Plan and literature reference for the lectures 1 and 8. November 2007.
Lecture 10: The open economy AD-AS
• Ch 23 and 24 in IAM
model–regime dependency of models.
• We start by reviewing the equations of the open economy model AD-AS
model in IAM.
— Exactly the same as in the book, but we simplify the notation somewhat
Ragnar Nymoen
Department of Economics, University of Oslo
• We spend some more time than the book on the model for the market
for foreign exchange, and on the interplay between the marked for foreign
exchange and the domestic money market.
October 31, 2007
2
1
The open economy AD-AS framework
• The analysis of the open economy AD-AS will focus on the difference
between monetary policy regimes, and on the difference between short-run
effects of shocks and policy changes, and the long-term effects of such
changes.
Using the symbols from IAM, Ch 23.3, with subscript t added, the condition
for equilibrium in the product market is defined as
Yt = Dt + Gt + N Xt
— We build on the concepts developed in the ”IDM” part of the lectures,
(1)
where:
— and on the analysis of the closed economy AD-AS model from the last
two lectures.
— This set of slides covers the presentation of Ch 23, and the “end product” is a suite of macro models for different policy regimes.
• Yt is real domestic GDP
• Dt is real domestic private demand (sum of private consumption and housing and business investment)
— The next slide set will cover Ch 24.
• Gt is real government expenditure.
• N Xt is the trade balance.
3
4
Since Dt includes both consumption and investment we include both private
disposable income, Yt − Tt, Tt being the real tax bill in period t, and the real
interest rate rt as explanatory variables, i.e. our theory of domestic demand
becomes
Real exports in period t is Xt and Mt is the quantity of imported foreign goods.
The real exchange rate in period t is defined as
f
Etr =
Dt = D(Yt − Tt, rt )
>0
<0
which is consistent with IAM, eq (17) on page 709 when note is taken that
1. We do not impose Gt = Tt.
2. We simplify by abstracting from the effects of the real exchange rate E r ,
foreign GDP Y f and confidence ε on domestic demand.
The trade balance, denoted, N Xt is defined in equation on page 707 in IAM.
EtPt
Pt
f
on page 704. Pt and Pt denote the domestic and foreign price level indices.
If there are no responses in Xt and Mt when Etr increases, Yt will be reduced
as a result of a real devaluation in period t. This may well be the case if the
time period is short and there are adjustment lags in Xt and Mt. In this case,
the terms-of-trade effect of a devaluation dominates. In the following we shall
however assume that the time period is long enough to allow the combined
quantity effect (an increase in Xt and a lowering of Mt) to knock out the
terms-of-trade effect.
N Xt = Xt − Etr Mt
6
5
Hence
Collecting the assumptions so far:
∂N Xt
>0
∂Etr
f
Yt = D(Yt − Tt, rt ) + Gt + N X(Yt − Tt, Yt ,Etr )
>0
subject to the Marhall-Lerner condition which is explained in detail on page
709 in IAM.
The theory of the trade balance is completed by assuming that Xt depends
f
positively on Yt and that Mt depends positively on Yt − Tt.
f
<0
<0
In IAM the following composite demand variable is defined (p. 706, equation
(17))
D̃ = D + N X.
In line with this, we re-write (2) as
f
N Xt = N X(Yt − Tt, Yt ,Etr )
Yt = D̃(Yt − Tt, rt, Yt , Etr ) + Gt
7
8
<0
>0 >0
(2)
>0 >0
(3)
The derivatives of the D̃ function become
∂D − ∂NX
D̃Y = ∂Y
∂Yt
t
D̃T = −D̃Y
D̃r = ∂D
∂r
t
D̃Y f = ∂NX
f
0 < D̃Y < 1
Equation (4) represents product market equilibrium in period t for given values
f
e
of Tt, Gt, Yt , rt, πt+1
and Etr . We note that it is a dynamic theory, by
definition, although we have abstracted from many sources of dynamics when
deriving (4).
