Aggregate demand and the marked for foreign
exchange IAM Ch 23.1-23-3.
Ragnar Nymoen
Department of Economics, UiO
20 October 2009
ECON 3410/4410: Lecture 8
Background for the open economy AD-AS model
In the AD-AS model for the open economy the emphasis is
going to be on the speci…cation of the demand side of the
economy
The AS schedule wil be the same as before— and the open
economy aspect is only incorporated in the steady-state
version of the model ( =foreign in‡ation)
This is not particularly realistic, and foreign factors are almost
certainly important for in‡ation in a medium-run perspective
(for example Norway 2003-2006), but it is done to simplify
the model is order to focus on other essential features of the
open economy:
Policy regimes, and the regime dependency of the
medium-term macroeconomic equilibrium.
Reference: IAM. Ch 23.1-23.3
ECON 3410/4410: Lecture 8
Open economy product market equilibrium I
Using the symbols from IAM, Ch 23.3, with subscript t added,
the condition for equilibrium in the product market is de…ned
as
Yt = Dt + Gt + NXt
(1)
where:
Yt is real domestic GDP
Dt is real domestic private demand (sum of private
consumption and housing and business investment)
Gt is real government expenditure.
NXt is the trade balance.
ECON 3410/4410: Lecture 8
Open economy product market equilibrium II
In the same way as for in Lecture 5 (closed economy) we write
Dt as
Dt = D(Yt ;Gt ; rt ; "t )
(2)
>0 <0 <0 >0
which is also with consistent with IAM, eq (17) on page 709
when note is taken that we abstract from any e¤ects of the
real exchange rate E r , foreign GDP Y f on domestic demand.
Remember the balanced budget assumption Tt = Gt .
The trade balance, denoted, NXt is de…ned in equation on
page 707 in IAM.
NXt = Xt
Etr Mt
ECON 3410/4410: Lecture 8
Open economy product market equilibrium III
Real exports (in the domestic currency) is Xt and Mt (!) is
the quantity of imported foreign goods. The real exchange
rate is de…ned as
Et Ptf
Etr =
(3)
Pt
as on page 704 in Ch 23 of IAM.
Et is the e¤ective nominal exchange rate (index), and Pt and
Ptf denote the domestic and foreign price level (indices).
Note that the …xed price value of imports is measured in
foreign currency units. To obtain real imports in the domestic
currency, it is multiplied by the real exchange rate.
Ceteris paribus, a real depreciation (E r increases) gives lower
trade balance NX , and GDP Y . This is due a negative
terms-of-trade e¤ect.
ECON 3410/4410: Lecture 8
Open economy product market equilibrium IV
As a rule of thumb for practical situations, the ceteris paribus
condition is thought to hold in the short-term. Adjustment
lags in the values means that the graphs of the cumulated
multipliers of NX has a J-form.
We shall however assume that the time period is long enough
to allow the combined quantity e¤ect (an increase in Xt and a
lowering of Mt ) to knock out the terms-of-trade e¤ect— we ar
on the upward part of the J-vurve.
Hence
@NXt
>0
@Etr
subject to the Marshall-Lerner Condition which is explained in
detail on page 709 in IAM.
The theory of the trade balance is completed by assuming
that exports depend positively on Ytf
ECON 3410/4410: Lecture 8
Open economy product market equilibrium V
and that imports depend positively on Yt , Gt and "t , and
negatively on rt :
NXt = NX (Yt ; Gt ; rt ; Ytf ; "t )
(4)
<0 <0 >0 >0 <0
Using (2) and (4) the product market equilibrium condition
can be written as:
Yt = D(Yt; G ; rt ; "t ) + Gt + NX (Yt ; Gt ; rt ; Ytf ; "t )
which de…nes the open AD function on implicit form
ECON 3410/4410: Lecture 8
(5)
Open economy AD function I
A linearization, following the same logic as in the closed
economy case, and see appendix to Ch 23 for details), of the
AD function de…ned by (5) gives
yt
y
r
1 (et
=
+
(see IAM eq (23)),
i
f
4 (yt
er )
2
f
y )+
(rt
|5
r) +
3
(gt
(ln "t ln ")
{z
}
vt
> 0 for all i, after control for “import leakage”.
All lower case latin letters, except rt , denote logs.
