Archive for the 'savings-iinvestment identity' Category

Savings and Investment Aren’t the Same Thing and There’s No Good Reason to Define them as Such

Scott Sumner responded to my previous post criticizing his use of the investment-savings identity in a post on the advantages NGDI over NGDP, and to my posts from three years ago criticizing him for relying on the savings-investment identity. Scott remains unpersuaded by my criticism. I want to understand why my criticism appears so ineffective, so I’m going to try to understand Scott’s recent response, which begins by referring to economics textbooks. Since it is well documented that economics textbooks consistently misuse the savings-investment identity, it would not be surprising to find out that the textbooks disagree with my position (though Scott doesn’t actually cite chapter and verse).

Economics textbooks define savings as being equal to investment:

S = I

To say that something is equal to investment doesn’t seem to me to be much of a definition of whatever that something is. So Scott elaborates on the definition.

This means savings is defined as the funds used for investment.

OK, savings are the funds used for investment. Does that mean that savings and investment are identical? Savings are funds accruing (unconsumed income measured in dollars per unit time); investments are real physical assets produced per unit time, so they obviously are not identical physical entities. So it is not self-evident – at least not to me — how the funds for investment can be said to be identical to investment itself. The two don’t seem to be self-evidently identical to Scott either, because he invokes another identity.

It’s derived from another identity, which says that in a closed economy with no government, gross domestic product equals gross domestic income:

GDI = C + S = C + I = GDP

But once again, it is not self-evident that GDI and GDP are identical. Income usually refers to earnings per unit time derived by factors of production for services rendered. Or stated another way, GDI represents the payments per unit time – a flow of money — made by business firms to households. In contrast, GDP could represent either a flow of final output from business firms to households and to other business firms, or the expenditures made by households and business firms to business firms. These two flows of output and expenditure are not identical, though, for the most part, representing two sides of the same transactions, there is considerable overlap. But it is clear that payments made by business firms to households in exchange for factor services rendered are not identical to the expenditures made by households and business firms to business firms for final output.

Bill Woolsey in a post commenting on my post and Scott’s earlier post to which I responded attempts to explain why these two flows are identical:

In a closed private economy, saving must equal investment. This is a matter of definition. Saving is defined as income less consumption. All output is defined as either being consumer goods or capital goods. Consumption is spending on consumer goods and investment is spending on capital goods. All expenditure is either on consumer goods or capital goods. Since income equals expenditure, and consumption is itself, then income less consumption must equal expenditure less consumption. By the definition of saving and investment, saving and investment are always equal.

I guess someone might think that is all insightful, but it comes down to saying that purchases equals sales.

Bill is very careful in saying that savings is defined as income less consumption, and all output is defined as either being consumer goods or capital goods, and all consumption is (presumably also by definition) spending (aka expenditure) on consumer goods and investment is spending (aka expenditure) on capital goods. So all expenditures are made either on consumer goods or on capital goods. Then Bill concludes that by the definition of savings and investment, savings and investment are always equal (identical), because consumption is itself and income equals expenditure. But Bill does not say why income equals expenditure. Is it because income and expenditure are identical? But, as I just pointed out, it is not self-evident that income (defined as the earnings accruing to households per unit time) and expenditure (defined as the revenues accruing to business firms in payment for final output produced per unit time) are identical.

Now perhaps Bill (no doubt with Scott’s concurrence) is willing to define expenditure as being equal to income, but why is it necessary to define income and expenditure, which don’t obviously refer to the same thing, as being equal by definition? I mean we know that the Morningstar is Venus, but that identity was not established by definition, but by empirical observation. What observation establishes that income (the earnings of factors of production per unit time) and expenditure (revenues accruing to business firms for output sold per unit time) are identical? As Scott has himself noted on numerous occasions, measured NGDI can differ and has frequently differed substantially from measured NGDP.

It is certainly true that we are talking about a circular flow: expenditure turns into income and income into expenditure. Expenditures by households and by business firms for the final output produced by business firms generate the incomes paid by business firms to households and the income paid to households provides the wherewithal for households to pay for final output. But that doesn’t mean that income is identical to expenditure. Chickens generate eggs and eggs generate chickens. That doesn’t mean that a chicken is identical to an egg.

