Relative PPP - Another Derivation • The relationship can be simplified as follows: e f ≈ I h _ I f This formula is appropriate only when the inflation differential is small. Old Data, Old Data, Old Data Example: Suppose that the inflation rate in U.S. is 9%, while U.K.’s rate is 5%. Then PPP suggests that the exchange rate should appreciate by about 4%. U.S. will import more, while U.K. will import less, until the exchange rate has risen by about 4%. At this point, U.K. goods will cost 5+4=9% more to U.S. consumers, while U.S. goods will cost 9-4=5% more to U.K. consumers. 4-31 Madura
Graphic Analysis of Purchasing Power Parity Inflation Rate Differential (%) home inflation rate - foreign inflation rate 4 PPP line 2 % Δ in the -3 -1 1 3 foreign currency spot rate -2 -4 4-32 Madura
Graphic Analysis of Purchasing Power Parity Inflation Rate Differential (%) home inflation rate - foreign inflation rate 4 PPP line Increased purchasing power of 2 foreign goods % Δ in the -3 -1 1 3 foreign Decreased currency purchasing spot rate -2 power of foreign goods -4 4-33 Madura
Purchasing Power Parity • If the actual inflation differential and exchange rate % change for two or more countries deviate significantly from the PPP line over time, then PPP does not hold. • A statistical test can be developed by applying regression analysis to the historical exchange rates and inflation differentials: e f = a 0 + a 1 { (1+ I h )/(1+ I f ) - 1 } + μ The appropriate t -tests are then applied to a 0 and a 1 , whose hypothesized values are 0 and 1 respectively. 4-34 Madura
Purchasing Power Parity • PPP may not occur consistently due to: ¤ the existence of other influential factors like differentials in income levels and risk, as well as government controls; and ¤ the lack of substitutes for traded goods. • A limitation in testing PPP is that the results may vary according to the base period used. • PPP can also be tested by assessing a “real” exchange rate over time. If this rate reverts to some mean level over time, this would suggest that it is constant in the long run. 4-35 Madura
The Real Exchange Rate • For a country which relies heavily on trade to maintain living standards, it is arguable that the exchange rate that is important is not the rate at which the country’s currency exchanges for another, but the rate at which the country’s goods exchange in international trade. • One such calculation of this is the real exchange rate, which relates the effective exchange rate to the price of domestic goods relative to the price of foreign goods. 4-36 International Business Economics: Piggott and Cook
The Effective Exchange Rate • Since a currency varies against other currencies, it sometimes makes little sense to refer to one particular bilateral rate intended to represent the foreign exchange value of that currency. • What is needed is some kind of average foreign currency value, of, say, the pound or Deutsche mark against several other currencies, and indeed this is what is currently computed for all major currencies. • These “average exchange rates” are termed effective exchange rates and are calculated as an index. 4-37 International Business Economics: Piggott and Cook
The Effective Exchange Rate Effective exchange rates (1991=100) Sterling US$ DM Yen 1985 107.4 130.6 81.2 68.3 1986 99.5 113.9 89.8 89.9 1987 97.9 105.2 96.0 97.5 1988 103.8 100.1 95.8 106.5 1989 100.6 102.8 95.1 99.9 1990 99.1 101.0 100.4 91.8 1991 100.0 100.0 100.0 100.0 1992 96.5 98.6 103.8 105.4 1993 88.4 100.7 107.9 126.6 1994 89.2 100.1 109.7 136.3 1995 85.4 101.0 116.8 143.9 1996 87.3 107.6 115.0 125.5 4-38 International Business Economics: Piggott and Cook
The Effective Exchange Rate • The effective exchange rate is an index of the weighted-average foreign exchange value of a currency against a basket of other currencies. ¤ This index summarizes in one number the value of the currency against a number of other currencies. • The weights are usually based on a country’s trade against its trading partners. 4-39 Extra-Man
The Effective Exchange Rate Example Suppose the U.S. only trades with Japan and Germany. Year 1 yen 100/$ index 100 DM 1.50/$ index 100 Year 2 yen 105/$ index 105 DM 1.65/$ index 110 Year 3 yen 110/$ index 110 DM 1.65/$ index 110 Total U.S. trade = $1000 billion with Japan $ 600 billion weight: 60% with Germany $ 400 billion weight: 40% Effective exchange rate for the $: Year 1: 100 Year 2: 107 Year 3: 110 4-40 Extra-Man
Openness in Goods and Financial Markets Opening the Economy to International Transactions Two dimensions of openness: 1. Openness in Goods Markets 2. Openness in Financial Markets 4-41
