Chapter XIX (1)

STATISTICAL DEMONSTRATIONS OF THE QUANTITY THEORY--THE REDISCOVERY OF A BURIED CITY

In the following chapter, as in most of the preceding chapters, constructive doctrine is aimed at, even though the discussion takes, in considerable part, the form of critical analysis of opposing views. We shall seek to set forth the facts, as far as may be, regarding the relations of banking transactions to trade, the relations of clearings to amounts deposited in banks, the relation of New York City clearings to country clearings, and of New York bank transactions to bank transactions in the rest of the country. We shall seek to ascertain the extent of variability in that highly elusive magnitude, "velocity of circulation," particularly "V'." We shall indicate something of the bearing of index numbers of prices on the theory of the value of money as here presented. In reaching conclusions on these and related matters, we shall build on the investigations of Dean Kinley, on the very interesting statistical studies of Kemmerer and Fisher based on Kinley's figures, on investigations more recently made by the American Bankers' Association regarding the relation of bank transactions and bank clearings, on figures from reports by the Comptroller of the Currency, as well as on other sources. One purpose of the chapter is to criticise the statistics which purport to prove the quantity theory. The bulk of the chapter is given to this. But the work of Fisher and Kemmerer thus criticised yields rich rewards for the study. The conclusions they have drawn from their figures are, in the judgment of the writer, untenable, but the figures themselves are of immense interest and importance.

The controversy over the quantity theory has been waged with many weapons. Theory, history, and statistics--to say nothing of invective!--have been freely employed. In large measure, the statistical studies have been concerned with the direct comparison of quantity of money and prices, in their variations from year to year. One of the best of these studies, that of Professor Wesley C. Mitchell, in his _History of the Greenbacks_ (followed by his _Gold, Prices and Wages under the Greenback Standard_), has, to the minds of many students, including the present writer, put it beyond the pale of controversy that the fluctuations in the gold premium, and in the level of prices, in the United States during the Greenback period, both for long periods and for daily changes, were not occasioned by changes in the quantity of money,[373] but rather, primarily, by military and political events, and other things affecting the credit of the Federal Government, together with changes affecting the values of gold and of goods. Professor Mitchell's discussion is so detailed and thorough, that what controversy remains relates, not to his facts, but rather to the possibility of interpreting those facts in harmony with the quantity theory, by repudiating the notion that the direct comparison of gold premiums or of prices with quantity of money gives a valid test.[374]

Recent defenders of the quantity theory have undertaken the examination of more complex statistics than those concerned with the simple concomitance of quantity of money and prices. Two of these studies, the first by Professor Kemmerer[375] and the second by Professor Fisher, are so elaborate, have commanded such general attention, and have been accepted by so many students as conclusive demonstrations, that I feel it proper to give them detailed examination. I do this especially because highly important facts for our construction argument emerge from this critical examination. Kemmerer's and Fisher's studies reach high-water mark in the effort to give statistical demonstrations of the quantity theory. If they are invalid, then I know no other attempts which many students would suppose to be possible substitutes. The theory involved in both these studies is clearly stated by Professor Kemmerer: "A study of this kind, to be of any value, must cover the monetary demand as well as the monetary supply. Any test of the validity of the quantity theory consisting merely of a comparison of the amount of money in circulation with the general price-level is as worthless as would be a test of the power of a locomotive by a simple reference to its speed without taking into account the load it was carrying or the grade it was moving over." This criticism of many previous studies is, in general, I think, valid, though I should except from this list such detailed studies as that of W. C. Mitchell, who takes account, as far as may be, of all the variables involved, and who considers day by day and week by week changes. I think the older studies of Tooke,[376] may also be excepted. In point of fact, if one wishes to know how much reliance may be placed in the quantity theory as a basis for prediction, when one knows that money is increasing, the simple comparison of money and prices is a fair test. If the "other things" which must be "equal" are so numerous and complex that the quantity theory cannot manifest itself in a direct comparison, much of its significance _as a basis of prediction_ is gone.

It is perfectly true, however, that studies running through long periods, which give simply figures for general prices and figures for quantity of money, omitting volume of trade, are not very relevant either for proof or disproof.[377] And the conception underlying the studies of Kemmerer and Fisher, that not merely money and prices, but also volume of bank-credit, volume of trade, velocity of monetary circulation, and velocity of bank-credit, must be measured, undoubtedly represents a big advance in the conception of the statistical problem involved. The mere stating of the problem is an intellectual achievement of no mean order, and the ingenuity and scholarship involved in seeking data for concrete measurement of these highly elusive elements must command the admiration of every student of monetary problems. Volume of trade, velocity of money and velocity of bank-credit had been generally supposed, until these studies were undertaken, to be beyond the reach of the statistician. There can be no doubt at all that the efforts to measure them, or to measure variations in them, by Kemmerer and Fisher, have greatly advanced our general knowledge of the phenomena of money and credit.

With great admiration for the magnificence of the problem undertaken, and for the industry, ingenuity and scholarship which have been devoted to its solution, I have nevertheless reached the conclusion that the figures assigned by these writers to the magnitudes of their "equations of exchange" are, with the exceptions of the figures for money and deposits, widely at variance from the real facts in the case, and second, that if they were correct, they could in no sense be said to constitute proof of the quantity theory.

