The Purchasing Power of Money

APPENDIX TO CHAPTER XII

§ 1 (TO CHAPTER XII, § 1)
Professor Kemmerer's Calculations

Professor Kemmerer (Money and Prices, p. 99) estimates the money in circulation (M) by deducting from the money in the United States, as estimated by the Comptroller of the Currency, two items, viz. the money in the United States treasury and that in banks (reported and estimated). He then estimates the velocity of circulation of money as 47 times a year, and assumes, in the absence of any data by which to estimate its variations, that it remains constant. He arrives at the figure 47 as follows: The amount of check transactions he first estimates for 1896, at 143 billions (p. 111). This estimate is based on figures taken from Kinley's investigation, made through the Comptroller of the Currency in 1896. Referring to Kinley's estimate that check transactions are at least three times money transactions, he takes one third of 143 billions, or 47.7 billions, as the amount of money transactions. Estimating the amount of money in circulation at 1.025 billions for 1896, he divides 47.7 by 1.025 and obtains (p. 114) 47 times a year as the velocity of circulation of money. This figure, as we shall see, is probably nearly three times too large, the error arising from the fact that Professor Kemmerer does not accept the opinion expressed by Professor Kinley that his (Kinley's) estimate for the percentage of check circulation in 1896 was a "safe minimum," but expressed the contrary opinion that it was rather a safe maximum. We shall give reasons for believing that Kinley was quite right in concluding that the estimate of check transactions at three fourths of total transactions was a "safe minimum." The calculations which we shall presently offer prove nine tenths rather than three fourths to be the probable figure.

Professor Kemmerer, as already indicated, estimates check transactions (what we have called M'V') at 143 billions in 1896. For other years than 1896, there being no corresponding data, he estimates check transactions by assuming that bank clearings are always 35 per cent thereof (p. 118). He makes no attempt to estimate M' (bank deposits) and V' (their velocity) separately. The volume of trade (T) Professor Kemmerer estimates relatively (i.e. he estimates what we have called Q in the Appendix to Chapter X). This is confessedly one of the roughest parts of all his estimates. He seeks to get as many indicators as possible of the growth of trade (p. 130), without much regard to their suitability. His indicators are fifteen in number, viz. population, foreign tonnage entered and cleared, exports and imports of merchandise (values), revenues of Post Office Department, gross earnings from operation of railroads in the United States, freight carried by railroads, receipts of Western Union Telegraph Company, consumption of pig iron, bituminous coal, wheat, corn, cotton, wool, wines and liquors, and market value of reported sales on New York Stock Exchange. Representing each of these sets of figures by index numbers, he takes their simple average as the index number of trade for each year in question.

Of course, as Professor Kemmerer well realized, many of these figures are open to more or less serious objections. Population is a poor index of trade when trade per capita is changing. Values are inappropriate unless the prices are supposed constant, which cannot be the case for exports and imports, railroad earnings, or stocks, and can be only partially the case for post office revenues and telegraph receipts.

Having thus computed for 1879-1908 the various elements theoretically determining price levels (viz. MV + M'V' and T), Professor Kemmerer uses these to calculate an index number of prices. The index number thus calculated from the other magnitudes in the equation of exchange, he calls the "relative circulation." He then compares the figures for relative circulation (virtually from the formula P = (MV + M'V') ÷ T) with the actual statistics of price levels.

These directly calculated index numbers of prices he takes as an average of index numbers of wholesale prices (Common's figures and those of the Bureau of Labor, p. 137), wages (those of reports of Bureau of Labor, p. 137), and of the Industrial Commission), and prices of railroad stocks (Industrial Commission and Wall Street Journal), weighting them as follows: wages, 3 per cent; stocks, 8 per cent; wholesale commodities, 89 per cent.

The two sets of figures—"relative circulation" and "general prices"—presented visually by curves (p. 149), show a general agreement.

