We conclude, then, that money must have value to start with, from some source other than the money function, and that there must always be some source of value apart from the money function, if money is to circulate, or to serve as money in other ways. But this is not to assert the doctrine of the commodity school, that its value must arise from the metal of which it is made, or in which it is expected to be redeemed. Nor is it to deny that the money function may add to the original value. On the contrary, the services which money performs are valuable services, and add directly, under conditions which we shall analyze more fully in a later chapter on the functions of money, to the value derived from non-pecuniary sources. Value is not physical, but psychical. And value is not bound up inseparably with labor-pain or marginal utility.
CHAPTER VIII
THE "EQUATION OF EXCHANGE"
In Professor Irving Fisher's Purchasing Power of Money[130] we have the most uncompromising and rigorous statement of the quantity theory to be found in modern economic literature. We have, too, a book which follows the logic of the quantity theory more consistently than any other work with which I am acquainted. The book deals with the theory more elaborately and with more detail than any other single volume, and sums up most of what other writers have had to say in defence of the quantity theory. Professor Fisher's book has, moreover, received such enthusiastic recognition from reviewers and others as to justify one in treating it as the "official" exposition of the quantity theory. Thus, Sir David Barbour cites Professor Fisher as the authority on whom he relies for such justification of the theory as may be needed,[131] while Professor A. C. Whitaker declares that he adopts "without qualification the whole body of general monetary theory" for which Professor Fisher stands.[132] Professor J. H. Hollander has recently referred to Professor Fisher's work on money and prices as a model of that combination of theory and inductive verification which constitutes real science.[133] The American Economic Review presents as an annual feature Professor Fisher's "Equation of Exchange."
Not all, by any means, of those who would call themselves quantity theorists would concur in Professor Fisher's version of the doctrine—Professor Taussig, notably, introduces so many qualifications, and admits so many exceptions, that his doctrine seems to the present writer like Professor Fisher's chiefly in name. But there is no other one book which could be chosen which would serve nearly as well for the "platform" of present-day quantity theorists as The Purchasing Power of Money. Partly for that reason, and partly because the book lends itself well to critical analysis, I shall follow the outline of the book in my further statement and criticism of the quantity theory, indicating Professor Fisher's views, and indicating the points at which other expositions of the quantity theory diverge from his, setting his views in contrast with those of other writers. We shall find that this method of discussion will furnish a convenient outline on which to present our final criticisms of the quantity theory, and parts of the constructive doctrine of the present book.
First, Professor Fisher presents in the baldest possible form the dodo-bone doctrine. The quality of money is irrelevant. The sole question of importance is as to its quantity—the number of money-units.[134] I shall not here discuss this point, as a previous chapter has given it extended analysis, except to repeat that it is in fact an essential part of the quantity theory. If the quality of money is a factor, a necessary factor, to consider, then obviously we have something which will disturb the mechanical certainty of the quantity theory. Professor Fisher is thoroughly consistent with the spirit of his general doctrine on this point.
Second, Professor Fisher has no absolute value in his scheme. By the value of money he means merely its purchasing power, and by its purchasing power he means nothing more than the fact that it does purchase: the purchasing power of money is defined as the reciprocal of the level of prices, "so that the study of the purchasing power of money is identical with the study of price levels." (Loc. cit., p. 14.) In this, again, Professor Fisher is absolutely true to the spirit and logic of the quantity theory doctrine. The equilibration of numbers of goods, and numbers of dollars, in a mechanical scheme, gives prices—an average of prices, and nothing else. Any psychological values of goods or of dollars would upset the mechanism, and mess things up. They are properly left out, if one is to be happy with the quantity theory. Fisher, in discussion of Kemmerer's Money and Credit Instruments, has criticised the exposition of the utility theory of value with which Kemmerer prefaces his exposition of the quantity theory, as "fifth wheel." I agree thoroughly with Fisher's view in this, and would add that the only reason that it has made Kemmerer little trouble in the development of his quantity theory is that he has made virtually no use of it there! The two bodies of doctrine, in Kemmerer's exposition, are kept, on the whole, in separate chapters, well insulated. Coupled with this purely relative conception of the value of money, however, there is, in Fisher's scheme, an effort to get an absolute out of it: the general price-level is declared to be independent of, and causally prior to,[135] the particular prices of which it is an average. I mention this remarkable doctrine here, reserving its discussion for a later chapter.[136]
A further feature of Professor Fisher's system, to which especial attention must be given, is the large rôle played in it by the "equation of exchange." This device has been used by other writers before him, notably by Newcomb, Hadley, and Kemmerer, receiving at the hands of the last named an elaborate analysis. But Fisher, basing his work on Kemmerer's, has made even more extensive use of the "equation of exchange," and has given it a form which calls for special consideration.[137] The "equation of exchange," on the face of it, makes an exceedingly simple and obvious statement. Properly interpreted, it is a perfectly harmless—and, in the present writer's opinion, useless—statement. It gives rise to complications, however, as to the meaning of the algebraic terms employed, which we shall have to study with care. The starting point is a single exchange: a person buys 10 pounds of sugar at seven cents a pound. "This is an exchange transaction in which 10 pounds of sugar have been regarded as equal to 70 cents, and this fact may be expressed thus: 70 cents = 10 pounds of sugar multiplied by 7 cents a pound. Every other sale and purchase may be expressed similarly, and by adding them all together we get the equation of exchange for a certain period in a given community."[138] The money employed in these transactions usually serves several times, and hence the money side of the equation is greater than the total amount of money in circulation. In the preliminary statement of the equation of exchange, foreign trade, and the use of anything but money in exchanges are ignored, but later formulations of the equations are made to allow for them. "The equation of exchange is simply the sum of the equations involved in all individual exchanges in a year.... And in the grand total of all exchanges for a year, the total money paid is equal in value to the total value of the goods bought. The equation thus has a money side and a goods side. The money side is the total money paid, and may be considered as the product of the quantity of money multiplied by its rapidity of circulation. The goods side is made up of the products of quantities of goods exchanged multiplied by their respective prices."