ECON 3410/4410: Lecture 8
g)
(6)
Open economy AD function II
The log of the real exchange rate
etr = et + ptf
pt
(7)
can be expressed in “law of motion” form
etr =
et +
f
t
|{z}
t
|{z}
+ etr
(8)
1
pt
p tf
Regarding the real interest rate, we use the same de…nition as
before:
e
rt = it
t+1
yt
y
=
1
h
( et +
2
+
it
f
4 (yt
f
t
e
t+1
f
r
t ) + et
r +
3
1
(gt
y ) + vt
ECON 3410/4410: Lecture 8
er
i
g)
(9)
Open economy AD function III
In the short-run,
for predetermined etr 1 , …xed et+1 ,
and given steady state values e r , r , g , and y f
we have a negative relationship between GDP and in‡ation.
Call this our preliminary AD function, because to make the
SRAS more precise, we need more theory for
In‡ation expectations.
How the nominal interest rate is determined in the model.
How the rate of nominal currency devaluation, et , is
determined in the model
The two …rst are exactly the same “loose ends” that we had
in the closed economy case.
The new element is that interest rate determination must be
analyzed jointly with exchange rate determination and this
creates new, genuinely open economy features.
ECON 3410/4410: Lecture 8
Open economy AD function IV
So we need to consider the market for foreign exchange,
and how it interacts with other …nancial markets
Speci…cally: Joint equilibrium with 3 markets: The FEX
market, the domestic bonds market and the domestic money
market.
After this “excurs” to the FEX and money market, we will
return to the speci…cation of the AD schedule— which we will
show becomes regime dependent.
ECON 3410/4410: Lecture 8
The FEX market in the short-run I
The participants in the market for foreign exchange (FEX) are:
1
2
Investors: Private banks and …nancial institutions, as well as
foreign central banks and domestic and foreign (production)
…rms.
The domestic monetary authority, usually, the central bank.
The central bank decides the demand for foreign exchange
The investors’decisions determine the net supply of foreign
exchange to the central bank (the exact counterpart to the
net demand for kroner).
In the very short-run (the daily to monthly horizon), the net
supply is dominated by capital movements: foreign currency is
supplied as a result of the investors’management of huge
…nancial portfolios.
ECON 3410/4410: Lecture 8
The FEX market in the short-run II
In the medium-run: the supply of currency is also a¤ected by
the ‡ow of currency generated by current account surplus or
de…cit (exporting …rms get paid in USD, and they will
exchange USD to kroner).
We start by …rst reviewing the basic characteristic of the FEX
market when we abstract from the trade balance e¤ect.
This is the pure stock or portfolio model of the FEX market.
We then explain how we can modify the framework by the
e¤ects of the ‡ow foreign currency resulting from international
trade.
ECON 3410/4410: Lecture 8
Basic short-run model of the FEX market
Price (kr/$)
Demand
Supply
E
Fg
Quantity ($)
FG denotes the net
demand of foreign
currency = foreign
currency reserves at the
central bank.
The supply of foreign
currency us here drawn as
curve that is increasing in
the price of the good.
ECON 3410/4410: Lecture 8
Stock and ‡ow determinants
In this model, known as the portfolio theory of the FEX
market (see ECON4330 for more) the whole stock of foreign
currency is determined
What determines net supply of foreign currency?
It cannot be the trade balance, because this is a ‡ow
variable, and a change in the ‡ow does not a¤ect the stock
much in the short-run
Instead, it must be factors that can, at any point in time,
e¤ect a revaluation of existing assets. One such variable is the
price of the commodity, the nominal exchange rate E , which,
for this reason is in the vertical axis of the graph.
ECON 3410/4410: Lecture 8
The role of the risk-premium
Other variables with an immediate e¤ect on the net supply of
foreign currency, are:
The domestic interest rate, it .
The foreign interest rate, itf
The expected rate of currency depreciation,
e
E t+1
Et
e
ln(Et+1
=Et ).
Et
These term are collected in a term known as the risk-premium
rpt = it
itf
e
ln(Et+1
=Et )
ECON 3410/4410: Lecture 8
E¤ect of changed risk-premium
An increased risk premium affects the
supply of FEX immediately (no lags)
The supply shift is
due to
Price (kr/$)
Demand
Supply
E
Fg
1
an increase in it ,
2
or a reduction in
itf ,
3
or a shift down
in the expected
rate of
depreciation.
