Savings Equals Investment - AP Lerner

SAVING EQUALS INVESTMENT

SUMMARY I. Why SI4, 297.-Difficulties of seeing this: the confusion between

stocks and flows, 299; the paradox of individual freedom and social necessity, 300; the habit of labeling expenditure as "out of" particular income receipts, 302; the failure to recognize the mathematical or analytical nature of the proposition, 304; a misunderstanding of argu- ments about equilibrium, 305. - II. Miss Curtis' condition that "all income is spent," 305; her failure to see the place of "wishes" in economic analysis, 307.- III. An attempt to salvage one of Miss Curtis' results, 308.

In a recent article I in this Journal, Miss Myra Curtis attacks the formulation put forward by Mr. Keynes in his book,2 and repeated by me in an article,3 according to which saving and investment, for a whole economy, are always equal. This equality has appeared paradoxical to many economists, and many difficulties have hindered its general acceptance. In the first part of this article I shall endeavor to clear up some of these difficulties. In the second part I shall consider two of Miss Curtis' criticisms at greater length; and in the concluding section I shall discuss the possibility of salvaging one point which does not rest entirely upon misunderstanding of Mr. Keynes' argument.

Mr. Keynes and I and most people would say that a man saves something in a given period, if he spends on consumption (consumes) in that period less than his income in the period. The only unambiguous measure of the amount of his saving is obtained by subtracting his (expenditure on) consumption in. the period from his income in the period. y (Income) - c (Consumption) = s (Saving) by definition. If he consumes more than his income, he is doing the opposite

1. "Is Money Saving Equal to Investment?" Quarterly Journal of Economics, August, 1937.

2. The General Theory of Employment Interest and Money. 3. "Mr. Keynes"General Theory of Employment,"' I. L. 0. Review,

October, 1936. 297

298 QUARTERLY JOURNAL OF ECONOMICS

of saving, dissaving, and we similarly measure the amount of his dissaving by subtracting his income from his consumption. c-y= -s is the same equation (with the signs changed) in which - s can be called dissaving.

Investment is the expenditure of money on things other than consumption. There is no reason why, for any individual, there should be any particular relationship between his investment (i) and the items y, c, and s mentioned above. But when we consider a whole (closed) economy, we see that there emerges a relationship between these items that does not appear to exist for the individual.

The equation y- c = s, since it is true for every individual in the economy, is also true for any two

Y2-c2=82

(YI+Y2) - (CI+C2) = (81+82)

or any other number of individuals in the economy. If we take all the individuals together and add up their incomes and consumptions and savings (using capital letters to rep- resent these sums for the whole economy), we get Y- C = S. In this respect, then, the whole economy is like any individual.

But for the whole economy there is another relationship. The sum of the incomes of all the individuals in the economy, Y. is equal to the sum of the expenditures of all kinds by the individuals of the economy, since these expenditures are nothing but the payments, the receipt of which constitutes all the incomes. The sum of all the payments must be equal to the sum of all the receipts in the same period, since these are the same thing, only looked at from different angles. The sum of expenditures of all kinds, which is equal to Y, must consist of C, the sum of expenditures on consumption, plus I, the sum of expenditures on things other than consumption, since these two make up all possible expenditures. This gives us the equation Y=C+I or Y-C=I. We know that Y-C is also equal to S, and since quantities that are equal to the same quantity are equal to one another, we get the result

SAVING EQUALS INVESTMENT 299

that S = 1. The sum of the savings of all individuals is equal to the sum of their investments in the same period.

The resistance that this piece of very simple arithmetic arouses in many people can usually be traced back to one or more of the following five causes:

(1) A failure to recognize that all the items considered are payments (or differences between payments) over a period, and never amounts existing at some point of time (such as the beginning or the end or some intermediate point within the period to which our proposition relates). They are all of the nature of flows which can be measured either as so much in a given period (as in the simplest case examined above) or as so much per unit of time (if we suppose the flows to continue at an unchanged rate over several units of time). They can never be measured as so much existing at any moment of time. That can only be done of stocks, not of flows, and our proposition deals only with flows.

This failure to keep clear of irrelevant considerations of stocks (of money) may take the form of

(a) An insistence on the discussion of the velocity of circulation of money. The velocity of circulation is nothing but the ratio between some total of money payments in a period (which, being a flow, may be relevant to our proposition) and some stock of money existing at some point of time (which, since it is a stock, is on a different plane and can have no relevance to our proposition).