In the critical analysis which follows, chief attention will be devoted to Fisher's statistics. His is the later study, and it follows, in main outlines, the methods laid down by Kemmerer. He has employed Kemmerer's statistics in considerable part, amplifying them for later years, using some data not available when Kemmerer wrote, and undertaking a fuller solution of certain problems than Kemmerer did. I shall, however, from time to time make reference to Kemmerer's figures, and show points of difference between the two studies.

Let me first briefly state the second point of my criticism of these studies: namely, that even if the statistics are correct, they do not constitute proof of the quantity theory. The statistics purport to be concrete data filling out for different years the equation of exchange.[378] But the equation of exchange, as we have seen, does not prove the quantity theory. The quantity theory is a _causal_ theory, and causation involves an order _in time_. The concrete figures for the equation do not prove that. Even Kemmerer's concluding chart on p. 148, showing a rough concomitance between "relative circulation" and general prices does not show that changes in relative circulation are _causes_ of changes in general prices. The causation might be the reverse for anything his figures tell us. Fisher himself recognizes this, in considerable degree: "As previously remarked, to establish the equation of exchange is not completely to establish the quantity theory of money, for the equation does not reveal which factors are causes and which are effects."[379] Again: "But, to a candid mind, the quantity theory, in the sense in which we have taken it, ought to appear sufficiently secure without such checking. Its best proof must be _a priori_."[380]

The main criticism here, however, relates to the figures themselves, rather than to their meaning. The figures given by Professor Fisher are concrete magnitudes to fill out his equation of exchange, MV + M'V' = PT[381] for the years since 1896. Thus, for 1909, the figures are: M = 1.61 billions; M' = 6.68 billions; V = 21.1; V' = 52.8; P = $1; T = 387 billions.[382]

Now in what follows, I shall challenge all these estimates except P for 1909, V for 1896 and 1909, and M and M' for all years. The figures for M and M', being the results of fairly simple computations based on Governmental statistics, need not be questioned. P for 1909 is arbitrarily placed at $1.00. V for 1896 and 1909, for reasons which will later appear, is better based than for other years, though Kemmerer and Fisher have differed greatly in their estimates for V, the former placing it at 47 and the latter at 18 or 20.[383] My criticisms with reference to V, however, will relate to the years other than 1909 and 1896.

The sources from which these absolute magnitudes are drawn are, primarily, two investigations by Dean David Kinley, one in 1896 and the other in 1909, in cooeperation with the Comptroller of the Currency.[384] The purpose of these investigations was to ascertain the proportions of checks and money in payments in the United States. Banks of all kinds, national and State banks, trust companies, private banks, etc., were requested by the Comptroller to supply data for a given day (March 16 in 1909) showing what their customers deposited on that day. They were asked to classify these deposits as cash, on the one hand, and as checks, drafts, etc. on the other. They were also asked to give a cross classification of the same deposits, as "retail deposits," "wholesale deposits," and "all other deposits." In 1909, over 12,000 banks of all kinds, out of about 25,000 banks, replied, and of these replies 11,492 were in available form. These replies showed a total of deposits of over 688 millions of dollars. Of this total, 647 millions were in checks, so that checks made up 94.1% of the whole. About 60 millions of this total were retail deposits, about 125 millions were wholesale deposits, and the rest, about 503 millions, were classed in the "all other" category. Kinley's use of these figures, _for his purpose_, seems to me in every way conclusive and safe. He was interested merely in the question of the _proportions_ of checks and money in _payments_, retail, wholesale, and "_all other_." The absolute magnitudes of the elements in the equation of exchange he was not trying to measure. Professor Fisher's use of the figures presents a different problem.[385]

Let us consider, first, Professor Fisher's estimate of M'V', taken together. M'V' is considered to be equal to the total amount (in dollars) of checks deposited during the year.[386] To get this, for 1909, Kinley's figure, above, for checks deposited in 11,492 banks on March 16, 1909, is used. This figure is 647 millions. As half the banks had not reported, an estimate for the non-reporting banks was obtained from Professor Weston, who had aided Dean Kinley in the investigation, and who had access to the original data. Professor Weston estimated the total checks deposited during the day at 1.02 billions.[387] The question then arose as to whether this day was typical for the year. Professor Fisher found New York City bank clearings of March 17 (the day after, on which these checks would get into the clearings) to be 28% below the average for the year. He assumed the rest of the country to be half as abnormal as New York City, and increased the 1.02 billions to 1.20 billions, getting what he conceived to be the daily average of checks deposited in the United States in 1909. Multiplying this figure by 303, the number of banking days in New York City (and so, presumably, a fair average for the number of banking days in the country), he obtained 364 billions for the checks deposited in 1909. This figure he considered to be M'V', the volume of bank deposits,[388] multiplied by its velocity of circulation. To obtain V', therefore, his problem was simple: he divided the figure for M'V' by the figure for M' previously obtained from government statistics, and obtained V'.

