Chapter 9
Taking a Bite Out of the Purchasing Power Parity (PPP)
In This Chapter
Understanding the relationship between the PPP and the MBOP
Exploring the relationship between inflation differentials and changes in exchange rates
Deriving the PPP
Estimating the PPP-suggested future spot rate
Understanding the Big Mac standard
The models of exchange rate determination in Chapters 5, 6, and 7 predict the direction of change in the exchange rate in terms of appreciation or depreciation. This chapter aims to attach a number to the direction of change in the exchange rate. In other words, using the purchasing power parity (PPP), you can predict that, for example, the dollar will depreciate by 2 percent.
Whereas the interest rate parity (IRP; see Chapter 8) looks at the interest rate differential between two countries, the PPP considers the inflation rate differential to predict changes in the exchange rates. Therefore, as in the case of the IRP, the PPP also provides a “best guess” regarding the future spot rate.
In this chapter, using the PPP formula and the current spot rate, I show you how to calculate the estimated future spot rate. This chapter also discusses an interesting but sometimes misunderstood concept of the Big Mac Standard. This discussion focuses on different prices of Big Macs around the world and the interpretation of these differences.
Getting a Primer on the Purchasing Power Parity (PPP)
In this section, I cover the basics of the PPP. An important component is the connection between the PPP and the Monetary Approach to Balance of Payments (MBOP). As in the case of the interest rate parity (IRP), the PPP has a connection with the MBOP. It is important to think about these connections to realize that theories and concepts explaining the changes in exchange rates are connected.
Additionally, this section examines two approaches to the PPP: absolute and relative PPP. Distinguishing between absolute and relative PPP is important, especially when the discussion is about whether the PPP holds.
Linking the PPP, the MBOP, the IRP, and the IFE
The PPP implies the relationship between inflation differentials and changes in the exchange rate. This relationship is related to the monetary approach to balance of payments (MBOP), the interest rate parity (IRP), and the international Fisher effect (IFE). Chapters 6–8 predict the effect of inflation on exchange rates in the same way.
In Chapters 6 and 7 (the monetary approach to balance of payments), the focus is mainly on monetary policy. In these chapters, changes in monetary policy lead to changes in the price level in the long run. Those chapters show changes in the exchange rate following changes in the price level. The monetary approach to balance of payments predicts depreciation in the higher inflation country’s currency and appreciation in the lower inflation country’s currency.
Chapter 8 highlights the interest rate parity and the international Fisher effect. The interest rate parity relates the nominal interest rate differential to changes in the exchange rate. In this concept, higher nominal interest rates imply higher inflation rates because the international Fisher effect assumes that investors have the same real rate in all countries. Therefore, predictions of the interest rate parity are also such that the currency of the country with higher nominal interest rate is expected to depreciate.
A similarity between the interest rate parity and the purchasing power parity (PPP) is that the PPP also implies a long-run relationship between inflation differentials and changes in the exchange rate.
Figuring the absolute and relative PPP
The PPP implies that the changes in two countries’ price levels affect the exchange rate. According to the PPP, when a country’s inflation rate rises relative to that of the other country, the former’s currency is expected to depreciate. In terms of the different PPP concepts, such as absolute and relative PPP, the nature of the change in the exchange rate is different.
The absolute PPP
The absolute PPP is similar to the Law of One Price. The concept of the Law of One Price means that the prices of the same products in different countries should be equal when they’re measured in a common currency. Consider the dollar–British pound exchange rate. The absolute PPP indicates the following:
where $/£, PUS, and PUK indicate the dollar-British pound exchange rate, the price level in the U.S., and the price level in the U.K., respectively. Note that the absolute PPP can also be shown as the equality of the price levels in both countries where, using the dollar-British pound exchange rate (E), the U.K. price level is expressed in dollars:
Therefore, for the absolute PPP to hold, the dollar–British pound exchange rate should reflect the ratio of the price levels in the U.S. (PUS) and the U.K. (PUK).
