Regime dependent AD-AS models (Part II), Ch
25.
Ragnar Nymoen
Department of Economics, UiO
13 November 2009
ECON 3410/4410 Lecture 10
Monetary independence with perfect capital mobility
Recall the “money supply function” of the open economy:
Mt =
Bt + E t
Fg ;t +
Et Fg ;t
In R-I, Fg ;t = 0 and Fg ;t = Fg . Revaluations of the stock of
foreign currency Fg a¤ects Mt , but according to the theory
of R-I, such movements are countered by market operations
( Bt ). Changes in the net supply of bonds can also be used
to increase or lower Mt independently of the market for foreign
exchange. Hence, monetary policy independence in R-I: the
interest rate is determined on the domestic money market.
No such independence in R-VI, because the interest rate is
determined in the market for foreign exchange.
Remember that the discussion of R-I and R-IV was based on
the assumption of perfect capital mobility (as in the IAM
book).
ECON 3410/4410 Lecture 10
From money targeting to in‡ation targeting I
In practice R-I failed to live up to its theoretical properties. In
practice, it turned out to be di¢ cult to control money supply.
Two issues in particular seem to have been important:
Which operational de…niton of the money stock? M1, M2 or
M3? Reduced transparency.
In practice central also banks rode two horses: Intervene in
FEX market (dirty ‡oat), which a¤ect money supply unless
sterized, which often proved di¢ cult in practice.
When several small open economies started ‡oating their
exchange rates in the 1990’s, most countries chose an
alternative ‡oating exchnge rate regime called in‡ation
targeting.
ECON 3410/4410 Lecture 10
From money targeting to in‡ation targeting II
In our typology, in‡ation targeting can be seen as an
extension of R-III: The interest rate is the used as an
instrument to achieve a certain in‡ation rate (the target).
Therefore, it is “exogenous in the domestic money market”.
However, it , is of course endogenous in the full
macroeconomic model.
ECON 3410/4410 Lecture 10
The open economy policy response function I
Let
denote the in‡ation target. The response function in
IAM is:
it = r f +
e
t+1
+ h(
t
), h > 0
(IAM 2)
where the main di¤erence from the closed economy case is:
The output-gap is omitted. Which means formally, that we
have a model with strict in‡ation targeting here. As we known:
‡exible in‡ation targeting entails that yt y is in the Taylor
rule.
The domestic steady-state real interest rate, r , has been
f
replaced by r f
if
, the real interest rate abroad.
We want to change the detail about r , in order to avoid that
the in‡ation target “must be” f , see discussion on page
769-770 for example.
ECON 3410/4410 Lecture 10
The open economy policy response function II
This makes the formulation more relevant for real-world
in‡ation targeting, since one rationale for that regime is that a
country can choose its own in‡ation rate.
Replacing r f by r , creates no logical problems in the model.
We just need to remember that the steady-state solution can
entail non-constant depreciation expectations since i 6= i f .
This does not represent a serious problem in a ‡oating
exchange rate regime, And as long as the real-exchange rate is
constant, the long-run solution for in‡ation and GDP can be
described with the aid as the same graph as the other two
regimes.
We therefore prefer the following formulation of the response
function
it = r +
e
t+1
+ h(
t
) h > 0.
(Policy response)
ECON 3410/4410 Lecture 10
In‡ation targeting: system of equations
yt
mt
t
pt
r
1 (et
y
=
rt
=
it
=
etr
=
t
=
it
=
1
= m0
er )
r ) + 3 (gt
2 (rt
f
f
+ 4 (yt
y ) + vt ;
e
it
t+1 ;
e
r + t+1 + h( t
) h>0
r
et + ft
t + et 1 ;
e
y ) + st
t + (yt
f
e
it + ( et + et 1 )
m1 it + m2 yt
g )(1)
(2)
(3)
(4)
(5)
(6)
(7)
Compared to R-I (‡oat with money targeting), one more
equation and one more endogenous variable, which is mt .
Note: On page 771, also IAM introduces the idea of regressive
expectations.
