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).