Unlock document.
This document is partially blurred.
Unlock all pages and 1 million more documents.
Get Access
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:
