Lecture 7
Money, Exchange Rates and Purchasing Power Parity
In Figure 7.1, the UK money market and the £/$ foreign exchange market are
in equilibrium at r£ and E£$. Money market equilibrium holds at A, and the
interest rate parity at B.
Figure 7.1
B
E£$
r£
L(r£, YUK)
MUK/PUK
A
Figure 7.2, shows the money market exchange rate market linkages:
Figure 7.2
Bank of
England
Fed
Reserve
UK MS
US MS
UK
Money
Market
US
Money
Market
r£
r$
FE Market:
E£$
When the UK money supply increases, r£ falls, and exchange rate rises (£
becomes weaker). When the US money supply rises, r$ falls; r$£, the rate of
$ return in £ falls, and the exchange rate falls (£ becomes stronger).
Money and Prices
Real money demand is L(r,Y) and money demand Md=P×L(r,Y). In
equilibrium: Ms=Md and so:
Ms
MS
= L( r , Y ) ⇒ P =
(1)
P
L(r , Y )
In the short run, P and Y are fixed and so changes in money supply are
reflected in changes in the rate of in interest.
However, given r and Y, an increase in a country’s money supply causes a
proportionate increase in its price level, ceteris paribus.
But can we assume that changes in money supply do not affect the long run
values of r and Y?
The long run value of Y is the full-employment level of Y: this level depends
on the country’s endowments of capital and labour. The interest rate
expresses the relative price of future £ to present £: [1/(1+r)]. So both are
unaffected by change in money supply which is fully reflected in an equiproportionate price change
A permanent increase in the UK money supply leads to a long-run rise in all £
prices, including the exchange rate.
So the expected rate of depreciation rises, raising r£$ so the exchange rate
rises from B to E.
Then the price level rises from P0 to P1. In the long run, r£ is unchanged but if
exchange rate expectations are unchanged, the long run equilibrium
3
exchange rate is higher: E£$
> E£$0 .
3
Notice that the exchange rate moves from: E£$0 → E£$2 → E£$
. The fact that the
short term equilibrium exchange rate > the long term equilibrium exchange
rate is known as exchange rate overshooting. When the money supply
increases, the expectations about the future exchange rate change before the
price level can adjust.
US Money Supply
UK Price Level
M1UK
P1UK
M0UK
P0UK
time
UK Interest Rate
time
UK Exchange Rate
E2£$
r0£
E1£$
E0£$
r1£
time
time
Figure 7.3A
Figure 7.3
E2£$
E
E1£$
D
E0£$
B
r1£
M0/P0
M1/P0
E2£$
r0£
A
C
E3£$
E0£$
r1£
M1/P1
M1/P0
r0£
The Law of One Price and Purchasing Power Parity (PPP)
When trade is free, identical goods must sell for the same price in different
currencies, when their prices are expressed in a common currency.
If a BigMac costs $1.50 in the USA and the exchange rate is 0.60/£, then it
must sell for £0.90 in the UK. Any deviation from this price opens up the
possibility of arbitrage.
i
£ PUK
= $ PUSi × E£$
(2)
Equivalently when the exchange rate between two countries equals the ratio
of the countries’ price levels, it is said to be the PPP rate:
P
E£$ = UK
(3)
PUS
If PPP=£0.50/$, then £100 would buy the same basket of goods and services
as $200 would in the USA.
The difference between PPP and LOP is that PPP applies to the general price
level while LOP applies to individual commodities.
Equation (3) represents absolute PPP. Relative PPP asserts that the change
in the exchange rate is the difference between the inflation rates in the two
countries:
E£$t − E£$t −1
= π tUK − π tUS
(4)
t −1
E£$
The Monetary Approach to the Exchange Rate
In the long-run the foreign exchange markets set rates so that PPP of
equation (3) holds. But we have:
s
s
M UK
M US
PUK =
and PUS =
(5)
L(rUK , YUK )
L(rUS , YUS )
Consequently, the exchange rate is fully determined by the relative supply
and demand for money in the two countries:
s
PUK M UK
L(rUS , YUS )
E£$ =
= s ×
(6)
PUS M US L(rUK , YUK )
1. A permanent rise in the UK money supply causes the exchange rate to
depreciate in proportion to the rise in the money supply.
