The Stock

A stock is a quantity measured at a single instant; a flow is a quantity measured over an interval of time. The difference is in the very unit. A stock's unit carries no reference to time — a sum of dollars, a number of machines, a tonnage of grain, a holding of money: what one has, frozen at a moment. A flow's unit carries a span of time within it — dollars per year, machines built per quarter, grain harvested per season: what passes, reckoned over an interval. The stock is a photograph, capturing what stands at an instant; the flow is the film, recording what moves through time. What you own is a stock; what you earn is a flow. The two are as different as a quantity and its rate of change, and keeping them distinct is the beginning of all clear economic thought.

The distinction sounds elementary, and confusing its two sides is nonetheless the commonest serious error in the subject. Wealth is a stock and income a flow, and a person may hold great wealth while earning little, or earn a large salary while holding nothing, so that to judge a person's standing by their income alone is to mistake the flow for the stock. The public debt is a stock and the deficit a flow, and to speak as though reducing the deficit reduced the debt is to confuse the level of a reservoir with the rate at which it fills. Money is a stock and spending a flow; capital is a stock and investment a flow. In each pair the same trap waits: to read a quantity at a moment as though it were a quantity through time, or the reverse — and to misunderstand, at the root, both who has what and how it came to be.

Yet stock and flow, though distinct, are inseparably bound, and the bond is time. The flow accumulates into the stock: every stock is the running sum of the flows that have fed and drained it, the integral of its own history. And the stock generates flows: capital yields the flow of output, wealth the flow of income, a reservoir the flow drawn from it. A quantity at a moment and a quantity through time are the two faces of a single thing seen in two ways — the level and the motion, the standing and the passing. The plates that follow examine the great stocks of economic life — capital above all, and wealth, and money, and inventory — tracing how each is accumulated by the flows that fill it, how each is valued by the flows it will yield, how each wears away, and what discipline it takes to keep the stocks and the flows from ever being confused.

A stock comes to be by accumulation — the piling up, over time, of the flows that feed and drain it. The image that holds the whole idea is the reservoir, or the humble bathtub: the level of water in it is a stock, a quantity at a moment; the tap pouring in and the drain running out are flows, quantities through time; and the level rises whenever the inflow exceeds the outflow, falls whenever the outflow exceeds the inflow, and holds steady when the two are matched. The figure draws it. The stock standing in the tub at any instant is nothing other than the running sum of every inflow it has received, less every outflow it has lost — the net flow, accumulated over all past time.

Every economic stock is such a reservoir. The capital of a nation is the accumulation of its past net investment, filled by the building of new plant and drained by the wearing-out of the old. The public debt is the accumulation of its past deficits, filled each year that spending exceeds revenue. A household's wealth is the accumulation of a lifetime's saving, filled by what is set aside and drained by what is drawn down. In every case the stock is the past made present — the whole history of the flows, congealed into a single quantity that can be held and counted at an instant. To know the level is to hold a summary of everything that has flowed; the reservoir remembers what the flows themselves, passing, forget.

The relation is, in exact terms, that of the integral and the derivative. The stock is the integral of the flow — its accumulation over time — and the flow is the derivative of the stock — its rate of change at each moment. This is why a stock can be vast though its current flow is a trickle, a great reservoir filled drop by drop across ages; and why a stock can be falling even as a positive flow continues, if the drain exceeds the tap. The level tells the history; the flow tells the present motion. To know a stock fully, one must know the whole past that accumulated it; to foresee its path, one must know the flows that will move it. The calculus of accumulation is the grammar that binds every stock to its flows.

Capital is the central economic stock — the produced means of production, the tools and machines and buildings and structures accumulated by past investment and set to work making more. What sets it apart from the other factors of production, from the labor of the wage and the land of the rent, is that capital is itself produced: it is at once an output of past production and an input to future production, a stock that the economy makes in order to make with. Eugen von Böhm-Bawerk caught its essence in a phrase — capital is roundaboutness, the productive detour through time. We forgo consuming now in order to build the tools that will let us consume more later; the deferral, embodied in a stock of equipment, is what capital is.

