The Growth

The first fact of growth is the fact of compounding, and the mind resists it. A quantity that grows at a steady rate does not climb in a straight line but in a curve that bends ever upward, doubling in a fixed span no matter how large it has already become — and small differences in the rate, given enough time, open into chasms. A rule of thumb captures the arithmetic: a quantity growing at a rate of so many percent a year doubles in roughly seventy divided by that rate. Two percent doubles output in thirty-five years; three percent in twenty-three. Over a single century, two percent multiplies output sevenfold, three percent nineteenfold — so that two nations beginning together, separated by a single point of growth, end the century one barely richer than its great-grandparents and the other transformed beyond recognition. The whole drama of growth is contained in that gap, which patience and compounding pry open from almost nothing.

The second fact is historical, and more startling. For nearly the whole of human existence there was essentially no growth in living standards: the output per person of a farmer in the year one thousand differed little from that of his ancestors a thousand years before, or his descendants centuries after. Generation upon generation lived and died at much the same material level, near the edge of subsistence. Then, in the last two centuries — a sliver at the very end of the human story — output per person in the nations that industrialized rose not by a fraction but by a factor of ten, twenty, thirty, and went on rising. Plotted across the millennia the line is flat, flat, flat, and then, abruptly, nearly vertical: the shape economists call the hockey stick, whose long handle is the poverty of all the ages and whose short blade is the whole of modern prosperity. The figure draws it.

This is the trend the previous volume's cycle merely rides. Where The Cycle studied the tremor — the boom and the slump, the deviations above and below — this volume studies the path those deviations deviate from: the long rising of potential output, the blade itself. And over any horizon that matters for human welfare, the trend dwarfs the tremor. A severe recession costs a tenth of output for a year or two and is made up; growth at a few percent a year, sustained, remakes the material world every generation. To separate the two — the trend that climbs and the cycle that wobbles around it — is the first move of macroeconomics, and it tells us where to look: not at the wobble, painful as it is, but at the slow, compounding, civilization-altering ascent.

Before we ask what bent the blade, we must ask why the handle was so long — why all the ingenuity of the ages, the plow and the wheel and the sail, writing and gunpowder and the printing press, left the mass of humanity living near the same bare edge millennium after millennium. The puzzle is real and deep: invention plainly occurred, and yet living standards barely stirred. The answer that organized the question came in 1798 from Thomas Malthus, in an essay on population that gave the long stagnation an iron logic, and gave the young science of economics the epithet it has never quite shed.

The mechanism is pitiless in its simplicity. Output, in a world that runs on land and labor, is bounded by the fixed earth and its diminishing returns to additional hands. Let some improvement — a better crop, a wetter decade, a cleverer tool — raise income above the subsistence minimum, and more children survive; the population grows; and the additional mouths, pressing on the unyielding land, drive income per head back down to the floor at which a population merely replaces itself. The long-run living standard is therefore not set by productivity at all, but by demography: it settles where the birth rate, rising with prosperity, meets the death rate, falling with it — and that meeting point is subsistence. The figure draws the trap. Every gain in productivity shifts the curves and shifts the population, but the equilibrium income returns, as if pulled by gravity, to the bare minimum.

The corollaries are as dismal as the name suggests. In a Malthusian world the only way to raise the living standard of the survivors is to thin their ranks or to stay their fertility: plague, war, and late marriage made people richer, while peace and plenty made them poorer by making them more numerous. The Black Death, carrying off a third of Europe, raised the wages of those it spared to heights not seen again for centuries — misery as the perverse engine of prosperity. This was the foundation of Malthus's gloom, and the origin of the discipline's reputation as the dismal science: that population would forever press against the means of feeding it, condemning most of humankind to live at the edge of want. For the whole of recorded history before his own lifetime, the verdict was simply correct.

Around the year 1800, in Britain, something happened that had never happened before: output per person began to rise, steadily, and did not fall back. The Industrial Revolution — steam and the factory, the machine and the harnessing of fossil energy buried in coal — loosed production from the ancient constraint of land and muscle, and growth rates that had hovered near zero for ten thousand years climbed to one and two percent a year and stayed there. This is the elbow of the hockey stick, the hinge on which the whole of economic history turns: the great escape, the moment a sliver of humanity broke out of the snare that had held all of it since the beginning.