4-42 Openness in Goods Markets
Openness in Goods Markets Observations of U.S. Exports and Imports • Exports and imports in the U.S. were 5% of GDP in 1960, are 12% (11.2% exports, 13% imports) of GDP today. • Decline in exports and imports from 1929-1936 was due in large part to the Smoot-Hawley Act of 1930, which led to sharp increases in tariffs with the hope of increasing the demand for domestic goods, thereby helping the U.S. economy recover from the Great Depression. • Large trade surpluses occurred in the 1940s, while large trade deficits occurred in the 1980s. 4-43
Openness in Goods Markets Measuring the Degree of Openness • Volume of Trade: Ratio of exports or imports to GDP (U.S. = 12%) • Tradable Goods Ratio: Percent of output that competes in foreign markets (U.S. = 60%) 4-44
Openness in Goods Markets A Look Around the World Country Export Ratio (%) Country Export Ratio (%) United States 12 Switzerland 40 Japan 10 Austria 38 Germany 23 Belgium 73 United Kingdom 29 Luxembourg 91 4-45
Openness in Goods Markets What Do You Think... Can exports exceed GDP? The trick is to realize that exports and imports may be exports and imports of intermediate goods. E.g., a country imports intermediate good for $1 billion and transfers them into final goods using only labor, which costs $200 million. Assume that there is no profit. The value of final goods is thus equal to $1,200 million. Assume that $1 billion worth of goods is exported and the rest is consumed in the country. Recall that GDP is value added in the economy ($200 million here), so that the ratio of exports to GDP is equal to 5. 4-46
Openness in Goods Markets The Choice Between Domestic and Foreign Goods Real Exchange Rates: Price of foreign goods in terms of domestic goods Nominal Exchange Rates: The relative prices of currencies 4-47
Openness in Goods Markets The Choice Between Domestic and Foreign Goods Nominal Exchange Rates: Two Views 1. The price of domestic currency in terms of foreign currency. 2. The price of foreign currency in terms of domestic currency. For Example: December 1998: Nominal exchange between U.S. dollar and German Deutschemark (DM) $ in terms of DM: 1$ = 1.67 DM DM in terms of $s: 1DM = 0.60 $ 4-48
Openness in Goods Markets The Choice Between Domestic and Foreign Goods Nominal Exchange Rates--Choosing a Definition: Nominal exchange rates ( E ): price of foreign currency in terms of domestic currency For Example: E between the U.S. (domestic) and Germany (foreign) is the price of DM in terms of $ E = .60 (December 1998) 4-49
Openness in Goods Markets The Choice Between Domestic and Foreign Goods Measuring Changes in the Nominal Exchange Rate ( E ) • Appreciation of domestic currency corresponds to a decrease in E • Depreciation of domestic currency corresponds to an increase in E 4-50
Openness in Goods Markets The Nominal Exchange Rate, Appreciation, & Depreciation: Germany and the United States* Nominal Exchange Rate, E (Price of DM in terms of dollars) Appreciation of the dollar Price of dollars in DM increases Equivalently: Price of DM in dollars decreases Equivalently: Exchange rate decreases: E ↓ Depreciation of the dollar Price of dollars in DM decreases *Note that E is in the Equivalently: form of “American Price of DM in dollars increases Quote” or “Direct Equivalently: Quote” here. Exchange rate increases: E ↑ 4-51
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Openness in Goods Markets The Nominal Exchange Rate between the DM and the Dollar 1978 - 1998 A sharp dollar appreciation in the first half of the 1980s was followed by an equally sharp dollar depreciation in the second half of the 1980s. 4-53
Openness in Goods Markets The Choice Between Domestic and Foreign Goods Observations on E between U.S. and Germany: The trend increase in E 1. 1975 DM = 40 cents 1998 DM = 60 cents The large fluctuations in E 2. Early 1980s the value of DM dropped 57 cents to 30 cents Late 1980s the value of DM rose to 60 cents 4-54
Openness in Goods Markets The Choice Between Domestic and Foreign Goods Question: Does a decrease in E of U.S. $s for DMs necessarily mean U.S. citizens can buy more German goods with their dollars? Hint: What is the inflation rate in Germany? 4-55
Openness in Goods Markets The Choice Between Domestic and Foreign Goods Calculating Real Exchange Rates The price of one German good (Mercedes SL) in terms of one U.S. Good (Cadillac Seville) 1. Convert the price of the Mercedes from DM to $s P DM = 100,000 DM = .60$s P$s = 100,000 x .60 = $60,000 2. Compute the ratio of the $ price of the Mercedes to the Cadillac (Cadillac price = $40,000) Real exchange rate between U.S. & Germany = $ 60 , 000 = 1 . 5 $ 40 , 000 4-56