How much capital should be held? The figure gives the marginal answer. Capital, like any factor, is subject to diminishing returns: the marginal product of capital — the extra output won from one more unit of it — falls as the stock grows, the curve sloping downward. Against this stands the cost of capital — the price of using a unit of it for a period, which is the interest forgone on the funds it ties up plus the depreciation it suffers, together its user cost, drawn here as a horizontal line. The desired capital stock is where the two meet: hold capital up to the point where the marginal product of the last unit just equals what it costs to hold, and no further. Beyond that point each added unit costs more than it yields; short of it, another unit would more than pay its way.

The concept has grown far beyond machines, and the growth is one of the great facts of modern economics. Human capital — the skills and knowledge embodied in people, accumulated through education and experience, the subject of the wage — is now reckoned the largest stock of all in advanced economies, dwarfing the physical. Intangible capital — software, knowledge, brands, patents, the organizational capacity of firms — has come to rival and surpass plant and equipment in value, and is far harder to see, let alone to count. Natural capital — the stock of environmental resources of the commons — is increasingly entered in the accounts. In every case the logic of the stock is the same: an asset accumulated by past investment, yielding a flow of services across time. But the further the concept stretches from the visible machine, the harder the stock becomes to measure — which is the trouble the next plates pursue.

The deepest question about any stock is what it is worth, and Irving Fisher gave the answer that organizes the whole of asset valuation: the value of a durable asset — any stock that yields a flow of income or service over time — is the present value of that future flow. The asset is worth the sum of all the yields it will deliver, each one discounted back to the present by the rate of interest, so that a dollar promised next year counts for somewhat less than a dollar in hand, and a dollar promised in a distant year for much less. A stock's value, on this principle, is simply its future, brought back to now and added up.

The principle is universal, the single key to the price of everything durable. A machine is worth the discounted stream of the outputs it will produce; a bond, the discounted stream of its coupons and its repayment; a parcel of land, the discounted stream of its rents, which is the capitalization of the rent volume; a share, the discounted stream of its dividends; a whole firm, the discounted stream of its profits; even the human capital embodied in a person, the discounted stream of their future earnings. In every case the price of the stock today is a forecast of flows tomorrow, collapsed into a single number by the act of discounting. The figure shows why the horizon matters so: one dollar received far in the future is worth very little today, the discount factor falling away toward nothing as the years recede.

This is the exact mirror of accumulation, and together the two complete the stock's relation to time. The reservoir showed the stock as the past made present — the integral of the flows that have filled it. Valuation shows the stock as the future made present — the discounted sum of the flows it will yield. The rate of interest of an earlier volume is the hinge between them, the rate at which the future is converted into the present and the present compounded into the future. A stock thus stands at the meeting of two times, accumulated out of the past and valued by the future, and its physical quantity — so many machines — and its money value — so many dollars — are bridged only through the interest rate and a forecast of what is to come. The stock is a knot tied in time.

To speak of "the capital stock" of a firm or a nation as a single number — the quantity of capital that enters a production function and earns its marginal product — one must add the capital up. And here the most basic of the stocks meets its most basic difficulty: capital is heterogeneous. Lathes and looms, locomotives and office towers, drills and warehouses cannot be summed in physical units, for there is no common physical measure of a press and a building. They can be added only in value — in dollars, by their prices. The capital stock, unlike a tonnage of grain or a count of workers, exists as a single quantity only when reckoned in money. And in that necessity lies the trouble.

For to value the capital goods, one needs their prices; and the price of a capital good is, by the valuation of the last plate, the present value of the future income it will yield — which depends on the rate of interest. But the rate of interest is itself the rate of return on capital, the very thing the quantity of capital was supposed to help determine. So the measurement of the capital stock presupposes the rate of interest, and the rate of interest presupposes the capital stock: the aggregate quantity of capital cannot be measured independently of the distribution of income between capital and labor that it was invoked to explain. The measuring rod is made of the very substance it is meant to measure, and the circle will not open.

