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r

Preliminary

f

Not

to

be Quoted

I
r

I
Working

I

A NOTE ON THE NEUTRALITY

I

I

79-2

OF TEMPORARY MONETARY DISTURBANCES

Marvin
Federal

Paper

S.

Reserve

Goodfriend
Bank of Richmond

Robert G. King
The University

of Rochester

(
(
March 1979

I

I
I

,
I
I

,

The views expressed here are solely
those of
the authors and do not necessarily
reflect
the
views of the Federal Reserve Bank of Richmond.

I

,
~-"

"

-""

"--"~-

-~

I
I
I

In the

I

(1972,1975)
generated

I

that

classical

and Barro

monetary

construction

of

I

relationship

between

I

result

I

rational

believed

For
a classical

tI

following

11

a fixed

of

on the basis

studies
of

shocks,

the

temporary

was the

the contemporaneous

prices

technical

relaxing

to be generally

the purposes

of the

macroeconomic

and output,

convenience.

random walk

monetary

inconsistent

specification

disturbances,

with

of the discussion

(zero)

rate,

(3) markets

sense

note,

models

of

a

incorporating

Sargent

rate
rate

and

the
(2)

only

output

Barro
store

Within
can alter
decisions.

--induced

real

this

framework,

output

However,

by changing
the

by a temporary
the real

balance

effect

extent

monetary
in

form

(1976)

within

with

of value

depends

on money, i.e.,

(4) agents

be working

and bears

positively

the expected

temporary
the

real

to which

anticipations

rationally

monetary

disturbances

the

on
deflation

of Muth (1961).

~

clear,

of return,
of return

we shall

resembling

(1) money is

nominal
real

present

model closely

characteristics:

the anticipated

-

and (b) permanent.

chosen for

effects

implies

(1975).

II

II

specification

models

monetary

by Lucas

are assumed to be

of these

consistent

of model,

to real

expectations,

.Wallace

~

type

This

focus

unobservable

this

leads

widely

analytical

constructed

aggregates

(a) unanticipated

was presumably

within

potentially

monetary

expectationally

specification

However,

is

primary

I

models

random walk.

growth

As the

I

(1976),

by a logarithmic

all

this

macroeconomic

yields

yields

depends on specification

demand and supply

--"

~

the

potentially

to agents'

movements in real

disturbance

commodity

relevant

in

schedules.

.-,.

are
of

I
I

-2 -

I

The organization
we make the notion

I

of

three

I

section

we derive

a rational

commodity

balances.

case,

In this

movements in

do not have real

I

link
.income

between

I

monetary

I

permanent

I

theoretical
-Section

I

Three
will

processes

I

independent

for

disturbances

(1957)

in which

only

the

of

In section

permanent

the

IV

monetary
temporary

we discuss

behavioral

strict

permanent

and demand functions,

of the alternative

or

some

specifications.

remarks.

(la)
and Barro

(1976).

autoregressive
stock,

in

specifications

the discussion

the natural
normal

-Specification

-

temporary

we break

from Friedman's

of

money

cause

III,

quantities--irrespective

some concluding

in

a version

monetary

section

supply

by means

depend on current

permanent

of the disturbances.

alternative

be considered

I

II

to

for

I,

MoneySupply Specifications

I

I

real

solution

specification,

relevant

precise,

disturbances

in

working

this

interpretations
V contains

I.

are

do not alter
character

while

By contrast,

Under

magnitudes

aggregates

monetary

In section

Subsequently,

demand and supply

money and prices,

perspective.

disturbance

expectations

temporary

effects.

as follows.

specifications.

commodity production,

I

is

monetary

money supply

the model in which
I

discussion

of a temporary

alternative
II,

of the

logarithm

the

of the
~t'

in

(lb)

the level

policy

The impulse
money stock

with

constant

random walk process,

Specifications

processes

respectively,

below.l

random variable,
is

of exogenous

and (lc)
and first

where p and A are positive

as in
are

to

behavior

these

(m ) is
t
variance

a serially

difference
constants

2

a ~.

Lucas (1972,
first

stochastic

1975)

order

,

of the money
less

than unity.

r
r

-3

r

(la)

m
t

r

(lb)

m -in. = p(m
t
t-1

f

(lc)

m -m
t
t-l

I

In specification
Defining

the

I

(lb),
growth

(2a)

x

(2b)

f

= ~

x

t

+ m
t-

t

rate

= ~

=

1
-in.)

