Ch8e8Inflation Interest Exchange Rate Relationships

8/22/2019 Ch8e8Inflation Interest Exchange Rate Relationships

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Relationships among Inflation,Interest Rates, and Exchange Rates

8

Chapter

South-Western/Thomson Learning 2006


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8 - 2

Chapter Objectives

To explain the purchasing power parity

(PPP) and international Fisher effect (IFE)

theories, and their implications for

exchange rate changes; and

To compare the PPP, IFE, and interest rate

parity (IRP) theories.


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Purchasing Power Parity (PPP)

When a countrys inflation rate risesrelative to that of another country,

decreased exports and increased importsdepress the high-inflation countrys

currency.

Purchasing power parity (PPP) theoryattempts to quantify this inflation

exchange rate relationship.


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Interpretations of PPP

The absolute form of PPP is an extensionof the law of one price. It suggests that the

prices of the same products in different

countries should be equal when measured

in a common currency.

The relative form of PPP accounts formarket imperfections like transportationcosts, tariffs, and quotas. It states that the

rate of price changes should be similar.


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Rationale behind PPP Theory

Suppose U.S. inflation > U.K. inflation.

U.S. imports from U.K. and U.S. exports to U.K.

Upward pressure is placed on the .

This shift in consumption and the s

appreciation will continue until in the U.S.: priceU.K. goods priceU.S. goods in the U.K.: priceU.S. goods priceU.K. goods


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Derivation of PPP

Assume that PPP holds.

Over time, inf lation occurs and the

exchange rate adjusts to maintain PPP:

Ph Ph (1 + Ih )where P

h= home countrys price index

Ih

= home countrys inflation rate

Pf Pf(1 + If) (1 + ef)where Pf = foreign countrys price index

If

= foreign countrys inflation rate

ef

= foreign currencys % in value


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Derivation of PPP

Ih > If ef > 0 i.e. foreign currency appreciatesIh < If ef < 0 i.e. foreign currency depreciatesExample: Suppose IU.S. = 9% and IU.K. = 5% .

TheneU.K. =

(1 + .09 ) 1 = 3.81%(1 + .05 )

PPP holds Ph = Pf andPh (1 + Ih ) = Pf(1 + If) (1 + ef)

Solving foref : ef =(1 + Ih ) 1(1 + If )


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Simplified PPP Relationship

When the inflation differential is small, the

PPP relationship can be simplified as

ef Ih IfExample: Suppose IU.S. = 9% and IU.K. = 5% .

Then eU.K. 9 5 = 4%U.S. consumers: PU.S. = IU.S. = 9%PU.K. = IU.K. + eU.K. = 9%U.K. consumers: PU.K. = IU.K. = 5%PU.S. = IU.S. eU.K. = 5%


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Graphic Analysis of Purchasing Power Parity

PPP line

Inflation Rate Differential (%)home inflation rate foreign inflation rate

% in theforeign

currencysspot rate-2

-4

2

4

1 3-1-3

Increasedpurchasing

power of

foreigngoods

Decreasedpurchasingpower offoreigngoods

A

B

C

D


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Testing the PPP Theory

Conceptual Test

Plot actual inflation differentials and

exchange rate % changes for two or morecountries on a graph.

If the points deviate significantly from the

PPP line over t ime, then PPP does nothold.


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Statistical Test

Apply regression analysis to historical

exchange rates and inflation differentials:e

f= a0 + a1 [ (1+Ih)/(1+If) 1 ] +

Then apply t-tests to the regression

coefficients. (Test for a0 = 0 and a1 = 1.) If any coefficient dif fers signif icantly from

what was expected, PPP does not hold.



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Empirical studies indicate that therelationship between inf lation differentials

and exchange rates is not perfect even in

the long run.

However, the use of inflation differentialsto forecast long-run movements in

exchange rates is supported.

A limitation in the tests is that the choice

of the base period will affect the result.



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Tests of PPP based on annual data from 1982 to 2004


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Why PPP Does Not Occur

PPP does not occur consistently due to:

confounding effects

Exchange rates are also affected bydifferences in inflation, interest rates,

income levels, government controls and

expectations of future rates.

a lack of substitutes for some traded

goods


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PPP in the Long Run

PPP can be tested by assessing a realexchange rate over t ime.

The real exchange rate is the actual

exchange rate adjusted for inflationary

effects in the two countries of concern.

If the real exchange rate follows a randomwalk, it cannot be viewed as being a

constant in the long run. Then PPP does

not hold.


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International Fisher Effect (IFE)

According to the Fisher effect, nominalrisk-free interest rates contain a real rate

of return and anticipated inflation.

If all investors require the same real return,differentials in interest rates may be due to

differentials in expected inflation.