This circularity erupted into one of the great disputes of twentieth-century economics, the Cambridge capital controversy — Cambridge in England, where Joan Robinson and Piero Sraffa pressed the attack, against Cambridge in Massachusetts, where Paul Samuelson and Robert Solow defended the aggregate. The English Cambridge showed that the textbook production function, with its single quantity of capital earning a well-defined marginal product, rests on assumptions that need not hold. The phenomenon of reswitching settled it in logic: the same technique of production can be the most profitable one at both a low and a high rate of interest and yet not at the rates between, so that there is no orderly, one-directional relation between the "quantity of capital" and the rate of return — and hence no coherent aggregate capital that behaves like a factor with a definite marginal product. The Massachusetts Cambridge largely conceded the logic, and largely went on using aggregate capital all the same.

Investment is the flow that builds the capital stock — the construction of new plant, the purchase of new equipment, the raising of new structures. Gross investment is the whole of it; net investment is gross investment less depreciation, the actual addition to the stock once the wearing-out of the old is allowed for. What determines how much is undertaken? At the margin, the answer is the desired-stock logic of the capital plate: a firm invests up to the point where the return on the marginal unit of new capital equals its cost. James Tobin gave the same condition a financial face in the ratio that bears his name — invest while the market value of installed capital exceeds the cost of replacing it, while his q stands above one — for then the market is saying that a dollar of new capital is worth more than a dollar.

But the most striking fact about investment is its violence, and the accelerator explains it. Suppose firms hold a capital stock proportional to their output — so much plant for so much production. Then investment, which is the change in the capital stock, depends not on the level of output but on its change. The figure draws the consequence, and it is dramatic. When output grows steadily, investment is positive but steady; when output's growth merely slows — not output falling, only its rise flattening — investment drops sharply; and when growth resumes, investment surges. A small wobble in the rate at which output grows becomes a large swing in investment. Investment is, in effect, the derivative of a desired stock that tracks output, and the operation of differentiation magnifies every change.

This is why investment is the most volatile component of output and a principal engine of the business cycle of a later volume. Because investment responds to the change in output, and its own swings in turn change output, the accelerator and the multiplier can drive each other into booms and slumps: rising output spurs investment, which lifts output further, which spurs investment more — until growth slows, investment collapses, and the spiral runs in reverse. The flow that builds the patient, slow-moving stock of capital is itself the most impatient and restless quantity in the whole economy, and its restlessness, amplified by the accelerator and broadcast through the multiplier, is much of what makes the aggregate economy lurch from expansion to contraction and back.

Every capital stock wears out. Machines age, break, and fall obsolete; buildings decay; equipment is used up in the using. Depreciation is the flow of this wearing-away — the consumption of capital, the rate at which the stock would shrink were nothing done to replace it. It is a flow, so much capital consumed per year, and it is the dark twin of investment: where investment is the inflow that builds the stock, depreciation is the outflow that drains it, the second pipe on the reservoir. No stock of capital simply endures; left untended, it runs down, and standing still requires effort.

On this turns the distinction between gross and net investment. Gross investment is all the new capital built; net investment is gross investment minus depreciation — the actual change in the stock once replacement of the worn-out is subtracted. A nation may invest heavily in gross terms and yet add almost nothing to its capital, if most of that building merely makes good what has decayed. The difference is large in the measurement of an economy: gross product counts the building of replacement capital as output, and rightly, since the work is really done — but a society that builds only enough to replace what wears out is, in net terms, standing perfectly still, running hard to stay in place. The flow can be furious while the stock holds constant, because the inflow is exactly swallowed by the drain.

This defines the rest point of all accumulation, the steady state. The steady state is where net investment is zero — where gross investment exactly equals depreciation, and the capital stock holds constant, neither growing nor shrinking. It is the level toward which a stock tends once the forces that build it and the forces that wear it come into balance, and it is the organizing idea of the theory of growth in a later volume: an economy left to its own devices approaches a steady-state capital stock at which just enough is invested to offset depreciation and to equip its new workers. The steady state is the stock at rest — the equilibrium of the reservoir, inflow matched to outflow, the level standing still though both pipes run full. It is where the bathtub settles when the tap and the drain are reconciled.