But sustained growth in output was not enough; the Malthusian link had also to be broken, or the new bounty would have been swallowed by new mouths as every bounty before it had been. It was broken by the demographic transition, the great reordering of births and deaths that accompanies industrialization. First the death rate fell — better nutrition, cleaner water, the slow conquest of disease — while the birth rate stayed high, and the gap between them opened into the population surge that swelled the industrializing nations. Then, crucially, the birth rate fell too: as children turned from farm hands into costly dependents to be schooled, as infant mortality dropped so that fewer births secured a surviving family, as women's prospects widened, families chose to have fewer. With both rates low, population growth subsided — and output per head, no longer outrun by population, could rise. The figure traces the passage: the death rate falling first, the surge between, the birth rate following, the gap closing at last.

Why then, and why there? This is among the great unsettled questions of the discipline, and the candidate answers are many and quarrelsome. Some point to coal — cheap, abundant energy at the very spot industrialization began. Some to institutions — the secure property and the patents that let an inventor profit from invention. Some to geography and empire — the resources and markets of a colonial reach. Some to culture and ideas — the Enlightenment's turn toward useful knowledge, the culture of growth in which experiment and improvement became respectable, the peculiar combination of high wages and cheap fuel that made labor-saving machines pay in Britain before anywhere else. Why Britain and not the equally clever Netherlands or China, why 1800 and not 1500 or 1900, the historians contest without resolution. And the escape, once begun, spread unevenly across the globe — which is the story, later in this volume, of who has caught up and who has not.

The first formal theories of modern growth, framed by Roy Harrod and Evsey Domar on either side of the Second World War, gave the natural answer: growth comes from accumulation. A society that saves and invests a larger share of its output builds more capital — more factories, machines, roads, and tools — and more capital, set to work, yields more output. The relation can be written as a single ratio: the rate of growth equals the share of output saved, divided by the amount of capital it takes to produce a unit of output. Save a fifth of output, with four units of capital behind each unit of product, and the economy expands at five percent a year. Growth, on this view, is the reward a society earns for its thrift — for consuming less now so as to build the apparatus of producing more later.

Here a paradox from the previous volume must be faced and reconciled. There, thrift was a danger: in a slump, a society that tried to save more only cut its own spending, deepened the shortfall of demand, and impoverished itself — the paradox of thrift, by which the virtue of the household becomes the vice of the nation. Here, across the long run, thrift is the very engine of advance. The contradiction is only apparent, and its resolution is one of the deepest lessons in macroeconomics. In the short run, when resources stand idle, saving subtracts from the demand that would put them to work; in the long run, at full employment, saving is precisely what frees resources from making consumption goods to make the capital goods that enlarge tomorrow's output. The same act — abstaining from consumption — is a withdrawal of demand on one horizon and a fund for investment on the other. Thrift ruins the year and makes the century, and which face it shows depends entirely on whether there is slack to be taken up or scarcity to be eased.

The Harrod-Domar theory carried a troubling feature within it, though, that hinted at its incompleteness. Its growth was unstable — balanced, in Harrod's image, on a knife-edge. The rate at which firms' past investment turns out to have been justified need not equal the rate at which the labor force and its productivity actually grow, and any gap between the two does not close but widens: invest a touch too little and the economy spirals down into idleness, a touch too much and up into overheating, with no restoring force to return it to balance. The model gave no account of how an economy might find and hold a path of steady growth — and the suspicion it raised, that there might be something missing from a theory in which capital simply piled up in fixed proportion to output, was the opening through which Solow would walk.

The answer came in 1956, in a model by Robert Solow — built at much the same time by Trevor Swan — that has organized the study of growth ever since. Output is made from capital and labor; capital is subject to diminishing returns, so that each new machine added to a fixed workforce yields a little less than the one before; saving, a fixed fraction of output, funds the investment that adds to the capital stock; and the stock is eaten at the edges by depreciation, and diluted as it is spread across a growing population. The model poses one question and answers it with unusual force: where does this process of accumulation finally come to rest?