D̃r < 0
0 < D̃Y f < 1
∂Yt
D̃E = ∂NX
D̃E r > 0
∂Etr
which is the same signs as on page 710 of IAM.
We will follow the book and work with a linearized version of (4). You do not
need to read the appendix in Ch 22, just accept
f
yt = β0 + β1 ert − β2 rt + β3 gt + β4 yt
The (ex ante) real interest rate rt is defined as
>0
e
rt = it − πt+1
e is the
where it, is the domestic nominal interest rate in period t, and πt+1
expected rate of inflation in period t + 1. Substitution in (3) gives
f
e , Y , Er) + G
Yt = D̃(Yt − Tt, it − πt+1
t
t
t
(4)
>0
>0
(5)
>0
at face value. yt = ln(Yt) and so on, so βi > 0 (i = 1, 2, 3, 4) are elasticities.
Compared to equation (23) on page 710 in IAM we have dropped the terms ȳ
etc. Think of them as subsumed in β0.
Equation (4), and its derivatives, is the first building block in our open economy
macro model.
9
10
To complete the model we need to add more assumptions and equations, notably for
1. The supply-side. This will be an expectations augmented Phillips curve,
of the form in equation (41) on page 716 in IAM (its derivation on page
712-715 in Ch 23.4 can be skipped):
πt = πte + γ(yt − ȳ) + st
(6)
where ȳ is the level of output consistent with πt = πte and no supply shocks
st = 0.
Remark. In the light of what we have learnt about wage-price dynmaics
probably means that the model understates the role of demand shocks.
3. The domestic money market, because this is where the nominal interest it
is determined (in most regimes, but not under inflation targeting).
Moreover, the domestic money market and the market for foreign exchange
are closely related, so it is necessary to take an ‘excurs’ to the theory of the
foreign exchange market and how it is related to the domestic financial markets:
Money and domestic bonds.
2. The market for foreign exchange, because this is where the nominal exchange rate Et in Etr =
regime.
EtPtf
Pt is determined in a floating exchange rate
11
12
The market for foreign exchange (a primer, or a review of what you know)
Definition and basic analytical framework
The joint (but uncoordinated) decisions of the investors determine the net
supply of foreign exchange to the central bank (the exact counterpart to the
net demand of 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 financial portfolios.
The participants in the market for foreign exchange (FEX) are
• Investors: Private banks and financial institutions, as well as foreign central
banks and domestic and foreign (production) firms.
• The domestic monetary authority, usually, the central bank.
— decides the demand of foreign exchange
13
Price (kr/$)
Demand
Supply
• in the intermediate-run: the supply of currency is also affected by the flow
of currency generated by current account surpluses or deficits (exporting
firms get paid in USD, and thus will exchange USD to kroner).
We start by first reviewing the basic characteristic of the FEX market when
we abstract from the trade balance effect. This is the pure stock or portfolio
model of the FEX market. We then explain how we can modify the framework
by the effects of the flow foreign currency resulting from international trade.
14
In the graph, we have drawn the (government’s) demand for foreign currency
as a vertical line. A synonym is the foreign exchange reserve and it is denoted
Fg in the graph (this notation is not in IAM)
Fg is the whole stock of foreign currency deposited in the central bank, less
any debt (incurred by the government) in foreign currency.
E
The supply schedule is market “S” and is upward sloping, i.e., as usual the
supply of foreign currency is increasing in price.
Demand and supply relate to the whole stock of foreign currency
What determines net supply of foreign currency?
Fg
Quantity ($)
• As noted, in the short-run, it cannot be the trade balance (primary current
account), because this is a flow variable.
Figure 1: The market for foreign exchange in terms of demand and supply
curves
15
• instead factors that can, in any point in time, effect 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 in the graph.
16
An increased risk premium affects the
supply of FEX immediately (no lags)
Other variables with an immediate effect (at any point in time) on the net
supply of foreign currency is
Price (kr/$)
Supply
Demand
E
1. The domestic interest rate, it.
f
2. The foreign interest rate, it
3. The expected rate of currency depreciation,
Fg
e −E
Et+1
t
e /E ).
≈ ln(Et+1
t
Et
In the so called portfolio model of the FEX market, detailed in the course
ECON4330, this term are collected in a term dubbed the risk-premium
f
e /E )
rpt = it − it − ln(Et+1
t
which has a positive (and immediate!) effect on the supply of foreign currency.
Quantity ($)
Hence the line representing a supply shift is due to either
1. an increase in it,
f
2. or a reduction in it ,
3. or a shift down in the expected rate of depreciation.
18
17
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 interest rates
and expected depreciation, as well as the nominal exchange rate itself.
A trade surplus which lasts for several periods
will shift the supply of FEX gradually (with lags)
Price (kr/$)
Supply
1 month with surpluss
Demand
2 months with surplus
1 year with surplus
E
This is true wether capital mobility is perfect or not: Even with less than perfect
mobility we expect that in the short-term, the changes in currency supply is
dominated by the terms that make out the risk premium on investment in
kroner.
Perfect capital mobility: The supply schedule becomes horizontal. The impact
multiplier of supply with respect to a small change in Et is infinite.
We will talk more about perfect capital mobility below, but we first consider
the role of the trade surplus/deficits
19
Fg
Quantity ($)
In the longer term, the trade balance becomes of importance, since persistent
surplus in N Xt means that a private and government savings are building up
which will have to be allocated to foreign or domestic assets.
Graphically, we represent this by small and gradual horizontal shifts in the
supply schedule.
20
The degree of capital mobility
Price (kr/$)
Mathematically, the degree of capital mobility is given by the derivative of the
f
supply function S(Et, it, it ....), graphically by the slope of the supply curve:
Supply
Demand
E
C
A
B
Supply curve with
low capital mobility
Fg
kroner/$
Quantity ($)
E
Initial situation is A. Then a positive (horizontal) shift in the S-curve. The new
equilibrium depends in the exchange rate regime:
A →B
Floating exchange rate.
Supply curve with
high capital mobility
quantity ($)
A →C
Fixed exchange rate. The central bank intervenes in the market
and increases its demand for USD (the foreign exchange reserves increases)
21
22
Covered interest rate parity.
Perfect capital mobility and the UIP condition
Capital mobility is perfect when a small change in E leads to an infinite change
in the supply of foreign exchange: mathematically: SE = ∞. Graphically: A
horizontal supply schedule in the market for foreign exchange.
In terms of economics, this means that with perfect capital mobility there are no
separate demand functions for kroner and dollar denominated assets. Instead
we have the arbitrage condition:
f
e /E )
it = it + ln(Et+1
t
(7)
saying that under perfect capital mobility, investors are indifferent 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.
(7) is known as the uncovered interest rate parity condition, UIP for short.
Note that (7) is the same as setting the risk premium rpt equal to zero.
UIP is a (strict) assumption about the characteristics of the spot market for foreign exchange. It equates the return of buying assets denominated in different
currencies.
To avoid exposure to exchange rate risk, consider paying the known price of
Ẽt+1 kroner today for the 1 USD needed at the start of next period (e.g.
month). This is using the forward market for foreign currency, rather than the
spot market.
An alternative way to avoid risk is to loan
Et
f
(1 + it )
kroner today, to have 1 USD available next period. At the start of next period
(when I need the USD), I have to repay the loan
Et
f
(1 + it )
23
× (1 + it)
24
The covered interest rate parity hypothesis says that arbitrage (“elimination of
profits by competition”) will secure that the two ways of hedging against risk
have the same cost:
Et
× (1 + it).
Ẽt+1 =
f
(1 + it )
This condition can be written as
Why do we not “see” the forward market in the model?
It is because all forward contracts can be “translated” to the spot marked.