Now I wish to call attention to three important errors involved in this calculation of M'V' for 1909. (1) The assumption that the total check circulation is the same as the volume of checks actually used in _trade_ is a violent one. _Payments_ may be tax payments, loans and repayments, gifts, what not. Many checks may be used in a single transaction. Surely not all of this is properly to be counted in the M'V' of the equation of exchange. But this topic is better discussed in connection with the estimate for T, and I reserve its fuller discussion till then. (2) The assumption that the rest of the country was abnormal in its clearings on March 17, 1909, is a pure assumption, which investigation does not verify. The rest of the country was, in fact, nearly normal! The error that comes for the year from increasing the total on this assumption amounts to at least 31 billions! The total for the year, on Professor Fisher's method of computation, with the correction to make the assumption regarding outside clearings correspond with the facts, is 333 billions, instead of 364 billions! As the figure for 1909 is a basic figure, on which figures for other years are calculated, this error is extremely significant.[389]

(3) A yet more serious error in this computation is the assumption that New York City was complete in Kinley's figures, while the rest of the country was incomplete. This error, as we shall see, largely neutralizes the error above, so far as the "finally adjusted" figure for 1909 is concerned, but it makes a vital difference in the figures for other years, as will appear, since it affects the "weighting" of New York clearings and outside clearings in the index of variation by means of which M'V' for years other than 1909 is determined. The assumption that New York is complete, in Kinley's figures, and that all of the extra hundreds of millions added by Professor Weston in his estimate for the non-reporting banks belongs to the country outside New York, is made by Professor Fisher both on pp. 444-445, in estimating M'V' for 1909, and on p. 446, in finding an index of variation for M'V'. The only reason given, so far as I can find, is the following: "This figure, _being for New York_, [Italics mine], is probably nearly complete." (_Loc. cit._, p. 446.) With this as a basis, Professor Fisher proceeds in his calculations to treat the figure for New York, 239 millions, as absolutely complete, and gives the rest of Professor Weston's 1.02 billions for the day, or 786 millions, to the country outside. The error above mentioned, of assuming the rest of the country to be abnormally low on March 17 in its clearings, still further increases the amount assigned to the rest of the country in the total figures for the year.[390] The conclusion finally is that New York had deposits of 93 billions in checks for the year, while the rest of the country had deposits of 271 billions in checks. As New York clearings for the year were 104 billions, while clearings for the rest of the country were only 62 billions, Professor Fisher concludes that New York clearings overcount New York check deposits, and outside clearings greatly undercount outside check deposits, so that, in the index of variation of check deposits, for years other than 1909 and 1896, New York clearings should be given a weight of only 1, while outside clearings should be weighted by 5. "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." (P. 447.) All this rests on the assumption that New York figures for March 16, 1909, were complete, and the only reason assigned is, "being from New York!"

Now the figures from New York were not complete. And New York clearings do not overcount New York check deposits. Outside clearings do not undercount outside check deposits nearly to the extent that Professor Fisher assumes. For each of these three statements I shall offer what would seem to be conclusive evidence, and I shall attempt to get an estimate of the real relation between New York check transactions and check transactions for the rest of the country.

First, the figures for New York were far from complete. It may be noted that Dean Kinley, in his volume for 1909,[391] is very careful to repudiate the assumption that the cities were complete more than the country: "Moreover, it is a mere assumption that the non-reporting banks are mainly the small banks in the country districts. _A great many city banks also did not report._" (Italics mine.) That this is true for New York is abundantly evident from figures there given for the private banks and the trust companies, not to consider at all the State and national banks. New York shows only $1,751 in checks deposited in the "all other deposits" in private banks! This is a city which includes among its private bankers J. P. Morgan & Co., Kuhn, Loeb and Co., J. & W. Seligman & Co., and others! Figures from these banks appear nowhere in Kinley's totals, since deposits made _by_ these banks in other banks are also excluded from Kinley's figures.[392] Of course, exact figures cannot be given to show how much New York would be increased had the private banks made full reports. We have no reports of any kind from these institutions. Every feature of their business is kept from the lime light, as far as possible--a practice which is much to be regretted, since it arouses hostility and suspicion, where a statement of the facts in the case would frequently entirely dispel them. We have, however, some information regarding the magnitude of their deposits, meaning by deposits, not what Kinley means in this investigation, namely, checks, etc., _deposited_ on a given day, but rather, deposits in the balance sheet sense of demand obligations to depositors. In Nov. 1912, J. P. Morgan and Co. held deposits of $114,000,000, exclusive of 49 millions on deposit with their Philadelphia branch of Drexel & Co. About half of these were deposits of interstate corporations. Kuhn-Loeb held, on the average, for the six years preceding 1913 over 17 millions of deposits of interstate corporations. What their aggregate deposits were, we do not know. These figures are obtained from the report of the Pujo Committee.[393] Morgan's deposits were equalled by only three banks and two trust companies in New York (as of April 3, 1915), and Kuhn-Loeb's deposits for interstate corporations alone exceeded the total deposits of any one of the great majority of the New York Clearing House banks and trust companies. Of course, large deposits in the balance sheet sense need not mean large deposits made on a given day. Private bankers' deposits may be inactive. But we know, first, that half of these figures for Morgan, and the whole of the figures given for Kuhn-Loeb, represent the deposits of active business corporations, engaged in interstate business. They are not mere trust funds lying idle, or awaiting investment in securities. What the rest are we can only conjecture. That they are deposits of men and firms connected with the Stock Exchange in some way is highly probable. The whole drift of the statistics presented in this book, and of the argument developed in this book, would serve to show that such deposits are likely to be more than ordinarily active.[394] I refrain from assigning any figures as to the amount of checks deposited in private banks in New York on March 16, 1909. It must have run high into the millions.[395] It certainly exceeded the two thousands, or less, reported to Kinley! The figures for New York were, thus, incomplete.

