For this reason practical applications of the theory are not thus restricted. The standard set of commodities selected is not confined to goods which are exported from and imported into the countries under comparison, but is the same set, generally speaking, as is used for compiling index numbers of general purchasing power or of the working-class cost of living. Yet applied in this way—namely, in a comparison of movements of the general index numbers of home prices in two countries with movements in the rates of exchange between their currencies—the theory requires a further assumption for its validity, namely, that in the long run the home prices of the goods and services which do not enter into international trade, move in more or less the same proportions as those which do.[27]

[27] “Our calculation of the purchasing power parity rests strictly on the proviso that the rise in prices in the countries concerned has affected all commodities in a like degree. If that proviso is not fulfilled, then the actual exchange rate may deviate from the calculated purchasing power parity.” Cassel, Money and Foreign Exchange after 1914, p. 154.

So far from this being a truism, it is not literally or exactly true at all; and one can only say that it is more or less true according to circumstances. If capital and labour can freely move on a large scale between home and export industries without loss of relative efficiency, if there is no movement in the “equation of exchange” (see below) with the other country, and if the fluctuations in price are solely due to monetary influences and not to changes in other economic relationships between the two countries, then this further assumption may be approximately justified. But this is not always the case; and such a cataclysm as the war, with its various consequences to victor and vanquished, may set up a new equilibrium position. There may, for example, be a change more or less permanent, or at least as prolonged as the reparation payments, in the relative exchange values of Germany’s imports and exports respectively, or of those German products and services which can enter into international trade and those which cannot. Or, again, the strengthening of the financial position of the United States as against Europe, which has resulted from the war, may have shifted the old equilibrium in a direction favourable to the United States. In such cases it is not correct to assume that the coefficients of purchasing power parity, calculated, as they generally are calculated, by means of the relative variations of index numbers of general purchasing power from their pre-war levels, must ultimately approximate to the actual rates of exchange, or that internal and external purchasing power must ultimately bear to one another the same relation as in 1913.

The Index Number calculated for the United States by the Federal Reserve Board illustrates how disturbing may be the influence of the change since 1913 in the relative prices of imported goods, exported goods, and commodities generally:

Goods
Imported.		Goods
Exported.		All
Commodities.
1913100100100
July 1922128165165
April 1923156186169
July 1923141170159

Thus the theory does not provide a simple or ready-made measure of the “true” value of the exchanges. When it is restricted to foreign-trade goods, it is little better than a truism. When it is not so restricted, the conception of purchasing power parity becomes much more interesting, but is no longer an accurate forecaster of the course of the foreign exchanges. If, therefore, we follow the ordinary practice of fixing purchasing power parity by comparisons of the general purchasing power of a country’s currency at home and abroad, then we must not infer from this that the actual rate of exchange ought to stand at the purchasing power parity, or that it is only a matter of time and adjustment before the two will return to equality. Purchasing power parity, thus defined, tells us an important fact about the relative changes in the purchasing power of money in (e.g.) England and the United States or Germany between 1913 and, say, 1923, but it does not necessarily settle what the equilibrium exchange rate in 1923 between sterling and dollars or marks ought to be.

Thus defined “purchasing power parity” deserves attention, even though it is not always an accurate forecaster of the foreign exchanges. The practical importance of our qualifications must not be exaggerated. If the fluctuations of purchasing power parity are markedly different from the fluctuations in the exchanges, this indicates an actual or impending change in the relative prices of the two classes of goods which respectively do and do not enter into international trade. Now there is certainly a tendency for movements in the prices of these two classes of goods to influence one another in the long run. The relative valuation placed on them is derived from deep economic and psychological causes which are not easily disturbed. If, therefore, the divergence from the pre-existing equilibrium is mainly due to monetary causes (as, for example, different degrees of inflation or deflation in the two countries), as it often is, then we may reasonably expect that purchasing power parity and exchange value will come together again before long.

When this is the case, it is not possible to say in general whether exchange value will move towards purchasing power parity or the other way round. Sometimes, as recently in Europe, it is the exchanges which are the more sensitive to impending relative price-changes and move first; whilst in other cases the exchanges may not move until after the change in the relation between the internal and external price-levels is an accomplished fact. But the essence of the purchasing power parity theory, considered as an explanation of the exchanges, is to be found, I think, in its regarding internal purchasing power as being in the long run a more trustworthy indicator of a currency’s value than the market rates of exchange, because internal purchasing power quickly reflects the monetary policy of the country, which is the final determinant. If the market rates of exchange fall further than the country’s existing or impending currency policy justifies by its effect on the internal purchasing power of the country’s money, then sooner or later the exchange value is bound to recover. Thus, provided no persisting change is taking place in the basic economic relations between two countries, and provided the internal purchasing power of the currency has in each country settled down to equilibrium in relation to the currency policy of the authorities, then the rate of exchange between the currencies of the two countries must also settle down in the long run to correspond with their comparative internal purchasing powers. Subject to these assumptions comparative internal purchasing power does take the place of the old gold parity as furnishing the point about which the short-period movements of the exchanges fluctuate.

If, on the other hand, these assumptions are not fulfilled and changes are taking place in the “equation of exchange,” as economists call it, between the services and products of one country and those of another, either on account of movements of capital, or reparation payments, or changes in the relative efficiency of labour, or changes in the urgency of the world’s demand for that country’s special products, or the like, then the equilibrium point between purchasing power parity and the rate of exchange may be modified permanently.

This point may be made clearer by an example. Let us consider two countries, Westropa and the United States of the Hesperides, and let us assume for the sake of simplicity, and also because it may often correspond to the facts, that in both countries the price of exported goods moves in the same way as the price of other home-produced goods, but that the “equation of exchange” has moved in favour of the Hesperides so that a smaller number than before of units of Hesperidean products exchange for a given quantity of Westropean products. It follows from this that imported products in Westropa will rise in price more than commodities generally, whilst in the Hesperides they will rise less. Let us suppose that between 1913 and 1923 the Westropean index number of prices has risen from 100 to 155 and the Hesperidean index number from 100 to 160; that these index numbers are so constructed in each case that imported commodities constitute 20 per cent and home-produced commodities 80 per cent of the whole; and that the “equation of exchange” has moved 10 per cent in favour of the Hesperides, that is to say a given quantity of the goods exported by the Hesperides will buy 10 per cent more than before of the goods exported by Europe. The state of affairs is then as follows:[28]