Quantity ($)
ECON 3410/4410: Lecture 8
Implications of the portfolio approach
Hence on daily and monthly basis, almost all the variation in
the net supply of currency to the central bank is explained by
the factors that determine the expected short-term return on
kroner denominated assets, namely the risk-premium and the
nominal exchange rate itself.
This is true wether capital mobility is perfect or not: Even
with less than perfect mobility we expect that in the
short-term, the changes in currency supply is dominated by
the terms that make out the risk premium on investment in
kroner.
Perfect capital mobility: The supply schedule becomes
horizontal. The impact multiplier of supply with respect to a
small change in Et is in…nite.
We will talk more about perfect capital mobility below, but we
…rst consider the role of the trade surplus/de…cits.
ECON 3410/4410: Lecture 8
E¤ect of sustained trade surplus
A trade s urplus whic h las ts for s everal periods
will shift the s upply of FEX gradually (with lags )
Price (kr/$)
Supply
Demand
1 month w ith surpluss
2 months w ith surplus
1 y ear with surplus
E
Fg
A period of trade surplus
(or expected positive
trade balances) lead to
currency appreciation
Often refer to this kind of
appreciation as due to
“fundamentals”
Quantity ($)
ECON 3410/4410: Lecture 8
The degree of capital mobility
Supply c urve with
low capital mobility
kroner/$
E
Supply curve with
high c apital mobility
The derivative of the S function
to E .
SE low: cap mob is low
SE high: cap mob is high
quantity ($)
ECON 3410/4410: Lecture 8
Uncovered interest rate parity UIP
When capital mobility is perfect, the FEX supply function,
S(E ; :::), becomes horizontal.
A small change in E leads to an in…nite change in the supply
of foreign exchange: mathematically: SE = 1.
Hence the whole model of the FEX market can be collapsed
to one arbitrage condition:
e
it = itf + ln(Et+1
=Et )
(10)
which the same as zero risk-premium:
rst = 0
With perfect capital mobility, investors are indi¤erent between
kroner assets and $ assets: the return on 1 mill invested in
kroner assets is the same as the expected return on 1 mill
invested in $ assets.
ECON 3410/4410: Lecture 8
The two main regimes: Fixed and ‡oating exchange rates
Initial situation A
Price (kr/$)
Floating exchange rate:
Supply
Demand
E
A !B
No intervention in the
FEX market
C
A
Fixed exchange rate:
B
Fg
A !C
Quantity ($)
The central bank
intervenes in the FEX
market.
ECON 3410/4410: Lecture 8
Capital mobility and the …xed exchange rate regime I
Price (kr/$)
Fgt a¤ects money
supply, Mt :
With very high captal mobility, shifts in the supply
of foreign currency leads to large endogenous
movements in foreign currency reserves, if a
fixed E is the policy target.
Demand
Supply
E
Fg
Quantity ($)
Very high cap mobility
makes it impossible to
control money supply, as
required in the money
targeting regime.
International capital
market liberalization
increased cap mobility
during the 1980s and
reduced the possibility of
combining …xed exchange
rate with money supply
ECON 3410/4410: Lecture 8
Capital mobility and the …xed exchange rate regime II
However, a …xed exchange rate regime can be operated with a
high degree of capital mobility if the interest rate is used as
the instrument (instead of foreign currency reserves).
Note that in (10):
e
it = itf + ln(Et+1
=Et )
Et can be exogenous along with itf (determined abroad). If in
e
addition Et+1
is exogenous also, then it is determined by the
UIP condition.
If it is the policy instrument, perfect capital mobility per se,
does not rule out the operation of a …xed exchange rate
regime.
e
This continues to hold if Et+1
is endogenous, as shown on the
next slide
ECON 3410/4410: Lecture 8
Typology of depreciation expectations
As simple way of endogenizing expectations:
e
ln(Et+1
=Et ) = e e +
e
ln Et
e
<0
regressive expectations
e
>0
extrapolative
e
=0
constant ( = e e )
(11)
Using (11) in (10) gives:
it = itf + e e +
e
ln Et
ECON 3410/4410: Lecture 8
(12)
The Ei-curve
Since itf and e e in (12)
are exogenous, (12)
de…nes a curve between
Et and it , the Ei-curve.
With perfect capital mobility, the slope of the Ei
curve depends only on expectations.
T he curve is shifted by changes in foreign
interest rates and by 'expectations shocks'
it
With perfect capital
mobility the slope only
depends on the parameter
e
i
f
ae
itf and e e shift the curve
e
e
ln E t
With imperfect capital
mobility the slope
depends on other factors
than e .
And a longer list of
factors can shift the
curve.
ECON 3410/4410: Lecture 8
Sterilized interventions
Imperfect capital mobility allows, in principle, a central bank
to maintain control of the domestic money supply.
In an open economy the change in the supply of money (M) is
given by:
Mt =
Bt + E t
Fg ;t +
Et Fg ;t
where Bt is the stock of domestic bonds in period t.
In a …xed exchange rate regime Et = 0.
Mt
Bt
=
+1
Et Fg ;t
Et Fg ;t
By market operations, the stock of bonds can be changed
“1-1” with the change in foreign currency reserves. Thus,
money supply is isolated from the market for foreign
exchange. This is called sterilization. However sterilization is
only possible when capital mobility is imperfect.
ECON 3410/4410: Lecture 8
Joint equilibrium in capital markets
The Ei curve is convenient for analyzing equilibrium in capital
markets: Money (M), domestic bonds (Bt ) and foreign
assets (Fg ).
This is because the Ei curve shows the foreign exchange
market equilibrium values of it and Et . We can show the
money market equilibrium in the familiar graph of
M
= m(i; Y )
P
(13)
where M is nominal money supply and m(i; Y ) is the money
demand function.
Finally, from Walras’Law, when 2 markets are in equilibrium,
also the third market (for bonds!) is in equilibrium.
ECON 3410/4410: Lecture 8
Joint equilibrium in the money and FEX markets
interest rate
money supply
money demand
Ei-curve
it
Money
Mt
Et
exchange rate
ECON 3410/4410: Lecture 8
Monetary policy regimes I
Foreign exchange rate market
exogenous variable
Foreign reserves
E
Money market
exogenous
variable
M
i
None
I
III
V
II
IV
VI
ECON 3410/4410: Lecture 8
Monetary policy regimes II
Regime I: Floating exchange rate: Money targeting. (“dirty
‡oat” if Fg and sterilization is used discretionaly, which
assumes imperfect capital mobility)
Regime II: Fixed exchange rate. Exchange rate targeting with
Fg as instrument, with sterilizing monetary policy. Requires
imperfect capital mobility.
Regime III: Floating exchange rate. For example: interest
rate is exogenous in the money market because, it is used
instrument to target in‡ation. Taylor ruled based monetary
policy belongs here.
Regime IV: Fixed exchange rate. Exchange rate targeting with
Fg as instrument but without sterilization (even though have
imperfect cap mob)
Regime V: Floating exchange rate without a “nominal anchor"
Regime VI: Fixed exchange rate. Exchange rate targeting
with it as instrument.
ECON 3410/4410: Lecture 8
Regime I: M reduced by
market operations.
i0 ! i1 , and E0 ! E1
interest rate
Regime III: i0 ! i1 in
order to reduce in‡ation
for example M0 ! M1
and E0 ! E1 .
i1
i0
Money
M0
M1
E1
E0
E'0
exchange rate
Regime VI: Ei shifts, due
to i f % for example.
E0 ! E00 avoided by
i0 ! i1 (the same
change as in i f ).
M0 ! M1 since demand
for money falls.
ECON 3410/4410: Lecture 8
The collapse of exchange rate targeting in Sweden I
100
A huge speculative attack
on SEK in September
1992 market the end of
exchange rate targeting in
Sweden
17 and 18 September 1992
Swe 1 month
90
80
70
60
50
The graph shows the
1-month money market
interest rate
40
30
20
2 January 1991
31 December 1993
10
0
100
200
300
400
500
600
700
See next graph for
exchange rate
ECON 3410/4410: Lecture 8
The collapse of exchange rate targeting in Sweden II
Similar development in
Norway.
The Swedish effective exchange rate index.
1.4
With change in regime a
little later
1.3
1.2
1.1
Seen as typical for small
open economies with own
currencies in the age of
capital market
liberalization
Sep temb er 1 9 9 2
1.0
0.9
0.8
0.7
1975
1980
1985
1990
1995
2000
2005
Was replaced by in‡ation
targeting— not money
supply targeting.
ECON 3410/4410: Lecture 8