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