VI. Purchasing Power ParityRead Chapter 4, pp. 1021111. The Law of One Price (LOP)LOPConditions for LOP to hold2. Purchasing Power Parity (PPP)Absolute PPPRelative PPPEmpirical evidenceReal Interest Rate Parity and international Fisher effect3. Real Exchange Rate Definition Effective exchange ratesExchange rate pass-through

Overview: International Parity ConditionsSome fundamental questions that managers of MNEs, international portfolio investors, importers, exporters and government officials must deal with every day are:What are the determinants of exchange rates?Are changes in exchange rates predictable?The economic theories that link exchange rates, price levels, and interest rates together are called international parity conditions.These international parity conditions form the core of the financial theory that is unique to international finance.We look at the relation between exchange and price levels.0

1. The Law of One Price (LOP)1.1. The Law of One Price (LOP) LOP: Commodity arbitrage should equalize the prices of a same good in two countries, when measured in the same currency (except for transportation costs).So, for spot rate St measured as ($/), Pt = St PtPt:$-price of an iPod in Canada Pt:-price of an iPod in U.K.

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1.1. The Law of One Price (LOP)Example: Pt = $100, Pt = 50.Q1: What is spot rate at which the LOP holds?St(LOP) = $100/50 = $2/.Q2: What happens if St moves to $1/? St Pt = ($1/)(50) = $50, while Pt=$100. Arbitragers buy in U.K. and sell in Canada.Then St Pt goes up (e.g. $75) and Pt goes down (e.g. $75): At this point, there is no incentives for further arbitrage. 0

1.2 Conditions for LOPHomogeneity of the goodNo barriers to trade (tariffs, import duties and quotas.)No transportation costs.0

2. Purchasing power parity (PPP)2.1 Absolute purchasing power parityArbitrage in price levels leads to absolute PPP. The price level refers to an weighted average price of all goods and services in the economy. Pt: price level in Canada measured in $ Pt: price level in U.K. measured in .Then arbitrage ensures, Pt = St Pt.

2.2 Relative purchasing power parityInterpret Pt as price index.0

2.2 Relative purchasing power parityQ: SPPP? (200/100) = (150/100) [St+1/3.00]. St+1= $4.00/.0

2.2 Relative purchasing power parityRecall that inflation rates are defined as0Rewrite the relative version of the PPP, using and *:

Exhibit 4.2 Purchasing Power Parity (PPP)Percent change in the spot exchangerate for foreign currencyPercent difference inexpected rates of inflation(foreign relative tohome country)24-5-4-1-3-1-4-22413531-2-3-660

2.2 Relative purchasing power parityRelative PPP describes the linkage among domestic and foreign inflation, and exchange rates. The percentage change in the exchange rate is approximately equal to the difference between domestic and foreign inflation. In other words, the depreciation or appreciation of the exchange rate offsets the difference in inflation rates. Justification for the PPP: Imagine a high inflation in Canada but no change in spot exchange rate. Then imports will become more competitive, and exports less competitive, leading to a deficit on current account, and exerting downward pressure on dollar.

2.2 Relative purchasing power parityExample: Suppose $(Canada)=5% p.a., and (U.K.)=2% p.a. Then the is expected to appreciate roughly by 3% p.a.This relation holds fairly well for high inflation countries.Example: In early 1980s, Israel began running high inflation. First 2 quarter of 1984:Israel = 197.2% p.a.$= 4.2% p.a.(St+1 - St)/St = - 192.8% p.a.

2.3 Empirical evidence2.3 Empirical evidence Q: Is St = Pt/P*t ? A: No. Reasons:Different basket of goods for price indexes.Non-traded goods.Barriers to tradeTransportation costsLong adjustment timePPP is still useful asa long-run benchmark exchange ratea basis to make a more meaningful international comparisons of economic data.

2.3 Empirical evidence GDP in 2002 measured in market and PPP exchange rate(column 3 is based on market, and column 5 based on PPP exchange rate.)

Rank

Country

GDP (US$ billion)

Country

GDP (US$ billion)

1

US

10,416

US

10,138

2

Japan

3,978

China

5,732

3

Germany

1,978

Japan

3,261

4

UK

1,552

India

2,694

5

France

1,409

Germany

2,171

6

China

1,237

France

1,554

7

Italy

1,180

UK

1,510

8

Canada

715

Italy

1,481

9

Spain

649

Brazil

1,311

10

Mexico

637

Russia

1,141

2.4 Real interest parity and international Fisher effect[Beginning of optional material]Q: How are interest rates in foreign money markets related to dollar interest rates? We will first look at the "Uncovered Interest Parity" (UIP).Uncovered Interest ParityRecall covered interest parity: (1+i$)=(1+i)(Ft/St)Replace Ft with EtSt+1 to get the uncovered interest parity: (1+i$) = (1+i)(EtSt+1/St)

2.4 Real interest parity and international Fisher effectExample: An investor with $1 million .i : 9.0% p.a. i$ : 4.5% p.a.Spot: $1.6689/ Expected spot rate: $1.6000/(1) Investor can invest $1 m at dollar interest rate and earn,(1 + i$)($1 m) = (1.045)($1 m) = $1.045m(2) Or, convert $1m into at the spot market, receiving,$1 m*/($1.6689/) = 0.5992 m.(3) Then invest these proceeds in a deposit to receive:(1 + i) * 0.5992 m = 1.09 * 0.5992 = 0.6531 mHis expected return in dollars is:(1/St)*(1+i)*Et St+1= 0.6531m*($l.60/) = $1.045 mNote that the expected returns are the same regardless of the currency invested.

2.4 Real interest parity and international Fisher effectThe relation equalizing expected returns is called the Uncovered Interest Parity (UIP):(1 + i$) = (1 + i) (EtSt+1/St)UIP: The return in $ deposits is the same as the expected return on deposits (e.g. i + expected capital loss on holding ).Investors are willing to hold dollar bonds with yield lower than bonds, because dollars are expected to appreciate.The UIP says that approximate link between interest rates (absent capital controls) is given by i$ - i E(e), where e (EtSt+1 St) /StThis is also known as the international Fisher effect.

2.4 Real interest parity and international Fisher effectConditions Underlying Uncovered Interest Parity:a. No Capital Controlsb. No Default Riskc. No Political RiskThese are also the conditions underlying Covered Interest Parity (CIP). However, for UIP, we also must add:d. No Risk Aversion.

Implication of PPP and UIP combined:Combining PPP and UIP

Recall UIP: (1 + i$) = (1 + i)(EtSt+1/St) or i$ - i E(e)Relative PPP:or $ - E(e), where e Et(St+1-St)/StNow combine UIP and PPP: i$ - i $ - , or i$ - $ i - , But by Fisher relation, the last equation is equal to Et(r$) Et(r), where r denotes real interest rate.It says that the expected real interest rate is the same across countries. [End of optional material]

3. Real exchange rateHow can we measure the relative competitiveness of a country's goods? Example: Competitiveness in Canada's timberRelative competitiveness of Canada's timber depends ona) the change in price level in two countries and b) the change in exchange rates The price of Canadian timber: $2 per unit in Canada.at $2/: selling price in U.K. is 1.at $1/: selling price in U.K. is 1/2.

3.1 Definition: real exchange rateThe real exchange rate for $ [the currency in numerator], q, is defined as Assume Pt = P,tSt, P$,t+1= price of a hamburger in Canada.Pt+1=$4, St+1 = $2/, P,t+1 = 2.50:With $Pt+1: you can buy 1 hamburger in Canada, butyou can buy q = 0.8 hamburgers in U.K.

3.1 Definition: real exchange rateIf q < 1 then it means that the inflation at home has been less than inflation abroad, after adjusting for the change in the exchange rates. there has been an improvement in export competitivenessAlternative interpretation Suppose the annual inflation rate is 5% in Canada, and 3% in UK. PPP relation predicts that $ will depreciate about 2% against . If $ indeed depreciates 2%, the PPP holds, and the real exchange rate, q, is equal to one.

3.1 Definition: real exchange rateIf U$ indeed depreciates 6%, the $ depreciates by more than the inflation differential, and the real exchange rate, q, is equal to 0.96, strengthening the Canadian competitiveness in export market.Real exchange rate, q, measures the extent to which the actual exchange rates deviate from PPP. Whether PPP holds or not has an important implications for international trade.Real exchange rate is an useful tool in predicting upward or downward pressure on a country balance of payments and exchange rate.

Example: Swiss firm selling product in Canada:Q. Has Canada gained or lost competitiveness in this example?Relative Price in year t: P /(P*t St) = $120/$100 = 1.2Case 1: no change in $ price: Pt+1/( P*t+1 St+1) = $120/$80 = 1.5. q=1.25 in year t+1. In this case, the Canadian firm lost competitiveness.Case 2: decrease in $ pricePt+1/( P*t+1 St+1) = $96/$80 = 1.2. q=1 in year t+1

Exhibit 4.3 IMFs Real Effective Exchange Rate Indexes for the United States & Japan (1995 = 100)Source: International Financial Statistics, International Monetary Fund, monthly, 1995=100.0198119831985198719891991199319951997199920012003180160140120100806040200United StatesJapan

3.2 Effective exchange ratesWhat happens to the competitiveness of Canada in international trade if dollar appreciates with respect to some trading partner's currencies, but depreciates with respect to others?We look at the trade-volume-weighted average of real (nominal) exchange rates, called the real (nominal) effective exchange rates. An increase in the real effective exchange rates signifies a loss in average competitiveness in international trade.

Exchange rate pass-throughPass-through is the measure of response of imported and exported product prices to exchange rate changes. Suppose a BMW cost $70,000 in Canada and 70,000 in Germany, and spot rate of $1.00/.Assume the euro appreciates 20% to $1.20/. If the price of the BMW in Canada rises only by 7.14% (rather than by 20%) to $75,000, then the degree of pass-through is partial: degree of pass-through = 7.14%/20% = 35.7%.The remaining 64.3% of the exchange rate change has been absorbed by the BMW.