The relative PPP
The relative PPP, on the other hand, indicates that the changes in the dollar–British pound exchange rate reflect the changes in the ratio of the U.S. and U.K. price levels (PUS and PUK):
Note the difference between the absolute and relative PPP. The absolute PPP indicates that the exchange rate has to reflect the ratio of two countries’ price levels. However, this is not easy. In reality, there are market imperfections such as nontransferable inputs, transportation costs, tariffs, quotas, and so forth. Therefore, the relative PPP takes these market imperfections in consideration and relaxes the relationship between the exchange rate and the price levels of two countries. It does so by considering the relationship between the changes in the exchange rate and the changes in the ratio of the price levels. All the relative PPP requires is the changes in the exchange rate equal the changes in the ratio of the price level.
From now on, when you read about the PPP in this chapter, it implicitly means the relative PPP, unless indicated otherwise.
Working with the PPP
This section explains how the PPP is derived. Understanding the relationship between inflation differentials and changes in the exchange rate enables you to attach a number to the change in the exchange rate, such as 2 percent depreciation. Then because spot exchange rates are observable, you can apply the expected change in the exchange rate to the spot rate, to predict the future spot rate.
Derivation of the PPP
Suppose that πH and πF indicate the home and foreign country’s inflation rates, respectively. In the following equations, you work with inflation factors of home and foreign countries, (1+ πH) and (1+ πF), respectively.
Remember, the relative PPP implies that changes in an exchange rate follow the changes in both countries’ price levels. You can express this relationship first by realizing that you cannot compare home and foreign country’s inflation factors:
One way to express the relationship between the home and foreign countries’ inflation factors is to adjust the foreign inflation factor with the expected change in the exchange rate. In this case, you have the following:
Here, e indicates the percent change in the exchange rate and is defined as the number of home currency per foreign currency. You can solve this equation for e by dividing both sides of the equation by (1+ πF) and moving 1 to the other side:
This equation indicates that if the home inflation rate is larger than the foreign inflation rate, the ratio of the two inflation factors becomes larger than 1, making e a positive percent change in the exchange rate. This scenario implies a depreciation in the home currency.
On the other hand, if the home inflation rate is smaller than the foreign inflation rate, the ratio of the two inflation factors becomes smaller than 1, making e a negative percent change in the exchange rate. It implies an appreciation in the home currency.
The idea behind the relationship between the change in the exchange rate and the inflation differential is related to the exchange rate determination introduced in Chapter 5. For example, when home inflation rate is higher than foreign inflation rate, you are inclined to buy foreign goods, which leads to exchanging domestic currency for foreign currency. Therefore, domestic currency depreciates.
As an approximation, for a smaller inflation differential between home and foreign country, you can use this formula as the difference between the home and foreign inflation rates:
The previous equation means that the percent change in the exchange rate should approximately equal the difference between the home and foreign inflation rates.
In 2010, the inflation rates based on the Consumer Price Indices of the U.S. and Turkey were 1.64 and 8.52 percent, respectively. Based on these inflation rates, the PPP indicates an expected change in the exchange rate of:
The U.S. and Turkish inflation rates imply a 6.34 percent appreciation in the U.S. dollar. If you use the approximation (1.64 – 8.52 = –6.88), the appreciation in the U.S. dollar becomes 6.88 percent. These two rates of appreciation are considered as similar for most purposes.
Application of the PPP
If you know the current spot rate, you can use the expected change in the exchange rate given in the previous example to predict the next period’s future spot rate. The dollar–Turkish lira exchange rate in 2009 was $0.67. Look at this rate as the spot rate in 2009, and suppose you want to guess the spot rate in 2010. For simplicity, further assume that the mentioned U.S. and Turkish inflation rates for 2010 reflect your expectations for 2010 in 2009.
The following equation connects the current and expected spot rate next period:
Here, the components of the equation imply the expected spot rate at time t+1, the current spot rate at time t, and the change in the exchange rate. Using this formula, calculate your expected exchange rate for 2010:
Based on the inflation differential between the U.S. and Turkey, your expected dollar–Turkish lira exchange rate for 2010 is $0.63, which implies appreciation in the dollar. (By the way, the actual dollar–Turkish lira exchange rate in 2010 was $0.65.)
This numerical example doesn’t constitute a test for the PPP. It aims to show the interpretation of the relevant equations. Clearly, you need to collect decades of data and apply suitable econometric techniques to test for the PPP or use the PPP for forecasting. Also, this example is closer to the future spot rate than what is often observed.
