Economics Chapter 14 Homework If the exchange rate was initially £0.57 per dollar

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14 Exchange Rates I: The Monetary Approach in the Long Run

Notes to Instructor

Chapter Summary

This chapter develops the long-run model of exchange rate determination that will be

used in later chapters. Beginning with the theory of purchasing power parity, exchange

rates are linked to prices and inflation rates via PPP. Then, using the monetary approach,

these variables are linked to the money supply, real income, and eventually interest rates.

The chapter concludes with a discussion of nominal anchors, using the monetary

approach to analyze the choice of monetary regime.

Comments

In the textbook, the authors use the case of the United States and the Eurozone as a

template for understanding relative prices and exchange rates in two different regions.

Here, a more generic notation (home versus foreign) is used in place of the region-

specific notation. This presents a broader set of examples and case studies to student. The

case of the United States and the Eurozone can easily be substituted for this generic

notation.

This chapter contains several important concepts that will be used in later chapters.

There are three broad topics covered here: (1) purchasing power parity, (2) the monetary

approach, and (3) monetary regimes. The textbook organizes these topics with a section

covering empirical evidence on the monetary approach inserted between the simple and

general models of the monetary approach. The lecture notes below follow the

1), one covering the monetary approach (Sections 2 and 4), and a final lecture covering

empirical applications (the last parts of Section 1 and all of Section 3) and regimes

(Section 5).

An outline of the chapter follows.

1. Exchange Rates and Prices in the Long Run: Purchasing Power Parity and Goods

Market Equilibrium

a. The Law of One Price

b. Purchasing Power Parity

c. The Real Exchange Rate

d. Absolute PPP and the Real Exchange Rate

e. Absolute PPP, Prices, and the Nominal Exchange Rate

f. Relative PPP, Inflation, and Exchange Rate Depreciation

g. Summary

h. Application: Evidence for PPP in the Long Run and the Short Run

i. How Slow Is Convergence to PPP?

j. What Explains Deviations from PPP?

k. Side Bar: Forecasting When the Real Exchange Rate Is Undervalued or

Overvalued

l. Headlines: The Big Mac Index

2. Money, Prices, and Exchange Rates in the Long Run: Money Market Equilibrium

in a Simple Model

a. What Is Money?

b. The Measurement of Money

c. The Supply of Money

3. The Monetary Approach: Implications and Evidence

a. Exchange Rate Forecasts Using the Simple Model

i. Forecasting Exchange Rates: An Example

ii. Case 1: A One–Time Decrease in the Home Money Supply

iii. Case 2: A Decrease in the Money Growth Rate

b. Application: Evidence for the Monetary Approach

c. Application: Hyperinflations

i. PPP in Hyperinflations

ii Money Demand in Hyperinflations

d. Side Bar: Currency Reform

4. Money, Interest, and Prices in the Long Run: A General Model

a. The Demand for Money: The General Model

b. Long-Run Equilibrium in the Money Market

d. The Fischer Effect

e. Real Interest Parity

f. Application: Evidence on the Fischer Effect

g. The Fundamental Equation Under the General Model

h. Exchange Rate Forecasts Using the General Model

i. Looking Ahead

5. Monetary Regimes and Exchange Rate Regimes

a. The Long Run: The Nominal Anchor

Lecture Notes

The prices of goods and services in different countries are related to the exchange rate.

When the relative prices of goods change, the exchange rate adjusts to reflect this change.

For example, consider the prices of a basket of goods in two countries: the United

States and the United Kingdom. Initially, the price of this basket is £100 in the United

Kingdom and $175 in the United States. The exchange rate is currently $1.75 per pound,

or £0.57 per dollar. Note that this implies the U.K. basket and the U.S. basket cost the

same amount in U.S. dollar terms. A U.S. resident buying the U.K. basket of goods will

pay $175 (= $1.75 per £ × £100). Similarly, a U.K. resident will pay £100 for the U.S.

basket (= $175/$1.75 per £).