But the trust companies were also incomplete. The national banks in New York reported checks totaling 186.5 millions, for all three classes of deposits; the State banks reported only 38.1 millions; the trust companies only 14.2 millions. With aggregate deposits, as shown by their balance sheets, exceeding the deposits of national banks[396] the New York City trust companies reported, as deposited on March 16, 1909, less than half as much as the State banks, less than a tenth as much as the national banks, and only 6.8% of the two combined--5.9% of the total from all three classes of institutions!

These figures are hard to reconcile with the assumption that the trust companies in New York were complete on that date.

It is, of course, possible that the trust companies, though having large deposits, have inactive deposits. This is sometimes held to be the case. But that the difference is so great in activity of deposit accounts between banks and trust companies is hardly credible. I have looked into this matter with considerable care, and have secured information and opinions from men intimately acquainted with the trust companies of New York from the inside. The only available quantitative measure of the activity of deposits would seem to be the volume of a bank's clearings. This is not perfectly accurate, by any means, but it is the best available test. Through the courtesy of a Vice President of one of the largest New York trust companies, I have obtained figures from an official of the Clearing House, which show that in New York trust company clearings run from 20 to 25% of the whole. On this basis, the trust company figures for 1909 were incomplete to the extent of from 33 millions to 46 millions, on the day in question. These clearings figures, however, are for the year, 1915, and not for the period before May, 1911, when the trust companies were admitted to the Clearing House. Prior to that time they did not deal directly with the Clearing House, but _through_ the member banks. Do these figures, therefore, represent the situation as it existed in 1909? The possibility was entertained that entering the Clearing House had made a difference in the reserve policy of the trust companies, and so had made them change the character of their business, in such a way as to bring about greater activity of accounts. This question was put to the official of the trust company before mentioned, and his reply is that the State law regarding reserves (passed after the Panic of 1907) had already brought about this change in reserve policy, and so no difference was made upon entering the Clearing House.

The same gentleman, by the way, replying to a question regarding the deposits in private banks in New York, and the influence of such deposits on clearings, writes: "The actual figures could not be obtained from the Clearing House..., consequently can only say that deposits made with these houses add to the Clearing House totals very large sums."

There is one piece of evidence which would seem to negative these conclusions regarding the trust companies. In the Report of the New York State Superintendent of Banks, for Dec. 31, 1907, p. xxxv, is a statement that during the two years, 1903-05, the trust companies of New York cleared only 7% as much as the banks. The statement relates, however, to a period during which the trust companies not only had no Clearing House membership, which of course was true up to 1911, but also had largely withdrawn from the privilege of clearing _through_ member banks.[397] Under these circumstances, even 7% would seem quite high. Inquiry was made of the Honorable Clark Williams, who was State Superintendent of Banks at the time the report was made, as to the source of the figures.[398] Mr. Williams, in reply, defends the figures as correct for that period, but authorizes the writer to quote him as in no way surprised at the percentages given above, 20 to 25% of the total clearings, in view of developments and changes in trust company business.

I conclude that the trust company figures for March 16, 1909, were exceedingly incomplete. The national bank figures were probably more nearly complete than any others, first because they are large, and second, because national banks would feel more obligation than other banks to reply to questions from the Comptroller. The State bank figures, 38.1 millions, as against national bank figures of 186.5 millions, were probably incomplete also, to a considerable extent, though State banks are not dominating factors in New York City. That they should exceed the figures for trust companies is surely evidence of the incompleteness of the trust company figures. The private banks are incomplete, with absolute certainty, since they are virtually not represented at all.

Further evidence that the New York figures were incomplete, however, will appear in the data regarding our second thesis, namely, that New York clearings do not overcount New York check deposits. The aggregate check deposits reported from New York, on the date in question, is 239 millions. Clearings for that day were 268 millions,[399] substantially exceeding the reported check deposits. Now do clearings exceed check deposits in New York City?

Evidence with reference to outside clearings, in connection with bank transactions, we now have in very definite and abundant form, and it will be convenient to approach the question of New York clearings, first, indirectly, _via_ country clearings. We shall, therefore, take up first the thesis that clearings outside New York do not undercount bank deposits outside New York nearly as much as Professor Fisher thinks. According to his estimate, checks deposited during the year in banks outside New York (exclusive of checks deposited by one bank in another) were 271 billions. (_Loc. cit._, 446.) Outside clearings were only 62 billions, and his conclusion is that the ratio of deposits to clearings is 4.4 to 1, or, in other words, that outside clearings amount to less than 22.8% of outside check deposits.

