Regime dependent AD-AS models (Part I).
Ragnar Nymoen
Department of Economics, UiO
27 October 2009
ECON 3410/4410 Lecture 9
The main dividing line is between ‡oating and …xed exchange
rate regimes.
Traditionally the main ‡oat regime has been money targeting
(R-I).
IAM downplay that regime and move to in‡ation targeting
(which will be a development of R-III in our typology)
However, important to keep a wide perspective of possible
regimes.
Sometimes the money market which plays a central role in
R-I, also becomes relevant under in‡ation targeting (compare
credit crisis).
Reference for these slides is IAM ch 23. 24.1-24.4.
ECON 3410/4410 Lecture 9
Open economy AD-AS, system of equations I
yt
mt
t
pt
r
1 (et
y
=
rt
=
etr
=
t
=
it
=
1
= m0
er )
r)
2 (rt
f
f
+ 4 (yt
y ) + vt ;
e
it
t+1 ;
r
et + ft
t + et 1 ;
e
y ) + st
t + (yt
f
e
it + ( et + et 1 )
+
m1 it + m2 yt
(1)-(3) refer to the aggregate demand.
IAM p. 713 set e r = 0 (choice of units)
and r = r f .
ECON 3410/4410 Lecture 9
3
(gt
g )(1)
(2)
(3)
(4)
(5)
(6)
Open economy AD-AS, system of equations II
(4) is the PCM for the supply side, despite that we are now
looking at the open economy. We will re-consider this during
the last lectures. In the present model, foreign in‡ation will
a¤ect domestic i‡ation only through expectations.
(5) is UIP condition for the FEX marked, as explained in
Lecture 8. Have omitted e e , so now constant depriation
expectations entails it = itf )
(6) is the equilibrium condition for the money market.
ECON 3410/4410 Lecture 9
Regime VI I
The model for this regime is de…ned by choosing
et .as exogenous, along with
gt , ytf , st ; vt , ft , itf , etr 1 , et 1 and pt 1
We also consider et and et+1 as exogenous since we now focus
on the short-run and “static expectations”.
Substitute from (2), (3) and (5) into (1):
h
f
r
yt y =
t ) + et
1 ( et + t
2
itf +
+ 3 (gt
|
e
( e t + et
g) +
(y f
{z4 t
zt
the AD function for regime VI.
1
1)
er
i
e
t+1
y f ) + vt
}
ECON 3410/4410 Lecture 9
(7)
r
Regime I (money targeting) I
Regime dependent exogenous variable: mt :
et is endogenous in this …rst ‡oating exchange rate regime.
Money market and FEX market are now interlinked
(remember earlier graph!)
Solve (5) and (6) for
et =
it =
1
e
et and it .
(it
1
(mt
m1
itf )
et
t
pt
1
1)
+
m0
m2
+
yt
m1
m1
ECON 3410/4410 Lecture 9
Regime I (money targeting) II
and substitute in (1):
yt =
1
1
1
e
1
(mt
m1
if
e t
+ etr
2
1
(mt
m1
1
et
t
pt
t
1
+
pt
f
t
1)
1)
t
+
+
m0
m2
+
yt
m1
m1
(8)
er
m2
m0
+
yt
m1
m1
+ zt :
ECON 3410/4410 Lecture 9
e
t+1
r
Regime I (money targeting) III
Since the same SRAS applies in both regimes, the di¤erence
between regime I and VI is captured the slope of the
short-run AD curves (7) and (8):
@ t
@yt
@ t
@yt
=
1
=
AD ;rI
<0
(9)
1
AD ;rVI
1
1
1
+
m2
em +
1
1
1 e m1
m2
2 m1
1
2 m1
(10)
Note …rst that (10) hinges on e 6= 0. The interpretation is
that with constant depreciation expectations and perfect
capital mobility, it is determined by the UIP condition alone.
Hence e = 0 would introduce an internal inconsistency with
the assumption that in this regime, mt is exogenous.
ECON 3410/4410 Lecture 9
Regime I (money targeting) IV
Second, in most expositions, (10) is simpli…ed to
@ t
@yt
=
1
1
m2
em
1
+
m2
2 m1
(11)
1
AD ;rI
which amounts to abstracting from the e¤ect of t on real
money supply. This is convenient since it is easy to see that
using (11),
@ t
@yt
>
AD ;rI
@ t
@yt
, when
e
<0
(12)
AD ;rVI
meaning that with regressive depreciation expectations, the
slope of the short-run AD curve is steeper in Regime I than in
Regime VI.
ECON 3410/4410 Lecture 9
Regime I (money targeting) V
The simpli…ed expression is tantamount to replacing (6) with
mt
pt = m0
m1 it + m2 yt
(13)
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 una¤ected
by the rate of in‡ation: They are assumed to be exogenous
since they can reasonably be interpreted as pre-determined in
the short run.
ECON 3410/4410 Lecture 9
Regime I and regime VI AD curves
In R-VI,
increased t
leads to real
appreciation and
lower yt .
π
R-I AD curve
In R-I, the
reduced yt gives
lower it .
So fall in yt is
less in R-I
R-VI AD curve
y
ECON 3410/4410 Lecture 9
Note the role of
the money
market!
Graph showing RI and R-VI equilibrium
Assume, for
both regimes,
the initial
equilibrium:
e and
t =
yt = y :
π
R-I AD curve
SR AS curve
π
e
Supply shocks,
policy changes
and demand
shocks
R-VI AD curve
Full employment
y
y
ECON 3410/4410 Lecture 9
will a¤ect the
two equilibria
Fiscal policy in regime I and VI
From (7) and (8) we see that for a given yt , the derivative of
t with respect to gt is identical in the two regimes
d t
dgt
=
yt =y ;rI
d t
dgt
=
yt =y ;rI
3
>0
1
The is because the di¤erence between the regimes has to do
with how the money market reacts to changes in y .
The graphical analysis of the short-run e¤ects of …scal policy
is therefore represented by the identical vertical shifts in the
AD curve of the two regimes.
ECON 3410/4410 Lecture 9
Short-run e¤ects of …scal expansion (R I and VI)
π
R-I AD curve
New equilibrium
in R-VI is in A
SR AS curve
B for R-I
A
π
e
Fiscal policy is
most e¤ective in
the …xed
exchange rate
regime.
B
R-VI AD curve
Full employment
y
y
ECON 3410/4410 Lecture 9
Later, we will
extend the
comparison to
include R-III.
The long-run model (IAM ch 23.4) I
In both regimes, the models’steady-states are de…ned by,
e
t
=
f
, expectation equal to the world in‡ation rate
yt = y ,
etr = etr
1
= e r , PPP property
gt = g , gov exp on trend,
ytf = y f , world GDP on trend
{f = constant world interest rate
st = vt = 0, no supply or demand shocks
Since etr = etr
1
= e r and
etr =
that
t
et +
f
=
f
t
it follows from
t
+ etr
1
et = 0 in steady-state.
ECON 3410/4410 Lecture 9
The long-run model (IAM ch 23.4) II
e =E ) so we
It is logical that in a steady-state et = ln(Et+1
t
add
e
ln(Et+1
=Et ) = et = 0
to the list of steady-state conditions.
Hence, from the UIP condition we then have:
i = {f
and
rt = r = {f
f
.
in steady-state.
Now consider the possibility of a permanent change in gt .
This implies an increase in g , so from the AD side of the
economy.
y AD =
1e
r
f
2 ({
f
)+
3g
+
ECON 3410/4410 Lecture 9
4y
f
The long-run model (IAM ch 23.4) III
However the supply side determined steady-state output-level
y is unchanged, meaning that the long-run equilibrium
condition can be written
y=
1e
r
f
2 ({
f
)+
3g
+
4y
f
(14)
which determines the long-run steady-state real-exchange rate.