Recall that PPP theory suggests thatexchange rate movements are caused by

inflation rate differentials.


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The international Fisher effect (IFE) theorysuggests that currencies with higher

interest rates will depreciate because the

higher nominal rates reflect higher

expected inflation.

Hence, investors hoping to capitalize on a

higher foreign interest rate should earn areturn no higher than what they would

have earned domestically.


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InvestorsResiding in

Japan

U.S.

Canada

Japan

U.S.

Canada

Japan

U.S.

CanadaJapan

U.S.

Canada

Attempt toInvest in Ih

3

3

3

6

6

611

11

11

%

If

3

6

11

3

6

113

6

11

%

ef

0

3

8

3

0

58

5

0

%

if

5

8

13

5

8

135

8

13

%

Return inHome

Currency

5

5

5

8

8

813

13

13

%

Ih

3

3

3

6

6

611

11

11

%

RealReturnEarned

2

2

2

2

2

22

2

2

%


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According to the IFE, E(rf), the expectedeffective return on a foreign money market

investment, should equal rh , the effective

return on a domestic investment.

rf = (1 + if)(1 + ef) 1if =interest rate in the foreign country

ef =% change in the foreign currencysvalue

rh = ih = interest rate in the home country

Derivation of the IFE


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Setting rf = rh : (1 + if)(1 + ef) 1 = ih

Solving foref : ef =(1 + ih ) _ 1

(1 + if )


ih > if ef > 0 i.e. foreign currency appreciatesih < if ef < 0 i.e. foreign currency depreciates

Example: Suppose iU.S. = 11% and iU.K. =12%.

TheneU.K. =

(1 + .11 ) 1 = .89% .(1 + .12 )

This will maker

f =r

h .


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When the interest rate differential is small,the IFE relationship can be simplified as

ef

ih

_ if


If the Brit ish rate on 6-month depositswere 2% above the U.S. interest rate, the

should depreciate by approximately 2%

over 6 months. Then U.S. investors would

earn about the same return on British

deposits as they would on U.S. deposits.


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Graphic Analysis of the International Fisher Effect

IFE line

Interest Rate Differential (%)home interest rate foreign interest rate

% in theforeign

currencysspot rate-2

-4

2

4

1 3-1-3

Lowerreturns frominvesting in

foreigndeposits

Higherreturns frominvesting in

foreigndeposits

A

B

C

D


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Graphic Analysis of the IFE

The point of the IFE theory is that if a firmperiodically tries to capitalize on higher

foreign interest rates, it wil l achieve a yield

that is sometimes above and sometimes

below the domestic yield.

On average, the yield achieved by the firm

would be similar to that achieved byanother firm that makes domestic

deposits only.


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Tests of the IFE

If actual interest rates and exchange ratechanges are plotted over time on a graph,

we can see whether the points are evenly

scattered on both sides of the IFE line.

Empirical studies indicate that the IFEtheory holds during some time frames.

However, there is also evidence that itdoes not hold consistently.


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Tests of the International Fisher Effect

Interest Rate Differential (%)home interest rate foreign interest rate

-2

-4

2

4

1 3-1-3 % in theforeign

currencysspot rate

IFE line


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To test the IFE statistically, applyregression analysis to historical exchange

rates and nominal interest rate

differentials:

ef = a0 + a1 [ (1+ih)/(1+if) 1 ] + Then apply t-tests to the regression

coefficients. (Test for a0 = 0 and a1 = 1.)

IFE does not hold if any coefficient differssignificantly from what was expected.

Tests of the IFE


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Why the IFE Does Not Occur

Since the IFE is based on PPP, it wil l nothold when PPP does not hold.

In particular, if there are factors other thaninflation that affect exchange rates,

exchange rates may not adjust in

accordance with the inflation differential.


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Comparison of the IRP, PPP, and IFE Theories

Exchange RateExpectations

Inflation RateDifferential

Forward RateDiscount or Premium

Interest RateDifferential

Purchasing

Power Parity(PPP)

Interest Rate Parity

(IRP)

Fisher

Effect

International

Fisher Effect (IFE)


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Comparison of the IRP, PPP, and IFE Theories

Interest rate parityForward rate premium p

Interest rate differential ih i

f

( )( ) fh

f

h iii

ip

+

+= 1

1

1

Purchasing power parity

% in spot exchange rate efInflation rate differential I

h I

f

( )( ) fh

f

hf II

I

Ie

+

+= 1

1

1

International Fisher effect

% in spot exchange rate efInterest rate differential i

h i

f

( )( ) fh

f

hf ii

i

ie

+

+= 1

1

1

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Ch8e8Inflation Interest Exchange Rate Relationships