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The Nordhaus model

William Nordhaus has been at the forefront of modeling the economic impact of CO2 emissions. In 1979, he devoted an entire chapter to this topic in his Cowles Commission Monograph.[1] In a chapter entitled, “Strategies for the Control of Carbon Dioxide,” he expounded a method that would model the economic impact of different levels of CO2 production. He also calculated the (shadow) price of carbon for controlling CO2 emissions at different levels. However, his model was not yet a fully fledged economic growth model, which he later developed.

Nordhaus developed the Dynamic Integrated Climate Economy (DICE) model, which takes into account CO2 in a full general equilibrium economic model (see Appendix to this chapter for a full description of the model). In the usual economic model, the economic agent solves an intertemporal problem of maximizing a utility function u that depends on her consumption every year of her life subject to certain lifetime constraints such as income during her working life. Formally, the utility function depends on consumption c at every period: u(ct) where t is a time period index. However, future utility is discounted at some rate (p). Nordhaus introduced an additional environmental factor T (i.e. temperature) so that the utility function at every period depends on two components: c and T. Thus, the utility function at any time t is written as u(ct, T). While higher consumption gives higher utility, a higher value of T reduces the utility.[2] In addition, there is a production function for the economy. This function, in the usual economics literature, depends on labor and capital only.[3] Formally, the output Y in the economy depends on two factors: capital K and labor L (Y = F(K, L)). The output increases when either capital or labor increases. The capital comes from savings that are not consumed in any period. In its simplest form: K = Y — C. This process links the utility to the production function in the model. In the Nordhaus model, the output Y = F(K, L, T). The output now depends on an additional environmental factor T. Moreover, any increase in T leads to a decrease in output. The DICE model has been used in many studies since Nordhaus introduced it. Nordhaus himself introduced more detailed and disaggregated versions of it.[4]

In the latest version of the model, called the Regional Integrated model of Climate and the Economy (RICE) model,[5] Nordhaus considers four different scenarios:

  • (1) Baseline: No climate-change policies.
  • (2) Optimal: Climate-change policies maximize economic welfare with full participation starting in 2010 and no climatic constraints.
  • (3) Limit temperature to 2°C: The optimal policies are taken subject to a further constraint that global temperature would not increase more than 2° C above the 1900 average.
  • (4) Copenhagen Accord: High-income countries implement deep emissions reductions (similar to those included in the current US proposals), with developing countries following in the next two to five decades.
  • (5) Copenhagen Accord with only rich countries: This policy assumes that high income countries implement deep reductions as in case (4), but developing countries do not participate (as in the current Kyoto Protocol).

Nordhaus concludes as follows:

Using a discount rate of 5 percent, the optimal program raises the present value of world income by USD 8.05 trillion, or 0.35 percent of discounted income. This is the equivalent to an annuity of USD 402 billion per year at a 5 percent discount rate. Imposing the 2°C temperature constraint is quite costly, reducing the net benefit by almost half, because of the difficulty of attaining the 2° C target. The Copenhagen Accord with phased in participation of developing countries has substantial net benefits, but lack of participation reduces these substantially.

He goes on to suggest that charging a carbon price to USD 100 per ton upfront, as suggested by some,[6] is counterproductive. It should be raised gradually over the decades:

The estimated 2°C-limiting carbon price for 2010 is estimated to be USD 64 per ton carbon (2005 prices), whereas the effective globally average carbon price today is around USD 5 per ton.

Nordhaus shows net costs and benefits to different countries and regions for complying with the Copenhagen Accord (2009). He demonstrates that large developing countries like India and China will benefit from it but there will be a net cost to the developed world.[7] That does not mean all developed countries will incur a net cost. Canada, for example, could expand landmass under agricultural production due to warmer months. The effect could be a net gain from climate change.[8]

  • [1] William Nordhaus, The Efficient Use of Energy Resources (Cowles Foundation for Research inEconomics, Yale University Press, New Haven 1979).
  • [2] William Nordhaus, “An Optimal Transition Path for Controlling Greenhouse Gases” (1992)258 Science 1315.
  • [3] See e.g. Robert Solow, Growth Theory: An Exposition (Oxford University Press, Oxford 1988).
  • [4] William Nordhaus, A Question of Balance: Weighing the Options on Global Warming Policies (YaleUniversity Press, New Haven 2008).
  • [5] William Nordhaus, “Economic Aspects of Global Warming in a Post-Copenhagen Environment” (2010) 107(26) Proceedings of the National Academy of Sciences 11721 (accessed March 15, 2013).
  • [6] For example, in the documentary produced by Al Gore, An Inconvenient Truth (2006).
  • [7] Nordhaus, “Economic Aspects of Global Warming.”
  • [8] Afshin Amiraslany, The Impact of Climate Change on Canadian Agriculture: A RicardianApproach, PhD thesis, University of Saskatchewan, 2010.
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