Openness in Goods Markets The Choice Between Domestic and Foreign Goods Expanding the Real Exchange Rate Calculation to the Entire Economic System If: P = U.S. GDP Deflator P* = German GDP Deflator E = DM-dollar nominal exchange rate Then: Price of German goods in US$ = EP* Real exchange rate ( ε ) = EP* P NOTE: Real exchange rates ( ε ) are index numbers and measure only relative change. 4-57
Openness in Goods Markets The Choice Between Domestic and Foreign Goods The Construction of the Real Exchange Rate Price of German Price of German goods in DM goods in dollars Real exchange P* EP* rate ε = EP* Price of U.S. P goods in dollars P 4-58
Openness in Goods Markets The Real Exchange Rate and Real Appreciation and Real Depreciation* Real Exchange Rate, ε (Price of German goods in terms of U.S. goods) Real Appreciation Price of U.S. goods in terms of German goods increases Equivalently: Price of German goods in terms of U.S. goods decreases Equivalently: Real exchange rate decreases: ε ↓ Real Depreciation Price of U.S. goods in terms of German goods decreases Equivalently: Price of German goods in terms of U.S. goods increases Equivalently: Real exchange rate decreases: ε ↑ *From the view of United States looking at Germany 4-59
4-60
Openness in Goods Markets The Choice Between Domestic and Foreign Goods Real and Nominal Exchange Rates Between Germany and the U.S., 1975-1998 4-61 4-61
Openness in Goods Markets The Choice Between Domestic and Foreign Goods The Real and Nominal Exchange Rates Between Germany and the U.S. 1975-1998 Observations: • The real 1998 exchange 0.60 was the same as 1975. * E and P both rose, so remained unchanged. P ∈= E P Movements in ε are driven primarily by change in E • 4-62
Openness in Goods Markets The Choice Between Domestic and Foreign Goods The Country Composition of U.S. Merchandise Trade, 1998 Exports to Imports from Countries $ BillionsPercent $ BillionsPercent Canada 156 23 177 19 Western Europe 159 24 193 21 Japan 57 8 121 13 Mexico 78 12 95 11 Asia* 126 19 247 27 OPEC** 15 2 19 2 Others 80 11 67 7 Total 671 100 919 100 *Not including Japan. **OPEC: Organization of Petroleum Exporting Countries. 4-63
Openness in Goods Markets The Choice Between Domestic and Foreign Goods Country Composition of U.S. Merchandise Trade, 1998 Observations: • Canada and Western Europe account for 40-47% of U.S. trade. • Large trade deficit with Japan: Exports to = $57 Billion Imports from = $121 Billion 4-64
Openness in Goods Markets The Choice Between Domestic and Foreign Goods Real Multilateral Exchange Rates • The real exchange rate when considering many countries • Calculate by using each country’s share of trade as the weight for that country 4-65
Openness in Goods Markets The Choice Between Domestic and Foreign Goods The U.S. Effective Real Exchange Rate 1975 - 1998 The multilateral real U.S. exchange rate is also called the U.S. trade- weighted real exchange rate, and the U.S. effective real exchange rate. 4-66 4-66
The Real Exchange Rate Real magnitudes are constructed from nominal magnitudes by adjusting for the appropriate price levels (P) or inflation rates. nominal income Real income = $ per market basket $55,000/year = $250/market basket = 220 market baskets/year in 1990 (define this as 100) So, real income is measured in terms of real goods and services. 4-67
The Real Exchange Rate In 1991, nominal income rises by 10% (to $60,500) while the price of a market basket rises by 8% (to $270). To express real income in 1991 as an index: real income (1991) index (1991) = real income (1990) (60,500/270) = 220 = 1.0185 Real income has increased by 1.85%. 4-68
The Real Exchange Rate The nominal exchange rate (e.g., S=$0.60/DM) measures the rate of exchange between the currencies of two countries. Currency traders quote nominal exchange rates. The real exchange rate is calculated by correcting the nominal exchange rate for the price levels in two countries. 4-69
The Real Exchange Rate Assuming the case that absolute purchasing power parity holds: ($600 Price/USgood) $0.60/DM = (DM 1000 Price/GermanGood) LHS = 1 = US good / German good RHS In other words, when PPP holds, identical US goods and German goods exchange for each other on a one-for-one basis; and the real exchange rate is constant. 4-70
The Real Exchange Rate Spot (Nominal, t ) Spot (Real, t ) = Spot ( PPP , t ) If real exchange rate index = $0.60/DM / $0.50/DM = 1.2 => DM is "overvalued" on a PPP basis, since DM 1 exchanges for $0.60 > PPP spot exchange $0.50 or 1.0 German good can be exchanged for 1.2 US goods and sellers of German goods have lost competitiveness. 4-71
