Here, I talk about capital theory as a path for macroeconomics. Some recent posts are relevant. Tyler Cowen talks about the saving-investment balance. Paul Krugman implicitly says that investment follows what I call in the installment below the “accelerator model” of investment. He seems to think that with a single graph he can prove that this model is correct, as if all problems of simultaneous equations bias and serial correlation that plague macroeconometrics can be swept under the rug by plotting two variables together. My post the other day on saving and accounting identities is, along with the installment below, my comment on the controversy that Cowen and Krugman are talking about.Capital Theory: Saving and Investment

In microeconomics, the analysis of saving and investment is called capital theory. The capital theory path is important in macroeconomics because Keynes offered a theory of economic fluctuations based on an excess of desired savings relative to investment. Austrians also explain economic fluctuations in terms of capital theory.

Suppose that an economy has a consumption good (fish) and a capital good (fruit trees). One unit of labor in the fishing industry can produce one unit of fish for consumption today. Alternatively, one unit of labor in the fruit tree industry can produce one fruit tree, which in turn produces one unit (basket?) of fruit for consumption next year. There are 100 units of labor in the economy, and consumers would like to allocate 80 percent of their income to present fish consumption and 20 percent of their income to next year’s fruit consumption.

In an economy with complete markets, also known as an Arrow-Debreu economy, the allocation of labor would be settled in a market in which consumers sign contracts today for fruit to be consumed next year. Markets will clear at prices such that 80 units of labor will be allocated to fishing and 20 units of labor will be allocated to planting fruit trees.

In a Keynesian economy, the Arrow-Debreu contracting process is not available. Instead, consumers use a rule of thumb for allocating income between consumption and saving. Meanwhile, investors undertake capital investment independently, on the basis of what Keynes called “animal spirits.”

Suppose that our Keynesian consumers allocate 80 percent of their income to consumption (fish) and 20 percent of their income to saving. Suppose that investors decide to employ 20 units of labor planting fruit trees. This decision generates 20 units of income in the “first round.” A “round” is not a period of time–I use it is a way of illustrating the multiplier process.

With an 80 percent consumption rule, consumers allocate 16 of their 20 units of their first-round income to fish. This generates another 16 units of income in the “second round.” Consumers allocate 80 percent of this to fish, which generates more income, and so on. This multiplier process will end when total consumer income is 20/0.2, or 100 units of income. At that point, saving is 20 units, investment is 20 units, and there is full employment. That is because I chose a rule of thumb for saving and a level of investment that result in exact balance.

However, what happens if the rule of thumb for saving and the level of investment are mismatched? For example, suppose that consumers have a 25 percent saving rate and investors plant 20 units of fruit trees. Then the multiplier process will be less expansive, because each unit of income will generate only 0.75 units of consumption. The initial 20 units of income will generate only 15 units of demand for fish in the “second round,” which in turn will generate (15)(.75) more units of demand in the next round, and so on. When the multiplier process is finished, total income will be 20/0.25, or 80, rather than 100. The economy will produce 20 units of fruit for next year, but only 60 units of fish for this year. The unemployment rate, or the shortfall from potential output, will be 20 percent.

Back in the Arrow-Debreu world, if consumers want to allocate 25 percent of their income to fruit next year, they sign contracts with investors to plant 25 fruit trees. This allows the economy to reach an equilibrium with 75 units of labor allocated to fish and 25 units of labor allocated to fruit trees.

The Arrow-Debreu world and the Keynesian world represent two extremes. In the Arrow-Debreu world, the signals between consumers and investors work perfectly. It is as if consumers are shopping in a market today for all the goods that they will want in the future as well as for goods today. This market tells investors exactly which capital goods they should build today.

In the Keynesian world, there is no signal whatsoever between consumers and investors. Only if the plans of consumers and investors happen by chance to match will there be full employment of resources.