Now an extensive investigation, covering the period from June, 1913, to Oct. 1914, inclusive, has been made by the American Bankers' Association, through Mr. O. Howard Wolfe, Secretary of the Clearing House Section. This investigation covered cities of various sizes, in various parts of the country. Its results are immensely more trustworthy than any results based on a single day, as Professor Fisher's results are, could be, even had Professor Fisher's method been otherwise correct. An account of this investigation is to be found in the _Annalist_ of Dec. 7, 1914.[400] This investigation involves, for the period in question, a comparison of "total bank transactions" in each city with the clearings of that city, together with a summary covering all the cities. "Total bank transactions" consist of all debits against deposit liabilities of each member of the Clearing House, whether they come through the Clearing House or over the counter. They include payrolls, for example, which, of course, never get into clearings. They include drafts on deposits of one bank in another. In a letter to the Editor of the _Annalist_, Mr. Wolfe states that "total bank transactions include all debits against deposit liabilities, whether by check, draft or charge ticket. The only exceptions are certified checks and certain cashier's checks, both of which to an extent represent a duplication." For the period in question, clearings amounted, on the average, for all cities, to 40% of "total transactions." The cities did not include New York City, as stated.

Now we cannot apply this 40% at once to the question in hand. Professor Fisher's 22.8% relates to the relation between clearings and checks and drafts _deposited_, _excluding_ items deposited by banks, and excluding, of course, cash deposited. What is the relation between Kinley's "deposits" and Wolfe's "total transactions"?

It is clear that "total transactions" must, in a period of time, _exceed_ Kinley's "deposits" very considerably. In a general way, what goes out of a bank, and what comes into a bank, must approximately equal one another in a period of time. In a general way, a depositor finds his income and his outgo balancing. Of course, some accumulate, paying in more than they withdrew, but in general such accounts are made with savings banks. The business man borrows from his bank, getting a "deposit credit" (without "depositing" in Kinley's sense), then checks against his "deposit," then receives checks in payments to himself, "deposits" them, building up his deposit balance again, and then checks against his deposit balance, in favor of the bank, to pay off his loan. What comes in and what goes out--abstracting from the growth of a rapidly expanding bank--balance. But notice, in the case cited above, that "total transactions" include more items than Kinley's "deposits" show. When the bank makes a loan, and gives a deposit credit, this does not, usually, show in Kinley's deposits. When, however, the loan is paid off by a check to the bank, it does show in "total transactions." Moreover, when a man deposits cash in the bank, it does not show in Kinley's figures for checks deposited. When, however, he withdraws cash from the bank, or his check to another is "cashed," it does appear in "total transactions." Further, checks deposited to the credit of one bank in another do not appear in Kinley's figures. Checks drawn, however, by one bank on another do appear in total transactions. How great the difference is between "total transactions" and "deposits" in the banks outside New York we cannot say precisely. The cash items alone, on the basis of Kinley's figures, would make a difference of about 9%.[401] To allow 11% excess to "total transactions" over "deposits" for the other reasons listed, is surely not to make an exaggerated allowance. We thus count "deposits" in Kinley's sense, for the banks outside New York City, as 80% of "total transactions." Since, then, clearings are 40% of "total transactions," they will be 50% of "deposits." This figure is more than twice as great as Professor Fisher's figure of 22.8%. Even if we counted deposits as equalling total transactions, Professor Fisher's estimate would be clearly very much too low.

How, then, do we stand? On Professor Fisher's showing, the overwhelming bulk of checks deposited were in the country outside New York--271 billions for the year, outside, as against 93 billions in New York City. If the ratio (50%) for outside clearings to deposits was the same for 1909 that it was in 1913-14 for the outside banks, we shall have to revise this radically. We have 62 billions of country clearings in 1909; we would have, then, 124 billions[402] of country check deposits! If Fisher's total figure for the country is correct, 353 billions as "finally adjusted," the balance, or 229 billions, would belong to New York! New York clearings, 104 billions, would thus be less than half of New York deposits! If we count outside clearings for 1909 as only 40% of outside check deposits, outside deposits would be, for 1909, only 155 billions, as against Professor Fisher's 271 billions, _a difference of 116 billions_! I am sure that his error in estimating outside check deposits is at least as great as that, and that we cannot assign to New York City less than a major part of the total check deposits of the whole country.

This result fits in with the figures actually reported to Dean Kinley, corrected to fit the known facts about March 17 clearings, better than Professor Fisher's estimate, by a good margin. According to Professor Fisher's estimate, New York City checks deposited are only 25.5% of the total. Kinley's actual figures give 239 millions to New York City, and 408 millions to the country outside. But New York clearings were 28% below normal on March 17, while country clearings were only 2.45% below normal. Adding 28% to the figure for New York checks, we get 306 millions. Adding 2.45% to the outside checks, we get 418 millions. Of the total, 724 millions, New York checks would be, then, 42.3%. We have shown reasons for considering New York deposits to be very incomplete for March 16, particularly as regards the private banks and trust companies. Comparison of the New York figures with the results indicated by the ratio of country clearings to country deposits would thus indicate that New York was much less complete than the country as a whole. Even so, I need to add but 7.3% of the total to Kinley's actual figures for New York, corrected in the light of next day clearings, to give New York half of the check deposits. Professor Fisher must subtract 16.8% of the total from the actual figures for New York, as corrected in the light of next day's clearings, in order to get his figure of 25.5%. To vary as widely from the actually reported figures as Professor Fisher does, I should have to assign 59.1% of total check deposits to New York City. I refrain from making an exact estimate. I am content with the conclusion that something more than half of the checks deposited in 1909 were in New York. This seems to be too clear for serious controversy.