= A(m
t-1

in. is
x

(2c)

f

Under
and serially

I

is

zero.2

I

x

t

("1 -p)

= AX
t-

the

correlation
being
shocks

imply

,

is nonstationary).
to a positive

(2b)

(~=
t+.
_J

0,

2b and 2c.3

t

1

I

j

) +

imply

~

t
specification,

at which

however,

a permanent

~t>O,

money shocks

in time,

a fixed

deviations

from average,
like

the

expected

target

implies
with

the expected

I shows the response
when all
for

the

other

shocks

monetary

permanent

future

target
positive

a fraction

random walk

are

money stock

from the

specification

change in

Figure

= 1,2,3...),

money stock.

t

implies

The third

shock,

of the

1, these rules

at any point

of money growth

t

1
i

1 + ~

rapidity

anticipated:

O<A<l
t

run level

(m -m

random walk

by the authorities.
,

) + ~
t-2

t-l

Specification
the

O<p<l

t

t

independent:

p measuring

-m

= m -m
t
t-

t
t

+ ~

the long

t

-

money growth
(m) with

are corrected
serial

of abnormal

specification,

level

growth

random

of money (the

process

of money and money growth
are assumed zero

policy

specifications

I
I

-4

-

I
I

Xt+j

mt+jlll

I

I

1..-

I
I

j

012345

j
x

= (1 -p)(m

t

-m

01
t-l

2345

) + E;
t

I
I

Xt+j

mt+j

I

I
j

0

1 2

3 4 5

j

I

x

= A(X
t

t-l

I

I

II.

to

I

and demand schedules,

that

rational

I

constructed

section

introduces

by Barro

(1976).

a market

expectations.

5

6

7

) + E;
t

real

money price

balances.

4

p.

model

The main elements
condition,

and demand for
one period

The normal

of the good y is

a log-linear

clearing

The supply

good y depends on the anticipated
current

I

3 4

A Basic Equilibrium ~

I

I

2

Figure 1

The present

I

0 1

level

real

of output

are

closely

commodity

and the hypothesis
the single,
return
is

related
supply
of

nonstorable

to money and on
denoted

y

and the

I
I

-5 -

I

(3)

ySt = Y + as(pt -EPt+l)
ydt = Y -ad(pt

-(4)

-",here

+ Bd(mt -Pt)

following

Barro all

market clearing

-(5

condition

Pt -a+B

Pt+l

the following

+~
a+B

recursive

with

t

(8)

y

solution

technique.

-L
Pt -(a+B)

the corresponding

I

of the

and output equations:

In the discussion

expectations

substitution

(7)

Solution

a = as + ad'
that follows,

the case

for concreteness.

rational

-the

price

compound parameters have been defined:

be treated

-A

,

as positive.5

+ ~t

= Bs + Bd' and H = asBd -adBs.
H>O will

-Pt)

parameters are treated

y t = Y --~Pt+l

where following

-B

-EPt+l)

yields

-~

)

(6)

-

-Bs(mt

for

prices

The result

may be obtained

by

is

E
~j
6,
j=O (a+B) Emt+j

solution

for

output

~

being

.

= -!!-[m
-L
E (~)JEm
t
a+B t
a+B j=O a+B
t+j+l

] + Y,

Case 1.
I

Consider

-walk

specification

first

the behavior

(la).

In this

contemporaneous information,
"

,

I

output

exhibit

a neutral

Em
t+j
solution

(9)

Pt = mt;

Yt = Y

of prices

and output under the random

case, given the assumption of complete
= m
t

for all

j.

Thus, prices

and

11

I)

(!

Ii

-6

f

and the

expected

r

is

equal

to mt

(10)

Ep
t+l

also

f
Thus,

the

(

present

yield

on money is zero,

= Em
t+l

as the expected

price

level

= m = p
t
t

model reproduces

the characteristic

result

of Lucas

and Barro.

f

real

-

Case2
By contrast,

(

behavior

(

eliminated,

in which
the jth

(11)

I
I ,'

(lb)

under

deviations

period

t+j

and output

is

specification

from a target

prediction

for

money stock

from (11) into

(7) and (8),

the

Pt = ffi + S+a(~=p)(mt-ffi)

I

(13)

Ep t+j

I

(14)

y t = ]¥£t~T

(15)

Ey
t+j
real

= Ii + ":Bfu~I:p)"Pj (mt-ffi)

=

(mt-

H(l-p)pj
~+a(l-p)

return

Ii) + Y

(m -in) + Y
t

on money is

given

by

I
I

I
I

(16)

Er

m ,t

gradually

money is

7

(12)

and the expected

are

t

I

I

of monetary

-j
= m + p (m -m)

Em

Substituting
prices

the alternative

= p

t

-Ep

t+1

=

~(I-p)(m
I3+a(l-p)

t

-Ii)

implied

behavior

of

(I
;
! 1
;

,

I
!

