Front Page Titles (by Subject) APPENDIX TO CHAPTER XII - The Purchasing Power of Money, its Determination and Relation to Credit, Interest and Crises
Return to Title Page for The Purchasing Power of Money, its Determination and Relation to Credit, Interest and Crises
The Online Library of Liberty
A project of Liberty Fund, Inc.
APPENDIX TO CHAPTER XII - Irving Fisher, The Purchasing Power of Money, its Determination and Relation to Credit, Interest and Crises 
The Purchasing Power of Money, its Determination and Relation to Credit, Interest and Crises, by Irving Fisher, assisted by Harry G. Brown (New York: Macmillan, 1922). New and Revised Edition.
About Liberty Fund:
Liberty Fund, Inc. is a private, educational foundation established to encourage the study of the ideal of a society of free and responsible individuals.
The text is in the public domain.
Fair use statement:
This material is put online to further the educational goals of Liberty Fund, Inc. Unless otherwise stated in the Copyright Information section above, this material may be used freely for educational and academic purposes. It may not be used in any way for profit.
APPENDIX TO CHAPTER XII
§ 1 (TO CHAPTER XII, § 1)
|CHECKS DEPOSITED (IN MILLIONS)|
|(1)||(2) NEW YORK CITY||(3) OUTSIDE NEW YORK CITY||(4) TOTAL U.S.|
|March 16, 1909||239||786||1025|
|Daily average if New York were alone abnormal||306||786||1092|
|Ratio average to actual = 1092/1025 = 1.07|
Splitting the difference between our extreme limits, 1.07 and 1.28, we get, as our estimate of the correction factors, 1.17 in 1909 as compared with .68 for 1896. The range of possible error on either side is about 10 for 1909 and 8 for 1896. As the limits are all very extreme, the probable error must be much less—perhaps half as much. We may judge that the correction factors, .68 and 1.17, are probably correct within 5 or 6 per cent.
We conclude, then, that the 468 millions estimated as the actual check deposits made on July 1, 1896, must be multiplied by .68 in order to obtain the estimated average daily deposits in 1896. The result is 318 millions; which, multiplied by the 305 (settling days), gives 97.0 billions as our estimate for the check transactions in the United States for the year 1896.
Likewise, multiplying the estimated volume of actual check transactions in the United States on March 16, 1909 (viz. 1025 millions), by the correction factor, 1.17, we obtain 1.20 billions as the estimated daily average check deposits and transactions. Multiplying this by 303 (the number of clearing days of the New York clearing house and presumably the average number of banking days in the country), we obtain 364 billions as our estimate of the check transactions in the United States in 1909.
§ 5 (TO CHAPTER XII, § 3)
Method of Calculating M'V' for 1897-1908
Although New York clearings constitute two thirds of all clearings for the country, it cannot be imagined that the check transactions in and about New York form two thirds of the check transactions of the United States. We have already seen that the reported check deposits in New York on March 16, 1909, amounted to 239 millions. This figure, being for New York, is probably nearly complete and indicates, as we have seen, an estimated average for the daily deposits in New York City in 1909 of 306 millions. This gives 306 × 303 or 93 billions for New York City, for the entire year. Our estimate for the entire country was 364 billions, leaving 271 billions outside of New York City. Let us compare these estimated figures for checks deposited with the figures for clearings. The New York clearings in 1909 amounted to 104 billions and those outside New York, to 62 billions.
The New York clearings (104) thus exceed the New York check deposits (93), probably because the clearings on account of outside banks include clearings representing banking transactions as distinguished from commercial transactions, since New York City is the chief central reserve city. The New York City deposits were thus only 93/104 or about 90 per cent of the New York clearings. Outside of New York, on the other hand, the deposits far exceeded the clearings, being in the ratio 271/62 or 4.4. These ratios between check transactions and clearings, viz. .90 for New York and 4.4 for "outside," would indicate that the published figures for clearings should be weighted in the ratio of 4.4 to .9 or about 5 to 1. That is, on the basis of 1909 figures, five times the outside clearings plus once the New York clearings should be a good barometer of check transactions.
Of 1896, unfortunately, we lack the figures for New York City deposits. We have, however, figures for the deposits in New York state in both 1896 and 1909; and a study of these figures indicates that the ratio of weighting for 1896 should be something over 3 to 1. Not to put too fine a point upon it, we shall use the weighting 5 to 1 for all the years. The difference in the results between this system of 5 to 1 and a system of 3 to 1, or any intermediate system, will be small. but 5 to 1 is chosen because (1) the data for 1896 on which the number 3 is based are less certain than those for 1909, and (2) the New York clearings are not as good a representative of New York deposits as the outside clearings are of outside deposits; the New York clearings being somewhat vitiated by an element extraneous to New York and especially by the banking transactions connected with adjustments of bank reserves. We prefer, therefore, to give as much weight as possible to the "outside" clearings.
Having obtained our "barometer" of check transactions, viz. New York clearings plus five times outside clearings, we merely need to multiply this by the proper ratio in order to obtain the check transactions themselves. Absolute knowledge of this ratio of check transactions to the barometer exists only for 1896 and 1909, in which years we know the check transactions as well as the barometer. These ratios are .69 and .88. But we cannot err greatly in assuming that the intermediate years have intermediate ratios, varying regularly each year. The result is the following table:—
|CLEARINGS AS BAROMETER OF CHECK TRANSACTIONS|
NEW YORK CLEARINGS
BAROMETER (2) + 5 × (3)
RATIO OF CHECK TRANSACTION TO BAROMETER
CHECK TRANSACTIONS (4) × (5)
VELOCITY OF CIRCU. OF DEPOSITS (V') (6) ÷ M'
As already indicated, only the first and last figures in column (5) are independently calculated, the rest being interpolated.
The other figures in the table explain themselves. The last column gives the very important magnitude which we have called the velocity of circulation of bank deposits subject to check, or the "activity" of checkable accounts. The probable errors of the last column are believed to range between about 5 and 10 per cent.
§ 6 (TO CHAPTER XII, § 4)
General Practical Formula for Calculating V
I. An Approximate Formula
For the purpose of tracing the circulation of money, and measuring it by bank records, we may classify the persons who use money in purchase of goods into three groups:—
- 1. Commercial depositors, i.e. all engaged in business—firms, companies, and others—who have bank deposits mainly or wholly apart from personal accounts.
- 2. All other depositors, chiefly private persons.
- 3. All who, like most wage earners, are not depositors at all. These three classes we shall distinguish as "Commercial depositors," "Other depositors," and "Nondepositors," or C,O, and N. The money in the possession of "Commercial depositors" we shall call "till money," and the rest "pocket money."
The three groups necessarily include all in the community who circulate money. By circulating money is meant expending it in exchange, not for some other circulating medium, as checks, but for goods.
The nature of these three groups of people must now occupy our attention. In countries advanced in the art of banking, "Commercial depositors" include practically all business establishments, and little else; "Other depositors" include most persons in the professional and salaried classes and proprietors, and little else; while the class of "Nondepositors" is almost coterminous with wage earners.
It is true that these characterizations of the three classes are not quite complete. "Commercial depositors," for instance, do not include some small business dealers, like street vendors, for these usually have no bank accounts. But the number of such is comparatively small in comparison with the number of business men or corporations who do have accounts, and, what is more to the point, the business they do is still smaller. It follows that the money they handle is negligible. In the United States, at least, excepting those rural parts of the South and a few other places where the money expenditures are very small, the custom of having bank accounts is practically universal among business men, firms, and corporations.
To keep a bank account is, in fact, a practical necessity of business. Without such an account a business man practically deprives himself of three of the most essential aids in modern business: the use of circulating credit; the use of remittance by mail; and the use of time credit.
Unless a dealer is obliged to pay "spot cash" or prefers to do so—and such cases are both few in number and insignificant in the amounts of money involved—he will almost invariably find it easier to make payment by check. Moreover, the very fact that most other business men use banking facilities creates in his mind the desire to have an account himself, both because he dislikes to appear "different," and because, when others pay him by checks, he finds it necessary to cash these checks,—a procedure which is always more trouble than to deposit them.
Cash payments are especially inconvenient when business is done at a distance. Remitting money by post, express, or personal delivery is troublesome, risky, and expensive as compared with posting a letter containing a check. Even a post-office money order is a clumsy and expensive substitute, and its use proclaims the user an insignificant financial factor.