Holding a stock is costly. It ties up resources that might have earned a return, occupies space, courts spoilage and obsolescence, and must be financed and guarded. So why hold one? Because a stock buffers the mismatch between flows. Inventory is the clearest case: production and sales are two flows that rarely match moment to moment, and inventory is the reservoir set between them, absorbing the difference — filling when production runs ahead of sales, drawing down when sales run ahead of production. The stock is held as insurance against the unevenness and the unpredictability of the flows it stands between, a cushion that lets production proceed steadily though sales arrive in fits, and lets sales be met though production comes in batches.

How much to hold balances the cost of holding against the cost of running out. Too thin a stock courts stockouts — lost sales, idled production lines, customers turned away; too thick a stock wastes the carrying cost. The optimal inventory minimizes the sum of the two, and the classic figure of inventory management — the sawtooth shown here — captures its rhythm. The stock is drawn down steadily as sales deplete it, then replenished all at once when it falls to a reorder point, then drawn down again, tracing a sawtooth across time; the average stock held works out to about half the size of each order. The economic order quantity strikes the balance between the fixed cost incurred each time one orders and the running cost of carrying what one holds.

Small as inventories are in the total stock of a nation's wealth, they play an outsized part in the business cycle of a later volume. Because firms hold inventory in proportion to their expected sales, a change in sales — or even in expected sales — triggers a magnified change in inventory investment, the accelerator over again, now applied to stocks of goods. When demand softens, firms not only produce less but run their inventories down, so production falls by more than sales did; when demand recovers, they rebuild their stocks, so production rises by more than sales. This inventory cycle — the swing from destocking to restocking — is among the sharpest and most regular of all short-run fluctuations, a small stock whose adjustments amplify the motion of the whole economy far beyond their own modest size.

Wealth is the stock of which income is the flow — the accumulated value of all that a person or a society owns, the capital and land and housing and financial claims, net of debts. It stands apart from income at every turn, as the snapshot plate insisted: one may hold a great fortune and earn little from it, an idle estate; or earn a large salary and hold nothing, a high flow spent as fast as it comes. Wealth is accumulated saving, the deposit the past has made in the present, and the way it is distributed across a society is among the most consequential of all economic facts — more consequential, in some respects, than the distribution of the income flow, because it determines not what people currently receive but what they securely command.

Wealth is almost everywhere far more concentrated than income — the stock more unequal than the flow. The reason is partly arithmetic and partly historical. Wealth accumulates, and small differences in the rate of saving and the rate of return compound over a lifetime, and across generations, into vast differences in the stock; and inheritance passes the accumulated stock forward intact, so that the distribution of wealth carries the inequalities of the past into the present in a way the distribution of income, earned afresh each year, does not. The concentration of the stock confers not merely consumption but position — security, independence, power, freedom from the discipline of the wage — so that the shape of the wealth distribution structures a society as deeply as the shape of the income distribution rewards its current effort, the theme the volume on the share will take up directly.

Thomas Piketty has pressed a relation between this stock and its flow with large consequences. When the rate of return on wealth exceeds the rate of growth of income — when r runs ahead of g — the stock of accumulated wealth tends to grow faster than the flow of income against which it is measured, and so to loom ever larger relative to it. Past accumulation then outpaces present effort: the wealth amassed and inherited from earlier times grows more important than the income earned in the present, the ratio of wealth to income climbs, and wealth concentrates further still, since the largest fortunes are the ones that compound the fastest. Whether the return reliably exceeds the growth rate, and what follows if it does, is much disputed — but the kernel is a pure piece of stock-and-flow logic: when a stock grows faster than the flow it is measured against, the stock comes in time to dominate, and a society of inherited position quietly displaces a society of earned reward.

