The economics of discounting climate change

April 26, 2022

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Environmental economics is a study at the intersection of both ecological and economic processes. After all, one of the reasons the earth is warming is because of the continuing growth of our economy and our reliance on fossil fuels. Although numerous efforts have been made so far to switch to sustainable sources, mankind has to make decisions regarding the usage of exhaustible resources over time. This brings with it several interesting questions. For instance, should we use more fossil fuels now in order to invest capital in breaching for the consequences of climate change? Should we rely on usage of capital to invest in greener alternatives to slow down global warming? Or, more succinctly formulated, how should optimal consumption of resources vary over generations?

As discussed in my previous article on Frank Ramsey (which you can find here), when analyzing the Ramsey growth model we find the following optimal rule:

(1)   \begin{equation*}    r = \delta + \eta g. \end{equation*}

Here, r is the rate at which you can borrow. Second, \delta is the pure rate of time preference, which measures the trade-offs in utility for present and future generations. When \delta=0, each generation is of equal importance, whereas when delta approaches one, future generations are not as valuable to the social planner as they are discounted heavily. Third, \eta is the elasticity of marginal utility w.r.t. consumption, which is defined as \eta = -\frac{U''(C(t))}{U'(C(t))}C(t). When \eta=1, marginal utility will follow a proportional decrease as consumption goes up. When \eta=0, there is no need for redistribution at all. In that case, it does not matter who consumes, as long as total consumption goes up. When we have a high \eta, there should be a lot of redistribution to those who have a low level of consumption. Finally, g is the growth rate of consumption. Now that we’ve introduced the Ramsey Rule and the parameters associated with this, we will turn to the economic aspect of climate change.

The biggest externality society faces

According to British Economist Nicholas Stern, climate change distinguishes itself from other externalities present in economic theory in a number of ways. First, uncertainty (regarding among others magnitude, impact and timing of effects of global warming) and risk in the outcomes are highly important. Second, spillovers and consequences are definitely not limited to specific regions (e.g. an unit of carbon dioxide emitted in The Netherlands has the same impact as one emitted in the USA, as the greenhouse gasses taken up into the atmosphere). In general, rich countries will be the largest polluters, whereas poor countries will be more vulnerable to consequences of climate disasters such as extreme drought. Third, there are most likely irreversible processes at play (think of melting icecaps). On top of that, one interesting feature of the economics of climate change is the timing of costs and benefits in mitigating climate change, which is highly non-linear. Greenhouse gasses that are emitted into the atmosphere right now will stay there for a long time. For instance, methane (CH_4) will stay in the atmosphere for around 12 years. Determining how long carbon dioxide will remain in the atmosphere is a bit more difficult. Around 65\% to 80\% of carbon dioxide emitted dissolves into the ocean over a period of 20 to 200 years, whereas the other part dissolves by a much lengthier process that spreads over hundreds of thousands of years. However, reducing emissions right now has high costs. More importantly, the benefits of costly reductions right now will be visible only decades, if not centuries, later. Thus, the economic incentive to the emitter himself is non-negligible. The market itself can in this case not correct for this externality.

Because of the timing of costs and benefits, we are left with evaluating a stream of utilities, which turns out to be an inter-generational comparison. Thus, we have to make ethical decisions regarding the value we assign to future generations. Trying to take into account future generations introduces several uncertainties. For instance, can we assume future generations have more goods? Does this offset the fact that they will probably suffer more from carbon dioxide emitted now than current generations? Will future generations still exist? Will there be better technology available, such as carbon scrapers, which will make future generations less vulnerable to climate change? Which regions will suffer most from climate disaster, and is the timing of these disasters such that we can take appropriate measures?

Stern versus Nordhaus

It comes as no surprise that there is a lot of disagreement regarding the appropriate discount factor among economists. For instance, Yale economist William Nordhaus sets \delta=0.03 and \eta = 1, whereas Stern sets \delta=0.001 and \eta=1 which results in an advocated carbon tax which differs by a magnitude of 10. Proponents of a zero discount rate find it ethically indefensible to dismiss the well-being of future generations solely because of the fact that they do not exist yet. A problem with this would be that current generations have to suffer a lot for future generations, more specifically generations that they will actually never meet. Since capital is productive, saving up right now and thus consuming relatively little would take into account future damages from climate change. Is this justified?

There are economists who are in favor of setting a positive discount rate. For instance, there is Nordhaus, who in his famous DICE models sets a discount factor of around 2-3\%. A back of the envelope calculation shows that this implies that welfare of people living 35 years from now only have half the weight of current humans in the calculation of the social planner. Note that setting a high delta shifts the burden to future generations, that is, abatement will be delayed as the future benefits are weakly weighted.

The ethics behind setting the appropriate discount factor

In his review of the Stern review, William Nordhaus further tries to dismantle the ethics behind the decision of Stern to set a near-zero discount rate. He proposes numerous alternatives. First, we should act according to a simple rule-of-thumb. Generations should leave behind at least as many resources, environmental quality and capital as they started with. The reasoning behind this is that it will ensure that each generation is at least as well off as its previous one. With this in mind, each generation will choose a consumption profile such that they will leave the planet in good hands for the next generation. Over consumption for that matter is not possible as it would violate the rule of thumb. Second, we could follow John Rawls, who argued that we should act as if we are behind a Veil of Ignorance. The argument all together discards the idea of discount rates as Rawls argues that mankind should act as if he would not know his own position (i.e. he does not know to which generation he will belong and where he is located on the globe). This implies that the optimal path the social planner lays out has to be consistent with the decision he would make when he would be behind the Veil of Ignorance. This implies that current consumption, in order to match anticipated increases in technological progress and future well-being, should increase sharply. One objection to this can be that increasing consumption heavily right now, especially with the ecological (irreversible) processes at play, might as well trigger something we definitely do not want to trigger if our predictions are wrong. The uncertainty involved in the future development of both climate and economics makes this a highly infeasible strategy.

I hope this article gave you insight into the philosophical and economic discussions at play with the issue of climate change. If you are interested, you can find more information in the sources below.

Sources

Archer, D., Eby, M., Brovkin, V., Ridgwell, A., Cao, L., Mikolajewicz, U., . . . others (2009). Atmospheric lifetime of fossil fuel carbon dioxide. Annual review of earth and planetary sciences, 37 , 117–134.

Dasgupta, P. (2008). Discounting climate change. Journal of Risk and Uncertainty, 37 (2), 141-169.

Mintz-Woo, K. (2021). A philosopher’s guide to discounting. In M. B. Budolfson,

T. McPherson, & D. Plunkett (Eds.), Philosophy and climate change (pp. 90–110). Oxford University Press.

Nordhaus, W. D. (2007). A review of the “stern review on the economics of climate change”. Journal of Economic Literature, 45 (3), 686–702.

Ramsey, F. P. (1928). A mathematical theory of saving. The economic journal , 38 (152), 543–559.

Rawls, J. (1971). A theory of justice (1st ed.). Cambridge, Massachussets: Belknap Press of Harvard University Press.

Stern, N. (2007). The economics of climate change: the stern review. Cambridge University Press.

van der Ploeg, F., & de Zeeuw, A. (2016). Non-cooperative and cooperative responses to climate catastrophes in the global economy: A north-south perspective. Environmental and Resource Economics, 65 (3), 519–540.

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