Again, a business man without a bank account cannot usually obtain time credit, either from dealers or from banks. In the United States a bank likes to lend only to its own depositors. A business man who asks for a bank loan usually meets with the request to open an account. If he should seek a loan from another dealer, as for instance, his supply house, the absence of a bank account would arouse suspicions as to his business standing, and might lead to a refusal.
These facts, confirmed by observation and inquiry, have led to the belief that practically all business transactions in the United States, certainly over 99 per cent (measured, not by their number, but by their aggregate size), make some use of bank accounts. Even in localities where there are no banks, traders usually like to have a bank account in the nearest town, in order to facilitate their dealings as purchasers. We conclude, therefore, that the category of "Commercial depositors" coincides for all practical purposes with the category of business establishments.
"Other depositors" include most proprietors, professional, and salaried persons. Almost no wage earners are included, and almost no business establishments or business men in a business capacity. When a single individual conducts a business, he usually separates carefully his business self from his personal self. John Smith, the individual, and the John Smith Shop are distinct. The pocket money of the one and the till money of the other are not often confused. Where payments of money are made from one to the other, the transaction is regarded as of the same nature as the payments between the shop and any other person. Originally, and under primitive conditions, it is of course true that no such distinction was observed, and even to-day the differentiation is sometimes unmarked, e.g. in the case of hucksters, peddlers, fruit-stand dealers, and small country shopkeepers. But, as we have seen, these persons are not usually depositors anyway. Moreover, their number is small; and since by the nature of the case the money they handle is also small, their classification is, for practical purposes, a matter of indifference. It is true that occasional cases exist of ordinary business men who have the exclusive ownership of a business and do not take care to separate clearly their business and their personal accounts. Yet we may, in such cases, perform the separation in thought. When such a person withdraws money from his till and puts it in his pocket, we may say his business self has paid his personal self some dividends of the business. Likewise, his checks drawn are usually distinguishable as between his business or his personal expenses, even though he himself fails to keep two separate bank accounts. But such cases are rare and unimportant, because modern business of size is usually conducted by partnerships and corporations, where a strict separation of accounts is necessary to safeguard conflicting interests.
So much for the line of demarcation between "Other depositors" and "Commercial depositors." As to the line separating "Other depositors" and "Nondepositors," it should be observed that, although "Other depositors" include most proprietors and professional and salaried persons, yet some proprietors and professional men, especially in rural communities, and some salaried persons, chiefly small clerks, are "Nondepositors."
Finally, "Nondepositors" consist chiefly of those who are classed in statistics as wage earners. While there are some wage earners who are depositors,41 they are rare; and while there are some "Nondepositors" who are not wage earners, especially (as just indicated) the agricultural proprietors (farmers) and small clerks, the amount of money circulated by them is small in comparison with the total circulation. While the line separating wages and salaries is not definitely marked in theory, it is usually easily recognized in practice.
Children under, say, twelve years need not be included in any of the three categories, as they are not handlers of money; at least, not to a sufficient degree to have any appreciable influence on the total circulation.
We may now picture concretely the main currents of the monetary flow, including the circulation of money in exchange for goods. Figure 18 illustrates the three principal types.
The corners of the triangle, C, O and N, represent the three groups of "Commercial depositors," "Other depositors," and "Nondepositors," and the B's represent banks. The arrows represent the flow of money from each of these four categories to the others. Thus Bo represents the annual withdrawals from banks by "Other depositors," Oc the spending of this withdrawn money by "Other depositors" among "Commercial depositors," and Cb the return of the money from the "Commercial depositors" to the banks. This circuit (BoOcCb) of three links is very common. A second type of circuit is represented by a chain of four arrows (BoOcNcCb. It is illustrated by private depositors drawing money (Bo), and paying wages (On) to servants who in turn spend the money (Nc) among tradesmen who finally deposit it (Cb). A third type of circuit, also fourfold, is represented by the arrows BcCnNcCb. It is illustrated by commercial firms cashing their checks at banks (Bc) for pay rolls, with the cash so obtained paying wages (Cn) to workmen who spend it (Nc) among other tradesmen who redeposit it in banks (Cb). These three types are not the only ones, but they are so much more important than any others that they merit our undivided attention before a completer study is undertaken. Figure 18 has been constructed for the purpose of exhibiting them uncomplicated by other details.
It will be noted that not all of the flows described are examples of the circulation of money. As already indicated, money may be said to circulate only when it passes in exchange for goods. Its entrance into and exit from banks is a flow, but not a circulation against goods. In the diagram the horizontal arrows represent such mere banking operations, not true circulation. On the other hand, the arrows along the sides of the triangle represent actual circulation. The diagram shows four such arrows, representing the four chief types of circulation: Oc payments of money from "Other depositors" to "Commercial depositors" in the purchase of goods; On payments from "Other depositors" to "Nondepositors," as when a housewife pays wages; Cn payments from "Commercial depositors" to "Nondepositors," as when a firm pays wages; and Nc payments from "Nondepositors" to "Commercial depositors," as when a wage earner buys goods of a merchant.
These four types of circulation of money occur in the three circuits already described, being sandwiched between the flows from and to the banks. The first, Oc, is contained within the circuit BoOcCb, and since no "Nondepositors" intervene, represents money changing hands once between its withdrawal from bank and its re-deposit there. The remaining types (On,Cn, and Nc) are contained within the two other circuits (BoOnNcCb and BcCnNcCb), and, owing to the fact that "Nondepositors" intervene, represent money circulating twice between withdrawal and re-deposit.
In short, one of the three circuits (BoOcCb) shows money circulating once out of bank. Both the others pass through N, and show money circulating twice out of bank. The diagram, then, represents all circulating money as springing from and returning to the banks; all of it as circulating at least once in the interim; and that portion handled by "Nondepositors" as circulating once in addition. Therefore, the total circulation exceeds the total flow from and to banks by the amount flowing through "Nondepositors." In other words, the total circulation in the diagram is simply the sum of the annual money flowing from and to banks and the money handled by "Nondepositors." The quotient of this sum divided by the amount of money in circulation will give approximately the velocity of circulation of money.
II. The Complete Formula
We have, however, still to consider the correction to be made for the less important forms of monetary circulation excluded from Figure 18.
In order to estimate the degree of accuracy of the first approximation just made for the circulation of money, we need to compare this approximation with a complete formula framed to include all possible transfers of money against goods.42 There are nine possible kinds of transfers, three being respectively within each one of the three groups C, O, and N, and six being between each pair of these three, in either direction.
The exchanges possible within a class are (1) those between one "Commercial depositor" and another "Commercial depositor" (2) those between one "Other depositor" and another; and (3) those between one "Nondepositor" and another. The transfers possible between classes are (4 and 5) those between "Commercial depositors" and "Other depositors" in either direction; (6 and 7) those between " Other depositors" and "Nondepositors" in either direction; and (8 and 9) those between "Nondepositors" and "Commercial depositors" in either direction. Thus there are three interclass kinds and six interclass kinds of transfers of money against goods.
Figure 19 gives a complete picture of all these nine flows of money in exchange for goods; that is, of the entire "circulation of money." The nine flows are represented in the diagram by the nine arrows about the triangle, six being along the three sides of the triangle and representing interclass circulation, and three (c, o, and n) at the corners to represent interclass circulation. The remaining six arrows on the horizontal lines represent, of course, mere banking operations. The total circulation or monetary flow (F) in exchange for goods is, therefore, the sum of the magnitudes represented by these nine arrows, viz.
F = Oc + Co + Nc + Cn + On + No + c + o + n. (1)
This is an exact formula for the circulation of money. We shall now compare it with the inexact first approximation, namely, "money deposited plus expenditures of 'Nondepositors.'" This comparison will express the error of the first approximation, and will suggest a method of transforming the exact formula (1) into a shape more suitable for statistical application. First, we need to express algebraically the first approximation. This may easily be done by inspecting Figure 19.
The total money deposited is Cb + Ob + Nb, while the total expenditure of "Nondepositors" is Nc + No. The sum of these two expressions we shall call F'. It is:—
F' = Cb + Ob + Nb + Nc + No, (2)
which is, therefore, the algebraic expression for the first approximation.
