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.
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.
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
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?
2. Money, Prices, and Exchange Rates in the Long Run: Money Market Equilibrium
in a Simple Model
a. What Is 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
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
5. Monetary Regimes and Exchange Rate Regimes
6. Conclusions
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
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
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
frictionless trade. Later, we will consider how frictions limit arbitrage.
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
Mathematically, LOOP for a particular good, g, is traded in two regions: home (H)
and foreign (F):
If qgH/F > 1, this implies that the good is less expensive in the home country. If qgH/F < 1,
this implies that the good is less expensive in the foreign country.
It is important to keep track of the units on each side of the LOOP equation.
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.
A common measure of nationwide prices is the Consumer Price Index (CPI). This
qgH/F = (EH/FPF)/PH
where the superscript g is redefined as a basket of goods. This version of PPP, known as
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
relative prices in terms of goods (or baskets of goods). The nominal exchange rate
measures the relative prices of currencies, a purely nominal, or monetary, concept.
How do we interpret changes in the real exchange rate?
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,
In the previous expression, we see that absolute PPP implies the exchange rate is equal to
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
inflation rate. To see why it does, first note the percentage change in the exchange rate:
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
the inflation differential (home less foreign inflation rate). Just as we could use absolute
PPP to forecast future prices and exchange rates, we can use relative PPP to forecast
changes in the exchange rate based on inflation differentials.
changes in exchange rates. Absolute PPP is a stronger hypothesis because it predicts a
relationship between the level of prices and the level of exchange rates. Therefore,
absolute PPP implies relative PPP, but relative PPP does not imply absolute PPP.
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
relative PPP, the percentage change in the exchange rate should be equal to the inflation
differential. Therefore, all countries should be on a 45-degree line. Along the 45-degree
line, a one-percentage-point increase in the inflation differential implies a one–
percentage-point increase in the exchange rate.
periods of time, there are dramatic deviations between exchange rates and relative prices.
However, over long periods of time, the two appear to move in the same direction. (A
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
rate movements in the long run. First, note that the real exchange rate and nominal
exchange rate are related according to relative PPP:
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
die out at a rate of 15% per year. This tells us how quickly the real exchange rate is
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
obtain copyright or patent protection, giving them market power and the
accompanying control over price and output.
■ Price stickiness. A common assumption in macroeconomic models is that prices
are slow to adjust, or sticky, in the short run. If prices are sticky in domestic
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:
3.42 yuan per U.S. dollar; therefore, the yuan is undervalued by 56% (7.77 − 3.42/7.77).
This index gives us a rough forecast of how exchange rates should move in the long
run. Those currencies that are undervalued should appreciate; those that are overvalued
should depreciate. The Big Mac Index is a very rough guide, however, because it
includes nontradable elements, such as rent and labor.
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
■ Can you think of other products that are purchased worldwide through a franchise
such as McDonald’s? Describe how one could use such a product to test the
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
supply in each country will determine its relative prices, and therefore its exchange rate.
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
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
even recognize it with a name. Instead, the Fed refers to the monetary base, M0, which is
currency held by the nonbank public, currency held by banks (vault cash), and bank
The Supply of Money
The amount of money in the economy is determined by the country’s central bank. 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
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:
These expressions are examples of the fundamental equation of the monetary
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: