Plate x in print

The Discount

present value and the valuation of the future; the ethics of the discount rate, from Ramsey to the price of the climate.

We ought not to weigh a future enjoyment for less than a present one merely because it lies in the future; to do so is no principle of reason but a narrowing of the sympathies. The welfare of one not yet born counts, in the sum we are bound to weigh, for exactly as much as the welfare of one now alive — and the rate at which we discount the unborn is the precise measure of our injustice toward them.

— the ethics of this plate, after Frank Ramsey, 1928

The volume has taken the rate as a market price — the reward for waiting, the yield of capital, the cost of money, the number a committee now sets. But there is a second rate, and it is not read off any market at all. When a government weighs a dam whose cost falls now and whose benefit falls in a century, or an effort against a warming climate whose worst harms land on the unborn, it must turn those distant gains and losses into present terms; it must discount the future. The rate it uses for this is the social discount rate, and it is not discovered but chosen. And because what it weighs is the welfare of generations who can neither bargain nor vote for themselves, the choosing is not arithmetic but conscience. The plate puts the question the whole volume has circled in its sharpest form: at what rate may the living rightly discount the lives of the unborn?

The framework that governs the question was set down by Frank Ramsey, a Cambridge prodigy dead at twenty-six, in a study of how much a nation ought to save. He showed that the rate at which a society should discount future consumption rests on two grounds, and only two. The first is growth: if those who come after will be richer than we are, an added pound will mean less to them than to us, and a benefit reaching them may fairly be weighed a little below the same benefit today. This ground is a matter of fact, and almost no one disputes it. The second is the contested one — discounting future welfare simply because it is future, apart from any expectation that the future will be richer at all. On this Ramsey was unbending: it has no rightful place in the reckoning.1 To count a life for less because it falls later is not a finding of economics but a failure of moral vision; the just rate at which to discount the unborn for their lateness alone, he held, is zero.

1. The social discount rate rests on two grounds. One is growth: if the future is richer, an added pound means less to it, and its benefits may be weighed a little below ours — a factual ground, scarcely disputed. The other is the discounting of future welfare merely because it is future; this is the contested ground, and Ramsey held its just rate to be zero.

The distinction can sound like a scholar's quibble until one sees what rides on it, for a discount rate compounds, and across the long horizons of the climate — a century, two centuries — a small difference in the rate swells into an immense difference in present worth. At a rate near zero, a calamity that strikes two hundred years hence is one we are bound to spend heavily now to prevent; at a few percent a year, the same calamity, discounted across two centuries, dwindles to a sum scarcely worth notice today.2 The rate chosen does not merely adjust the answer; it very nearly is the answer. And folded inside it, doing its quiet work, sits the one term Ramsey marked as moral: the rate at which we discount the welfare of people simply for being born after us.

2. A rate compounds, so over a century or two a small difference in it becomes an enormous difference in present worth. Near zero, a distant calamity is one we must pay heavily now to prevent; at a few percent, the same calamity discounted across two centuries shrinks to almost nothing. The rate does not adjust the answer so much as fix it.
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The clearest place to watch the stakes is the long argument over climate change, where Ramsey's rule became the hinge on which policy turned. Almost the whole cost of a warming world falls on the future, so the case for spending now to spare it rests on the rate at which that future is discounted. The Stern Review, reporting to the British government in 2006, set the discounting of future welfare close to zero — close, that is, to Ramsey's ethics — and concluded that the harm to come was so vast, reckoned in present terms, that the world ought to act at once and on a great scale. William Nordhaus, working the same arithmetic, set a higher rate, drawn from the returns people actually earn in markets, and concluded a steadier, more gradual course the wiser.3 The two were not divided over the science of warming, nor over the economics of its damage. They were divided over a single ethical number, and everything else followed from it: how much a harm to the unborn is worth to us now.

3. The Stern Review of 2006 set the discounting of future welfare near zero, after Ramsey, and judged the case for urgent, large-scale action overwhelming. William Nordhaus used a higher rate, drawn from market returns, and judged a gradual course wiser. They agreed on the science of warming and the economics of harm; they differed on the ethical number folded into the rate.

What the quarrel lays bare is that the discount rate is the seam where economics runs out and ethics begins. No measurement can settle how much the present owes the future; that is a question of justice between the generations, and a number cannot answer it, only carry an answer chosen elsewhere. And there lies the quiet danger: a moral verdict upon the claims of the unborn is made to wear the plain coat of a technical parameter, when it is in truth a judgment that ought to be argued in the open.4 The rate hides the choosing, just as the market rate hides the contest between lender and borrower — save that here the contest runs between those now alive and those not yet, who can lodge no complaint against the terms we set them.

4. The disagreement cannot be settled by data, for it turns on how much the present owes the future. A high rate says the unborn count for little; a low rate, that they count nearly as much as we do. And the verdict hides inside a number, so that a question of intergenerational justice comes dressed as a technical choice an analyst hands over.

So the rate, which opened this volume looking like the most impersonal of magnitudes — a fact of arithmetic the market merely reports — closes it as the most personal of all: a measure of how much the living care for the unborn. The market rate, the volume has argued, is a verdict in the oldest contest of money, between those who have it and those who need it; the social discount rate, a verdict in a contest older still, between the generation that acts and those that inherit what it does. Ramsey's answer was not a theorem but a conviction — that a life is a life whenever it falls, that the lateness of a birth grants no licence to weigh it for less, and that a positive rate of pure time preference is only the arithmetic of a narrowed sympathy.5 The volume asked who decides what an hour of waiting is worth. Its last plate asks the harder thing: by what right the living set the price of a world they will not live to see.

5. The market rate is a verdict in the contest between creditor and debtor; the social discount rate, a verdict in the contest between the present and the unborn. Ramsey's answer — that a life counts for as much whenever it is lived — was a claim in ethics, not economics, and marks the point where the price of time becomes a question of justice.