On the social cost of carbon and discounting in the DICE model

i

This article has been updated. A Correction to this article was published on .

i

The Original Article was published on

i

The Original Article was published on

i

This article has been updated

i

This article was retracted on

i

This article has been updated

Abstract

The social cost of carbon (SCC) has emerged as one of the relevant measures in integrated assessment models in climate economics, to quantify costs related to global warming and climate change. While the SCC is used in different models, including DICE (Dynamic Integrated model of Climate and Economy), PAGE (Policy Analysis of the Greenhouse Effect), and FUND (Climate Framework for Uncertainty, Negotiation, and Distribution), its exact definition and computation depend on the reference and, frequently lacking consistency within research streams whether focusing on a single model or on different models. In this study, we investigated three different methods for the computation of the SCC using the integrated assessment model DICE. While the first two methods are commonly known and used, the novel formula derived for the third method allows a direct analysis of the impact of the discount factor in the calculation of the SCC. We provide a detailed proof for the correctness of the third method and validate the consistency of all three methods by numerical experiments.

Keywords

economics of climate change / DICE / optimal control / social cost of carbon / sensitivity analysis

CHANGE HISTORY

A Correction to this paper has been published:
https://doi.org

The Retraction Note was updated to reflect reception of statements of disagreement from all authors.

This article has been retracted.Please see the Retraction Notice for more detail:
https://doi.org

References

[1] Archer D, Eby M, Brovkin V, et al. (2020) Atmospheric lifetime of fossil fuel carbon dioxide. Annu Rev Earth Planet Sci 37: 117-134. https://doi.org/10.1146/annurev.earth.031208.100206

[2] Eby M, Zickfeld K, Montenegro A, et al. (2009) Lifetime of anthropogenic climate change: Millennial time scales of potential CO₂ and surface temperature perturbations. J Clim 22: 2501-2511. https://doi.org/10.1175/2008JCLI2554.1

[3] Marten A L, Kopits E A, Griffiths C W, et al. (2015) Incremental CH₄ and N₂O mitigation benefits consistent with the US Government’s SC-CO₂ estimates. Clim Policy 15: 272-298. https://doi.org/10.1080/14693062.2014.912981

[4] Nordhaus W (2014) Estimates of the social cost of carbon: Concepts and results from the DICE-2013R model and alternative approaches. J Assoc Environ Resour Econ 1: 273-312. https://doi.org/10.1086/676035

[5] Hope C, Newbery D (2008) Calculating the social cost of carbon. In M. Grubb, T. Jamasb, and M. G. Pollitt, editors, Delivering a Low Carbon Electricity System: Technologies, Economics and Policy, chapter 2, 31-63. Cambridge University Press, Cambridge, 2008.

[6] Anthoff D, Tol R S J, Yohe G W (2009) Discounting for climate change. Economics: the Open-Access, Open-Assessment e-Journal, 3: 1-24. https://doi.org/10.5018/economics-ejournal.ja.2009-24

[7] D. Nordhaus W, Sztorc P (2013) DICE 2013R: Introduction and User’s Manual , second edition, 31 October 2013.

[8] Ramsey FP (1928) A mathematical theory of saving. Econ J 38: 543-559. https://doi.org/10.2307/2224098

[9] Anthoff D, Tol RSJ (2013) The uncertainty about the social cost of carbon: A decomposition analysis using FUND. Clim Change 117: 515-530. https://doi.org/10.1007/s10584-013-0706-7

[10] Anthoff D, Tol RSJ, Yohe GW (2009) Risk aversion, time preference, and the social cost of carbon. Environ Res Lett 4: 1-7. https://doi.org/10.1088/1748-9326/4/2/024002

[11] Hope C (2013) Critical issues for the calculation of the social cost of CO₂: why the estimates from PAGE09 are higher than those from PAGE2002. Clim Change 117: 531-543. https://doi.org/10.1007/s10584-012-0633-z

[12] Kögel T (2012) The rate of change of the social cost of carbon and the social planner’s Hotelling rule. Economics: the Open-Access, Open-Assessment e-Journal 1-26. 2012-37.

