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.