(b) An insistence on the discussion of "hoarding" (and "dishoarding"). Sometimes "hoarding" means a reduction in the velocity of circulation, the irrelevance of which has been shown. Sometimes it means simply holding stocks of money. Sometimes it means increasing one's stock of money. And most frequently it mysteriously means all three of these simultaneously, as well as a lengthening of the period an individual holds particular coins or notes. The concept of stocks inherent in all of these usages renders irrelevant any validity that the particular meaning of "hoarding" may retain.

Lack of clarity as to whether stocks or flows are being dis-


cussed has played a great part in feeding useless discussions in economics in the past. The Wages Fund is a conspicuous example of an ambiguous word used to cover such a confusion, and in modern theory of capital the same confusion is a great stumbling block. The proposition that I=S is a proposition about flows and has nothing to do with stocks.

(2) A failure to understand the paradox that, while each individual separately is free to save either more or less than he invests, all the individuals together are not so free, since the sum of the investments I is always equal to the sum of their savings S. How does this compulsion work? If it does not affect any individual, how can it affect the whole economy, which is simply the sum of the individuals?

To understand paradoxes of this nature is the special province of the economist, and many other similar paradoxes have by their familiarity ceased to terrify and become part of the stock in trade of all economists. Any country is free to import more goods than it exports or vice versa, but world imports always equal world exports (plus freight charges, etc.). Any individual can take his money out of the bank tomorrow morning, but all individuals together cannot. And we have the converse paradox. One bank or one country cannot expand its credit indefinitely; all the banks, or all the countries, keeping in step, can do so. To insist that what is true of each individual must be true of all individuals together is the simple fallacy of composition.

But how does the compulsion work, if it does not affect individuals? This question leaves many students uneasy. The answer is that the individual is by no means as free to decide how much he is going to save as has been suggested. There are very few individuals who would not like to have larger incomes than they actually have and to save more out of these larger incomes. Each individual is constrained to save the amount that he does by the size of his income; and the size of his income is determined by other people's expenditures on the goods that he produces. Each individual considers his own income as given and independent of his own expenditure (since in a large community the repercussions


on his own income of any variations in an individual's expenditure are in general likely to be small enough to be legiti- mately neglected); and, not being interested in the effect of his expenditure in creating income for somebody else, he sees no connection between income and expenditure. This does not mean that the connection does not exist for the individual. It merely means that he is not interested in it, insofar as his own expenditure affects other people's incomes (tho he may have a lively interest in the effect of other people's expenditure on his own income). The economist has a wider outlook, must concern himself equally with the incomes of all the individuals, and so must recognize that for the whole community the excess of total incomes over that part of incomes that is created by expenditure or consumption must have been created by investment (or expenditure on other things), so that I =S.

The failure to face up to the paradox of social necessity with apparent individual freedom sometimes takes the form of trying to extract from the total of an individual's actual saving (i.e., the excess of his income in a period over his consumption in the period) some part of it that really is "free" or "voluntary" or "ex ante" and declaring that the rest of his saving is "forced" or "involuntary" or "really saved by somebody else" (i.e., the investor who produced something that cannot be consumed) so that it should not be counted. All such attempts necessarily fall to the ground for the lack of any situation, to serve as a basis for comparison, in which the individual can with any plausibility be said to be uncon- strained in his saving or even less constrained than in the period discussed. It is much more satisfactory to recognize that in a determinate universe all saving, like everything else, is "forced" and that free will is nothing but a pleasant illusion.

Related to this difficulty is the unconscious assumption- taken from the point of view of the individual and illegiti- mately transferred to society - that while expenditure is varied, income remains the same. From this it would follow that an increase in saving always means a reduction in con-


sumption4 (and never an increase in income, consumption remaining constant). The assumption of constant income is then dropped and the fall in consumption is allowed to diminish income, so that any increase in saving appears necessarily to involve a diminution of income.5 From this type of argument any number of surprising results naturally follow, such as that altho there is an increase of saving (to which the fall in expenditure is due) there is no change in saving (since income has fallen as much as consumption).6

(3) A tendency to regard expenditure, not as a flow during a period coincident with the flow of income during the same period, but as something coming "out of" the income received in the period. "Saving" is on this view the income received in a period minus the expenditure made "out of" that income.