To obtain the difference, F - F', between the exact and the approximate formula, we subtract (2) from (1), canceling Nc and No and placing the negative terms first. We thus obtain for a remainder (r) the following:—
r = F - F' = - Cb -Ob - Nb + Oc +Co + Cn +On + c + o + n.(3)
That the value of F - F' is small may be seen clearly by transforming (3). We shall transform it by means of another equation (4) given below. In order to derive this new equation (4), we shall need to make a digression. This new equation is merely a special application of the general principle that the net outflow (i.e. outflow minus inflow) from the contents of any reservoir must equal the net decrease in its contents during the same time, or (algebraically expressed) that the net outflow (positive or negative) plus the net increase in contents (negative or positive) must be zero. We may apply this principle to any reservoir or store of money, but shall here find it most helpful to apply it to the reservoir of money contained among the "Commercial depositors" and "Nondepositors" taken together as one group. Let us designate the combination of these two as the "CN group." The total outflow indicated in the diagram from this "CN group" is evidently Cb + Co + Nb + No, and the total inflow Bc + Oc + Bn + On. Hence, the net outflow, so far as the diagram shows us, is:—
Cb + Co + Nb + No - Bc - Oc - Bn - On.
This, plus the net outflow not shown in the diagram, is the true net outflow. Since the diagram was constructed to show only flows against goods (monetary circulation), and flows to or from banks, we have still to take account of money flowing in the community in exchange for something else than goods, and that flowing without any exchange at all, as well as any net outflow outside of the community.
We have thus to take account of three undiagramed flows. The first is the net outflow of money from the "CN group" to the "O group," which, though in exchange, is not in exchange for goods. This means simply cashed checks, for, according to the classification we are here using, "goods" are taken to include anything exchangeable, not either money or checks. Our first correction is, therefore, the net outflow of money from the "CN group" for cashing checks, i.e. the difference between the checks cashed by the "CN group" for the "O group" and those cashed in the opposite direction.
It will be understood that we have nothing to do here with the cashing of checks at banks, for this is included in the diagram (Bo,Bn, and Bc). Moreover, we have nothing to do here with cashing of checks within the "CN group," as when a storekeeper cashes a check presented by a "Nondepositor." We have only to do with the net outflow for cashed checks from CN to O. This net outflow (which may be positive, negative, or zero) we shall designate by the letter a, to stand for "accommodation" checks.
For the second correction, we have to designate the net outflow of money given away by the "CN group" in gifts, taxes, thefts, etc., for which no specific goods are received in return. This net outflow may be designated by g.
We have, thirdly and lastly, the net outflow of money with respect to the "CN group" outside of the community, i.e. the net amount of money which is lost to the country by export, fire, shipwreck, melting, etc., in excess of that imported, minted, etc. This net outflow may be designated by e, to stand for "external" outflow. Adding the net undiagramed outflow (a + g + e) to the net diagramed outflow, we have, for the total net outflow,
Cb + Co + Nb + No - Bc - Oc - Bn - On + a + g + e.
Now, on the reservoir principle already explained, the algebraic sum of this net outflow from the "CN group" and the net increase of the money in that group must be zero. That is, representing this net increase by i, we have
O = Cb + Co + Nb + No - Bc - Oc - Bn - On + a + g + e + i. (4)
We now place this new equation (4) under the old equation (3), giving the value of r = F - F' in the following manner:—
Adding and canceling the terms of (3) and (4) indicated in parentheses, and rearranging the remaining terms, we have
The letters are grouped in parentheses forming six terms, arranged, as far as can be judged, in the order of descending importance.
By using the expression just obtained for r, the complete formula (1) for the circulation of money may now be put in a form suitable for statistical application. Since r = F - F', then F = F' + r. Substituting for F' and r the expression already given in equations (2) and (3)', we have, as a transformation of (1),
= (1) all money deposited
+ (2) money expenditures of "Nondepositors"
+ (3) C's money expenditures from tills (i.e. money expenditures in excess of money withdrawn from bank)
+ (4) O's money receipts pocketed (i.e. money receipts in excess of money deposited in bank)
+ (5) intraclass monetary circulation
+ (6) CN's undiagramed net outflow of money
+ (7) CN's net increase of money on hand
- (8) N's withdrawals of money from bank.
This is a complete and universal formula for the circulation of money in any community. Its first two terms constitute the first approximation, and the other six terms constitute r, which may be called the "remainder term."
The first and second terms are by far the most important. The last three terms—sixth, seventh and eighth—are doubtless quite negligible under all circumstances actually met with. I am also reasonably confident that, in the United States, the 3d, 4th, and 5th terms amount to less than 10 per cent of the total and probably less than 5 per cent. Therefore, the complete omission of all except the first two terms would still give us a fairly good figure for the total F; for any one familiar with the inaccuracies of statistics knows that 5 or 10 per cent is a small error, especially for a magnitude which has hitherto eluded any attempt at measurement.
We may, therefore, distinguish three successive stages in our approximations. The first approximation comprises only the first two terms, viz. money deposited plus expenditures of "Nondepositors"; the second includes, in addition, terms (3), (4), and (5), viz. till-paid money expenditures of C, pocketed money receipts of O, and intraclass circulation; while the third is rendered absolutely complete by including terms (6), (7), and (8), none of which has practical importance. The complete formula is presented in the hope of arousing discussion and investigation which will disclose in particular to what extent it may be applied in countries where data exist for the first two terms, viz. money deposited and expenditures of "Nondepositors." The former is to a large extent a matter of daily record in most civilized countries, and the latter consists chiefly of wages, a magnitude which has for long been a favorite subject for statistical estimate.
§ 7 (TO CHAPTER XII, §4)
Application of Formula to Calculation of V for 1896 and 1909
We shall now exemplify the use of our formula by means of actual figures for the United States. The Report of the Comptroller of the Currency for 1896, already referred to, and the special report of the National Monetary Commission for 1909, give a basis for estimating the first term (Cb + Ob + Nb), the annual money deposited in banks in those years. Both reports were made under the direction of Professor David Kinley of the University of Illinois. We shall consider first the figures for 1896. The total money deposited in banks on the settling day nearest July 1, 1896, was 7.4 per cent of the total deposits of all kinds. This total for all reporting banks was 303 millions, of which 7.4 per cent would make $22,400,000. It was made up of over $16,200,000 from 3474 national banks, and the remainder from 2056 other banks. There were, all together, according to the Comptroller's Report, about 13,000 banks in the country at that time. On the basis of these figures, the Comptroller attempts to estimate the (retail) deposits of all kinds for all these 13,000 banks, assuming that the average deposit was the same as for the country banks replying. This average was $2375 for banks in places of 12,000 inhabitants or less. Applying this average to the unreporting banks, we would increase the retail deposits (which were $26,500,000) by an additional $17,800,000.
If we assume the same ratio of increase for the total money deposits, the sum of 22.4 millions would be increased by 15.0 millions, making a total of 37.4 millions, as the amount of money deposited in banks on the settling day nearest July 1, 1896. This figure represents at least a rough approximation to the inflow of cash into, and, therefore, also the outflow of cash from, the banks of the country. Multiplying by 305 settling days for the year, we obtain 11.4 billions as the total annual amounts deposited. The figures, being for the settling day nearest the first of July, are probably above the daily average for the year. Thus 11.4 is an upper limit rather than an estimate. Later we shall also set a lower limit.
The preceding figures relate to the year 1896. Similar calculations for 1909 have been made by Professor David Kinley43 with the assistance of Professor Weston. The resulting figure for money deposited in 1909 is 19.1 billions.44
But if it is necessary to adjust the figures for deposits of checks in 1896 and 1909 because the days selected are exceptional (see § 4 of this Appendix), it is also necessary to adjust the figures for the deposits of money. On July 1, 1896, many June bills must have been paid by cash as well as by check and on March 16, 1909, the middle of a month, there must have been slackness of settlements by cash as well as by check. Consequently, like the total deposits of checks, the total deposits of money made on July 1, 1896, were in all probability above the daily average for 1896, and on March 16, 1909, they were below the daily average for 1909. In other words, without adjustment for the abnormality of the days selected, the figure expressing monetary circulation for 1896 would be too large, and that for 1909, too small. That is, without such adjustment our calculations merely set an upper limit in 1896 and a lower limit in 1909.