Money is a stock — a quantity held at a moment — and spending is the flow that money finances. The money stock of an economy, the quantity of money in being at an instant, is distinct from the flow of spending it supports, the two related by the speed at which money changes hands, the subject of the volume on money. But the sharpest puzzle is at the level of the single holder. Money in its pure form earns no interest, while the bonds and assets one might hold instead do; to hold a stock of money is therefore to forgo a return. Why, then, hold any — why keep a hoard of barren cash when wealth could be held in forms that grow?

John Maynard Keynes gave the answer in his theory of liquidity preference: money is held for its liquidity — its immediate and certain usability, its readiness to be spent at any moment without conversion, delay, or loss. People hold money for transactions, to bridge the gap between income received at intervals and spending made continuously; for precaution, as a reserve against unforeseen needs and shocks; and, Keynes argued, for speculation, to wait in safety for a better moment to buy other assets. Money is the buffer stock of the previous plate in its most liquid form, a reserve held against the unevenness and uncertainty of the flows of receipt and payment. The figure shows the demand to hold it: the higher the rate of interest, the greater the return given up by holding money rather than bonds, and so the less money is held — the demand for money slopes downward against the interest rate.

The rate of interest is thus the price of holding money — the opportunity cost of liquidity, the yield surrendered for the convenience of keeping wealth in instantly spendable form. This makes the demand for money the bridge between the money stock and the interest rate, and so a hinge of monetary policy and of the determination of the interest rate itself, in the volumes on the level and on money. When money is made more plentiful, its holders, finding they now hold more liquidity than they wish at the going rate, bid for other assets, and that bidding drives the interest rate down until they are content to hold the larger stock. The willingness to hold the money stock, at each rate of interest, is the lever that monetary policy works upon. Liquidity is a service the stock of money renders, and the interest rate is the price the holder pays for it.

The discipline the whole volume has been building toward is stock-flow consistency: the requirement, simple to state and ceaselessly violated, that the stocks and the flows in any account fit together exactly — that the change in every stock equal the net of its flows, with nothing created or lost in the gap between them. Every flow comes from somewhere and goes somewhere; every stock is the accumulation of the flows that have moved it. A consistent account leaves no flow without a stock it changes and no change in a stock without a flow that caused it. This is mere bookkeeping — and it is, all the same, the most reliably violated principle in public argument about the economy.

The gravest and most familiar violation is the confusion of the deficit with the debt. The deficit is a flow — the amount by which spending exceeds revenue in a single year. The debt is a stock — the accumulated total owed, the running sum of all past deficits net of all past surpluses. The figure sets the two side by side: the deficit is the annual flow into the debt, and the debt is the integral of the deficits, the reservoir they fill. And here is the implication so constantly missed: as long as the deficit is positive, the debt grows, even when the deficit is shrinking. A falling deficit is still a rising debt — the inflow into the reservoir is slowing, but the level is still climbing. "The deficit fell this year" and "the debt has never been higher" are both true, at the same moment and forever, and the failure to hold the stock and the flow apart muddles very nearly every public argument about the public finances.

Stock-flow consistency is not a fact about governments alone but a universal accounting discipline that binds the whole of macroeconomics together. One sector's deficit is another's surplus; one agent's borrowing is another's lending; the flow of saving accumulates into the stock of wealth, the flow of investment into the stock of capital, the flow of the current account into the stock of foreign assets. The modern macroeconomic models that take this seriously — the stock-flow consistent models — insist that every flow be traced to the stock it changes and every stock to the flows that move it, so that the accounts close and nothing leaks. The discipline is humble and powerful at once: a great deal of economic confusion, and not a little bad policy, comes from losing track of whether a quantity is a stock or a flow, and from accounts that fail to balance because a flow was forgotten or a stock was counted twice. To keep the books consistent is, in the end, simply to think clearly.

A stock is the quantity held at a moment, and this volume has followed it through its forms: the snapshot set against the film; the reservoir of accumulation; capital and its valuation; the sum that cannot quite be taken; the flow that builds and the flow that wears away; the buffer held against uncertainty; wealth, and money, and the accounting that keeps them straight. It remains to ask what a stock is, taken whole — and, this being the last plate of the last volume, what the atlas of which it is the end has been.

