Discounting in the Economics of Climate Change

It was frequently argued that the discount rate is the most important single figure in the economics of climate change. Due to this figure we observe large differences in policy recommendation between different economists of climate change (most notably, the choice of the discount rate determines the difference in what William Nordhaus on the one hand, and Nicholas Stern, on the other, call for). There is no concrete recommendation in standard economics how to discount long run benefits and losses. But it is clear that, if you want to compare benefits from the future with costs today, you need a discount rate. So far agreement prevails. The problem is the definition (or: choice) of the “right” discount rate, which involves economic forecasts as well as ethical decisions. In the following I shall present an overview about the main arguments in the discussion.

First it is appropriated to give a short overview about what a discount rate is. There are many different discount rates. The one we are talking about here is the so called “social discount rate” (also called “consumption interest rate”). It is a parameter which we can use to compute the “present value” of a given amount of money from the future (be it positive – a benefit – or negative – a cost):

PV = X/(1+r)^t,

with PV being the present value of X, r is a discount rate and t is time. The reasons why we need the net present value are mainly: (1) impatience (people prefer to get something now instead of getting the same tomorrow) or, as it is sometimes interpreted, the possibility of extinction, and (2) equity concerns (see the following).

That the choice of the discount rate is important, can be seen in the modern economics of climate change: while one group of economists (the most prominent being William Nordhaus) recommends reservation (claiming that it wouldn’t pay to invest heavily in climate change mitigation now – we should wait until about the middle of the century), others (especially Nicholas Stern) recommend decisive action now. The main reason for this discrepancy is, indeed, discounting: while Nordhaus is working with social discount rates of about 4-5% per year, Stern used one of 1,4%. So the question is: who is right? Or, at least, who is nearer at the right figure? And is there such?

The social discount rate is defined as follows (according to the economist and mathematician Frank Ramsey, 1928; simplified):

ρ = δ + ηg,

ρ (rho) being the discount rate, δ (delta) the so called pure time preference (mathematical expression of (1) above), η (eta) the elasticity of marginal consumption ((2) above; the grade of our valuation of relative changes in consumption/well-being), and g the rate of growth in consumption/well-being (a forecast).

Nicholas Stern used this equation to explicitly “ethically” define his discount rate. He chose δ = 0,001, arguing that generally we should value the well-being of future generations equally as compared to ours (then delta would be 0), but since there is some probability that humanity will cease to exist every next year, he chose an ad hoc value of this probability being 0,1% p.a. Further, Stern set the elasticity of marginal consumption at 1 (I will comment on that later, since Nordhaus made exactly the same choice), and g (assumed to be well approximated by the forecast of world GDP growth) at 1,3% per year. Thus he arrived at a social discount rate of 1,4% – a rather small one, many would argue, implying a halving of the discounted sum every 50 years though (e.g., a benefit 50 years ahead of US$100 would have a net present value of about US$50).

Meanwhile, William Nordhaus chose a completely different approach. Arguing that in aggregate (and the social discount rate is an aggregate number) the social discount rate is reflected by the market rates of return to investment – a surprisingly common approach in economics -, he set η at 1, g at about 1,5% p.a., and derived from that an “empirical” value for the pure time preference of about 3% p.a. (consider: with an exemplary ρ = 4,7%, the sum discounted is halving every 15 years) There are many downsides of this approach, though. First, the assumption that the market rates of interest equal social discount rates holds only in perfect market economies – an artifact, since our economies are deeply imperfect and distorted (e.g., only a rather small part of the population is active at financial markets, where market rates of interest are determined; there are distortionary taxes; information asymmetries etc.). Second, if we decide to make this assumption, we have the problem of choosing a single interest rate, since there are many (and they differ substantially in magnitude). Third, market rates of return to investment can be used to value investments in the short up to the middle run. But most of the expected consequences of climate change will occur in the long run (100 years and more). Markets don’t deal with such time spans (meanwhile, there are empirical studies showing that people tend to discount the long run much lower, when they don’t “deal” with their own lives any more).

It was argued elsewhere (see here for an comprehensive discussion) that, while Stern may be right in setting the pure time preference at nearly 0 (which implies that we generally value the well-being of future generations equal to our own), the choice of the elasticity of marginal consumption made by both Stern and Nordhaus was wrong. Setting this parameter at 1 is equal to saying that the same absolute change in consumption/well-being of a person is always to be valued equally – without regard to the initial level of consumption/well-being of the person. For instance, it would imply that we are indifferent between giving US$100 to a person having an income of, say, 100,000, and a person having one of 1000. The higher η, the higher our concern for relative changes in well-being and thus, our concern for inequality. It was argued that a more proper value for η would be in the range of [2,4] (this is also what has been observed in empirical studies). In fact, Stern admitted that this critique is generally justified.

Another problem of common approaches to the economics of climate change is the assumption that, even in business as usual, consumption/well-being will be growing at a constant rate. This assumption has at least two downsides: first, it is a long run forecast. Assuming a constant rate is highly arbitrary, since there are many sources of uncertainty in this area (indeed, it was shown by Partha Dasgupta that when we take these uncertainties into account, the social discount rate will be lower). Second, it is often argued that GDP growth doesn’t at all reflect growth in well-being (see my discussion here), and there are numerous studies that reached the conclusion that global well-being is actually declining, or at best stagnating.

The arguments presented here are the most common ones. The literature on social discounting is huge and there are many more aspects not mentioned here (see, e.g., chapter 6 of the TEEB study for a substantial overview). It is clear that the choice of a proper social discount rate is essential for the comparison of costs and benefits of action against climate change. What the “right” discount rate is, is a highly controversial issue – nevertheless, it can be shown that some approaches clearly are wrong, while others seem to be more appropriate.

There is one question left: do we actually need social discounting in the economics of climate change? As I wrote in the beginning, you need them if you want to compare benefits from the future with costs today – i.e., if you want to conduct a cost-benefit-analysis. Yet, there are reasons for believing that a cost-benefit-analysis in the field of climate change is futile and misleading: there are many aspects of this phenomenon that cannot be monetized (as I already wrote here and here), e.g. lives lost, disrupted societies, biodiversity losses etc. There is an alternative though – based on the Price-Standard approach by William Baumol and Wallace Oates. It has been proposed to let the climate science define a threshold we don’t want/should not pass (economics could have an advising role here – but not more). The main part for the economics of climate change would be then to find efficient ways to achieve the goal set by others. No cost-benefit-analyses would be needed, and thus no social discount rates. Thus far, though, this is only a rather unpopular approach – therefore it is good to understand the working and meaning of social discount rates.



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