Money Mischief_ Episodes in Monetary History - Milton Friedman [113]
As to silver countries, the estimate of the 16 to 1 U.S. price level in Table 1 falls 4 percent, of the hypothetical price level (discussed in point 4 of this chapter) rises 4 percent, consistent with Fisher's "if at all" (1911, pp. 244–45).
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* A footnote to the Warren and Pearson tables says that for 1865 to 1932 the index was prepared by Carl Snyder of the Federal Reserve Bank of New York. Warren and Pearson report similar index numbers of U.S. physical volume of production. The trend of the index of U.S. production is steeper than the trend of U.S. real income (estimates from Friedman and Schwartz 1982). On the other hand, the general ups and downs are very similar. Accordingly, I experimented with adjusting the Warren and Pearson index by subtracting out a trend at a rate equal to the difference between the logarithmic trends of U.S. production and U.S. real income, which was four-tenths of 1 percent per year. However, the effect on the final results was trivial and, if anything, rendered them slightly less significant statistically, so I have simply used the original index.
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* However, it is not clear that it is preferable to use the U.S. rather than the U.K. deflator. I experimented with both. The difference in results was small, trivially in favor of the U.S. deflator. Still, a more decisive consideration was that I wanted to use the equation to estimate the hypothetical U.S. price level, so it was encouraging that substituting the U.K. deflator did not produce a statistical improvement.
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* The year 1874 is the first for which I have an estimate for EWMDS, which explains why the first year for which I can estimate the first approximation is 1874.
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* A major sticking point is to specify precisely how the U.S. gold stock would have been disposed of. My earlier rough approximation evades this question. For a full solution, however, we cannot evade it. Demand functions for gold and silver refer to annual quantity demanded, and we need to equate that demand function with annual supply; this means that we would need to add to total gold production the amount of gold that the United States would have released to the rest of the world from its stock on a year-by-year basis. I see no way to estimate the annual release except by purely arbitrary assumptions.
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†The calculated demand functions for nonmonetary use of gold are as satisfactory as those for silver in terms of goodness of fit, but not in terms of economic logic. The logarithmic and linear demand functions are as follows:
where WNMG is the world nonmonetary demand for gold. As with silver, both equations give high multiple correlations (adjusted R2s of .98 for the log equation and of .97 for the linear equation) and relatively small standard errors. The standard error of the log correlation is .031. The corresponding estimate for the linear equation of the coefficient of variation is .037, whether the denominator is an arithmetic mean or a geometric mean.
An appendix to chapter 4 of the Report of the U.S. Commission on the Role of Gold reports estimates of demand equations that are linear in the logarithms of the variables for the industrial demand for gold for 1950–80 and 1969–80 (1982, [>]). The independent variables are conceptually the same as those that I used: the real price of gold, the real price of silver, and real income. Both sets use two alternative deflators to estimate the real prices, the U.S. wholesale price index and the world consumer price index. The difference between the two sets of equations is that the one for the longer period