§ 2 (TO CHAPTER XII, § 2)
Method of Calculating M

The estimates for M, or money in circulation in the United States, are based on the reports of Comptroller of the Currency. The calculations are shown in the following table:—

Column (2) gives the money in the United States in the middle of each calendar year according to the official estimates of the director of the mint. In 1907 these official estimates were corrected by subtracting an estimated error of $135,000,000 from the gold believed to be in the United States, this correction being made in view of the investigations of Maurice L. Muhleman. The mint corrections were made, however, only for the ends of calendar years.*36 In order to make the corrections apply to the middle of a given calendar year, the corrected figures for gold in the United States at the beginning and end of it were averaged. The average thus obtained was assumed to be the corrected figure for gold at the middle of the year. This corrected figure was then compared with the official figure for gold for the middle of the year and the difference assumed to be the correction for that date. This correction was then deducted from the figures for money in the United States given in column (2) above. We thus obtain the figures in column (3). Mr. Muhleman has made independent corrections for the middles of the years 1896-1900 inclusive. These are slightly smaller than those calculated from the mint figures as given above, the differences being in successive years, .05, .03, .00, .03, .05. Columns (4) and (5) of our table give the money in the federal treasury and the money reported in banks as stated in the annual reports of the Comptroller of the Currency. Column (6) gives the estimated percentage not reported. This estimate is found by assuming that the unreported reserves bear the same ratio to the reported reserves as unreported deposits bear to reported deposits, the latter ratios being calculated from the table given in the next section (§ 3) of this Appendix.

This estimated percentage being calculated and the correction found by it being added to the money in reporting banks, (column 5), we get the total estimated money in banks, (column 7). Column (8) is then found by subtracting from the corrected money in the United States (as given in column 3), the sum of the money in treasury (column 4), and estimated money in banks (column 7). These estimates of money in nonreporting banks are of course subject to some error; but even a 50 per cent error in the largest of them would not affect the last column much more than 2 per cent. A more important possible source of error is in column (2), which depends upon hypothetical estimates of gold in the United States. Mr. Muhleman writes me that in his opinion the corrections made by the Mint Bureau are not adequate. The corrections as made by that Bureau and here adopted affect several of the figures in column (8) by as much as 10 per cent. The errors in these corrections would presumably be much smaller than this. There are few other sources of error and, taking all things into account, it seems likely that the results are in general trustworthy—subject to a probable error of perhaps 2 or 3 per cent. This is fair accuracy as ordinary statistics go.

§ 3 (TO CHAPTER XII, § 2)
Method of Calculating M'

The calculations for obtaining M', or individual deposits subject to check, are shown in the table on page 49.

The figures of column (2) are those of "Individual Deposits" taken from the annual reports of the Comptroller of the Currency (see Report for 1909, pp. 64-66). For the years 1896-1899 correction is made for deposits of trust companies and savings banks misclassified as individual deposits. Prior to 1900 many banks included such deposits of bankers as individual deposits. They should be deducted because such deposits in one bank by other banks are not generally used for commercial purchases, but for banking operations. These deposits, to be deducted from column (2), are given in column (3).

The figures in column (3) are estimates based on the fact that the deposits of savings banks and trust companies in national banks are (whenever comparison is possible, viz. 1900-1908) found to be approximately equal to the deposits of state banks in national banks. As the state bank figures are available for 1896-1899, they are taken in lieu of the missing trust and savings figures. Since the original edition of this book was printed, consultation with the Comptroller has convinced the writer that these corrections are too large and that it would have been better to have omitted them altogether. They are retained, however, in order not to necessitate numerous changes in the plates. Fortunately, as will be seen on page 492, the net error thus retained is very small.

After deducting the correction of column (3), our next step is to add the correction of column (4), the estimated deposits unreported.