The long-e¤ect of a permanent change in gt is therefore:
de r
dg
3
=
rI ;rVI
<0
1
if we can assume the dynamic process is stable.
Unlike the short-run equilibria. The long-run equilibrium is not
regime dependent.
IAM call this “the long-run" neutrality of the exchagne rate
regime”.
ECON 3410/4410 Lecture 9
The long-run model (IAM ch 23.4) IV
Compare with the steady-state in the closed economy case.
The it was the real-interest rate that “secured” crowing out of
private demand.
In the open economy case, that role is “taken over” by the
real-exchange rate.
ECON 3410/4410 Lecture 9
Long-run e¤ects of …scal expansion (R I and VI)
e
r
LRAS
LRAD
er
e
Slope of LRAD
is 1 .
r
0
1
Shift is
y
3
1
Graph illustrates
the e¤ect of
…scal
contraction.
y
ECON 3410/4410 Lecture 9
Dynamic stability— Regime VI I
See 739-741 in ch 24.3 of IAM.
Use the short-run model above, with the additional
assumptions:
e
t+1
e
et+1
=
e
t
=
f
et = 0
et = 0
So that rt = rtf , and r = r f , the model in more compact form
is
yt
y=
1( t
f
2 (rt
zt =
t
f
t
etr
= (yt
=
(
f
t)
r
1 et 1
+
r) +
3
(gt
+ zt ,
g) +
(15)
f
4 (yt
y ) + st
t
f
t)
+
f
y ) + vt
(16)
etr 1
ECON 3410/4410 Lecture 9
(17)
Dynamic stability— Regime VI II
Use (15) and (16) to express etr
f )):
for ( t
t
etr
1
=
(1 +
1
)
1
(yt
by yt
y (i.e., substitution
zt
y ) + st
1
1
which is equation (14) on page 739 in IAM. We also have:
etr =
(1 +
1
)
(yt+1
y ) + st+1
zt+1
1
1
Using these two expressions in (17), together with (16), gives
the …nal equation for (yt+1 y ):
(yt+1 y ) =
1
1+
(yt
1
y )+
1
(1 +
1
)
zt+1
ECON 3410/4410 Lecture 9
1
(1 +
1
)
st
Dynamic stability— Regime VI III
or, for yt :
(yt
y) =
1
1+
(yt
1
y) +
1
1
(1 +
1
)
zt + ::::
(18)
which is dynamically stable since
1
1+
which holds since
1
<1
1
> 0.
The essential equilibrating mechanism is the real exchange
rate in the AD curve.
In R-I further stabilization since increased GDP gives higher
interest rate.
ECON 3410/4410 Lecture 9
Temporary …scal expansion R-VI
π
Graph illustrates
the dynamics of
temporary …scal
expansion in
R-VI
π1
π
π
f
2
R-VI AD curves
y2
y1
y
ECON 3410/4410 Lecture 9
SRAS does not
shift because of
e = f
t
Systematic …scal policy
If …scal policy is systematically counter-cyclical
gt
g=
a(yt
y );
a > 0.
(19)
The AD curve becomes steeper, because real appreciation due
to higher gives less reduction in y , compared to case with
a = 0.
The applies to both R-I and R-VI, Figure 24.4 and discussion
covers R-VI
ECON 3410/4410 Lecture 9
Devaluation
A devaluation is only relevant in the …xed exchange rate
regime.
An unanticipated and permanent increase in et , shifts the
AD-curve out— because in the short-run a nominal
devaluation is also a real depreciation.
Because in‡ation in increased, the domestic price level grows
over time, and the AD curve“ glides back” along the AS
curve, see …gure 24.7.
Remark: The way we have formulated the UIP condition, a
devaluation leads to a lower interest rate (the e < 0
assumption).
However, unclear if this is relevant when there is a discrete
devaluation.
Quite possible that investors may “punish” the currency by
demanding a higher risk premium, at least temporarily.
ECON 3410/4410 Lecture 9