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The Stern model

The British economist Nicholas Stern was asked by the British Treasurer to do a “review” of the impact of climate change on the economy and what can be done to mitigate the problem in economic terms. Stern produced a report that amounted to “a call to action.”[1] It argued that, by incurring modest costs today (in the order of one to two percent of the gross world product), it is possible to reduce future high cost if no action is taken at all (in the order of ten to twenty percent of the world gross product). After reviewing the evidence, the Stern Report concluded that, given the 2005 rate of emissions, it is impossible to stabilize carbon emissions at a level any lower than 450 ppm. On the other hand, any level of carbon emissions above 550 ppm will be catastrophic.

The basis for calculating the impact of climate change in the Stern Report is the PAGE2002 model.[2] The model itself is not all that different from the DICE/ RICE models used by Nordhaus. However, the difference in the outcomes and the consequent recommendations arise from the way the future is “discounted” in the

The impact of discounting

Figure 6.3 The impact of discounting

Stern Report. Let us consider the simple question of how discounting the future matters with a graphical illustration.

Suppose we start with USD 100 in different decades starting with 2010. How much would USD 100 in 2030 be worth in 2010? The answer depends critically on the discount rate used to bring that USD 100 in 2030 to 2010. Figure 6.3 illustrates this point. If we do not discount the future at all (that is, if our discount rate is 0 percent), then (and only then) USD 100 in 2100 has the same value in 2010. However, with a discount rate of 1.5 percent per year, the present value in 2010 of USD 100 at future dates keeps falling. For example, USD 100 in 2060 is worth less than USD 48 in 2010 at that discount rate of 1.5 percent. At a discount rate of 10 percent per year, the value of USD 100 in 2020 is less than USD 39 in 2010. With discount rates of 10 and 5 percent, the value of USD 100 in 2090 is virtually zero in 2010. Even with a low discount rate of 1.5 percent per year, in 80 years, almost 70 percent of the value is lost. This exponential decay is a characteristic of compounding.

The discount rate for consumption, p, can be expressed by the simple formula, p = 8 + grj, where 8 is the social rate of time preference, g is the projected growth rate of average consumption, and ^ is the elasticity of the “social weight” attributed to a change in consumption. The parameter ^ is there to account for the following: as consumption grows, the marginal unit of consumption may be considered as having less social value. It is similar to diminishing marginal private utility of private consumption. The appropriate value to assign to ^ is not without controversy, but a value in the range of 2 or 3 seems reasonable. The Stern Report puts the value of ^ at 1,[3] but this level does not seem compatible with other evidence.

There is a big disagreement surrounding the appropriate value for 8, the social rate of time preference. This parameter allows for discounting the future simply because it is the future, even if future generations were no better off than we are. Therefore, the Stern Report adopts a value of zero for 8—the social rate of time preference. The reason is that Stern did not want to treat the welfare of future generations with any less weight than the current generation. This approach has been underpinned by theoretical argument in terms of generational equity questions.[4] It is also consistent with the principle of sustainable development. Thus, in the Stern Report, the value of p ends up being small, making discounting of future values low relative to the Nordhaus model. Therefore, it is not surprising that the Stern Report advocates strong action now.

  • [1] Kenneth Arrow, “Global Climate Change: A Challenge to Policy” Economists’ Voice, June 2007.
  • [2] PAGE2002 is a Microsoft Excel-based model to be used with the risk management programcalled @RISK as an add-in. The model calculates the impact at regional and global level of climatechange. It also has a component to calculate social costs of different greenhouse gases. It calculates thecosts of abatement and adaptation. It belongs to the class of Integrated Assessment Models.
  • [3] Nicholas Stern, The Economics of Climate Change (Cambridge University Press, Cambridge 2007).
  • [4] John Quiggin, “Equity between Overlapping Generations” (2012) 14 Journal of Public Economic Theory 273.
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