Chapter 8

Relationships among Inflation, Interest Rates,
and Exchange Rates
A. Purchasing Power Parity (PPP)
B. International Fisher Effect (IFE)
C. Comparison of the IRP, PPP, and IFE Theories
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 the theory of interest rate parity (IRP),
which was introduced in the previous
chapter
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¥)

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
P¥
S $
P




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 “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 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
=
$3.41
Yuan
3.23/$
◦ 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/$
Yuan 7.60/$
=
-58%
1. Interpretations of Purchasing Power
Parity
b. Relative Form of PPP

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
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.
1. Interpretations of Purchasing Power
Parity
b. Relative Form of PPP
General equation:

ef = 1+Ih
-1
1+If
Simplified equation:
ef= Ih- If
Ih: Home nominal inflation.
If: Foreign nominal inflation.
ef: Changes in exchange rate. ef can be defined as: ef = (St+1- St)/St
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
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%.



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
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
Why Purchasing Power Parity Does Not Occur
a. Confounding Effects – other factors are
determinants to exchange rate.
b. No Substitutes for traded goods

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

formula,
The Fisher Effect is

each country are equal to the required real rate of
return plus compensation for expected inflation. As a
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

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.
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:
1 + i¥
-1 = 1 + I¥
1 + i$
1 + I$
6-25
-1 = ef
1.
Interpretations of International Fisher Effect
General equation:

ef = 1+ih
-1
1+if
Simplified equation:
ef= ih- if
ih: Home nominal interest rate.
if: Foreign nominal interest rate.
ef: Changes in exchange rate. e
f
can be defined as: ef = (St+1- St)/St
St: spot exchange rate
St+1: expected exchange rate or exchange rate at the next period

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.
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 currency
appreciate
IFE: high interest rate  high inflation  by PPP,
currency depreciate
Question: which theory is correct? How shall we apply
these theories?
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.


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
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
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
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
8.7

13, 14, 15, 18, 20, 25.