2. A rise in the UK interest rate, causes UK money demand to fall; UK price
level rises and the £/$ exchange rate depreciates; a rise in the US interest
rate, causes US money demand to fall; US price level rises and the £/$
exchange rate appreciates
3. If UK output rises, UK price level falls and the £/$ exchange rate
appreciates; If US output rises, US price level rises and the £/$ exchange
rate depreciates
Monetary Growth
The interest rate parity condition (Lecture 6) combined with relative PPP
yields:
e
e
rUK − rUS = D£$e = π UK
− π US
(7)
where: π e = ( Pt e − Pt −1 ) / Pt −1 is the expected inflation rate over period t.
So, if relative PPP is expected to hold, the difference in UK-US interest rates
will be mirrored in the difference between the expected UK and US inflation
rates.
Consequently, a rise in UK expected inflation rate will be mirrored in an equal
rise in the UK interest rate. This long-run relation between the expected
inflation rate and the interest rate is known as the Fisher effect.
Figure 7.4
UK Money Supply
UK interest rate
r£+∆π
Slope=π+∆π
r£
M0
Slope=π
0
time
Panel A
UK price level
0
Panel B
t ime
£/$ exchange rate
Slope=π+∆π
Slope=π
0
Panel C
Slope=π+∆π
Slope=π
time
0
time
Panel D
At time 0, money supply growth rate increases π% per year to (π+∆π)% per
year (Figure 7.4: Panel A). As a consequence the expected inflation rate in
the UK rises from π% per year to (π+∆π)% per year. Under relative PPP, £ is
expected to depreciate (π+∆π)% per year instead of the earlier π% per year
and so UK interest rates rise from rUK to rUK+∆π (equation (7)). This is shown
in Figure 7.4: Panel B.
The interest rate rise reduces real money demand in the UK: L(rUK,YUK). This
causes the UK price level to jump at time=0 (equation (1)) before growing at
the higher rate of (π+∆π)% per year. PPP implies (equation (6)) that the £/$
exchange rate jumps before being expected to depreciate at (π+∆π)% per
year, instead of π% per year.
The Big Mac Index
PPP does not stand up well to empirical scrutiny, either in absolute or in
relative form. The Economist's Big Mac index is based on the theory of
“purchasing-power parity”. Under PPP, exchange rates ought to adjust to
equalise the price of a basket of goods and services across countries. The
Economist’s basket is the Big Mac. Dividing the April 2001 American price of
a Big Mac, $2.49, by the British price, £1.99, implies a PPP exchange rate of
$1.25. The market rate is $1.45, making sterling 16% overvalued. By this
measure, the South African rand is undervalued by 64%.
The Economist (25/4/02) reports “Every time we update our Big Mac index,
readers complain that burgernomics does not cut the mustard. The Big Mac is
an imperfect basket. Hamburgers cannot be traded across borders; prices
may be distorted by taxes, different profit margins or differences in the cost of
non-tradable goods and services, such as rents. Yet it seems to pay to follow
burgernomics. In 1999, for instance, the Big Mac index suggested that the
euro was already overvalued at its launch, when nearly every economist
predicted it would rise. Several studies confirm that, over the long run,
purchasing-power parity—including the Big Mac PPP—is a fairly good guide
to exchange-rate movements. Still, currencies can deviate from PPP for long
periods. In the early 1990s the Big Mac index repeatedly signalled that the
dollar was undervalued, yet it continued to slide for several years until it
flipped around. Our latest figures suggest that, sooner or later, the mighty
dollar will tumble: relish for fans of burgernomics”.