One possible meaning of this is simply that only that expenditure is to be counted which takes place after some or all of the income is received. If the ambiguities in this are overcome - as they can be - by some arbitrary ruling as to when we are -to begin counting the expenditure, we will, of course, find that "SS" so defined is greater than I by all the expenditure that took place too early in the period to be considered to be "out of" the income received in the period, so that we did not count it. If this procedure were carried to its logical conclusion, this expenditure, not beng "out of income," would have to be considered as dissaving and sub- stracted from "S" and so reduce it to exactly the same value as I. It is, however,. not usually carried to its logical conclusion, and is considered to be a demonstration of the falsity of our proposition that I =S.

4. E.g., "An increase in S must be accompanied by a reduction in expenditure on consumption goods."-Miss Curtis, Quarterly Journal of Economics, August, 1937, p. 617.

5. E.g., "An increase in S depresses income."- Ibid., p. 617. 6. Miss Curtis seems to hold that the converse of the proposition

quoted in footnote 4 above is also true, and to suppose that I hold the same view. Thus she says that when I speak of a diminution of consumption I must mean an increase of S ("or why the reduction in total consumption and in income?"- Ibid., p. 617). This enables her, when she realizes that the contradiction between the two propositions quoted

SAVING EQUALS IN VESTMENT 303

Another meaning of the insistence on counting C, I and S only insofar as they come "out of" the income received during the period is that we must count only the expenditure (or laying up) of the particular notes or coins received as income during the period. Thus if something is bought with money received before the period began, it is not expenditure "out of" income. On this line of analysis, Peter, who took his wages bag to the grocer, has spent all his income and saved nothing, while Paul, who put his wages bag into his safe and took last week's bag to the grocer, has saved all his income. At this stage of the argument it is again not necessary for I to equal S. Of course, if this method of counting were carried to its logical conclusion and the expenditure of coins other than those received as income in the period were regarded as dissaving, we would find ourselves back at our arithmetical result that I=S; but to do that would be to destroy the whole purpose of this new method of counting.

Correlative with the objection to counting spending that is not "out of income" is an objection to counting as saving the unspent income with which a man is caught at the end of a period, even tho he may not have the slightest intention of saving it.7 This looks like a serious divergence from the ordinary man's idea of what is meant by saving, and has inspired Mr. Robertson to another of his delightful quota- tions from "Alice."8 This would be justified if by saving were meant particular coins or notes received as income and not spent. But we are not interested in particular notes or coins, and what is included in the saving of an individual, apart from the saving that he has used to buy assets other than money, is the excess of the money he holds at the end of a period over the money he had at the beginning. If a man started a period with ?20 and finds himself at the end of the period with ?25, it does not conflict with commonsense leads to the absurdities noted in the text of my article, to attribute the same confusion to me.

7. I am grateful to Dr. H. W. Singer for drawing my attention to this form of my third type of difficulty - an important form which I had overlooked.

8. Economic Journal, September, 1937.


to say that he has saved ?5 in that period, even if it is his intention to spend the whole ?25 (or more) in succeeding periods. Of course if we take highly artificial periods - say, of ten minutes each - our definitions acquire an artificial flavor too. We would then have to say that in the ten- minute period in which a man receives his weekly wage he saves (nearly) all of it, and that in all the other ten-minute periods in which he makes any expenditures he dissaves. But if we take reasonable periods, this artificiality disappears.

There is, of course, a sound idea underlying the notion of considering only such expenditure as comes after or "out of" income. It is that an individual's expenditure is determined more by income in the past, which is known and has been received, than by income in the present, which is uncertain. This may be true to a certain extent, altho the effect of expected income on a man's expenditure must not be left out altogether. It is important for the real economic prob- lems of forecasting expenditure and income, and has its place in economic theory, much more important than our piece of simple arithmetic; but it cannot be used to show that two and two are five.