Letting M represent quantity of money, and V its velocity or rapidity of circulation, p, p´, p´´, etc., the average prices for the period of different kinds of goods, and Q, Q´, Q´´, etc., the quantities of different kinds of goods, we get the following equation:
MV = pQ + p´Q´ + p´´Q´´ + etc.[139]
"The right-hand side of this equation is the sum of terms of the form pQ—a price multiplied by the quantity bought."[140] The equation may then be written,
MV = Σ pQ (Sigma being the symbol of summation). The equation is further simplified[141] by rewriting the right-hand side as PT, where P is the weighted average of all the p's, and T is the sum of all the Q's. "P then represents in one magnitude the level of prices, and T represents in one magnitude the volume of trade."
It may seem like captious triviality to raise questions and objections thus early in the exposition of Professor Fisher's doctrine. And yet, serious questions are to be raised. First, in what sense is there an equality between the ten pounds of sugar and the seventy cents? Equality exists only between homogeneous things. In what sense are money and sugar homogeneous? From my own standpoint, the answer is easy: money and sugar are alike in that both are valuable, both possess the attribute of economic social value, an absolute quality and quantity. The degree in which each possesses this quality determines the exchange relation between them. And the degree in which each other good possesses this quality, taken in conjunction with the value of money, determines every other particular price. Finally, an average of these particular prices, each determined in this way, gives us the general price-level. The value of the money, on the one hand, and the values of the goods on the other hand, are both to be explained as complex social psychological forces. But when this method of approach is used, when prices are conceived of as the results of organic social psychological forces, there is no room for, or occasion for, a further explanation in terms of the mechanical equilibration of goods and money. Professor Fisher, as just shown, very carefully excludes this and all other psychological approaches to his problem of general prices, and has no place in his system for an absolute value. In what sense, then, are the sugar and the money equal? Professor Fisher says (p. 17), that the equation is an equation of values. But what does he mean by values in this connection? Perhaps a further question may show what he must mean, if his equation is to be intelligible. That question is regarding the meaning of T.
T, in Professor Fisher's equation, is defined as the sum of all the Q's. But how does one sum up pounds of sugar, loaves of bread, tons of coal, yards of cloth, etc.? I find at only one place in Professor Fisher's book an effort to answer that question, and there it is not clear that he means to give a general answer. He needs units of Q which shall be homogeneous when he undertakes to put concrete figures into his equation for the purpose of comparing index numbers and equations for successive years. "If we now add together these tons, pounds, bushels, etc., and call this grand total so many 'units' of commodity, we shall have a very arbitrary summation. It will make a difference, for instance, whether we measure coal by tons or hundred-weights. The system becomes less arbitrary if we use, as the unit for measuring any goods, not the unit in which it is commonly sold, but the amount which constitutes a 'dollar's worth' at some particular year called the base year" (p. 196). If this be merely a device for the purpose of handling index numbers, a convention to aid mensuration, we need not, perhaps, challenge it. The unit chosen is, in that case, after all a fixed physical quantity of goods, the amount bought with a dollar in a given year, and remains fixed as the prices vary in subsequent years. That it is more "philosophical" or less "arbitrary" than the more common units is not clear, but, if it be an answer, designed merely for the particular purpose, and not a general answer, it is aside from my purpose to criticise it here. If, however, this is Professor Fisher's general answer to the question of the method of summing up T, if it is to be employed in his equation when the question of causation, as distinguished from mensuration, is involved, then it represents a vicious circle. If T involves the price-level in its definition, then T cannot be used as a causal factor to explain the price-level. I shall not undertake to give an answer, where Professor Fisher himself fails to give one, as to his meaning. I simply point out that he himself recognizes that the summation of the Q's is arbitrary without a common unit, and that the only common unit suggested in his book, if applied generally, involves a vicious circle.
What, then, is T? Perhaps another question will aid us in answering this. What does it mean to multiply ten pounds of sugar by seven cents? What sort of product results? Is the answer seventy pounds of sugar, or seventy cents, or some new two-dimensional hybrid? One multiplies feet by feet to get square feet, and square feet by feet to get cubic feet. But in general, the multiplication of concrete quantities by concrete quantities is meaningless.[142] One of the generalizations of elementary arithmetic is that concrete quantities may usually be multiplied, not by other concrete quantities, but rather by abstract quantities, pure numbers. Then the product has meaning: it is a concrete quantity of the same denomination as the multiplicand. If the Q's, then, are to be multiplied by their respective p's, the Q's must be interpreted, not as bushels or pounds or yards of concrete goods, but merely as abstract numbers. And T must be, not a sum of concrete goods, but a sum of abstract numbers, and so itself an abstract number. Thus interpreted, T is equally increased by adding a hundred papers of pins,[143] a hundred diamonds, a hundred tons of copper, or a hundred newspapers. This is not Professor Fisher's rendering of T, but it is the only rendering which makes an intelligible equation.
We return, then, to the question with which we set out: in what sense is there an equality between the two sides of Professor Fisher's equation? The answer is as follows: on one side of the equation we have M, a quantity of money, multiplied by V, an abstract number; on the other side of the equation, we have P, a quantity of money, multiplied by T, an abstract number. The product, on each side, is a sum of money. These sums are equal. They are equal because they are identical. The equation asserts merely that what is paid is equal to what is received. This proposition may require algebraic formulation, but to the present writer it does not seem to require any formulation at all. The contrast between the "money side" and the "goods side" of the equation is a false one. There is no goods side. Both sides of the equation are money sides. I repeat that this is not Professor Fisher's interpretation of his equation. But it seems the only interpretation which is defensible.
