Transcript Lecture 7 Intermediate Targets, Money Supply or Interest rates? • Examine the problems related to the pegging of the rate of interest • Examine.

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
   (   )
e
e
A dynamic analysis- let
R = R*
y   ( R *  )
e
y   e
e



  y  
    e   e
e

  (  1) (   )

0

A positive IS curve shock
R
LM
R*
IS(e)’
IS+u
IS
Y
Y*
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
m td  Pt  y t  cR t
(1)
mts  m   t
(2)
y ts  y   ( Pt  E Pt )
(3)
y td  rt
(4)
t 1
Rt  rt  E Pt 1  E Pt
t 1
t 1
(5)
Price level is determined
equating money demand and money supply

m   t  Pt  y t  c rt  E Pt 1  E Pt
 Pt  y t 
c


t 1
t 1
y t  c E Pt 1  E Pt
t 1
t 1


taking expectations

c

mt  E Pt  y  1    c E Pt 1  E Pt
t 1
t 1
t 1
 

or
c

m  1   y

c

E Pt 

E Pt 1
t 1
1 c
1  c t 1
By continuous forward substitution
 

1 N
 c 
E Pt 
m  1  c y 


t 1
 1  c
1  c i 0
c

lim N  , E Pt  m   1   y
t 1


N
 c 


 1  c
N 1
E Pt  N 1
t 1
so P is determined.
If R is pegged - P is
indeterminate
If R is pegged, then take the conditional expectation of the IS curve.


E y t    E Rt  E Pt 1  E Pt 
t 1
t 1
t 1
t 1
E Pt  1 E y t  E Rt  E Pt 1
t 1
t 1
t 1
t 1
say
E Rt  R then by substituting forward
t 1
E Pt 
t 1
1

N
E y
i 0
t 1
t i
 NR  E Pt  N 1
lim N   , lim E Pt  
t 1
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 = 2v
• 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
LM+v
LM
IS+u
IS
y
Solving for the equilibrium
R and y (eqns 1 & 2)
( y0  u )  ( m  v )
R
(   )
 ( y0  u )   ( m  v )
y
(   )
Loss function LR =
2
(R-R*)
 ( y0  u )  ( m  v )
*
LR  
R 
(   )


2
Minimising the loss function
 y  u (m  v)
  1
LR
 2 0

 R * 
m

  
   
Which gives:
m  y 0  u  v  (   ) R *

  0

The variance of output
  ( y0  u )   ( m  v )
*
E ( y  y )  E 
 y 
(   )


* 2
2
With an interest rate
intermediate target
  ( y0  u )   ( y0  u  v  (   ) R  v)
*
E ( y  y )  E 
 y 
(   )


 E ( y0  u  R*  y * ) 2   u2
*
* 2
 y2 R  R   u2
*
2
R* with only IS shocks
R
R*
IS+u
IS
IS-u
Y
R* with only LM shocks
LM+v
LM
• R
LM-v
R*
Y
Y*
Variance of output with a
money supply intermediate
target
  ( y0  u )   ( m  v )
*
  E( y  y )  E 
y 
(   )


*
2
y
* 2
 y0  u  m  v
*
 E
y 
(   )


*
2

2
y m  m*
2
2
   2    2
  u  
  v
 
   
   
2
M* with only IS shocks
• R
LM
IS+u
IS
IS-u
Y
M* with only LM shocks
• R
LM+v
LM
LM-v
IS
Y
If only IS shocks - which is
best intermediate target?
• R
LM
IS-u
R*
IS+u
IS
Y
If LM shocks only - which
is best intermediate target?
• R
LM+v
LM
LM-v
R*
IS
Y*
Y
Combination policy
• R
LM if IS shocks only
LM if IS & LM
shocks
LM if LM shocks
only
IS
Y
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