!

-7

I:

A positive
operating

r

the

characteristics

determination

(

exists

I

balances

demand for

in

this

in

to fall,

raise

goods supply

to

additional

income.

I

and taking

a capital

I

for

I

by the

current

I

anticipated

gain

market

I
I

The right
on impact
there.

I

level

character,

because

Notice

that

level

goods

must rise
eliminate

is

rises

incipient
level

shown in

frame

the solutions

goods supplied

p-7l,

monetary
those

but

the

of Figure

of real

output.

of deflation
shocks

is

leisure,

next

period

sum over

with
not

the

money

affected

due to

the

is increased.
we assume

than

the

current

2.
It
at its

is

greatest

maximum

,

become more permanent

of the previous

the

to the market.8

Since

by less

is

some of his

goods supply

frame

path

rate

approach

However,

current

left

shows the

current

equiproportionately
is

future

level

buy more goods in

must rise,

the anticipated
as

money into

excess supply.

the

for

and hoard

increase.

desired

anticipated

the price

future

goods demand and supply

the price
This

him to

amount of

deflation,
exhibits

money stock.

substitute

money supply

The goods market
clearing,

demand for

implies
that

additional

enables

real

nominal

level

above normal,

this

total

then

future

means that,

back down and thereby

price

to

the market

Carrying

on impact,

This

the price

an agent believes

the price

supply

I

current

If

a given

Now if

The

by examining

excess

Therefore,

balances

he has incentive

I

unchanged.

and an incipient
y.

2.

level.

remains

real

the

case.

going

two periods

rise,

in Figure

goods.

But a rise
deflation

level

current

illustrated

1'011price

1'0" at output

to bring

the excess

I

I

real

is

model may be illustrated

of the period

in period

on impact

shock

of the

Suppose the price
on impact,

I

monetary

-

case.

in

I
I

-8-

I
I
I
I

Case

~

Behavior

I

Response

of

Prices

to

2

and

~t>O

Output

~t+.=O,
-J

I

P

t+j

"

",mt+j

Y t+j

:

,

r'~~~~:-:-::..:::.::..::.::.-::~-~,

01234567

8
Figure

,
I
I

-

,

2

under

all

(lb)

j>O

I
I

I

-9

Case3

I

The third
these

I

-

solutions,

run expected
of

monetary

specification

as a given

value

of the

money growth.

contains

innovation

yields

money stock

The relevant

jth

both

period

the

correlated

prediction

long

pattern
as 9

may be written

.+1
(17)

I

of each of

a change in

and a serially

I

I

elements

where

Em
t+j

.

the

f~rst

the latter

= m
t-l

two terms

term

is

+ -1-(m -m
1-1. t t-l
represent

the jth

) -~

the expected

period's

~ -m
t t-l

1-1.

discrepancy

)

new long

run level

from the expected

and
long

run level.lO
I
I

Substituting
solutions

I

for

(18)

from

price

I

(19)

Pt = [mt-l

(20)

I

(21)

I

I

I
I

Ep t+j

with

price

the rational

Ey

t+J

S
-S+a(l-l.)

>..
(I=r)(mt-mt-l)

-

(2-+ B+a.(T-"1)\l-1. ) (mt mt-l )
+ ~(mt-

solution

rm,t

.=

real

expectations

are:

for

mt-l)]
output

-B+a1r=IrI.

is

-H(l-l.)
I.
.Yt = y -S+a.(l-I.)(~)(mt-mt-l)

the one period

(22)

(7) and (8),

1
+ ~(mt-mt-l)]

= [mt-l

and the corresponding

I

into

and expected

-~(1-1.)
-mt-l

I

(17)

y -Q~~~~~,(A)l.j~
.,+a\l-l\j
J.-I\
return

= Pt -EPt+l

t

-m 1 )
t-

on money in period
-S(l-l.)
>..
= S+a(l-I.)(I=r)(mt-mt-l)

t

.