It rests at the steady state. As capital per worker rises, output per worker rises too, but along a curve that flattens — diminishing returns again — so that the saving drawn from that output also rises ever more slowly. Against this stands the investment merely required to stand still: enough to replace what depreciates and to equip each new worker, a requirement that climbs in steady proportion to the capital already in place. Where the slowing curve of saving meets the rising line of this break-even requirement sits a single level of capital per worker — call it k-star — that the economy approaches and then holds. Below it, saving more than covers the upkeep, and capital deepens; above it, saving falls short, and capital thins. At k-star itself, all investment goes to mere maintenance, and growth in output per head comes to a stop. The figure assembles the pieces: the production curve, the saving curve beneath it, the straight break-even line, and the rest where the last two cross.

The implication is profound and deflating. A higher saving rate raises the level of the steady state — a thriftier nation comes to rest richer, on a higher plateau — but it does not raise the long-run rate of growth, which, absent something the model has not yet named, is zero. Thrift buys a once-and-for-all ascent to a loftier resting place, not a permanently swifter climb. The accumulation that the previous plate's theory had enthroned cannot, by itself, be the engine of sustained growth: an economy that does nothing but save and build arrives, however richly, at a standstill. And since the world plainly does not stand still — since output per head has risen without pause for two centuries — there must be some other force, outside the accounting of capital and labor, that drives the endless rise the hockey stick records. Solow's own measurements would put a name to it.

Having shown in theory that accumulation must run out, Solow turned in 1957 to measurement, and gave the field a tool as durable as the model: growth accounting. The growth of output can be carved into parts. Some of it comes from more capital, and that part is weighted by capital's share of income — by how much of what is produced is paid out to capital. Some comes from more labor, weighted by labor's share. And whatever remains, the growth in output not accounted for by the growth in measured inputs, is a residual: a rise in the productivity of inputs taken together, the same hands and machines somehow yielding more. The residual has a name, total factor productivity, but the name conceals more than it reveals.

When Solow ran the numbers for the United States across the first half of the twentieth century, the result was a quiet bombshell. The residual was not a minor correction but the main event: something like seven-eighths of the growth in output per worker was explained by neither more capital nor more labor, but by the unaccounted remainder. Most of growth, that is, came from a source the inputs did not capture — from technological progress, broadly read: better techniques, better tools, better ways of organizing work, the steady learning of how to do more with the same. Moses Abramovitz, finding the like, gave the residual the phrase it has worn ever since — a measure of our ignorance — a name for what we cannot explain, costumed as a quantity we can. The figure shows what the residual is: not a movement along the production curve, which is mere accumulation, but the curve itself rising, lifting output at every level of capital.

The finding remade the subject. Growth is mainly about productivity, not accumulation; about ideas and technique, not thrift alone — the engine is not the building but the knowing what and how to build. Yet the triumph was also a confession. In Solow's model the technological progress that drove almost everything was exogenous — manna falling from outside the economy at a rate the model took as given and never explained. To attribute most of growth to a residual is to admit that most of growth is unexplained. And the residual is a capacious sink: it swallows not only true invention but every input mismeasured — the rising quality of machines and workers, the shifting of resources from farm to factory to office, the loosening or tightening of competition and regulation — so that it is less a clean reading of technology than a holding pen for all we have failed to count. To open it, and to see what lay inside, became the great project of the generation that followed.

To open the residual was the work of endogenous growth theory, framed by Paul Romer in the nineteen-eighties and pursued alongside Robert Lucas and others. Its ambition was to bring technological progress inside the model — to make it something the economy produces rather than receives. If growth is driven by technology, and technology is at bottom a stock of ideas, then the rate of growth is the rate at which a society discovers new ideas; and that rate is not manna but a choice, depending on how many people and how much of its resources the society devotes to the search, and on the incentives that reward or starve it. Technology, on this view, is endogenous — an outcome of economic decisions, sensitive to the price of research and the protection of its fruits.