In a fully specified model of financial portfolios one can therefore include the
forward market within one and the same analytical framework.
Ẽt+1
f
(1 + it ) − 1
Et
and is sometimes called the forward parity condition.
In terms of solution, we can think of Et (and it) as determined first, given that
Ẽt+1 is determined.
Unlike UIP, covered interest rate parity has empirical support.
A good reference is Ch1 in Asbjørn Rødseth (2000): Open Economy Macroeconomics, Cambridge University Press.
it =
26
25
Price (kr/$)
Capital mobility and the fixed exchange rate regime (2)
With very high captal mobility, shifts in the supply
of foreign currency leads to large endogenous
movements in foreign currency reserves, if a
fixed E is the policy target.
Demand
Supply
However, in principle at least, a fixed exchange rate regime can be operated
with a high degree of capital mobility if the interest rate is used as instrument
(instead of foreign currency reserves). Note that in (7):
E
f
e /E )
it = it + ln(Et+1
t
f
Fg
Quantity ($)
Capital mobility and the fixed exchange rate regime (1)
The degree of capital mobility is important for the operation of exchange rate
regimes. The classical “impossibility” is to operate a fixed exchange rate with
(near) perfect capital mobility and using foreign currency reserves as policy
instrument.
27
e
Et can be exogenous along with it (determined abroad). If in addition Et+1
is exogenous also, then it is determined by the UIP condition (7).
Hence if is it is the policy instrument. Then perfect capital mobility per se,
does not rule out the operation of a fixed exchange rate regime.
e
This continues to hold if Et+1
is endogenous, as shown on the next slide
28
The Ei-curve
Typology of depreciation expectations:
e /E ) = ee + αe ln E
ln(Et+1
t
t
αe < 0
regressive expectations
αe > 0
αe = 0
extrapolative
(8)
f
Since it and ee in (9) are exogenous, (9) defines a curve between Et and it,
the Ei-curve.
With perfect capital mobility, the slope of the Ei
curve depends only on expectations.
The curve is shifted by changes in foreign
interest rates and by 'expectations shocks'
constant ( = ee)
it
Using (8) in (7) gives:
f
it = it + ee + αe ln Et
(9)
Hence if capital mobility is perfect, and the exchange rate is fixed, the domestic interest rate is determined from (9), which is consistent with endogenous
depreciation expectations.
i
f
ae
ee
ln E t
29
Imperfect capital mobility and the Ei-curve.
In the case of imperfect capital mobility, the Ei-curve continues to hold, but
with important modifications
30
Imperfect capital mobility is important since it allows, in principle, if not necessarily in practice, 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:
• The slope is no longer 1-1 with the expectations parameter αe (but αe < 0
still secures a downward sloping Ei-curve).
• Several other factor may cause shifts in the Ei-curve.
— Interventions in the market for foreign exchange: if the foreign currency
reserve (Fg ) increases, there is a positive horizontal shift in the Ei-curve.
— A trade surplus which lasts for some time will cause a gradual negative
horizontal shifts in the Ei-curve.
31
∆Mt = −∆Bt + Et · ∆Fg,t + ∆Et · Fg,t
where Bt is the stock of domestic bonds in period t.
In a fixed 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.
32
The Ei curve is convenient for analyzing equilibrium in capital markets: Money
(M ), domestic bonds (Bt) and foreign assets (Fg ).
interest rate
money supply
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 )
(10)
P
where M is nominal money supply and m(i, Y ) is the money demand function.
money demand
Ei-curve
it
Money
Mt
Et
exchange rate
Finally, from Walras’ Law, when 2 markets are in equilibrium, also the third
market (for bonds!) is in equilibrium.
Figure 2: Joint equilibirum in the domestic money market and in the marked
for foreign exchange.
34
33
Regime I: Floating exchange rate. Money targeting. (“dirty float” if Fg and
sterilization is used discretionaly, which assumes imperfect capital mobility)
Table 2: Regimes in the domestic money market and the market for foreign
exchange.
Regime II: Fixed exchange rate. Exchange rate targeting (Fg as instrument)
with sterilizing monetary policy. Requires imperfect capital mobility.
Foreign exchange rate market
exogenous variable
Foreign exchange reserves Exchange rate
Regime III: Floating exchange rate. For example: interest rate as instrument to
target for example inflation. Note: Taylor ruled monetary policy also belongs
here.
Money market Money supply
exogenous
Interest rate
variable
None
I
III
V
II
IV
VI
Regime IV: Fixed exchange rate. Exchange rate targeting (Fg as instrument).Requires
imperfect capital mobility
Regime V: Floating exchange rate (“dirty float” if Fg is used discretionaly)
Regime VI: Fixed exchange rate. Exchange rate targeting with it as instrument.
35
36
Regime II: Ei shifts, due to if % for example. E0 −→ E00 avoided by Fg &.
Money market stays at (i0, M0) because of sterilization.
interest rate
Regime IV: Ei shifts, due to if % for example. E0 −→ E00 avoided by Fg &.
Money market changes i0 −→ i1 and M0 −→ M1, because of sterilization is
not possible. Note: loose monetary policy independence.
i1
i0
Money
M0
M1
E1
E0
E'0
exchange rate
Regime III: i0 −→ i1 in order to reduce inflation for example M0 −→ M1 and
E0 −→ E1.
Figure 3: Regime dependent response to changes in exogenous variables.
Regime VI: Ei shifts, due to if % for example. E0 −→ E00 avoided by i0 −→ i1
(the same change as in if ). M0 −→ M1 since demand for money falls.
37
38
A closer look at Regime VI.
Per annum, this corresponds to a interest rate differential of
Assume again that if increases. From the eq. condition, i must increase by
the same amount, irrespective of the degree of capital mobility (since both Fg
and E are exogenous in the market).
Another source of change in i in the case of this regime is expectations driven
runs of speculative attacks.
If a situation occurs with large probability of devaluation in the near future,
the rise in short interest rates (overnight, monthly) may be huge.
Example
P rob(10% devaluation within one month) = 0.5.
0.5 × 10% × 12 = 60%
If this is to be compensated completely, the domestic one-month interest rate
(annualized rate) must increase by 60 percentage points!
In practice, governments have often tried to defend the exchange rate by a
combination of Fg and i policies. Sweden and Norway in the autumn of 1992
are good examples.
In Sweden in particular short-term interest rates shoot-up to the hundreds.
Interest on loans with longer maturity (house loans) did not increase as much,
because the high short term rates did not last long for long
0.5 × 10% = 5% expected rate of depreciation over the next month.
39
40
100
17 and 18 September 1992
Swe 1 month
The Swedish effective exchange rate index.
90
1.4
80
1.3
70
1.2
60
1.1
September 1992
50
1.0
40
0.9
30
0.8
20
2 January 1991
0.7
31 December 1993
10
1975
1980
1985
1990
1995
2000
0
2005
100
200
300
400
500
600
700
Figure 4: Swedish exchange nominal effective rate.
Figure 5: Sweden. 1-month yield on treasury bills.
41
42
Regime dependent macro models
Short-run models
f
yt = β0 + β1ert − β2rt + β3gt + β4yt
e
rt = it − πt+1
f
ert = ∆et + πt − πt + ert−1
πt = πte + γ(yt − ȳ) + st
f
it = it + ee + αe(∆et + et−1)
mt − πt − pt−1 = m0 − m1it + m2yt, mi > 0, i = 1, 2
f
(11)
(12)
(13)
(14)
(15)
(16)
(11) has been explained above. (12) is the definition of the real interest rate.
e is the expected rate of inflation, one period ahead.
πt+1
(13) is a definition equation for ert , see IAM, p 704 and 711.
(14) is the PCM.
e /E ) ≡ ee
e
e
(15) is UIP with ln(Et+1
t
t+1 − et = e + α (∆et + et−1) inserted.