The indirect approach to the relation between New York clearings and New York deposits, _via_ the study of outside clearings in 1913 and 1914, taken in conjunction with the figures for check deposits in 1909, would seem to make it quite clear that New York clearings do not exceed New York deposits, or, indeed, constitute a substantially higher percentage of them than is the case with country clearings and deposits.[403] Logically, assuming the correctness of the estimate for checks deposited, the case is complete: we have a simple problem in arithmetic: given country clearings for 1909, 62 billions; given the ratio of country clearings to country deposits (and a minimum for this ratio is clearly given, in the 40% which country clearings are of "total transactions"), we can fix a maximum for country deposits, which is 155 billions. Then, given our estimate of 353 billions for total check deposits, we subtract the maximum possible for country deposits from it, and get a minimum possible for New York City of 198 billions of check deposits. Comparing this with the known clearings of 104 billions in New York, we find that New York clearings constitute, as a maximum possible, 52.5% of New York check deposits. If the reasons given for holding check deposits in the country to be less than total transactions are accepted, the ratio of clearings to deposits in New York City is lower.

Indirect calculations, however, even when logically complete, ought to be checked up by other methods, when possible. We have some further data, drawn from an earlier period, 1890-91-92, which suggest the same conclusion.

The reason commonly offered for holding that New York clearings exaggerate local New York transactions, as compared with country clearings and country transactions, is that New York is the clearing house for the country. Country banks send their idle cash there; country banks pay other banks by drafts on their New York balances; country banks send out of town checks to New York for collection; business men in St. Louis pay business men in Chicago with New York exchange, etc. These items are supposed greatly to swell New York clearings.

Now several of these reasons are not at all valid. Cash shipped back and forth between New York and the interior does not get into clearings. Secondly, New York, because of the charges made for collecting out of town checks, has tended to lose much of the collection business. Chicago probably does a great deal more of it than New York does.[404] However, even if checks on out of town banks were sent largely to New York for collection, they would not get into the clearings. New York banks send checks on country banks directly to country correspondents. Checks on out of town banks sent in for collection do swell clearings in Boston and Kansas City, where arrangements have been made, to the advantage of all concerned, to have the clearing houses handle this business. But New York has not made provision for it.[405] The only checks that get into New York clearings will be checks drawn on New York banks.[406]

These checks will be of two kinds: (1) checks drawn by individuals and firms on New York banks. These checks will commonly be drawn by people in New York, and, in so far as they come from out of town, will represent business between New York and other places, hence, New York business. (2) Drafts by banks on their New York balances. These will be of three kinds: (a) drafts sold, especially by country banks, to their customers who need to make payments in other cities. Many of these will represent payments to New Yorkers for transactions between New York and the country, hence New York business, and will appear in the check deposits of individuals, firms, and corporations in New York, (b) There will also be drafts from one country bank, on New York, to another country bank, in which New York is truly being used as a clearing house, New York exchange taking the place of an intercity shipment of cash.[407] (c) Drafts by New York banks on New York banks, to avoid deficits at the Clearing House, or--especially in the case of private bankers, between whom and brokers the line is hard to draw,--for general purposes.

Now, fortunately, we have some data, trustworthy, even though old, for the volume of bank-drafts on New York, and, more important, for the proportion of drafts on New York to drafts on banks in other cities. These figures are, as stated, from the three years, 1890, 1891, and 1892. For the purpose in hand, however, they are relevant, since then, as now, New York clearings were nearly twice as great, on the whole, as country clearings, and if this excess of New York clearings is due to that cause, it should have manifested itself in these figures. If the proportion of these drafts on New York to the total of bank-drafts was greater than the proportion of New York clearings of total clearings, we might find reason for supposing that New York clearings were unduly swelled by this fact. But in fact, drafts on New York are not out of proportion. The figures are virtually complete for drafts drawn by all the national banks on national and other banks for the years in question. They will be found in the Comptroller's _Reports_ for the three years, under the caption, "Domestic Exchanges." For 1890 the figures are:

Drafts on (000,000 omitted)
New York $ 7,284 (63.07%)
Chicago 1,084 ( 9.30%)
St. Louis 188 ( 1.64%)
Other reserve cities 2,537 (21.88%)
Other cities 464 ( 4.02%)
Total 11,550 ( 100%)

The Comptroller (_Report_ of 1890, p. 19) gives an estimate for drafts drawn by State and private banks of an additional 6,089 millions. He does not try to apportion these among New York and the other cities. There is no reason to suppose that the percentage for these banks of drafts drawn on New York would be higher than for national banks, and there is some reason for supposing that they would be lower: namely, that these institutions would lack the incentive supplied by the National Bank Act for depositing reserves in a Central Reserve City. The Comptroller's figures probably do not include the great private banks in New York, which deposit in New York commercial banks, and draw huge checks against their deposits. These checks, probably, however, chiefly represent stock exchange collateral loans to brokers, and so appear in brokers' deposits as well as in New York clearings--represent New York deposits. I do not use this estimate in my computations. If I did, the results, so far as proportions are concerned, would be the same, since I could do nothing but assign the same proportions to them. It will be seen that my argument rests on the proportions, chiefly.

