Article

The Purchasing-Power-Parity Theory of Exchange Rates: A Review Article

Author(s):
International Monetary Fund. Research Dept.
Published Date:
January 1976
Share
  • ShareShare
Show Summary Details

The concept of purchasing power parity (PPP) has two applications in economics. The first use is as a conversion factor to transfer data from denomination in one national currency to another. The data are generally in a national accounts framework, but the level of detail can range from the gross domestic product (GDP) itself to highly disaggregative categories of expenditure. This use of PPP boasts a body of theory (mainly index-number theory) and applications (predominantly to intercountry comparisons of GDP and its components) that have steadily improved over the years, and pathbreaking studies in the area continue to appear.1 There is now general recognition that, for certain purposes of data conversion, it is preferable to use PPPs rather than current exchange rates.

The second application of PPP has no such widespread acceptance among economists. The reference here is to the PPP theory of exchange rates, which has remained a relatively unsophisticated theory, hardly advanced in complexity over three fourths of a century. Yet the PPP approach is resurrected from time to time, ushering in a period distinguished both by empirical applications and renewed criticisms of the theory, whereupon again the approach falls into disuse. Lutz (1966, pp. 13–14) notes that, in spite of its limitations, “the purchasing-power-parity theory … still has many supporters especially among journalists and among government and international officials.” He refers to “the apparently indestructible popularity of this theory.” It is this second application of PPP, its use as an exchange rate theory, that is the subject of this review article. Sections I and II explore conceptual issues of PPP, while Sections III and IV consider its empirical aspects. Section V presents conclusions of the review and offers suggestions for further research in the area.

I. Theories of Purchasing Power Parity

methodology

The purchasing power parity between two countries is defined as either the ratio of the countries’ price levels (absolute PPP) or the product of the exchange rate in a base period and the ratio of the countries’ price indices (relative PPP). Let A and B be two countries, t the current time period, and o a base period. Then, by definition

PLji=price level in country i in period j
Pji=price index in country i in period j, with base period o
PPPjabs=absolute PPP in period j (number of units of country B’s currency per unit of country A’s currency)
PPPjrel=relative PPP in period j (number of units of country B’s currency per unit of country A’s currency)
Rj=actual exchange rate in period j (number of units of country B’s currency per unit of country A’s currency).

PPP theory consists of two definitions and two propositions, all involving equilibrium exchange rates. The short-run equilibrium exchange rate is defined as the rate that would exist under a freely floating (i.e., unmanaged) exchange rate system. The long-run equilibrium exchange rate is defined as the fixed exchange rate that would yield balance of payments equilibrium over a time period incorporating any cyclical fluctuations in the balance of payments (including those related to business cycles at home and abroad). Furthermore, the latter definition assumes the absence of special policies to avoid balance of payments disequilibrium (e.g., the use of monetary and fiscal restraint or trade and payments restrictions to prevent or suppress a deficit). The balance of payments concept used is an inclusive one, generally the official settlements or basic balance, rather than the current account or trade balance.2

The propositions of PPP theory are (1) that the short-run equilibrium exchange rate is a function of the long-run equilibrium exchange rate in the sense that the former variable tends to approach the latter, and (2) that the PPP is either the long-run equilibrium exchange rate or the principal determinant of it. Then PPP theory in its most general form is

RSt=f(PPPt,…), where
RSt=short-run equilibrium exchange rate in period t (number of units of country B’s currency per unit of country A’s currency)
PPPt=PPPtabsorPPPtrel
f=an arbitrary increasing function with respect to the explicit independent variable, with the ellipsis denoting space for additional explanatory variables.

PPP is not a single theory but rather consists of many alternative theories. One can consider a three-way classification of these theories. First, the absolute form of PPP is distinguished from the relative form. Second, a variety of product-price or factor-cost measures may be used in the definition of PPP. Examples (for absolute or relative PPP, respectively) are the GDP price level or the GDP deflator; the cost of living (COL) price level or COL price index, that is, the consumer price index (CPI); a wholesale price level or wholesale price index (WPI); and wage rates, unit labor cost (ULC), or unit factor cost (UFC), the last three measures in either absolute-level or index-number form.

The third dimension of any PPP theory is the form of the f function. The central tenet of all PPP theories is a tendency for the short-run equilibrium exchange rate to approach the PPP.3 Factors, if any, that are recognized as inhibiting this tendency (and space for which in the function is indicated by the ellipsis) may be either short-run or long-run in nature, with the classification in certain cases depending on one’s time horizon. As examples, a possible short-run inhibiting influence might be exchange market speculation; a possible long-run factor a persistent unidirectional flow of long-term capital.

Where does a PPP theory end and an eclectic theory of the (short-run) equilibrium exchange rate begin? Consider two extreme cases. First,

RSt = PPPt

In this formulation, the exchange rate4 cannot deviate even temporarily from the current value of the PPP. This relationship is the most extreme form of the PPP theory, but it has never been advocated by a proponent of the theory. As noted by Holmes (1967 b), this formulation of PPP was repeatedly rejected by Cassel himself, the greatest proponent of the theory.5

In the second case, the PPP is but one variable with no overriding importance in a multivariable multiequation explanation of the exchange rate.6 Obviously, this formulation cannot be considered as falling within the rubric of the PPP theory.

What of the intermediate cases? Working from the first extreme, one can replace PPPt by a weighted average of the current and past values of PPP. Again, this distributed-lag relationship, with no other explanatory variable and no error term, has not been advocated by any proponent of the PPP theory. The introduction of a random error term in the f function would come closer to Cassel’s theory but still not describe it accurately.7

Cassel’s form of the f function involves PPPt not as the only systematic variable explaining the exchange rate but as the most important such variable. He allows room both for random influences and for other (though less important) explanatory variables in the f function. Cassel writes that the rate of exchange is “primarily determined” by the PPP (e.g., 1918, p. 413) or “essentially determined” by it (e.g., 1925 c, p. 17). Holmes (1967 b, p. 692) notes that “Cassel always had such qualifying phrases. …” Cassel suggests even weaker versions of PPP in his later writings, arguing that (relative) PPP is “satisfactory for a first rough calculation of the new equilibrium level of the rates of exchange after big monetary changes have occurred” (1932 b, p. 661). Cassel recognized several variables other than the PPP as systematic influences on the exchange rate;8 and even if these other variables happened to be dormant or absent, he allowed for divergences (described as small and/or temporary) of the exchange rate from the PPP, that is, for a random error term.9 Following Cassel, the criterion for a PPP theory adopted in this review is that the PPP be the most important determinant of the exchange rate.

origins of the purchasing-power-parity theory

The term “purchasing power parity” was originated by Cassel (1918, p. 413), but he presented his PPP theory nearly three years earlier using the equivalent term “theoretical rate of exchange” (1916, p. 64). While many credit Cassel as the originator of the PPP theory, some observers 10 consider the founders to be the English economists writing at the time of the floating pound during the so-called Bank Restriction Period, 1797–1821. Specifically, they credit Wheatley, writing in 1803, with the earliest complete formulation of the theory.11 Other writers assert that the theory was anticipated even earlier. Brisman (1933, p. 72) claims that the PPP theory appeared first in Sweden more than 20 years prior to the Bank Restriction Period. Einzig (1970, pp. 145–46) traces the origins of the theory to Spanish writers in the sixteenth and seventeenth centuries.

Yet Cassel was the first economist to place PPP within a systematic framework so that it clearly became an operational theory. As noted by Viner (1937, pp. 379–80), Cassel was the first to express the theory in terms of statistical averages of prices. Not only did Cassel make PPP an operational theory—he was also the first to test it empirically, and he certainly was the most active proponent of PPP. Most impressive of all, Cassel’s theoretical analysis and empirical tests of PPP are remarkably similar to those current in later periods, up to and including the present. Therefore Cassel’s contributions, and not those of preceding writers, are the earliest analyses and applications of PPP discussed in this review. The focus on Cassel here, in view of the modernity of his work, is analytical rather than historical.12

absolute price parity

Cassel’s theory of PPP is appropriately named, for its foundation is the idea that the value of a currency—and therefore the demand for it—is determined fundamentally by the amount of goods and services that a unit of the currency can buy in the country of issue, that is, by its internal purchasing power, the latter defined as the inverse of the price level for goods and services. With this statement applying to two countries, the value of one country’s currency relative to the other’s is the short-run equilibrium exchange rate, and the ratio of the internal purchasing powers or price levels defines the absolute PPP (PPPabs). Thus, a theory of absolute price parity results.13

The internal purchasing power of a currency is sometimes referred to merely as its “purchasing power,” and is called “buying power” or “paying power” in Cassel’s early writings. It is clear that the price levels used to define the absolute PPP are general price levels of the countries, representing prices of all goods and services available for purchase, or, as Cassel writes, of “the whole mass of commodities marketed in the country” (1928 a, p. 33). Cassel is explicit on this point.14 Indeed, he is emphatic that only a general price level can represent the purchasing power of money in a country and that price measures limited to traded goods (exports and imports) are unsuitable.15

Cassel does not directly identify the kind of general price level that would be optimal in computing PPP, but the most logical interpretation would be a price measure of a country’s GDP. National accounts had not yet been developed at Cassel’s time of writing, so the concept of GDP was alien to him. Yet Cassel surely means to exclude import prices from the measure and to include export prices.16 The purchasing power of a currency must refer to the country’s own production of goods and services. Moreover, Cassel (1928 b, pp. 7–8 and 10–11) describes the process whereby an exchange value for a country’s currency below (above) the PPP leads to an increase (decrease) in demand for the currency, followed by an increase (decrease) in its commodity exports and a decrease (increase) in its commodity imports.

Thus, the ability to use currency to purchase goods and services in the country of issue is the foundation of Cassel’s PPP theory. So he notes that the theory works best, that is, that the short-run equilibrium exchange rate is expected to have minimum deviation from the PPP, under conditions of free international trade. Cassel also states that the theory holds when trade restrictions are of equal severity in both directions, that is, on both imports and exports of a country.17

Cassel’s justification of absolute price parity has not been superseded to the present day.18 Both critics 19 and supporters 20 exposit the theory in terms virtually indistinguishable from those of Cassel. Thus Yeager writes, with approval: “People value currencies primarily for what they will buy and, in uncontrolled markets, tend to exchange them at rates that roughly express their relative purchasing powers” (1958, p. 516). Some critics, however, use a reductio ad absurdum to destroy the theory:

Of course, under perfect competition, free trade without tariffs, quotas, or exchange controls, relative prices of one good could not deviate regionally if transport costs were zero. In that case only, each competitive good’s international price ratio … would have to equal the official free exchange rate exactly, as a result of quick acting competitive arbitrage; and what is true for each and every good, must be true for the average index number of price …21

Under the extreme conditions outlined by Samuelson (and others before him),22 the existing exchange rate—whether freely floating, managed floating, or pegged—cannot deviate even infinitesimally from the PPP, except to the extent that there are imperfections in the arbitrage process. This removes all operational content from the theory. In contrast, Cassel’s absolute price parity does not rely on the unrealistic assumption that all commodities are traded and without transport costs, tariffs, or quantitative restrictions. In particular, the theory accepts the fact that there are nontraded goods but notes that the prices of traded and nontraded goods are closely related through various links, as described by Yeager, for example.23 Haberler, although critical of PPP, describes its basis correctly: “The proposition that general price levels in different countries are connected through the prices of internationally traded goods is the foundation of the purchasing-power parity doctrine” (1975, p. 24).

Although acknowledging the existence of both traded and nontraded goods, proponents of PPP emphasize that these two groups are not unvarying collections of commodities. Cassel notes: “There is never a definite group of commodities that can be exported. Even a small alteration in the rate of exchange may widen or restrict the group of exportable goods” (1928 a, p. 33). This view is supported by Yeager: “Actually, the line between domestic and internationally traded goods is a fuzzy and shifting one” (1958, p. 522).

relative price parity

Cassel’s theory of relative, like that of absolute, price parity is consistently presented throughout his writings.24 The actual exchange rate in a base period, which for Cassel must be a “normal” period, is multiplied by the ratio of proportionate changes in price levels in the countries concerned. The result is the (relative) PPP in the current period. The ideal base period would be one in which the exchange rate is equal to the absolute PPP.

The question arises as to whether the PPP calculated in this fashion, that is, the relative PPP in the current period, is equal to the absolute PPP newly calculated for this period. The answer is affirmative, according to Cassel, only if the changes in the economies that occurred since the base period were purely monetary in nature. In this respect, Cassel is at one with his critics. Viner writes: “The one type of case which would meet the requirement of exact inversely proportional changes in price levels and in exchange rates would be a monetary change in one country … which would operate to change all prices and money incomes in that country in equal degree, while every other element in the situation, in both countries, remained absolutely constant” (1937, p. 384). Similar discussions of the case of proportionate changes in exchange rates and price levels with no real changes are provided by Samuelson (1948, p. 399), Vanek (1962, p. 84), and Stern (1973, pp. 144–46).

Samuelson points out that this ideal result, founded on the neutrality of money, can occur only in the long run.25 In the short run (and also in the long run if the ideal conditions are not fulfilled), real changes will take place in the economies and the relative PPP theory will not hold exactly. However, if the monetary changes dominate the real changes, relative PPP still applies, although in an approximate fashion. This is certainly the position of Cassel.

