The Numéraire

in print · The Money · plate i

Money does three things, and the third is the strangest: it is the unit of account, the rod in which every price is told and against which every other worth is measured. This plate asks what it means for one thing to be the measure of all the others — whether a yardstick can be cut from outside the world it measures, why the classical economists searched in vain for a standard that would hold still, and how the measure of value came, in the end, to be made of the very stuff it counts.

Money has become by convention a sort of representative of demand; and this is why it has the name nomisma — because it exists not by nature but by law. Aristotle, Nicomachean Ethics, Book V · c. 350 bce

Of the three things money is said to do, the quietest is the one the schoolbooks list last, and it is the one this volume has taken for its name. Money is a medium of exchange, the thing handed over; it is a store of value, the thing held back; and it is a unit of account — the numéraire, the rod against which every other worth is measured and in which every price is told. The first two offices money shares, in some degree, with a sack of grain or a bar of silver. The third it shares with nothing, for to be the measure of all values a thing must somehow stand outside the press of valuation even while it takes part in it — must be at once the yardstick and one of the lengths laid against it. No other object in economic life is asked to be both, and the quiet strain of that demand, hidden in plain sight at the foot of every price, is where the mystery of money begins.

Begin with the order of things, since it is contested and the contest decides much. The common account, the one the commodity theory tells, makes the medium of exchange the root: money is first the good one takes in trade and passes on, and its service as a measure rides along behind. But there is an older and stranger possibility — that the measure comes first, that before money is a thing handed over it is a unit things are reckoned in, a standard in which a debt is named and a price set, and that the coin is only what one reaches for to settle accounts already kept in the unit. The question is not antiquarian. If the measure is primary, then money begins as an abstraction, a way of counting, and the metal is incidental — and a thing that begins as a way of counting is a very different object from a commodity that won a popularity contest.

Grant the measure its dignity and one sees at once how much it accomplishes. In a market without a common unit there is no such thing as the price of a good; there is only a swarm of separate exchange ratios — bread for wool, wool for iron, each struck on its own — and the swarm grows monstrous, for a hundred goods generate not a hundred prices but nearly five thousand pairwise ratios, more than any market could clear. The numéraire dissolves it. Choose one thing as the unit and every good has a single price in it; the thousands of ratios collapse to one figure apiece, and values that were merely tradeable become commensurable — rankable, addable, set on a single scale. Aristotle had seen it twenty-three centuries ago: money is the measure that makes all things commensurable, and does so not by nature but by convention. What he stated calmly conceals a vast claim — that the worth of anything whatever can be reduced, without remainder, to a quantity of one chosen thing.

Pressed to its limit, the idea of the measure becomes pure abstraction, and it is worth seeing in that bare state, for it shows what the measure is when nothing else clings to it. In the mathematical theory of general equilibrium the numéraire is the most innocent object imaginable: one commodity, chosen arbitrarily, whose price is fixed at one, every other price written as its ratio to that one. Nothing rides on the choice — pick gold or pick wheat, the real pattern of exchange is identical — and only relative prices are ever determined; the level as a whole floats free, so that to double every price at once changes nothing real. Here the unit of account is laid utterly bare, stripped of every other function: it does no exchanging, stores no value, bears no metal. It is a counting-stick and nothing more — the very emblem of the doctrine that money is a veil over a real economy that would run as it does whether reckoned in dollars or in shells.

But the numéraire of the equations is not money, and the gap between them is the whole of the trouble. Walras's unit does no work in the world; it is a device for pinning relative prices to a scale, and it neither circulates nor is hoarded nor commands a premium in a panic. Actual money is asked to be that serene abstraction and, in the same breath, a concrete thing — a coin, a note, a balance — that one holds and hands over, that exists in some definite quantity, that is wanted more in fear and less in confidence, and that therefore has a price of its own. The single syllable "money" welds together two natures that do not sit easily in one body: a pure unit of account, which to do its work ought never to vary, and a traded asset, which by its nature cannot help but vary. Almost every confusion in the theory of money can be traced to the seam where these two are joined and the join then forgotten — to the moment when the rod that measures is quietly assumed to be as fixed as the abstraction, while in truth it is as restless as the commodity.