Then Scott addresses my criticism:

David Glasner doesn’t like these definitions, but for some reason that I haven’t been able to figure out he doesn’t say that he doesn’t like the definitions, but rather he claims they are wrong. But the economics profession is entitled to define terms as they wish; there is no fact of the matter. In contrast, Glasner suggests that my claim is only true as some sort of equilibrium condition:

It’s not a question of liking or not liking, but one ought to be parsimonious in choosing definitions. Is there any compelling reason to insist on defining expenditure to be the same as income? On the contrary, as far as I can tell, there is a decent prima facie case to be made that expenditure and income refer to distinct entities, and are not just different names for the same entity. Perhaps there is some theoretical advantage to defining expenditure and income to be the same thing. If so, I have yet to hear what it is. On the contrary, there is a huge theoretical disadvantage to defining income and expenditure to be identical: doing so makes the Keynesian income-expenditure model unintelligible. Come to think of it, perhaps Scott, a self-described hater of the Keynesian cross, likes that definition. But even if you hate a model, you should try to make it as good and as coherent as possible, before rejecting it. This post is already getting too long, so I will save for a separate post a discussion of why defining income and expenditure to be identical makes the Keynesian income-expenditure model, and the loanable funds doctrine, too, for that matter. For now, let me just say that if you insist that the savings-investment equality (or alternatively the income-expenditure equality) is an identity rather than an equilibrium condition, you have drained all the explanatory content out of your model.

Scott objects to this statement from my previous post:

Scott begins by discussing the simplest version of the income-expenditure model (aka the Keynesian cross or 45-degree model), while treating it, as did Keynes, as if it were interchangeable with the national-accounting identities:

In the standard national income accounting, gross domestic income equals gross domestic output. In the simplest model of all (with no government or trade) you have the following identity:

NGDI = C + S = C + I = NGDP (it also applies to RGDI and RGDP)

Because these two variables are identical, any model that explains one will, ipso facto, explain the other.

Here is Scott’s response:

David’s characterization of my views is simply incorrect. And it’s easy to explain why. I hate the Keynesian cross, and think it’s a lousy model, and yet I have no problem with the national income identities, and believe they occasionally help to clarify thinking. The quote he provides does not in any way “discuss” the Keynesian cross model, just as mentioning MV=PY would not be “discussing” the Quantity Theory of Money.

OK, I believe Scott when he says that he’s not a fan of the Keynesian cross, but it was Scott who brought up consumption smoothing in response to a decline in aggregate demand caused by central bank policy. Consumption smoothing is a neo-classical revision of the Keynesian consumption function, so I was just trying to put Scott’s ideas into the context of a familiar model that utilizes the equality of savings and investment to determine equilibrium income. My point was that Scott was positing a decrease in saving and asserting, by way of the savings-investment identity, that investment would necessarily drop by the same amount that saving had dropped. My response was that the savings-investment identity does not allow you to infer by how much investment falls in response to an assumed decrease in savings, because savings and investment are mutually determined within a macroeconomic model. It doesn’t have to be the Keynesian cross, but you need more than an accounting identity and an assumption that savings falls by x to determine what happens to investment.

Scott then makes the following point.

[I]t seems to me that David should not be focusing on me, but the broader profession. If economics textbooks define S=I as an identity, then it’s clear that I’m right. Whether they should define it as an identity is an entirely different question. I happen to think it makes sense, but I could certainly imagine David or anyone else having a different view.

If I am focusing on Scott rather than the broader profession, that simply shows how much more closely I pay attention to Scott than to the broader profession. In this particular case, I think Scott is manifesting a problem that sadly is very widely shared within the broader profession. Second, that Scott shares a problem with the rest of the profession does not establish that Scott is right in the sense that there is any good reason for the profession to have latched on to the savings-investment identity.

In response to my reference to posts from three years ago criticizing him for relying on the savings-investment identity, Scott writes:

I have never in my entire life made any sort of causal claim that relied solely on an identity. In other words, I never did what David claims I did. Like all economists, I may use identities as part of my argument. For instance, if I were to argue that rapid growth in the money supply would increase inflation, and that this would increase nominal interest rates, and that this would increase velocity, I might then go on to discuss the impact on NGDP. In that case I’d be using the MV=PY identity as part of my discussion, but I’d also be making causal arguments based on economic theory. I never rely solely on identities to make a causal claim.