Deciding Whether the PPP Holds
As with the IRP, figuring out whether the PPP holds isn’t exactly straightforward. Sometimes you have to be careful about what a certain test implies. Case in point: the Big Mac standard, a concept whose meaning is sometimes misinterpreted. Additionally, this section examines the factors that interfere with the empirical verification of the PPP.
The PPP and the Big Mac Standard
It’s hard to believe, but we’re talking here about McDonald’s Big Mac. In 1986, a British magazine, the Economist, introduced the results of its worldwide survey at McDonald’s restaurants regarding the prices of Big Macs, to make a case about the PPP (actually, a case against the absolute PPP, as you see later in this section).
In terms of selecting the Big Mac for this purpose, clearly the magazine picked a highly standardized good with little variation (bun, hamburger patty, onion, lettuce, ketchup, and so on) so that the differences in Big Mac prices aren’t attributable to the differences in its content or quality.
After the Economist collected the prices of Big Macs around the world in local currency, it converted these prices into dollars at the market exchange rate. The results showed discrepancies of various sizes among the dollar prices of this seemingly standardized good.
The price of a Big Mac around the world
Think about the nature of the exercise. The Economist’s Big Mac standard is a test for the absolute PPP. The absolute PPP implies that the prices of similar goods around the world should be the same when their prices are expressed in a common currency.
However, the results indicated that Big Mac prices were much higher than in the U.S., especially in some of the European countries, such as France, and were lower in developing countries, such as Mexico.
Since 1986, the Economist has repeated this exercise every year, with similar results showing that the Law of One Price doesn’t hold. As you will read later in this chapter, finding evidence even for the relative PPP is difficult. Therefore, the fact that the Law of One price doesn’t hold isn’t surprising.
Obviously, choosing a standardized good doesn’t solve the problem. International price differences in the Big Mac stem from various circumstances. Based on tastes, demand conditions vary among countries. In some countries, eating at McDonald’s may be a status symbol; in others, a stigma may be attached to it. Among other things, such attitudes may affect the manager’s choice between a high volume/low margin and a low volume/high margin approach to profits.
Additionally, nonfood costs of production vary widely around the world. A variety of local taxes, labor laws and standards, government regulations of fast food, and costs of delivery, advertising, rent, electricity, and more certainly affect the prices of the Big Mac worldwide. These local conditions cannot be avoided by importing Big Macs from other countries: Big Macs are not a tradeable good.
Using the Big Mac standard to evaluate currencies
Every year, after reporting the worldwide dollar prices of Big Mac, the Economist attempts to examine whether currencies are trading at the “right” exchange rates. In other words, it asks whether currencies are overvalued or undervalued, based on the Big Mac standard.
This section first looks at the Economist’s approach to answering whether currencies are trading at the right exchange rates. Second, it raises a couple cautionary points regarding the use of the Big Mac standard for currency overvaluation or undervaluation.
For example, using the numbers from the Big Mac survey of July 2008, the price of a Big Mac was $3.57 in the U.S. and £2.29 in the U.K. Therefore, the implied PPP was calculated as:
In other words, the PPP-implied exchange rate was $1.56 per pound. At the time, the actual dollar–pound exchange rate was $2 per pound. Comparing the PPP-suggested exchange rate to the actual exchange rate, the Economist concluded that the pound was 28 percent overvalued against the dollar:
The extent of other currencies’ overvaluation and undervaluation against the dollar was calculated similarly based on the Big Mac standard. In these calculations, the Swiss franc appears one of the most overvalued currencies; the dollar price of a Big Mac in Switzerland is much higher than its U.S. price.
As another example, based in the 2004 Big Mac standard, the price of Big Mac in the U.S. and Switzerland was $2.90 and SFR3.92. Again, the PPP-implied exchange rate was this:
The PPP-implied exchange rate suggested $0.74 per dollar, but the actual dollar–Swiss franc exchange rate at the time of the publication was $1.25. Therefore, according to the Big Mac standard, the Swiss franc was overvalued by 69 percent in 2004:
According to the Big Mac standard, in most cases nominal exchange rates don’t reflect the ratio of the price levels. And in terms of the cases mentioned, we were paying too much for a British pound and a Swiss franc. The market dollar price of a pound or a Swiss franc exceeded the Big Mac–based PPP rates.
