Every discount rate this volume has weighed has been a market price — the rate the market sets, the lender charges, the central bank moves. This plate takes up a discount rate of another kind: the social discount rate, at which a society should weigh costs and benefits that fall not next year but next century, on generations not yet born. It is the hinge of every decision whose consequences reach far into the future — the warming of the climate, the burial of nuclear waste, the saving or the spending of an exhaustible world — and it turns out to matter more than almost any other number, for over long horizons the discount rate exerts a kind of tyranny: a high rate makes the far future vanish, shrinking a catastrophe three centuries hence to a rounding error today; a low rate makes the distant generation weigh almost as heavily as our own. This plate will set out the formula by which the social rate is reckoned, and the deep ethical quarrel at its heart — over whether a society may rightly be impatient, may discount the welfare of future people merely because they are future — a quarrel made vivid in the great debate of Stern against Nordhaus over the worth of a warming world; and it will find the volume's question carried here to its furthest and gravest form: no longer is this price just, but how much do we owe those who come after.
Begin with why the social rate matters so enormously, which is a fact of arithmetic before it is a question of ethics. Discounting compounds, and over long spans it compounds ferociously. Take a harm of a trillion dollars falling two centuries from now. Discounted at five per cent a year — an ordinary market rate — its present value is some sixty dollars: a trillion dollars of future suffering, shrunk by the arithmetic of compounding to the price of a dinner. Discounted instead at one and a half per cent, the same trillion is worth some sixty billion today — a billionfold more weighty, enough to command serious present sacrifice. The two rates differ by three and a half points; the present values they yield differ by a factor of a billion. This is the tyranny of the discount rate: over the horizons that matter for the climate or the deep future, the choice of rate does not merely adjust the answer but very nearly determines it, settling before any other argument is heard whether the far future shall count for much or for almost nothing. The rate is no technical parameter buried in the model; it is the model's hidden conscience — the place where a civilization quietly decides how much the unborn are worth to it.
The rate is no technical parameter buried in the model; it is the model's hidden conscience — where a civilization quietly decides how much the unborn are worth to it.
The formula for the social rate was given, in essence, by Frank Ramsey, in a paper on saving written when he was twenty-five. It holds that the rate at which we should discount future consumption has two parts. The first is the rate at which a richer posterity diminishes the worth of a marginal good: if those who come after will be wealthier than we — if consumption grows — then an extra unit of consumption will mean less to them than to us, just as a loaf means less to the full than to the hungry, and so future benefits may be discounted in proportion to that growth and to the speed with which added wealth loses its savour. This part is little disputed; it is a matter of diminishing marginal utility, applied across time. The second part is the one that has set the world by the ears: the pure rate of time preference, the rate at which we discount future welfare itself — not because posterity will be richer, but simply because their welfare lies in the future and is therefore, somehow, worth less to us now. The whole moral weight of the social discount rate rests on this second term: on whether a society may, like the impatient individual of an earlier plate, prefer its own welfare to a later generation's merely on account of the date.
And here the ethical objection is old and sharp. To discount a future person's welfare because he is born later is not, the objectors say, like an individual's preferring jam today to jam tomorrow; it is preferring one's own generation to another, a partiality, a discrimination by date of birth. Ramsey himself, the very author of the formula, called pure time preference "ethically indefensible," a thing arising "merely from the weakness of the imagination"; and a line of thinkers from Pigou to Parfit has agreed that from an impartial moral standpoint all generations count equally, and the pure rate should be zero — or near it, allowing only a sliver for the bare chance that there will be no future generation at all, that humanity may not survive to collect. Against this stands a case no less serious. People do discount the future, and markets reveal a positive rate; a social rate pinned near zero, the answer runs, would impose upon the living a duty of saving and sacrifice that no actual person would accept, demanding that the present beggar itself for a posterity it cannot see. And there is the plain fact of the opportunity cost of capital: a dollar invested today grows, so a dollar of distant benefit must be weighed against what that dollar would have become — to discount the future at less than the return on capital is to leave the future poorer than a simple investment would have made it. The quarrel, then, is between an ethics that forbids discounting persons by their birthdate and a realism that reads the rate from the market and the deed.
