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.