(4) The failure to realize that the proposition S=I is only an analytical proposition, and not about the real world at all. What is taken to be a statement about the real world excogi- tated from an armchair is naturally looked upon with sus- picion. Our proposition is not based upon observation of the real world. It therefore cannot tell us anything we did not know; neither can it turn out to be mistaken. It follows from and is implicit in our definitions of income, consumption, savings and investment, and the postulate that in any period moneys paid out are equal to moneys received. It is a proposition of the same order as the proposition that the area of the square of the hypotenuse of a right-angled triangle is equal to the sum of the areas of the squares on the other two sides. It has been called a truism, often in tones of contempt, telling us nothing but that something is equal to itself. In a sense this accusation is justified. All the propositions of mathematics are similarly truisms, since they tell us nothing


that is not implied in the basic definitions and postulates. To one who sees these implications in the postulates themselves the enunciation of the propositions of mathematics are nothing but an array of truisms and a waste of time, and I understand that there are born mathematicians for whom propositions like Pythagoras' and the multiplication table are unnecessary encumbrances. The usefulness of propositions of this mathematical nature is an inverse function of their obviousness. The abundant discussion that has grown up around the proposition, made famous by Mr. Keynes, that S=I is abundant proof that its truth is not instantaneously obvious to all men; and if without adducing any new informa- tion it leads them to see some implications previously overlooked, it carries out the purpose for which it was designed.

(5) A belief that the short period equilibrium which is discussed in the analysis that makes use of our proposition is a necessary condition for the realization of the equality. This would indeed be suspicious, since the proof of the equality-e.g., as given in the first pages of this article does not mention equilibrium. This seems to go with a belief that it is the ultimate goal of Mr. Keynes and his followers to show that I = S and then to retire from the field of economics. The equality of I to S has nothing whatever to do with any kind of equilibrium. Equilibrium is discussed as a condition for some kind of stability of Y and C (and con- sequently also of I and S). The equation of I to S is always true and serves as a check, since any result that makes them unequal must involve a mistake either in logic or in counting.

II A first reading of Miss Curtis' article gives the impression

of a daring attack on the proposition that I= S. A closer examination shows, however, that Miss Curtis puts forward all of the objections and difficulties discussed in the first first section of this paper (as well as some minor confusions more peculiar to herself) and in order to be able to dismiss the proposition as a truism she has ultimately to admit it as true. This she does on page; 616 where for the first time she


defines saving in the way Keynes does (S" in her notation), having spent more than half of the article in trying to show that the equation does not hold for other definitions of S (saving "out of income" as discussed in I (3) above, not carried to its logical conclusion; and a hybrid between this and a stock of money as discussed in I (1) above - "total amount withheld from consumption in the period," p. 615). There are, however, two points in her article that I should like to discuss further.

Miss Curtis' main slip is to be found in her statement that "a hidden condition is attached to the equations - namely that all income (and nothing from other sources) is spent in the period" (p. 607). "The condition is, however, not one that can be expected to be uniformly fulfilled. For if it were, spending would be constant and incomes would never change." (p. 610)

This looks at first like a denial that total income must be equal to total expenditure (i.e., C+I). Miss Curtis shows, however, that she does not make as simple a mistake as this. She says, indeed, "Tho all expenditure becomes income, all income need not become expenditure" (p. 608), and in her arithmetical examples which are designed to show the falsity of our proposition, she wisely avoids any internal contra- dictions by making income (Y) equal throughout to spending (C+I) in the same period. She does not deny that incomes and total spendings in any period must be equal to each other.; What she denies is that incomes must be equal to spending "out of" the incomes received. This condition, she says, "cannot be expected to be uniformly fulfilled" (p. 610); "receipts of income . .. may be passed on during the period either wholly, or in part, or not at all, to form the income of others." (p. 608)

In this Miss Curtis does not go far enough. It is impossible for all income receipts "to be passed on" during any period, for the act of passing income on by one person is the act of receiving income by the other person, and whenever the gong goes to mark the end of our period, there must always be somebody left with unspent income. In a game of musical


chairs, the players cannot beat the band, however fast they run. The condition described by Miss Curtis as one that "cannot be expected to be uniformly fulfilled" is one that can never be fulfilled. Fortunately there is no need for the fulfillment of this impossible condition. The meaning behind Miss Curtis' conclusion that if this (as we have seen impossible) condition were fulfilled, "spending would be constant and income would never change" will be examined in the next section.