Of course, in some countries, the dollar price of a Big Mac is much lower than the price in the U.S. One of these countries is China. In 2004, the price of a Big Mac in the U.S. and China was $2.90 and CNY10.41, respectively. Therefore, the PPP-suggested exchange rate should be $0.279 per Yuan:
In 2004, whereas the PPP-suggested dollar–yuan exchange rate was $0.279, the actual rate was $0.121 per yuan. According to the Big Mac standard, the yuan was undervalued by 57 percent:
Therefore, the Economist concluded that we all should pay more dollars per yuan. The results from other developing countries, such as the Philippines, are similar to the results in China. Again in 2004, the Big Mac standard calculated the market dollar price of the Philippine peso to be about 58 percent below the level of the burger price parity!
The Big Mac standard implies that the Law of One Price, or the absolute PPP, doesn’t hold. You can’t go around the world and expect similar goods to be sold at the same price expressed in a common currency. The example countries in this section (the U.K., China, and the Philippines) widely vary in terms of their labor laws and standards, wage rates, and other possible nonfood production costs, so their Big Mac prices in dollars also vary.
Be careful when using the results of the Big Mac standard to comment on overvaluation or undervaluation. First, using the terms overvaluation and undervaluation in terms of (almost) freely traded currencies such as the British pound or the Swiss franc is misleading. Do you really want to conclude that foreign exchange markets cannot price them correctly?
Second, other factors are at work. Consider the Swiss case. In Chapter 8, I mention the fact that, especially in terms of short-term investment decisions, the Swiss franc is the go-to currency during global economic downturns. Additionally, the fact that the cost of living is higher in Switzerland has nothing to do with higher inflation rates. In fact, Switzerland is one of the lower-inflation countries with lower nominal interest rates. Therefore, there’s no reason for the Swiss franc to be overvalued.
You can conclude from this examination that, in countries such the U.K. and Switzerland, higher nonfood production costs and various government restrictions are likely factors that increase the price of the Big Mac.
In China, the yuan is a pegged currency. The Chinese government implements extensive controls over the yuan and determines the yuan–dollar exchange rate. In this case, one can talk about overvaluation or undervaluation of the yuan. In fact, you know that the Chinese government has undervalued the yuan, to enhance the country’s export performance.
Empirical evidence on the (relative) PPP
The PPP implies a long-run relationship between the changes in the exchange rate and inflation rate differential between two countries. The idea is that these variables should move together in the same direction. Generally, the evidence for the PPP isn’t overwhelming because the empirical verification of the PPP seems to be sensitive to the choice of the base period and the size of the inflation differential between two countries. For example, everything else constant, a larger inflation differential seems to be helpful in verifying the PPP. This is because variation in inflation is necessary for inflation to be a helpful predictor. With low inflation that varies little, the forces assumed to be important in PPP are overwhelmed by tariff changes, changes in transportation costs and other real factors.
Other obstacles to finding empirical support for the PPP exist. These obstacles weaken the connection between the prices of similar goods in different countries, making it difficult for the PPP to hold. Some of these barriers are nontradable goods, government control of prices, restrictions on international trade, and transportation costs.
Some goods and services are called nontradables because their transportation costs are prohibitively high (housing and haircuts, for example). Prices of nontraded goods and services aren’t linked among countries because domestic market conditions solely determine their prices. When the domestic market conditions change, prices of nontraded goods change. However, these changes in prices may not reflect the changes in the price of a similar nontraded good in other countries. This situation leads to deviations from the PPP.
Even if a good is tradable, a large increase in its transportation cost or the introduction of a government restriction on its trade in the form of tariffs, quotas, and so on increase the price of this good and, therefore, limit its trade. For example, in November 2012, the U.S. International Trade Commission decided to impose a tariff between 24 and 36 percent on Chinese-made solar panels. The reason was the government provided subsidy to solar panel production in China, which was believed to have provided an unfair advantage to Chinese suppliers. Any type of trade impediment as in this example weakens the relationship between changes in the exchange rate and inflation differential, which also leads to deviations from the PPP.