We have a bit of a semantic issue here about what it means to rely on an identity. As I understand him, Scott is asserting that because savings is identical to investment he can make a causal statement about what happens to savings and then rely on the savings-investment identity to infer directly, by substituting the word “investment” for the word “saving” into a causal statement about investment. I don’t accept that the savings-investment identity allows a causal statement about savings to be transformed into a causal statement about investment without further explanation. My claim is that savings and investment are necessarily equal only in equilibrium. A causal statement about savings can’t automatically be transformed into a causal statement about investment without an explanation of how savings and investment were brought into equality in a new equilibrium.

Scott had trouble with my expression of puzzlement at his statement that Keynesians don’t deny that (ex post) less savings leads to less investment. I found that statement so confusing that apparently I wasn’t able to articulate clearly why I thought it was confusing. Let me try a different approach. First, if savings and investment are identical, then less savings can’t lead to less investment, less savings is less investment. A pound is defined as 2.2 kilograms. Does it make sense to reducing my weight in pounds leads to a reduction in my weight in kilograms? Second, if less savings is less investment, what exactly is the qualification “ex post” supposed to signify? Does it make sense to say that ex post if I lost weight in pounds I would lose weight in kilograms, as if I might plan to lose weight in pounds, but not lose weight in kilograms?

In the same post that I cited above, Bill Woolsey makes the following observation:

To say that at the natural interest rate saving equals investment is like saying at the equilibrium price quantity supplied equals quantity demanded. To say that savings always equals investment is like saying that purchases always equals sales by definition.

To compare the relationship between savings and investment to the relationship between purchases and sales is clearly not valid. The definition of the activity called “purchasing” is that a commodity or a service is transferred from a seller to a buyer. Similarly the definition of the activity called “selling” is that a commodity is transferred to a buyer from a seller. The reciprocity between purchasing and selling is inherent in the definition of either activity. But the definition of “saving” does not immediately tell us anything about the activity called “investing.” As Bill concedes in the passage I quoted earlier, the identity between saving and investment must be derived from the supposed identity between income and expenditure. But the definition of “income” does not immediately tell us anything about “expenditure.” Income and expenditure are not two reciprocal sides of the same transaction. When I buy a container of milk, there is a reciprocal relationship between me and the store that has no direct and immediate effect on the relationship between the store and the factors of production used by the store to be able to sell me that container of milk. I don’t deny that there is a relationship, just as there is a relationship between chickens and eggs, but the relationship is not at all like the reciprocal relationship between a buyer and a seller.

UPDATE: (2/18/2015): In a comment to this post, Bill Woolsey points that I did not accurately characterize his post when I said “Bill does not say why income equals expenditure,” by which I meant that he did not say why income is identical to expenditure. If I had been a more careful reader I would have realized that Bill did indeed explain why income is identical to output and output is identical to expenditure, which (by the transitive law) implies that income is identical to expenditure. However, Bill himself actually concedes that the identity between output and expenditure is arrived at only by imputing the value of unsold inventory to the profit of the firm. But this profit is generated not by an actual expenditure of money, it is generated by an accounting convention — a perfectly legitimate accounting convention, but a convention nonetheless. So I continue to maintain that income, defined as the flow of payments to factors of production per unit time, is not identical to either expenditure or to output. Bill also notes that, as Nick Rowe has argued, in a pure service economy in which there were no capital goods or inventories, output would identically equal expenditure. I agree, but only if no services were provided on credit. There would then be a lag between output and the expenditure corresponding to the output. It is precisely the existence of lags between output, expenditure and income that allows for the possibility of non-instantaneous adjustments to changes, thereby creating disequilibrium transitions between one equilibrium and another.

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About Me

David Glasner
Washington, DC

I am an economist in the Washington DC area. My research and writing has been mostly on monetary economics and policy and the history of economics. In my book Free Banking and Monetary Reform, I argued for a non-Monetarist non-Keynesian approach to monetary policy, based on a theory of a competitive supply of money. Over the years, I have become increasingly impressed by the similarities between my approach and that of R. G. Hawtrey and hope to bring Hawtrey's unduly neglected contributions to the attention of a wider audience.

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