The other point is concerned with a criticism both of Mr. Keynes and of myself for speaking of "attempts" to save and "wishing" to save amounts different from the amount of investments. Miss Curtis is, of course, absolutely right in suggesting (p. 619) that "attempting" and "wishing" to spend have in themselves no effect on anything, except insofar as they are translated into actual spending. She is not on such firm ground when she applies the same argument to saving or, in her language, "withholding of income." Saving, or the "withholding of income," is not an action that has effect and that can be contrasted with the mere "attempting" or "wishing" to save in the same way as actually spending money can be contrasted with merely wishing to spend. Income receivers are free to spend on consumption as much or as little as they wish (within certain limits, of course), but they are not, taken altogether, able to save any desired amount as simply as they are able to spend any desired amount. This is because their saving depends, not only upon their spending, but also upon income, since it is the difference between these. With the rate of investment given (it being undertaken by other people, or at any rate determined by other forces), income receivers are not able to save either more or less than is being invested. They may wish to save more and may try to implement this wish by actually spending less. This, however, has the effect of diminishing incomes by exactly the same amount, so that while there has been an actual diminution in expenditure (and a corresponding actual diminution of Incomes), the increase in saving has neverthe- less remained a wish. In the same way a wish to save less may result in increased spending and increased incomes, but


not in any diminution in saving - that decrease always remains in the realm of wishes.

An equilibrium is reached, but not by translating the wish for a larger (or smaller) amount of saving into an actuality and so satisfying the wish and thereby dispelling the driving force that is incompatible with equilibrium. Equilibrium is reached by a fall (rise) in incomes and consumption as far as is necessary to make the income receivers give up their wish. If they are obstinate, they merely make a greater fall (rise) in incomes necessary before they change their mind. When they acquiesce, we have equilibrium. Reality has not been adjusted to fit the wish; the wish has been adjusted to fit reality.

Equilibrium here merely means that there is no longer any tendency for Y and C to move down (or up) together. To suppose, as Miss Curtis does (p. 620), that this equilibrium is necessary to make I=S is to misunderstand the whole point. That equality has nothing to do with equilibrium, and is undisturbed however violent may have been the movement towards equilibrium, if indeed it is ever reached. For the parallel movement of Y and C does not in the least affect the gap between them which is S and equal to I. The examination of all this movement towards equilibrium is not carried out in the least for the purpose of demonstrating our little bit of arithmetic (tho it may be observed there as any- where else), but to consider the effect on the economy of wishes on the part of individual income receivers to vary the amount they are saving - not by telepathy but through the changes in actual spending that result from those wishes.

III

There seems to be one point that Miss Curtis is perhaps trying to make which does not rest entirely upon misunderstanding. When she says that Mr. Keynes' definition of saving (the excess of income over expenditure on consumption goods) "has nothing to do with saving in the ordinary sense of withholding money income from consumption expenditure" (p. 616), she may mean that people's expenditure is a more stable function of income received at some time or in


some period in the past than of income received in the same period. Individuals consider, say, last week's income when they make their decisions as to how much they are going to spend, and consider themselves to have saved the difference between last week's income and this week's spending.

Some such interpretation gives sense to Miss Curtis' impossible condition "If ... all income of the period (and no more than income) is spent and recreates itself as income in the period" (p. 610), and gives validity to her otherwise baseless conclusion "spending would be constant and incomes would never change." For if spending (here total expenditure, C2+I2) in period Two is equal to income (Y1) in period One, income in period Two (Y2=C2+I2) is equal to income in period One (Y1) and income is unchanged.

Such a salvaging of Miss Curtis' argument, however, involves the adoption of a technique of analysis in terms of successive periods, of the kind developed by Mr. Robertson and the Swedish writers. Of this there is no trace in Miss Curtis' article, which throughout considers simply "the period." Again the difference between these writers and Mr. Keynes and his followers is on quite another level. I am rather skeptical concerning the usefulness of analysis in terms of successive periods or "days," because it seems to me to complicate and confuse matters rather than to clarify them. But that is merely a hunch on my part as to which is the more promising (or perhaps more pleasant!) road for research. I may easily be mistaken in this and am ready to welcome any results that those who like this technique may produce. There is no question here of right or wrong or of logical errors committed.

Miss Curtis claims, however, not a difference of technique adopted but the correction of an error. It is therefore prob- ably best to give up our attempt at salvage and to say that Miss Curtis' denials that S=I are simply the result of confusion of thought. Her various definitions of saving, if carried through to their logical conclusions, all come to the same as Mr. Keynes' definition, and the equation applies just as much to these as to Mr. Keynes'. LONDON SCHOOL OF ECONOMICS A. P. LERNER.

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Savings Equals Investment - AP Lerner

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