A stock, first, is the past made present. It is the integral of bygone flows: capital the sum of past investment, wealth the sum of past saving, debt the sum of past deficits, every reservoir the running total of all that has flowed into it less all that has drained away. To hold a stock is to hold the accumulated history of the flows that made it — the present quantity is the past, congealed and counted. Stocks have inertia and memory; they move slowly where flows move quickly, and they carry forward, into every present moment, the whole record of what has been.

A stock, second, is the future made present. Its value is the discounted sum of the flows it will yield — the asset worth its coming outputs, the bond its coupons, the land its rents, the firm its profits, each pulled back to now by the rate of interest. A stock thus stands at the meeting of two times, accumulated out of the past and valued by the future, a knot tied in time and bound by the rate at which time is priced. To weigh a stock is to weigh, at a single instant, an entire history behind it and an entire imagined future before it — which is why the calmest identity in economics, that a stock is worth its discounted future, governs in practice its most restless quantity.

From this the volume's practical lesson follows, the plainest the atlas has to give: to think clearly in economics is, above all, to know whether one is looking at a stock or a flow, and never to confuse the photograph with the film. Wealth is not income; the debt is not the deficit; capital is not investment; the money stock is not spending. The commonest and most consequential errors in the subject — in public argument most of all — are confusions of a quantity at a moment with a quantity through time, and the simple discipline of asking which one is before us dissolves a remarkable quantity of muddle.

What, then, is known of the stock, and what is not? The framework is a triumph of clarity: accumulation understood as integration, valuation as discounting, consistency as bookkeeping, and from these few clean ideas the whole of capital theory, asset pricing, growth, and macroeconomic accounting is organized. And the humility is just as real: the most basic stock, capital, cannot be coherently aggregated, as the Cambridge controversy showed; the value of any stock rests on an unknowable future and a volatile discount rate, as the bubbles of the asset plate attest; and the largest stocks of the modern world, the human and intangible capital embodied in skills and knowledge, are the hardest of all to measure. The framework is lucid; the quantities it organizes remain elusive.

The Stock is the fourth and last of The Quantities, and the one most deeply bound to time. It completes the group: it stands beneath The Margin, where capital is hired to its marginal product and the stock is optimized at its edge; beside The Surplus, the value a market realizes from its trades; beneath The Utility, where the discounting of a future satisfaction is the very operation that values a stock. And it reaches across the whole atlas — to The Rate, the interest that prices time and bridges every stock to its flows; to The Wage, where labor's own stock is its human capital; to The Growth, where accumulation is the engine of all advance; to The Share, where the distribution of the stock of wealth is the deepest question of justice; to The Money and The Cycle, where the money stock and the inventory stock move the whole. The stock is the quantity in which all the times of economics meet.

What is a stock? The quantity held at a moment — and, like every quantity this atlas has weighed, a verdict on a hidden contest: between the stock and the flow, between the past accumulated and the future redeemed, between what is held and what is earned, between the moment and the time that gives it worth. To hold a stock is to hold a knot of time, the whole past poured into it and the whole future discounted back, reckoned at a single instant. The argument, here as in every volume before it, remains open.

And here a word is owed to the whole, for this is the last plate of the last volume. Twenty-six elements, ranged in six groups — the prices and the quantities, the failures and the institutions, the aggregates and the behaviors — have been set out as a periodic table of economic life: the wage and the rent and the rate, the premium and the spread; the margin, the surplus, the utility, the stock; the powers and frictions that break the markets, and the firms and contracts and monies and rules that build them; the cycles and growth and levels and shares of the whole; and the choices, biases, games, and norms of the minds within it. Each was a quantity that some price or number is supposed to measure, and each, examined closely, was found to be not a simple fact read off the world but a verdict — the settled-for-now outcome of forces held in tension. What the atlas has tried to show, element by element, is that the numbers economics reports are not neutral readings but the results of contests, and that to take them for bare facts is to miss the argument folded inside each one. The table is now full. It is offered not as a set of answers but as a way of seeing: a claim that beneath every economic quantity there lies a question, and that the question stays open. Here the atlas ends. The argument does not.