Money Mischief_ Episodes in Monetary History - Milton Friedman [32]
1. Objective. To estimate the price level and gold-silver price ratio that would have prevailed if the Coinage Act of 1873 had contained provision for the free coinage of the standard silver dollar of 371.25 troy grains of pure silver, so that the legal and market price of silver had remained $1.2929....
2. Naive Estimate. The real price of silver is simply the nominal price divided by the price level (PS/P). On the naive assumption that this price remained unchanged, the real price of silver would have been 1.2929/PHN, where PHN is the naive estimate of the hypothetical price level under a silver standard. Equating the two and solving for the naive hypothetical price level gives
where P is the actual price level and PS is the actual nominal price of silver.* (For subsequent definitions of notation, see the Record of Notation at the end of the chapter.) The naive estimate is less than the actual price level from 1865 to 1876. In 1876 the two are equal; hence, if the fateful line had not been omitted from the Coinage Act of 1873, resumption on the basis of silver would have occurred in 1876, a year after the passage of the Resumption Act. Figure 3 of chapter 3 plots the subsequent naive estimate of the price level; Table 1 gives the numerical values.
Defects of the naive estimate: (1) The United States would probably have added to its silver stock under a silver standard even more than it did in response to the silver interests under a gold standard. That would have tended to raise the real price of silver. (2) The United States would also have exported gold rather than accumulating gold, which would have added to the rest of the world's monetary and nonmonetary stocks of gold and raised nominal prices in the gold-standard world. That would have lowered the real price of gold. (3) On both scores, the gold-silver price ratio would have been lower than it actually was.
3. 16 to 1 Estimate. Assume that the adoption of a silver standard by the United States would have been effective in establishing 16 to 1 as the actual gold-silver price ratio and that the United States stayed on a strict silver standard (that is, the ratio was trivially above 16 to 1). As we shall see, this is not as farfetched as it seems.
To estimate the hypothetical U.S. price level under this assumption, we need an estimate of the hypothetical real price of gold. Assume that the United States disposed of the whole of its monetary gold stock when it adopted a silver standard and that the gold released was divided between nonmonetary use (by the United States and the rest of the world) and the monetary gold stock of the rest of the world in the proportion that actually prevailed between these two components of the total gold stock.*
Table 1
Estimated Effect on U.S. and U.K. Prices of U.S. Being on Silver Standard, 1865–1914
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Assume further that the world price level rose in proportion to the increased stock of gold. We then have
Since the real price of silver is by assumption -fa the real price of gold and by definition equal to the nominal price (= legal price) divided by the price level, we have
The actual U.S. monetary gold stock became a steadily increasing fraction of the world's monetary gold from 1879 on, so that the 16 to 1 price roughly parallels the actual price, with the differential rising somewhat over the period (see Figure 3 of chapter 3). In 1876, when resumption on silver would have taken place, the price level as estimated from equation (3) was a trifle below the actual price level. By 1877, it was a trifle above.
The hypothetical real price of gold is also all that is needed to estimate the effect on the price level of the gold-standard world of the United States' being on a silver standard throughout the period. If we take the U.K. price level as representative of the price