Money Mischief_ Episodes in Monetary History - Milton Friedman [33]
(See Figure 4 of chapter 3.) The effect is clearly appreciable.*
4. A More Sophisticated Estimate. To go beyond these simple estimates requires finding a way to estimate the real price of silver, since we can use the counterpart of equation (3) to convert such an estimate into an estimate of the hypothetical price level.
The real price of silver is determined by (a) the supply of and (b) the demand for silver for nonmonetary use in the world as a whole. The U.S. adoption of a bimetallic or silver standard would presumably not have significantly affected the world demand function for silver for nonmonetary use. To estimate that demand function (section b below) requires data on the actual nonmonetary use of silver (section al). On the other hand, the U.S. adoption of a bimetallic or silver standard would clearly have altered significantly the supply of silver for nonmonetary use (section a2) because it would have increased the monetary demand for silver. Constructing acceptable estimates for the period in question (1875–1914) proved by far my most troublesome problem.
a1. Actual Nonmonetary Use of Silver. The supply of silver for nonmonetary use is equal to (1) the production of silver minus (2) the demand for silver for monetary use by the rest of the world minus (3) the demand for silver for U.S. monetary use. Or,
(5) SNM = SPROD - EWMDS - UMDS.
Estimates for SPROD, the annual production of silver, and EWMDS, the increment in the monetary stock of silver by other countries, are readily available. I have constructed estimates for UMDS, the increment in the U.S. monetary stock of silver, for the fiscal years 1873 to 1894 from a report of the Treasury Department listing the U.S. purchases under the successive silver purchase acts and for later years from estimates of the total dollar value of the monetary stock of silver.
a2. Hypothetical Supply of Silver for Nonmonetary Use. Equation (5) gives actual nonmonetary use. Add an H to the relevant symbols and the equation gives hypothetical nonmonetary use under a silver standard. Item (1), silver production, depends in principle on the real price of silver. However, during the period in question the actual production of silver rose sharply, nearly tripling from 1880 to 1914, while at the same time the real price of silver fell to less than half its initial level. Supply was clearly being driven by exogenous discoveries and innovations. Moreover, much silver is a by-product of the mining of other metals and so is relatively inelastic in supply. Hence, I have assumed that silver production would have been what it actually was. This assumption introduces an error leading to an upward bias in the estimated real price of silver.
Regarding item (2), I have assumed that other countries would not have been affected by the U.S. adoption of a silver standard, either by themselves adopting silver rather than gold or by changing the amount of silver added to their monetary stocks. This assumption seems eminently justified. The major move from silver to gold by Germany, France, and others came before the United States would have moved to a silver standard and, indeed, was part of the reason why the United States itself moved to a gold standard. Hence, I have simply used the actual monetary demand by other countries as the hypothetical.
Item (3), the hypothetical increment in the U.S. monetary stock of silver, is the most difficult. We can tautologically express the hypothetical U.S. monetary silver stock (in ounces) as the product of the ratio maintained between specie and money (SPR) times the quantity of money divided by the legal price of silver, or, expressing the quantity of money by the ratio of nominal income to velocity and expressing nominal income as the product of real income and the price level, as follows:
y/V is the real money stock; multiplication by P converts it into nominal dollars. Only the product of SPR and y/V, which I have designated by k1 and which equals the real value of the specie reserve, enters into the subsequent