~~)

(mt-mt-l

)

I
I

-10

I

In interpreting

-~

anticipated

I

mechanism,

I

current

are

monetary

relevant

monetary

future
just

future

equal
as the

these

serially

times

I

first

two terms

and are

Figure

3.

In this

increases
is ~
I

the

short

long
t

its

Again,

of the

I

real

balances

period

rise,

to

limit

I

excess

the

rise

demand for

y.

the

current

cannot
I

rise

I

reduce

-

further
current

periods

and this

in

a
the

fraction

worksII

real

by the

on money.

increase

in money implies

illustrated

run equilibrium,

level.

remains

the

converges

1'011price

an excess
the price

balances

to

its

in

new higher
by a verbal

level.
This

demand for
level

money stock,

increases

illustrated

unchanged.

in
further

The money stock
as it

basis

means that
goods in

must rise

and eliminate

the

on impact
incipient

goods.

end of the
in

j

shock is

implies

Therefore

money stock.

be the

yield

Specifically,

on a one-to-one

of the model is

level

Suppose the price
I

yield

of the period

current

the

real

money as captured

in prices

to increase

this

the

monetary

operation

but

of

in

and the real

determination

"0, II at output

I

changes

original

Suppose the price

only

movements in case 2.

a current

run and continues

discussion

movement,

In the new long

back to

run level.

current

of a positive

in the future.

brought

money

are reflected

case,

through

a movement in

the

to output

The effect

operating

that

of output.

permanent

(18)

irrelevant

I
I

in

first

determination

correlated

In addition,

notice

increments,

implies

H Aj

to

solutions,

to the

shock

-

level
Current

story

the future.
goods supply

rises
real

on impact
balances

because

are unchanged,

the money stock

The anticipated
below normal

equiproportionally

inflation

and raise

but

and prices
induces

current

with
this
will

agents

to

goods demand

-11-

Case 3
Behavior of Prices and Output under (lc)
Response to ~t>O

P t+j

/---::-::~-;--:::::-;-::~

.,.

."
Pt-1

= mt-1

,.. If;..

ttj:j=O,

all

j>O

Yt+j

mt+j

01234567

012345

Figure 3

.0

.

I

m
'"

I

~,

:
-

-12

I

above normal.

I

Therefore

But this

the current

stock increase.
I

price

the left

I

output.
III.

level

level

as is evident

The right

level

is bounded

by reasoning

alternative

paths are shown in

frame shows the path of real

specification

considered in the present section

only permanent monetary magnitudes appear in the commodity supply

and demand schedules.U
respecification

Denoting permanent money balances as m*t'

(23)

ySt = Y + as(pt-EPt+l)

I

(24)

yd

where all

t

= Y -0.

d

-8s(m*t-Pt)

(p -Ep
) + 8 (m* -p )
t
t+l
d
t t

parameters are assumed positive.

The market clearin~

implies

I

(25) p = ~p

I

(26)

t

A rational

I

a+8

t+l

+ ~*

0.+8 t

Yt = y + ~(m*t-EPt+l)

expectation
(27)

solution

-6-'"

for

o.j

prices

then has the form

*

Pt = a+B j~O (a+B) Em t+j

I

I
~y;;

this

implies

I

I

along

The Permanent Balance Model

is that

I

price

money

11

~e

-I

must exceed the current

The money stock and price

frame of Figure 3.

I
I

rise

excess demand for goods.

in the current

above by the new long run price

I

an incipient

level

Note the rise

the above lines.

I

implies

-

,",

~."

condition

c""""~?,,,"::iii',
;",i'~~c;,§~~i1

I
I

-13

I

I

Consistency
absence

of trend

the behavior
I

P

I

output

equal

policy
forecasts

I

yield

the

* +'

= m

and,

correspondingly,

Em

t J

*

in

t

.Thus,

to

on money is

permanent

simply

monetary

are obtained

the previous

zero

values

by letting

for

j

the

go to

three

infinity

alternative
for

the

section.