The Real Exchange Rate
Suppose the price of a “basket” of the goods and services bought by the
“typical” UK and US household costs, respectively, PUK (in the UK) and PUS in
the USA. The real £/$ exchange rate, denoted, R£$ , is the £ value of the US
basket, relative to the UK basket:
E ×P
R£$ = £$ US
(8)
PUK
where: E£$ is the nominal exchange rate. The real £/$ exchange rate
expresses the pound’s purchasing power over US goods and services relative
to its purchasing power over UK goods and services.
Suppose E£$ = £0.80 / $ and PUK=£100 and PUS=$150: then
R£$ = (0.80 ×150) /100 = 1.2 . This means that one would need 20% more £ to
buy the US basket than one would need to buy the UK basket.
So a real depreciation occurs when the value of R£$ rises. This means that
the purchasing power of £ in the USA declines or equivalently, the price of US
products relative to UK products rises. This can occur because of:
(i)
A nominal depreciation as E£$ rises (£ becomes weaker).
(ii)
A change in the world relative demand for UK, relative to US, output: if
this goes down (a shift in UK demand towards US products; a shift in
US demand away from UK products) then PUS/PUK will rise, leading to a
real depreciation of £/$
(iii)
A change in the relative supply of UK, to US, output: if UK productivity,
relative to US, rises then PUS/PUK will rise, leading to a real depreciation
of £/$.
PUK
⇒ R£$ = 1 . If absolute PPP does not hold,
PUS
but relative PPP does hold, the real exchange rate is constant: if PUS/PUK rises
– reflecting a difference in US-UK inflation rates – the nominal exchange rate
will fall by the same proportion.
If absolute PPP holds then E£$ =
Equation (8) can be solved to yield:
R£$ × PUK
(9)
PUS
Comparing equation (8) to equation (3) shows that the determination of the
nominal exchange rate has monetary aspects – encapsulated in the fact that
changes in relative money supply and demand in the UK and US affect their
relative price levels – and also non-monetary aspects consisting of the
amalgam of factors affecting the real exchange rate.
E£$ =
The Real Interest Rate
From equation (8):
d log R£$ d log E£$ d log PUS d log PUK
e
e
=
+
−
⇒ F£$e = D£$e − (π UK
− π US
) (10)
dt
dt
dt
dt
where: F£$e is the expected rate of depreciation in the real exchange rate; D£$e is
the expected rate of depreciation in the nominal exchange rate; and
e
e
π UK
and π US
are the expected rates of inflation in the UK and the US.
Consequently, the interest rate parity condition (equation (7)) can be rewritten
as:
e
e
)
r£ − r$ = D£$e = F£$e + (π UK
− π US
(11)
The £-$ interest rates are the sum of two components:
1. The expected rate of real appreciation
2. The difference in inflation rates
The expected real interest rates in the UK and the US, denoted R£ and R$
respectively, are defined as:
e
e
R£ = r£ − π UK
and R$ = r$ − π US
(12)
Consequently, using equation (11):
e
e
R£ − R$ = (r£ − π UK
) − (r$ − π US
) = F£$e
(13)
Equation (13) – which says that the difference in UK-US real interest rates
depends on the expected rate of depreciation in real interest rates – is known
as the real interest rate parity condition.
Factors Affecting the Nominal Exchange Rate: Summary
1. The monetary approach to the exchange rate uses PPP (either
absolute or relative) to explain exchange rate movements entirely in terms
of shifts in money supply and demand.
2. Under absolute PPP, changes in money supply and demand in the UK,
relative to the US, change the relative price level, PUK / PUS and hence
change E£$ = PUK / PUS The exchange rate rises in proportion to the price
level changes. The real exchange rate is unchanged.
3. Under relative PPP, differences between the UK and the US in their
money supply growth leads to differences in their (expected) inflation rates
and hence in D£$e the expected depreciation in £. This changes interest
rates in the two countries. The real exchange rate is unchanged.
4. The theory of real exchange rates can be grafted on to the monetary
approach based on PPP. The real exchange rate measures the extent to
which the nominal exchange rate deviates from PPP (absolute or relative).