C HA P T E R 8 Relationships

C HA P T E R 8 Relationships among Inflation, Interest Rates, and Exchange Rates

Chapter Overview A. Purchasing Power Parity (PPP) B. International Fisher Effect (IFE) C. Comparison of the IRP, PPP, and IFE Theories

Chapter 8 Objectives This chapter will: A. Explain the purchasing power parity (PPP) theory and its implications for exchange rate changes B. Explain the International Fisher effect (IFE) theory and its implications for exchange rate changes C. Compare the PPP theory, the IFE theory, and theory of interest rate parity (IRP), which was introduced in the previous chapter

Purchasing Power Parity (PPP)-- Prices and Exchange Rates Interpretations of Purchasing Power Parity a. Absolute Form of PPP The Law of one price states that all else being equal (no transaction costs) a product’s price should be the same in all markets Even if prices for a particular product are in different currencies, the law of one price states that P$ S = P¥ Where the price of the product in US dollars (P$), multiplied by the spot exchange rate (S, yen per dollar), equals the price of the product in Japanese yen (P¥)

Prices and Exchange Rates Conversely, if the prices were stated in local currencies, and markets were efficient, the exchange rate could be deduced from the relative local product prices ¥ $

Purchasing Power Parity & The Law of One Price If the Law of One Price were true for all goods, the purchasing power parity (PPP) exchange rate could be found from any set of prices Through price comparison, prices of individual products can be determined through the PPP exchange rate This is the absolute theory of purchasing power parity Absolute PPP states that the spot exchange rate is determined by the relative prices of similar basket of goods

The Hamburger Standard The “Big Mac Index, ” as it has been christened by The Economist is a prime example of this law of one price : ◦ Assuming that the Big Mac is identical in all countries, it serves as a comparison point as to whether or not currencies are trading at market prices ◦ Big Mac in China costs Yuan 11. 0 (local currency), while the same Big Mac in the US costs $3. 41 ◦ The actual exchange rate was Yuan 7. 60/$ at the time

The Hamburger Standard ◦ The price of a Big Mac in Chinese Yuan in U. S. dollar-terms was therefore: Yuan 11. 0 Yuan 7. 60/$ = $1. 45 ◦ The Economist then calculates the implied purchasing power parity rate of exchange using the actual price of the Big Mac in China over the price of the Big Mac in U. S. dollars: Yuan 11. 0 = $3. 41 Yuan 3. 23/$

The Hamburger Standard ◦ Now comparing the implied PPP rate of exchange, Yuan 3. 23/$, with the actual market rate of exchange at that time, Yuan 7. 60/$, the degree to which the Chinese yuan is either undervalued or overvalued versus the U. S. dollar is calculated: Yuan 3. 23/$ - Yuan 7. 60/$ = -58%

Exhibit 6. 1 Cash and Carry: The Hamburger Standard

Exhibit 6. 1 Cash and Carry: The Hamburger Standard (cont. )

Relative Purchasing Power Parity 1. Interpretations of Purchasing Power b. Relative Form of PPP Parity If the assumptions of absolute PPP theory are relaxed, we observe relative purchasing power parity ◦ This idea is that PPP is not particularly helpful in determining what the spot rate is today, but that the relative change in prices between countries over a period of time determines the change in exchange rates ◦ Moreover, if the spot rate between 2 countries starts in equilibrium, any change in the differential rate of inflation between them tends to be offset over the long run by an equal but opposite change in the spot rate

Relative Purchasing Power Parity 1. Interpretations of Purchasing Power Parity b. Relative Form of PPP For example: 1£=1. 6$. US inflation rate is 9%. UK inflation is 5%. What will happen? Answer: US inflation is 4% higher than UK US products are 4% higher than UK US customers convert $ to £ to purchase cheap UK products This buying pressuring of £ and selling pressure of $ will force £ to appreciate until the prices in UK are the same as in US No benefits for US customers to buy from UK market.

Relative Purchasing Power Parity 1. Interpretations of Purchasing Power Parity b. Relative Form of PPP General equation: ef = 1+Ih -1 1+If Simplified equation: ef = I h - I f Ih: Home nominal inflation. If: Foreign nominal inflation. ef: Changes in exchange rate. ef can be defined as: ef = (St+1 - St)/St

Relative Purchasing Power Parity 1. Interpretations of Purchasing Power Parity b. Relative Form of PPP Previous example: 1£=1. 6$. US inflation rate is 9%. UK inflation is 5%. What is the new exchange rate? ef = 1+Ih -1 =(1+0. 09)/(1+0. 05)-1 ≃ 4% 1+If So, new £ worth (1+0. 04)*1. 6 = $1. 66/£ Simplified equation: ef= Ih- If =0. 09 -0. 05= 4% Ih: Home inflation rate. If: Foreign inflation rate. ef: Changes in exchange rate.

Illustration of Purchasing Power Parity 8. 1

Identifying Disparity in Purchasing Power 8. 2

Relative Purchasing Power Parity 1. Interpretations of Purchasing Power Parity b. Relative Form of PPP Explanation of Point A, B, C and D. A: Ih is 4% higher than If. Foreign currency appreciate 4% to offset inflation differentials. PPP holds and exchange rates are at equilibrium. B: Ih is 5% lower than If. Foreign currency depreciate 5% to offset inflation differentials. PPP holds and exchange rates are at equilibrium. C: Ih is 4% higher than If. Foreign currency appreciate 1%, not enough to offset inflation differentials. PPP does not holds and foreign currency should appreciate by another 3%. D: Ih is 3% lower than If. Foreign currency depreciate 2%, not enough to offset inflation differentials. PPP does not holds and foreign currency should depreciate by another 3%.

