Download Section 4 The Exchange Rate in the Long Run

Section 4
The Exchange Rate in the Long Run
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Content
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•
•
•
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Objectives
Purchasing Power Parity
A Long-Run PPP Model
The Real Exchange Rate
Summary
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Objectives
• To understand the law of one price and purchasing
power parity (PPP).
• To understand PPP as a theory of long-run
exchange rate determination.
• To understand the real exchange rate.
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Purchasing Power Parity
• The Law of One Price:
– Identical goods must be priced identically.
• Commodity Price Parity:
– Goods in different countries must sell for the
same price, when their prices are expressed in
the same currency.
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Purchasing Power Parity
• Commodity Price Parity:
PkUS  S (USD / CAD) PkC
Where Pkus is the USD price of commodity k in the U.S.,
Pkc is the CAD price of commodity k in Canada,
S(USD/CAD) is the price of CAD in USD.
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Purchasing Power Parity
• In the real world, CPP may not hold for the
following reasons:
• Transaction Costs:
– Tariffs, transportation costs, insurance fees, and other
such costs mean that it may not be possible to make
arbitrage profits even in the presence of price
differences across countries.
• Nontraded Goods:
– Several goods, such as services (haircuts) are
nontradable.
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Purchasing Power Parity
• Quotas:
– Quotas and other such barriers to trade restrict
the ability to make arbitrage profits.
• Imperfect Competition:
– Imperfect competition in commodity markets
may prevent prices from being equalized across
countries. For example, price discrimination,
entry costs, and menu costs would prevent CPP
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Purchasing Power Parity
• In an economy with many goods, purchasing
power is defined in terms of a representative
bundle of goods. It describes the number of
baskets of goods you can buy.
• The price level is the price of a particular basket of
goods. The most common price index is the
Consumer Price Index (CPI).
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Purchasing Power Parity
• Absolute Purchasing Power Parity:
– Identical baskets of goods in different countries
must sell for the same price, when their prices
are expressed in the same currency.
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Purchasing Power Parity
• Absolute Purchasing Power Parity:
US
P
 S (USD / CAD) P
C
Where Pus is the USD price of a basket of goods in the U.S.,
Pc is the CAD price of a basket of goods in Canada,
S(USD/CAD) is the price of CAD in USD
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Purchasing Power Parity
• In the real world, Absolute PPP may not hold for
the following reasons:
• Violations of CPP:
– Absolute PPP is unlikely to hold if CPP is
violated. That is, if the individual goods in the
representative consumption basket do not
satisfy CPP, then PPP is likely to be violated.
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Purchasing Power Parity
• Differences in Baskets:
– Absolute PPP will not hold if the composition
of the baskets differs across countries. For
example, the presence of non-traded goods
would make baskets different across countries
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Purchasing Power Parity
• The Relative PPP hypothesis states that the
percentage change in the exchange rate reflects the
difference between inflation at home and abroad.
• Relative Purchasing Power Parity:
PTUS ST (USD / CAD) PTC

 C
US
Pt
St (USD / CAD) Pt
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Purchasing Power Parity
• Relative PPP can also be expressed as:
1 
US
t ,T
 [1  (ST  St ) / St ]  (1   )
C
t ,T
• The linear version of relative PPP is:

US
t ,T

C
t ,T
 (ST  St ) / St
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Purchasing Power Parity
• Where  is the inflation rate:
 t ,T  ( PT  Pt ) / Pt
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Purchasing Power Parity
• Relative PPP states that inflation differences
between countries should be reflected in
percentage changes in the exchange rate.
– For example, if the inflation rate is 5 % in the
US and 2 % in Canada, then the Canadian
dollar should appreciate by 3 %.
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Purchasing Power Parity
– If prices in the US are rising faster than in Canada,
Canada's exports are becoming relatively cheaper.
– This should attract importers, thereby increasing
Canadian net exports and reducing US net exports.
– This should generate a relatively higher demand for
CAD and promote an appreciation of the CAD against
the USD.
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A Long-Run PPP Model
• The Monetary approach to the exchange rate
• The Fundamental Equation:
– Price levels and the Demand for Money:
P  M / L(i , Y )
h
h
h
h
P  M / L(i , Y )
f
f
f
f
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A Long-Run PPP Model
• Specific predictions from the monetary approach to longrun exchange rate determination:
– Money supplies
• An increase in the USD money supply causes a proportional
long-run depreciation of the USD against foreign currencies.
– Interest rates
• A rise in the interest rate on USD assets causes a depreciation
of the USD against foreign currencies.
– Output levels
• A rise in U.S. output causes an appreciation of the USD against
foreign currencies.
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A Long-Run PPP Model
– The international interest rate difference is the
difference between expected national inflation rates.
– Recall UIP:
h
t ,T
i
 i  (S  St ) / St
f
t ,T
e
T
– Recall Relative PPP:

h
t ,T

f
t ,T
 (S  St ) / St
e
T
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A Long-Run PPP Model
– So,

eh
t ,T

ef
t ,T
 (S  St ) / St
e
T
– And the interest differential is:
i i
h
t ,T
f
t ,T

eh
t ,T

ef
t ,T
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A Long-Run PPP Model
• The Real Interest Rate:
(1  rt ,T )  (1  it ,T ) /(1   t ,T )
rt ,T  it ,T  
e
t ,T
• The Fisher Relation (Real Interest Parity):
r r
h
t ,T
f
t ,T
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A Long-Run PPP Model
• A simple numerical example.
– Assume that:
• Pt = USD 100/Basket,
• PT = USD 101/Basket and
• it,T=0.03
• Today, period t
– If I have USD xt = USD 100, I can buy 1 basket:
• B yt = USD xt / Pt = (USD 100)/(USD 100/Basket) = B 1
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A Long-Run PPP Model
– If invest, I get USD xT = USD 103:
• USD xT = (1+ it,T) USD xt = (1+0.03)USD 100 = USD 103
– If I have USD xt = USD 103, I can buy 1.02 basket:
• B yT = USD xT / PT = USD 103/USD 101/Basket = B 1.02
– Inflation is 1+t,T =1.01
• (1+t,T)=PT/Pt =(USD 101/B)/(USD 100/B) = 1.01
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A Long-Run PPP Model
• USD rate of return is 3 percent:
– 1+ it,T =USD xT /USD xt = 1.03
• Real rate of return is 2 percent:
– (1+rt,T) = B yT / B yt = b1.02/b1 = 1.02
• Thus,
(1+rt,T) = (1+ it,T) Pt /PT = (1+ it,T)/ (1+t,T)
Or rt,T = it,T -t,T = 0.03 – 0.01 = 0.02
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A Long-Run PPP Model
•
The Fisher Effect
–
A rise in a country’s expected inflation rate
generates an equal rise in the interest rate:
it,T = rt,T + et,T
–
In the long run, inflation is a monetary phenomenon:
1+t,T = MT /Mt
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A Long-Run PPP Model
The Fisher Effect
M
i
i2 = i1 + 
growth =  + 
i1
growth = 
t0
P
Time
t0
S
Slope =  + 
Slope = 
Time
Slope =  + 
Slope = 
t0
Time
t0
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Time
A Long-Run PPP Model
– Jump in prices:
1   t ,T  PT / Pt 
M T / L(iT ,TT , YT )
M t / L(it ,T , Yt )
• Jump in interest rate for constant also force prices to
jump.
– USD constantly depreciates and jumps because of
absolute PPP.
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The Real Exchange Rate
• Recent empirical evidence suggests that
– PPP does not hold in the short run.
– It is a good approximation for the currencies of
countries experiencing hyperinflation.
– Prices of identical goods differ substantially across
countries (the Economist and the Big Mac Index).
– PPP (or something like it) appears to hold in the longrun. That is, the real exchange rate is trend reverting.
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The Real Exchange Rate
• This empirical evidence also suggests that
domestic and foreign baskets of goods on which
price levels are computed are different across
countries.
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The Real Exchange Rate
• The information summarized by PPP may still be
useful to determine the competitive position of a
particular country.
• The Real Exchange Rate summarizes this
information. The Real Exchange Rate is:
S (USD / CAD) P C
Q(US / C ) 
PUS
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The Real Exchange Rate
• The real exchange rate is the relative price of a
foreign basket of goods in terms of a domestic
basket of goods.
– For example, assume that the price level is CAD 150
per basket of Canadian goods in Canada and USD 100
per basket of US goods in the US. Also assume that the
exchange rate is USD 0.65/CAD.
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The Real Exchange Rate
– The real exchange rate is then:
USD0.65 / CAD  CAD150 / B C
Q(US / C ) 
USD100 / BUS
Q(US / C )  BUS 0.975 / B C
– That is, the Canadian basket is cheaper than the
American basket, which suggests that the American
economy is somewhat less competitive than the
Canadian economy.
– Another interpretation is that the costs of living are
lower in Canada.
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The Real Exchange Rate
• Real depreciation of the USD
– A rise in the real home price of a foreign basket
of goods.
– A rise in the real USD/CAD exchange rate
• A fall in the purchasing power of a USD in Canada
relative to the purchasing power of the USD in the
U.S.
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The Real Exchange Rate
• The real exchange rate is the relative price of a
foreign basket of goods. In the long run, this
relative price is determined by the supply and
demand for baskets of goods.
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The Real Exchange Rate
• These market forces can be summarized by:
– An increase in world relative demand for
Canadian goods causes an increase in the price
of the Canadian basket of goods and an increase
in the real exchange rate.
– An increase in world relative supply of
Canadian goods causes a reduction in the price
of the Canadian basket of goods and a reduction
in the real exchange rate.
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The Real Exchange Rate
• Nominal and Real Exchange Rates
– The real exchange rate is mean reverting.
• The half life of changes in the real exchange rate is
several years long.
• So, relative PPP holds in the long-run.
– The real and nominal exchange rates are highly
correlated.
S (USD / CAD) P C
Q(US / C ) 
PUS
• This suggests that prices are sticky.
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The Real Exchange Rate
• The real exchange rate and real interest parity.
– The relative version of the real exchange rate is:
– or
QT ST PTC / PTUS