Cassel’s recognized limitations of purchasing power parity

Cassel’s acknowledged limitations of PPP are an integral part of his theory. The qualifications and exceptions are presented throughout his writings on PPP, so that a comprehensive citation of references is not manageable. However, the following reasons why a floating exchange rate may diverge from the PPP are gleaned from Cassel’s writings: 26

1. Trade restrictions may be more severe in one direction than in another. For example, if a country’s imports are more restricted than its exports, the exchange value of the country’s currency may exceed the PPP.

2. Speculation in the foreign exchange market may be against a country’s currency and therefore may reduce its exchange value below the PPP.

3. Anticipation of greater inflation in a country than abroad may lower the exchange value of its currency below the PPP.27

4. Changes in relative prices within a country are an indicator of real changes in the economy from a base period, and so involve a divergence between relative PPP and the exchange rate.

5. Long-term capital movements can move the exchange rate away from the PPP. For example, a net long-term capital outflow may depress a country’s currency below the PPP.

6. The government can intervene in the foreign exchange market, bidding up the price of foreign exchange above the PPP by demanding a certain amount of foreign currency irrespective of price. Cassel considers the purpose of the government intervention to be procuring foreign exchange as a replacement for capital inflows rather than influencing the course of the exchange rate.

cost parity

Arguments in favor of cost over price parity theories have been presented even by critics and evaluators of PPP, and are outlined as follows. (1) Costs of production are less subject to adjustment to exchange rate changes than are prices of traded goods.28 (2) Costs exclude the volatile component of profits and so are more likely than product prices to represent long-run prices (for absolute parity) and to reflect permanent rather than temporary changes in prices upon inflation or deflation (for relative parity).29 These arguments, however, do not justify a cost parity as such, only its superiority in certain respects over a price parity.

The earliest proponent of cost parity is Sven Brisman (1933). He rejects price parities mainly on the grounds that they do not measure a country’s competitiveness (“ability to compete”) on the world market. In their place, he proposes an absolute cost parity calculated from the “effective cost of production” at home and abroad. It is clear that Brisman has a UFC concept in mind, for he explicitly states the elements of effective cost as wages, interest, rent (which can be ignored because of its small magnitude), and changes in productivity. Brisman notes that his parity concept cannot generally be employed in a quantitative fashion, because UFC is impossible to calculate statistically owing to the unavailability of data.

Hansen (1944) also proposes an absolute cost parity, but in vaguer terms than Brisman. He calls it a “cost structure parity” and does not discuss its component cost measures. Further, unlike Brisman, Hansen does not reject the price-parity concept outright. Rather, he indicates that “cost structure parity” is a preferred way of stating the PPP theory. The cost structure parity provides the correct exchange rate that assigns factors of production to those export industries, and only those export industries, where the country has a comparative advantage.

A cost-parity theory that reduces to a price parity is offered by Houthakker (1962 a; 1962 b; 1963). He begins with an absolute-parity theory that is founded on UFC, which (he states) may be approximated by ULC, since labor is the most important factor of production. Again, the justification is in terms of competitiveness. Houthakker mentions, however, that the existence of long-term capital movements and unilateral transfers may cause the long-run equilibrium exchange rate to differ from the UFC parity. A net outflow would require greater competitiveness for the country’s exports, that is, a lower exchange value for the currency than that given by the parity. He notes that this modification is not required to the extent that the capital flows are themselves caused by the deviation of the current exchange rate from the UFC parity.

Officer (1974) interprets Houthakker’s theory as follows. Abstracting both from factors of production other than labor and from labor costs other than wages, the UFC parity (number of units of B-currency per unit of A-currency) is given by

where Wi=wage rate in country i
PRi=productivity in country i

Officer’s justification of the ULC parity theory is that, to retain long-run balance of payments equilibrium, a rise in the wage rate relative to that abroad, if not compensated by an increase in productivity, requires a reduced exchange value of the country’s currency.

Houthakker (1962 a, p. 296) demonstrates that his ULC parity is equivalent to a COL price parity. His argument, however, is highly condensed and involves stronger assumptions than he recognizes. Relying on Officer’s interpretation (1974, pp. 868–73), let

MPLi=marginal product of labor in country i
Pi=price level in country i

Assume that (1) aggregate production functions of the two countries differ only by a neutral and constant efficiency factor, namely, PRA/PRB, so that

and (2) there is long-run pure competition in factor markets, so that the marginal productivity theory of wages applies, that is,

Then, in the long run, factor-price equalization would exist at the aggregate level except for the efficiency factor; this factor is carried over into the international relationship of real wage rates:

Reordering equation (3),

Thus, the absolute UFC parity is equal to an absolute price parity, but what kind of price levels (PA and PB) compose the latter parity? Each country’s price level is a production-weighted average of commodity prices in that country, where the weights are specific to each country, that is, they refer to the country’s own production pattern. The reason is that the intercountry relationship of marginal products of labor (equation (1)) and the marginal productivity theory of wages (equation (2)) both refer to production within each country. Thus, the price levels pertain to the GDP in each country, and the result is an absolute GDP price parity theory.

What are the additional requirements to transform the ULC parity further, into a COL price parity? In other words, what are the conditions under which household consumption weights (again specific to each country) can be substituted for production weights in the computation of the price levels without altering the value of the GDP price parity?

First, there must be international equalization, at the parity rate, not only of the GDP price level but also of individual prices for all commodities. For traded commodities, international arbitrage guarantees this result at any current exchange rate, whether or not it is equal to the parity rate, providing that one abstracts from trade restrictions and transportation costs. For nontraded commodities, either pure competition or “equal degrees of monopoly” in domestic product markets are necessary for price equalization. The former assumption ensures that price is equal to ULC, the latter that the same percentage deviation between price and ULC occurs in each country. Second, production and household consumption patterns must be the same both within each country and between countries. Only then can one be assured that the calculated parity is invariant with respect to the choice of production or household consumption weights for the price levels.

Obviously, these additional assumptions are unlikely to be fulfilled, so that Houthakker’s switching from production to household consumption weights in computing the price levels for absolute price parity entails some index-number problems, at the least—given that one begins with the absolute ULC parity theory. In fairness to Houthakker, it should be noted that it was lack of data on UFC or ULC parities and, presumably, also on GDP price parities that induced him to re-express his theory in terms of the COL price parity.

Friedman and Schwartz (1963, pp. 62–63, fn. 66) offer the unique viewpoint of rejecting price parity on the grounds that product price indices include the effect of changes in productivity. They argue that the logic of PPP is that the indices used to compute the parity should refer to monetary changes alone and not incorporate changes in productivity, which are real (nonmonetary) in nature. Implicitly, Friedman and Schwartz are also rejecting a UFC or ULC parity, and indeed they advocate that the parity be constructed from indices of factor prices weighted by employment (and with no allowance for changes in productivity). As a second best, a price parity may be calculated from product price indices, where the prices of individual commodities are weighted by the volume of domestic production “as a proxy for volume of resources employed.”

II. Criticisms of Purchasing Power Parity

price parity

Index-number problems

One set of limitations of PPP is statistical in nature, relating to the method of computing the parity itself. Pigou (1922, pp. 67–68) noted that actual price indices are calculated from individual prices of only a sample of commodities rather than all commodities in the economy. Therefore, any computed price parity is an imperfect representation of the true theoretical parity.

A related difficulty is present even if the entire population of commodities is used to construct the price measure in each country. The value of the parity will, in general, depend on the kind of price level (or price index) selected. In other words, the parity will vary with the weighting pattern of the price measures. The sole exception, as noted by Vanek (1962, p. 84), is when (1) the ratio of the price of a given commodity in one country to its price in the other country is the same for all commodities and (2) the identical weighting pattern is used for the computation of each country’s price measure. Even if the price measures refer to traded goods alone and there is costless international arbitrage of these goods (no trade restrictions or transport costs and no imperfection in the arbitrage process), different weighting schemes for the countries’ price levels (or price indices) will, in general, lead to different parities, none of which can be expected to equal the “true” parity (namely, the current exchange rate, in this case), which equalizes all individual commodity prices internationally. Condition (1) is satisfied, but not condition (2). Samuelson (1964, p. 147) declares that this point is widely overlooked; but Keynes (1930, pp. 73–74) certainly had it in mind, and Viner (1937, pp. 383–84) stated it quite clearly.

Keynes (1930, pp. 72–74) was the first to point out that a PPP calculated from traded-goods prices alone is close to a truism, drawing the implication that WPIs are a poor basis for computing PPP. The reason is that such indices are heavily weighted with traded goods (“the staple commodities of international trade”) and therefore relative price parities calculated from these indices come close to the actual exchange rate, resulting in a spurious verification of the theory. The bias in the test was overlooked, Keynes (1930, pp. 73–74) notes, just because the results could not be perfect:

Since, however, these index-numbers generally include two or three commodities which do not enter freely into international trade, and since the systems of weighting and the grades and qualities of the selected articles are various, there has been just that degree of discrepancy in the “verifications” to make the Theory seem prima facie interesting.

Keynes’ observation led subsequent observers to recommend against calculating parities with price indices weighted entirely or heavily with internationally traded goods and, in particular, to reject export and import price indices and WPIs for this purpose.30 With traded-goods price indices and WPIs unsuitable, evaluators of PPP generally suggest that parities be constructed with COL price measures.31 For some observers, this recommendation carries with it the requirement that the weighting pattern be the same for each country’s price level, that is, that an identical basket of goods be priced in each country. Thus Stern writes: “In principle, the calculation of PPP on the basis of the absolute interpretation requires taking a common basket of goods with a standard system of weighting for the individual countries” (1973, p. 143). Yeager takes the same position in stronger terms: “The ‘absolute’ or ‘positive’ approach to rate calculation ideally envisages the pricing in local currency in each of two countries of a standard assortment of goods and services, the same for the two countries and yet duly representative of economic life in each” (1958, p. 517). As this dual requirement is impossible (unless the countries happen to have identical consumption or production patterns), Yeager rejects absolute PPP as nonoperational.

Insofar as price parity is founded on a factor-cost or UFC parity, however, Officer (1974, pp. 868–70) argues that each country’s own pattern of production is the ideal source of weights to construct its price measure for the parity computation.32 This position is also taken implicitly by Houthakker (1962 a, p. 296), and explicitly by Friedman and Schwartz (1963, pp. 62–63, fn. 66).

If the foundation of absolute price parity on UFC parity is to be rejected, the problem arises of selecting the common bundle of commodities. An obvious possibility is to take the consumption pattern in one of the countries and apply it to the prices of both. It is well known and now commonly pointed out in the literature that the two alternative weighting patterns entail divergent biases in the computed parity.33 Consumption expenditure in each country will be concentrated on those commodities with lower relative prices. Consider the country the weighting pattern of which is used for the computation of both countries’ price levels. The calculated parity will involve an exchange value for that country’s currency greater than that given by the “true” parity.

The usual practice is to apply Irving Fisher’s ideal index-number formula, that is, to take the geometric mean of the parities calculated alternatively using the one and then the other country’s expenditure weights.34 The solution is reasonable because the biases are in opposite directions. As implied by Officer (1974, pp. 872–73), there is a case in which these biases do not exist; namely, if, at the current exchange rate, prices of all commodities are equalized in the two countries (the Vanek example noted earlier). In this event, all relative prices are the same in each country. Unless demand patterns happen to be identical in the two countries, the use of the consumption weights of one country or the other to construct both countries’ price levels will, in general, still give rise to different computed parities; but there is now no reason to expect these parities to have divergent or even systematic biases with respect to an ideally constructed parity.

Absolute parity

Criticisms of absolute price parity fall neatly into two categories: (1) those that suggest a reduced accuracy with which the short-run equilibrium exchange rate approaches the PPP, without refuting the proposition that this tendency exists; and (2) those that deny the basic premise of PPP theory, namely, that a freely floating exchange rate tends to the PPP. The first group of criticisms can be incorporated within the existing framework of PPP theory, and indeed some are admitted modifications of the theory according to its proponents. The second group is incompatible with PPP as it stands; if these criticisms are correct, fundamental changes in the theory are needed to preserve its validity.

The existence of tariffs and transport costs may be expected to give rise to a deviation of the short-run equilibrium exchange rate from the PPP, the amount of this deviation varying directly with the severity of the imperfections.35 In particular, when trade restrictions take the form of sufficiently high and comprehensive tariff walls, quotas, or exchange control, a freely floating (or any maintained) exchange rate may bear virtually no relationship to the PPP, because the price responsiveness of imports and exports is greatly reduced.36 PPP becomes all the more inapplicable if controls are extended to the domestic sector in the form, for example, of price and wage controls, rationing of consumer goods, and industry allocation of raw materials and primary factors of production. Under these conditions, the buying power of the country’s currency is but poorly reflected in market prices.37

PPP theory emphasizes the role of prices in exchange rate determination; yet incomes are also relevant. Yeager (1958, p. 518) counters this criticism by arguing that deviations of the exchange rate from the PPP owing to income forces will bring about price-determined trade flows to reduce the deviations. Furthermore, he notes, movements in prices over the business cycle tend to correspond to movements in income. A point overlooked by Yeager is that PPP represents the long-run equilibrium exchange rate, which should not be responsive to cyclical variations in income. So the neglect of income considerations cannot be considered a fundamental weakness of the theory.