[13] A. L. Marten . (2011) Transient temperature response modeling in IAMs: The effects of over simplification on the SCC. Economics: the Open-Access, Open-Assessment e-Journal 1-44. https://doi.org/10.5018/economics-ejournal.ja.2011-18

[14] Marten A L, Newbold S C (2012) Estimating the social cost of non-CO₂ GHG emissions: Methane and nitrous oxide. Energy Policy 51: 957-972. https://doi.org/10.1016/j.enpol.2012.09.073

[15] Tol RSJ (2009) An analysis of mitigation as a response to climate change. Technical report, Copenhagen Consensus Center, 2009.

[16] Moyer E J, Woolley M D, Matteson N J, et al. (2014) Climate impacts on economic growth as drivers of uncertainty in the social cost of carbon. J Leg Stud 43: 401-425. https://doi.org/10.1086/678140

[17] Tol RSJ (2014) Climate Economics: Economic Analysis of Climate, Climate Change, and Climate Policy . Edward Elgar, 2014.

[18] Economides G, Papandreou A, Sartzetakis E, et al. (2018) The Economics of Climate Change . Bank of Greece, 2018.

[19] Newbold S C, Griffiths C, Moore C, et al. (2013) A rapid assessment model for understanding the social cost of carbon. Clim Change Econ 4: 1-40. https://doi.org/10.1142/S2010007813500012

[20] Ploeg F (2020) Discounting and climate policy, 2020. CESifo Working Paper no. 8441, Available at SSRN: https://ssrn.com/abstract=3657977.

[21] Arrow K, Cropper M, Gollier C, et al. (2013) Determining benefits and costs for future generations. Science 341: 349-350. https://doi.org/10.1126/science.1235665

[22] Groom B, Hepburn C, Koundouri P, et al. (2005) Declining discount rates: The long and the short of it. Environ Resour Econ 32: 445-493. https://doi.org/10.1007/s10640-005-4681-y

[23] Farber DA (2015) Gambling over growth: Economic uncertainty, discounting, and regulatory policy. J Leg Stud 44: S509-S528. https://doi.org/10.1086/676690

[24] Kellett C M, Weller S R, Faulwasser T, et al. (2019) Feedback and optimal control in climate economics. Annu Rev Control 47: 7-20. https://doi.org/10.1016/j.arcontrol.2019.04.003

[25] Hassell MP (1975) Density-dependence in single-species populations. Journal of Animal Ecology 44: 283-295. https://doi.org/10.2307/3863

[26] Wächter A, Biegler LT (2006) On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Mathematical programming 106: 25-57. https://doi.org/10.1007/s10107-004-0559-y

[27] Drud AS (1994) CONOPT-a large-scale GRG code. ORSA Journal on computing 6: 207-216.

[28] Bertsekas DP (1999) Nonlinear Programming . Athena Scientific, 1999. https://doi.org/10.1287/ijoc.6.2.207

[29] Grass D, Caulkins J P, Feichtinger G, et al. (2008) Optimal Control of Nonlinear Processes: With Applications in Drugs, Corruption, and Terror . Springer, 2008. https://doi.org/10.1007/978-3-540-77647-5

[30] Seierstad A, Sydsaeter K (1986) Optimal Control Theory with Economic Applications . Elsevier North-Holland, 1986.

[31] Campbell J Y, Viceira L M (2002) Strategic Asset Allocation: Portfolio Choice for Long-Term Investors . Oxford University Press, 2002. https://doi.org/10.1093/0198296940.001.0001

[32] Faulwasser T, Kellett C M, Weller S R (2018) MPC-DICE: An open-source Matlab implementation of receding horizon solutions to DICE. In Proc. 1st IFAC Workshop on Integrated Assessment Modeling for Environmental Systems, Brescia, Italy, May 2018.

[33] Fiacco AV (1983) Introduction to Sensitivity and Stability Analysis in Nonlinear Programming . Academic Press, 1983.