Valuing the Future: Recent advances in social discounting

Valuing the Future: Recent advances in social discounting,
David Pearce, Ben Groom, Cameron Hepburn & Phoebe Koundouri,
WORLD ECONOMICS, Vol. 4, No. 2, April–June 2003

" ... One of the problem areas concerns timediscounting—the process whereby society places a lower value on a futuregain or loss than on the same gain or loss occurring now. The rationale fortime-discounting follows logically from the basic value judgement of welfareeconomics. If people’s preferences count and if people prefer now tothe future, those preferences must be integrated into social policy formulation.Time-discounting is thus universal in economic analysis, but itremains, as it always has, controversial.

...

The tyranny of discounting

It is comparatively easy to illustrate the moral dilemma in discounting. Letthe weight that is attached to a gain or loss in any future year, t, be wt.Discounting implies that wt 1. Moreover, discounting implies that theweight attached to, say, 50 years hence should be lower than the weightattached to 40 years hence. The discounting formula is then:

W(t) = 1 / t-squared of (1 + s)

Inspection of this equation shows that it is simply compound interestupside down. This is why the approach is often called ‘exponential discounting’.The weight wt is the discount factor and s is the discount rate. It isimportant to distinguish the two, as we will see. The discount factor isoften represented as a fraction, and the discount rate as a percentage. Forexample, if s = 4%, then the discount factor for 50 years hence would be:

W(50 years) = 1 / 50-squared of (1 + 0.04) = 0.14

In practical terms, this would mean that a gain or loss 50 years hencewould be valued at only 14% of its value now. Transposed to the kinds ofglobal environmental problems now faced by the world, the arithmeticillustrates the ‘tyranny’ of discounting. Keeping to the 4% discount rate,global warming damage one hundred years from now would be valued atjust one-fiftieth of the value that would be assigned to it if it occurredtoday. Imagine a cost of $1 billion one hundred years from now. The useof discounting means that this loss would appear as just £20 million in anyappraisal of the costs and benefits of global warming control. Indeed,cost–benefit models of global warming have been shown to be highly sensitive to assumptions about the discount rate. ...

Not discounting is discounting at 0%, and it isn’t good

The dilemma of discounting seems easily resolvable—simply don’t do it.But not discounting is formally equivalent to discounting at a particularnumber which happens to be zero per cent. In terms of the discountingequation, if s = 0, wt = 1 and everyone is ‘equal’ now and in the future. Thisoutcome would not matter much for the debate but for some very unnervingimplications of using zero discount rates. The first is transparently simple.Zero discounting means that we care as much for someone not justone hundred years from now as we do for someone now, but also someoneone thousand years from now, or even one million years from now. It seemsat least legitimate to ask: do we care about someone one million yearshence (we already know we do not), and should we care about someoneone million years from now? We suspect that the answer to the secondquestion would also be negative if there was a poll of people to determine it. ...

The notion of a social discount rate is usually presentedin the form of the following equation, known as a Ramsey equation(after Frank Ramsey, (Ramsey, 1928)):

s = r + m.g

What this says is that the social discount rate is equal to the sum of twofactors: r which is the ‘pure’ rate of time preference, reflecting people’simpatience; and the product of m (to be explained) and g, the growth rate offuture (per capita) consumption. m is known as the elasticity of the marginalutility of consumption, the percentage change in the well-being derivedfrom a percentage change in consumption (or income). The intuition behindm is that it expresses individuals’ aversion to fluctuations in their incomelevels. While there is a substantial debate about the value of m, recentreviews suggest that it takes a convenient value of about 1.0 (Cowell andGardiner, 1999). Notice that there is a simple intuition behind m.g. Peoplein the future will (almost certainly) be richer and hence the ‘utility’ theyattach to one more dollar of income is likely to be lower than that attached to the same dollar today. Effectively, then, discounting is justified simplyby the fact that future people will be better off than today’s people. ... (본문 중에서)