A further point must be made: Sigma pQ, where the Q's are interpreted as abstract numbers, is a summary of concrete money payments, each of which has a causal explanation, and each of which has effected a concrete exchange. Mathematically, PT is equal to ΣpQ, just as 3 times 4 is equal to 2 times 6. But from the standpoint of the theory of causation, a vast difference is made. Three children four feet high equal in aggregate height two men six feet high. But the assertion of equality between the three children and the two men represents a high degree of abstraction, and need not be significant for any given purpose. Similarly, the restatement of ΣpQ as PT. One might restate ΣpQ as PT, defining P as the sum (instead of the average) of the p's, and T as the weighted average (instead of the sum) of the Q's. Such a substitution would be equally legitimate, mathematically, and the equation, MV = PT equally true. ΣpQ might be factorized in an indefinite number of ways. But it is important to note that in PT, as defined by Professor Fisher,[144] we are at three removes from the concrete exchanges in which actual concrete causation is focused: we have first taken, for each commodity, an average, for a period, say a year, of the concrete prices paid for a unit of that commodity, and multiplied that average by the abstract number of units of that commodity sold in that year; we have then summed up all these products into a giant aggregate, in which we have mingled hopelessly a mass of concrete causes which actually affected the particular prices; then, finally, we have factorized this giant composite into two numbers which have no concrete reality, namely, an average of the averages of the prices, and a sum of the abstract numbers of the sums of the goods of each kind sold in a given year—a sum which exists only as a pure number, and which, consequently, is unlikely to be a causal factor! It may turn out that there is reason for all this, but if a causal theory is the object for which the equation of exchange is designed, a strong presumption against its usefulness is raised. Both P and T are so highly abstract that it is improbable that any significant statements can be made of either of them. As concepts gain in generality and abstractness, they lose in content; as they gain in "extension" they lose (as a rule) in "intension." On the other side of the equation, we also look in vain for a truly concrete factor. V, the average velocity of money for the year, is highly abstract. It is a mathematical summary of a host of complex activities of men. Professor Fisher thinks that V obeys fairly simple laws, as we shall later see, but at least that point must be demonstrated. Even M is not concrete. At a given moment, the money in circulation is a concrete quantity, but the average for the year is abstract, and cannot claim to be a direct causal factor, with one uniform tendency. Of course Professor Fisher himself recognizes that his central problem is, not to state and justify, mathematically, his equation[145]—that is a work of supererogation, and the statistical chapters devoted to it seem to me to be largely wasted labor. Professor Fisher recognizes that his central problem is to establish causal relations among the factors in his equation of exchange. It is from the standpoint of its adaptability as a tool in a theory of causation that I have been considering it. It should be noted that "volume of trade," as frequently used, means not numbers of goods sold, but the money-price of all the goods exchanged, or PT. It is in this sense of "trade" that bank-clearings are supposed to be an index of volume of trade. The sundering of the p's and Q's really is a big assumption of many of the points at issue. Indeed, it is absolutely impossible to sunder PT. It is always the p aspect of the thing that is significant, Fisher himself finally interprets T, statistically, as billions of dollars.[146] As a matter of mathematical necessity, either P must be defined in terms of T or T defined in terms of P. The V's and M and M´ may be independently defined, and arbitrary numbers may be assigned for them limited only by the necessity that MV + M´V´ be a fixed sum.[147] But P and T cannot, with respect to each other, be thus independently defined. The highly artificial character of T has been pointed out by Professor E. B. Wilson, of the Massachusetts Institute of Technology, in his review of Fisher's Purchasing Power of Money in the Bulletin of the American Mathematical Society, April, 1914, pp. 377-381. "Various consequences are readily obtained from the equation of exchange, but the determination of the equation itself is not so easy as it might look to a careless thinker. The difficulties lie in the fact that P and T individually are quite indeterminate. An average price-level P means nothing till the rules for obtaining the average are specified, and independent rules for evaluating P and T may not satisfy [the equation.] For instance, suppose sugar is 5c. a pound, bacon 20c. a pound, coffee 35c. a pound. The average price is 20c. If a person buys 10 lbs. of sugar, 3 lbs. of bacon, and 1 lb. of coffee, the total trading is in 14 lbs. of goods. The total expenditure is $1.45; the product of the average price by the total trade is $2.80; the equation is very far from satisfied." Wilson thinks it necessary, to make the matter straight, to define T, arbitrarily as (MV + M´V´)/P in which case, the equation is true, but so obviously a truism that no one would see any point in stating it. T no longer has any independent standing. Fisher has, however, an escape from this status for T, but only by reducing P to the same position. He defines P as the weighted average of the p's (27), and fails, I think, to see how completely this ties it up with T. The only method of weighting the p's that will leave the equation straight is to weight the different prices by the number of units of each kind of good sold, namely, T. Thus, in Wilson's illustration, we would define P as [(5c.×10) + (20c.×3) + (35c.×1)]/14 P is then 105/14 c., while T is 14. PT is, then, equal to $1.45, which is the total expenditure, or MV + M´V´. Be it noted, here, that P is defined in terms of T, i. e., P is defined as a fraction, the denominator of which is T. No other definition of P will serve, if T is to be defined independently.
But notice the corollary. P must be differently defined each year, for each new equation, as T changes in total magnitude, and as the elements in T are changed. The equation cannot be kept straight otherwise. Suppose that the prices remain unchanged in the next year, but that one more pound of coffee, and two less pounds of sugar are sold. P, as defined for the equation of the preceding year would no longer fit the equation. P, as previously defined, would be unaltered, since none of the prices in it had changed. P, defined as a weighted average with the weights of the first year, would, then, still be 105/14 cents. The T in the new equation is 13. The product of P and T is $1.349/14. But the total expenditure, (MV + M´V´) is $1.70. The equation is not fulfilled. To fulfill the equation, it is necessary to get a new set of weights for P, in terms of the new T of the new equation. From the standpoint of a causal theory, this is delightful. P is the problem. But you are not allowed to define the problem until you know what the explanation is! Then you define the problem as that which the explanation will explain!
Fisher, however, appears unaware of this. At all events, he does not mention it. And he ignores it in filling out his equation statistically, for he assigns one set of weights to the particular prices in his P throughout.[148]
The causal theory with which the equation of exchange is associated is as follows: P is passive. A change in the equation cannot be initiated by P. If P should change without a prior change in one of the other factors, forces would be set in operation which would force it back to its original magnitude. M and T are independent magnitudes. A change in one does not occasion a change in the other. An increase or decrease in M will not cause a change in V. Therefore, an increase in M must lead to a proportionate increase in P, and a decrease in M to a proportionate decrease in P, if the equation is to be kept straight. Changes in T have opposite proportional effects on P.
Before examining the validity of the causal theory, and the arguments by which it is supported, it will be best to state the more complex formula which Professor Fisher advances as expressing the facts of to-day. The original formula ignored credit, and ignored the possibility of resort to barter. It also failed to reckon with certain complications which Fisher deals with as "transitional" rather than "normal."