The figures for nonreporting banks for 1900 and 1902-1909 are the official estimates of the Comptroller of the Currency. (Those for 1900 and 1902 are entered in the Comptroller's tables under the rubric "reporting capital only" instead of "nonreporting," but I am assured by the Comptroller's office that this is a distinction without a difference.) The figure for 1901 is interpolated between those of 1900 and 1902. The figure for 1896 is estimated by the aid of two assumptions. The first assumption is that the unreported deposits in that year should be larger relatively to all deposits than was the case in 1903, as the table shows that the farther back we go the larger is the percentage of missing deposits. This consideration indicates that the correction exceeds .28. The second assumption is that the correction should be less absolutely than in later years; because the total deposits were then much less than later; and because the official figures in column (4), viz. those for 1900 and 1902-1909 show, as we proceed backward in time, that there is a slight tendency for them to grow less in absolute amount. (The chief exception is for 1909, when the special investigation of April 28 reached an unusual degree of accuracy.) This consideration would make the correction less than .50. Therefore, between .28 and .50 we select .40 as a rough mean. The error involved is not likely to affect the final column more than 3 or 4 per cent. The corrections for 1897-1899 are interpolated.

Column (5) gives a correction to be subtracted, viz. the deposits in savings banks. These deposits, by the nature of the case, are not used as a circulating medium, but are nevertheless included in the official "individual deposits" of column (2). The item for 1909 as here given includes, besides the reported figures, an additional item of .20 (i.e. $200,000,000), being the savings accounts of the state banks of Illinois. The inclusion of this Illinois item is simply in order to make the figures for 1909 comparable with those of the preceding years in which the same item had always been included (see Comptroller's Report, 1909, pp. 43-44).

Column (6) contains another, though small, subtractive correction, viz. the "exchanges for clearing house." In general, these exchanges represent checks which have been deposited by the persons receiving them but which have not yet reached the home bank and been charged against the persons who drew them. Any one (except a sharper or a blunderer) will, as soon as he has drawn a check, deduct the amount of it (say $100) from his deposit balance and refrain from drawing against it again. Such a person—say Smith—regards the $100 as transferred to his drawee—say Jones—and no more Smith's than money would be which he had paid out. But it takes time before the bank on which Smith draws knows of this transfer of Smith's deposits to Jones. In the meantime the bank books still include this $100 among Smith's deposits. The total figure for deposits is not disturbed by the inclusion of the $100 in Smith's account provided it is not included in Jones's account also. But when Jones deposits the check in his bank, this (Jones's) bank adds $100 to Jones's account before Smith's bank can deduct it from Smith's account. That is, the $100 is temporarily counted as both Smith's and Jones's. If both sides of this transfer were recorded at the same time, there would be no double counting. But until the check reaches Smith's bank the only record of the deduction which should be made from Smith's account is in the "exchanges for clearing house" which, accordingly, we must deduct in our statistics.

These figures, however, have to be estimated. Only for April 28, 1909, are they given for all banks, the figures being those of the special Report of the Monetary Commission already referred to. Of this amount, four fifths are of national banks; and as national banks report annually their exchanges against clearing houses, we assume that the total each year is five fourths of that reported by the national banks (see Comptroller's Report, 1908, pp. 514-522). The whole correction is so small that any error in this assumed ratio is quite negligible in the final result.

Column (7) is derived by applying to column (2) the above mentioned corrections,—deduction of items in column (3), addition of those of column (4), deduction of column (5), and deduction of column (6).

But even yet we have not reached the desired item,—deposit currency, or deposits subject to check. The net individual deposits which we have estimated include, not only current accounts, but deposits on certificate and other deposits which are considered investments rather than media of exchange. The first published attempt to give the true deposits subject to check is that of the National Monetary Commission. In their valuable special Report as of April 28,1909, constructed through the Comptroller of the Currency, the checkable deposits are given as 6.94 billions.*37 This 6.94 is subject to an addition for "nonreporting banks" and a deduction for "exchange against clearing house." The unreported deposits of all kinds are estimated for 1909 in the table at .39, of which, by proportion, only 6.94/14.01 of .39 or .19, is probably checkable. The .38 exchanges against clearing houses must be assumed to be almost wholly against deposits subject to check. The net corrected figure is therefore 6.94 + .19 - .38 or 6.75 billions as the checkable deposits in 1909. These constitute about 67 per cent of the "net individual deposits" of column (7).

