A Tract on Monetary Reform: Chapter III - II. The Theory of Purchasing Power Parity

A Tract on Monetary Reform, by John Maynard Keynes is part of HackerNoon’s Book Blog Post series. You can jump to any chapter in this book here. Chapter III: II. The Theory of Purchasing Power Parity.

The Quantity Theory deals with the purchasing power or commodity-value of a given national currency. We come now to the relative value of two distinct national currencies,—that is to say, to the theory of the Foreign Exchanges.

When the currencies of the world were nearly all on a gold basis, their relative value (i.e. the exchanges) depended on the actual amount of gold metal in a unit of each, with minor adjustments for the cost of transferring the metal from place to place.

When this common measure has ceased to be effective and we have instead a number of independent systems of inconvertible paper, what basic fact determines the rates at which units of the different currencies exchange for one another?

The explanation is to be found in the doctrine, as old in itself as Ricardo, with which Professor Cassel has lately familiarised the public under the name of “Purchasing Power Parity.”26

26 This term was first introduced into economic literature in an article contributed by Prof. Cassel to the Economic Journal, December 1918. For Prof. Cassel’s considered opinions on the whole question, see his Money and Foreign Exchange after 1914 (1922). The theory, as distinct from the name, is essentially Ricardo’s.

This doctrine in its baldest form runs as follows: (1) The purchasing power of an inconvertible currency within its own country, i.e. the currency’s internal purchasing power, depends on the currency policy of the Government and the currency habits of the people, in accordance with the Quantity Theory of Money just discussed. (2) The purchasing power of an inconvertible currency in a foreign country, i.e. the currency’s external purchasing power, must be the rate of exchange between the home-currency and the foreign-currency, multiplied by the foreign-currency’s purchasing power in its own country. (3) In conditions of equilibrium the internal and external purchasing powers of a currency must be the same, allowance being made for transport charges and import and export taxes; for otherwise a movement of trade would occur in order to take advantage of the inequality. (4) It follows, therefore, from (1), (2), and (3) that the rate of exchange between the home-currency and the foreign-currency must tend in equilibrium to be the ratio between the purchasing powers of the home-currency at home and of the foreign-currency in the foreign country. This ratio between the respective home purchasing powers of the two currencies is designated their “purchasing power parity.”

If, therefore, we find that the internal and external purchasing powers of the home-currency are widely different, and, which is the same thing, that the actual exchange rates differ widely from the purchasing power parities, then we are justified in inferring that equilibrium is not established, and that, as time goes on, forces will come into play to bring the actual exchange rates and the purchasing power parities nearer together. The actual exchanges are often more sensitive and more volatile than the purchasing power parities, being subject to speculation, to sudden movements of funds, to seasonal influences, and to anticipations of impending changes in purchasing power parity (due to relative inflation or deflation); though also on other occasions they may lag behind. Nevertheless it is the purchasing power parity, according to this doctrine, which corresponds to the old gold par. This is the point about which the exchanges fluctuate, and at which they must ultimately come to rest; with one material difference, namely, that it is not itself a fixed point,—since, if internal prices move differently in the two countries under comparison, the purchasing power parity also moves, so that equilibrium may be restored, not only by a movement in the market rate of exchange, but also by a movement of the purchasing power parity itself.

At first sight this theory appears to be one of great practical utility; and many persons have endeavoured to draw important practical conclusions about the future course of the exchanges from charts exhibiting the divergences between the market rate of exchange and the purchasing power parities,—undeterred by the perplexity whether an existing divergence from equilibrium will be remedied by a movement of the exchanges or of the purchasing power parity or of both.

In practical applications of the doctrine there are, however, two further difficulties, which we have allowed so far to escape our attention,—both of them arising out of the words allowance being made for transport charges and import and export taxes. The first difficulty is how to make allowance for such charges and taxes. The second difficulty is how to treat purchasing power over goods and services which do not enter into international trade at all.

The doctrine, in the form in which it is generally applied, endeavours to deal with the first difficulty by assuming that the percentage difference between internal and external purchasing power at some standard date, when approximate equilibrium may be presumed to have existed, generally the year 1913, may be taken as an approximately satisfactory correction for the same disturbing factors at the present time. For example, instead of calculating directly the cost of a standard set of goods at home and abroad respectively, the calculations are made that $2 are required to buy in the United States a standard set which $1 would have bought in 1913, and that £2·43 are required to buy in England what £1 would have bought in 1913. On this basis (the pre-war purchasing power parity being assumed to be in equilibrium with the pre-war exchange of $4·86 = £1) the present purchasing power parity between dollars and sterling is given by $4 = £1, since 4·86 × 2 ÷ 2·43 = 4.

The obvious objection to this method of correction is that transport and tariff costs, especially if this term is taken to cover all export and import regulations, including prohibitions and official or semi-official combines for differentiating between export and home prices, are notoriously widely different in many cases from those which existed in 1913. We should not get the same result if we were to take some year other than 1913 as the basis of the calculation.