*

(29a)

I

that

requires,

to y.

specifications
in

the money supply,

reduces

The relevant
I

of expectations

t

the expected
is

in

formation

= m*
t

Further,

the

growth

of prices

(28)

I

in

-

m t = mt

(29b) m* = m
t

I

(29c)

I

I

Thus,
balances,
without

I

m* = m
t
t-l

m -p
t
affecting

of measured real

in
t

this

+ -l-(m
I-A

behavioral

, adjust
real

to

)

specification,

accommodate

output

balances

-m
t-l

t

transitory

or consumption.

then

(30a)

Emt+j

-Pt

= 0

I

(30b)

Emt+j

-Pt

= pj(mt-m)

(30c)

Em

-p

=--

I

I
I

t+j

t

.+1
AJ (m-m
I-A
t
t-l

monetary

The expected

is 13

I

measured

)

real
movements
behavior

I
I

-14

I
I

The consequence
make a large
with

I

class

to their

respect

balances--as

of

this

effect

on real

limit

The short

I

to change any of
long

I

run monetary

stock

real

Consequently,

and the price

level

I

assumed to know this.

I

their

real

I

real

and demand only
permanent

I

real

or measured

I

I

short
long

run level

I

terms

I

from

this

is

and stays
(23)

level.

If

short

then

to

affect

behavior,

the

level

there.

and (24)

only

This

is

and solving

equilibrium

in this

supplies

changes

case is

The only
zero

no

current

or demand.

path

immediately

is

in

consistent
to

on the anticipated

Pt.

in

or

there

and convergence

jumps

are

goods supply

time

seen by eliminating
for

money
Agents

realize

level

foresight,

level

the

goods supply

price

conditional

Therefore,

run changes

excess

allow

as follows.

run monetary

affect

not

real

in

are assumed not

short

and agents

their

perfect

price

that

they will

briefly

run effects.

balances

effect,

rules

between

permanent

real

one where the price

goods market

the price

effect,

balances

run equilibrium

I

I

wealth

15

create

a wealth

run equilibrium,

money stock

with

through

real

Given
.with

money wealth.

three

by short

run relation
to

independence

functions.

unaffected

invariant

rule

is available.

run behavior

is

do not

all

to

permanent

a serial

responses

Agents realbE,therefore,

money balances

demands for

and policy

long

because

may be described

the long
is

under

is

random walk

is

information

the solution

balances

the

exhibit

be neutral

disturbances

specification

This

forecast--must

the underlying

run demand for

disturbances.

of

to

output.

contemporaneous

The economics

balance

equivalent

money will

accurate

I

permanent

rules

an optimal

case if

the

policy

of increments.14Hence,
I

of

-

long

to

the

its

last

solution

anticipated

the
run

long
two
consistent

change in

I
I

-15 IV.

Money

t

The models
of the real

,

purpose
to

of section

balance

of

the

present

the economic

,

If
decisions

effect

in

should

is

held

purely
only

,

to be permanent.16If

agents

,

and lengthy
monetary

movement cannot

response

in

the future,

(

to real

II

then

a given

held

to future

periods,

a factor

in

In our view,
interpretation
of section
while
with

the
the

along
III

is

current

to

supply.

take

advantage

in

of

consumption

that

temporary

budget constraint.
as a medium of

balances

could

be relevant

money reduces

of commodities.
an anticipated

shift

Alternatively,

from present,

the lower

to the

Then,,
temporary

expenditure
of

the

net costs

extent

that

current

balances

could

of the previous

sections

these lines.

invite,

The permanent

a purely
specification

asset

balance

theoretic

of section

II

lead

specification,
view of money,

,

is

of money as a medium of exchange.

of,

money

17

the models

balance

current

might

flow

a countervailing,

renders

the purchase

balances

utility

lifetime

it

suppose

a reduction

essentially

interpretation

that

real

anticipated

necessitates

who suffers

these periods.

current

The

specifications

to an anticipated

the services

with

in order

of production,

a reduction

for

balances

an unchanged

an individual

in measur,ed real

is

specification

schedules.

current

marginal

response

For example,

reduction

in

in the

alternative

then

in real

as it

satisfy

associated

wealth,

transactions

a real

becomes plausible

costs

these

as an asset,

be optimal,

flow decisions.

transactions
for

it

relate

have diminishing

to

When money is
exchange,

only

demand and supply

to changes

horizons,

I

to

differ

of money.