But we may easily set the opposite limits. We may be reasonably sure that deviations from the average are less for money deposits than for check deposits. It cannot be expected that daily money deposits fluctuate as greatly as daily check deposits. Practically all check payments are influenced by the periodicity in receipts of checks by the depositors (as of their salary, interest, or dividend checks), or by the periodicity of credit extended to them (as of the tradesmen who render them monthly bills). While the fluctuations to which money payments are subject are more or less similar, they are much less in extent for two reasons: First, the payment or credit cycles which influence the fluctuations of money deposits are usually shorter than those which influence the fluctuations of check deposits; the wage earner usually gets his money weekly as against the salaried man who receives his check monthly, or the stockholder who receives his dividends quarterly. Secondly, unlike check payments, many, if not most, money payments have no payment or credit cycle. There is no credit cycle in what are called "cash" payments, for they imply that no credit is given. The receipts at "cash stores," the smaller receipts at all stores, the receipts of tramway, railway, and steamship offices, the receipts at theaters and many miscellaneous establishments are almost wholly on a cash basis and result in daily and fairly steady money deposits made by these establishments. These are facts of every-day experience and are confirmed by inquiry of bankers, who state that their money deposits are far steadier day by day than their check deposits. Confirmatory and conclusive evidence is also obtainable from Kinley's investigation in the Comptroller's Report for 1896 (p. 95). If check and money deposits were to fluctuate in perfect sympathy with each other, the percentage of the total which consists of checks would remain constant. But if, as we shall endeavor to show, the excess or abnormality of check deposits on July 1 is greater than the excess or abnormality of money deposits on that date, then we ought to find that the percentage of check deposits is greater on July 1 than usual. The figures of the Comptroller's Report indicate that this is the case. They show that the percentage of checks received (unfortunately not quite synonymous with "deposits") was on September 17, 1890, 91.0 per cent and on July 1 of the same year, 92.5 per cent, or 1½ per cent higher. Again, comparing July 1, 1896, with the nearest available date for another season of the year, namely, September 15, 1892, we find the figures to be as follows: for September 15, 1892, check receipts, 90.6 per cent; for July 1, 1896, check deposits, 92.5 per cent, or 1.9 per cent higher. The excess would have been still greater if both the figures were for receipts instead of one of them being for deposits; for, as the Comptroller says, the inclusion of other receipts than deposits tends to exaggerate the percentage of checks. That July 1 has a far larger proportion of checks than June 30 is indicated by the figures for retail deposits for June 30, 1894, and July 1, 1896, the former being 58.5 per cent and the latter 67.6 per cent, or 9.1 per cent higher. We should be cautious, however, in drawing any quantitative conclusion from this difference, since the investigations for 1894 and 1896 were conducted somewhat differently. But the difference, as we find it, harmonizes with all the facts at hand. Similar confirmation may be drawn from the absence of any contrast between the figures for June 30 and September 17, 1881, as compared with the sharp contrast already noted between July 1 and September 17, 1890. The credit receipts in 1881 on June 30 and September 17 were 91.77 per cent and 91.85 per cent, respectively, which figures are substantially equal, while, as above noted, for July 1 and September 17, 1890, we find a difference of 1½ per cent.
We feel, therefore, safe in concluding that check deposits are subject to greater fluctuations or abnormalities than money deposits. Consequently the deposits of money on July 1, 1896, while they may have exceeded the daily average, were probably not so far above the daily average as were the deposits of checks; also on March 16, 1909, the deposits of money were probably not so far below the average daily deposits of money as were the deposits of checks.
Now, if this were not true,—if the money deposits fluctuated exactly parallel with check deposits,—we should need to assume the same correction-factors for money as for checks, viz. .68 in 1896 and 1.17 in 1909, with the results given in column (1) of the following table:—
|ESTIMATED MONEY DEPOSITS OF YEAR|
MONEY DEPOSITED ON DAY SELECTED (IN MILLIONS)
ASSUMING DAY AN AVERAGE ONE (IN BILLIONS)
ASSUMING CORRECTION FACTORS EQUAL TO THOSE FOR CHECK DEPOSITS
MEAN BETWEEN TWO PRECEDING COLUMNS
We see that the true value of the money deposited in banks in 1896 must in all probability lie between 7.8 and 11.4 billions, and in 1909, between 19.1 and 22.3 billions. If, in each case, we split the difference, the estimates become for 1896, 9.6, and for 1909, 20.7. The truth cannot be far from these figures, for there are only narrow limits on either side. The probable error, judged roughly from the calculated limits and from the character of the estimates of these limits, is placed at about 1 billion in each case. It will be noted, of course, that this error is larger proportionally in 1896 than in 1909.
We have now estimated the first term (total deposits) of the formula for the total circulation of money.
The next term (Nc + No) is the expenditure of the "Nondepositors" made to other classes. This is practically the expenditure of wage earners. The Census gives the average wages in manufacturing industries as $430. Mr. William C. Hunt of the Census Bureau, in an unofficial memorandum which he has kindly allowed me to see, has estimated that the laborers in the United States number about 18,400,000. Let us assume, as a reasonable approximation, that their average wages are the same as the average in manufacturing industries, namely, $430. We first apply this to the 8.5 millions of people which Mr. Hunt estimates are engaged in manufacturing and mechanical pursuits and trade and transportation. These persons, therefore, receive about 3.7 billions of dollars in wages.
The remaining classes of laborers are domestic servants and agricultural laborers. These, however, receive board and lodging as part pay. Since food and rent form about 60 percent of workingmen's budgets, we may assume that the actual money paid to domestic and agricultural workers is only about 40 per cent of that paid to manufacturing laborers, i.e. about $170. Mr. Hunt estimates the number of domestic and agricultural laborers at 9.9 millions. Hence the total money they handle in a year is probably about 1.7 billions. This, added to the previous 3.7 billions, gives 5.4 billions as the total money paid in wages in the United States All these figures relate to the year 1900, while the figures for our first term relate to 1896. In the interim both the number of laborers and their wages doubtless increased somewhat and we must, therefore, make a correction for each. We shall assume that the number of laborers increased in the same ratio as population, and that population increased between 1896 and 1900 at the same rate per annum as between 1890 and 1900. This would reduce the 5.4 billions to 5.0 billions. If, instead of population, we use the number of employees in manufacturing and mechanical pursuits as given by the Bureau of Labor,45 the result is lower, viz. 4.6. The truth probably lies between, since agricultural labor, for which we have no statistics, has probably not increased as fast as manufacturing labor, and, therefore, even if labor as a whole increased in the same ratio as population, the relative increase of manufacturing labor, as compared with agricultural labor, would mean a greater payment of money wages. We may select 4.8 billions as close to the truth. As to the rate of wages, the index numbers of the Bureau of Labor46 for 1896 and 1900 are 99.5 and 104.1 respectively. On this account, therefore, we should still further reduce our estimate of money wages paid in 1896,—in the ratio of 104.1 to 99.5 or from 4.8 billions to 4.6 billions. Furthermore, a small fraction of these laborers are prosperous enough to have bank accounts, and the expenditures of these should not be included among the expenditures of "Nondepositors." About 4½ billions is probably as close to the truth as we can expect to get.
But we must now add to this an allowance for "Nondepositors" other than wage earners. Some of the 2.1 million clerks and 8.6 million proprietors and professional men in Mr. Hunt's estimates, though not laborers, are nevertheless "Nondepositors." As to the clerks, it is said by business men that most clerks who receive over $100 a month, and some who receive less, have bank accounts. Probably, the great bulk of the 2 millions of persons estimated as clerks are far below $100 a month, and many are doubtless included who, like office boys, have less than what are ordinarily called wages. To make a guess sure to be large enough, let us say that three-fourths of the clerks have no bank account and average $60 a month. Even then the total cash-paid clerk hire would scarcely exceed a billion.
Among the proprietors and professional men, the only group we need to consider is agricultural proprietors (5.7 millions). The remainder consists of classes among which bank accounts are practically universal. Of these agricultural proprietors, those who have no bank accounts are doubtless smaller ones, living in districts where little money changes hands. Their number could certainly not exceed four millions, which would be over two thirds of the whole. The problem is, What cash do these farmers pay to depositors, commercial and other? Practically, this means, What do they pay to country storekeepers? Their payments to laborers or other farmers are payments to other "Nondepositors" and do not concern us here. For rent, food, or such farm supplies as they can raise themselves, they pay little or nothing. Thus, the hay crop of the nation is said to exceed in value the wheat crop; but so little hay is marketed that it is seldom quoted or thought of as a market commodity. Even the trade of these farmers with the storekeeper is conducted largely by barter or book credit. Their expenditures in actual money may be conjectured to average less than $250 a year for each farmer, making less than a billion dollars at most (even if the number of such farmers be counted at 4 millions).
It seems safe to say, then, after allowing a billion for clerks and a billion for farmers, that the total expenditures of "Nondepositors" cannot exceed 4½ + 1 + 1 = 6½ billions.