The formula which includes credit is as follows:
MV + M´V´ = PT
Here, MV and PT have the same significance as before. M´ is the average amount of bank-deposits in the given region for the given period, and V´ is the velocity of circulation of those deposits. M, money, consists of all the media of exchange in circulation which are generally acceptable, as distinguished from those which are acceptable under particular conditions, as by endorsement. M excludes money in bank reserves and government vaults. Money, specifically, includes gold and silver coin, minor coins, government paper money, and bank-notes; M´ consists of deposits transferable by check. This version would not satisfy such a writer as Nicholson,[149] who would limit money to gold coin, and would include in M´ not only deposits, but also bank-notes, and other credit instruments. I may suggest here, what I shall later emphasize, that Fisher's "money," though he doubtless is using the most common definition of money, is really a pretty heterogeneous group of things, concerning which it is possible to make few general statements safely. In economic essence, e. g., bank-notes are much more like deposits than like gold, and if one wishes to separate money and credit, bank-notes belong with M´ rather than with M. But we must take the theory as we find it! Again, credit is by no means exhausted when bank-deposits are named. Why should not book-credits, and bills of exchange be included? Why not postal money-orders, why not deposits subject to transfer by the giro-system? M´ is defined[150] as "the total deposits subject to transfer by check," and would, thus, exclude the giro-system of Germany. It is surely a very provincial equation of exchange, with which Fisher and Kemmerer seek to set forth the universal laws of money! Fisher's reason for excluding book-credits is that book-credits merely postpone, and do not dispense with, the use of money and checks.[151] Book-credits, unlike deposits, have no direct effect on prices (Ibid., 82, n.; 370), but only an indirect effect, by increasing the velocity of money. (Ibid., 81-82; 370-371.) Book-credit, indeed "time-credit" in general thus has no direct effect on prices, and is properly excluded from the equation of exchange. These distinctions seem to me highly artificial. In the first place, the use of checks, in part, merely postpones the use of money: money is moved back and forth from one part of the country to another, and from one bank to another, to the extent that checks fail to offset one another, and in the case of book-credit, while there is less of this offsetting, there is a good deal of it, especially between stockbrokers in different cities, and in small towns and at country stores, and particularly in the South, where the country storekeeper and "factor" are also dealers in cotton, etc., and where they advance provisions during the year to the small farmers, receiving their pay, in considerable degree, not in money, but in cotton, which they credit on the books in terms of money to the customer—a point which Fisher mentions in an appendix. (Ibid., p. 371.) The difference on this point is a difference in degree merely.[152] Further, Fisher makes the same point with reference to deposits subject to check that he makes with reference to book-credits, namely, that their use increases the velocity of money. To say that one has a direct effect on prices, and the other only an indirect effect is absolutely arbitrary. If buying and selling are what count, if prices are forced up by the offer of money or credit for goods, and forced down as the amount of money and credit offered for goods is reduced, then one exchange must count for as much as any other of like magnitude in fixing prices. The same is true of transactions in which bills of exchange or other credit devices serve as media of exchange. Of course these considerations do not render the equation of exchange, as presented by Fisher, untrue. The equation simply states that the money and bank-deposits used in paying for goods in a given period are equal to the amount paid for those goods in a given period. It makes no assertion concerning payments for other goods, and makes no assertion as to the amount of other transactions which are paid for in other ways. General Walker, presented with the problem of credit phenomena, simplifies the thing even more.[153] He rules out all exchanges which are effected by credit devices, counting only those performed by coin, bank-notes and government paper money, and insists that the general price-level is determined in those exchanges in which money alone (as thus defined) is employed. His equation—if he had considered it worth while to use one—would then have been simply
MV = PT
where T would be merely the number of goods exchanged by means of money. One could make a similar equation, equally true, by defining money as gold coin, and reducing T correspondingly. Is there any reason for limiting the equation at all?[154] Is there any reason for supposing that any one set of exchanges is more significant for the determination of the price-level than any other set of exchanges? Does not the logic of the quantity theory require us to include all exchanges which run in terms of money?—If one wishes a complete picture of the exchanges, some such equation as this would be necessary:
MV + M´V´ + BV´´ + EV´´´ + OV´´´´ = PT,
where B represents book-credit, V´´ the number of times a given average amount of book-credit is used in the period, E bills of exchange, and V´´´ their velocity of circulation, and O all other substitutes for money, with V´´´´ as their velocity of circulation. Even then we have not a complete picture, if direct barter or the equivalents of barter can be shown to be important.
For the present, I waive a discussion of the comparative importance of these different methods of conducting exchanges. The situation varies greatly with different countries. Fisher's and Kemmerer's equations are at best plausible when presented as describing American conditions, are much less plausible when applied to Canada and England, and are caricatures when applied to Germany and France.
So much for the statement of the equation of exchange, except that it is important to add that the period of time chosen for the equation is one year. Just why a year, rather than a month or two years or a decade should be chosen, may await full discussion till later. I shall venture here the opinion that the yearly period is not the period that should have been chosen from the standpoint of Fisher's causal theory, and that it probably was chosen, if for any conscious reason at all, because of the fact that statistical data which Fisher wished to put into it are commonly presented as annual averages. The question now is, however, as to the use to be made of the equation in the development of a causal theory.
