§ 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 1909inclusive.

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,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 investigationof 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.

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.