The heart of the theory is an observation about what kind of good an idea is. Ordinary goods are rival: if I use this machine or eat this loaf, you cannot. Ideas are nonrival. A blueprint, a formula, a method, once discovered, can be used by everyone at once, everywhere, forever, without being consumed or diminished — a theorem proved in antiquity is as available to us today as to the day of its proof, undimmed by all the using. Nonrivalry is the deep reason ideas escape the diminishing returns that doom mere accumulation: one cannot exhaust an idea by applying it, and each new idea adds permanently to a common stock that the next discoverer may build upon. Growth powered by nonrival ideas need never reach a plateau, because its fuel, unlike capital, does not deplete with use — it accumulates without bound, and compounds.

But nonrivalry exacts a price, and the price is paid in the coin of competition. If an idea costs a great deal to discover and almost nothing to use once discovered — the marginal cost of an existing blueprint being near zero — then it cannot be both priced at that marginal cost and made to repay its discovery. Sell the idea for what an extra copy costs, and the inventor never recovers the cost of inventing; let the inventor charge more, and one has stepped outside the world of perfect competition in which everything sells at marginal cost. Ideas therefore bring increasing returns — double every input and reuse the existing stock of knowledge, and output more than doubles — and they require some shield of monopoly, a patent or a secret or the lead of the first mover, to make their creation pay. Here the theory of growth runs headlong into the theory of market failure: the production of ideas is inescapably imperfectly competitive, bound up with the market power of The Power; and because knowledge spills beyond its maker, its return to society exceeding its return to the maker, a free market left alone will discover too little of it — the externality of The Externality, met now as the central fact about the engine of growth.

The capital of an economy is not only its machines and its buildings. It is also its people — or rather, the productive capacity lodged within them: the skills, the knowledge, the health, the experience accumulated through schooling and training and care. This is human capital, named and developed by Theodore Schultz and Gary Becker, measured against earnings by Jacob Mincer, and made an engine of growth by Robert Lucas. The insight is to see a year of schooling or a course of training as an investment like any other — a cost borne now for a return reaped later, in the higher output a more capable worker produces — so that the worker becomes, in the cool eye of the theory, a stock of capital that happens to be embodied in a person, built up at expense and yielding a return over a working life.

Folded into the theory of growth, human capital earns its place. The Solow model augmented with it — the work of Mankiw, Romer, and Weil — fits the cross-country record better than the bare model, for rich nations are rich in both kinds of capital, and much of the gap between nations in income tracks the gap between them in schooling and skill. Lucas made human capital an engine in its own right, and gave it an externality: an educated person raises not only her own productivity but, by the knowledge she shares and the example she sets, the productivity of those around her — so that human capital, like the ideas of the previous plate, throws off spillovers and increasing returns that a market acting on private motives alone will underprovide. Education is thus a double thing: a private investment, undertaken for the earnings it brings, and a public good, conferring benefits on others that the investor neither captures nor counts.

The doctrine ties this volume to others and reaches its own limits. It binds growth to The Wage, where the return to a year of schooling — the Mincer return — is the very price the labor market sets on human capital, and where the hard question waits whether schooling builds productivity or merely signals a talent the worker already had. If education chiefly signals, sorting the able from the rest rather than making anyone more able, then its private return to the individual exceeds its return to society, and its power to drive growth is weaker than the wage data suggest. Health, too, is human capital — a population freed from disease is a more productive one, and the long conquest of illness is a growth story as much as a humane one. Yet human capital, like physical, meets its own diminishing returns: a society cannot raise its income without end merely by adding years to its schooling, and the endless climb, here as everywhere, finally requires the nonrival ideas of the plate before.

The Solow model makes a clean and hopeful prediction. Because capital meets diminishing returns, a poor country — starting with little of it — should earn a higher return on each new unit than a rich country already sated with it, and so should draw investment and grow faster, catching up. Poverty, on this logic, is a disequilibrium: a country below its steady state, climbing toward it, and climbing fastest when it is furthest below. The poor should converge upon the rich, the gap between them closing as the latecomers run the steeper part of the curve. The figure draws the hope: a poor economy growing faster than a rich one and gaining on it over time.

