Topic 6. Purchasing Power Parity


The concept of purchasing power parity has had a long history in open-economy macroeconomics and still forms a basis for some contemporary policy arguments. The essence of this idea is that one can determine what the nominal exchange rate between two countries' currencies should be by looking at the ratio of their price levels. A deviation of the actual exchange rate from this purchasing-power-parity level would thus indicate that the currency is over- or under-valued in the market.

The equation defining the real exchange rate

        Q  =  P  /  Π P*

where  Q  is the real exchange rate,  Π  is the nominal exchange rate, defined as the domestic currency price of foreign currency, and  P  and  P*  are the domestic and foreign price levels, can be manipulated to yield

        Π  =  P  /  Q P*.

It is immediately evident from the second of these equations that a domestic inflation that increased the domestic price level by 25 percent would predictably raise the nominal exchange rate---that is, depreciate the currency---by 25 percent. And failure of the exchange rate to adjust would leave the domestic currency overvalued. It is a further short step to argue loosely that the eventual movement of the exchange rate to its purchasing-power-level is a return to equilibrium.

It should be easy for you to detect the crucial assumption in this argument. It is that the equilibrium real exchange rate is constant. The view that  Q  should be constant in equilibrium is based on the notion that every commodity should have the same price, measured in a single currency, in every country---otherwise people would conduct arbitrage by buying the good in the country where it is cheap and selling it in the country where it is dear.

It might seem obvious that this law of one price must be true, barring government intervention, for products like wheat, crude oil and soybeans after tariffs and transport costs are taken into account. It is less obvious that it must be true for automobiles and cook stoves because these commodities are not homogeneous---a Chrysler Newport is not the same as a Nissan Centra. And it is clearly not true for services like haircuts. One would pay the equivalent of, say, $13 U.S. dollars for a haircut in Canada as compared with, maybe, 75 cents in India. The reason for this, of course, is that wages are much lower in India than in Canada and Indian barbers cannot easily migrate to Canada. Nor can Canadians profitably fly to India to get their hair styled. The prices of non-traded goods will thus differ between countries while the prices of (identical) traded goods will be the same net of tariffs and transport costs. We are, of course, measuring prices here in a single currency.

Actually, the distinction between traded and non-traded goods is not really a very useful one, because every good has traded and non-traded components. Haicuts have a traded component because the stylist may be using scissors, or a chair, that was imported from abroad. And wheat has a non-traded component in that domestic labour must be used in transporting it and arranging for its storage and eventual export. It is thus more accurate to talk, not about traded and non-traded goods, but about the traded and non-traded components of a country's output.

Since the advance of technology and associated growth of real income in different parts of the world will cause the prices of the non-traded relative to traded components of output to change, there is no reason to expect that the price of any particular country's output in terms of other countries' outputs---that is, its equilibrium real exchange rate---will be constant through time. Moreover, countries do not all produce the same traded goods, so a rise in the prices of natural resource based goods relative to the prices of manufactured goods, for example, will increase the real exchange rates of countries specializing in resource intensive goods.

So there is no reason to expect a movement of the nominal exchange rate that results from a change in the equilibrium real exchange rate, with price levels constant, to be a movement away from equilibrium. A high nominal value of a country's currency will thus reflect a high equilibrium value of its real exchange rate and not a deviation from equilibrium. At the same time, the fact that the equilibrium real exchange rate may change through time should not be allowed to cloud the principle that countries having more inflation will experience devaluations of their nominal exchange rates with respect to countries having less inflation.

Let us now have a look at the real exchange rate movements of some major industrial countries. Figure 1 plots the real and nominal exchange rates and the nominal price level ratio of the United Kingdom with respect to the United States for the 19th and 20th centuries. Figure 2 plots the real and nominal exchange rates and the nominal price level ratio of Canada with respect to the United States for the period 1873 through 2007. And Figure 3 plots the same series for Canada with respect to the United Kingdom over the same period.