CHAPTER IX
THE VOLUME OF MONEY AND THE VOLUME OF CREDIT
John Stuart Mill, who first among the great figures in economics gives a realistic analysis of modern credit phenomena, thought that credit acts on prices in the same way that money itself does[155] and that this reduces the significance of the quantity theory tendency greatly, and to an indeterminate degree. The quantity theory is largely whittled away in Mill's exposition of the influence of credit. In Fisher we have a much more rigorous doctrine. The quantity of money still governs the price-level, because M governs M´. The volume of bank-deposits depends on the volume of money, and bears a pretty definitely fixed ratio to it. Just how close the relation is, Professor Fisher does not say, but the greater part of his argument, especially in ch. 8,[156] rests on the assumption that the ratio is very constant and definite indeed. At all events, the importance of the theory, as an explanation of concrete price-levels, will vary with the closeness of this connection, and the invariability of this ratio. It is not too much to say that the book falls with this proposition, to wit, that M controls M´, and that there is a fixed ratio between them. We would expect, therefore, a very careful and full demonstration of the proposition, a care and fullness commensurate with its importance in the scheme. But the reader will search in vain for any proof, and will find only two propositions which purport to be proof. These are: (1) that bank reserves are kept in a more or less definite ratio to bank deposits; (2) that individuals, firms and corporations preserve more or less definite ratios between their cash transactions and their check transactions, and between their cash on hand and their deposit balances.[157]
If these be granted, what follows: the money in bank-reserves is no part of M! M is the money in circulation, being exchanged against goods, not the money lying in bank-vaults![158] The money in bank-vaults does not figure in the equation of exchange. As to the second part of the argument, if it be granted, it proves nothing. The money in the hands of individual and corporate depositors is by no means all of M. It is not necessarily the greatest part. The money in circulation is largely used in small retail trade, by those who have no bank-accounts. A good many of the smallest merchants in a city like New York have no bank-accounts, since banks require larger balances there than they can maintain. Enormous quantities of money are carried in this country by laborers, particularly foreign laborers. "The Chief of the Department of Mines of a Western State points out that when an Italian, Hungarian, Slav or Pole is injured, a large sum of money, ranging from fifty dollars to five hundred or one thousand, is almost always to be found on his person. A prominent Italian banker says that the average Italian workman saves two hundred dollars a year, and that there are enough Italian workmen in this country, without considering other nationalities, to account for three hundred million dollars of hoarded money."[159] I do not wish to attach too great importance to these figures, taken from a popular article in a popular periodical. It is proper to point out, too, that these figures relate to hoarded money, rather than to M, the money in circulation. But in part these figures represent, not money absolutely out of circulation, but rather, money with a sluggish circulation. And they are figures of the money in the hands of poor and ignorant elements of the population. Outside that portion of the population—larger in this country than in any other by far[160]—which keeps checking accounts, are a large body of people, the masses of the big cities, the bulk of rural laborers, especially negroes, the majority of tenant farmers, a large proportion of small farm owners, especially nominal owners, and not a few small merchants in the largest cities, who have no checking accounts at all. A very high percentage of their buying and selling is by means of money. Kinley's results[161] show that 70% of the wages in the United States are paid in cash, and, of course, the laborers who receive cash pay cash for what they buy. (Not necessarily at the time they buy!) Money for payrolls is one of the serious problems in times of financial panics.[162] To fix the proportion between money in the hands of bank depositors and non-depositors is not necessary for my purposes—a priori I should anticipate that there is no fixed proportion. But it is enough to point out that money in the hands of depositors is not the whole of Fisher's M. Of what relevance is it, then, to point out, even if it were true, that an unascertainable portion of M tends to keep a definite ratio to M´, when the thing to be proved is that the whole of M tends to keep a definite ratio to M´? Fisher's argument is a clear non-sequitur. If it proves anything, it proves that a sum of money,[163] not part of M, and another sum of money, an unknown fraction of M, each independently, for reasons peculiar to each sum, tends to keep a constant ratio to M´. This gives us l'embarras des richesses from the standpoint of a theory of causation! Two independent factors, bank-reserves and money in the hands of depositors, each tending to hold bank-deposits in a fixed ratio, and yet each moved by independent causes! By what happy coincidence will these two tendencies work together? Or what is the causal relation between them? And if, for some yet to be discovered reason, Professor Fisher should prove to be right, and there should be a fixed ratio between M as a whole and bank-deposits, would it not indeed be a miracle if all three "fixed ratios" kept together? Bank-deposits, indissolubly wedded to three independent variables[164] (independent, at least, so far as anything Professor Fisher has said would show, and independent in large degree, certainly, so far as any reason the present writer can discover), must find their treble life extremely perplexing. May it not be that Professor Fisher has pointed the way to the real fact, namely, that bank-deposits are subjected to a multitude of influences, no one of which is dominant, which prevent any fixed ratio between bank-deposits and any other one thing? At a later point, I shall maintain that this is, indeed, the case.
Be it noted further, however, that even if we grant a fixed ratio, on the basis of Fisher's argument, between M and M´, Fisher has offered no jot of proof that the causation runs from M to M´. He simply assumes that point outright. "Any change in M, the quantity of money in circulation, requiring as it normally does a proportional change in M´, the volume of deposits subject to check." (Ibid., p. 52, Italics mine.) For this, no argument at all is offered. A fixed ratio, so far as causation is concerned, might mean any one of three things: (a) that M controls M´; (b) that M´ controls M; (c) that a common cause controls both. Fisher does not at all consider these alternative possibilities. I shall myself avoid a sweeping statement as to the causal relations among the factors in the equation, because I do not think that any of the factors is homogenous enough, as an aggregate, to be either cause or effect of anything. But if a generalization concerning these magnitudes were required, I should be disposed to assert that the third alternative is the most defensible, and that to the extent that M and M´ vary together it is under the influence of a common cause, namely, PT! That is to say, that the volume of bank-deposits and the volume of money tend to increase or decrease in a given market—and Fisher's theory is a theory of the market even of a single city[165]—because of increases or decreases in PT (considered as a unitary cause rather than as two separate factors) in that market. But I shall not put my proposition in quite that form, as I find the factors in the equation of exchange too indefinite for satisfactory causal theory.
So much for the validity of Fisher's argument, assuming the facts to be as he states them. Are the statements correct? Do banks tend to keep fixed ratios between deposits and reserves? Do individuals, firms, and corporations tend to keep fixed ratios between their cash on hand and their balances in bank? Regarding this last tendency, Professor Fisher says in a footnote on p. 50, "This fact is apparently overlooked by Laughlin." I think it has been generally overlooked. I have found no one who has discovered it except Professor Fisher. Certainly no depositor whom I have consulted can find it in his own practice—and I have put the question to "individuals, firms, and corporations." The further statement which Professor Fisher adduces in its support does not prove it, namely, that cash is used for small payments, and checks for large payments.[166] It would be necessary to go further and prove that large and small payments bear a constant ratio to one another, and further, that velocities of money and of bank-deposits employed in these ways bear a constant relation. If Fisher has any concrete data, of a statistical nature, to support the doctrine of a constant ratio between bank-balance and cash on hand in the case of individual depositors, he has failed to put them into his book. Nor is there any statistical evidence offered in the case of banks. It should be noted here that finding a general average for a whole country or community would not prove Fisher's point. General averages give no concrete causal relations. Fisher's argument, moreover, starts with individual banks and individual deposit-accounts (pp. 46 and 50) and generalizes the individual practice into a community practice. He would have to offer data as to individual cases.
While general averages could not prove the contention of a constant ratio between reserves and deposits for individual banks, general averages can disprove the contention. A constant general average would be consistent with wide variation in individual practices, on the principle of the "inertia of large numbers." But if the general average is inconstant, it is impossible that the individual factors making it up should be constant. This disproof is readily at hand, both for the ratio of deposits to reserves in the United States, and for the ratio of demand obligations to reserves among European banks (most of which do not make large use of the check and deposit system).