Evidence: The Law of One Price • One test of the Law of One Price is the Big Mac index, which has been published annually in The Economist since 1986. http://www.economist.com/markets/Bigmac/Index.cfm • The Big Mac index (burgernomics) was devised as a light-hearted guide to whether currencies are at their “correct” level, based on PPP – the notion that a dollar should buy the same amount in all countries. • Thus in the long run, the exchange rate between two countries should move towards the rate that equalizes the prices of an identical basket of goods and services in each country. • In other words, a dollar should buy the same amount everywhere. 4-72 The Economist
Evidence: The Law of One Price ¤ Our “basket” is a McDonalds’ Big Mac, which is produced and consumed in 120 countries around the world. ¤ The Big Mac PPP is the exchange rate that would leave hamburgers costing the same in America as abroad. ¤ Comparing actual exchange rates with PPPs signals whether a currency is under- or over- valued. 4-73 The Economist
Evidence: The Law of One Price • The result of the 2000 survey suggested that the average price of a Big Mac in the U.S. was $2.51, but was as little as $1.19 in Malaysia, and as much as $3.58 in Israel. • Hence the Israeli shekel is the most overvalued currency (by 43%), while the Malaysian ringgit is the most undervalued (by 53%). 4-74 The Economist
25/04/00 Big Mac foreign-currency price = PPP rate US($) price (of the US$) convert into dollars at the spot rate 4-75 The Economist
4-76 25/04/00 The Economist
The first column of the table shows local-currency prices of a Big Mac, while the second converts them into dollars. The third column calculates PPPs. foreign currency price Big Mac PPP rate = (of the US$) US($) price US($) price Big Mac PPP rate = (of the foreign foreign currency price currency) spot rate Big Mac PPP rate – Under (-) / Over (+) (of foreign currency) (of the foreign currency) x 100 valuation against = Big Mac PPP rate the dollar, % (of the foreign currency) 4-77
Evidence: The Law of One Price Example 1. Canada Purchasing power of C$2.85 = Purchasing power of $2.51 = a Big Mac Hence Big Mac PPP implies 1 C$ = $ (2.51/2.85) However from the market spot rate, 1 C$ = $ (1/1.47) (-)/(+) valuation against $, % (based on Big Mac PPP) (1/1.47) - (2.51/2.85) (1/1.47) = = = - 1 (2.51/2.85) (2.51/2.85) = - 22.8% 4-78
Evidence: The Law of One Price Example 2. Denmark Purchasing power of 24.75 DKr = Purchasing power of $2.51 = a Big Mac Hence Big Mac PPP implies 1 DKr = $ (2.51/24.75) However from the market spot rate, 1 DKr = $ (1/8.04) (-)/(+) valuation against $, % (based on Big Mac PPP) (1/8.04) - (2.51/24.75) (1/8.04) = = - 1 (2.51/24.75) (2.51/24.75) = + 22.6% 4-79
4-80 17/04/01
4-81 17/04/01
The average price of a Big Mac in the U.S. is $2.54 (including sales tax). In Japan, Big Mac scoffers have to pay ¥294, or $2.38 at current exchange rates. Dividing the yen price by the dollar price gives a Big Mac PPP of ¥116. Comparing that with this week’s rate of ¥124 implies that the yen is 6% undervalued. (1/124 - 1/116)/(1/116) = -0.0645 = -6% The cheapest Big Macs are found in China, Malaysia, the Philippines and South Africa, and all cost less than $1.20 – these countries have the most undervalued currencies, by more than 50%. The most expensive Big Macs are found in Britain, Denmark and Switzerland – they have the most overvalued currencies. Sterling, for example is 12% overvalued against the dollar – less than two years ago, it was overvalued by 26%. 4-82
Overall, the dollar has never looked so overvalued during 15 years of burgernomics. In the mid 1990s the dollar was cheap against most currencies; now it looks dear against all but three. The most undervalued of the rich-world currencies are the Australian and New Zealand dollars, which are both 40-45% below McParity. They need to ketchup. All the emerging-market currencies are undervalued against the dollar on a Big Mac PPP basis. That, in turn, means that a currency such as Argentina’s peso, which is undervalued only a tad against the dollar, is massively overvalued compared with other currencies, such as the Brazilian real and virtually all of the East Asian currencies. 4-83
4-84 25/04/02
25/04/02 4-85