This figure for checkable deposits in 1909 is found at the bottom of column (9) in the table. As it is only 67 per cent of the net individual deposits, and as it could not be assumed that the same ratio obtained for other years, I was unwilling to guess at the deposits subject to check for these other years without further light. Accordingly I wrote to Mr. A. Piatt Andrew, then Director of the Mint, and asked him whether, in his capacity as advisor to the Monetary Commission, he could not have a search made among the Comptroller's records for 1896 and a few other years in order to obtain the corresponding ratio for such years. Through his kindness and that of the Commission and Comptroller, in acceding to my request, it has been made possible to work out the corresponding ratio for 1896 as 85 per cent; for 1899 as 89 per cent; and for 1906 as 78 per cent.

Mr. Andrew gives 4.97 billions as the total (uncorrected) deposits of all banks as of July 14, 1896. This figure is slightly more complete than what I had already used from the Comptroller's Report (viz. 4.95), doubtless because, for this particular inquiry, a larger number of banks were included than had originally been used in the Comptroller's tables. Mr. Andrew gives the checkable deposits as 2.59 billions. This figure is subject to two corrections: one to account for unreporting banks, and one to account for exchanges for clearing house. We have estimated the deposits of nonreporting banks at .40; and, since Mr. Andrew has discovered in such banks .02 more total deposits (4.97) than the Comptroller reported, we must assume that there are .02 less unreported deposits in his figures than in the Comptroller's. This would make the estimated unreported deposits for Andrew's figures .38 instead of .40 which we assumed for the Comptroller's. The part of this ascribable to the deposits subject to check (2.59) is (2.59/4.97) × .38 or .20. This is the first (and additive) correction. The second (and subtractive) correction is the exchanges for clearing house, viz. .11. The final corrected figure is therefore 2.59 + .20 - .11 or 2.68. The ratio of this to the "net deposits" is 2.68/3.17 or 85 per cent.

For 1899, Andrew's figures for total net deposits are 4.38 and for checkable deposits 4.09. His figures for total deposits (7.07) are .30 completer than those of the Comptroller employed in the first column of the above table, and thus reduce the estimate for nonreporting banks applicable to Andrew's figures from .44 to .14, of which (4.09/7.07) × .14 or .08 are ascribable to the deposits subject to check. The correction consisting of exchanges for clearing house is .27. The figures for checkable deposits are therefore 4.09 + .08 - .27 or 3.90, which is 89 per cent of the "net deposits" (4.38).

For 1906 Andrew's figures for total net deposits are 8.75 and for checkable deposits, 6.90. His figures for total deposits (12.37) are less complete than those of the Comptroller, thus increasing the estimate for unreporting banks applicable to his figures from .41 to .61, of which (6.90/12.37) × .61 or .34 are ascribable to the deposits subject to check. The exchanges for clearing house were .40. The figures for checkable deposits are therefore 6.90 + .34 - .40 or 6.84, which is 78 per cent of the "net deposits" 8.75). We thus have figures for column (9) and column (8) for the years 1896, 1899, 1906, 1909.

If now, for intervening years, we interpolate evenly between these percentage figures for the years 1896, 1899, 1906, 1909, we shall have column (8) of the preceding table.

Column (9) may next be formed for the remaining years by applying the percentages in column (8) to the net individual deposits in column (7). Thus the table is made complete.

The results are of course subject to a probable error which, however, is believed to be only some 2 or 3 per cent for the years 1896, 1899, 1906, 1909, and perhaps double as much for years midway in the intervals between these four years.