Now what difference would be made if we wiped out all these draft transactions, and reduced clearings to correspond? New York clearings in 1890 were 37,660 millions; country clearings were 21,184 millions. Let us subtract the drafts on New York from New York clearings, and the drafts on other places from the country clearings. The result is: New York clearings, 30,376 millions; country clearings, 16,918 millions. New York clearings still retain their former status! New York clearings are still nearly twice as great as country clearings! It is not the bank drafts used in making New York the "clearing house" for the country that swell New York clearings as compared with the rest of the country! It is something else! The main explanation, as we have in part seen, and shall further see, is a mass of speculative transactions, chiefly Stock Exchange transactions, and loan transactions connected therewith! New York clearings grow out of New York business, primarily.

The figures for the other two years vary little from those of 1890. What variation there is shows a growth of drafts on interior cities, and a decline of drafts on New York. New York showed 63.07% of these drafts in 1890, 61% in 1891, and 60.77% in 1892.[408]

As we have seen, the only checks or drafts that get into New York clearings are those drawn on New York banks. The checks on New York banks probably almost all represent business in which one party is a New York individual, firm, or corporation. The drafts by out-of-town banks will contain all the items, virtually, that represent "clearings" through New York. Not all of these, by any means, will represent such clearings. A very substantial part of them will represent exchange sold to customers to make payments in New York. We exaggerate the "clearing through New York" when we subtract all these drafts from New York clearings. Since, however, we treat country clearings in the same way, no error results, so far as the proportions between them are concerned.

The two sets of data converge. Both from the figures of 1913-14, in conjunction with estimated check circulation in 1909, and from the figures of 1890-92, can we conclude that New York clearings do not overcount New York transactions. The conclusion would seem to be inevitable that New York is really as important in our volume of banking transactions as its clearings would indicate. This may be qualified by a recognition of the possibility that New York clearings are more efficient in handling check deposits than are clearings in other cities. Some scattering data from national banks for single days at a time indicate that a higher percentage of checks is cleared in New York than elsewhere in the country,[409] and one observation for five national banks for a ten-day period shows 67% of checks deposited cleared.[410] These checks include deposits made by other banks, as do the figures of Kemmerer's observations. But there are no direct observations covering New York for a long enough period, or for enough institutions, to warrant any definite conclusions.[411]

The error of assuming clearings of March 17 in the country outside New York to be abnormally low, swelled Professor Fisher's total figure for check circulation by 31 billions, as we have seen. On the other hand, the error of assuming New York City to be complete in Kinley's figures tended to make the total smaller than it would have been, since New York City was 28% below normal, and an increase of 28% applied to half of Professor Weston's figure of 1.02 billions, gives about 70 millions more for the day, or 21 billions more for the year, than when the 28% increase is applied to only a quarter of Professor Weston's figure. These two errors roughly neutralize one another, and we may accept Professor Fisher's "finally adjusted" estimate of 353 billions[412] for the year as roughly approximating the amount of checks deposited.[413] How "rough" an estimate one gets by taking a single day as the basis for a year need not be here discussed. I should be disposed to think that an indirect calculation, _via_ clearings, in view of our more extensive knowledge of the relation of clearings to "total transactions," might well be worth more, so far as deposits outside New York are concerned. Since, however, we lack any extended figures for the relation of transactions and clearings in New York, and since even for the country we are obliged to make guesses as to the relation of "checks deposited" to "total transactions," I refrain from trying to improve further on Professor Fisher's estimate for checks deposited in 1909--even though questioning that "check deposits" and M'V' are identical.

What, however, shall we say of M'V' for other years? In the calculation of this, Professor Fisher relies on the absolute figures for 1909 (and 1896, similarly calculated), together with an "index" based on New York and country clearings. In this index he weights country clearings by 5,[414] and New York clearings by 1. The result is, of course, that country clearings dominate the index. But New York clearings are much more variable than country clearings. The range of variation in New York clearings for the years 1897 to 1908, inclusive, is from 33.4 billions in 1897, to 104.7 billions, in 1906; the latter figure being more than three times as great as the former. The range in country clearings is from 23.8 billions, in 1897, to 57.8 billions, in 1907, the latter figure being 2-10/23 as great as the former. But more significant is the degree of _year by year_ variability. The country clearings, with the exception of 1908, always rise,--a steady, if not quite symmetrical, increase. New York clearings, however, go up and down, 42 billions in 1898, 60.8 billions in 1899, 52.6 billions in 1900, 79.4 billions in 1901, 66.0 billions in 1903, 104.7 billions in 1906, 87.2 billions in 1907, 79.3 billions in 1908. New York clearings are highly variable in both directions, while country clearings vary almost wholly in one direction, with a maximum difference of 6.4 billions between any two consecutive years, and with an average yearly variation of only 3.5 billions.[415] When country clearings are weighted by 5, almost all of the high degree of variability of New York clearings is covered up, and volume of checks deposited for years other than 1909 and 1896 is thrown hopelessly away from the facts. It is too large by far in most years. In 1905, 1906 and probably 1901 it is too small. It does not vary nearly enough. As V' for years other than 1909 and 1896 is determined, for Professor Fisher's equation, by dividing the M'V' thus estimated by the M' for the year, it is clear that V' as estimated by Professor Fisher is very much less variable than it is in fact. It is pretty variable even in his figures, but his figures do not nearly show how variable it is.[416]

