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

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  • Christian Traeger

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Abstract

We introduce a version of the DICE-2007 model designed for uncertainty analysis. DICE is a wide-spread deterministic integrated assessment model of climate change. Climate change, long-term economic development, and their interactions are highly uncertain. The quantitative analysis of optimal mitigation policy under uncertainty requires a recursive dynamic programming implementation of integrated assessment 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 function approximations, and reductions of the uncertainty domain. The paper promotes a state-reduced, recursive dynamic programming implementation of the DICE-2007 model. We achieve the reduction by simplifying the carbon cycle and the temperature delay equations. We compare our model’s performance and that of the DICE model to the scientific AOGCM models emulated by MAGICC 6.0 and find that our simplified model performs equally well as the original DICE model. Our implementation solves the infinite planning horizon problem in an arbitrary time step. The paper is the first to carefully analyze the quality of the value function approximation using two different types of basis functions and systematically varying the dimension of the basis. We present the closed form, continuous time approximation to the exogenous (discretely and inductively defined) processes in DICE, and we present a numerically more efficient re-normalized Bellman equation that, in addition, can disentangle risk attitude from the propensity to smooth consumption over time. Copyright Springer Science+Business Media Dordrecht 2014

Suggested Citation

  • Christian Traeger, 2014. "A 4-Stated DICE: Quantitatively Addressing Uncertainty Effects in Climate Change," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 59(1), pages 1-37, September.
  • Handle: RePEc:kap:enreec:v:59:y:2014:i:1:p:1-37
    DOI: 10.1007/s10640-014-9776-x
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    1. Lemoine, Derek M. & Traeger, Christian P., 2010. "Tipping Points and Ambiguity in the Economics of Climate Change," CUDARE Working Papers 98127, University of California, Berkeley, Department of Agricultural and Resource Economics.
    2. Christian Traeger, 2014. "Why uncertainty matters: discounting under intertemporal risk aversion and ambiguity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(3), pages 627-664, August.
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    8. Derek Lemoine & Christian Traeger, 2014. "Watch Your Step: Optimal Policy in a Tipping Climate," American Economic Journal: Economic Policy, American Economic Association, vol. 6(1), pages 137-166, February.
    9. Kelly, David L & Kolstad, Charles D, 2001. "Solving Infinite Horizon Growth Models with an Environmental Sector," Computational Economics, Springer;Society for Computational Economics, vol. 18(2), pages 217-231, October.
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    16. Crost, Benjamin & Traeger, Christian P., 2013. "Optimal climate policy: Uncertainty versus Monte Carlo," Economics Letters, Elsevier, vol. 120(3), pages 552-558.
    17. Christian Traeger, 2014. "Why uncertainty matters: discounting under intertemporal risk aversion and ambiguity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(3), pages 627-664, August.
    18. Kelly, David L. & Kolstad, Charles D., 1999. "Bayesian learning, growth, and pollution," Journal of Economic Dynamics and Control, Elsevier, vol. 23(4), pages 491-518, February.
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    20. Leach, Andrew J., 2007. "The climate change learning curve," Journal of Economic Dynamics and Control, Elsevier, vol. 31(5), pages 1728-1752, May.
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    22. Traeger, Christian P., 2010. "Intertemporal risk aversion – or – wouldn’t it be nice to tell whether Robinson Crusoe is risk averse?," CUDARE Working Paper Series 1102, University of California at Berkeley, Department of Agricultural and Resource Economics and Policy.
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    Cited by:

    1. In Chang Hwang & Richard S.J. Tol & Marjan W. Hofkes, 2013. "Active Learning about Climate Change," Working Paper Series 6513, Department of Economics, University of Sussex.
    2. repec:eee:appene:v:205:y:2017:i:c:p:428-439 is not listed on IDEAS
    3. Ian Bateman & Hassan Benchekroun & Christian Vossler, 2015. "EAERE Award for the Best Paper Published in Environmental and Resource Economics During 2014," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 62(1), pages 1-2, September.
    4. Lemoine, Derek & Traeger, Christian P., 2016. "Ambiguous tipping points," Journal of Economic Behavior & Organization, Elsevier, vol. 132(PB), pages 5-18.
    5. repec:eee:resene:v:48:y:2017:i:c:p:1-18 is not listed on IDEAS
    6. Jensen, Svenn & Traeger, Christian P., 2014. "Optimal climate change mitigation under long-term growth uncertainty: Stochastic integrated assessment and analytic findings," European Economic Review, Elsevier, vol. 69(C), pages 104-125.
    7. Drupp, Moritz A. & Hänsel, Martin C., 2018. "Relative prices and climate policy: How the scarcity of non-market goods drives policy evaluation," Economics Working Papers 2018-01, Christian-Albrechts-University of Kiel, Department of Economics.
    8. Armon Rezai & Frederick Van der Ploeg, 2016. "Intergenerational Inequality Aversion, Growth, and the Role of Damages: Occam's Rule for the Global Carbon Tax," Journal of the Association of Environmental and Resource Economists, University of Chicago Press, vol. 3(2), pages 493-522.
    9. Baker, Erin & Olaleye, Olaitan & Aleluia Reis, Lara, 2015. "Decision frameworks and the investment in R&D," Energy Policy, Elsevier, vol. 80(C), pages 275-285.
    10. Delavane B. Diaz, 2015. "Integrated Assessment of Climate Catastrophes with Endogenous Uncertainty: Does the Risk of Ice Sheet Collapse Justify Precautionary Mitigation?," Working Papers 2015.64, Fondazione Eni Enrico Mattei.
    11. repec:wsi:ccexxx:v:08:y:2017:i:02:n:s2010007817500063 is not listed on IDEAS
    12. Tamaki, Tetsuya & Nozawa, Wataru & Managi, Shunsuke, 2017. "Evaluation of the ocean ecosystem: climate change modelling with backstop technology," MPRA Paper 80549, University Library of Munich, Germany.
    13. David García-León, 2016. "Adapting to Climate Change: an Analysis under Uncertainty," Working Papers 2016.10, Fondazione Eni Enrico Mattei.
    14. Howard, Peter H. & Derek, Sylvan, 2016. "The Wisdom of the Economic Crowd: Calibrating Integrated Assessment Models Using Consensus," 2016 Annual Meeting, July 31-August 2, Boston, Massachusetts 235639, Agricultural and Applied Economics Association.
    15. Erin Baker & Olaitan Olaleye & Lara Aleluia Reis, 2015. "Decision Frameworks and the Investment in R&D," Working Papers 2015.42, Fondazione Eni Enrico Mattei.
    16. Rick Van der Ploeg & Armon Rezai, 2015. "Intergenerational Inequality Aversion, Growth and the Role of Damages: Occam's rule for the global tax," Economics Series Working Papers OxCarre Research Paper 15, University of Oxford, Department of Economics.
    17. KEVIN DAYARATNA & ROSS McKITRICK & DAVID KREUTZER, 2017. "Empirically Constrained Climate Sensitivity And The Social Cost Of Carbon," Climate Change Economics (CCE), World Scientific Publishing Co. Pte. Ltd., vol. 8(02), pages 1-12, May.
    18. repec:wsi:ccexxx:v:08:y:2017:i:02:n:s2010007817500075 is not listed on IDEAS
    19. J. Farmer & Cameron Hepburn & Penny Mealy & Alexander Teytelboym, 2015. "A Third Wave in the Economics of Climate Change," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 62(2), pages 329-357, October.

    More about this item

    Keywords

    Climate change; Uncertainty; Integrated assessment ; DICE; Dynamic programming; Risk aversion; Intertemporal substitution; MAGICC; Basis; Recursive utility; Q54; Q00; D90; C63;

    JEL classification:

    • Q54 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Climate; Natural Disasters and their Management; Global Warming
    • Q00 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - General - - - General
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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