On the other hand, it can scarcely be less than 5 billions. To reduce it to this figure would require us practically to ignore the existence of "Nondepositors" other than wage earners, or to assume a large error in the estimate of wages.
We conclude that for 1896 the second term lies somewhere between 5 and 6½ billions. Placing it midway, we obtain approximately 5.7 billions with a possible error of .7 or. 8. Similar calculations for 1909 show 13.1 billions for the second term with a possible error of 1.0. To quote from Professor Kinley's article already referred to:47 —
"The second term of the formula is the money payments of 'Nondepositors,' made up principally, as Professor Fisher thinks, of the wages of working people. The following table shows an estimate of the increase from 1900 to 1909 in certain pursuits on the basis of the percentage of increase from 1890 to 1900 and on census and railroad returns since 1900. As far as possible salaried officers are eliminated.
|Domestic and personal service||4,220,812||5,580,657||32.2||7,377,628|
|Trade and transportation||1,977,491||2,617,479||35.2||4,275,913|
|Manufacturing and mechanism||4,251,613||5,208,406||6,935,113|
"A rough calculation based on the figures of Census Bulletin No. 93 gives us about $550 as the average yearly wages of people in manufacturing. If we should include mechanical pursuits, probably the average should be raised a little. Very likely $600 would be more nearly correct for this class.
"Again the Report of the Interstate Commerce Commission for 1907 gives figures from which it appears that the average yearly wage is about $640. It is more difficult to get a ground for making an estimate of the money wages of those engaged in agricultural and domestic pursuits. Doubtless it is more than, at first thought, might be believed. The money wages of domestic servants at present probably will average not less than $250 a year. Agricultural laborers are certainly receiving a good deal more than formerly, and $300 or $350 probably will not be too large a sum to assign to these. Accordingly, we may recapitulate as follows:—
|Trade and transportation||4.3 millions at $640||$2,752 millions|
|Manufacturing and mechanical pursuits||6.9 millions at $550||$3,790 millions|
|Agricultural pursuits||12.4 millions at $300||$3,720 millions|
|Domestic and personal service||7.4 millions at $250||$1,850 millions|
|Clerks, etc., having no bank account||$1,000 millions|
"This gives us the second term of the formula."
We have now estimated the first two terms (constituting together what has been called the first approximation) for both 1896 and 1909.
To this first approximation must be added the remainder, r, consisting of the many terms already explained, most of which are not known with exactness, but all of which are known to be small. The term "small" is always relative, and in this case a term is small for 1896 which is small compared to 16 billions. For instance, 160 millions is a mere trifle, being only 1 per cent of 16 billions, while 16 millions is only one tenth of 1 per cent. For purposes of comparison we do not need exact statistics for the various terms of which r is composed. All we need to know is that r is small and that it varies approximately as the rest of circulation varies. Under these circumstances a large mistake in estimating it will make a small error in comparisons. Only in case r were at once large and variable relatively to the other terms could a mistake in its estimation greatly affect the comparisons. Our attempt to estimate r has been made, not so much for the purpose of obtaining its absolute value, as to set for it wide and safe limits.
The magnitude r consists of all the five terms of our formula beyond the second. We shall take these up in order.
The third term of the formula is (Co + Cn - Bc). This represents the till-paid commercial expenditures, or the excess of the money paid out by "Commercial depositors" over the money withdrawn by them from banks. Personal inquiry shows that the great bulk of the money withdrawn by "Commercial depositors" from the banks is drawn for the purpose of paying wages; also that the great bulk of the actual money expended by "Commercial depositors" is expended for wages. In other words, Co is very small compared with Cn, and the sum of the two is nearly the same as Bc. Hence the difference (Co + Cn - Bc), or till-paid expenses, is nearly zero. Till-paid expenses, being mostly wages and, as all observation shows, only a small part of total wages (4½ billions)—certainly not over one tenth—can be set down as less than half a billion in 1896 and less than a billion in 1909.
The fourth term (Co + No - Ob) is O's money receipts which are pocketed instead of being deposited. Now O's money receipts, Co + No, are small in the first place, for O, being depositors, usually receive their dividends, interest, and salaries by check. The chief exception is found in the rents and the professional fees paid by workingmen to landlords, physicians, etc., payments which constitute most of No. But these rents and fees paid by workingmen to private individuals are only a part of total rents and fees of workingmen, and the total rents and fees themselves are known by statistics of workingmen's budgets to be only about 20 per cent of wages. From this and other clews, we may safely set half a billion as an upper limit for the fourth term in 1896. Professor Kinley places .8 billion as the upper limit in 1909.
The fifth term (c + o + n) is the circulation within each of the three groups. Obviously only in trifling cases does money circulate between one "Commercial depositor" and another, between two "Other depositors," or between two "Nondepositors." Half a billion is put as an extreme upper limit for the total for 1896 and .8 by Professor Kinley for 1909. This would mean that about one dollar out of every thirty-five expended is passed on to other persons who are within the class to which the expender belongs. In fact, the universal testimony of such few representatives of c,o, and n as I have been able to interrogate personally is that the true ratio is less than this.
The remaining three terms are even more insignificant. In the normal state of equilibrium for the "CN group" it is evident that the sixth and seventh terms would both be substantially zero. The eighth term, withdrawals from banks by people who have no bank accounts, represents very exceptional conditions, such as where workmen cash checks at banks. Workmen seldom have checks to cash and, when they have, usually cash them in stores or saloons.
We shall summarize the estimates for each of the eight terms in the following table. Each term is placed midway between upper and lower limits estimated as safe, and the possible variation in either direction is indicated after a "±". Thus, $300,000,000 ± $300,000,000 means simply that, though $300,000,000 is assigned as the estimate, the true value may be more or less by an amount not exceeding $300,000,000, in other words, that the truth lies between $600,000,000 and zero. Instead of half billions we have used in the table $600,000,000 as being more easily divisible by two. The results for both years are given in the following table, in which generous estimates are given for the "probable error" in each case. In fact most of these "probable" errors are improbably large.
|1. Money deposited (Cb + Ob + N||9.6 ± 1.5||20.7 ± 1.5|
|2. Expenditure of "Nondepositors" (Nc + No)||5.7 ± .7||13.1 ± 1.0|
|3. C's expenditure, till paid (Co + Cn - Bc||0.3 ± .3||0.5 ± .5|
|4. O's receipts, pocketed (Co + No - Ob)||0.3 ± .3||0.4 ± .4|
|5. Intraclass circulation (c + o + n)||0.3 ± .3||0.4 ± .4|
|6. Net undiagramed outflow from CN (a + g + e)||0.0 ± .1||0.0 ± .2|
|7. Net increase of money of CN (i)||0.0 ± .1||0.0 ± .2|
|8. Money withdrawn from banks by "Nondepositors" (- Bn)||-0.001±.001||-0.001±.001|
|16.2 ± 2||35.1 ±2|
The first two terms (F') constitute the great bulk of the total. The remaining six terms (r) make up less than a billion more for either year. The total reaches about 16 billions as the estimated circulation of money in the United States in 1896. This estimate is subject to error, but not as much as the total of the possible errors of individual terms, which is over 3 billions. Even if each of the possible errors indicated were as likely as not to occur, the chance that in all eight cases they should all simultaneously occur in the same direction is (½)8, or one chance in 256. We may, therefore, "trust to luck" that the errors will, to some extent, offset each other. In fact, the chance of the error reaching the sum of those of the first three terms, or 3 billions, is less than a half. The "probable error" can therefore be placed with some confidence as less than 2 billions.
Dividing the figures we have obtained for the total circulation of money by the figures for the amount of money in circulation, we obtain figures for the velocity of circulation. These are 18.6 in 1896 and 21.5 in 1909, which show remarkably little change.
Reverting now to the remark with which we began the discussion of money velocity, namely, that it circulates but seldom outside of banks, let us picture our statistical results in the light of this fact.
Evidently, if all money circulated once only, then the bank record for 1896, showing about 9½ billions annually flowing into and out of the banks, would also exactly indicate the volume of the intervening work done. This would then be 9½ billions. But the true figure is, as we have shown, probably about 16 billions, and consequently we infer that some of the 9½ billions emanating from banks changes hands more than once before it returns.
Next let us suppose that all of the 9½ billions circulate once, except the part passing through the hands of "Nondepositors" (6 billions), and that the latter circulates twice. Then 3½ billions circulate once only. Under this assumption we can account for 3½ + 2 × 6 = 15½ billions of exchange work. But we have found in fact 16 billions. The difference of about half a billion is chiefly due to the existence of some money which circulates more than twice outside of banks.
The entire 16 billions may be roughly accounted for by dividing the 9½ billions flowing from banks into three streams; 3½ billions circulating once and once only; 5½ billions, twice and twice only; and ½ billion, three times. This makes 3½ + 2 × 5½ + 3 × ½ = 16 billions. Of the three parts, the first (3½ billions) is mainly the spending money drawn by "Other depositors," the second (5½ billions) is money withdrawn from bank for wages and other payments to "Nondepositors," and the third (½ billion) is the small amount not otherwise accounted for. This is only a rough scheme of division. A very small part circulates oftener than three times.48
Similarly, for 1909, of the 21 billions flowing into and out of the banks, the 13 billions passing through the hands of "Nondepositors" must have circulated twice or more and thus have accounted for 26 billions or more of the total circulation (35 billions), leaving 21—13, or 8, to have circulated only once. This would account for 26 + 8 or 34 billions. The entire 35 billions may be accounted for by supposing the 21 billions flowing from banks to be divided into the following three streams:—
- 8 billions circulating once, making 8 billions,
- 12 billions circulating twice, making 24 billions,
- 1 billion circulating three times, making 3 billions.
The whole 21 billions, bank outflow, perform 35 billions of circulation before returning to bank.
The first two terms of the formula for the monetary circulation evidently give 15½ billions out of our estimated total of 16 billions for 1896, and 34 out of 35 for 1909; showing that the remainder, unless it has been greatly underestimated, is relatively small. The significance of this fact is that the terms most difficult to estimate statistically are least important. Of the two terms constituting the "first approximation," the first and most important is susceptible of the most accurate determination of all, while the second is made up chiefly of wages, which also are susceptible of statistical determination, or seem destined to become so.
In fact, if we should, as a statistical makeshift for the first approximation, merely add the amount of money annually withdrawn from bank to the annual money wages, we should, as to the year 1896, account for 9½ + 4½ or 14 out of 16 billions, leaving only 2 billions to be otherwise accounted for. In other words, this makeshift—the part most adapted to statistical measurement—accounts for about 88 per cent of the total circulation, leaving only 12 per cent for the part which can only be determined within wide limits. For 1909, deposits plus wages make up about 32 billions out of 35, or over 90 per cent. A still simpler makeshift is to add the deposits to the total wages without attempting to ascertain the part which is paid in money. This makeshift might be justified on the ground that total wages are more exactly ascertainable than the part paid in money, and that presumably the money part will maintain a fairly constant ratio to the total wages from year to year. The two parts here indicated may be distinguished as the measurable part (comprising the first term of our formula (1)' and most of the second term), and the conjectural part, comprising the remainder of the second term and the other six terms. Even if the allowance for the conjectural part should prove to be but half the truth, the measurable part would still constitute the great bulk of the total. The measurable part would therefore still be a safe practical index, or barometer of changes in the volume of circulation. Any excess of variation in the conjectural part, as compared with the measurable part, would, when spread over the whole, produce a disturbance only one fourth as great. It is reasonable to suppose that the conjectural and measurable parts will ordinarily vary together. If the measurable part varies 10 per cent, it is natural to suppose that the conjectural part, and therefore also the total of both, will vary likewise. But suppose this assumption erroneous and that, while the measurable part varies 10 per cent, the conjectural part really varies 14 per cent or 6 per cent. The difference between these and 10 per cent, i.e. 4 per cent, representing a supposed excess or deficiency of variation of the conjectural part, would produce a difference of only 1 per cent in the total! That is, the total, instead of varying 10 per cent, would vary 11 per cent or 9 per cent. Evidently, therefore, any unknown variation in the conjectural part can cause only a trifling variation in the result. In other words, the measurable part will always be a good index of the total—a reliable barometer of circulation. If we divide this by the quantity of money in circulation, we obtain a figure indicating the relative velocity of circulation of money from year to year. We conclude, therefore, that money deposits plus wages, divided by money in circulation, will always afford a good barometer of the velocity of circulation.
It is not always the absolute value of any magnitude we find most useful, but its relative value under different conditions. We may compare the relative length of two ships by measuring their water lines, although this method omits the overhang at either end. Such a comparison will apply roughly to any two vessels, and with great exactness to two ships of the same build. Similarly, our proposed barometer will afford rough comparisons for any two countries using banking facilities in comparable degrees, and will afford fairly exact comparisons for two successive years in the same country.
The proper statistical procedure would, therefore, seem to be to provide for the conjectural part by an estimated percentage correction, to be applied to the measurable part as a constant factor. Different correction factors will presumably apply in different countries, as, let us say, 10 per cent in the United States, 20 per cent in England, 30 per cent in France, etc. The chief value of such conjectural corrections would be to enable us to compare roughly the circulations and velocities of different countries. For comparisons in the same country at different times it would be almost immaterial what percentage correction were adopted or whether none at all were employed.
By means of the method which has been explained, it is believed that some interesting and valuable results can in the future be obtained, if statisticians in various lands will obtain (1) the total money deposited each year in banks (except by other banks), or, what is normally the same thing, the total money withdrawn from banks (except by other banks); (2) the total wages expended, or, what is practically the same thing, the total wages received; (3) if desired, a conjectural percentage addition to allow for the remaining and less known part of our formula; (4) the total money in circulation. The sum each year of (1) and (2) corrected by (3) and divided by (4) will be a very accurate barometer of the velocity relatively considered, as well as a fair approximation to its absolute value. The omission of (3) will not invalidate the results for purposes of relative comparison.
The importance of such accurate determinations can scarcely be overestimated, as the remarks on the subject by Jevons, Landry, and others have shown. When we know statistically the velocity of circulation of money, we are in a position to study inductively the "quantity theory" of money, and to discover the significance of that velocity in reference to crises, accumulation of wealth, density of population, rapid transit, and communication, as well as many other conditions. In fact a new realm in monetary statistics is laid open.
§ 8 (TO CHAPTER XII, § 4)
Interpolating Values of V for 1897-1908
To interpolate values for V we split the difference between two extreme hypotheses: the one of extreme steadiness; the other of extreme variability.
The first of these hypotheses is that V changes in a steady progression from its value of 18.6 in 1896 to its value of 21.5 in 1909. This would imply a perfectly steady growth with time, with no temporary fluctuations. But it seems unlikely that the velocity of circulation of money should not fluctuate somewhat from year to year. We have seen that, theoretically, there is a tendency under normal conditions for money expenditures (MV) to keep pace with check expenditures (M'V'). If this correspondence were perfect, we should have the ratio of MV to M'V', if not constant, at least changing in a perfectly even manner with time. Now this ratio for 1896 is 16.7 per cent and in 1909, 9.6 per cent. If we were to assume a perfectly steady change in this ratio during the intervening 13 years, the resulting value for V would have to vary considerably. This assumption is our second hypothesis of extreme variability. The following table shows the results of the two extreme hypotheses. It will be seen that in general there is no great difference between them.
HYPOTHESIS OF EXTREME STEADINESS
HYPOTHESIS OF EXTREME VARIABILITY V VARYING AS NEEDED TO PRESERVE EVENLY CHANGING RATIO OF MV TO M'V'
MEAN OF TWO PRECEDING
A supplementary calculation reveals the interesting fact that the "hypothesis of extreme variability" would make money velocity fluctuate approximately with deposit velocity. Splitting the difference between the two extreme hypotheses,—that of extreme steadiness and that of extreme variability,—we have what would seem to be an approximately correct estimate of actual velocity. It is probably correct in most cases for the first two digits. We cannot assume even for 1896 and 1909 that the third digit, that beyond the decimal, is correct, much less can we assume this to be true for the intervening years. But it is sometimes advisable to carry out the calculations to one digit beyond "the last significant figure."
§ 9 (TO CHAPTER XII, § 5)
Method of Calculating T
The table in the text is taken from the final column of the following more complete table:—
This table is constructed as follows:—
Column (2) is constructed for 1900-1909 from monthly figures on Internal Commerce published in the Monthly Summary of Commerce and Finance of the United States. By taking the monthly figures it was possible to obtain results for calendar years. This column is an average of separate indices for the following articles for which records were available. The original figures give the quantities of each article brought into the principal cities of the United States. These quantities were each multiplied by an assumed price which remained as a constant multiplier for every year. The products were then added together and the figures thus obtained taken to represent the total trade in these commodities, and to be a barometer of the relative internal commerce in the United States.
The articles referred to, and the dates for which data were used (as well as the price factors employed as explained below) are as follows:—
These articles are representative for the trade of the country and may well serve as a barometer of that trade. Yet the amount of trade, actually consisting of the sales of these articles in the few cities concerned, constitutes of course only a very small part (probably less than one tenth of 1 per cent) of the total trade of the country.
The actual figures first obtained were all divided by two before being entered in column (2) in order to bring them down to a scale more comparable with the figures of column (3). Since not all of the commodities were quoted in all the years, the table had to be "pieced out" for the defective years by the principles of proportion as already exemplified. As the statistics of the Monthly Summary go back only to 1900, the table had to be "pieced" back to 1896. This was done by using data from the statistical abstract of the United States and the abstract of the United States Census for 1900. The only figures obtainable for important articles in internal trade were those for grain, received during calendar years at fifteen principal primary markets, and for the estimated national consumption during fiscal years of the following articles, chiefly, or largely, of domestic production: cotton, wool, bituminous coal, pig iron, iron and steel railroad bars, and "distilled spirits, wines, and malt liquors."
The fiscal year figures were taken from 1896 to 1901 inclusive and reduced to calendar years on the assumption, for instance, that the true figure for the calendar year 1896 is the average of those for the two fiscal years ending June 30, 1896, and June 30, 1897. In this way we get hypothetical calendar year figures for 1896 to 1900. These figures and those for grains, which were already for calendar years, were then reduced by a factor so that each was made to be 111 for 1900, the number for that year found by the calculations involving the articles in the series, 1900-1909. The figures thus found were then averaged with weights selected to correspond with the estimates of their respective importance as judged from the estimates of their national consumption values and from the fact that some of them are indicators of large related businesses. The weights chosen were: for grains (including wheat, wheat flour, corn, rye, oats, barley, malt, and pease49 ), 20; for bituminous coal, iron and steel, liquors, and cotton, 5 each; and for pig iron and wool, 1 each.
The data for 1896-1899 are far inferior to those for 1900-1909 taken from the Monthly Summary, and this for three reasons: (1) because they are so few in number; (2) because all except the grains are for fiscal years and the hypothetical correction to calendar years is subject to error; and (3) because all except the grains are very rough estimates of consumption, not based on shipments or receipts, but based on estimated production, corrected for exports and imports, which three elements are all subject to error.
We should not be surprised, therefore, to find larger errors in the resulting figures for 1896-1899 than for 1900-1909. In fact, we shall see that such is probably the case.
For carrying out the laborious operations involved in ascertaining the index numbers from 1900 to 1908, I am indebted to one of my undergraduate students, Mr. Robert N. Griswold, and for bringing them down to 1909, to one of my graduate students, Mr. W. Y. Smiley.
Column (3) is also based on laborious calculations which were performed by Mr. Griswold. The materials were also taken from the Monthly Summary of Finance and Commerce and covered 23 staple articles of import and 25 for export. The quantities of each were multiplied by a uniform price, and the sum of the resulting figures for imports and exports was taken. The articles of imports (with the price multipliers used) were:—
The articles of exports were:—
The statistics of exports and imports are probably fifty times as full as those of internal commerce and therefore (on the principle that probable errors vary inversely as the square root of the fullness of returns) some seven times as accurate. But, on the other hand, exports and imports represent less than 1 per cent as much trade as the internal commerce of the United States, and, by the principles already explained in previous chapters, should count in the equation of exchange only at half its value, one of the parties in the exchange being a foreigner. In spite, however, of the diminutive character of external commerce, it is to some extent an index of internal commerce; since a vast amount of internal business is a preliminary to exports and a sequel to imports, while perhaps a still larger amount is in other ways indirectly related to such commerce. By balancing these and other considerations, the relative weights to be assigned to the external and internal trade were selected as given in column (5).
Column (4) gives the sales of stocks according to the ordinary figures as given, for instance, in the Financial Review. These figures are, of course, not for values, but for amounts.
Column (6) gives the figures for tons of freight carried by railroads according to Poor's Railroad Manual for fiscal years.
Column (7) gives the figures for pieces of first-class mail matter carried in fiscal years. These figures were kindly supplied by the Post Office Department. They are lacking for 1896.
We have still to describe the method employed for combining columns (2), (3), (4), (6), (7).
The first three are regarded as constituting a group by themselves, representing direct indices of trade: and the last two are regarded as constituting another group of indirect indices.
The direct indices are combined by weighting the internal commerce, twenty, the exports and imports, three, and sales of stocks, one. These weights are, of course, merely matters of opinion, but, as is well known, wide differences in systems of weighting make only slight differences in the final averages.
In this way, column (5) is found.
As to the relative weights to be given to the railroad and post office statistics, the former were weighted as two and the latter as one. Railway tonnage represents almost every conceivable commodity in commerce and comes far closer to actual trade than post office letters.
After railroad and post office indexes are thus combined, the transition from fiscal to calendar years is made on the assumption that the figures for a calendar year are the mean of the figures for the fiscal years ending June 30 of that year and June 30 of the next year.
In this way column (9) is obtained.
From columns (5) and (9) column (10) is obtained by weighting (5) two, and (9) one.
Finally, column (11) is found by magnifying the figure of column (10) in the ratio 399/155 in order to make the figure for the base year, 1909, equal to 399 billions of dollars,—the total value of the left side of the equation (MV + M'V').
The probable errors in the values of T which have been calculated are believed to be some 5 to 10 per cent for the years 1900-1909 and 10 to 15 per cent for the years 1896-1900.
§ 10 (TO CHAPTER XII, § 5)
Method of Calculating P
The table in the text for index numbers of prices is taken from the last column of the table on page 487.
Column (2) gives the index numbers of the United States Labor Bureau (No. 81, March, 1909, p. 204).
I am under obligations to the Commissioner of Labor, Mr. Neill, for his courtesy in supplying me with the figure for 1909 in advance of publication.
Column (3) is taken from the Bulletin of the Bureau of Labor, July, 1908, p. 7.
Column (4) is from "The Prices of American Stocks, 1890-1909," by Wesley C. Mitchell, Journal of Political Economy, May, 1910. These figures are doubtless the best yet available in this difficult subject.
|INDEX NUMBERS OF PRICES|
WHOLESALE, 258 COMMODITIES
WAGES PER HOUR
COLUMN (5) REDUCED TO BASIS OF 100 IN 1909
The general index number in column (5) is a weighted average of the figures in the three preceding columns, the weights being essentially the same as those used by Professor Kemmerer and for the same reasons.50 For ease in computation the weights are taken in integers, viz. 30 for column (2), 1 for column (3) and 3 for column (4). This calculation brings the table down through 1907. As column (3) is defective for 1908-1909, these years and 1907 are worked out as averages of columns (2) and (4), the weights being the same as already mentioned. The result is two series of figures, one for all three columns ending in 1907, and the other for two columns beginning in 1907. As in this case it happens that both series have the same figure (137) for 1907, no corrections need be made in 1908 and 1909. The probable errors in the figures for P may be placed as about 5 to 10 per cent.
§ 11 (TO CHAPTER XII, § 7)
Mutual Adjustments of Calculated Values of M, M', V, V', P, T
There are various methods of calculating the best adjustments, involving the theory of least squares. But the problem may be greatly simplified by dividing the process into a few separate steps. First, we ascertain the best adjustments of the calculated values of each side of the equation of exchange considered as a whole. We shall need to exercise judgment in deciding the relative errancy of the two sides, but the total adjustments are so small that differences in judgment could not make much difference in the results.
After a careful weighing of all the evidence, it is believed that the errors in the right side (PT) are liable to be about double those in the left (MV + M'V'). Accordingly, the discrepancy between the two sides is corrected by changing PT twice as much as MV + M'V'; that is, by applying to PT a correction equal to two thirds of the total discrepancy, and by applying the remaining one third to MV + M'V', the two corrections being, of course, opposite and such as to bring the two sides into agreement. Thus, for 1899, the total discrepancy is 5 per cent, of which we assign about a third, say 2 per cent, to MV + M'V', and the remaining 3 per cent to PT. That is, we propose to increase the calculated figures for MV + M'V', by 2 per cent and decrease those of PT by 3 per cent. The result will bring them nearly into agreement at 185 billions. Sometimes the results will not exactly agree, as this method of adding and subtracting percentage corrections is only approximately correct; but any remaining slight discrepancies are readily adjusted by slight empirical changes in the factors. The result is shown in the Figure 20, which gives MV + M'V' and PT (reduced by dividing by 1.11) as originally calculated, and a mean (dotted) curve which is the revised estimate of both MV + M'V' and PT.