For the United States, from 1890 to 1911, taking yearly averages, we have a variation in the ratio of reserves to deposits of over 73% of the minimum ratio. The ratio was 26% in 1894, and 15% in 1906. "The juxtaposition of these extreme variations shows how inaccurate is the assumption that the deposit currency may be treated as a substantially constant multiple of the quantity of money in banks."[167] For New York City, the annual average percentage of reserves of Clearing House banks to net deposits varies from 24.89% in 1907 to 37.59% in 1894.[168] The extreme variations[169] in weekly averages are (for the sixteen years, 1885-1900) 20.6% in August, 1893 and 45.2% in February, 1894. These figures are extreme, since the number of occurrences is small for them, but there are numerous occurrences of deviations from the mean as wide apart as 24% and 42%.[170] The yearly fluctuation in all these ratios is very great.
The ratio of money held by the banks and money held by the people also shows wide variation, and considerable yearly fluctuation. There is a further complication, for the United States, of varying proportions of the total monetary stock held by the Federal Treasury. As between the banks and the public, the banks held about a third in 1893 (average for the year), and nearly half in 1911.[171] Whatever may be the relations between money in the hands of the people, money in banks, and volume of deposits, in "the static state," there is no statistical evidence whatever to justify the notion of fixed relations among them in real life.[172] We shall later show that there can be no static laws whatever governing the relations of credit and reserves.[173]
For European banks, the case is equally clear. European bankers deny any intention of keeping any definite reserve ratio. This appeared very clearly in the "Interviews" obtained for the Monetary Commission with leading European bankers.[174] The Banque de France increased its gold reserves, between 1899 and 1910, by 75%, but increased its discounts and advances during the same period by only 5%.[175] J. M. Keynes[176] points out that the reserves of the great banks of the world, and of Treasuries which act as central banks, have absorbed an enormous part of the gold produced in the fifteen years before the War, increasing their holdings from about five hundred million pounds sterling in 1900 to one billion pounds sterling at the outbreak of the War. "The object of these accumulations has been only dimly conceived by the owners of them. They have been piled up partly as the result of blind fashion, partly as the almost automatic consequence, in an era of abundant gold supply, of the particular currency arrangements which it has been orthodox to introduce.... The ratios of gold to liabilities vary very extremely from one country to another, without always being explicable by reference to the varying circumstances of those countries.... The contingencies, against which a gold reserve is held, are necessarily so vague that the problem of assessing the proper ratio must be, within wide limits, indeterminate. It is natural, therefore, that bankers, who must act one way or the other, should often fall back on mere usage or accept that amount of gold as sufficient which, if they are chiefly passive, the tides of gold bring them. [Italics mine.] At any rate, the management of gold reserves is not yet a science in most countries. There is no ideal virtue in the present level of these reserves. Countries have got on in the past with much less, and under force of circumstances could do so again."
It will be noticed that Keynes, in the passage cited, is speaking of gold reserves, while Fisher's contention relates to all kinds of money available for reserves, which in this country would include gold, silver dollars, greenbacks, and, for many State banks, the notes of national banks. He is also talking of the relation of reserves to demand liabilities, which for most great European banks are primarily notes, rather than of reserves to deposits. But as an exposition of the theory of the ratio of reserves to deposits (the chief liability of American banks), it is applicable to American conditions, and as a statement of the facts, it of course gives a basis for testing Fisher's doctrine generally. I do not think that Fisher's fixed ratio, as between reserves and deposits, or even the ratio which more moderate quantity theorists might seek to find between gold and demand liabilities, will find any justification in the facts of banking history.[177]
A factor which has developed on a grand scale in recent years has tended still further to weaken any tendency that may be supposed to exist toward a fixed ratio between money-reserves and demand-liabilities. I refer to the gold exchange-standard, in India, the Philippines, and elsewhere, and to the practice of the great banks of the continental countries of Europe, particularly the Bank of Austria-Hungary, of holding foreign gold bills, rather than gold exclusively, as reserve to cover note issue. In the case of the Austro-Hungarian Bank, which has carried this practice to the extreme, all possibility of a fixed ratio between gold reserves and demand-liabilities has vanished. The ratio is highly flexible. When bills are cheap, i. e., when the exchange is "in favor" of Austria-Hungary, the Bank buys bills with gold; when bills are high, when the exchanges have turned "against" Austria-Hungary, the Bank sells bills for gold. Commonly, the holder of a note of the Austro-Hungarian Bank does not ask for it to be redeemed in gold, but in foreign exchange. The reason for this practice on the part of the Bank is primarily economy. A large holding of gold would represent idle capital—a heavy burden for the Bank of a debt-ridden and poorly developed country. Foreign bills, however, serve equally well for maintaining the value of the bank-notes, and at the same time bear interest.[178] A similar practice has been employed by the Reichsbank, by the National Bank of Belgium,[179] by virtually all the debtor countries of Europe, and the great trading countries of Asia.
