Why the future is cheap
One number decides whether a catastrophe a century out is worth spending money on today. It is chosen, not measured, and reasonable people choose it differently. Move it below and watch what it does.
Anything that happens later is worth less now. That is not a moral claim, it is what a positive interest rate means: given the choice between a hundred euro today and a hundred euro in a year, the first is better because it can be turned into more than a hundred by the time the year is out. Run that forward far enough and the arithmetic does something violent.
Below is a single benefit of a hundred euro, delivered in one future year. The curve is what it is worth today at every horizon from now to three hundred years out. Move the rate and watch the curve collapse against the axis.
01One hundred euro, later
02The formula is an ethical statement
The rate is not usually picked out of the air. The standard construction is the Ramsey rule, which builds it out of three quantities, and it is the reason the three sliders above are separate rather than one.
discount rate = pure time preference + (elasticity x growth rate) The second term is uncontroversial. The first is not.
The second term is a statement about wealth. If people in the future are richer, an extra euro means less to them than it does to somebody today, so a benefit that lands on them counts for less. The elasticity is how quickly the value of a euro falls as you get richer. Both parts of that are empirical questions, at least in principle, and disagreement about them is ordinary disagreement.
The first term is different. Pure time preference is the rate at which you discount a person's wellbeing purely because it happens later. Not because they will be richer. Not because the world might end before then. Simply because they are further away in time. Set it to two per cent and you have said that a person alive in a hundred years counts for about an eighth of a person alive now, and you have said it in a spreadsheet rather than out loud.
There is no measurement that settles this. It is a position about how much a stranger who does not exist yet is owed, and it goes into an equation that then produces a number that looks technical. That is the whole difficulty with discounting: the ethics enters early, gets multiplied by three hundred years of compounding, and comes out the other end looking like arithmetic.
03The same damage, two answers
Here is what that does to a policy question. Suppose an unmitigated climate produces damage of a fixed size in every year from some point onward, for ever. The most that would be rational to spend today to prevent it is the present value of that damage. That is one calculation and one damage, priced at four different rates.
Nothing about the physical world changed between those bars. The damage is the same damage. What changed is a parameter that no experiment can settle, and the answer to whether the problem is worth acting on moved by an order of magnitude. Goulder and Williams make the point with a clean arithmetic example: a given loss of consumption a hundred years from now is about seventeen times smaller under a discount rate of 4.3 per cent than under one of 1.4 per cent. Those two rates are not invented for the illustration. They are the two positions.
04Stern and Nordhaus, side by side
The disagreement has two names attached to it. Both are set out below as their own parameters, with the sources underneath. I am not going to tell you which is right, because the disagreement is not the kind that gets settled by being told.
| Pure time preference | Elasticity | Growth | Discount rate | |
|---|---|---|---|---|
| Stern, 2007 | 0.1 % | 1.0 | 1.3 % | 1.4 % |
| Nordhaus, 2007 | 3.0 % | 1.0 | 1.3 % | 4.3 % |
| United States regulatory guidance, 2023 | estimated as a social rate of time preference, updated every three years | 2.0 % | ||
Sources for every figure in the table are in section seven. The two positions share the same elasticity and the same assumed growth. The entire gap between them is the first column.
What each position holds
Stern takes pure time preference to be very close to zero, and the small remainder to represent the chance that there is no future generation at all rather than any lower claim on our concern. The argument is that every generation counts equally, and that discounting a person because they are born later is not defensible as ethics whatever it may be as description. The consequence is a low rate, a large present value for distant damage, and a case for spending substantially now.
Nordhaus takes the position that the parameters should be disciplined by what people and markets actually do. Real interest rates and savings rates reveal how societies in fact trade the present against the future, and an analysis built on parameters that contradict observed behaviour will recommend a level of saving that nobody would accept. In his review of the Stern Review he argues that its conclusions depend decisively on the near zero discount rate and would not survive assumptions consistent with market interest rates. The consequence is a higher rate, a smaller present value for distant damage, and a case for acting more gradually.
Both of those are coherent. The first says that an ethical parameter should be argued from ethics. The second says that a parameter used to make real decisions should be consistent with the revealed choices of the people the decisions are for. Neither of them is making an arithmetic mistake, and no amount of better data will resolve it, because the question is not empirical. What you can do, and what this page is for, is see exactly how much rides on it before you take a side.
05The same arithmetic in a suit
This is not a problem peculiar to climate. It is the same problem that sits in the middle of every discounted cash flow, where it wears better clothes and attracts less scrutiny. A valuation forecasts a few years explicitly, then reduces everything after that to a single terminal value, and discounts the lot. The terminal value is the same object as the distant damage above: a long tail of the future, collapsed into one figure by a rate somebody chose.
The number to watch is the share carried by the terminal value. On ordinary settings, most of what a company is said to be worth is the part of the forecast that was never actually forecast. The five year model that took three weeks is the small piece. The perpetuity assumption typed into one cell is the large one. Move the terminal growth rate by half a point and see how much of the valuation moves with it.
The instrument I built for that work, the analyst desk, prints that share on every run for exactly this reason, along with the arithmetic that produced it. It is here, and the reasoning behind it is written up as the dcf lab case study. A valuation that does not tell you how much of itself is the terminal value is not telling you what it is.
06Where the model stops
Assumptions and limits
- A constant rateEvery calculation here uses one rate applied to every year. Much of the serious literature argues that the rate should decline with the horizon, because of uncertainty about future growth, and the 2023 United States regulatory guidance in the table does exactly that. A declining rate raises the weight on distant damage substantially and this page does not model it.
- CertaintyThe damage arrives with certainty and in a known amount. In reality both the size and the timing are deeply uncertain, and a large part of the case for acting rests on the tail of that distribution rather than on the central estimate. Nothing on this page carries a probability.
- One consumption goodThe Ramsey rule assumes a single good whose quantity grows. It has no way to express the possibility that some of what is lost, a coastline or a species, is not substitutable for anything the extra growth buys. If some damages cannot be compensated by being richer, the whole framework understates them.
- The damage is a flat streamReal climate damage is neither flat nor starting at a single date. The stream in figure two is a shape chosen so that the effect of the rate is visible, not an estimate of anything.
- Numbers, not estimatesThe hundred euro, the damage of a hundred a year, and the cash flows in figure three are units chosen for legibility. They are not measurements, and no figure produced on this page belongs in a real appraisal.
- Two positions, not the fieldSection four sets out two named positions because they are the two most cited. There is a wide literature between and beyond them, including arguments for rates below Stern's and above Nordhaus's, and the table should not be read as the range of respectable opinion.
07Sources
- The parameters in the table. Stern: pure time preference 0.1 per cent, elasticity of marginal utility 1.0, growth 1.3 per cent, giving a consumption discount rate of 1.40 per cent. Nordhaus: pure time preference 3.0 per cent, the same elasticity and growth, giving 4.30 per cent. The same paper states that a given loss of consumption a hundred years from now is seventeen times smaller at 4.3 per cent than at 1.4 per cent. Lawrence H. Goulder and Roberton C. Williams III, The Choice of Discount Rate for Climate Change Policy Evaluation, NBER Working Paper 18301, 2012. nber.org/system/files/working_papers/w18301/w18301.pdf Checked 2026 08 21.
- The same two figures, 1.4 per cent for Stern as 1.3 per cent of productivity growth plus 0.1 per cent for the risk of extinction, and 4.3 per cent for Nordhaus, with the framing of the disagreement as ethical rather than technical. The CORE Econ Project, The Economy, microeconomics, section 9.5, Discounting, external effects, and the future of the planet. books.core-econ.org Checked 2026 08 21.
- The Stern Review's own parameters: a pure rate of time preference of 0.1 per cent per year, justified by the risk of extinction, and an elasticity of marginal utility of one. House of Commons Library, The Stern Review and the discount rate, Standard Note SN/EP/4739. researchbriefings.files.parliament.uk/documents/SN04739/SN04739.pdf Checked 2026 08 21.
- Nordhaus's own statement of his objection: that the Stern Review's conclusions depend decisively on the assumption of a near zero time discount rate combined with a specific utility function, and would not survive the substitution of assumptions consistent with market real interest rates and savings rates. William D. Nordhaus, A Review of the Stern Review on the Economics of Climate Change, Journal of Economic Literature, volume 45, number 3, 2007, pages 686 to 702. aeaweb.org/articles?id=10.1257/jel.45.3.686 Checked 2026 08 21.
- The regulatory figure: the November 2023 revision of Circular A-4 adopts a 2.0 per cent real social rate of time preference for near term analysis, updated every three years, with a schedule of declining rates for long horizons reaching 1.1 per cent for the years 2164 to 2172. Office of Management and Budget, Circular No. A-4 discount rate history and appendix, 9 November 2023. whitehouse.gov/wp-content/uploads/2023/11/CircularA-4DiscountHistory.pdf Checked 2026 08 21.