The existence of noncurrent account items is a well-known limitation of PPP theory. As noted earlier,38 Cassel himself assigned a role to both short-term speculation and long-run capital movements as determinants of the short-run equilibrium exchange rate. Others (e.g., Houthakker (1962 a) and Officer (1974)) see long-term capital flows as influencing exchange rate long-run equilibrium as well. Again, the impact of this factor on the PPP theory is a function of the magnitude and persistence of the flows involved. To have a long-run impact on the exchange rate, the flows must persist in significant magnitude net in one direction.39 Furthermore, as Houthakker (1962 a, p. 294; 1962 b, p. 12) emphasizes, not all capital movements are autonomous variables in an extended PPP theory; some may be induced by the divergence of a pegged exchange rate from the PPP. Finally, Yeager (1958, p. 518) notes again that a deviation of the actual exchange rate from the PPP, caused now by capital movements, will give rise to the corrective force of price-induced trade flows.

A criticism of a different nature is that PPP views the exchange rate as the determined variable and price levels as causal variables, whereas there are also chains of causation running from exchange rates to prices. This is a long-standing criticism of PPP; so its advocates are numerous. Among them are Keynes (1923, pp. 95–96), Whittaker (1940, pp. 668–69), Machlup (1964, p. 27), Samuelson (1948, pp. 405–406), and Balassa (1964, pp. 591–92). Yeager (1958, pp. 520–22; 1966, pp. 181–84) presents the most creditable defense of the theory against this criticism. He declares that mutual causation of exchange rates and prices is compatible with PPP theory providing that the line of causation is stronger from price levels to the exchange rate, which he argues is true under normal circumstances (these circumstances guaranteed by a responsible monetary policy). A point in his favor overlooked by Yeager is that influences of the exchange rate on price levels are generally short run in nature, whereas the PPP theory asserts that price levels are long-run determinants of the equilibrium exchange rate. This reasoning suggests that proper timing in calculating the PPP is crucial to obtain a good representation of the long-run equilibrium exchange rate. In particular, the parity should not be computed while the exchange rate is affecting domestic prices, for example, while the effects of a devaluation on internal prices are working themselves out. It is also clear that the mutual-causation criticism would be less applicable to a cost than to a price parity, for the reasons given in cost parity in Section I.

Pigou (1922, pp 64–65) was the first to criticize absolute price parity on the grounds that, if one decomposes the general price level of each country into the price level of nontraded and that of traded commodities, there is no reason for the ratio of the former component price level to the latter (call it the internal price ratio) to be the same in each country. Pigou and later Ellsworth (1950, pp. 593–94), quoting Pigou approvingly, reject absolute PPP for this reason. If the criticism goes no further, however, then its implication concerns only the random error to which the PPP theory is subject. A bias in a parity computed from general price levels would require that a systematic divergence in the countries’ internal price ratios exist, that is, a divergence explainable in terms of other variables.

Hagen (1957; 1960) offers the proposition that the internal price ratio is an increasing function of the per capita income of a country. His rationale is that in a low-income country, where labor is relatively cheap, nontraded commodities are labor intensive and exports are capital intensive or land intensive. Therefore, exports are higher priced relative to nontraded goods, compared with a high-income country. Also, the low-income country’s imports are representative of prices in high-income countries. Therefore, the country’s relatively cheap labor is reflected only in the price level of its nontraded goods. Beckerman (1966, p. 25) points out that Hagen’s argument is questionable, for the exports of many low-income countries are labor intensive, with textiles as an example.

It remained for Balassa (1961; 1964) to offer what many regard as the definitive reason why the internal price ratio increases with per capita income, both across countries at a given point in time (the relevant comparison to assess absolute parity) and for a given country over time. A high-income country is more productive technologically than a low-income country; but the efficiency advantage of the former country is not uniform over all industries. Rather, it is greater for traded goods (especially manufactured goods and agricultural products) than for nontraded goods (taken by Balassa to be consumer services—he does not mention the public sector).40 Advances in productivity proceed in this asymmetric fashion for all countries.

Now, prices of traded goods are equalized across countries (abstracting from trade restrictions and transport costs); but this is not so for nontraded goods. With the wage rate higher in the more productive (higher-income) country and with wages equalized domestically across all industries, the internal price ratio must be higher in the higher-income country.

The prices of nontraded goods (relatively higher in the more productive country) are not directly relevant for balance of payments equilibrium. Therefore, a price parity calculated from general price levels yields an exchange value of the high-income country’s currency that is lower than its true long-run equilibrium value, and this systematic bias increases with the overall productivity difference (represented by the per capita income difference) between the countries involved.

Balassa’s argument has been accepted by Maddison (1967, p. 297), Yeager (1968, pp. 77–80), Harry Johnson (1968, p. 92; 1973, p. 514), Kindleberger (1973, pp. 391–92), and Samuelson (1974, pp. 604–605). At first sight, the hypothesis deals a severe blow to an absolute PPP theory applicable to countries at diverse levels of development. Officer (1974), however, has challenged Balassa’s theoretical analysis on the grounds that it ignores quality differences in consumer services among countries. Admittedly, these differences are minimal for highly laborintensive consumer services; but they would appear significant for professional services, such as education and medical care. The labor involved in such higher-level services embodies human capital and/or works with physical capital, including advanced technology. It is only logical to expect the more productive (higher-income) country to have an efficiency advantage in these services.

Balassa’s response (1974 a) is that, for Officer’s criticism to hold, the asserted quality difference between a high-income and a low-income country would have to be large enough to offset the observed price differences over all consumer services (not just those services subject to an international quality difference). The validity of Balassa’s argument thus reduces to an empirical question, the investigations of which are discussed later.41

Even if Balassa’s analysis is confirmed empirically, absolute price parity is not thereby destroyed as a workable theory. First, the theory would remain applicable as it stands for exchange rate analyses among countries at approximately the same level of technological advancement. Second, to consider countries at diverse levels of development, the theory could be amended by including the effect of international productivity differences on the internal price ratio, thus correcting the bias of the simply computed parity.

Relative parity

Relative price parity has one problem that absolute parity avoids: a base period is required for calculating relative parity. Ideally, the base-period exchange rate should be in long-run equilibrium; but unless the exchange rate was freely floating in the base period, there is no guarantee that it was in even short-run equilibrium. Furthermore, even if the exchange rate was freely floating, its value may have been influenced by temporary factors (for example, short-term capital flows) that pull it away from the long-run equilibrium.42 Under these circumstances, the base-period exchange rate may have been in disequilibrium, and the relative price parity perpetuates this disequilibrium.

Traditionally, the problem of selecting the appropriate base period is the first one mentioned by evaluators of relative parity.43 The difficulty of finding a “normal” or equilibrium base period is sometimes viewed as so overwhelming that the theory becomes virtually unusable, a position taken by Bunting (1939, p. 285) and Bacha and Taylor (1971, p. 220).

Remaining criticisms of relative price parity center around the fact that economic conditions may have changed in some manner since the base period. The great advantage of relative over absolute PPP is that relative parity is not affected by the various limitations and biases of absolute parity, providing that these factors are invariant from the base to the current period.44 Any change in these factors, however, will give rise to a deviation of the computed relative parity from the long-run equilibrium exchange rate.

One condition that may have changed is the height of trade restrictions and the level of transport costs. Beginning with Pigou (1922, pp. 66–67), many have mentioned this deficiency of relative price parity.45 The extent to which the theory is affected, of course, depends on the magnitude of the changes, and an assessment analogous to that of the impact of tariff and transport-cost levels on absolute parity is applicable.

Conditions determining international capital flows, unilateral transfers, and investment income may have changed since the base period. For example, capital flows may have become increasingly mobile over time (Kindleberger, 1973, p. 391), or a country may have lost overseas assets since the base period, owing, for example, to an intervening war (Haberler, 1945, pp. 312–13; Hicks, 1959, p. 131). To the extent that affected balance of payments flows have shifted in direction or magnitude since the base period, the long-run equilibrium exchange rate has changed in a way not captured by the relative-parity computation.

Changes in income would affect a country’s short-run equilibrium exchange rate even without a change in price levels, a fact emphasized by Nurkse (1950, pp. 10–12) and Metzler (1947, pp. 19–20) and mentioned by many others.46 Therefore, the selection of base and current period at different phases of the business cycle would reduce the accuracy of the PPP theory. However, Scammell’s statement (1961, p. 59, fn. 2) that relative PPP requires the assumption of constant national income is too strong, for the reasons mentioned earlier, in Absolute parity.

Structural changes in the economies may produce a relative price parity that would diverge from the absolute parity for the current period and therefore from the long-run equilibrium exchange rate. Except under a neutrality condition (as noted by Bacha and Taylor (1971, p. 220)), these structural changes would be reflected in changes in relative prices domestically. As Ellsworth states: “a general rise or fall of prices is always accompanied by a dispersion of prices, that is to say, by an unequal rate of movement… [This] would be almost certain to result in a different total demand for and supply of exchange in the foreign-exchange markets, with a different equilibrium rate of exchange as a consequence” (1950, p. 597). Changes in tastes, technology, factor supplies, and market form are the structural changes typically mentioned in the literature.47

The implication for relative PPP is that the base period should be as close as possible to the current period in order to minimize the scope for structural changes, as first indicated by Bunting (1939, p. 285). The problem with this prescription is that it may conflict with the requirement of selecting a base period in which the exchange rate is in (or close to) long-run equilibrium. Thus the “‘ancient-history’ element in comparative-version parity calculations” (Yeager, 1958, p. 527) is perhaps the principal defect of the theory. Yeager comments that the problem is mitigated by trade flows responding to price changes; but these flows are secondary effects, and so they may be expected to move the new long-run equilibrium only partway back to the relative parity.

The type of structural change most damaging to PPP is one that involves a differential shift in the internal price ratio as between countries. Any systematic country differences in movements of this ratio give rise to a definite bias in relative PPP. The Balassa argument of a nonuniform productivity advantage (greater for traded than for non-traded goods) enjoyed by the technologically advanced country involves a bias in absolute PPP. An increase (decrease) over time in the advanced country’s productivity advantage, as indicated by a higher (lower) rate of growth in per capita income compared with the less advanced country, imparts a similar bias to relative PPP.48Balassa (1964) applied his analysis to relative PPP after making the case against absolute PPP, while an earlier study by Hicks (1959, pp. 66–84) anticipated the Balassa argument in a dynamic sense, hence as applicable to relative PPP alone. Since Balassa’s contribution, the dynamic form of his argument has been accepted by Yeager (1968, p. 80), Kindleberger (1973, pp. 391–92), and Haberler (1975, p. 25).

Cost parity

Criticisms of the cost-parity theory fall into two groups: those that point out the weaknesses of cost parity in comparison to the price-parity concept, and those that concentrate attention on the UFC parity. An early critic of the general idea of a cost parity is Haberler (1944 b, p. 192; 1945, p. 312, fn. 4). He sees cost parity as having all the problems of price parity and the additional disadvantage of being vague and ambiguous, arguing that “cost level” or “level of cost of production” is a price level of a set of prices that is not clearly defined. Replacing cost parity by wage parity is no solution, he argues, because allowance would still have to be made for other factors of production. Also, a relative wage parity would require that changes in the productivity of labor be incorporated into the measure.

Objections of a more specific nature are offered by Metzler (1947, pp. 21–22) and repeated by Ellsworth (1950, pp. 596–97) and Stern (1973, p. 147, fn. 31). First, there is the need to select the firms whose costs are to be reflected in the economy’s cost level or index. Costs vary among firms not only between industries but also within an industry; so the choice is not obvious. A related issue is that a firm’s costs vary with its volume of output; therefore, there is also the need to determine the appropriate output level at which to measure cost. To complete the argument, one should add that either competition or oligopolistic price setting leads to uniform prices among the firms in an industry and also keeps prices stable over a single firm’s output range. Thus, these problems are not apparent in the computation of price parity.

Finally, there is the problem of the availability of data. Information on factor prices and productivity is less comprehensive—if available at all—than is information on product prices. With the possible exception of wage data, this statement remains true today.

The UFC or ULC parity as developed by Houthakker (1962 a; 1962 b; 1963) and later Officer (1974) has been subjected to direct criticism. Samuelson (1964, pp. 149–53) has two lines of attack against the concept. First, he has a series of objections that, in effect, coalesce into the observation that the trade-off between increases in ULC at home relative to abroad and depreciations of the domestic currency in the exchange market can be accepted while denying the rigid framework of the ULC parity. The latter theory locks the equilibrium exchange rate (price of foreign currency in terms of domestic currency) into equality with the ratio of ULC at home to ULC abroad. An explanation of this criticism is offered by Officer (1974, p. 869), who suggests that Samuelson views the cited trade-off as a short-run relationship, while the ULC parity represents the long-run equilibrium exchange rate.

Samuelson also attacks Houthakker’s analysis for its dependence on a factor-price equalization model, which he rejects as unrealistic.49 The use of a production function involving neutral productivity differences between countries and therefore allowing factor prices to differ internationally by this efficiency factor does not remove Samuelson’s criticism, because he considers this model hardly more realistic than that of pure factor-price equalization.

Officer (1974, p. 870) responds to this criticism by noting, first, that Arrow and others (1961) provide econometric evidence that intercountry differences in production functions take the form of a neutral efficiency factor.50 His second point is that the UFC model uses factor-price equalization only as a long-run phenomenon. He cites Hicks (1959, pp. 266–67) for an argument that factor-price equalization has validity as a long-run tendency when the many kinds and qualities of factors of production are aggregated into the two broad factors, labor and capital. Officer suggests that it is within the spirit of Hicks’ analysis to aggregate commodities as well as factors, so that an aggregate production function may be considered for each country. However, it is not necessary to retain Hicks’ condition of equal productivity throughout the world. The weaker assumption of neutral productivity differences between countries means that the “long run” need not be as long as that envisaged by Hicks; and the amended form of factor-price equalization—wage rates differing internationally by a relative-efficiency factor—is quite sufficient for the ULC theory.

