Irving Fisher

“ Therefore, if deposits had increased just as fast as money and no faster, we should ascribe the whole increase to money alone. In that case no part of the rise of prices would be ascribable to any increase in deposits; for there would have been no increase except what was due to the increase in money. The increase of deposits subject to check can be considered independently of the increase of money only in so far as the deposits have increased relatively to money. We have seen that mere increase of money would of itself normally cause a proportionate increase of deposits ”

“ We must remember, however, that such persons as economists, who are most apt to think about the circulation of money, have a rapid turnover. They are usually city dwellers and the comparatively well to do, who, as we know, do not keep their cash inactive long. Laborers, especially thrifty laborers and laborers paid monthly, will keep cash on hand for several weeks without spending it. Farmers and others living in sparsely settled districts will even keep it for months. Probably the velocity of circulation of money differs widely among different classes and different localities. ”

“ XII.97 It would take us too far afield to discuss all the other factors which have been held more or less responsible for the increase in prices. We have already made it clear that none of these could influence prices except by increasing the quantity of money in circulation, the relative deposits, or their velocities, or by decreasing trade. As trade has increased greatly, the last possibility may be ignored. ”

“ In other words, there has been a greater increase in money than appears from the United States figures by the amount which has overflowed into foreign lands. The United States is only a small part of the world's market, and its price level is largely determined by the world's price level. ”

“ XII.20 For two years, 1896 and 1909, thanks to the efforts of Professor Kinley of the University of Illinois, we have voluminous and unique data collected originally for the purpose of calculating the ratio of money-transactions to check-transactions in the United States, i.e. the ratio of MV to M'V'. We shall see that these data, in conjunction with other official statistics, are sufficient for something more important than computing this ratio; for they enable us to calculate with a tolerable degree of exactness the magnitudes V and V' for both the years mentioned. ”

“ If we know the amount of exchanges effected, and the quantity of currency used, we might get by division the average number of times the currency is turned over; but the data, as already stated, are quite wanting" XII.29 As we shall see, however, data now exist, capable of revealing the "amount of exchanges effected," or, MV. In fact, this is equal to the total money deposited in banks, plus the total money-wages paid, plus a small miscellaneous item. From MV and M it is of course easy to obtain V by division. ”

“ XII.7 But Persons's method of testing agreement by means of a coefficient of correlation is not really applicable to two curves representing magnitudes changing in time. For it practically ignores a most essential factor, their order in time. A year-to-year comparison is better. If we consider the curves of prices and of "relative circulation,"*5 we see at a glance that almost every successive change in direction in the one curve is matched by a corresponding change in direction in the other. ”

“ Thereafter the tariff ceases to affect the price level, except as it interferes with trade and thereby prevents the price level at home from adjusting itself to the price levels abroad. This interfering effect may be in either direction; that is, the price level at home will be rendered more independent of foreign price levels than it would be if trade were free. The tariff merely isolates the protected country. ”

“ XII.55 It is to be emphasized that the coefficients of correlation as just given compare the price level with what it should be according to the statistics of the five magnitudes on which, by the so-called quantity theory, it is dependent. The correlation would be less if instead of these five magnitudes only one were taken. Thus the coefficient of correlation for 1896-1909 as between money, M, and prices, P, by the year-to-year-ratio method is 43 per cent (or .43 ± .13) .*27 Even this is a moderately high degree of correlation. ”

“ The treasury stock is excluded because it is a hoard which does not become adjusted to needs of payment in the sense—or at any rate in the degree—that the stocks in merchants' tills and in people's pockets become adjusted. ”

“ XII.74 These figures, or the dotted curves in the preceding diagram, show that money in circulation (M) has nearly doubled in thirteen years; that its velocity of circulation (V) has increased only 10 per cent; that the deposit currency has nearly tripled and its velocity of circulation (V') has increased 50 per cent; that the volume of trade has doubled; and that prices have risen two thirds. ”

“ This makes a grand total for business done at present prices (MV + M'V' or PT) of 387 billions, or more than a billion a day. The size of this aggregate will probably astonish most readers. In the absence of actual statistics we have heretofore little realized the colossal proportions of our trade. Probably few persons outside of statisticians would have imagined that our import and export trade, which has filled so large a place in our political vision, sinks into utter insignificance as compared with the internal trade of the country. ”

“ So far as our prices have risen faster than prices have risen in other countries, like England, in the period here considered, it seems fair to attribute a part of this additional rise to our tariff system. ”

“ Thus, the inflections of 1899, 1900, 1901, for "relative circulation," although all counted as cases of disagreement, are strikingly similar respectively to the inflections of 1900, 1901, 1902, for "general prices." From the fact that the statistics are partly for calendar and partly for fiscal years, such one-year shifting of correspondence is to be expected, as Professor Kemmerer points out.
§ 2 XII.10 I shall now attempt to make as precise statistical estimates of the magnitudes in the equation of exchange for the years 1896-1909 as the data available will allow. ”

“ The correlation coefficient for Kemmerer's figures 1896-1908 is 83 per cent, which is far higher than that obtained by Persons for the period beginning in 1879.
25. For instance, no one would deny that the length and breadth of nuts are highly correlated. The coefficient of their correlation is 57 per cent. The height of a man and the breadth of his face are correlated to the extent of 35 per cent. ”

“ We have still to interpolate figures for intervening years. For the period between these two years, we have, unfortunately, no such data as those of Professor Kinley for 1896 and 1909. However, we can find an excellent barometer in the clearing house transactions,—a barometer dependent partly on the clearings in New York City, but more on those outside of New York City. ”

“ The changes made in the various factors are made in proportion to their assumed relative liability to error.
XII.67 The results are shown in Figures 14, 15, 16, and the previous Figure 13, each of which relates to one of the factors in the equation of exchange as originally calculated and as finally adjusted (dotted lines) . When they are all thus adjusted, they conform exactly to the equation of exchange.*28
XII.68 In Figure 14 we see that the alterations made in the figures for M and M' are so trifling as to be almost negligible, being usually much less than 1 per cent. ”