The prediction is half right, and the half it gets wrong is the larger. Convergence holds, but only conditionally: among countries with similar fundamentals — like rates of saving, like institutions, like schooling — the poorer do grow faster and close the gap, as Western Europe and Japan closed theirs upon the United States after the war, as the East Asian tigers and later China and India have closed theirs in a single generation. But unconditional convergence, convergence across all countries regardless of their fundamentals, simply fails. For two centuries the dominant fact ran the other way: the great divergence, the fanning-out of national incomes as the industrializers raced ahead and much of the world stood still, widening the ratio between the richest and the poorest from perhaps four to one into something nearer fifty to one. The poor catch up only if they come to share the conditions that sustain growth — which throws the question back upon why those conditions are so unevenly held.

Why might a poor country fail to converge, and stay poor? The answer is the poverty trap — a self-reinforcing low equilibrium, the long-run cousin of the multiple equilibria met in the volume on the cycle. Low income yields low saving and little schooling, which yield little capital and skill, which yield low income again, the circle closing on itself. Or low income breeds poor health and high fertility, which press income per head back down — the Malthusian snare, modernized. Or no firm invests because no other firm does, and no infrastructure is built because no demand awaits it — a coordination failure, in which each waits for the others. A trap of this kind cannot be escaped by small steps; it wants a great coordinated leap, a big push, to vault the economy from the bad equilibrium to a good one. Whether such a push can be supplied from outside is among the bitterest disputes in development economics — Jeffrey Sachs urging that aid can lift the poorest over the wall, William Easterly answering that aid more often entrenches the very institutions that built the trap.

The engines this volume has studied — capital, ideas, human capital — are proximate causes. They tell us how output grows, but not why some societies set the engines running while others, no less able, leave them idle. The deepest question of growth is the question of ultimate causes: what fundamental features of a society determine whether it accumulates, invents, and educates — whether, in the phrase that names the whole subject, its effort compounds across the generations or merely repeats. Three families of answer have long contended for the place, and they go by the names of institutions, geography, and culture.

The leading modern answer is institutions, descended from Douglass North and pressed hardest by Daron Acemoglu and James Robinson. Growth, on this account, requires arrangements that secure property, enforce contracts, reward enterprise, and restrain the powerful from simply seizing what the productive create — inclusive institutions, which open opportunity to the many. Where institutions are instead extractive, built to funnel a society's wealth to a narrow elite, with property insecure and power unchecked, no one has reason to invest or to innovate, and the society stagnates or preys upon itself. Institutions explain, on this view, why the same technology yields prosperity in one place and poverty in another; why North and South Korea, one people sundered by a line, diverged so totally from a common start; why a reversal of fortune left once-rich regions poor and once-poor regions rich, tracking the institutions that colonizers found it convenient to impose. Nations fail, on this telling, because their institutions are built to extract rather than to enable.

Against the institutional view stand its two great rivals. Geography — urged by Jared Diamond and by Jeffrey Sachs — points to what a society did not choose: its climate and its burden of disease, the fertility of its soil and its reach to the sea, the accident of which plants and animals could be domesticated where, advantages and afflictions that shaped which peoples could prosper and that linger in the divide between the temperate zones and the tropics. Culture — urged by Max Weber long ago and by Joel Mokyr and Gregory Clark more recently — points to values and beliefs: attitudes toward work and thrift, toward schooling, toward science and the new, the culture of growth that Mokyr argues underlay the European miracle, a willingness to tinker and to question that some societies nurtured and others suppressed. The trouble is that the three are knotted together past untangling — institutions shape culture and are shaped by geography, and all three are bound up with the very prosperity they claim to explain — so that to say which is cause and which effect defeats the ordinary instruments of the discipline. The deepest question of growth is also its least resolved.