Now suppose the price of a typical basket of goods increases by 10% in the United

Kingdom; this means that U.K. residents need more pounds to buy the same basket of

goods. If this basket previously cost £100, now it will cost £110. The purchasing power

of the British pound has decreased for U.K. residents. At the same time, U.S. residents

will find that the U.S. dollar has increased in value relative to the British pound, by 10%

to be exact. If the exchange rate was initially £0.57 per dollar, then the new pound‒dollar

exchange rate will be £0.63 (a 10% increase in the pound‒dollar exchange rate). How

1 Exchange Rates and Prices in the Long Run: Purchasing Power Parity and

Goods Market Equilibrium

Arbitrage in the goods market implies that the prices of goods in different countries

should be the same in same-currency terms. Why should we expect this to be the case? If

the price of a single good is different in two locations, everyone would rush to buy the

The Law of One Price

The law of one price (LOOP) means that, under a certain set of assumptions, identical

goods sold in two different markets must sell for the same price when these goods are

denominated in a common currency. The two assumptions are: (1) no trade frictions (e.

g., transportation costs or tariffs), and (2) free competition (no individual seller or buyer

has the ability to manipulate prices).

To see how LOOP works, consider the trade of Oriental rugs in Mumbai and Los

Angeles. Suppose that a rug of a given quality sells for 240,000 rupees in the Mumbai

market, and the exchange rate is 200 rupees per U.S. dollar. If the law of one price holds,

Mathematically, LOOP for a particular good, g, is traded in two regions: home (H)

and foreign (F):

qgH/F = (EH/FPgF)/PgH

(EH/FPgF) = PgH

Purchasing Power Parity

Purchasing power parity (PPP) applies LOOP to a basket of goods, rather than to a

single good. It is the macroeconomic counterpart to a microeconomic concept. According

to PPP, the price of a basket of goods should be the same in two different locations in

same-currency terms. If LOOP holds for all goods in the basket, then purchasing power

parity should hold.

absolute PPP, implies qgH/F = 1. If qgH/F > 1, then (EH/FPF) > PH and the basket of goods

is more expensive in the foreign country relative to the home country. If qgH/F < 1, then

(EH/FPF) < PH and the basket of goods is more expensive in the home country relative to

the foreign country.

The Real Exchange Rate

The real exchange rate is the relative price of two countries’ baskets of goods, qgH/F.

This tells us how many foreign baskets are needed to purchase one home basket. We can

see this from the PPP expression given previously.

The real exchange rate differs from the nominal exchange rate because it measures

Absolute PPP and the Real Exchange Rate

According to PPP, the real exchange rate should be equal to 1. If qgH/F deviates from 1,

this implies that one currency is below its equilibrium value (undervalued) and the other

is above its equilibrium value (overvalued).

■ qgH/F < 1 by x% → foreign currency is undervalued by x%. Foreign goods are

Absolute PPP, Prices, and the Nominal Exchange Rate

According to absolute PPP, the real exchange rate is equal to 1. Therefore,

Relative PPP, Inflation, and Exchange Rate Depreciation

Often, macroeconomists are more interested in the growth rate of prices, or inflation, than

the level of prices. The theory of purchasing power parity has implications for the

Using the PPP condition just shown, we can substitute prices into this expression:

Note that each exchange rate term in the previous expression is equal to the relative price

level in home versus foreign. This gives us the following relationship between inflation

and exchange rates:

According to relative PPP, the rate of depreciation in the nominal currency is equal to

Summary

Both absolute and relative PPP imply that prices and exchange rates across countries are

APPLICATION

Evidence for PPP in the Long Run and the Short Run

To test the validity of PPP, we study the relationship between exchange rate movements

and inflation differentials across countries. Figure 14-2 compares exchange rates and

inflation differentials relative to the United States from 1975 to 2005. According to

From the figure, we see that relative PPP appears to hold. Countries with small

inflation differentials tend to have smaller changes in the exchange rate. Those with large

How Slow Is Convergence to PPP?