The corrections which are thus made in MV + M'V' and PT, by which they are brought into mutual agreement, are small; but the corrections necessary in the individual factors, M,V,M', V', P,T, are smaller still. We assume, for simplicity, that the percentage corrections to be made in M and M' are equal to each other and also that the corrections to be made in V and V' are equal to each other. This is a reasonable assumption; but even if some other assumption were made, the final results would be scarcely changed.
A correction of 1 per cent simultaneously in M and M' will produce a correction of 1 per cent in MV + M'V'. Likewise a correction of 1 per cent simultaneously in V and V' will produce a correction of 1 per cent in MV + M'V'. We may then regard the correction of MV + M'V' as practically consisting of two parts: one, the correction of M and M' and the other, the correction of V and V'. As the M's are more accurately ascertained than the V's, their correction should be smaller. Thus, for 1897, the total correction assigned to MV + M'V' is 3 per cent, of which we assign 1 per cent to M and M', and the remaining 2 per cent to V and V'. That is, we increase the calculated values of M and M' by 1 per cent and those of V and V' by 2 per cent, thus effecting (approximately) the desired increase of 3 per cent in MV + M'V'. In like manner the total correction assigned to PT is distributed over P and T, assigning the major part to T. By thus distributing the corrections over (1) M and M', (2) V and V', (3) P, and (4) T, we find that only very slight individual corrections are needed, the maximum being only 5 per cent and the vast majority (50 out of 56 cases) not exceeding 2 per cent. In fact, a decided majority (35 out of 56 cases) are within 1 per cent. It is really astonishing to think that a correction of only 2 per cent or less is usually required in our calculated values of M,M', V,V', P,T, in order to make them conform perfectly to the equation of exchange. In fact, 2 per cent is less than what might naturally be considered the probable error in most of the figures as calculated. This fact justifies confidence in the general correctness of our results.
Having thus corrected, by mutual adjustment, all the factors in the equation of exchange, we are left with a figure for P which is not 100 per cent for any one year. As we prefer to call 1909 the unit year, the figures for P are adjusted on that basis and the figures for T accordingly. This change disturbs the system of corrections as measured relatively to the original figures. It reduces to zero the correction of P for 1909. In general, it makes smaller the corrections for P and T for years near 1909 and makes correspondingly larger those for years remote from 1909. But, even so, the corrections never exceed 10 per cent for T nor 6 per cent for P. As the entire scheme of corrections thus outlined is a matter of judgment and each figure was frankly "doctored" on its own individual merits in view of all the circumstances in the case, it seems inadvisable to burden these pages by any fuller statement of the voluminous details of the process. The results as shown in Figures 13, 14, 15, and 16, already given in the text, speak for themselves.
§ 12 (TO CHAPTER XII, § 17)
Credit and Cash Transactions. Comparison with Kinley's Estimates
These figures agree surprisingly well with what might be expected from a rougher calculation from Kinley's investigations. For July 1, 1896, he found that money deposits constituted 7.4 per cent of all deposits and, on March 16, 1909, 5.9 per cent. Both of these figures are too low to represent the percentage of money transactions, for the reason that money often circulates more than once before being deposited, whereas checks in general circulate but once. The figure for 1896, especially, is too low, because of the excessive amounts of checks deposited on July 1. In fact, it was largely because the 1896 figures had been criticized in this respect that Kinley made the 1909 investigation. He did not, of course, take the figures of deposits as indicating exactly the ratios of check and money transactions. He recognized the fact that these would give too low a ratio for money and too high a ratio for checks. He expressed the belief that a safe minimum for check transactions in 1896 was 75 per cent51 and in 1909, 88 per cent, implying that 25 per cent and 12 per cent were safe maxima for monetary circulation. Professor Kinley's purpose seems to be to establish safe maxima rather than to attempt exact estimates. Tabulating Kinley's figures, we have for money transactions expressed in percentage of all transactions:—
|Year||Maximum (Kinley's estimate)||Minimum (as indicated by deposits)||Mean of two preceding||Present estimate|
According to this table, if we take the percentage of money in bank deposits as a lower limit of the percentage of money transactions, and if we take Kinley's estimates as a safe upper limit, and if we split the difference between these two limits, we shall reach almost52 the same results as already reached by the more exact calculations in this book, which results are given, for comparison, in the last column. Thus the results of this book strikingly confirm those of Professor Kinley. They also agree remarkably well with the prevailing impression among business men that about 90 per cent of trade is now performed by means of checks.
[36.] See Report of the Director of the Mint, 1907,p. 87.
[37.] See Senate Document, 225, 61st Congress, 2d Session, Special Report from Banks of the United States, April 28, 1909, p. 261; also Report of Comptroller of the Currency, 1909, p. 835. The figures are exclusive of Hawaii, Porto Rico, and the Philippines, although the sum thus excluded is scarcely appreciable.
[38.] See Financial Review (the Annual of the Commercial and Financial Chronicle), 1906, p. 26 and 1910, p. 33.
[39.] Convincing proof that the clearings on July 2 exceeded those on July 1 is afforded by the fact that whereas the New York state clearings for July 1, 1896, were $140,000,000, as given in the Comptroller's Report for 1896 (p. 494), the New York City clearings alone on July 2 were $157,000,000.
For New York City the clearings, as Mr. Gilpin of the New York clearing house has informed me, were far larger on July 2, 1896, than on July 1, the two figures being 157 and 138 millions respectively.
[40.] Kinley, The Use of Credit Instruments in Payments in the United States, National Monetary Commission, 61st Congress, 2d Session, Doc. No. 399, 1910.
[41.] The term "depositors," as here used, does not, of course, include savings bank depositors. A savings bank is not a true bank of deposit, providing circulating credit.
[42.] That is, all transfers within the community considered. If it is desired to include as part of a community's circulation the sums exported or imported in foreign trade, these may most conveniently be added at the end. But even if they be included, they will be of trifling significance, partly because foreign trade is usually very small compared with domestic, and partly because money is so little used in foreign trade, especially if we exclude bullion from the category of money.
[43.] See "Note on Professor Fisher's Formula for Estimated Velocity of Circulation of Money." Publications American Statistical Association, March, 1910. The calculation are based on data taken from Professor Kinley's valuable monograph on "Credit Instruments," 61st Congress, 2d Session, Doc. No. 399 in Reports of National Monetary Commission.
[44.] Professor Kinley gives 18.3. The difference is due to the fact that Professor Kinley, while estimating the daily deposits as 62.9 millions, calls this in round numbers 60 millions. It seems preferable to use the estimate as it stands and make any allowances for errors at the end rather than the beginning. Professor Kinley also takes 305 settling days for the year, this being the number used by Professor Kemmerer for 1896. But Mr. Gilpin of the New York clearing house tells me that the clearing house business days, though 305 in 1896, were 303 in 1909. I have therefore used 303 as the number of settling days in 1909. The product 62.9 millions, times 303, is 19.1 billions.
[45.] Bulletin of the Bureau of Labor, No. 77, July, 1908, p. 7.
[46.] Ibid., p. 7.
[47.] Publications of the American Statistical Association, March, 1910.
[48.] It may avoid some confusion to remind the reader that we are dealing with sums of money expended for goods, not with individual coins. Many coins remain "in circulation" a long time without returning to bank, because used "in change." But money used in change enters as a subtractive term in monetary expenditures. When $10 are given for an $8 purchase, and $2 are received back in change, $12 have changed hands, but only $8 of monetary circulation against goods have been effected.
[49.] See Statistical Abstract of United States, 1908, p. 523.
[50.] See Money and Credit Instruments, New York (Holt), 1909, p. 139.
[51.] His original estimate for a safe minimum was 80 per cent. But in the Journal of Political Economy, Vol. V, p. 172, and in "Money," p. 44, and pp. 108, 14, he takes 75 per cent as safer.
[52.] If we take Kinley's original "safe minimum" for checks of 80 per cent, and consequently the "safe maximum" for cash as 20 per cent, we shall obtain in the above table 14 per cent, instead of the figure 16½, which would make the last two columns agree absolutely.