Growth consumes resources and burdens the world that yields them; can it continue against a finite planet? The fear is Malthus returned in modern dress. The Limits to Growth, the much-debated report of the Club of Rome in 1972, projected that exponential growth in output and population would overshoot the earth's carrying capacity and collapse — the old snare set on a planetary scale. Against it stands a stubborn record: every prior prophecy of resource exhaustion has so far been confounded by ingenuity, by new resources and substitutes and rising efficiency, as the famous wager between Julian Simon and Paul Ehrlich was confounded, the prices of the scarce metals falling rather than rising over the bet's ten years, the optimist collecting. The figure draws the contest: one path of growth unbounded, ingenuity forever outrunning scarcity; the other bending to a ceiling, the limit real at last. Climate change has sharpened the question to a point, for the very burning of fossil fuel that powered the escape from the Malthusian trap now threatens a ceiling of a different kind — not the exhaustion of an input but the accumulation of a harmful output, the atmosphere the global commons of The Commons and carbon the great externality of The Externality.

Even if growth can continue, should it be the overriding aim? Here the discontent turns from the possible to the desirable. The Easterlin paradox observes that above some threshold of income, rising output seems to buy little added happiness: within a nation the rich report themselves more satisfied than the poor, yet as whole nations grow richer across the decades their reported well-being climbs only feebly. The evidence is genuinely contested — others find that income goes on lifting satisfaction, if only in proportion to its logarithm — but if the paradox holds, if affluence past sufficiency does not make people happier because what they prize is their standing relative to others, or because their wants swell to meet their means, then the relentless chase after more output is in part a chase after nothing. The degrowth movement carries the thought to its end: that rich societies should aim not to grow but to flourish within limits already ample.

And the gains of growth may not be shared. An economy can grow while its median citizen stands still, the increase captured by a few — the question of The Share, which this group of volumes takes up next — and the costs of growth, the despoiling of nature and the disruption of settled communities by the creative destruction that drives it, fall unevenly on those least able to refuse them. Yet when all the discontents are weighed, the balance does not tip against growth so much as qualify it. Growth has been, on the whole, the greatest force for the relief of human misery the species has ever found: it has lifted billions out of the poverty that was, for all of prior history, the universal human condition, and in the still-poor world the moral case for more of it is overwhelming. Growth is a means, though, not an end — its only warrant is human flourishing — and where it ceases to serve that end, where it wrecks the planet or buys no happiness or enriches only the few, the case for it weakens. The volume holds both truths at once: growth as humanity's great escape, and growth as a process with costs and limits that the escape must yet reckon with.

Eleven plates have circled the long ascent, and it is time to say plainly what the circling has found. Economic growth — the sustained rise of output per person — is, at bottom, the discovery and diffusion of useful ideas, embodied in ever more capable tools and ever more skilled people, and either nurtured or stifled by the institutions a society happens to have built. It is the one economic process that compounds, and in compounding it remakes the material world. The ascent and the long stagnation behind it; the Malthusian snare and the great escape; accumulation and the plateau at which it halts; the residual and the ideas found within it; human capital, the worth built into people; convergence and the great divergence; the deep roots of institution and geography and culture; the ceiling that may or may not bound it all — each was a facet of this single, civilization-altering thing.

Where, mechanically, does the climb come from? The engines fall into an order the volume has established. More capital matters, but capital meets diminishing returns and carries a society only to a richer rest — the plateau, not the endless climb. More skilled people matter, but human capital meets limits of the same kind. The endless rise is sustained, in the end, by one thing only: rising productivity, the getting of more from the same — and that is ideas, the nonrival knowledge that escapes the diminishing returns which bind everything physical. Growth, measured, is mostly a residual; the residual, opened, is mostly ideas. Accumulation builds the body of an economy; ideas are its growing mind, and it is the mind that does not stop growing.

Beneath the engines lie the ultimate causes — the institutions, the geography, the culture that decide whether a society runs its engines or lets them rust, whether its effort compounds across the generations or merely repeats. This is the deepest layer the subject has reached and the least settled: we know that institutions matter, that geography and culture matter, but not how to disentangle the three, nor how to plant the good ones where they do not already grow. The frontier of growth is the frontier of why some societies grow at all — and it remains, for all the discipline's labor, largely dark.