Another critic of the UFC parity is Balassa (1974 a), whose case against absolute price parity is directly applicable to absolute UFC parity, as both he and Officer (1974) note. For UFC parity to be an unbiased measure of the (long-run) equilibrium exchange rate, international efficiency differences must not vary systematically as between traded and nontraded industries. If one accepts the validity of Balassa’s observation that the advanced country’s productivity superiority is greater in the former than in the latter industries, then the absolute UFC parity understates the equilibrium exchange value of the advanced country’s currency in the same way that absolute price parity does (although not necessarily by the same amount).

Correspondingly, if Balassa’s argument is applicable to relative price parity, it would also be relevant for a relative version of UFC parity. Any limitations of Balassa’s case against the price-parity theories are, of course, also applicable as a defense of the cost-parity theories.

residual validity of purchasing power parity

Most critics of PPP, after making their case against the theory, do not reject it outright. They recognize what may be termed the “residual validity” of PPP, the theory’s range of applicability that remains even granted the criticisms that have been raised. Haberler sees three situations in which the PPP theory has applicability.51 First, “under normal circumstances … the P.P.P. theory holds in an approximate fashion in the sense that it would hardly be possible to find under such circumstances a case where an equilibrium rate is, say, 15–20 percent off purchasing power par” (1961, p. 51). Second, when general price movements dominate changes in relative prices, relative PPP is a useful concept: “if cautiously used, along with other evidence, P.P.P. calculations have considerable diagnostic value, especially in periods of severe inflation” (1961, p. 50). Finally, when trade relations between countries have been interrupted (owing to war, for example) or have been reduced to a barter or government-to-government basis, PPP can provide an indication of the equilibrium exchange rate that would apply when normal trade relationships are resumed.

Metzler writes: “In my opinion, the criticism of the parity doctrine went too far, and the theory was rejected even for situations in which it was valid” (1948, p. 223, fn. 31). When large inflations have taken place in different countries, relative PPP provides an approximate measure of the new pattern of equilibrium exchange rates.52

Ellsworth notes that, in spite of the criticisms directed against it, PPP “continues to be widely used as a basis for estimating equilibrium exchange rates … for purchasing power par alone are data available which will permit the calculation of a concrete rate … Therefore purchasing power par has almost irresistible attractions, in spite of its pitfalls” (1950, p. 600). He agrees with Metzler that PPP is legitimately applicable to situations in which general price movements are dominant.

Other writers adopt a more restrictive scope for PPP, even while adopting the same line of argument. For example, Machlup accepts relative PPP as valid only when great changes in exchange rates are to be explained. He implies that the general movement of prices must be so large as to approach hyperinflation; for only then can one be certain that it dominates structural changes. “While changes in tastes, changes in productivity, changes in capital movements, etc., can change exchange rates somewhat (or even by substantial percentages), inflation in one of the countries can change the rates by huge multiples” (1964, p. 27). Stern also (1973, p. 147) would not apply PPP to periods of merely moderate inflation; for only under rapid inflation are changes in relative prices likely to be minimal. In the same vein, Lutz (1966, p. 23) notes that if “the purchasing-power-parity theory contains an important kernel of truth,” the theory nevertheless applies only when disturbances in the balance of payments are due to monetary as distinct from real factors.

On the other hand, Kindleberger is in accord with Haberler in seeing a wider applicability of PPP, at least in its relative form. The computed parity provides an approximation to the new equilibrium exchange rate after an interruption of trade. More generally, “it helps suggest what changes are necessary in the exchange rate (or in price levels) when inflation is proceeding at different rates in different countries” (1973, p. 392). The implication is that even if rates of inflation are only moderate, nevertheless they provide scope for the theory to operate. Finally, Harry Johnson (1968, pp. 92–93) observes that relative PPP “is a reasonable approximation for the analysis of short-run monetary disturbances of the type with which Cassel was concerned and provides a rough guide for policy makers obliged to decide the magnitude of exchange-rate changes. As a matter of fact, the exchange rates of the major countries do not depart very far (typically less than 20 per cent) from purchasing power parity.”

III. Empirical Applications of Purchasing Power Parity

use by policymakers

Three known cases exist of the apparent use of PPP by national governments in connection with the setting of a new exchange rate. All occurred in the period between the two World Wars. Two cases (the United Kingdom and Czechoslovakia) involved the use of PPP to calculate the amount of overvaluation of the currency that would remain at a predecided new exchange value of the country’s currency, that is, to measure the amount of price-level adjustment at home or abroad that would be required to maintain the new exchange rate. The third situation (Belgium) involved the application of PPP actually to compute the new exchange rate. The most famous case is the United Kingdom’s return to the gold standard in 1925 at the prewar mint parity with the dollar. This event had followed an appreciation of the floating pound from 10 per cent below parity to less than 2 per cent below it, an appreciation of a temporary speculative nature, caused by the anticipation of a return to parity. Immediately after the return to the gold standard, Keynes castigated the advisors of Winston Churchill (then Chancellor of the Exchequer) for using WPIs to compute a relative PPP for the pound based on the prewar mint parity with the dollar.53 (Presumably the computation was made at the time following the speculative appreciation of the pound.) As discussed earlier,54 the use of WPIs for this purpose tends to validate the existing exchange rate. Keynes correctly points out that the preponderance of traded goods in such indices makes them a poor choice for relative-parity calculations. Index numbers of domestic (e.g., COL) prices or wages would have been a better measure, as they do not “adjust themselves hour by hour in accordance with the foreign exchanges” (1932, p. 249). Keynes declares that whereas a relative price parity computed from WPIs indicated an overvaluation of the pound of only 2 or 3 per cent at its appreciated exchange value, the use of other indices would have revealed the true figure of 10 or 12 per cent. The outcome for the United Kingdom, as Keynes predicted, was deflation and unemployment.

Haberler notes that the same mistake was made by the Czechoslovakian authorities in 1934.55 In this case the currency was recognized as overvalued; but with attention apparently paid to the movement of WPIs at home and abroad, the extent of the overvaluation was understated.56 The currency was depreciated, but by an insufficient amount, and a further devaluation had to be carried out in the following year.

A case does exist in which policymakers apparently acted on the basis of a PPP calculated using COL price indices, thus avoiding some of the difficulties inherent in the WPI. The Belgian franc was devalued by 28 per cent at the end of March 1935. Triffin (1937) notes that this figure is precisely the amount of overvaluation of the franc with respect to the pound calculated for January 1935 by the Belgian central bank using a PPP computation, with the result later published by the bank. The base year is 1930, when both Belgium and the United Kingdom were on the gold standard, so the mint parity between the franc and the pound is the base-period exchange rate.57

It is unlikely that the bank’s figure is coincidentally equal to the amount of devaluation or that it represents an attempt at ex post rationalization of the devaluation decision, for a reference to the use of relative PPP to indicate the degree of currency overvaluation was included in the official report to the legislature at the time of the devaluation decision. The central bank found an overvaluation of 28 per cent using COL price indices in the parity calculation and 26 per cent using wage indices. Triffin writes that only the cost of living indices were used to determine the devaluation rate (1937, p. 47), suggesting that the action of the Belgian Government was indeed contingent upon the results of a PPP calculation.

use by private economists

Measuring the disequilibrium of a pegged exchange rate

Cassel (1925 b; 1925 d) put his relative PPP theory to work in assessing the equilibrium status of the Swedish krona and the pound sterling following these countries’ postwar return to the gold standard, Sweden in April 1924 and the United Kingdom one year later. For Sweden, Cassel adopts two alternative base periods: October 1923 and March 1924. In each of these months, the krona (then floating) was 2 per cent below its gold par. In December 1924, the krona was ½ of 1 per cent above par, and yet in the interim Swedish prices and U. S. prices moved so as to imply a reduction in the purchasing power of the krona by 3.7 per cent from the first base period and more than 6 per cent from the second. He concludes that, as of December 1924, the krona was surely overvalued with respect to the U. S. dollar. The reason given is an inflow of capital to Sweden from the United States.

A similar analysis indicates a 4–5 per cent overvaluation of the pound with respect to the dollar upon the return of the United Kingdom to the gold standard in April 1925. Cassel notes that this overvaluation was removed by June via a decline in British prices owing to two influences. First, the overvaluation of the pound involved a decrease in the prices of traded goods in England, which dampened the internal price level. Second, the Bank of England pursued a restrictive monetary policy.

Metzler (1947) calculates WPI and CPI parities in an attempt to indicate the extent to which the initial par values announced by the International Monetary Fund in 1946 made allowance for wartime inflation. The base period is October 1936-June 1937, and he justifies it on the grounds that it is close to World War II but free of the war’s influences, and that it represents a period of relative stability in exchange markets following the devaluations earlier in the 1930s. The current period is November or December 1946 for most countries, and the U. S. dollar is the standard currency for the calculations.

The technique is to compare parity (PPP) with official rates (number of dollars per unit of domestic currency). About half the countries examined have par values substantially above parity, that is, are significantly overvalued in relation to the dollar. For nonmember countries and member countries whose official rates had not yet been agreed upon, there is the same tendency for official rates to exceed parity rates, that is, for a general overvaluation of currencies against the dollar.

Samuelson (1948), in commenting on Metzler’s results, sees the neglect of PPP considerations in the establishment of initial par values as a reasonable course to follow. World War II brought massive structural changes to the world economy, making relative PPP based on prewar exchange rates a dubious measure of new equilibrium exchange rates.

Fifteen years later, absolute PPP was applied by Houthakker (1962 a) to show the changed equilibrium status of the dollar, now overvalued with respect to the mark. Cost of living (i.e., household-consumption-weighted) price parities published by the Statistical Office of the Federal Republic of Germany are the source of Houthakker’s computations. These parities (for various countries) are based, alternatively, on the weighting pattern of the Federal Republic of Germany and the domestic weighting pattern. Houthakker takes the geometric mean (Fisher ideal index) of each pair of parities and compares it with the official deutsche mark/domestic currency exchange rate in March 1962. Among other results, he notes that the U. S. dollar is overvalued by 22 per cent with respect to the deutsche mark. He also makes a dollar/pound comparison, using results of a PPP study of the data-conversion genre. Paige and Bombach (1959) computed an absolute gross national product (GNP) price parity for the pound in terms of the dollar. Their calculated parity for 1957 was 3.9, taking the geometric mean of the U. S.-weighted and U. K.-weighted parities. Houthakker (1962 a) compares this result with the official exchange rate of 2.8 to reach the conclusion that the dollar, was overvalued by 28 per cent against the pound in 1957.58

Measuring the disequilibrium of a floating exchange rate

The use of PPP to measure the amount of disequilibrium of a floating exchange rate implies that some force is keeping the floating rate from its long-run equilibrium (assumed to be the PPP). In the literature with this theme, speculation is always cited as the explanation of disequilibrium. However, the concept of speculation has different meanings to the various authors.

Cassel (1925 d) examined the floating currencies of Denmark and Norway. Taking Sweden as the standard country, he computes PPPs and compares them with exchange rates (number of units of Swedish currency per unit of domestic currency). For each country, the percentage increase in the exchange rate during 1925 is greater than that in the PPP: the external value of the currency increased more than the internal value. Cassel’s explanation: “a very intense and widespread speculation, on the part of those who believed in the restoration of the gold parity, had forced up the external value of the currency” (1925 d, p. 57). The reason for this “speculation” was the announced goal, on the part of the Danish and Norwegian authorities, of a return (appreciation) of their currencies to their former gold parities.

In 1931, the United Kingdom and Sweden, followed by other countries, abandoned the gold standard and let their currencies float. Letting the U. S. dollar be the standard currency, 1926–28 the base period, and January 1932 the current period, Cassel (1932 a, pp. 85–87) computed PPPs for the pound and the krona and compared them with the exchange rate (number of dollars per unit of domestic currency). In each case the PPP is far above the exchange rate, that is, the currency is substantially undervalued on the exchange market. The explanation, according to Cassel, is an “exaggerated distrust” of paper standards (i.e., floating currencies) in relation to currencies still on the gold standard (represented by the dollar).

Tsiang (1959) suggests that the deviation of a floating exchange rate from the PPP can be taken as a measure of the amount of speculative activity in the foreign exchange market. Without accepting the theory that the long-run equilibrium exchange rate is the PPP, one can infer that a widening divergence of the actual exchange rate from the PPP within a short time period is due to speculation, unless changes in “nonspeculative factors” (such as supply and demand conditions for traded goods and nonspeculative capital movements) are present. Tsiang uses WPIs to compute the PPP, with the base year 1913 and the dollar as the standard currency. The subjects of the analysis are the post-World War I floating exchange rates of the United Kingdom, Norway, and France.

Tsiang’s results are not discussed here—only his approach is of interest—for he is not prepared to use PPP/exchange rate comparisons to form a judgment about the overvaluation or undervaluation of a currency. The selection of WPIs to construct the PPPs may have resulted in smaller deviations of the actual exchange rates from the PPPs and therefore, in Tsiang’s framework, less speculation than if a price index less weighted with traded goods had been used. Indeed, a related study by Aliber (1962), who uses retail as well as wholesale price indices to construct PPPs, finds greater evidence of “speculation.” Countries examined are the United Kingdom, France, Belgium, the Netherlands, and Switzerland.

