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By Root 325 0

a trend for k1. Any systematic bias arises primarily from the assumption that the same specie reserves would have been maintained under a silver standard in the early and late years of the period as those maintained under a gold standard. The possible sources of error are different for the specie reserve ratio and the real stock of money. The desired specie reserve ratio might have been affected by a different pattern of prices. A rise in prices under a gold (silver) standard means that the real value of gold (silver) is falling, and conversely. A falling real value makes it less expensive to hold the specie reserves, and conversely. It is doubtful, however, that any such price effect has a significant influence on the decision by the monetary authority on how large a specie reserve is desirable—any financial benefit or loss is subtle and accrues to the government at large and not specifically to the monetary authority. A more important factor is surely the threat of a specie drain, which would have been largely absent under a secure silver standard.

Figure 2

Actual and Hypothetical Gold Reserves (k1), 1875–1914 (in billions of 1929 dollars)

The real stock of money would have been affected by the reduction in uncertainty as a result of settling on a definitive silver standard. The reduced uncertainty would have tended to lower velocity and raise real income, both of which would have raised the real money stock—as appears to have happened after 1896. Neglect of these effects produces an underestimate of the hypothetical silver stock. Such an underestimate introduces a downward bias in estimating the real price of silver, or a bias in the opposite direction from the possible bias introduced in estimating item (1), the production of silver.

b. Demand for Silver. The quantity of silver demanded for nonmonetary use depends primarily on world real income, the real price of silver, and the real price of gold. I have estimated a demand curve with these variables in two variants: linear and logarithmic. As a general rule, the logarithmic form is preferable. However, in this particular case I do not believe it is. The logarithmic form forces the nonmonetary demand for silver to be positive, yet it is easily possible for additions to monetary stocks of silver to exceed the world production of silver (as happened most recently under the silver purchase program of Franklin Delano Roosevelt in the 1930s). In that case, the quantity of silver available for nonmonetary purposes is negative if it is estimated in accordance with equation (5), which gives the nonmonetary supply of silver out of current production, not the nonmonetary use of silver.

As an estimate of world real income, I have used an index number of the physical volume of world production given by Warren and Pearson (1933).* For the real price of silver and the real price of gold, I simply used the actual prices divided by the U.S. deflator. This procedure assumes that the real price of silver and the real price of gold were the same throughout the world, surely not an unreasonable assumption for those two monetary metals.*

The two equations are as follows for 1880–1914:

where WI stands for world income. As usual, the values in parentheses are the absolute t-values. In the log equation, the coefficients are all highly significant; in the linear equation, only the coefficients of world income and the real price of silver are. However, there is little to choose between the equations in terms of the goodness of fit, as can be seen graphically in Figure 3 as well as from the adjusted R2s, which are .949 for the log equation and .950 for the linear equation. The standard error of estimate for the log equation is .180, which is comparable to an estimate of the coefficient of variation for the linear equation. That is .138 if the denominator of the coefficient of variation is the arithmetic mean of the dependent variables and .177 if it is the geometric mean. Both estimates for the linear equation are lower than that for the log equation.

Figure 3

Nonmonetary Demand for