Which brings us to capital theory. In capital theory, markets are not so complete that consumers are telling investors exactly what goods they would like next year. Instead, the interest rate is a general signal about how much consumers prefer goods in the present to goods in the future. Firms can use this signal to decide how much to invest. If the interest rate is high, then only a few investment projects will yield a high enough return to cover the cost of borrowing funds, and investment will be low. If the interest rate is low, then many investment projects will be able to cover the cost of borrowing, in which case that investment will be high.

To explain economic fluctuations in terms of investment using capital theory, one needs a story for why the interest rate would not act as an appropriate signal. For example, one way to think of the Austrian theory is that when the interest rate is too low (artificially held down by the central bank, for example), firms choose production methods that are highly roundabout. That is the Austrian way of saying that there is too much investment. When the tide of low interest rates goes out, these roundabout production methods are left stranded on a beach of unprofitability. A slump ensues.

Both the Keynesian story and the Austrian story describe economic fluctuations as resulting from changes in the estimates of the profitability of investment. For Keynesians, investment moves up and down due to changes in “animal spirits.” For Austrians, the main driver is deviations of the interest rate from its natural value, with central bank manipulation being the most common source of such deviations.

Keynes saw entrepreneurs as relatively insensitive to interest rates. Instead, their investment decisions were based on “the state of long-term expectations.” Absent the Arrow-Debreu markets, beliefs about the future have no firm anchor in reality. Optimistic entrepreneurs will invest, and pessimistic entrepreneurs will not, regardless of the interest rate.

In fact, it is possible that expectations of the future are closely linked with current economic circumstances. That is, when output is high, entrepreneurs expect demand to be high in the future, and conversely. If this is the case, then the economy will be highly unstable. That is, when output is high, investment will be exuberant, leading to more output. However, once the economy decelerates, investment will slow down, leading to further deceleration and even to declines in output. This is the “accelerator model” of investment.

In the story of fish and fruit trees, suppose that every increase in total output causes investment in fruit trees to rise by 25 percent, and suppose that consumers spend 80 percent of their income on fish. If we start in the first round with investment of 20 fruit trees, the increase in output next round is 16 fish (80 percent of 20) plus 5 fruit trees (25 percent of 20, for a total increase of 21. In the next round, output increases by more than 21, and in each round it increases by more, ultimately leading to infinite output. This is not always a property of the accelerator model, but in general the accelerator model is one in which the Keynesian multiplier is very high (because investment is “crowded in” rather than “crowded out”) and the economy is not very stable. There was a time when many economists thought that they could discern an accelerator model in the data.

Some economists make a point of distinguishing planned investment from unplanned investment. If firms are surprised by low sales, unwanted inventories accumulate. This is technically an investment in inventories, but it is unplanned.

My view of inventories is that they affect the way that a recession unfolds, but I would not put inventories at the center of a theory of economic fluctuations. Instead, the way that I think of it, if there were no unplanned inventory accumulation when demand declines unexpectedly, firms would cut back production immediately. With unplanned inventory accumulation, the production cutback is delayed until firms realize that they have excess inventory.

The challenge for explaining macroeconomic fluctuations can be thought of in the following terms. Ordinarily, we think of shifts in demand as relative, meaning that when people want less of one thing they want more of something else. From the perspective of capital theory, if people want less consumption today it is because they want more consumption in the future, and this should induce more investment in order to accommodate this desire for future consumption. Instead, the Keynesian model says that entrepreneurs make their investment decisions with little or no regard for what consumers are doing. Thus, a change in preferences that leads consumers to want more output of future goods will not get properly transmitted to the market and will not lead to more investment.

A difficulty with the Keynesian story is how to account for idle saving. When people save, financial intermediaries put those savings to work by funding capital investment. An excess of savings should drive down interest rates. If most entrepreneurs are insensitive to interest rates (because they are focused on the “state of long-term expectations”), then interest rates should fall a lot when savings increase. With a sufficiently large drop in interest rates, some long-term investment should be induced. Unless the interest rate elasticity of investment is zero across the board, it would seem that more saving should call forth more investment, rather than stand idle.

Of course, part of the Keynesian story is that the demand for saving is satisfied in part by the hoarding of money, which is not a produced good. However, the story of money balances as idle saving leads us down yet another path: monetary theory.