Figure 1

Figure 2

Figure 3

It should be obvious from the above graphs that the real exchange rate, represented by the solid line, is not a constant. The evidence also suggests that the real exchange rates in question do not trend upward or downward over the very long run, although downward trends are apparent for Canada with respect to both the U.S. and U.K. in recent decades. The absence of long-term trends would seem reasonable---on-going technology growth may increasingly favour the resource base of particular countries for extended periods of time but one would expect that, over a couple of centuries, positive and negative shocks should tend to average out.

The fact that the real exchange rate exhibits no trend through time does not mean that it's equilibrium level is constant and that exchange rates tend to deviate from and then return to that equilibrium in the long-run. Rather, it simply means that the equilibrium value of the exchange rate rises and falls through time---the absence of a long-run trend is a purely statistical phenomenon reflecting the tendency of positive and negative shocks to the equilibrum level to eventually average out.

Notice that during the gold standard period before 1914 when the nominal exchange rate was fixed the real exchange rates and nominal price level ratios of Canada with respect to the U.S. and U.K. tended to be perfectly correlated. This was also true of the United Kingdom with respect to the United States between 1880 and 1914 and, to a rough approximation, in the three decades prior to the U.S. Civil War. In the early 19th century, the gold standard was in the process of being established, and as a result of the Civil War the United States broke with the gold standard, as can be seen from the spike in the nominal exchange rate in Figure 1, returning to a rigid parity in 1879. During the post-Bretton-Woods period from 1973 onward the nominal and real exchange rates were highly correlated, with the price level ratios showing much smoother variations.

Finally, Figure 4 plots the real and nominal exchange rates and nominal price level ratio of Denmark with respect to Norway from January 1967 to mid-2009. And Figure 5 plots the same series for Japan with respect to the United States for the period from January 1957 through mid 2009.

Figure 4

Figure 4

It is clear that Denmark's real exchange rate with respect to Norway is quite variable, ranging between 80 and 110 percent of its average level in 2005. And the overall movement in the Japanese real exchange rate with respect to the U.S. was remarkable. It went from 50 to more than 150 percent of its 2005 level between the late-1960s and the mid-1990s, then fell thereafter.

The Japanese real exchange rate with respect to the United States was highly correlated with the price level ratio during the period before the collapse of the Bretton-Woods system of fixed exchange rates. After 1973, the real and nominal exchange rates are highly correlated with the price level ratio declining rather smoothly as the difference between the real and nominal exchange rates gradually disappeared. The real and nominal exchange rates of Denmark with respect to Norway are also highly correlated during the period from 1973 onward with the price level ratio moving upward more slowly as the difference between the nominal and real exchange rates slowly disappeared.

The strong correlations between the real exchange rate and price level ratios during periods of fixed exchange rates and the strong correlations between the real and nominal exchange rates when the latter was flexible are exactly what we would expect, given the definition of the real exchange rate. Also, it is clear from the data plotted above that any notion that the equilibrium real exchange rate can be viewed as constant is a figment of the imagination. The evidence against purchasing power parity is overwhelming.

Some might still try to argue, since the real and nominal exchange rate tend to move in step with each other when the latter is flexible, that observed movements in the real exchange rate are the caused by nominal exchange rate movements arising from differences in monetary policy between countries. The problem with this view that real exchange rate movements were caused by policy induced nominal exchange rate changes is that it implies price level rigidity---if prices are flexible, monetary policy will be reflected in the price level and nominal exchange rates but not in output and the real exchange rate. Full price level adjustment usually takes place within two or three years (which is the maximum length of the typical business recession) while the observed real exchange rate movements are much longer-term. And not a shred of evidence of price level adjustment in response to real exchange rate movements appears under flexible exchange rate conditions in the charts we have plotted above.

Our conclusion is thus that the bulk of the major observed movements in real exchange rates are changes in the equilibrium levels in response to technological change, economic growth and shifts of world investment flows between countries. This, of course, does not rule out the possibility that short-term month- to-month adjustments could result from overshooting monetary shocks.

Time for a test. As always, think up your own answers before looking at the ones provided.

Question 1
Question 2
Question 3

Choose Another Topic in the Lesson.