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A 4-stated DICE: quantitatively addressing uncertainty effects in climate change

  • Traeger, Christian

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.

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Paper provided by Department of Agricultural & Resource Economics, UC Berkeley in its series Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series with number qt9034k05t.

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Date of creation: 01 Dec 2013
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Handle: RePEc:cdl:agrebk:qt9034k05t
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  1. Garth Heutel, 2012. "How Should Environmental Policy Respond to Business Cycles? Optimal Policy under Persistent Productivity Shocks," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 15(2), pages 244-264, April.
  2. Christian Traeger, 2012. "Why Uncertainty Matters - Discounting under Intertemporal Risk Aversion and Ambiguity," CESifo Working Paper Series 3727, CESifo Group Munich.
  3. Fischer, Carolyn & Springborn, Michael R., 2011. "Emissions Targets and the Real Business Cycle: Intensity Targets versus Caps or Taxes," Discussion Papers dp-09-47-rev, Resources For the Future.
  4. Christian P. Traeger, 2009. "Recent Developments in the Intertemporal Modeling of Uncertainty," Annual Review of Resource Economics, Annual Reviews, vol. 1(1), pages 261-285, 09.
  5. Crost, Benjamin & Traeger, Christian P., 2010. "Risk and aversion in the integrated assessment of climate change," CUDARE Working Paper Series 1104R, University of California at Berkeley, Department of Agricultural and Resource Economics and Policy, revised Jul 2011.
  6. Derek M. Lemoine & Christian P. Traeger, 2012. "Tipping Points and Ambiguity in the Economics of Climate Change," NBER Working Papers 18230, National Bureau of Economic Research, Inc.
  7. Leach, Andrew J., 2007. "The climate change learning curve," Journal of Economic Dynamics and Control, Elsevier, vol. 31(5), pages 1728-1752, May.
  8. John Y. Campbell, 1993. "Understanding Risk and Return," NBER Working Papers 4554, National Bureau of Economic Research, Inc.
  9. Epstein, Larry G & Zin, Stanley E, 1989. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: A Theoretical Framework," Econometrica, Econometric Society, vol. 57(4), pages 937-69, July.
  10. Hoel, Michael & Karp, Larry, 2000. "Taxes and Quotas for a Stock Pollutant with Multiplicative Uncertainty," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt9v86p5s7, Department of Agricultural & Resource Economics, UC Berkeley.
  11. 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.
  12. Keller, Klaus & Bolker, Benjamin M. & Bradford, D.F.David F., 2004. "Uncertain climate thresholds and optimal economic growth," Journal of Environmental Economics and Management, Elsevier, vol. 48(1), pages 723-741, July.
  13. Hoel, Michael & Karp, Larry, 2001. "Taxes versus Quotas for a Stock Pollutant," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt5fx9p7kf, Department of Agricultural & Resource Economics, UC Berkeley.
  14. Weil, Philippe, 1990. "Nonexpected Utility in Macroeconomics," The Quarterly Journal of Economics, MIT Press, vol. 105(1), pages 29-42, February.
  15. Karp, Larry & Zhang, Jiangfeng, 2006. "Regulation with anticipated learning about environmental damages," Journal of Environmental Economics and Management, Elsevier, vol. 51(3), pages 259-279, May.
  16. Crost, Benjamin & Traeger, Christian P., 2013. "Optimal climate policy: Uncertainty versus Monte Carlo," Economics Letters, Elsevier, vol. 120(3), pages 552-558.
  17. Emi Nakamura & Jón Steinsson & Robert Barro & José Ursúa, 2010. "Crises and Recoveries in an Empirical Model of Consumption Disasters," NBER Working Papers 15920, National Bureau of Economic Research, Inc.
  18. Kelly, David L., 2005. "Price and quantity regulation in general equilibrium," Journal of Economic Theory, Elsevier, vol. 125(1), pages 36-60, November.
  19. 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.
  20. Kelly, David L & Kolstad, Charles D, 2001. "Solving Infinite Horizon Growth Models with an Environmental Sector," Computational Economics, Society for Computational Economics, vol. 18(2), pages 217-31, October.
  21. 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 137-66, February.
  22. Yongyang Cai & Kenneth L. Judd & Thomas S. Lontzek, 2012. "Continuous-Time Methods for Integrated Assessment Models," NBER Working Papers 18365, National Bureau of Economic Research, Inc.
  23. Ravi Bansal & Amir Yaron, 2000. "Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles," NBER Working Papers 8059, National Bureau of Economic Research, Inc.
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