Again, this undue weighting of country clearings, swallowing up New York, vitiates Professor Fisher's estimates for V, the velocity of money, for years other than 1909 and 1896. One of the elements in the calculation of V is the estimated V'.[417] Since V' is wrong, V will also be wrong. V is probably much more variable than Professor Fisher's figures would indicate. With great admiration for the ingenuity of Professor Fisher's speculations regarding V, I find too many elements of conjecture, and too many arbitrary assumptions, to give me confidence in the figure for any year. I refrain from going into any general criticism of his method of calculating V, however, contenting myself with the one clear point that, to the extent that the values of V for years other than 1909 and 1896 depend on the estimated M'V' for those years, they are less variable than they ought to be.[418]

The same conclusion regarding Professor Fisher's estimates for V' have been reached, by a different method, by Professor Wesley C. Mitchell. He, too, concludes that V' is, in fact, more variable than Professor Fisher would indicate.[419]

I conclude, therefore, that neither V' nor V has been correctly calculated, for years other than 1909 and 1896. I pass now to a consideration of T, the volume of trade, after which I shall consider P, the price-level, in the equation of exchange.

Let us first recall the point made in the chapter on "The Equation of Exchange," that P and T, the price-level and the volume of trade, are not independent even in idea. If one is given an independent definition, the other cannot be given an independent definition. If the equation is to be true, then P must be weighted by the numbers of each item (as hats) exchanged. P is not a mere average, but is a _weighted_ average, and T is always the denominator in the formula for P. In developing statistics for P and T, therefore, this fact must be kept in mind, and the elements entering into each must coincide, and vary together year by year.

In our chapter on "The Volume of Money and the Volume of Trade," we showed that the great bulk of trade is speculation. We showed that the _indicia_ of variation which Fisher[420] and Kemmerer have constructed for trade, dominated by inflexible physical items of consumption and production, give wholly misleading results for every year except the base year. They give a steadily growing, inflexible figure, with little variation from its steady path. Trade, if chiefly speculation, is highly flexible, varies enormously from year to year, waxes and wanes. This point need not be further developed. At best Fisher's figure for trade can be accepted only for one year, 1909.

Is, however, the figure for 1909, 387 billions, an acceptable figure? Is it not decidedly too large? It is made up, it will be recalled, by taking the figures for MV and M'V', adding them together to get one side of the equation, and declaring them equal to PT. P is then declared to be $1, by the arbitrary device of taking as the unit of T one dollar's worth of every sort of good at the prices of 1909. T is, then, 387 billions, since MV plus M'V' equals 387 billions. The theory underlying this is that deposits made in banks correctly represent trade.[421] Our criticisms as to the absolute magnitude assigned to T (and hence to MV plus M'V') will rest in large measure in challenging this assumption. It is our contention[422] that deposits made in banks very greatly overcount trade.

Deposits made in banks include taxes and other public revenues; they include loans and repayments, and interest-payments; they include gifts and benevolences, money sent by parents to children away from home, pensions, payments of insurance losses, annuities, dividends on stocks, payments to and from savings and loan associations, fines, contributions to churches, and other non-commercial organizations, etc., etc. None of this represents trade.

But further, whether payments are in trade or not, many times indeed does it happen that several checks are drawn in connection with the same transaction. Professor Kemmerer, entertaining this possibility, thought it might be neutralized by cases where the same check passes through several hands, making payments in several different transactions. He calls this, however, a "gratuitous assumption of unverifiable accuracy,"[423] and makes no claim to have given the matter careful study.

In general, I think it safe to hold that the case where a single check passes through several hands is not important.[424] It will happen chiefly with small checks in small places, or with small checks paid to laborers. It is the pecuniary magnitude of checks, rather than their number, that counts here. I am informed by several bankers that large checks are almost universally deposited at once. This is for several reasons: (1) The recipient of the check wishes to make sure that it is good. (2) It is unlikely that the check is of the right size for another transaction, unless the recipient is a mere agent for a third party, in which case he should (but commonly does not) pass it on to his principal, if double counting is to be avoided. (3) Every person who handles sums of any size wishes a record of the transaction, and his own canceled check is a receipt which he would not have if he passed on the check of another.

This last point will go far toward explaining why bank transactions may multiply without a corresponding multiplication of trade. The banks do the bookkeeping for modern business in increasing degree. Checks are records, of high legal value. A colleague recently told me that he, in his own capacity, had just drawn a check to himself, as trustee, transferring a sum from one account to another. Another colleague, with eight different bank accounts, estimates that over 50% of the deposits in three of them represent transfers from other accounts. This kind of duplication, where trust relations are involved, is enormous. Intercorporate relations and separate bank accounts within a corporation complicate it still further.