It seems strange, since so much has been said of the relative importance of check and money circulation, that no attempt has previously been made to estimate or record the volume of the currency which circulates by check. This currency and its circulation are of many times the statistical importance of money and its circulation. Our wonder is the greater when we consider that "deposits subject to check" have been regularly reported by individual banks to the Comptroller of the Currency. The published figures began in the '60's to omit this category and lump all "individual deposits" together, and subsequent reports have simply followed the precedent thus established. The present Comptroller states that he intends, hereafter, to separate the item of deposits subject to check; so that we may hope from now on to have annual returns of the checkable deposits. We shall then know each year the magnitude of that item in our circulatory medium which, as we shall see, does nine tenths of the exchange work of the country.

§ 4 (TO CHAPTER XII, § 3)
Method of Calculating M'V' for 1896 and 1909

According to the Comptroller's Report for 1896, the total sum (money and checks) deposited in all reporting banks on the settling day nearest July 1, 1896, was 303 millions. Professor Kemmerer's allowance for nonreporting banks (op. cit., pp. 110-111) brings the figures up to 506 millions. The proportion of checks found in all deposits reported was 92.5 per cent, which, if applied to the estimated 506 millions of total deposits, will give 468 millions as the total checks deposited in one day. But July 1, being a first day of the month, would show exceptionally large deposits. In order to determine how much allowance to make for this fact, I have obtained, through the kindness of Mr. Gilpin of the New York clearing house, the figures for the New York clearings of July 2, 1896. July 2 was selected because the checks deposited in New York July 1 would appear in the clearing house statistics of July 2. The clearings for July 2 amounted to 157 millions, while the daily average for 1896 was only 95 millions or 60 per cent as much. Thus, the excessive clearings of July 2 have to be corrected by multiplying by .60 in order to reach a true average for the year. It is perhaps fair to assume that the deposits made on July 1 in New York require substantially the same correction. If we could assume that the abnormality of the day's deposits in the rest of the country were exactly like that of New York, requiring the same correction factor (.60), then this correction factor would apply to the whole country. But this assumption we cannot make. Doubtless .60 is too small an estimate of the true multiplier for the whole country outside of New York. The departure from the average was probably somewhat less than in New York City.

That this is the case appears likely for various reasons. In the first place New York is more sensitive to the variations in business activity than the country generally. Consistently with this view, we find that the percentage fluctuation in clearings from year to year is much greater in New York than in the rest of the country. By comparing each year with the next, we find this to be true of all except five of the twenty-seven years from 1883 to 1909*38 inclusive.

Again, the quarterly and semiannual dividends would cut a larger figure in a financial center like New York than in other places, in many of which few or no dividends are received.

Finally, in large cities like New York, checks are deposited more systematically and promptly, so that a fuller proportion of the first-of-the-month checks received on July 1 would be deposited on that day than in a smaller community. In the smaller community these checks straggle along to banks through several days after being received, thus tending to even up the daily flow and in particular to diminish the excess on and about July 1. We conclude that .60 is a minimum estimate for our multiplier for 1896.

Having obtained .60 as a minimum estimate, we next proceed to ascertain a maximum estimate. We may be reasonably sure that deposits outside of New York are so far subject to the influence of quarterly dividends, first-of-the-month payments, etc., that the volume of checks deposited outside of New York must to some extent exceed the average in 1896. We need to know to what extent we are safe in assuming that this outside volume of checks deposited on the day chosen exceeded the average. We can best reach such a safe estimate by means of some data on clearing houses in the Finance Report for 1896 (p. 493, Comptroller's Report). It is there shown that on July 1, or "the settling day nearest July 1," 66 out of the 78 clearing houses of the country had $228,000,000 of clearings. We are safe in assuming that the country's total clearings on that day were larger than this, because the returns as given include only 66 out of the 78 clearing houses of the country; and that on the following day they were larger still,*39 because it was then that occurred the bulk of the heavy July 1 deposits of checks. If the $228,000,000 clearings on July 1, 1896, were representative for each day of 1896, we could, simply by multiplying by the number of settling days of 1896, 305 days, find the total clearings of the country. But the result of this multiplication is 67.1 billions, whereas the actual clearings of the country for 1896 were only 51.2 billions. This is conclusive evidence that the clearings on July 1, and presumably still more those of July 2, exceeded the daily average and need to be reduced at least in the ratio 51.2/67.1 or .76.

