It is a peculiar thing to build a science around a residual — around, that is, the part of the answer that is left over when everything one can measure has been subtracted out. Yet that is very nearly what the study of growth has had to do. Add up the contribution of all the extra machines and all the extra workers to the rising output of a wealthy nation, and you find that they account for less than half of it; the larger share is a remainder, a quantity with no name of its own but the one the economists gave it in their chagrin — the residual, or, more honestly, the measure of our ignorance. The whole engine of modern prosperity sits inside that word, and the word is a confession.
The confession was wrung from the soberest kind of arithmetic. Faced with the great enrichment, economists wanted to know what had produced it, and they went at the question as accountants would, by sources. The rise in a nation's output, they reasoned, must come from some mix of more capital — tools, machines, buildings, roads — and more labor, more hands at work; so let us measure how fast each has grown, weight each by the share of the national income it commands, and add the two together to see how much of the growth they explain. The exercise is called growth accounting, and when Robert Solow first performed it with care, for the United States across the first half of the twentieth century, the result was startling. Capital and labor together accounted for only a small fraction of the rise in output per worker. The overwhelming majority of it — by his reckoning, some seven-eighths — was a remainder no one had expected and no one could, at first, explain.
To feel the force of the finding, one must see what it overturned. The natural assumption — of common sense, and of most economics before — was that a nation grows rich by accumulation: by saving and investing, piling up capital, equipping each worker with ever more to work with. On that view, wealth is stored-up thrift, and the richest nation is the one that has accumulated the most. The residual says otherwise. The bulk of the enrichment came not from working with more but from working better — from the rising efficiency with which the same labor and the same capital are turned into output, the quantity economists named total factor productivity. And productivity is a different sort of thing from a machine or a worker: not a stock one can count, but a ratio, a measure of how much comes out for what goes in. The engine of growth, the accounting said, was not the quantity of the inputs but the efficiency of their use — and that efficiency was the residual.
Behind the empirical surprise lay a theoretical reason why it nearly had to be so. Capital, like everything in economics, is subject to diminishing returns: the more of it a worker already commands, the less an added unit gives. Hand a man without tools his first spade, and you transform his output; hand a man who already runs a fleet of machines one more, and you change almost nothing. From this single fact the Solow model drew a stark conclusion. A society that grows only by accumulating will find each new tranche of saving buying less than the last, while the capital it holds wears out and the workers it keeps adding must themselves be equipped. Sooner or later, all that the society saves goes merely to maintaining and extending what it has, and capital per worker stops rising. It has reached a steady state, and there its growth in output per head must halt. Thrift can lift the plateau a nation stands on; it cannot keep the ground rising beneath its feet.
What, then, keeps the ground rising? In the Solow model the answer was technological progress — and here the theory made a strange and honest move. It did not explain the progress; it assumed it, writing into the equations a steady rate at which productivity improves and leaving wide open the question of where that rate comes from. Economists have called it manna from heaven, and the name is exact: an indispensable blessing descending on the model from outside, sustaining the growth that accumulation could not. The result is a structure of remarkable candor. The model proves, with full rigor, that lasting growth must come from the residual — from rising productivity, not from piling up capital — and then, the proof complete, falls silent on what the residual actually is. The deepest term in the whole theory of wealth was left, on purpose, a blank: an IOU drawn against the future of the science.
Set the two accounts of wealth side by side, and the argument of these volumes steps forward. On the first, a nation's wealth flows from its stock — from the capital it has piled up and the resources it holds, the endowment it possesses and enlarges by saving; this is wealth as a natural accumulation, the slow reward of a frugal and well-favored people, and on it a nation's riches are very nearly a fact of what it has. On the second, the account the residual forces, the wealth flows instead from productivity — from ideas, from technique, from the organization of work, and from the institutions that summon all of these into being. A price is a verdict on a hidden contest, mistaken for a fact of nature — and so, the residual reveals, is the wealth of nations: not the natural yield of an endowment, but the made fruit of productivity, and productivity is made only where the long contests over the rules have settled in the ways that reward making. What drives the enrichment is not what a nation has, but what it makes — and making is never a gift of nature.
The case for accumulation must be given its due, for it is not empty. Capital deepening is real and necessary; the residual is most of growth, not all, and no nation grew rich on no investment whatever. The growth miracles of East Asia, moreover, were on one celebrated reckoning driven more by sheer accumulation — prodigious saving, surging schooling, more of the people drawn into work — than by any rise in productivity: a triumph, it was said, of perspiration over inspiration. And a measurement worry cuts deep: the residual, being a leftover, silently absorbs every error in the measuring of capital and labor, so that what we credit to productivity may be, in part, our own mismeasurement. Each point has weight. But the Solow logic stands — accumulation-led growth exhausts itself in the end, as the Soviet Union's long stagnation after furious investment made plain — and beneath every adjustment a stubborn fact survives: nations with ample labor and capital do not on that account grow rich, or the poor world, with its teeming workers, would be wealthy. Whatever its exact size, the residual is where the wealth of nations has hidden itself. One scruple must be added, though: to call the residual "productivity," or "technology," is to name the box and not to open it — and a name passes too easily for an explanation it has not earned.
Notice, last, the quiet confession folded into the word itself. To call productivity the residual is to cast it as the leftover — what remains once the real factors, capital and labor, have been counted and credited. But the leftover is the main event and the counted factors the supporting cast; the accounting has the order of importance exactly inverted. We lavish our measurement on the things that look like solid facts of a nation's endowment — its stock of capital, its supply of hands — and consign to an unexplained balance the made and contested thing that does the actual work of enrichment. The frame itself enacts the error these volumes were written to expose. A price is a verdict on a hidden contest, mistaken for a fact of nature — and growth accounting, for all its rigor, makes the same mistake in reverse: it treats the natural-seeming stock as the substance and the made thing as the remainder, when the made thing is the substance and the stock the self-limiting remainder. The residual is misnamed; it is not what is left over, but what matters most.
This redeems, and deepens, the phrase the residual was given at its christening. It was called the measure of our ignorance, and so it is — but the ignorance is one we have manufactured. Growth is not in itself a mystery beyond the reach of explanation; we have made it mysterious by the shape of our reckoning — by building that reckoning around the inputs that wear the look of natural fact, capital and labor and land, and banishing to a nameless remainder the ideas and institutions that are the real engine. Having mistaken a nation's endowment for the cause of its wealth, we are left with no choice but to call the true cause a riddle. The residual is the exact measure of that mistake — the size of what escapes us when we hunt the wealth of nations in what they happen to hold, rather than in the contests, won and lost, that settled the rules under which they think and build.
The residual is misnamed: not the leftover after the real causes are counted, but the cause itself — left over because we counted the wrong things.
So the volume's two opening plates divide the work of beginning. The first set down the fact — that the modern world is, against all the prior history of the species, astonishingly and recently rich. This one has asked where that wealth comes from, and returned an answer that points beyond itself: not the stock a nation accumulates, which diminishing returns must exhaust, but the residual — the rising productivity that is the made and inexhaustible thing. And to ask what the residual is — what lies inside that confessing word — is to be handed the rest of the volume: the ideas productivity is built from, the institutions that decide whether it is built at all, the divergence between the nations that found the engine and those still seeking it. The enrichment of the modern world is not the yield of what its fortunate nations have. It is the fruit of what they have made, under rules that let them make it. The argument remains open.