Download Chapter 23. Aggregate demand and aggregate supply in the open

Chapter 23. Aggregate demand and
aggregate supply in the open
economy
ECON320
Prof Mike Kennedy
Key assumptions
• The economy is small and so cannot affect developments in
the rest of the world
• The economy is specialized and its goods are imperfect
substitutes for those in the rest of the world, implying that
domestic prices can vary relative to the rest of the world
• International capital mobility is perfect and accordingly
domestic and foreign assets are perfect substitutes
• Investors are risk neutral, caring only about returns and not
the stochastic variability of those returns
• These last two assumptions imply that rates of return are
equalised between countries
Capital mobility and nominal interest rate parity
• We define the nominal exchange rate (E) as the number of
domestic currency units needed to buy one unit of the foreign
currency
• Note that a rise (fall) in E is a depreciation (appreciation)
• With perfect capital mobility we get the arbitrage condition that
investors will be indifferent to investing in the home or foreign
economy
• Note that E+1e is the exchange rate expect to prevail in the next
period after the bond matures
• This arbitrage condition says that domestic and foreign
investments must generate the same returns
Interest rate parity: Uncovered
• In logs we get the following approximation of the IRP
• Note that the expected rate of depreciation is equal to the
expected capital gain on holding foreign bonds
• If the domestic currency is expected to depreciate then
domestic interest rates must rise by enough to make domestic
and foreign bonds equally attractive
• The above equation is referred to as the uncovered interest
parity condition or UIP:
– In this case the investor is bearing the exchange rate risk
Interest rate parity: Uncovered
• The investor could “cover” the risk by selling the proceeds of the
investment forward at an agreed upon forward rate
which is
known or agreed to at the beginning of the period
• The above is the covered interest parity condition
• Taking logs of both sides
• Covered and uncovered interest parity can hold at the same time if
• This condition holds if there is risk neutrality
The more exchange rates are fixed the less
volatile are interest rates
The real exchange rate
• The real exchange rate is defined as the nominal rate (E) times
the foreign price level (Pf) divided by the domestic price level (P)
• In log this becomes
• Looking at rates of change we get
• In the long run, the real exchange rate is constant (otherwise the
trade balance would keep changing) and the above becomes
• This condition is known as relative purchasing power parity which
implies that the real interest rate is equal to the foreign rate
The tri-lemma and its resolution
• Capital mobility and its effect on interest rates leads to the
“tri-lemma” for policymakers in which they can choose only
two of the following three
1.
2.
3.
Free capital mobility
Fixed exchange rate
Independent monetary policy
• Under the gold standard, countries chose mostly to opt for 1)
and 2)
• Under Bretton-Woods they chose 2) and 3) and used capital
controls
• With the breakdown of Bretton-Woods, we entered a period
of free floating
• Now exchange rate regimes have polarised
Exchange rate systems
70%
Number of countries as a percentage of total
62%
(98)
1991
60%
2006
50%
41%
(76)
34%
(63)
40%
26%
(48)
30%
20%
23%
(36)
16%
(26)
10%
0%
Hard peg
Intermediate
Float
Aggregate demand in an open economy
• Equilibrium in the goods market is
• The nominal value of imports measured in the domestic currency
is EPfM and the real value in terms of the domestic good is
EPfM/P = ErM
• The variable net exports is then
• Suppose we have the following equations for exports and
imports: X = X(Er, Yf ) and M = M(Er, Y, τ, r, ε) then
Aggregate demand and the Marshall-Lerner condition
• We want to know how changes in the real exchange rate will affect
trade balance (NX)
• We assume that initially X0 = Er0M0 which implies
¶X E r
hX = r
>0
¶E X
¶M E r
hM = - r
>0
¶E M
• The condition states that a rise in Er (a depreciation of the real
exchange rate) will improve the trade balance as long as the sum of
the export and import elasticities (ηX and ηM, respectively) is
greater than one, which we will assume
Aggregate demand in an open economy
• Using the above equations and what we know about the other
components of demand we can derive the AD curve
Y = D(Y, t , r, e, E r )+ NX(E r ,Y f ,Y, t , r, e )+ G
• The function measures total private demand from both the
domestic and foreign sectors
• Note that Er influences domestic demand through an income effect
• For the response of demand to income we will assume that only a
fraction of demand is devoted to imports
• Maintaining the condition that ∂D/∂Y < 1 then