Calculating par value changes in real terms

Purchasing power parity can have analytical value simply as a computational device. De Vries (1968) uses relative price parity to calculate depreciation or appreciation “in real terms” for the currencies of 64 countries compared with the dollar. Alternative base years are 1948 and 1955. The author stresses that PPPs are not equilibrium exchange rates and do not provide a guide for measuring the degree of overvaluation or undervaluation of a currency. Thus, it is not necessary that the base years be periods of equilibrium. The PPPs (calculated from COL price indices) enable a comparison of external exchange depreciation with the internal depreciation of the currency, both in relation to the dollar.

For each country, de Vries calculates the ratio of PPP to the exchange rate (number of units of domestic currency per dollar) in 1967. If this ratio is less than unity, it implies that the external depreciation has exceeded the internal depreciation for the currency in question, that is, depreciation in real terms has in fact occurred. Countries are grouped according to level of development and degree of inflation over the periods considered. The general conclusion is that less developed countries (LDCs) as a group had greater real depreciation of their currencies than did developed countries (DCs), especially with the 1948 base.

A similar analysis is applied by Paul Johnson (1970) to devaluations of the Colombian currency over the period 1958–65. He notes that Colombian price indices (WPI and COL) doubled over this period, while U.S. price indices were almost stable. “Naive purchasing power parity considerations would call for a doubling of the Colombian exchange rate. Comparing 1958 and 1965 … this is almost exactly what happened” (1970, p. 169). However, the 1965 exchange rate cannot be considered to be at the appropriate level because the exchange market was not in equilibrium in 1958.

Assessing the rationality of exchange rate policies of state-trading economies

The conventional wisdom is that the exchange rate systems of state-trading economies (STEs) are of little economic significance and indeed are irrational and artificial.59Amacher and Hodgson (1974) seek to test this view by taking the PPP as the norm and comparing the actual exchange rate with it. The idea is that the purchasing power of a currency in relation to that abroad represents fundamental factors that a rational exchange rate policy would take into account. The authors take Yugoslavia as the country of interest (for it is an STE that has become increasingly market oriented over time) and its major trading partners, namely, Italy and the Federal Republic of Germany, as the countries of comparison.

The model employed is one of relative price parity and is as follows. The epitome of a rational exchange rate policy over time requires that

Given a base period, Ro is a constant. Therefore, letting Pt=PtB/PtA and taking logarithms, one obtains the estimating equation:60

Rt and Pt are denominated in the number of dinar per lira or per deutsche mark. A successful testing of the hypothesis requires that β be positive and significant, and that the equation have a high explanatory power. The model consists of two equations (5), one for the dinar/lira, the other the dinar/deutsche mark comparison.

To construct the variable P, an index of “producer’s prices, industrial goods” is used for Yugoslavia, WPIs for Italy and the Federal Republic of Germany. The base period is 1952 and the current period 1971. The dinar/lira and dinar/deutsche mark exchange rates are not available directly; they are obtained through cross rates with the dollar. One might question the assumption of consistent cross rates as less valid for Yugoslavia than for a market economy.

It turns out that movements in price levels explain 40–45 per cent of the variation in exchange rates. The authors see the relationship as weakened by the fact that the base-period exchange rate is probably not in equilibrium. They conclude that the devaluations of the dinar in the 1950s and 1960s are in accordance with PPP theory.61 It is questionable, however, whether the result of a rational or partly rational exchange rate system can be projected to other STEs, which are further away from a market economy than is Yugoslavia.

IV. Tests of the Validity of Purchasing-Power-Parity Theory

absolute price parity

International differences in the internal price ratio

A fundamental criticism of absolute PPP is that the internal price ratio (defined as the ratio of the price level of nontraded commodities to that of traded commodities) may differ systematically between countries.62 Now, in empirical testing of this aspect of PPP theory, the ratio of a country’s internal price ratio to that of a standard country (say, the United States) is typically proxied by the ratio of absolute price parity to the actual exchange rate (number of units of domestic currency per dollar). Is this a justifiable procedure? Consider the following notation:

PLi=general price level in country i
PTi=price level of traded commodities in country i, with a weight of αi in the general price level
PNi=price level of nontraded commodities in country i, with a weight of βi in the general price level
R=actual exchange rate (number of units of domestic currency per dollar)
PPP=absolute purchasing power parity (number of units of domestic currency per dollar)

where αi + βi = 1, and the superscript “US” will be used to refer to the United States.

Then the issue concerns the legitimacy of the approximation

It is expected that

The exchange rate is only approximately equal to the ratio of the price levels of traded goods for two reasons. First, trade restrictions and transport costs prevent an exact equalization of prices of traded goods. Second, the weighting pattern within the traded-goods price level may differ in the two countries. If relationship (7) is accepted, then

Therefore, a deviation between a country’s (actual) exchange rate and PPP involves (a) a divergence between the country’s internal price ratio and that of the standard country and/or (b) a divergence between the relative weights of traded and nontraded commodities in the two countries’ price levels. Considering a multicountry comparison, a systematic deviation between exchange rates and PPPs among countries entails a systematic divergence either in their internal price ratios and/or in the relative importance of traded and nontraded goods in the countries’ economies. The latter difference in economic structure among countries is thus ignored by those who use PPP/R to represent the ratio of the internal price ratios at home and abroad. It is not obvious that a systematic difference in PPP/R among countries implies a corresponding difference in their internal price ratios, and hence a case against the validity of the PPP theory. To the extent that there is a systematic variation in the relative importance of traded and nontraded goods in the countries’ economies, the PPP/R differences may be a reflection of this fact.

Hagen tests the hypothesis “that the greater the difference between the two countries in per capita income, the greater the error caused by use of the exchange rate to compare their price levels” (1957, p. 383).63 He finds that, using data for the year 1950 developed by Gilbert and Kravis (1954), the hypothesis holds true among France, the Federal Republic of Germany, and Italy (with the United States as the standard country). However, the data point for the United Kingdom (the final country in the Gilbert-Kravis study) would fit the hypothesis only prior to the 1949 devaluation of the pound.

Balassa (1961) offers a hypothesis equivalent to that of Hagen and tests it using results of Gilbert and associates (1958). The variables PPP/R and per capita income have closely corresponding rankings for eight European countries in 1955.

Taking absolute PPP data from a variety of sources, Delahaut and Kirschen (1961) correlate R/PPP with per capita national income (converted into dollars at the actual exchange rate). The result, for the year 1957 with 18 countries providing data points, is a correlation coefficient of −0.86 (the correct sign, since the dependent variable is inverted). However, there is no discussion of a theory underlying this relationship.

Balassa (1964, p. 589) was the first to state explicitly the hypothesis of a systematic bias in (absolute) PPP as a measure of the equilibrium exchange rate: “the higher level of service prices at higher income levels leads to systematic differences between purchasing-power parities and equilibrium exchange rates.” He provides two kinds of evidence for this hypothesis. First, he uses sectoral PPP computations for the year 1950 64 to show that “services [i.e., nontraded goods] are by and large cheaper in countries with relatively low incomes” (1964, p. 588). Second, he regresses PPP/R on per capita GNP (converted into dollars using R) for 12 member countries of the Organization for Economic Cooperation and Development (OECD) for the year I960.65 The correlation coefficient is 0.92.

Later, a nonstructural form of this relationship was “rediscovered” by David (1972; 1973);66 and in commenting on David’s analysis, Balassa (1973) re-expresses his equation so that the independent variable is the ratio of domestic to U. S. per capita GNP and re-estimates the equation using revised data for the independent variable. He converts domestic currency GNP to dollars by means of, alternatively, the actual exchange rate and the PPP. Results are consistent with those of the original regression.

To counter Officer’s criticism (1974) that the first set of evidence assumes equal quality of services across countries,67Balassa (1974 a) calculates that the quality of education and medical care in the United States would have to exceed that in Europe by a factor ranging from 2.5 to 5 (depending on the country) for the criticism to be validated empirically. The data refer to the year 1950 and the computations assume that there are no international quality differences in other kinds of services.

Officer (1974) also questioned Balassa’s econometric test of PPP. One criticism concerns the choice of independent variable. The ratio of GDP to employment would appear to be a better measure of a country’s level of productivity than GNP divided by total population.

Another problem with Balassa’s test is common to the tests and empirical commentaries of Balassa’s predecessors (discussed earlier). The hypothesis of a systematic bias in PPP can be tested, strictly speaking, only by comparing PPP with the long-run equilibrium value of the exchange rate.68 Balassa and his predecessors substitute the actual (i.e., official) exchange rate (generally the par value) for the equilibrium rate. The validity of the test then hinges on the assumption that, across countries at a given point in time, the actual exchange rate is proportional to the long-run equilibrium rate. The test would be less powerful (but retain some validity) if the correlation between the actual and equilibrium exchange rate exceeded the correlation between the PPP and the equilibrium rate. Therefore, a judicious choice of the year to which the test is applied could assure a high correlation between the former set of variables and thus validate the test. Balassa suggests an alternative criterion to judge the applicability of his test. The test would be invalid only if “the ratio of the equilibrium to the actual exchange rate … [were] positively related to productivity in the same way as in the ratio of purchasing power parity to the actual exchange rate” (1974 a, p. 882, fn. 3).

Several authors have tested whether Balassa’s result is also applicable to LDCs. Grunwald and Salazar-Carrillo (1972) present PPPs for 11 Latin American countries in 1968, based on specially collected data. Letting Venezuela replace the United States as the standard country, they find that the rank correlation between PPP/R and per capita GDP has the wrong sign, irrespective of whether official exchange rates or free rates are used. The authors conclude that the Balassa hypothesis is not applicable to Latin America.

Clague and Tanzi (1972) extend Balassa’s analysis from a model in which labor is the only limiting factor of production to a three-factor model involving unskilled labor, human capital, and natural resources. Their theory results in an equation with the internal price ratio (represented by PPP/R) as the dependent variable, and human capital per worker and the ratio of natural resources to other factors of production as principal explanatory variables. The independent variables are not available directly; so, to proxy them, the authors engage in data construction of a rather rarefied kind.

They then test their model against that of Balassa, applying the models to Balassa’s sample of 12 OECD countries and to a sample of 19 Latin American countries, each pertaining to the year 1960. For the OECD countries, Balassa’s data are used where applicable, while for the Latin American countries, the PPP measures are obtained from ECLA (1967) and are absolute GDP price parities.69 For the Balassa model, per capita income (presumably GNP for the OECD countries, GDP for the Latin American countries) is expressed in U.S. dollars with R and PPP as alternative conversion factors.

The findings are that the Balassa hypothesis performs better for the OECD countries, but the Clague-Tanzi equation is far superior for the Latin American countries. In fairness to Balassa, he does not consider his equation to be applicable to LDCs, and indeed warns against such an extrapolation of his results. He mentions as reasons the differences between DCs and LDCs in the importance of nontraded goods, endowment of natural resources, height of tariffs, and amount of capital inflow. He criticizes the Clague-Tanzi selection of variables as inadequate attempts to take account of these differences.70

Certainly the most reliable absolute-PPP data computed to date are those assembled by Kravis and others (1975, especially ch. 13). A variety of countries are considered: three LDCs, five market DCs, and one STE, with the United States as the standard country. For purposes of this review, among the many PPPs computed by the authors, the relevant measure is the GDP price parity. As usual, the authors use the Fisher ideal index of the parities based upon the U.S. and domestic weighting patterns to obtain the parity measure for analytical purposes. They consider the year 1970 and plot, in effect, R/PPP (note the inverted form of the variable) against per capita GDP (converted to dollars using PPP).71 The variable R/PPP is greater than unity for all countries, because the United States, the richest country, is the standard country. The correlation of this variable with per capita GDP is negative, as expected, but not strong.

Kravis and others (1975) conclude that variables other than income are required to explain country differences in R/PPP. They suggest that one such variable is the importance of a country’s international trading relationships. A country with a higher ratio of trade (exports plus imports) to GDP is expected to have R/PPP closer to unity because its economy is more influenced by world prices. The authors find firm support for this hypothesis among the LDCs but only mixed support among the market DCs.

Finally, the authors plot R/PPP against the ratio of the PPP for traded goods to the PPP for nontraded goods,72 that is, the reciprocal of the internal price ratio in the domestic country to that in the United States. This is an extremely important relationship to consider; for, in effect (taking reciprocals of the variables), the relationship tests the fundamental assumption that PPP/R is a satisfactory proxy for the ratio of the internal price ratio at home to that in the United States; that is, it tests “equation” (6). It turns out that the observed relationship is positive and quite strong. Certainly, a scanning of the two graphs indicates that the R/PPP versus per capita GDP relationship is weaker in comparison.

Alternative computations of exchange rate disequilibrium

If a comparison of PPP with the official exchange rate is used to measure the amount of currency overvaluation or undervaluation, the result may be checked by computing the disequilibrium using another method. Houthakker (1962 a) had applied absolute PPP to reach the conclusion that the U.S. dollar was overvalued by about 20 per cent in 1962. Floyd (1965) questions this result as too high. He develops a model in which the disequilibrium of a country’s currency (i.e., the depreciation or appreciation percentage that would restore exchange rate equilibrium) is a specified function of various variables and parameters. He selects alternative sets of values of the parameters to show that the dollar is overvalued by only about 7 per cent. Obviously, however, one cannot judge between the Houthakker and Floyd results on the basis of divergent estimates alone.

relative price parity

Time-series comparisons of purchasing power parity with a floating exchange rate

An obvious test of PPP theory is the following: Calculate a time series of relative PPP during a period when the exchange rate is floating and compare it with the corresponding time series of the floating rate. PPP theory asserts that there is a tendency for the short-run equilibrium exchange rate, that is, a freely floating rate, to equal the PPP. Noticeable divergences between the actual rate and PPP are then explained in terms of other influences on the rate.

