§ 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 Kinleywith the assistance of Professor Weston. The resulting figure for money deposited in 1909 is 19.1 billions.

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:—

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,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 Laborfor 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:—

"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.

"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:—

"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.

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.

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:—

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.