Relative Purchasing Power Parity Empirical tests of both relative and absolute purchasing power parity show that for the most part, PPP tends to not be accurate in predicting future exchange rates PPP-determined exchange rates still provide a valuable benchmark. Two general conclusions can be drawn from the tests: ◦ PPP holds up well over the very long term but is poor for short term estimates ◦ The theory holds better for countries with relatively high rates of inflation and underdeveloped capital markets

A. Purchasing Power Parity (PPP) Testing the Purchasing Power Parity Theory Conceptual Tests of PPP 1. ) choose two countries (say, the United States and a foreign country) 2. ) compare the differential in their inflation rates to the percentage change in the foreign currency’s value during several time periods.

Comparison of Annual Inflation Differentials and Exchange Rate Movements For Four Major Currencies 8. 3

A. Purchasing Power Parity (PPP) Why Purchasing Power Parity Does Not Occur a. Confounding Effects – other factors are determinants to exchange rate. b. No Substitutes for traded goods

Interest Rates and Exchange Rates Prices between countries are related by exchange rates and now we discuss how exchange rates are linked to interest rates The Fisher Effect states that nominal interest rates in The Fisher Effect is each country are equal to the required real rate of return plus compensation for expected inflation. As a formula, i = (1+r)*(1+ ) -1= r+ + r ≃ r+ Where i is the nominal rate, r is the real rate of interest, and is the expected rate of inflation over the period of time The cross-product term, r , is usually dropped due to its relatively minor value

Interest Rates and Exchange Rates Applied to two different countries, like the US and Japan, the Fisher Effect would be stated as $ $ i = r $ + ; ¥ ¥ i = r ¥ + It should be noted that this requires a forecast of the future rate of inflation, not what inflation has been, and predicting the future can be difficult! Note: if real interest rates in two countries are the same, then, PPP can be described by interest rate. This is IFE.

International Fisher Effect If the Fisher effect holds in the U. S. 1 + i$ = (1 + r$ ) × (1 + I$) and the Fisher effect holds in Japan, 1 + i¥ = (1 + r¥ ) × (1 + I¥) and if the real rates are the same in each country r$ = r¥ then we get the International Fisher Effect: 6 -25 1 + i¥ -1 = 1 + I¥ 1 + i$ 1 + I$ -1 = ef

Interest Rates and Exchange Rates 1. Interpretations of International Fisher Effect General equation: ef = 1+ih 1+if -1 Simplified equation: ef = i h - i f ih: Home nominal interest rate. if: Foreign nominal interest rate. ef: Changes in exchange rate. e f can be defined as: ef = (S - St)/St t+1 St: spot exchange rate St+1: expected exchange rate or exchange rate at the next period

International Fisher Effect For example, if the interest rate of country A is 10% and that of country B is 5%, then the currency of country B should appreciate roughly 5% compared to the currency of country A. The International Fisher Effect observation holds that a country with higher interest rate will also be inclined to have a higher inflation rate.

International Fisher Effect (IFE) 1. Relationship with Purchasing Power Parity high Inflation (called PPP) high nominal interest rate (called IFE) Chapter 4: High interest rate high demand of the currency higher price of the currency appreciate IFE: high interest rate high inflation by PPP, currency depreciate Question: which theory is correct? How shall we apply these theories?

B. International Fisher Effect (IFE) 2. Implications of the IFE for Foreign Investors: If IFE holds, the returns to US investors are the same: a: invest in local market and earn ih b: convert to foreign currency which has depreciated by if-ih by IFE or PPP, and invest in foreign market and earn if (if>ih). The overall return is still ih. Take away: Returns are the same no matter where you invest your money.

Interest Rates and Exchange Rates Justification for the international Fisher effect is that investors must be rewarded or penalized to offset the expected change in exchange rates The international Fisher effect predicts that with unrestricted capital flows, an investor should be indifferent between investing in dollar or yen bonds, since investors worldwide would see the same opportunity and compete it away

Illustration of IFE Line (When Exchange Rate Changes Perfectly Offset Interest Rates Differentials) 8. 5

International Fisher Effect Explanation of Point A, B, C and D. E: ih is 3% lower than if. Foreign currency depreciate 3% to offset interest rate differentials. IFE holds and exchange rates are at equilibrium. F: ih is 2% higher than if. Foreign currency appreciate 2% to offset interest rate differentials. IFE holds and exchange rates are at equilibrium. G: ih is 3% lower than if. Foreign currency appreciate 2%, it cannot offset interest rate differentials. IFE does not holds and foreign currency should depreciate to 3%. H: ih is 3% lower than if. Foreign currency depreciate 5%, it cannot offset interest rate differentials. IFE does not holds and foreign currency should depreciate to 3%. J: omitted

B. International Fisher Effect (IFE) 5. Test of the International Fisher Effect a. Results from testing the IFE: similar to PPP b. Statistical Test of the IFE: Similar to PPP

B. International Fisher Effect (IFE) 6. Why the international Fisher Effect Does Not Occur a. PPP does not hold in certain times b. Since IFE based on PPP, it does not hold consistently either

C. Comparison of the IRP, PPP, and IFE Theories 8. 7

HW 13, 14, 15, 18, 20, 25.