How demand responds to changes in key variables
• That only a fraction of demand is directed towards imports implies
• Finally we assume that
• Since ∂D/∂Er < 0, this final relationship requires that the MarshallLener condition (∂NX/∂Er > 0) has a large enough margin to
overcome the negative income effect
How demand responds to changes in key variables
• Using the above and the same procedure as in Chapter 16 yields
y - y = b1 (er - e r )- b2 (r - r )+ b3 (g - g)+ b4 (y f - y f )+ b5 (ln e - ln e )
• We now show that there is a negative relationship between
output and actual inflation
• Recall the definition of the change in the real exchange rate (2nd
equation, Slide 7) and the final equation on Slide 7
e = e + De + p - p
e
e
e
r = i - p +1
= i f - p +1
+ Dee, Dee º e+1
-e
r
r
-1
f
• Assume that E r =1 which implies that e r º ln E r = 0
• In long-run equilibrium we have r = r f
How demand responds to changes in key variables
• Plugging these into the first equation on the previous slide
where
• To complete the model, we need to make assumptions about the
formation of expectations of inflation and exchange rate changes
• Exchange rate expectations will depend on the exchange rate
regime – fixed versus flexible
• Note that an increase in inflation will erode competitiveness,
thereby reducing output
– The first term in brackets is equal to er
– The response will be greater, the larger is β1, which in turn is dependent
on the Marshall-Lerner conditions
How demand responds to changes in key
variables
• Note as well that the AD curve will shift whenever relative
purchasing power parity fails to hold
• This can be seen by the presence of the lagged real exchange
rate in the curve
• In an open economy, shifts in the AD curve will be part of the
adjustment process
Aggregate supply
• We will assume that aggregate supply is given by an equation liked
that derived in Chapter 17
• When unemployment benefits are linked to the general price level,
wage setting will be characterised by relative wage resistance
• A trade-union model of wage setting leads to a short-run aggregate
supply curve for the open economy that is the same as in a closed
economy
• If unemployment benefits are indexed to the consumer price level,
then they will be affected by the exchange rate
• Without deriving we will assume that the SRAS is the familiar
p = p e + g (y - y)+ s, s º (1- g )(ln a - ln a)
where a is productivity
Long-run equilibrium in an open economy
• Even in the absence of an assumption about exchange rate
regimes we can find the long-run equilibrium AD
• Start by noting that in equilibrium the real exchange rate does
not change and this implies not only relative purchasing
power parity but that the real interest rate is equal to the
world real rate (r = rf)
e
e
• We also know that r º i - p +1
= i f +∆ ee - p +1
• Inserting these two relationship into the AD curve we get the
LRAD
e =
r
y-y -z
b1
z º -b2 (r f - r f )+ b3 (g - g)+ b4 (y f - y f )+ b5 (ln e - ln e )
Long-run equilibrium in an open economy con’t
• Note that the LRAD curve slopes upward in terms of the real
exchange rate – a higher value of e (a depreciation of the real
exchange rate) makes domestic goods more competitive
• The long-run equilibrium condition for supply occurs when
actual equals expected inflation and shocks are absent, which
gives
y=y
• The above implies that the LRAS is vertical
• Long-run equilibrium occurs at a real exchange rate given by
the intersection of the two curves (see next slide)
• Note that a permanent demand shock (z ≠ 0) will get
absorbed into the real exchange rate
Long-run equilibrium in an open economy
Long-run equilibrium in an open economy con’t
• The long-run equilibrium values of the real variables in the
economy are all independent of the exchange rate regime
– We did not have to make any assumption about the exchange rate
regime
• It follows that in the long run the exchange rate regime is
neutral in the sense that it does not have any impact on the
equilibrium values of the key variables
• Here the authorities can choose to have either a fixed or a
floating exchange rate, but they cannot determine the longrun value of EPf/P
• That said, it will turn out that the exchange rate regime is
important for determining the adjustment in the short run
Current accounts and wealth effects
• Not taken into account are wealth effects emanating from
abroad
• If a country is running a persistent current account deficit
(surplus) then its net foreign asset position is worsening
(improving)
• In Canada’s case, it has generally run current account deficits
(next slide) and its net foreign asset position has deteriorated
• These wealth effects typically take a long time to materialise
and will be ignored in this couse
Canada’s current account balance
4
Current account balance for Canada
3
2
Per cent of GDP
1
0
-1
-2
-3
-4
-5
-6
(as per cent of GDP)