Confidence in these conclusions is much increased by a study of the views of Professor Taussig.[180] Professor Taussig is, in his initial formulations of his doctrine, a quantity theorist. In a situation where only money is used, credit being excluded, in effecting exchanges, he would hold that the quantity theory correctly accounts for prices. He is fond of the old formulation, as a first approximation, even in dealing with the complex facts of modern banking. But he does not dodge the complex facts, and his theory becomes, substantially, first, a general formula, and second, an elaborate body of qualifications and exceptions, the latter making up the major part of the theory. His doctrine regarding the relation of money and credit is as follows: there is, in the long run, a real limitation on elastic credit instruments in the quantity of specie. (This is very different from the assertion that there is a fixed ratio between deposits and money in circulation, including paper, bank-notes, etc., in money. The present writer has no quarrel with the doctrine that the gold supply of the world imposes outside limitations on the possible expansion of credit.) The limitation, Taussig holds, comes in two ways: (1), in the connection between prices in any one country, and prices in the world at large; (2), in various links of connection between the volume of deposits (and of notes elastic like deposits) and the quantity of specie. I shall consider at a later point the relation between prices in different countries.[181] I shall there maintain that the quantity theory, which explains gold movements on the basis of price-levels in different countries, is inadequate; that not price-levels, but particular prices, of goods most available for international trade, are of primary importance, and that of these particular prices, one, namely the "price of money," or the short time money-rate, is most significant of all. For the present, I wish to analyze the linkages which Taussig finds between elastic credit instruments and specie, and to see how far they would go, not in proving Taussig's point (with which I have little quarrel) but in proving Fisher's contentions. The points involved are: (a) Direct necessity constrains the bankers to keep some cash on hand.[182] This fixes a minimum limit (Taussig's contention), but does not at all suggest a "normal ratio" (Fisher's contention). (b) Binding custom, as to the proper amount of reserve that banks should carry, particularly important in connection with the Bank of England, but also in evidence in the Banque de France and the Reichsbank. Here again, however, minimal, rather than fixed, ratios are suggested. Limitations on the expansion of credit these customs may impose, but they by no means determine a normal, or average amount of credit expansion—in England least of all, since there is so large a flexible element in the deposits of the Joint Stock Banks, whose reserves are largely secret. The statement supra quoted from Keynes, together with the testimony of European bankers, may be considered in connection with this point, also, as to the factors determining the reserve policies of the great European banks. The extent to which custom really binds is doubtful. (c) Direct regulation by law, peculiar to the United States. Here again, a minimum, rather than a fixed ratio, is indicated. Some limitation on credit expansion by the banks is caused by this at times, but Fisher's argument would require vastly more. (d) The interaction in the use of deposits, notes, and other constituents in the circulating medium. The point involved here is that different kinds of business call for different kind of media. Small retail business is not done with hundred dollar bills, nor are stocks and bonds bought with pennies. Limiting the size of bank-notes to five pounds in England compels the use of a large amount of gold for smaller transactions, and keeps a larger amount of gold in use than would otherwise be the case. Expanding business draws cash from the banks for circulation, trenching on reserves. That Professor Taussig has a point here is not to be doubted, but how closely it limits the expansion of credit will depend on the degree to which different kinds of media of exchange really are thus specialized. In a country like the United States, where checks may be used for virtually any transaction of over a dollar, and where small change for less than a dollar will be increased by the Government to meet the demands of trade, the point would not seem to involve a practically serious limitation.
Finally, Professor Taussig recognizes a coefficient with the quantity of specie in the temper of the business community. Whether or not deposits are to expand, depends not only on reserves, but also on the attitude of borrowers.
Taussig concludes: "Thus there is only a rough and uncertain correspondence of bank expansion with bank reserves; much play for ups and downs which have no close relation to the amount of cash in bank vaults, and still less direct relation to the amount of money afloat in the community at large. Where bank media, whether in the form of deposits or notes, are an important part of total purchasing power, the connection between general prices and quantity of 'money' is irregular and uncertain." (Italics mine.)
This conclusion would be of little service in supporting Fisher's rigorous contentions! Our constructive theory concerning the relations of reserves and deposits, or reserves and demand liabilities, must wait for later discussion, in the chapter on "Bank Assets and Bank Reserves" in Part III. It will there be maintained that there are no "normal" or "static" laws governing the percentage of reserves to demand liabilities, or to deposits, that the reserve function of money is a dynamic function, and that its whole explanation must be found in dynamic considerations. For the present, I am content to have analyzed two widely divergent views, one the extreme view of Professor Fisher, representing the quantity theory in its utmost rigor, and the other, the view of Professor Taussig, who virtually surrenders the quantity theory in complex modern conditions.
In between these two writers, verging more toward Fisher than toward Taussig, will be found, with great individual variation, the rest of the quantity theorists. The quantity theory, as an instrument of prediction, becomes important only to the extent that Fisher's view is maintained.
CHAPTER X
"NORMAL" VS. "TRANSITIONAL" TENDENCIES
The Quantity Theory, as a causal theory, is, then, little altered by the passage from a hypothetical, creditless economy to the actual world, where a vast deal of credit is used,—particularly in Professor Fisher's hands. Of the different kinds of credit, only deposits subject to check are recognized as directly influencing prices, and deposits subject to check are controlled by the volume of money. The causal theory[183] remains, then, as follows: if M be increased, it will increase M´ proportionately; it will not change the V's; it cannot increase T; to keep the equation straight, therefore, P must rise in proportion to the rise in M. A decrease of M, reducing M´ proportionately, leaving V's and T unchanged, must proportionately reduce P. P is passive. A change in P cannot sustain itself, unless it be due to a prior change in T, the V's, M or M´.
This theory is set forth with the qualification that these effects are the "normal" effects of the changes in question. The proportion between quantity of money and price-level is not strictly maintained during "transition periods." I now approach the most difficult question which I shall have to answer as to the meaning of Fisher's terms. The same problem arises for all quantity theorists. Precisely what is the distinction between "transition periods" and "normal periods"? What limitations and qualifications does he admit to the rigorous statement of his theory so far given? I may first express the opinion that the line shifts greatly in his own mind, or at least shifts greatly in the exposition. I do not find an explicit statement in which definitions are given. The matter is chiefly discussed by Fisher in ch. 4,[184] which is called "Disturbance of Equation and of Purchasing Power during Transition Periods." There we find, as I have stated, no definitions, but the initial statements would suggest the following: a transition period is the period following a change in any one of the factors in the equation during which a readjustment among all the others is taking place; the normal period is the period preceding such a change, or following the transition after such a change, and is characterized by the fact that all the factors are at rest, in stable equilibrium. Equilibria during transition periods are unstable. During the transition, the relations among the factors vary: M and M´ need not keep their fixed ratio; P need not be wholly passive; M and P need not keep the same proportion. But until M and M´ get back into the normal ratio, until P becomes proportional to M (in the proportion prior to the initial disturbance), there is no rest; the equilibrium is unstable. How long is a transition period? How realistic is the notion of a transition period? Is the transition period a theoretical device, to aid in isolating causes, or is it supposed to be a real period in time? Is the normal period a real period in time, or is it merely a theoretical hypothesis? It is not easy to answer these questions. Thus (p. 72) the seasonal fluctuations are declared to be "normal and expected," and, at the same time, one gets the impression that Fisher considers them illustrations of his "transitions," in which the normal theory does not strictly hold (pp. 72, 169). What is described chiefly in the chapter on transition periods is the business cycle—a theory of the business cycle, based primarily on the notion that the failure of interest to rise as fast as prices rise causes the "boom," and that the draining of bank reserves precipitates the crisis. I shall not discuss this theory, as a theory of business cycles, further than to say that Wesley Mitchell's study would indicate that the interest rate is a minor factor, and that, while as a theoretical possibility, the drains on bank reserves may check prosperity if something else doesn't do it first, practically something else always does come in ahead, so far as his studies have gone.