(16) is an equilibrium condition for the money market. Right hand side is a
linearization of the demand for money function.
43
f
In all the short-run models, the following variables are exogenous: gt, yt , st, πt ,
f
it , ert−1, et−1 and pt−1 (or pt, see discussion of Regime I below).
Regime VI
Regime dependent exogenous:∆et.
n
f
yt = β0 + β1 ∆et + πt − πt + ert−1
n
o
(17)
o
f
f
e
− β2 it + ee + αe(∆et + et−1) − πt+1
+ β3gt + β4yt
πt = πte + γ(yt − ȳ) + st
(18)
f
e
e
(19)
it = it + e + α (∆et + et−1)
mt − πt − pt−1 = m0 − m1it + m2yt
(20)
(17) is the AD curve. Note that the equilibrium condition on the market for
foreign exchange, (19), is included in this equation. (18) is the AS curve. If
e , and π e are exogenous, then (17) and (18) determines y and π . i is
πt+1
t
t
t
t
determined in (19) and mt in (20).
44
Regime I
The difference between regime I and VI is the slope of the AD curves (17) and
(21):
Regime dependent exogenous: mt
Money market and FEX market are now interllinked. Solve (15) and (16) for
it and the nominal exchange rate;
¯
1
f
(it − it − ee) − et−1
αe
−1
m
m
it =
(mt − πt − pt−1) + 0 + 2 yt
m1
m1 m1
"
1
αe
(
m
m
−1
(mt − πt − pt−1) + 0 + 2 yt
m1
m1 m1
¸
1
(23)
1
Note first that (23) hinges on αe 6= 0. The interpretation is that with constant
depreciation expectations and perfect capital mobility, it is determined by the
UIP condition alone. Hence αe = 0 would introduce an internal inconsistency
with the assumption that in this regime, mt is exogenous.
)
1 f
f
− e (it + ee) − et−1 + πt − πt
α (
)
m0 m2
−1
e
− β2
(mt − πt − pt−1) +
+
yt − πt+1
m1
m1 m1
f
+ β3gt + β4yt
πt = πte + γ(yt − ȳ) + st
(22)
m1
2
1 − β1 αm
e m + β2 m
∂πt ¯¯
1
2
=
¯
∂yt ¯AD,rI
−β1 + β1 αe1m − β2 m1
∆et =
yt = β0 + β1
¯
∂πt ¯¯
1
=
<0
¯
∂yt ¯AD,rV I
−β1
Second, in most expositions, (23) is simplified to
(21)
45
¯
m1
2
1 − β1 αm
e m + β2 m
∂πt ¯¯
1
2
=
¯
∂yt ¯AD,rI
−β1
(24)
46
which amounts to abstracting from the effect of πt on real money supply. This
is convenient since it is easy to see that using (24),
−
¯
¯
∂πt ¯¯
∂πt ¯¯
>−
, when αe < 0
¯
¯
∂yt ¯AD,rI
∂yt ¯AD,rV I
(25)
meaning that the slope of the short-run AD curve is steeper in Regime I than
in Regime 6, at least when αe < 0.
Note the difference in from the nominal exchange rate, et (in logs), and its
growths rate.
The simplified expression is tantamount to replacing (16) with
The rationale is that the price of foreign currency can change significantly even
within very short time periods. The is consistent with the portfolio approach
to the foreign exchange market. Hence it does not make good sense to treat
et as predetermined in regime I.
mt − pt = m0 − m1it + m2yt
(26)
and replacing pt−1 with pt in the list of exogenous variables. The rationale is
that, over short periods of time, the price level and the stock of real money
are more or less unaffected by the rate of inflation: They are assumed to be
exogenous since they can reasonably be interpreted as pre-determined inthe
short run.
47
48
p
Regime VI
Regime I
y
e
Figure 6: Short-run AD curves, fixed πt+1
in regime I and VI.
49