Purchasing-Power Parity: Definition, Measurement, and Interpretation Robert Lafrance and Lawrence Schembri, International Department • The concept of purchasing-power parity (PPP) has t has been argued that the Canadian dollar is two applications: it was originally developed as a undervalued because its current market value theory of exchange rate determination, but it is is below the purchasing-power-parity (PPP) I exchange rate calculated by the Organisation for now primarily used to compare living standards across countries. Economic Co-operation and Development (OECD) and Statistics Canada (Chart 1). While the deviation of • From the perspective of exchange rate determin- the value of the Canadian dollar from its purchasing- ation, PPP is useful as a reminder that monetary power-parity rate has been growing in recent years, policy has no long-run impact on the real exchange this article argues that this deviation cannot be inter- rate. Thus, countries with different inflation rates preted as implying that the Canadian dollar is under- should expect their bilateral exchange rate to adjust valued by a comparable amount. Instead, this deviation to offset these differentials in the long run. The indicates that the prices of goods and services are, on exchange rate, however, can deviate persistently average, lower in Canada than in the United States, from its PPP value in response to real shocks. when measured in the same currency at the prevailing exchange rate. • To compare living standards across countries, PPP exchange rates are constructed by comparing the national prices for a large basket of goods and Chart 1 services. These rates are used to translate different Canada’s PPP Exchange Rate currencies into a common currency to measure the purchasing power of per capita income in different US$/Can$ countries. A PPP exchange rate constructed in 0.90 0.90 Bilateral PPP this manner is not, however, an accurate measure (Statistics Canada) of the equilibrium value of the market-determined 0.85 0.85 exchange rate. 0.80 0.80 0.75 Multilateral 0.75 PPP (OECD) 0.70 0.70 Nominal 0.65 exchange rate 0.65 0.60 0.60 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 BANK OF CANADA REVIEW • AUTUMN 2002 27 PPP as a Theory of Exchange Rate • the composition of the basket of goods and Determination services included in measures of national price levels differs across countries, espe- While the origins of the PPP concept can be traced cially for producer-based as opposed to back to the Salamanca School in 16th-century Spain, consumer-based price indexes, and its modern use as a theory of exchange rate determi- nation begins with the work of Gustav Cassel • the fact that the real exchange rate is not (1918), who proposed PPP as a means of adjusting constant in the short run because aggregate pre–World War I exchange rates or parities for coun- price levels are sticky and the exchange rate tries intending to return to the gold standard system is affected by money or asset market shocks, after hostilities ended.1 Some adjustment was neces- or in the long run because of persistent real sary because countries that left the gold standard in shocks 1914 experienced significantly different rates of infla- tion during and after the war.2 As a theory of exchange rate determination, the sim- In practice . absolute PPP does not plest and strongest form of PPP (absolute PPP) is based on an international multi-good version of the law hold for a number of reasons, and of one price (Box 1). Absolute PPP predicts that the these undermine its usefulness as a exchange rate should adjust to equate the prices of theory of the determination of the national baskets of goods and services between two level of the exchange rate. countries because of market forces driven by arbitrage. Under absolute PPP, the exchange rate is simply equal to the ratio of the domestic to the foreign price of a given aggregate bundle of commodities, but this A weaker version of PPP, known as relative PPP, implies implies that the real exchange rate is constant.3 that the exchange rate between two countries should In practice, however, absolute PPP does not hold for eventually adjust to account for differences in their a number of reasons, and these undermine its useful- inflation rates. That is, countries that follow monetary ness as a theory of the determination of the level of the policies with different inflation-rate objectives should 4 exchange rate. The most important are expect to see this difference manifest itself in an • the existence of non-traded goods and exchange rate movement. To illustrate the circum- services that preclude arbitrage stances where relative PPP may provide useful explan- atory power, consider Table 1, which compares the • the presence of significant transactions cumulative inflation and exchange rate experiences of costs for traded goods, including transport Canada and Mexico relative to the United States over costs, tariffs, taxes, information costs, and the period 1975–2001. The table clearly shows that, for other non-tariff trade barriers that make 5 Canada, the exchange rate movement over the period arbitrage costly is largely due to a depreciation of the underlying real exchange rate because the cumulative inflation differ- 1. Dornbusch (1987) provides a historical overview and insightful discussion ential with the United States is only 6 per cent of the of PPP. total exchange rate movement. The opposite is true for 2. Like Cassel, Keynes believed that the exchange rate needed to be adjusted for inflation differentials because he recognized that wages and prices were Table 1 too sticky to adjust. Unfortunately, Winston Churchill, as Chancellor of the Exchequer, decided to return the United Kingdom to its pre-war parity in Relative Inflation and Exchange Rates, 1975–2001 1925. This move proved disastrous; exports fell and unemployment increased sharply. Country (1) (2) (3) Contribution CPI in Price Exchange of relative 3. The real exchange rate is defined here as the exchange rate deflated by 2001 ratiosa ratesb inflationc the ratio of the domestic to the foreign price index. 1975=1 1975=1 4. Perhaps the strongest criticism of the absolute version of PPP is by Canada 3.38 1.03 1.52 6% Paul Samuelson (1964, p. 153), “Unless very sophisticated indeed, PPP is a Mexico 2260 687 747 92% misleadingly pretentious doctrine, promising us what is rare in economics, United States 3.29 1 1 na detailed numerical prediction.” a. Canadian and Mexican price levels relative to the U.S. price level in 2001 5. Rogoff (1996) surveys evidence that the law of one price does not hold for b. Units of domestic currency per U.S. dollar most traded goods and services; he concludes that international markets for c. Proportion of exchange rate depreciation relative to the U.S. dollar that is explained by these items are much less integrated than domestic markets. higher rates of inflation in Canada and Mexico 28 BANK OF CANADA REVIEW • AUTUMN 2002 Box 1 Absolute and Relative Purchasing-Power Parity Absolute PPP is obtained by extending the law of As a theory of exchange rate determination, abso- one price to multiple commodities in an interna- lute PPP, given by equation (4), predicts that the tional setting. This “law” implies that, in the absence exchange rate will adjust to equalize price levels. of transactions costs, competitive arbitrage should Note that absolute PPP assumes that the real force the same good to sell for the same price, exchange rate—the nominal exchange rate adjusted expressed in a given currency, across countries. for differences in national price levels—is constant: ∗ EP∗ ⁄ P = 1. To illustrate the law of one price, letPi andPi be the domestic and foreign currency prices of com- In practice, absolute PPP does not hold because of modityiE (a good or service) and the exchange obstacles to international trade. If these trade fric- rate (expressed as the price of foreign exchange). tions, denoted byk , are assumed to be relatively Thus, the law of one price implies that constant, then (4) can be modified as ∗ ⋅ ⁄ ∗ Pi = EPi . (1) EkP= P , (5) To extend this illustration to PPP, letPP and ∗ and taking the ratio between timeto and time be the domestic and foreign price levels, which are gives constructed by taking a weighted average of the prices ofn commodities in the national production E P ⁄ P or consumption baskets: ------t = ---------------------t o . (6) E ∗ ⁄ ∗ o Pt Po n n Equation (6) represents a weaker version of PPP Pw= P and P∗ = w ∗P ∗, (2) ∑ i i ∑ i i (relative PPP) that predicts that the exchange rate ii= ii= will adjust to offset inflation differentials between ∗ wherewi andwi represent the weights of com- two countries over time. Thus, if most of the shocks modityi in the basket. If it is further assumed that affecting the exchange rate are monetary rather the weights are identical and the law of one price than real, then relative PPP will be able to explain a holds for all commodities, then substantial portion of the exchange rate movement between two countries. EP∗ = P (3) or EPP= ⁄ ∗ . (4) Mexico, where the cumulative inflation differential PPP and Standard-of-Living represents 92 per cent of the exchange rate movement relative to the United States. Therefore, relative PPP is Comparisons useful in explaining exchange rate movements only To compare living standards between countries, it is 6 when monetary, not real, shocks predominate. necessary to translate per capita income or expendi- ture values measured in the local currency into a com- 6. Keynes was perhaps the first to recognize this point; although he appreci- mon currency, normally the U.S.