The average American price has fallen slightly over the past year, to $2.49. The cheapest Big Mac is in Argentina (78 cents), after its massive devaluation; the most expensive ($3.81) is in Switzerland. By this measure, the Argentine peso is the most undervalued currency and the Swiss franc the most overvalued. The euro is only 5% undervalued relative to its Big Mac PPP, far less than many economists claim. The euro area may have a single currency, but the price of a Big Mac varies from euro 2.15 in Greece to euro 2.95 in France. However, that range has narrowed from a year ago. The Australian dollar is the most undervalued rich-world currency, 35% below McParity. No wonder the Australian economy was so strong last year. Sterling, by contrast, is one of the few currencies that is overvalued against the dollar, by 16%; it is 21% too strong against the euro. 4-86
Overall, the dollar looks overvalued. Over half the emerging-market currencies are more than 30% undervalued. That implies that any currency close to McParity (eg, the Argentine peso last year, or the Mexican peso today) will be overvalued against other emerging-market rivals. Adjustment back towards PPP does not always come through a shift in exchange rates. It can also come about through price changes. In 1995 the yen was 100% overvalued. It has since fallen by 35%; but the price of a Japanese burger has also dropped by one-third. In the early 1990s the Big Mac index repeatedly signalled that the dollar was undervalued, yet it continued to slide for several years until it flipped around. Our latest figures suggest that, sooner or later, the mighty dollar will tumble... 4-87
4-88 Apr 24th 2003
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4-91
Evidence: The Law of One Price • Some find the Big Mac index hard to swallow. Not only does the PPP theory hold only for the very long run, but hamburgers are a flawed measure of PPP. • Local prices may be distorted by trade barriers on beef, sales taxes, local competition and changes in the cost of non-traded inputs such as rents. • But despite its flaws, the Big Mac index produces PPP estimates close to those derived by more sophisticated methods. • A currency can deviate from PPP for long periods, but several studies have found that the Big Mac PPP is a useful predictor of future movements – “betting on the most undervalued of the main currencies each year is a profitable strategy.” 4-92 The Economist
Evidence: The Law of One Price ¤ Indeed, the Big Mac has had several forecasting successes. ¤ When the euro was launched at the start of 1999, most forecasters predicted that it would rise against the dollar. But the euro has instead tumbled – exactly as the Big Mac index had signaled. At the start of 1999, euro burgers were much dearer than American ones, suggesting that the euro had started off significantly overvalued. ¤ One of the best-known hedge funds, Soros Fund Management, admitted that it chewed over the sell signal given by the Big Mac index when the euro was launched, but then decided to ignore it. The euro tumbled, and Soros was cheesed off. 4-93 The Economist
Year 2000 Year 2001 2.51/2.56 = 0.98 2.54/2.57 = 0.99 (0.93-0.98)/0.98 = -5% (0.88-0.99)/0.99 = -11% € is undervalued by 5% € is undervalued by 11% The average price today in the 12 euro countries is euro 2.57, or $2.27 at current exchange rates. The euro’s Big Mac PPP against the dollar is euro 1=$0.99, which shows that it has now undershot McParity by 11%. That, in turn, implies that sterling is 26% overvalued against the euro. Please update the Big Mac Index at http://www.economist.com/PrinterFriendly.cfm?Story_ID=2708584 (also appear in this week’s reading list). 4-94
July 2007 4-95
July 2007 4-96 * *
July 2007 4-97
The price of a burger depends heavily on local inputs such as rent and wages, which are not easily arbitraged across borders and tend to be lower in poorer countries. For this reason PPP is a better guide to currency misalignments between countries at a similar stage of development. 4-98
The most overvalued currencies are found on the rich fringes of the European Union: in Iceland, Norway and Switzerland. Indeed, nearly all rich-world currencies are expensive compared with the dollar. The exception is the yen, undervalued by 33%. This anomaly seems to justify fears that speculative carry trades, where funds from low-interest countries such as Japan are used to buy high-yield currencies, have pushed the yen too low. But broader measures of PPP suggest the yen is close to fair value. 4-99
Carry Trade: borrow money at a cheaper rate than you can earn on an investment elsewhere 2007 The biggest risk is generally that the exchange rate moves against you – the higher-interest rate currency rapidly devalues, reducing the value of your assets relative to your borrowing. That's why these trades are often described as “picking up nickels in front of a steamroller” 4-100
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