The empirical evidence suggests that PPP holds in the long run, but not in the short run.

A natural question to ask is how long it takes for exchange rates and prices to adjust

according to PPP. To measure this, economists use the speed of convergence, a measure

S I D E B A R

Forecasting When the Real Exchange Rate Is Undervalued or Overvalued

Even if PPP doesn’t hold in the short run, we can still use this theory to forecast exchange

If PPP holds, then qH/F,t = 1 and ∆qH/F,t = 0, so the expression collapses to the relative PPP

condition.

If PPP does not hold in the short run, we can use information on the speed of

convergence to forecast changes in the real exchange rate. Recall that deviations in PPP

What Explains Deviations from PPP?

The deviations in PPP can be traced back to our assumptions about frictionless trade:

■ Transactions costs. In reality, it costs resources to transport goods. In our example

of Oriental rugs traded in Mumbai and Los Angeles, it might be too expensive for

traders to travel to Mumbai. If these costs are large enough, traders are willing to

■ Imperfect competition and legal obstacles. Many goods are differentiated; they

vary in quality, use, and the ability to distribute and produce. On the buyer side,

consumers prefer different brands and types. On the seller side, producers may

H E A D L I N E S

The Big Mac Index

The Economist publishes an index meant to evaluate the theory of PPP and which

currencies are undervalued or overvalued. To test the theory, it is important to find a

basket that is sold in many different markets. The Big Mac is the basket chosen for the

analysis.

The Big Mac Index is as follows:

The table reports which currencies are undervalued and which are overvalued

according to the Big Mac Index. Consider a currency that is undervalued, such as the

Chinese yuan. If the yuan exchange rate is 7.77 Chinese yuan per U.S. dollar, the

Discussion questions

■ In addition to the Big Mac Index including nontradable elements, are there other

reasons why the Big Mac Index may fail to predict future movements in exchange

2 Money, Prices, and Exchange Rates in the Long Run: Money Market

Equilibrium in a Simple Model

This section develops a monetary theory of exchange rate determination. The money

What Is Money?

Money is an object that serves three functions:

■ Store of value: Money is an asset that can be used to purchase goods and services

in the future.

■ Unit of account: Prices in the economy are quoted using the local currency, or

money.

The Measurement of Money

Based on the definition of money given in the preceding section, which assets should be

included in measures of money? The narrowest definition of money would include only

currency held by the nonbank public. That definition is so narrow that the Fed does not

The Supply of Money

The amount of money in the economy is determined by the country’s central bank. The

central bank controls the money supply by changing the monetary base. Although the

The Demand for Money: A Simple Model

The textbook presents two theories of money demand: the simple model (based on the

quantity theory of money) and the general model (based on interest rates).

PY measures nominal income, where P is the price level and Y is real income. is a

constant that measures how much demand for liquidity is generated for each dollar in

nominal income. In the general model, we relax the assumption that is a constant by

allowing it to depend on the interest rate. In the simple model shown earlier, we assume

The previous expression can be converted into real terms. The demand for real money

balances is

Equilibrium in the Money Market

Money market equilibrium is determined by money demand and money supply:

A Simple Monetary Model of Prices

The money market equilibrium condition shows that prices in the home country are

determined by the ratio of money supply to real money demand:

The same relationship holds for the foreign country:

approach to the price level. This relationship states that when prices are flexible (i.e., in

the long run), changes in money supply and real income affect the price level:

A Simple Monetary Model of the Exchange Rate

We can derive the fundamental equation of the monetary approach to exchange rates

from the fundamental equation of the monetary approach to the price level. The

theory of PPP shows us the relationship between the exchange rate and the price level:

We can substitute the fundamental equations for the price level into this expression:

The previous expression is the fundamental equation of the monetary approach to

exchange rates. We can use this expression to see how changes in money supply and real

income at home and abroad affect the exchange rate: