Wednesday, April 10, 2013

Saving and Investment

Scott Sumner wrote:

Saving is saving; it is defined in all the textbooks as the funds that go into investment.

I found this incredible.   "All" the textbooks define saving as the funds that go into investment?

I was quite sure that the textbooks that I have used recently define saving as income less consumption.

I have never once seen a textbook that has in bold face:

saving - funds that go into investment.  

But to refresh my memory, I checked out the appropriate part of my current text.   I am currently using Gwartney, Stroup, Sobel, and MacPherson.    On page 533, they write:

Saving is income not spent on current consumption. Investment and saving are closely linked. Saving refers to the nonconsumption of income, while investment refers to the use of unconsumed income to produce a capital resource.

Sobel just happened to pop into my office while I was looking it up.    He didn't think that saving was defined as funds going into investment.   Still, the text is a group effort, and he focuses more on micro--he's a public choice economist.  "Investment refers to the use of unconsumed income to produce a capital resource."   Income used for production.  Not the way I would frame it.

I checked the text that  I was using before.   Cowen and Tabarrok write on page  484:
Saving is income that is not spent on consumption goods. Investment is the purchase of new capital, things like tools, machinery and factories….. (they go on to explain that investment is not buying stocks and then finish up with)… Okay, let’s see how savings are mobilized and transformed into investments.

I could expand on their brief introductions, but I think the focus was on how saving is necessary to free up resources to produce capital goods, and capital goods allow for an increase in future output.    That makes great sense to me, but of course I would appreciate the approach of micro-oriented free market economists.  

So, I decided to check a few other texts from my shelf.   Mankiw has a definition in the margin on page 267:

private saving – the income that households have left after paying for taxes and consumption.

But the section immediately before is called “Some Important Identities,” where he uses algebra to find that S = I.    

I then checked out Krugman and Wells.   On page 258, they have a section on the Saving-Investment Spending Identity. Like Mankiw, they use algebra to show that S=I.   Only after that, on page 259, do they define private saving. It isn’t in bold or anything.   They write,

“National saving is equal to the sum of private saving and the budget balance, where private saving is disposable income (income after taxes) minus consumption.”   (I added the bold.)

So, the high Keynesians, from both the Republican and Democrat branches, do put the "identity" of saving and investment front and center, and only as an afterthought, do they bother to define saving as that part of income not spent on consumer goods.

It is interesting that the definition of investment as purchases of capital goods is treated as primary.   Why isn't investment defined to be that part of income not consumed?

I certainly don't deny that national income accounting implies that aggregate expenditure generates an equal aggregate income.   And that if aggregate saving is defined as aggregate income minus aggregate consumption, then it must equal aggregate investment, assuming it is the only sort of aggregate expenditure that is not aggregate consumption.

However, I would not start from expenditure equals income.   Rather I would start with an individual choosing to either spend income on consumer goods and services now or else save by adding to net worth.   Of course, that addition to net worth allows for an increase in consumption in the future.

Aggregate saving would not be found by taking aggregate income and subtracting off aggregate consumption.  It would be found by summing up the individual amounts saved.

Similarly, I would not find aggregate invesetment by taking aggregate expenditure and subtracting off aggregate consumption.   Instead, I would sum up the amounts that individual firms choose to invest.   Of course, the purchase of new capital goods exands the capital resources they will have available for future production.

No way is saving, either individual or aggregate, the same thing as investment, either individual or in aggregate.      They may be necessarily equal, but any kind of focus on individual choice screams they are different sorts of things.  

In my view, the interest rate is the price that coordinates saving and investment.   Why would there be any need for a price to coordinate two things that are necessarily equal?   Of course, it is desired saving and desired investment that need to be coordinated.

Is  that really so unusual?   Consider apples.   The supply of apples is the amount of apples that firms are able and willing to sell at various prices.   The demand for apples is the amount of apples that households are able and willing to buy at various prices.   The market supplies and demands are built up from the supplies of individual firms and the demands by individual households.  The price of apples coordinates the quantity supplied and demanded.

Of course, the actual amount of apples purchased is always exactly equal to the actual amount of apples sold.   If the demand for apples was identified with the number of apples purchased and the supply of apples was identified with the number of apples sold, then they would always be equal, by definition.   This would be exactly the same thing as the claim that saving is always equal to investment by definition.   But that wouldn't mean that the price of apples has no role in coordinating the desired purchases of apples with the desired sales.   And, of course,  quantity supplied and demanded are actually defined in terms of desired amounts.

Consider the labor market.   The demand for labor is the amount of labor firms choose to utilize at different real wages.   The supply of labor is the amount of labor households choose to provide at different  real wages.   The real wage coordinates quantity supplied and demanded.  

But suppose the demand for labor was defined to be the amount of labor firms were actually utilizing and the supply of labor was defined as the amount of labor actually being provided by households.   Those two amounts would be equal by definition.   What possible role would the real wage have in coordinating those "demands" and "supplies" of labor?     Of course, it would still be possible for the real wage to coordinate the desired "demand" for labor and the "desired" supply of labor.   And that is exactly how the supply and demand for labor are defined--in terms of the desired amounts.

The apples that are being supplied and the apples that are being demanded are the same thing.   It is the supplying of them that is not the same as the demanding of them.   Only by focusing on actual transactions does an empty tautology of apple purchases equaling apple sales cause confusion.

The labor being supplied and the labor being demanded are the same thing.   It is the supplying of the labor that is not the same thing as the demanding of it.   Again, only by focusing on actual transactions does an empty tautology of labor utilized and labor done cause confusion.

But saving and investment are different things.  And the supplying of saving and the demanding of investment are also different.   But somehow, a focus on the identity of the total amount of expenditure on goods and services and the total amount earned from selling goods and services, when combined by a subtraction of consumption, results in confusion.   

Somehow the equality of actual saving and investment is considered more important than the defined equality between the actual amount of apples sold and the actual amount of apples purchased.  It is considered more important that the equality between labor utilized and labor done.   But it is not.

The problem remains how interest rates coordinate desired saving and desired investment.

It is certainly possible (and I think likely) that a decrease in income can lead to a reduction in desired saving.   If desired saving was greater than desired investment, and desired investment was somehow maintained, then a contraction in income could lead to desired saving falling enough to become equal to desired investment.    This would be the paradox of thrift in terms of quantity of saving supplied and quantity of investment demanded.   That is, in terms of desired saving and desired investment.  

However, the interesting and important condition is the coordination of saving and investment when aggregate income equals the productive capacity of the economy.   That is, the allocation of resources between production of consumer goods and services and capital goods constrained by the scarcity of currently existing resources.  

A better way to use the algebra, or really the arithmetic, of consumption, saving, income and investment is to see that the interest rate that keeps the quantity of saving supplied equal to the quantity of investment demanded is also the interest rate that keeps the sum of the quantity of consumption demanded and the quantity of investment demanded equal to potential output--the productive capacity of the economy.  

That realized saving is equal to realized investment because realized expenditures equals realized income adds nothing but confusion.    I suppose that is another reason to avoid the textbooks written by high Keynesians.

The conventional wisdom is that Keynes confused identities with equilibrium conditions.   I am sure that Mankiw and Krugman keep them straight, but their approach to introducing saving and investment doesn't help.

As for Sumner, the answer is that no, not all of the textbooks define saving as the funds going into investment.


  1. Good article! It is very important for us to be clear about the different functions of these accounts and to be sure that our expectations match.

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  3. Thank you very much for this excellent article! I was very confused about the identity, mainly because a rise of the real interest rate would lead to a increase in savings but to a decline in investment.

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