The second difficulty—the treatment of purchasing power over articles which do not enter into international trade—is still more serious. For, if we restrict ourselves to articles entering into international trade and make exact allowance for transport and tariff costs, we should find that the theory is always in accordance with the facts, with perhaps a short time-lag, the purchasing power parity being never very far from the market rate of exchange. Indeed, it is the whole business of the international merchant to see that this is so; for whenever the rates are temporarily out of parity he is in a position to make a profit by moving goods. The prices of cotton in New York, Liverpool, Havre, Hamburg, Genoa, and Prague, expressed in dollars, sterling, francs, marks, lire, and krone respectively, are never for any length of time much divergent from one another on the basis of the exchange rates actually obtaining in the market, due allowance being made for tariffs and the cost of moving cotton from one centre to another; and the same is true of other articles of international trade, though with an increasing time-lag as we pass to articles which are not standardised or are not handled in organised markets. In fact, the theory, stated thus, is a truism, and as nearly as possible jejune.

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:

hus 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

For 10x = 11y
8y + 2x = 1550

        11x´ = 10y´
8y´ + 2x´ = 1600.

Thus it appears that the purchasing power parity of the Westropean currency in 1923 compared with 1913 is (160/155 = ); whereas the rate of exchange, compared with the 1913 parity, is (163/167 = 148/152 = ). If the worsening of Westropa’s equation of exchange with the Hesperides is permanent, then its purchasing power parity (on the 1913 basis) will also remain permanently above the equilibrium value of the market rate of exchange.

A tendency of these two measures of the value of a country’s currency to move differently is, therefore, a highly interesting symptom. If the market rate of exchange shows a continuing tendency to stand below the purchasing power parity, we have, failing any other explanation, some reason to suspect a worsening of the “equation of exchange” as compared with the base year.

In the charts and tables below, the actual results are worked out of applying the theory to the exchange value of sterling, francs, and lire in terms of dollars since 1919. The figures show that, quantitatively speaking, the influences, which detract from the precision of the purchasing power parity theory, have been in these cases small, on the whole, as compared with those which function in accord with it. There seems to have been some disturbance in the “equations of exchange” since 1913,—which would probably show up more distinctly if it were not that the index numbers employed in the following enquiry are of the type which is largely built up from articles entering into international trade. Nevertheless general price changes, affecting all commodities more or less equally, due to currency inflation or deflation, have been so dominant in their influence that the theory has been actually applicable with remarkable accuracy. In the case, however, of such countries as Germany, where the shocks to equilibrium have been much more violent in many respects, the concordance100 between the purchasing power parity based on 1913 and the actual rate of exchange has suffered, whether temporarily or permanently, very great disturbance.

The first of these charts, which deals with the value of sterling in terms of dollars, shows that whilst the purchasing power parity, calculated with 1913 as base, is often somewhat above the actual exchange, there is a persevering tendency for the two to come together. The two curves are within one point of each other in September-November 1919, March-April 1920, April 1921, September 1921, January-June 1922, and February-June 1923, which is certainly a remarkable illustration of the tendency to concordance between the purchasing power parity and the rate of exchange. On inductive grounds it would be tempting to conclude from this chart that the financial consequences of the war have depressed the equilibrium of the purchasing power parity of sterling as against the dollar from 1 to 2½ per cent since 1913, if it were not that this figure barely exceeds the margin of error resulting from the choice of one pair of index numbers rather than another from amongst those available.29 It will be interesting to see what effect is produced by the payment, just commenced, of the interest on the American debt.

29 Nevertheless, if I had used the Board of Trade or the Statist index number in place of the Economist index number in the table below, the presumption of a slight worsening of the “equation of index” against Great Britain would be somewhat strengthened.

This chart brings out clearly, as also do those for France and Italy, the susceptibility of the foreign exchange rates to seasonal influences, whereas the purchasing power parity is naturally less affected by them.

In the case of France the curves are together at the end of 1919, diverge in 1920, come together again in the middle of 1921, and keep together until a divergence occurred again in the latter part of 1922.

For Italy, rather unexpectedly perhaps, the relationship is extraordinarily steady, although here, as in the case of France and Great Britain, there are indications that the war may have resulted in a slight lowering of the equilibrium point, by (say) 10 per cent;30—the parity, calculated with 1913 as the base year, has been almost invariably somewhat above the actual rate of exchange. The Italian curve illustrates in a remarkable way the manner in which the external and internal purchasing powers of the currency fall together, when the main influence at work is a progressive depreciation due to currency inflation.

30 The use of any of the other Italian index numbers would have accentuated this indication. The table of American prices given on p. 94 above confirms the suggestion that the “equation of exchange” between the U.S. and the rest of the world as a whole has moved, say, 10 per cent in favour of the former.

The broad effect of these curves and tables is to give substantial inductive support to the general theory outlined above, even under such abnormal conditions as have existed since the Armistice. During this period the movements of the relative price level in France and Italy due to monetary inflation have been so much larger than any shifting in the “equation of exchange” (a movement of more than 10 or 20 per cent in which would be startling) that their foreign exchanges have been much more influenced by their internal price policy in relation to the internal price policies of other countries than by any other factor; with the result that the Purchasing Power Parity Theory, even in its crude form, has worked passably well.

Great Britain and the United States

31 Economist Index Number.

32 U.S. Bureau of Labour Index Number, as revised.

33 The U.S. Bureau of Labour Index Number divided by the Economist Index Number.

France and the United States

34 U.S. Bureau of Labour Index divided by French official wholesale Index.

Italy and the United States

35 U.S. Bureau of Labour Index Number divided by the “Bachi” Index Number.