Qt
St Pt C / PtUS
QT  Qt ( ST  St )

  tC,T   tUS
,T
Qt
St
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The Real Exchange Rate
• Uncovered Interest Parity
e
S
US
C
T  St
it ,T  it ,T 
St
• Real Exchange Rate:
QTe  Qt ( STe  St )
eUS

  teC


,T
t ,T
Qt
St
• Real Interest Rate:
rt ,T  it ,T  
e
t ,T
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The Real Exchange Rate
• Real Interest Parity (Part II)
e
Q
US
C
T  Qt
rt ,T  rt ,T 
Qt
• Uncovered Interest Parity
C
itUS

i
,T
t ,T
STe  St

St
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The Real Exchange Rate
• The real interest parity condition states that
differences in expected real interest rates depend
on expected movements in the real exchange rate.
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The Real Exchange Rate
• An interpretation of real interest parity
e
Q
*
T  Qt
rt ,T  rt ,T 
Qt
– The real interest rate is a measure or the real return to
capital. The higher that return, the higher the growth
rate of the economy.
– So, if r>r*, the home economy is growing faster and
must see its competitiveness improves. That is, the real
exchange rate (the price of a foreign basket of goods)
must rise.
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Summary
• Absolute PPP states that the purchasing power of any
currency is the same in any country:
P  S  P*
• Relative PPP predicts that percentage changes in exchange
rates equal differences in national inflation
 t ,T  
*
t ,T
 (ST  St ) / St
• The real interest rate is:
rt ,T  it ,T  
e
t ,T
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Summary
• The real exchange rate is the price of a foreign
basket of goods:
SP*
Q
P
• Real interest parity is:
– If both UIP and PPP hold:
– If only UIP holds:
rtUS
,T
rt ,T  r
*
t ,T
e
Q
C
T  Qt
 rt ,T 
Qt
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Summary
• There are sizeable movements in the real exchange
rate.
– These movements are long-lasting, but not permanent.
– Thus, relative PPP holds in the long run.
• The real and nominal exchange rates are highly
correlated.
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