In those studies that deal with the period during or after World War I, the base-period rate is always the prewar (generally 1913) mint parity of the two currencies involved. The early writers tend not to specify the nature of the price series used to construct the PPP (although some do cite the data sources); but it is reasonable to assume that WPIs are used, as these were the first general price indices available. Usually, the standard currency is taken to be the dollar, which remained on the gold standard while most European currencies floated after World War I.

The earliest such study is performed by Cassel (1916). Taking a prewar period as a base, he computes a PPP between the pound and the floating Swedish krona monthly for the year 1915. Cassel concludes: “The unmistakable conformity of the curves for the theoretical and actual rates may be regarded as a remarkably good proof of the theory here set forth” (1916, p. 64). Because of acknowledged data limitations,73 this was regarded as only a preliminary test of PPP theory. For Cassel, the definitive test was a comparison of the pound/dollar PPP and exchange rate during the floating-pound period that followed World War I.74Cassel (1925 c) computes R/PPP (both numerator and denominator expressed in number of pounds per dollar) monthly for the period 1919–24. He notes that the dollar is overvalued or undervalued with respect to the pound according as R/PPP is greater or less than unity. The average overvaluation is only 0.3 per cent, and Cassel’s explanation of the subperiods of overvaluation or undervaluation of the dollar centers on international capital movements. For example, he points out that dollar undervaluation occurs in periods of substantial capital outflow from the United States. Cassel is emphatic that the results imply rejection of the conventional explanation of exchange rate movements in terms of variations in the balance of trade, for the R/PPP series does not exhibit regular seasonal fluctuations.

This last conclusion is disputed by Crump (1925), who plots three R/PPP series monthly for the period 1920–24, one of which is Cassel’s series and the other two are computed from alternative price indices for the United States and the United Kingdom. Crump notes that all three series rise in the autumn and decline in the spring, following the known balance of trade pattern.

Keynes (1923, pp. 99–106) computes PPPs for the British, French, and Italian currencies versus the dollar monthly for the period 1919–23. The dollar/pound comparison provides “a remarkable illustration of the tendency to concordance between the purchasing power parity and the rate of exchange” (1923, p. 100), and the results for France and Italy show that “the Purchasing Power Parity Theory, even in its crude form, has worked passably well” (1923, p. 106).

Angell (1926, pp. 424–40) presents time series of the PPP and exchange rate for the floating pound and French franc versus the dollar for the period 1919–24. He sees the variation of both series as being due to a third force: the degree of confidence in a country’s currency, itself determined by the amount of government inflationary finance and by the past depreciation of the currency.

The floating Swedish krona during World War I is the vehicle for Heckscher’s time-series test of the PPP theory (1930, pp. 147–69 and 212–14). He finds that the krona depreciated generally less than half as much with respect to the pound on the foreign exchange market as in its relative internal purchasing power, and he rejects the PPP theory.

Results that confirm the PPP theory are reported by Graham (1930, pp. 117–26). He calculates WPI parities for 12 floating European currencies and computes PPP/R (both numerator and denominator expressed in number of dollars per unit of domestic currency) monthly over the period 1919–23. His result: “If we exclude Germany, the clustering around the 100% figure is marked and aberrations were apparently self corrective” (1930, p. 121). For Germany, where hyperinflation occurred, PPP/R is well over 100 per cent, that is, the exchange value of the deutsche mark was very low compared with its purchasing power.75 To the extent that deviations of R from PPP do occur in countries other than Germany, Graham explains them as being due largely to capital flows, expectations of exchange rate changes, and trade restrictions. He sees the determining factors in the German case as recurring fixed international liabilities and panic demand for foreign exchange in the face of a decline in the exchange value and purchasing power of the domestic currency.

White (1935) examines the floating exchange rates of the United Kingdom, Sweden, and Argentina over the period 1930–33. He concludes that the balance of payments, speculation, and capital flows—and not the PPP—determined the exchange rates. One notes that the 1930s were a period of severe world-wide deflation rather than a “normal” period or one of substantial inflation, and it is the latter situations to which the PPP theory has been viewed as applicable.76 The failure of PPP theory to predict exchange rate movements in the 1930s is reflected in a later study that spans both the 1920s and 1930s.

This longer-run test of PPP is presented by Katano (1957), who computes a Japanese/U.S. WPI parity annually for the period 1921–36. The yen was floating throughout that period except in 1930–31, so the base year selected is 1930, with the mint parity between the yen and dollar taken as the base-period exchange rate. Katano computes the correlation coefficient between the exchange rate and PPP for the entire period 1921–36 and for the subperiod 1925–29. The coefficient is −0.06 for the overall period and 0.93 for the subperiod.

Katano (1957) shows that these divergent correlations can be explained by the close approximation to pure price inflation in each country during the subperiod 1925–29. He takes six commodities for Japan and six commodity groups for the United States, all of which weigh heavily in the respective country’s WPI. For each commodity or commodity group, he computes the ratio of its price index to the WPI in the current year and compares it with the same ratio in the base year. There is no large divergence in these relative prices in the years 1926–29 but a substantial change in relative prices in the years 1932–36, during which time there is a large deviation of the exchange rate from the PPP.

Yeager (1958) tests how well movements of the floating Canadian dollar (with respect to the U.S. dollar) were explainable in terms of PPP during the period 1950–57. He finds a good correspondence of the exchange rate with a WPI parity but a low correlation with a CPI parity. The greater weight of traded goods in the WPI is not mentioned by Yeager as a possible cause of the differential result. Rather, he suggests as explanatory factors a slower response of retail than wholesale prices to monetary conditions and the narrow range of fluctuation of the U.S.-Canadian CPI ratio.

In a later study, Yeager (1969) looks back at the nineteenth century and correlates a WPI parity with the exchange rate of the floating Austrian gulden with respect to the pound. The correlation coefficient varies between 0.52 and 0.79, depending on the time period of the analysis and whether levels of the series or percentage changes are considered.

Another investigation of the PPP theory in the nineteenth century is performed by Friedman and Schwartz (1963, pp. 58–78). They consider the period of the floating dollar (“greenback”), computing a WPI parity between the dollar and the pound annually for the greenback period (1861–79) and comparing it with the greenback price of gold, representing the dollar/pound exchange rate (since the United Kingdom remained on the gold standard). Alternatively, the PPP (number of dollars per pound) may be considered the hypothetical price of gold. Friedman and Schwartz note that the actual price of gold (i.e., the exchange rate) varies over a range of more than 2 to 1, whereas the ratio of the actual to the hypothetical price (i.e., the ratio of the exchange rate to the PPP) varies over a range of only 1.3 to 1. They explain the residual movement in this ratio in terms of (1) the cutoff of trade during the U.S. Civil War and (2) international capital flows that occurred after the war.

The PPP model employed by Amacher and Hodgson (1974) to examine the exchange rate policy of Yugoslavia 77 was used in an earlier study, pertaining once more to the floating currencies after World War I. Letting R denote the exchange rate (number of dollars per unit of domestic currency) and P the ratio of the domestic to the U.S. WPI, Thomas (1973) fits equation (5) separately for 12 countries (10 European countries plus Canada and Japan) for which monthly data are available over the period 1920–24. He interprets the PPP theory in terms of percentage changes, that is, it predicts a unitary elasticity of the exchange rate (R) with respect to the purchasing power parity (P). Given his definition of the variables, the elasticity (β in equation (5)) is expected to be minus one.78 Certainly, β must be significantly negative for the PPP theory to receive some confirmation. It turns out that β is significantly negative for all countries, but only for one country (France) does the value of β exceed unity in absolute value. Thus, there is a systematic divergence between (percentage changes in) the exchange rate and PPP, which Thomas attributes to speculation.79

The same model is applied by Hodgson and Phelps (1975) to 14 countries with floating currencies in the period 1919–25. WPIs are used to construct the P variable for all countries except Austria, for which a retail price index is employed.80 The PPP variable (P) is significant with the correct sign in 9 of 14 cases. Hodgson and Phelps see this model as involving a severe test of PPP, for it requires a simultaneous movement of monthly exchange rates and prices, in contrast to a distributed-lag effect of PPP on the exchange rate.81

Where a pegged exchange rate is coupled with exchange control, a black market exchange rate may play the role of a floating rate. Culbertson (1975) uses a CPI parity along with other variables to explain the black market dollar exchange rates of India, the Philippines, and Turkey annually for the years 1952–71. Fitting his equations in logarithmic form, Culbertson finds that in all cases the PPP not only provides the largest elasticity but also is the most significant explanatory variable.

Comparative-static comparisons of purchasing power parities and exchange rates

A time-series comparison of the exchange rate and PPP may be distinguished from a comparative-static comparison of the variables at two points in time. Under the comparative-static framework, the earlier time point has the usual interpretation of the base period. The later time point may be an arbitrary “current period” if the exchange rate is floating, in which case the approach is a special case of the time-series analysis. However, if the exchange rate is fixed in the later period, then this period should have the same properties as the base period; that is, it should be one in which the exchange rate ideally is in long-run equilibrium, or, at the least, it should be a “normal” period. This symmetric property of the two time periods offers a balanced framework with which to test the PPP theory. A more difficult test to pass would result from choosing the later period quite arbitrarily. Such a test has some foundation; for if PPP does represent the long-run equilibrium exchange rate, then gold points or market intervention points must envelop the PPP for the country to avoid sustained gains or losses of international reserves.82

As with the time-series approach, Cassel (1916) was the first to test PPP theory in a comparative-static way. In all cases, he uses a prewar base period. His first test involved a comparison of the PPP and the actual exchange rate of December 1915 for each of three countries with floating rates (France, Germany, and Russia), with Sweden (also under a floating rate) as the standard country. “The divergencies between the theoretical and actual rates are very small, and all lie within the limits of the errors unavoidable in such a calculation as this and the occasional fluctuations of the rates of exchange” (1916, p. 64). The floating Swedish currency was the object of a similar test of PPP in the autumn of 1918. Cassel (1918) shows that the Swedish currency is overvalued with respect to the pound. His explanation is the much greater restrictions on Sweden’s imports than on its exports.

Finally, Cassel (1919) examines the extent of depreciation of the floating deutsche mark at the end of 1919. He describes his findings: “Thus, with all allowance for the uncertainty of our estimation of the purchasing power parity, an enormous undervaluation of the mark as compared with the Swedish crown must be taken as established” (1919, p. 493). Cassel offers two reasons for this result. First, with international credit unavailable, the German Government was able to obtain foreign exchange only from speculators abroad and at very disadvantageous exchange rates. Second, there was a flight of capital from Germany.

There is a long hiatus during which there is no comparative-static testing of the PPP theory. Then two studies apply the comparative-static test to currencies that are pegged rather than floating. Yeager (1958) computes PPPs for 35 countries 83 as of July 1957, taking a pre-World War II year as the base period and the United States as the standard country. He discusses his selection of the price measures used to compute PPP. The average of the CPI and WPI is used, except when only one index is available. Given various WPIs for a country, the one weighted most heavily with nontraded goods is chosen. The ratio of the actual exchange rate to the PPP is within the range 75–125 per cent for three fourths of the countries considered. Yeager concludes: “These results and those mentioned earlier [other studies] hardly leave room to doubt a broad correspondence between actual and purchasing-power-parity exchange rates, especially in comparison with the huge discrepancies to be expected if Cassel’s doctrine were quite wrong” (1958, p. 527).

While Caves and Jones (1973, p. 338) agree with Yeager that the PPP theory performs well in this test, Balassa (1964, p. 591) emphatically disagrees. His argument is threefold. (1) There is no statistical significance attached to the selected range. (2) The results depend on which country is selected as the standard. (Balassa sees no a priori reason for the United States to play this role.) (3) The cause-effect relationship between the exchange rate and PPP is not involved in the test.

A long-term comparative-static test of PPP is applied by Gailliot (1970) to seven industrial countries, with the United States as the standard country and WPIs as the price measure. The two periods selected are 1900–1904 and 1963–67, each of which involved pegged rather than floating exchange rates for the countries considered. However, the periods are carefully chosen to be “normal.” Gailliot points out that each period had relatively free international trade and capital flows and convertible currencies. Also, both were preceded by a long interval of relative peace and prosperity for the industrial countries.

The ratio of the exchange rate to the PPP is close enough to unity for all countries (except Japan) to enable Gailliot to conclude: “The results are exceptionally good when one considers the myriad social and economic upheavals that have occurred during the twentieth century and the difficulty of acquiring reasonably accurate estimates of wholesale prices, especially for the earlier periods. … It appears that Cassel’s theory receives significant support from the empirical evidence” (1970, pp. 351–52).

Gailliot computes the ratio of the exchange rate to the PPP on a decade-by-decade basis (again in the form of five-year averages). There are greater deviations from unity (as expected, because the periods are not chosen on the basis of “normality”), but a tendency to return to unity in the next period (with the exception of Japan). “Again, these figures offer significant support to Cassel’s thesis …” (1970, p. 353).

Lagged effect of purchasing power parity on the exchange rate

If PPP determines the exchange rate, there is no necessity for the relationship to be simultaneous. Allowance for a lagged influence not only is consistent with the theory but also may improve its explanatory power, especially if the lag is distributed through time.

The earliest study of this nature is Bunting’s examination (1939) of the French franc/dollar and pound/dollar exchange rates for the period 1919–36.84 Regarding the base period, Bunting selects the year 1926 rather than 1913, which he argues is too far in the past. He graphs WPI parities together with the exchange rate (a) unled, (b) led one month, (c) led two months, and (d) led three months. Bunting criticizes previous studies of PPP for considering only an unlagged relationship. “Not to allow a lag is to suppose that changes in domestic price levels will be immediately acted upon by foreign buyers” (1939, p. 293). For both the franc and the pound, Bunting finds substantial deviations of the exchange rate from the PPP even using lags. He concludes: “This is damaging statistical evidence against the purchasing power parity theory. … Professor Cassel’s theory finds meager support from a statistical analysis designed to show it in the most favorable light possible” (1939, p. 299).

Thomas (1973) suggests an adaptive-expectations model relating expected to actual PPP. Retaining the previous notation,85 and letting PE denote the expected PPP (ratio of WPIs) and the subscript “– 1” a one-month lag, he presents the following model:

Equation (8) expresses the theory that the current PPP determines the trade balance while the expected PPP determines speculative capital flows (because the optimal method of forecasting the exchange rate is to consider the future PPP). Thomas derives two alternative estimable equations from this model and fits the equations for 11 countries with floating currencies, using monthly data for the period 1920–24. It turns out that the estimated value of β is generally close to zero, implying a low elasticity of expectations. This result is favorable to the PPP theory, for a β substantially above zero would involve an increase in “measured” PPP leading to an increase in expected PPP, and thence to an increase in speculative capital flows.

Hodgson and Phelps (1975) extend the common model in another way. They consider two alternative lag distributions of the PPP in equation (5) as follows:

Equation (10) involves the lag weights declining geometrically from the current month; equation (11) allows the peak of the lag distribution to occur after the current month.

Both models are fitted to 14 floating currencies in the period 1919–25. The authors find that, in both models, movements in PPP explain more than 90 per cent of the variation in the exchange rate for 11 countries, and that the average lag is less than six months for the preponderance of the countries. They conclude: “with the passage of a relatively short period of time, currency purchasing powers begin to exert a dominant influence on exchange rates and explain a remarkably high percentage of their variation” (1975, p. 63).

Use of aggregate econometric models

Although his study is neither mathematical nor econometric, Stolper (1948) can be credited with the earliest use of an aggregate model to test the PPP theory. The subject of his analysis is the exchange value of the floating pound during the years 1919–25, with monthly observations of the exchange rate (number of dollars per pound) taken as percentages of the prewar mint parity. The exchange rate series is charted with, in turn, (a) three alternative PPP series (based on general WPIs, raw-material WPIs, and COL indices), (b) three trade balance series (bilateral U. S.-U. K. balance, overall U. S. balance, and overall U. K. balance), (c) U. S. employment and U. K. unemployment (used in the absence of national accounts data), and (d) short-term interest rates in the two countries. There are noticeable deviations of the exchange rate from each PPP, and comparison of the exchange rate with the employment variables leads Stolper to the conclusion that differences in timing of the business cycle in the two countries are the principal explanation of these deviations. Indeed, he argues that for much of the period relative income in the two countries has higher explanatory power for the exchange rate than do relative prices.

The floating pound after World War I is also examined by Hodgson (1972), who explains the monthly dollar/pound exchange rate in the context of an explicit econometric model. He derives the reduced form equation for the exchange rate as a function of U. S. and U. K. price levels (entered as separate variables), U. S. and U. K. real income, the short-term interest rate differential, money supplies in the two countries, gold flows, a trend term, and dichotomous variables to represent the seasons and special events. The price measures are not identified in the article; income is proxied by employment in the United States, unemployment in the United Kingdom (Stolper’s variables).

Hodgson’s purpose is to test the role of “fundamental determinants” of the exchange rate as against that of special events. In the final equation, the income variables are dropped (because they are imperfect measures and are collinear with the price variables) and the money variables and interest rate differential are lagged one month. The results are (1) “the exchange rate closely followed a path predicted by the ‘fundamental’ determinants;” (2) “price levels were the most significant of the ‘fundamental’ determinants” (Hodgson, 1972, p. 250). Because the price-level variables enter the equation independently rather than in ratio form, this is not a precise test of the PPP theory. Nevertheless, the findings are implicitly supportive of PPP.

The Hodgson model is adopted by Thomas (1973), who drops the money supply variables and (to reduce multicollinearity and to increase degrees of freedom) expresses price levels, income, and interest rates in ratio form. Monthly data are used to examine the exchange rates of six floating currencies with respect to the dollar in the period 1920–24. WPIs are used as the price measure, and various variables proxy income in the absence of national accounts data. The price variable (i.e., the PPP) is highly significant in all cases.

A unique model to test the PPP theory under special circumstances is presented by Holmes (1967 a). The approach requires that one country (A) be small in comparison to the other (B). Then, under the PPP theory, the external value of country B’s currency is adjusted to its internal value through changes in either the exchange rate (under a floating rate) or country A’s price level (under a fixed rate). Hence, whether the exchange rate is floating or fixed, the PPP theory takes the form of a relationship in which RPA is the dependent variable and PB the independent variable.86

More generally, RPA is a current endogenous variable and PB an exogenous variable in an aggregate model from which Holmes derives an estimable equation with RPA as the dependent variable and two groups of explanatory variables in addition to PB. The first group consists of variables that are recognized by Cassel as nonmonetary influences on the exchange rate: tariffs in each country, capital flows and unilateral transfers (into the small country), and a variable representing government intervention in the foreign exchange market (this variable is the official rate when applicable, the market rate otherwise). The second group includes variables that are influences on demand for commodities, but not mentioned by Cassel: real income and population in each country. For the test to be passed by the PPP theory: (1) PB should be the most significant explanatory variable; and (2) as regards other explanatory variables, the first group (those mentioned by Cassel) should be more significant than the second group.

Holmes takes Canada as the small country, the United States as the large country, and fits the equation to annual data for the period 1870–1960. It turns out that the U. S. price level (measured by the CPI) is the most significant explanatory variable, followed by the market intervention variable, the Canadian tariff, and capital inflow into Canada. Holmes concludes: “The Purchasing Power Parity Theory of Gustav Cassel as formulated by our model is confirmed by the evidence in this study” (1967 a, p. 52).

Given the dependence of the Canadian upon the U. S. economy, a high correlation between the Canadian price level in U. S. dollars (RPA) and the U. S. price level (PB) is to be expected irrespective of the validity of PPP theory. Therefore a weaker conclusion is indicated. Holmes’ test shows, rather, that the PPP theory cannot be rejected on the basis of the model and the data used.

Investigation of the movement of internal price ratios

If the difference between countries’ internal price ratios changes over time, a case is thereby made against the relative PPP theory. One reason for such an event is emphasized by Balassa: productivity increases occurring in a nonuniform fashion among countries. Balassa (1964) himself tests this hypothesis for seven industrial countries. For each country, he computes the ratio of the GNP price deflator (representing the general price index) to the WPI of manufactured goods (representing the price index of traded goods) for the year 1961, taking 1953 as the base year. The internal price ratio is thus proxied by the ratio of a price index of the nontraded plus traded sectors of the economy to a price index of the traded sector. The resulting variable is regressed on the increase in manufacturing output per man-hour—representing productivity change in the traded sector—over the same period. The correlation coefficient is 0.91, implying that disparate productivity advances among countries do in fact lead to the predicted divergent movements in their internal price ratios.

A similar test is performed by McKinnon (1971, pp. 21–23) and is cited approvingly by Haberler.87 Again taking 1953 as the base year, the CPI (a general price index), WPI, EPI (export price index), and an index of output per man-hour are calculated for the first quarter of 1970 for six industrial countries. The countries with high growth in productivity have substantially higher CPI/WPI and CPI/EPI ratios than do the countries with low growth in productivity. The divergence between the rapidly and the slowly growing economies is greater for the CPI/EPI ratio—an expected result, for the WPI incorporates some nontraded goods. The implication once more is that Balassa’s hypothesis is applicable to relative PPP.

cost parity

There is no literature involving direct testing of the cost-parity version of PPP theory, but there is a related empirical study. If the ULC parity is to yield the same value as a price parity, then the following relationship must hold: 88

Officer (1974) collected annual data for 10 DCs over the years 1952–70, with the Federal Republic of Germany (B) as the base country. The ratio of the price level of the Federal Republic of Germany to the domestic price level is measured as the geometric mean (Fisher ideal index) of the German-weighted and domestic-weighted COL PPPs computed by the Statistical Office of the Federal Republic of Germany. Wage rates are represented by hourly earnings in manufacturing and productivity by the ratio of GDP to employment, where GDP is converted into deutsche mark using the computed PPP (Fisher index). The equation

is fitted to the pooled cross-sectional and time-series data, with the result that the hypothesis “α = 0 and β = 1” cannot be rejected even at a high level of significance. Therefore, there are some grounds for using a price-parity measure as a proxy for a cost parity—a useful result, given the less favorable data situation regarding factor costs and productivity compared with product prices.

V. Conclusions

Perhaps the most salient result of this review is how Cassel’s theory qua theory has stood the test of time. Apart from the development of the cost-parity concept, there is nothing in the current state of PPP theory that was not embodied in Cassel’s writings. The failure of the theory to develop along sophisticated lines is in an important respect a favorable feature. Models of exchange rate determination outside the scope of this review have become increasingly complex. It is the principal virtue of the PPP approach that computations of equilibrium exchange rates can be performed “on the back of an envelope” without the need of sophisticated econometric or mathematical techniques. Such simple calculations may provide checks on the results of high-powered models that seek to explain the movement of the exchange rate or to find its equilibrium value. The PPP approach may also be of value in forecasting floating exchange rates. One requires only price indices for this purpose, and they may be forecast from existing econometric models.89

It is the virtue of PPP theory to be simple; but the theory would have to be rejected if it were simple-minded. The theory does have limitations, and the many criticisms leveled at the theory over the years reflect these limitations. Crucial to survival of the PPP approach is the ability to allow scope for the imperfections noticed by critics (and by proponents). These imperfections are of three kinds. Some refer to the fact that the PPP theory, like any theory, cannot make exact predictions, that is, results are subject to random error. While the distribution of this random error is of importance in empirical work, of course, for theoretical purposes acknowledgement of the approximate nature of PPP computations suffices.

A second kind of limitation is one that can be corrected by a simple alteration or extension of the theory. For example, one way to incorporate income movements in exchange rate determination is to let the PPP itself represent the role of income in addition to that of prices; thus, only the interpretation (and possibly the lag specification) of the theory is affected. Another approach is to include an income variable in addition to the PPP as determinants of the actual exchange rate. If the PPP remains the more important explanatory variable, the PPP theory has been amended but not eclipsed. Such techniques may be used to incorporate speculation, trade restrictions, and other influences on a floating exchange rate.

The third kind of limitation is the existence of a systematic bias in the PPP computation of the (long-run) equilibrium exchange rate. Fundamental alterations in the theory are required to cope with such a limitation, and the result might be a theory of the exchange rate that is no longer recognized as in the PPP tradition.

However, the existence of systematic biases need not destroy the empirical applicability of the theory. It might turn out that in practice PPP is a robust theory that predicts movements of floating exchange rates and estimates long-run equilibrium rates to a high degree of accuracy. In other words, systematic biases might exist but have only a small quantitative impact. In this respect, empirical testing of the theory for various countries and diverse time periods is essential, for a bias may show itself to be significant only in certain circumstances.

Even if a systematic bias does exist and is substantial, the PPP approach need not be abandoned, for the bias might be predictable in its effect. A relationship between the exchange rate, the PPP, and variables representing the impact of the bias may be used to determine equilibrium exchange rates, evaluate existing rates, and predict the movements of floating rates. As a theory, such an approach is haphazard; as a practical technique, it may have value.

Unfortunately, the existing empirical work on PPP is not yet at the stage where optimal treatment of biases can be performed. Much of the testing of the theory refers to periods in the distant past. Thomas (1973, p. 182) seems to be alone in warning against an unqualified projection of results based on historical periods to the current situation. Considering studies of the floating exchange rates that followed World War I, he notes that expectations of a return to the old mint parities, greater flexibility of wages and prices, and a small role for government macroeconomic policy are all elements that are not present in the current situation. Research on the present and recent experience of foreign exchange markets is necessary to gauge the relevance of PPP theory and to improve its applicability to existing conditions. In particular, the new era of floating—albeit managed—exchange rates affords useful data for such empirical work.

The nature of the testing of PPP theory also requires examination. One basic test that has yet to be documented involves a comparison of the theory’s forecasting ability with that of other exchange rate models, both sophisticated and naïve. Furthermore, the literature on the testing of PPP is flawed by the independent approach taken by many authors. Little attempt is made to build on the techniques and results of other authors—or indeed to refine and develop one’s own approach. A notable recent exception is provided by the various studies of Amacher and Hodgson (1974), Hodgson (1972; 1975), and Thomas (1973).

A prerequisite for usable results from research on PPP is careful attention to the basic components of the approach. For example, the base period for relative PPP must be chosen with care. In this respect it is unfortunate that the rationale of selecting a period in which the exchange rate is in long-run equilibrium is generally ignored. In particular, no researcher has used balance of payments data (or apparently any quantitative data) to determine an optimal base period. Also, the price measures used to compute PPP tend to be selected if not haphazardly, then without sufficient awareness of the advantages and disadvantages of the alternative measures available. For example, many authors use WPIs without acknowledging the inherent bias of these indices in favor of the PPP theory.

The selection of a standard country is another element in the PPP approach that requires re-examination. If a unique standard country is to be used in the computation of PPPs for a broad group of countries, then the usual choice of the United States seems appropriate. However, for individual-country analysis, the optimal standard country would be the one with which the former country’s trade and payments links are strongest. This reasoning suggests that the concept of effective exchange rates be applied to PPP, so that the standard currency is replaced by an appropriately weighted average of the currencies of the country’s principal partners in trade and payments.90

The tests of PPP to date are mixed in their results. Some researchers claim to demonstrate the existence of a systematic bias in PPP as a measure of the equilibrium exchange rate; others argue that the evidence indicates a close correspondence between PPP and the actual exchange rate. A balanced viewpoint suggests caution in applying PPP computations to measure currency overvaluation or undervaluation until the theory receives the careful empirical testing warranted by its tradition, simplicity, and adaptability.

BIBLIOGRAPHY

Mr. Officer, consultant in the Research Department, is a graduate of McGill University and of Harvard University. He was on leave from his post as professor at Michigan State University when this paper was written.

The most recent example is Kravis and others (1975).

There can be no objection to the definition of the short-run equilibrium exchange rate, except perhaps that some observers might consider a freely floating rate to be dynamically unstable. The definition of the long-run equilibrium exchange rate is more controversial. The concept was developed by Nurkse (1944, pp. 124–27; 1950), Haberler (1947), Triffin (1947), Meade (1951, pp. 13–16), and Machlup (1964, ch. Ill), and criticized by Haberler (1944 a), Yeager (1966, p. 47), and Balassa and Schydlowsky (1968, pp. 356–57). For discussions of the issues involved in the concept, see Scammell (1961, pp. 53–57), Kindleberger (1969), and Stern (1973, ch. 1). The definitions of exchange rate equilibrium are presented here solely for the purpose of expositing PPP theory.

Although only the current value of the PPP is included explicitly in the function, PPPt may be interpreted here as representing a distributed lag of this variable over past periods and the current period.

Unless otherwise stated or implied, the term “exchange rate” signifies the short-run equilibrium exchange rate.

For example, considering “the very possibility of exchanges deviating from the purchasing power parity being denied,” Cassel (1922, p. 183) declares himself to be “in opposition to such a point of view.”

Perhaps the earliest suggestion of this view can be ascribed to Terborgh: “As a self-sufficient and independent explanation of exchange phenomena it [PPP] is scarcely entitled to serious consideration. It must be reduced from the rôle of an independent theory to that of a component element in a comprehensive synthesis, where it has a proper and permanent place” (1926, p. 208).

Samuelson (1964, p. 153) asserts that the PPP theory is generally devoid of an error term: “Unless very sophisticated indeed, PPP is a misleading pretentious doctrine, promising us what is rare in economics, detailed numerical predictions.” Holmes (1967 b, pp. 693–94) argues, on the contrary, that Cassel’s equations do include random error terms, although Cassel described them only in a literary rather than mathematical fashion. Holmes’ position is supported by his own references to Cassel’s writings and by those cited later in the text.

See Cassel’s recognized limitations of purchasing power parity later in Section I.

See, for example, Cassel (1928 a, p. 32; 1928 b, p. 17).

For example, Angell (1926, pp. 49–52), Terborgh (1926, p. 198), Whittaker (1940, p. 656), and Haberler (1961, pp. 45–48).

Einzig (1970, p. 205) notes that Wheatley was the first to provide a name for the ratio of two countries’ price levels: “par of produce.”

For the latter viewpoint, one may consult Ellis (1937, pp. 207–15) on Cassel’s development of PPP theory over time, and Angell (1926, pp. 188–93 and 291–97) and Einzig (1970, pp. 264–72) on the early reaction that Cassel’s. theory had among other economists.

This exposition of absolute PPP theory is apparent throughout Cassel’s writings. See, for example, Cassel (1916, p. 62; 1921, p. 36; 1922, pp. 138–39; 1925 a, pp. 148–49; 1932 b, pp. 659–60).

See, for example, Cassel (1922, p. 182).

See Cassel (1925 c, p. 18; 1928 a, p. 32).

One cannot argue that Cassel’s selection of price indices in his empirical work contradicts this statement. He tested and applied PPP theory at a time when general price indices were few in number and primitive in concept.

See, for example, Cassel (1918, p. 413).

The sole exception is the derivation of absolute price parity from a UFC parity. See cost parity later in Section I.

For example, Terborgh (1926, pp. 197–98).

For example, Yeager (1958, p. 516; 1966, p. 170).

Samuelson (1974, p. 602).

See Index-number problems in Section II.

See Yeager (1958, p. 522) and the references cited there.

As representative examples of Cassel’s exposition, see Cassel (1918, p. 413; 1925 c, p. 17; 1932 b, p. 661).

See Samuelson (1964, p. 146; 1971, p. 6, fn. 4; 1974, p. 602).

Summaries of Cassel’s acknowledged limitations of his PPP theory are also provided by Bunting (1939, pp. 283–84) and Holmes (1967 b, pp. 686–90).

Points 2 and 3 are based on a sophisticated theory of price expectations. See, for example, Cassel (1923; 1924).

See Metzler (1947, p. 21), Ellsworth (1950, p. 596), and Stern (1973, p. 147, fn. 31).

See Metzler (1947, p. 21), Samuelson (1964, p. 149), and Stern (1973, p. 147, fn. 31).

See, for example, Haberler (1945, pp. 311–12; 1961, pp. 48–49), Ellsworth (1950, pp. 594–95), and Stern (1973, pp. 144 and 147). Bresciani-Turroni (1934), a critic of PPP, stated the theory in terms of export prices.

See, for example, Haberler (1945, p. 312; 1961, p. 49) and Ellsworth (1950, p. 596).

See cost parity in Section I.

See, for example, Houthakker (1962 a, p. 297), Yeager (1968, pp. 77–78), Stern (1973, pp. 143–44), and Officer (1974, p. 873).

This procedure is followed in the computation of PPPs both for providing international comparisons of standard of living and GDP (e.g., Kravis and others (1975)) and for indicating the long-run equilibrium exchange rate (e.g., Houthakker (1962 a) and Officer (1974)).

Scammell (1961, p. 59) seems to argue that the very existence of imperfections involves a breakdown in the PPP theory. Others (for example, Ellsworth (1950, pp. 591–92) and Yeager (1958, p. 517)) see moderate levels of tariffs and transport costs as reducing the accuracy of the theory but not destroying it outright.

See, for example, Haberler (1936, p. 38), Ellsworth (1950, p. 592), and Yeager (1958, p. 517).

See Haberler (1945, pp. 313–15).

See Cassel’s recognized limitations of purchasing power parity in Section I.

Also, their effect on the balance of payments must not be canceled through the associated cumulative reflow of interest and dividend payments.

The reasons for the higher productivity of the traded sector of the economy are not discussed by Balassa. Aukrust (1970, p. 53, fn. 3) suggests that the scope for technological progress afforded by the higher capital intensity of this sector is not the sole reason. Exposure to international competition itself may be a spur to increased efficiency.

See International differences in the internal price ratio in Section IV.

One solution is to calculate the absolute price parity in the base period and let it play the role of the base-period exchange rate. This technique requires that sufficiently comprehensive data be available to compute an absolute price parity that is a good approximation to the long-run equilibrium exchange rate. Use of the actual base-period exchange rate, on the other hand, has the statistical advantage that the only product-price data required are the countries’ own price indices.

See, for example, Haberler (1945, p. 311), Metzler (1947, p. 18), Yeager (1958, p. 517), Kindleberger (1973, pp. 391 and 392), and Stern (1973, p. 146).

It is assumed that the base-period exchange rate is correctly chosen.

For example, Haberler (1945, p. 312; 1947, p. 100), Scammell (1961, p. 59, fn. 2), and Caves and Jones (1973, p. 337).

For example, Haberler (1947, p. 100), Vanek (1962, p. 84), Balassa (1964, p. 591), and Stern (1973, p. 146).

See, for example, Haberler (1945, p. 312; 1947, p. 100; 1961, pp. 49–50), Metzler (1947, p. 19; 1948, p. 223), Machlup (1964, p. 27), Vanek (1962, pp. 84–85), Kindleberger (1973, p. 391), and Stern (1973, p. 146).

Differential technological change in the various sectors of an economy can also have important domestic implications. A model with this viewpoint has been presented by Baumol (1967). For comments and elaborations, see Birch and Cramer (1968), Robinson (1969), Keren (1972), and Baumol (1968; 1969; 1972).

It is interesting to recall that Samuelson is one of the originators of the factor-price equalization model.

This neutrality result is disputed by Gupta (1968) but defended by Minsol (1968).

See Haberler (1936, pp. 37–38; 1945, pp. 313–15; 1961, pp. 50–51).

See Metzler (1947, pp. 22–24; 1948, pp. 222–23).

Appropriately enough, the discussion is entitled “The Misleading of Mr. Churchill”—see Keynes (1932, pp. 244–53). For a contemporary analysis contrary to that of Keynes, see Gregory (1926, pp. 39–96). Later assessments of the U.K. return to the gold standard are offered by Moggridge (1972, ch. 4) and Yeager (1966, pp. 277–80). Moggridge (1972, ch. 3) also provides a comprehensive account of the elements in Churchill’s decision.

See Index-number problems in Section II.

See Haberler (1945, p. 312; 1961, p. 49, fn. 37). A different criticism is made by Nurkse (1944, p. 128), who points out that the precise application of PPP left no margin in the new rate for balance of payments pressure arising from expansion of output.

An analysis of the Czechoslovakian experience by the League of Nations implies that WPIs were so used: “the sole purpose of devaluation was to adjust Czechoslovak prices to world levels” (1936, p. 50). This statement is followed by a reference to the necessity of preventing “any considerable internal rise of prices lest the competitive capacity of Czech exporters be again impaired,” and then a discussion of rising wholesale prices in connection with the Belgian devaluation in the following year.

One might comment that this was not necessarily an equilibrium parity at the time and also that by taking into account only the pound, Belgium could not obtain optimal results.

Casual observation would suggest that this estimate is too high, whereas the dollar/deutsche mark result would appear more reasonable.

See, for example, Holzman (1968) and Wiles (1969).

The error term is omitted here and in subsequent equations.

This is the assessment also of Neuberger (1968, p. 362).

See Absolute parity in Section II.

For an early discussion of this hypothesis, with computations involving the Netherlands Indies guilder in relationship to the U.S. dollar, see Polak (1943, ch. 17).

The PPP concept used is that of an absolute GNP price parity. A geometric mean (Fisher ideal index) of U. S. and domestic quantity-weighted PPPs is used for most countries. The basic data come from a variety of sources and, where necessary, are extrapolated to bring them up to date.

See Absolute parity in Section II.

Equivalently, internal price ratios should be compared between countries only when exchange rates are in long-run equilibrium.

Presumably, the PPPs are the geometric means of the parities based on the average Latin American and on the U. S. weighting pattern. (The ECLA study uses average Latin American expenditure patterns rather than those for individual countries.)

For a description of the actual variables used, see Kravis and others (1975, pp. 186–87).

Both PPPs are Fisher indices of the respective U. S.-weighted and domestic-currency-weighted parities.

See, for example, Cassel (1922, pp. 181–82).

For Cassel’s view in his subsequent writing that this test provided definitive proof of the PPP theory, see Cassel (1925 a; 1932 b, pp. 678–79).

Angell did not calculate a PPP series for Germany apparently because “the grotesque size of the figures makes it almost impossible to handle them” (1926, p. 440).

See residual validity of purchasing power parity in Section II. Of course, a deflation predominantly in price rather than in output would be as applicable for PPP as is inflation.

See Assessing the rationality of exchange rate policies of state-trading economies in Section III.

It is unusual to express the exchange rate and PPP in units inverse to one another.

For an outline of his subsequent analysis, see Lagged effect of purchasing power parity on the exchange rate later in this section.

As in most empirical studies of PPP, there is no discussion of the selection of the price index.

Their distributed-lag model is discussed in Lagged effect of purchasing power parity on the exchange rate later in this section.

This point was clearly stated by Cassel, who viewed PPP as the principal determinant of the exchange rate under both floating rates and the gold standard. See Cassel (1922, pp. 185–86; 1925 a, pp. 149–50; 1928 a, pp. 31–32; 1932 b, pp. 519–24). For the same interpretation of PPP theory, see Yeager (1958, p. 526).

Of the countries considered, only Canada and Thailand had floating rates.

He makes no comment about the fact that the period spans intervals of both floating rates and the gold standard.

See Time-series comparisons of purchasing power parity with a floating exchange rate earlier in this section.

The notation followed is that set forth in methodology in Section I.

See Haberler (1973, pp. 91–92; 1975, pp. 16 and 24–25).

Equation (12) is simply a rearrangement of equation (4). For derivation of the equation and for notation, see cost parity in Section I.

In a distributed-lag formulation of PPP, much of the required price information may be available without forecasting.

This approach is taken in the International Monetary Fund’s Annual Report (1975, pp. 31–33), where, for seven industrial countries in the period 1973–75, an effective exchange rate index is compared with the ratio of the country’s (manufactured-goods) WPI to a weighted average of the WPIs of all seven countries.

Other Resources Citing This Publication