§ 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.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.