ECON 3410/4410 Lecture 10
The slope of the SRAD under in‡ation targeting I
From (6):
et =
1
e
itf )
(it
et
1
substitution of it from Taylor rule (3)
et =
=
1
e
1
e
e
t+1
r+
h(
t
+ h(
)+
1
if
e t
)
t
e
t+1
+
1
e
r
et
itf
ECON 3410/4410 Lecture 10
1
et
1
(8)
The slope of the SRAD under in‡ation targeting II
We therefore obtain the short-run AD schedule as
1
yt =
1
+
1
+
e
1
e
2
(h(
3
(gt
h(
t
)+
r
itf
et
1
e
t+1
+
(9)
f
t
t
+ etr
))
t
g) +
4
+
f
4 (yt
y f ) + vt ;
Implicit derivation:
1=
1
1
e
h
@ t
@yt
1
@ t
@yt
2h
@ t
@yt
giving
@ t
@yt
=
AD ;rIII
1
1 + h(
2
1
e
)
<0
ECON 3410/4410 Lecture 10
1
The slope of the SRAD under in‡ation targeting III
Remember that, for the …xed exchange rate regime VI:
@ t
@yt
=
AD ;rVI
1
<0
1
since the di¤erence is a positive term in the denominator, we have
that
@ t
@ t
>
, when e < 0
@yt AD ;rVI
@yt AD ;rIII
meaning that the SRAD curve under in‡ation targeting is less
steep than in the …xed exchange rate regime.
ECON 3410/4410 Lecture 10
Interpretation of the slope-di¤erence
The interpretation of the di¤erence has to do with how the
interest rate is determined in the two regimes: When t
increases, y -demand is reduced in both regimes through the
real exchange rate, e r . But there are additional e¤ects in R-III:
1
2
The interest rate is increased (monetary policy response) which
leads to further reduction in yt .
The nominal exchange rate appreciates because of the higher it
Hence, with h > 0, regime III is di¤erent from the …xed
exchange rate Regime-VI, but also from the ‡oating exchange
rate Regime-I (money as the target) where lower demand for
money reduces the interest rate in the domestic money
market.
Note that we have generalized …gure 25.3: AD(‡ex) represents
only one sub-category of ‡oating exchange rate regimes.
ECON 3410/4410 Lecture 10
Joint equilibrium in three regimes
Inflation
AS schedule is
the same in all
three regimes.
Can illustrate
short-term
equilibrium in 3
regimes with the
aid of a single
graph.
πf
R-III
R-VI
R-I
ȳ
Real GDP
ECON 3410/4410 Lecture 10
Have assumed
that
= f in
this graph.
Supply shock
π
Largest e¤ect on
GDP in R-III.
Least in R-I
SR A S cu rv e
π
e
Largest e¤ect on
t in R-I. Least
in R-III.
R-III
R-V I
R-I
Fu ll emp lo y men t
y
y
ECON 3410/4410 Lecture 10
Hence, the two
‡oat-regimes are
the extremes.
A temporary demand shock I
We already know that R-I and R-VI can be compared by
(identical) vertical shifts in the AD curves:
d t
dgt
d t
dgt
=
yt =y ;rI
=
3
>0
1
yt =y ;rVI
However, from (9)
0=
1
1
2h
e
h
d t
dgt
d t
dgt
d t
dgt
d t
dgt
1
yt =y ;rIII
+
yt =y ;rIII
3
yt =y ;rIII
=
yt =y ;rIII
3
1 + h(
2
1
e
)
ECON 3410/4410 Lecture 10
A temporary demand shock II
So, apart from the case of h = 0, vertical shifts are not
comparable (IAM p 782) across regimes.
However, for a given :
dyt
dgt
=
t=
3
;rIII
since there are no indirect demand side e¤ects of a change in
y in this regime (yt is not included in the policy response
function). The same is true in R-VI where the interest rate is
determined on the FEX marked. Hence, we have
dyt
dgt
=
t=
3
;rVI
and regime III and VI can be compared with the aid of a
horizontal shift of the AD schedule.
ECON 3410/4410 Lecture 10
Demand shock
Comparison of
R-III and R-VI
can be done with
horizontal shift.
π
SR A S cu rv e
Algebra on page
782.
A
B
π
e
Largest e¤ect on
both t and yt
in R-VI.
R-III
R-V I
Fu ll emp lo y men t
y
y
ECON 3410/4410 Lecture 10
The in‡ation
targeting regime
stabilizes both
variables in this
analysis.
Long-run
De…ne steady-state as in R-I and R-VI
With the exception noted above that we can drop
from the de…nition of the steady-state.
e
Because of the Phillips curve, if
from this equation.
=
et = 0
then y = y directly
The real-exchange rate e r is determined in the long-run AD
equation, and equilibriates aggregate demand to the full
employment capacity output y .
The constant equilibrium real exchange rate gives:
f
e=
which can be non-zero if
f
> 0 for example.
ECON 3410/4410 Lecture 10