Hence the true correction factor must lie between .60 and .76. Splitting the difference we have .68 as an estimate which cannot be far from the correct figures on either side; especially as .60 and .76 are so very safe or extreme limits. Figures very near either of them are improbable. The probable error is simply set at 5 or 6 per cent.

We turn now to similar calculations for 1909. At my request Professor Weston of the University of Illinois, through the kindness of Professor Kinley, has used substantially the same method for estimating the check circulation of 1909 based on Kinley's investigation*40 of that year for March 16. Professor Weston estimates the total check deposits of March 16, 1909, at 1.02 billions. This is below the daily average. A proof of this is found in the clearings of the New York clearing house on March 17, which reflect the deposits made in New York banks on the previous day; these were 268 millions, which was not representative of the year, as the average daily clearings were much greater, being 342 millions, or 28 per cent greater than those of March 17. 1.28 is therefore the correction multiplier we would apply if we could trust New York clearings to be a faithful barometer for the whole country. But since, as we have seen, New York is especially sensitive to speculative and other variations in banking operations, and as a part is usually more variable than the whole, it is reasonable to assume that the abnormality we find in New York of the deposits on March 16 exaggerates the abnormality of that day for the country at large, and that the correction multiplier should be less than 1.28. In order to set a safe lower limit, we may see what figure would result from the extreme assumption that outside of New York the day's deposits on March 16, 1909, were exactly the same as the daily average for the year. We can make a fairly good estimate of the resulting correction factor from the table on page 59.

This table is constructed from data taken from Kinley's report to the Monetary Commission on Credit Instruments (pp. 182, 186) together with the estimated corrections for the whole country's check deposits made by Professor Weston.

The figure for deposits in New York City is given for March 16, 1909. Deducting these figures from those estimated by Weston for the entire country, we have the deposits (786) outside New York. But the daily average in New York has been shown to be probably 28 per cent higher, or 306. These figures, added to those for deposits outside New York (786), give the daily average for the entire country, on the assumption that only New York City was abnormal on the day selected. The result (1092), compared with the actual deposits on the day selected (1025), shows the correction factor on the assumption that only New York was abnormal. This factor is 1.07. This furnishes a lower limit for the correction factor we are seeking.

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
(1) YEAR	(2) NEW YORK CLEARINGS	(3) OUTSIDE CLEARINGS	(4) BAROMETER (2) + 5 × (3)	(5) RATIO OF CHECK TRANSACTION TO BAROMETER	(6) M'V' CHECK TRANSACTIONS (4) × (5)	(7) V' VELOCITY OF CIRCU. OF DEPOSITS (V') (6) ÷ M'
1896	28.9	22.4	140.9	.69	97	36.2
1897	33.4	23.8	152.4	.70	106	37.9
1898	42.0	26.9	176.5	.72	127	39.8
1899	60.8	33.3	227.3	.73	166	42.6
1900	52.6	33.4	219.6	.75	165	37.5
1901	79.4	39.0	274.4	.76	208	40.6
1902	76.3	41.7	284.8	.78	222	40.9
1903	66.0	43.2	282.0	.79	223	39.1
1904	68.6	43.9	288.1	.81	233	40.2
1905	93.8	50.0	343.8	.82	282	43.1
1906	104.7	55.2	380.7	.84	320	46.8
1907	87.2	57.8	376.2	.85	320	44.9
1908	79.3	53.1	344.8	.87	300	45.5
1909	103.6	62.0	413.6	.88	364	53.9

