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Lecture 7
Intermediate Targets, Money Supply or Interest rates?
• Examine the problems related to the pegging of the rate of interest
• Examine Friedman’s argument in the context of adaptive expectations.
• Confirm the Sargent- Wallace finding for the instability of an interest rate peg with rational expectations
• Show that an interest rate target is feasible under RE
The Friedman critique of interest rate pegging
• Friedman showed that pegging the rate of interest leads to instability of inflation and output
• The argument owes a lot to Thornton (1806) and Wicksell
• A positive real shock can lead to accelerating inflation and above capacity growth.
The model
• Let m = money, y = output, r = real rate of interest, R = nominal rate of interest and = rate of inflation (e = expected inflation)
• R = r + e • Let the demand for money be given by md
- p = y - R • Let the IS curve be y = -r• Let the ‘Phillips’ curve be = (y-y*)+ e
Instability of of the interest rate peg with Adaptive
Expectations
)( ee
A dynamic analysis- let R = R*
0
)()1(
)*(
e
ee
e
e
e
y
y
Ry
A positive IS curve shock
R
R*
Y*Y
LM
ISIS+u
IS(e)’
Sargent & Wallace confirm the same result with RE
• Should the monetary authorities use the interest rate or the money supply as its instrument of control?
• It depends on the flexibility of prices and relative magnitudes of demand (real) versus nominal shocks
• S&W show that if money is the instrument of control, there is a determinate price level
• If R is the control variable, there is not.
The S-W Rational Expectations Model
tttd
t cRyPm ( 1 )
m mts
t ( 2 )
y y P E Pts
tt
t
( )1
( 3 )
y rtd
t ( 4 )
R r E P E Pt tt
tt
t 1
11
( 5 )
Price level is determinede q u a t i n g m o n e y d e m a n d a n d m o n e y s u p p l y
m P y c r E P E P
P yc
y c E P E P
t t t tt
tt
t
t t tt
tt
t
11
1
11
1
t a k i n g e x p e c t a t i o n s
m E P yc
c E P E Ptt
tt
tt
t
1 1
11
1
o r
E Pm
cy
c
c
cE P
tt
tt
1 11
1
1 1
B y c o n t i n u o u s f o r w a r d s u b s t i t u t i o n
E Pc
m c yc
c
c
cE P
tt
N N
i
N
tt N
1
1
01
1
1
11
1 1
l i m ,N E P mc
yt
t
1
1
s o P i s d e t e r m i n e d .
If R is pegged - P is indeterminate
I f R i s p e g g e d , t h e n t a k e t h e c o n d i t i o n a l e x p e c t a t i o n o f t h e I S c u r v e .
E y E R E P E Pt
tt
tt
tt
t
1 1 1
11
E P E y E R E Pt
tt
tt
tt
t 1 1 1 1
11
s a y E R Rt
t
1 t h e n b y s u b s t i t u t i n g f o r w a r d
E P E y N R E Pt
tt
t ii
N
tt N
1 10
11
1
l i m , l i mN E Pt
t 1
McCallum (1981) (1986)
• If the monetary authorities follow an interest rate rule, it is possible to obtain a determinate price level.
• mt = m* + a(Rt-R*)• In a simple model with a forward expectations IS
curve and a LM curve and a price surprise supply curve.
• There is a deterministic solution and a stochastic solution
Monetary Policy - intermediate targets
• The role of monetary policy in a stochastic environment
• The intermediate target - money supply or interest rate to stabilise output?
• When is the money supply the most appropriate intermediate target?
• When the interest rate?• When a combination?
Assumptions• Authorities know the structure of the economy• Uncertainty is additive• Shocks to the IS curve are given by u and E(u) =
0 and E(u)2 = 2u
• Shocks to the LM curve are given by v and E(v)=0 and E(v)2 = 2
v
• The price level is fixed and we are in the short-run
IS-LM Model
• IS Schedule y = y0 - R + u
• LM Schedule m = y - R + v
• A positive u shifts the IS curve up
• A positive v shifts the LM up to the left.
u, v > 0
R
yIS
IS+u
LM
LM+v
Solving for the equilibrium R and y (eqns 1 & 2)
)(
)()(
)(
)()(
0
0
vmuyy
vmuyR
Loss function LR = (R-R*)2
2
*0
)(
)()(
Rvmuy
LR
Minimising the loss function
W h i c h g i v e s :
*0 )( Rvuym
01)(
2 *0
R
vmuy
m
L R
The variance of output
2
*02*
)(
)()()(
yvmuy
EyyE
With an interest rate intermediate target
22
22**0
2
**
002*
*
)(
)(
))(()()(
uRRy
uyRuyE
yvRvuyuy
EyyE
R* with only IS shocks
R
Y
R*
IS
IS+u
IS-u
R* with only LM shocks
Y
• R
R*
LM
LM-v
LM+v
Y*
Variance of output with a money supply intermediate
target
2
2
2
2
*
2
2
**
0
2
**
02*2
)(
)(
)()()(
vummy
y
yvmuy
E
yvmuy
EyyE
M* with only IS shocks
• R
Y
LM
IS
IS+u
IS-u
M* with only LM shocks
• R
YIS
LMLM+v
LM-v
If only IS shocks - which is best intermediate target?
• R
Y
R*
LM
IS
IS+u
IS-u
If LM shocks only - which is best intermediate target?
• R
Y
IS
R*
LM
LM-v
LM+v
Y*
Combination policy
• R
Y
IS
LM if IS shocks only
LM if LM shocks only
LM if IS & LM shocks
Summary
• Interest rate is best intermediate target if LM shocks dominate
• Money supply is best intermediate target if IS shocks dominate
• Combination policy is superior to both if shocks come from both IS and LM