What, then, can the study of growth claim, and what must it concede? The triumph is real and large. It has named the proximate sources of the climb and established the primacy of productivity over mere accumulation; it has uncovered the strange economics of ideas, nonrival and increasing in their returns; and it has helped to guide the policies — of saving and schooling, of openness and secure property — that have accompanied the steepest reduction in poverty the species has ever known. The humility is just as real. Most of growth remains a residual we can name but not explain; we cannot reliably kindle growth where it is absent, as a hundred failed prescriptions attest; we did not foresee the miracles of East Asia or the long stagnations beside them; and the deepest question of all — why the Industrial Revolution came when and where it did, why some nations escaped the snare and others did not — is genuinely, stubbornly open. Growth is understood in its mechanics and mysterious in its ultimate springs.

Why does so much rest on the answer? Because growth compounds, and compounding, given time, dominates everything. The cycle of the previous volume subtracts for a year; growth multiplies for a century, and the century always wins. The chasm between the rich world and the poor, and the chasm between the present and the past, are overwhelmingly the work of growth — of who got the compounding engine running, and when. This is why, by the measure that finally matters, the welfare of human beings across the long run, growth is the most important subject in all of economics; and why getting it right, or wrong, in the regions where billions still live near the old subsistence, is among the highest-stakes questions any society will ever face.

The figures of this volume have all stood still. This last one moves, because compounding is best understood by watching it run. Below, a single sum is invested and left for forty years — once at compound interest, where each year’s gain itself earns in the years that follow (the bold curve), and once at simple interest, where only the original sum ever earns (the faint line). At a low rate the two scarcely part. Raise the rate and the bold curve pulls away and then leaps while the faint one plods; the doubling comes sooner and sooner, and the final multiple climbs out of all proportion to the rate. This is the whole of why a century of growth dwarfs a year of it, and why a small difference in the rate is, given time, an enormous difference in the end.

Annual rate of growth

Doubles in—

Compound, 40 yr—

Simple, 40 yr—

Compounding’s lead—

And yet the volume has refused to make growth an idol. It is a means, not an end; its sole warrant is the flourishing of human beings, and it must answer for its costs — the resources it draws down, the climate it unsettles, the communities its creative destruction uproots, the gains it may fail to share. Whether it can continue against a finite planet, and whether past sufficiency it still serves the flourishing that is its only justification, are questions the discipline cannot settle alone. The honest position holds both halves at once: growth as humanity's escape from the universal poverty of all the ages, and growth as a process whose continuation and desirability are not assured.

This is the second volume of The Aggregates, and it stands in a fixed relation to the first. The cycle is the wobble; growth is the trend the wobble moves around — and the two together, the long climb and the short oscillation, compose the real path an economy travels through time. The threads run outward in every direction. Back to The Cycle, whose recessions are dips in this volume's rising line, and whose real-business-cycle theorists read the slump itself as a stumble in the very residual studied here, seen at short range. Forward to The Level, the price level and its inflation — the nominal companion to this volume's real concern, the two of them the great trends of the macroeconomy. To The Share, which asks how the fruits of growth divide, for a growth that enriches only the few is a hollow triumph. Down to the institutions of The Firm, The Contract, and The Rule, where the inclusive arrangements that let a society's effort compound are studied close. And to The Wage, where the human capital this volume accumulates is, at last, given its price.

What, in the end, makes a people richer than their grandparents? Ideas, mostly — the slow, compounding accumulation of useful knowledge, nonrival and shared, embodied in better tools and abler hands, set running or stifled by the institutions a society has built. And what does it ask of them? Saving and schooling; openness to the new and the foreign; the security of property and the rule of law; and a tolerance for the creative destruction by which the better drives out the good. Growth is neither automatic nor assured — it is the rarest condition in human history, achieved by a sliver of societies in a sliver of time, and its springs are understood only in part. The aggregate, like every quantity this atlas has weighed, turns out to be a verdict on a hidden contest: between scarcity and ingenuity, between the diminishing returns that would halt every accumulation and the expanding returns of ideas that escape them, between the prosperity that growth confers and the costs that it exacts, between the freedom to create and the limits within which creation must finally work. The argument remains open.