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 B_o represents the annual withdrawals from banks by "Other depositors," O_c the spending of this withdrawn money by "Other depositors" among "Commercial depositors," and C_b the return of the money from the "Commercial depositors" to the banks. This circuit (B_oO_cC_b) of three links is very common. A second type of circuit is represented by a chain of four arrows (B_oO_cN_cC_b. It is illustrated by private depositors drawing money (B_o), and paying wages (O_n) to servants who in turn spend the money (N_c) among tradesmen who finally deposit it (C_b). A third type of circuit, also fourfold, is represented by the arrows B_cC_nN_cC_b. It is illustrated by commercial firms cashing their checks at banks (B_c) for pay rolls, with the cash so obtained paying wages (C_n) to workmen who spend it (N_c) among other tradesmen who redeposit it in banks (C_b). 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: O_c payments of money from "Other depositors" to "Commercial depositors" in the purchase of goods; O_n payments from "Other depositors" to "Nondepositors," as when a housewife pays wages; C_n payments from "Commercial depositors" to "Nondepositors," as when a firm pays wages; and N_c 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, O_c, is contained within the circuit B_oO_cC_b, and since no "Nondepositors" intervene, represents money changing hands once between its withdrawal from bank and its re-deposit there. The remaining types (O_n,C_n, and N_c) are contained within the two other circuits (B_oO_nN_cC_b and B_cC_nN_cC_b), and, owing to the fact that "Nondepositors" intervene, represent money circulating twice between withdrawal and re-deposit.

In short, one of the three circuits (B_oO_cC_b) 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 = O_c + C_o + N_c + C_n + O_n + N_o + 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 C_b + O_b + N_b, while the total expenditure of "Nondepositors" is N_c + N_o. The sum of these two expressions we shall call F'. It is:—

F' = C_b + O_b + N_b + N_c + N_o, (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 N_c and N_o and placing the negative terms first. We thus obtain for a remainder (r) the following:—

r = F - F' = - C_b -O_b - N_b + O_c +C_o + C_n +O_n + 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 C_b + C_o + N_b + N_o, and the total inflow B_c + O_c + B_n + O_n. Hence, the net outflow, so far as the diagram shows us, is:—

C_b + C_o + N_b + N_o - B_c - O_c - B_n - O_n.

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 (B_o, B_n, and B_c). 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,

C_b + C_o + N_b + N_o - B_c - O_c - B_n - O_n + 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 = C_b + C_o + N_b + N_o - B_c - O_c - B_n - O_n + 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 (C_b + O_b + N_b), 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 Kinley *43 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
(1)	(2) MONEY DEPOSITED ON DAY SELECTED (IN MILLIONS)	(3) ASSUMING DAY AN AVERAGE ONE (IN BILLIONS)	(4) ASSUMING CORRECTION FACTORS EQUAL TO THOSE FOR CHECK DEPOSITS	(5) MEAN BETWEEN TWO PRECEDING COLUMNS
1896	37.4	11.4	7.8	9.6
1909	62.9	19.1	22.3	20.7

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 (N_c + N_o) 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 Labor*46 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.

	1890	1900	Increase Per Cent	Estimate 1909
Agricultural pursuits	8,565,926	10,381,765	21.2	12,362,605
Domestic and personal service	4,220,812	5,580,657	32.2	7,377,628
Total				19,740,233
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
Total				11,211,026

"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
Total		13,112 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 (C_o + C_n - B_c). 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, C_o is very small compared with C_n, and the sum of the two is nearly the same as B_c. Hence the difference (C_o + C_n - B_c), 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 (C_o + N_o - O_b) is O's money receipts which are pocketed instead of being deposited. Now O's money receipts, C_o + N_o, 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 N_o. 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.

	1896	1909
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 bill