[185] My interest here is primarily in seeing the limitations Fisher imposes on his theory, and the qualifications he admits. If the business cycle is the typical transition period, during which his normal theory doesn't hold, when does the normal theory hold? When are the "normal periods"? There is no concrete period during which prices are neither rising nor falling, during which no important changes are taking place among the factors.[186] At times, Fisher seems to indicate that the normal period is imaginary (pp. 56, 159). Is, then, the contrast between a realistic "transition period" and a hypothetical "normal period" or are both hypothetical? Is the equation of exchange, too, a mere hypothesis? It should be, if it is to set forth a merely hypothetical theory. But no, Fisher insists on putting concrete data into it, and, indeed, gives an elaborate statistical "proof" of the equation. It, at least, is realistic. I confess that my certainty as to Fisher's meaning grows less, as I study his book with greater care. If the typical transition period be the business cycle, then the normal period could come only once, say, in ten years—or whatever period, regular, or irregular, one chooses to assign to the business cycle. The concrete price-levels for the greater part of the time are then surrendered to other causes. And the one-year cycle described in the equation of exchange is quite irrelevant. The equation of exchange should cover the whole business cycle, to fit in with the theory. Indeed, a realistic equation of exchange would then have no meaning at all, as the average price-level during the business cycle, played upon by a host of causes other than the factors described in the quantity theory, would not be the same as the average price-level which would have obtained had only the "normal" causes been in operation.[187]
The distinction between "normal" and "transition" periods suggests a dangerous fallacy: namely, that during one period one sort of causation is working, with the other in abeyance. In fact, whatever causes there are are working all the time. The only legitimate thing is to abstract from one set of causes, and see what the other set, if left to themselves, will bring about. But this sort of abstraction has many dangers, one of which is that the causes abstracted from are frequently thought of as non-existent. The chemist, in his laboratory, can in actual physical fact abstract impurities from his chemicals, and see what they will do. He can even perform experiments in what is practically a vacuum. But the economist has no right to think in vacuo! All that he has a right to do is to assume the factors which he does not wish to study constant. And even that he must not do if (1) changes in the factors which he wishes to study do in fact lead to changes in the factors abstracted from, or (2) if the factors which he wishes to study can only change because of prior or concomitant changes in the factors from which he is abstracting. Is it, for example, legitimate to assume an increase in M´ apart from its usual accompaniment, an increase in PT?
The notion, too, that causation can be seen in a state of stable equilibrium should be critically analyzed. Causation is only revealed by a course of events, when mechanical causation is involved. The relation of cause and effect may be a contemporaneous relation in fact, and it is possible, where conscious, psychological phenomena are involved, to discern causal relations among the elements in a mental state by direct introspection. It is the not uncommon practice, also, in the theory of mechanics, or in theoretical economics, where the method of investigation is deductive rather than inductive, to abstract from the temporal sequence, and to construe causal relations as timeless, logical relations. But even here, the cause of a change in the general situation precedes the change in time, and it is only by abstraction that the time element is left out. If there is no question as to the causal relations, this abstraction is legitimate, but if all that one knows about the situation be that in a stable equilibrium certain constant ratios obtain, then the question as to which term in the ratio is cause and which is effect remains unanswered. In Fisher's situation, then, assuming that it be true—which I shall deny—that the only stable equilibrium is that which the normal theory requires, it still remains true that the causal relations among the factors can only be revealed by a study of the transitions, by seeing the temporal sequence of changes in the factors of the equation. Even if it be granted that M, M´ and P tend to keep a constant relation to one another, the quantity theory falls if, for instance, it can be shown that a change may first occur in P, spread to M´, and finally reach M last of all, leading to a new normal equilibrium which is stable. I shall later show cases of this sort.[188]
The abstract formulation of Fisher's contrast will not, I believe, give us an answer as to the extent to which he thinks his quantity theory realistic. I find myself particularly in genuine uncertainty as to the point mentioned above: would an actual equation of exchange for the whole business cycle, made up of the averages of M, M´, V, V´, P and T for the whole period, exhibit the "normal" relations among these factors? Or would this "normal" relation only emerge concretely at some moment of time in the course of the cycle when the abnormal causes affecting the price-level happened to offset one another? Or is it true that no actual figures which might be found, either for a moment of time, or as averages for any given period, will exhibit the relations required, and that only a hypothetical equation, based on the figures for M, M´, V, V´, P and T that would have been realized had there been no "disturbing" causes, will show these "normal" relations? If, as Fisher at times indicates—as in his reference to Boyle's Law (p. 296)—he is stating only an abstract tendency, which may be neutralized by other tendencies in the situation, so far as concrete results are concerned, then it is this last doctrine which we must take, and the concrete equation of exchange has little if any relevance. If, moreover, this last interpretation be given, then the whole of Fisher's elaborate statistical "proof" is pointless. The only sort of statistical proof which would be relevant would be of a much subtler sort, not a mere filling out of the equation of exchange by means of annual figures, but an effort to disentangle and measure the importance of his tendency, as compared with other tendencies. But we have the other tendencies merely mentioned in qualitative terms, and we never find any definite statement, of mathematical character, as to how important they are.
It seems pretty clear, however, that on the whole, despite occasional suggestions that his theory is abstract, Fisher means his theory to be the overwhelmingly important point in the explanation of actual price-levels. He is particularly insistent on the high degree of the generality of his contention that P is passive. Thus: "So far as I can discover, except to a LIMITED extent during transition periods, or during a passing season, (e. g., the fall) (capitals mine, italics Fisher's), there is no truth whatever in the idea that the price-level is an independent cause of changes in any of the other magnitudes, M, M´, V, V´, or the Q's."[189] On p. 182 he enumerates in a series of propositions his general normal theory, and adds, as the first sentence of proposition 9: "Some of the foregoing propositions are subject to SLIGHT modification during transition periods." (Italics and capitals mine.) And the general drift of the argument, particularly in chapter 8, where the heart of Fisher's causal theory is presented, would indicate that the concessions he is disposed to make are very slight, indeed.