Consider what we ask of a measure, and set beside it what money is. A measure must be constant; a unit of length that swelled on Tuesdays and shrank on Fridays would be no unit at all, the whole point of a standard being that it holds while the things measured against it change, so that any difference may be charged to the thing and not the rule. This is what money cannot promise. As the unit of account the dollar is asked to stand perfectly still; as a held asset its purchasing power rises when prices fall and falls when they rise, so that the very rod in which all worth is told is forever lengthening and contracting in the hand. The merchant who prices his goods in money, the lender who writes a loan in it, the worker who signs a wage in it, all bind themselves against a yardstick that does not keep its length — and the slow theft and slow gift that follow are consequences not accidental to money but inherent in asking one object to be the measure and a thing measured at once.

The classical economists felt this difficulty in their bones, and the best of them spent themselves trying to escape it. If money would not hold still, perhaps some other standard might — some invariable measure of value, cut from outside the flux, against which the real changes in all other things could at last be read without distortion. Adam Smith reached for labor, the toil and trouble a thing could command, as the truest and most constant measure of worth. David Ricardo pursued an invariable measure through the whole of his Principles, returned to it again and again, and was still wrestling with it in an unfinished paper at his death — and his conclusion, reached honestly and against his own wish, was that no such measure can exist. For any commodity one might offer as the standard is itself a produced thing, made with labor and capital in some proportion, and its own value shifts whenever the conditions of its making shift; there is no good in the world whose worth is fixed, and so none that can serve as the fixed point against which the rest are weighed. The rod, wherever one cuts it, is cut from inside the forest it is meant to survey.

There is a further strangeness, and it cuts the other way, for if the measure cannot be made to hold still, neither need it be fastened to any thing at all. We picture the unit of account as riding on a particular coin — the dollar as the silver in it — but for most of European history the two came clean apart. Men kept their ledgers in pounds, shillings, and pence, a money of account handed down from Charlemagne, while paying in an unruly crowd of actual coins — florins, ducats, groats, écus — whose worth in the pound was declared by the authorities and revised whenever it suited them. The unit was indispensable and universally used; it answered to no coin one could carry; and a prince could alter the relation between the abstract pound and the concrete piece with a stroke, lightening every debt without touching a scrap of metal. The numéraire, it turns out, need not be incarnate at all — it can be a pure name, a column in a book, a convention floating above the jingling confusion it orders. And a measure that is in the end a name, kept by agreement and adjustable by power, is plainly no fact of nature.

Gather these findings and the numéraire stands revealed as something quite other than it pretends. It presents itself as the fixed and external reference, the neutral bedrock against which all values are read — and it is no such thing. It is itself one of the goods, with a quantity that can be enlarged and a worth that drifts; there is no invariable version of it to be had; and where it is most purely a measure it is least a thing, a mere name kept by convention. A plain consequence follows: a price stated in money is never a reading against a fixed scale but a ratio struck between two goods — the thing priced and the money it is priced in — a figure that can move because either term has moved. When a loaf costs more this year than last, the price alone cannot say whether the loaf has grown scarcer or the money more abundant; the two causes wear one face. Every price quoted in money is thus contingent twice over: on the hidden contest that fixes the worth of the thing, and on the drifting worth of the rod that worth is told in. The first contingency this table was built to expose; the second is the one the measure most quietly conceals — by seeming to be a measure, and not a thing.

This is the deepest reason money wears so convincingly the look of a natural fact. We do not measure the wage or the rent against the dollar as we measure a length against a fixed standard kept in a vault, indifferent and outside the things it gauges; we measure them against another good, as restless as they are, whose own value is set in the same press of supply and demand and trust and power that sets theirs. The rod is made of the very stuff it measures — and in this there is an irony the work cannot escape and had better own. This whole undertaking is named for the numéraire, and announces as its aim to fix a numéraire of honesty against which the verdicts of the market may at last be truly read. The plate on the numéraire returns the awkward answer that no such fixed and external measure exists: there is no place to stand outside the system of values from which to weigh it. The honest measure, if there is one, is not a rod cut from beyond the world but the steady recollection that the rod is within it, moving with all it counts.

The measuring rod is made of the very stuff it measures; there is no place outside the world of values from which to weigh them.

Money's first and subtlest deception, then, is not that it hides the contests behind particular prices, though it does that too. It is that money offers itself as the neutral ground on which all such contests are scored — the fixed unit, the given measure, the one quantity in economic life that simply is — when it is in truth as made, as moving, and as contestable as anything it is used to price. A price is a verdict on a hidden contest, mistaken for a fact of nature; and the unit in which the verdict is handed down is itself a verdict of the same uncertain kind, mistaken for the fixed and natural measure of all the rest. The numéraire is the rod the whole table is named for, and it does not stand still. The argument remains open.