The Steady State

If growth is the great exception, the first task of a theory is to ask where it comes from — what, exactly, makes output per person rise. The most natural first answer, and the one the first rigorous model of growth pursued, is accumulation: a people grows richer by building up its stock of capital — the tools, machines, buildings, and infrastructure with which it works. Give each worker more and better equipment, and each produces more; accumulate enough capital, and the whole economy's output per person rises. This is the intuition behind the Solow model, the foundation of modern growth theory; and the model's lasting achievement was to take this intuition seriously, follow it to its conclusion, and discover that it fails — that accumulation alone cannot account for sustained growth, and that the real source of growth lies elsewhere.

The flaw in accumulation as an engine of growth is diminishing returns. Give a worker who has no tools his first tools, and his output leaps. Give a well-equipped worker still more equipment, and his output rises by less; pile capital ever higher upon the same worker, and each additional machine adds less than the one before, until further capital adds almost nothing — a worker can use only so many machines. Capital, like any input added while others are held fixed, runs into diminishing returns, the principle the margin first taught. And this has a fatal consequence for growth by accumulation: as a country builds up its capital, the return to each new increment shrinks, so the boost to output from accumulation slows. Worse, capital wears out, and a richer economy with more capital must spend more just replacing what depreciates. Eventually the society reaches a point where all its saving goes merely to replace worn-out capital, with nothing left over to add to the stock — and there, accumulation stops, and with it the growth that accumulation produced.¹

This is the central prediction of the Solow model: the steady state. An economy growing by accumulation does not grow forever; it approaches a standstill, a steady state in which capital per worker, and output per worker, stop rising — held there because all saving goes to replacing depreciation, leaving no net accumulation. The economy can reach a higher steady state by saving more, since more saving builds more capital before depreciation eats it; but even then it merely climbs to a higher plateau and stops. A higher saving rate raises the level of income, not the permanent rate of growth, which returns to zero at the new steady state. The model makes a second, striking prediction: convergence. A poor country, with little capital, earns high returns on each new increment, capital being scarce there, and so should accumulate fast and grow fast, catching up to rich countries, whose abundant capital earns low returns and grows slowly. Among economies alike in all but their capital, the poor should grow faster than the rich and converge toward them. Both predictions — the steady state and convergence — follow from diminishing returns, and both turn out to be the model's undoing as a complete theory of growth.²

The trouble is that the world does not behave as a model of pure accumulation predicts. Rich countries have not slowed to a standstill; they have gone on growing, decade after decade, their output per person rising long past the point where diminishing returns to capital should have stopped them. If accumulation were the whole story, growth would have petered out as capital piled up; instead, sustained growth in output per person is the central fact of the modern world. And the convergence the model predicts is, at best, partial: some poor countries have caught up, but many have not, and the gap between the richest and poorest nations has widened over the past two centuries, not narrowed, contrary to what diminishing returns alone would imply. The Solow model, taken as a theory of what causes growth, is contradicted by the persistence of growth and the persistence of poverty alike. Something keeps the rich growing past the steady state, and something keeps the poor from converging — something the model of accumulation does not contain.³

Solow himself supplied the decisive evidence, and it is the model's most important legacy. He asked: of the growth in output per worker that America had actually experienced, how much could be explained by the accumulation of capital — by workers having more equipment? The answer, astonishingly, was: only a small fraction. Most of the growth — by his reckoning, the great majority — could not be accounted for by more capital, or more labor, at all. It was a residual, the part of growth left over after accumulation had been credited with all it could explain. Solow attributed this residual to technological progress — to workers producing more not because they had more tools but because they had better methods, better knowledge, better technology. This residual, the part of growth that accumulation cannot explain, came to be called total factor productivity, and, more honestly, the measure of our ignorance: a name for the source of most of growth, defined precisely by our inability to reduce it to the accumulation of things. The model's greatest achievement was thus a negative one — to prove, by careful accounting, that the engine of growth is not accumulation but something else, something the model could label but not explain.⁴

The steady state, then, leaves the theory of growth with a precise and pointed question. Accumulation — the building up of capital — cannot be the engine of sustained growth, because diminishing returns drive it to a standstill; and the accounting confirms that most of the growth we actually observe comes not from accumulation but from the residual, from technological progress, from the improvement of methods rather than the multiplication of machines. So the real question of growth is the question of the residual: what is this technological progress, where does it come from, why does it keep coming in some places and not others? The Solow model treats the residual as falling like manna — exogenous, unexplained, arriving from outside the economy at some given rate. The work of later growth theory was to open this black box, to ask what is inside the residual and why it grows; and the answer, when it came, was that the residual is the accumulation not of things but of ideas, which obey laws entirely different from the diminishing returns that doom accumulation. Before that deepest answer, two plates examine the residual at work: how new methods displace old, and how some nations acquire the methods others invent. The next plate is the churn.⁵

The Solow model is the foundation of growth theory and the proof of its central negative truth. Accumulation — giving each worker more capital — raises output, but by less and less, until diminishing returns bring the economy to a steady state, a standstill where saving only replaces what wears out and growth ceases. Save more, and the economy climbs to a higher plateau, but not to a higher permanent rate of growth. The model thus cannot explain the sustained growth of the modern world, which has run on long past any steady state; and Solow's own accounting showed why, by proving that most of the growth we observe is not accumulation at all but a residual — technological progress, the improvement of methods — that the model could name but not explain. The engine of growth lies in the residual, and the residual is a black box the rest of the volume must open. Accumulation builds the body of the economy; but the thing that makes it grow without end is not in the body. The next plate is the churn.