Intermediate Targets, Money Supply or Interest rates?

1
Lecture 7

• Intermediate Targets, Money Supply or Interest
  rates?

2

• Examine the problems related to the pegging of
  the rate of interest
• Examine Friedmans 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

3
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.

4
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

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Instability of of the interest rate peg with
Adaptive Expectations
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A dynamic analysis- let R R
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A positive IS curve shock
R
LM
R
IS(?e)
ISu
IS
Y
Y
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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
• SW show that if money is the instrument of
  control, there is a determinate price level
• If R is the control variable, there is not.

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The S-W Rational Expectations Model
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Price level is determined
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If R is pegged - P is indeterminate
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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

13
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?

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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

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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.

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u, v gt 0
LMv
R
LM
ISu
IS
y
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Solving for the equilibrium R and y (eqns 1 2)
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Loss function LR (R-R)2
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Minimising the loss function
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The variance of output
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With an interest rate intermediate target
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R with only IS shocks
R
R
ISu
IS
Y
IS-u
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R with only LM shocks
LMv

• R

LM
LM-v
R
Y
Y
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Variance of output with a money supply
intermediate target
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M with only IS shocks

• R

LM
ISu
IS
IS-u
Y
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M with only LM shocks

• R

LMv
LM
LM-v
IS
Y
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If only IS shocks - which is best intermediate
target?

• R

LM
IS-u
R
ISu
IS
Y
28
If LM shocks only - which is best intermediate
target?

• R

LMv
LM
LM-v
R
IS
Y
Y
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Combination policy

• R

LM if IS shocks only
LM if IS LM shocks
LM if LM shocks only
IS
Y
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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