No debate has shown the stakes of this choice so plainly as the quarrel over the warming of the climate, fought between two of its ablest economists. Nicholas Stern, in his review for the British government, chose a low rate — a pure time preference of a tenth of one per cent, near the ethical zero, on the ground that a future generation's welfare must count almost equally with our own. At so low a rate the harms of unchecked warming, falling though they do across centuries, loom vast in present value, undiscounted into significance; and the conclusion follows that the world should act now, hard and at once, for the cost of strong action today is small against the calamity it forestalls. William Nordhaus, who would later have the Nobel for his work on the economics of climate, chose a higher rate, calibrated to the returns the market actually pays; and at his rate the distant harms are discounted far more, so that the cost-benefit ledger counsels not inaction but a gentler, rising ramp — a modest carbon price now, climbing with the years. The two men worked from much the same science of the climate; what divided their conclusions, almost entirely, was the discount rate — the one ethical choice, of how to weigh a future life, that no thermometer can settle. The debate made unforgettable what the arithmetic had implied: that buried in this single parameter was the whole question of our duty to the future, masquerading as a technical assumption.
Honesty requires that the case for discounting the future not be caricatured, for it is stronger than the ethical objection alone would suggest. If our descendants will indeed be far richer than we — as growth, continued, would make them — then to impoverish ourselves for their sake is to transfer from the poorer present to the wealthier future, a strange charity that runs uphill; the growth term in Ramsey's rule is no evasion but a real reason to discount. The opportunity cost is real: resources sunk now into averting a distant harm cannot also be invested to make the future rich, and a future left a great endowment of productive capital may be better armed against its troubles than one left only a slightly cooler climate. And the deep future is radically uncertain: we do not know the growth, the technology, the very wants of those centuries off, and this uncertainty, some argue, ought itself to lower the rate we use for the farthest horizons — for if the rate that will prevail is unknown, the low-rate futures come to dominate the reckoning, and the schedule of discount should decline as it lengthens, a refinement that several governments have since adopted. None of this dissolves the ethical worry; but it shows that a positive social rate is not mere selfishness dressed as economics, and that the choice is a genuine dilemma and not a morality tale.
What, then, becomes of the volume's question, carried this far? It transforms. "Earned or extracted" was a question about the justice of a market price — the rate the lender charges, weighed against the service he renders. But the social discount rate is no market price; it is a choice, about how to weigh those who cannot bid in any market, cannot bargain, cannot consent, because they are not yet born. And so the question becomes a graver one: not whether a price is fair to the parties before us, but how much the living owe the unborn. Seen from the future's side, a high discount rate is a kind of extraction without limit and without recourse — the present generation consuming now and leaving the costs, the warmed world and the emptied mine and the buried waste, to those who came too late to object, the most powerless of all parties, more voiceless even than the desperate borrower or the worker with no other door, for they have not so much as a voice to raise. And yet a near-zero rate, its defenders' impartiality notwithstanding, would lay upon the present a burden of sacrifice for a richer posterity that looks, from the living side, like a tyranny of the unborn over the born. There is no market to settle this, no sovereign whose administered rate could be right or wrong by any standard but its own; there is only the living generation's conscience, reckoning in the dark what it owes those who come after. The social discount rate is the price of time stripped of every veil — no productivity, no impatience, no liquidity, no inflation, only the bare question of how much a person not yet born is worth to a person now alive.
The social discount rate is the price of time stripped of every veil — the bare question of how much a person not yet born is worth to a person now alive.
So the price of time, at the end of its long ascent through this volume, arrives at the gravest of its forms. It began as the discount of a single loan, the simple fact that a sum today outweighs the same sum tomorrow; it became the natural rate, the market rate, the curve, the real rate, the moral question, the strange negative rate of the slump; and here it becomes the rate at which a civilization values its own future — the worth it assigns to the children of its children, and to theirs. Whether a society may be impatient as a person may; whether the unborn are owed an equal place or only a discounted one; whether the warmed world and the spent earth are a debt we are running up against those who cannot collect — these the social discount rate decides, and decides for everyone, under the guise of a number in a model. The world we are asked to hold in trust for the unborn is the common inheritance the table met before in the value of land; and the harms we discount onto the future are the externalities a later volume must take up under their own name. What remains, after the far future, is to gather the whole volume into the one number from which the rest hang — the short rate the central bank sets each morning, and the architecture that depends upon it — and that the final plate must do. Through it, as the table says of every price, the argument remains open.