporal risk aversion and ambiguity
                • Article
                CUDARE Working Papers (2008)

                The paper explores the consequences of limited substitutability in welfare between environmental and produced goods for long-term evaluation. I show how the magnitude and time development of optimal social discount rates depend on the substitutability between the different classes of goods. The notions of weak and strong sustainability are translated into the degree of substitutability. I show that a strong notion of sustainability results in lower weights given to long-run service and consumption streams compared to a weak notion of sustainability.

                  Cover page: Sustainability, Limited Substitutability and Non-Constant Social Discount Rates
                  • Article
                  CUDARE Working Papers (2012)
                  The uncertainty of future economic development affects the term structure of discount rates and, thus, the intertemporal weights that are tobe used in cost benefit analysis. The U.K. and France have recently adopteda falling term structure to incorporate uncertainty and the U.S. is consideringa similar step. A series of publications discusses the following concern: Aseemingly analogous argument used to justify falling discount rates can alsobe used to justify increasing discount rates. We show that increasing anddecreasing discount rates mean different things, can coexist, are created bydifferent channels through which risk affects evaluation, and have the samequalitative effect of making long-term payoffs more attractive.
                    Cover page: What's the rate? Disentangling the Weitzman and the Gollier effect
                    • Article
                    CUDARE Working Papers (2011)
                    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.
                      Cover page: Risk and aversion in the integrated assessment of climate change
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