respond

planning

and III

commodity

section

functions

money is

II

consistent,

to,

It

I
I

-16 v. Conclusio~s
The present

analysis

I

proposition--the

81

in monetary

aggregates--depends

of

balance

demonstrates

II

the real

rational

independence

effect,

II

the

II

return
supply

present

on money,
schedules.

nonneutrality

alternative
the

of

It

assumed to be that

II

distinction
retains

enters
is

classical

invariance

from perceived

variations

manner on the specification

framework

store-of-value

that

incorporates

such as Barro
for

labor
with

for

a key element

disturbances

to stress

in

(1978)

supply

is

the

that

the

fixed

commodity

in

of

nominal

demand and

a model with

or King

(1978),

and commodity

a variable

money as wealth

importance

context,

as an argument

important

yield

nominal

where

decisions

yield,

is

this

and money as a medium of exchange

the hypothesis

of the invariance

of

magnitudes.
In a critique
(1968)

I

as a medium of exchange,

-to

pointedly

of the

~

asSign
extent

possible

II

the

II

monetary

remarked

a formal

to do this

for

relationship

or

that
if

in

a descriptive

the classical,
between

money and growth
I'it

is

in our

interpretation

disturbances

as an asset

I
I

a critical

monetary

of an asset

between
its

single

of value,

marginal

II

II

magnitudes

in a basic

transitory

which

stores

relevant

-real

in

the

expectations.
In the

II

of real

that

policy

on output

no good to

theoretical
to

literature,
assert

(nonoptimizing)

rules

depends

as a medium of exchange.

effect

on whether

Clower

money serves

we are unable
T0

analysis,

expectations
and the

that

analysis

th~s assert~on.
,
'fl18

rational

Robert

model.

t h e 1 ~m~te d
,.
we have tried
In particular,

of temporary
we interpret

money

I
II

-17 -

I
FOOTNOTES

I

(
I

1 Alternatively,
money

I
I

I

to

observed

conclusions

of

we could

serially
this

have concocted

correlated

variables,

feedback
with

no

rules

from

difference

in

the

paper.

2 This is popularly called a simple "base drift"

policy rule

because the level
of money stock at any point in time is irrelevant
for
intended
future
money growth.
In effect
the level
of the money stock is
allowed to wander or drift
over time) with no affinity
for a mean level.
Intended
money growth is always zero in this case.

lover

Our second policy
may be thought of as a version
of Milton
Friedman's
proposed constant
growth rule.
Here, the long run chosen growth
rate is zero and the monetary authority
is committed to removing any
deviations
of the money stock from its chosen long run level
gradually
time.

I

money growth.

Our third

policy allows "base drift"

3 These figures
policy

specifications

II

I

(lb)

4 A more general
for
y

interest

s

=
t

I

are

n

rate

L a (Ep
j=O j
t+j

expositional

autocorre1ated

of money and money growth

under

and (lc).
specification

effects

would

on commodity

-Ep

simplicity,

corre1ograms

with additional

) -S
t+j+l
since

s

for

a longer

demand and supply,

(m -p).
t
t

the

allow

qualitative

We treat

the

effects

horizon

as for
present

would

example)
case

for

seem to be the

same if

I

~

¥ a pj > O. Such a formulation
allows for larger
effects
of
j=O j
changes in interest
rates that are perceived
to be temporary.
In general,
one would anticipate
that the supply response to transitory
occurrences
would be larger
because of the greater
range of substitution
possibilities)
as Robert Lucas has stressed.
5 See Section
parameter

IV and footnote

I

-

a discussion

of

sign specifications.,

6 l'le are assuming here that
..This
~

16 below for

EPt+j+1 -mt+j~

constraint
guarantees
an equiproportional
and money supply in the long run.

0 as

j -7 m.

movement of the price

level

I
I

-18 -

II

I

I
I
I

7 The steps

involved

deriving

B
<»
.
= -Z
~
J Em
Pt
a+B j=O (a+B)
t+j'
= (1-0)

= (1-0)

H

Yt

I

Pt and Yt are summarized

= -m
a+B

(ffi ~
1

f

0
B

t

agents

<»

aj

--}:;
-Em
a+B j=O (a+B)

= -B-!(B+a)
(l-p)
a+B\S + a(l-p)
8 If

= -L
-a+B

+ (m -ffi)~
=
t
1 ep)

= -B-/m -m -p
a+B \" t

I

.0

't' ej[rn + pj(m -Iii)]
j=O
t

= Lim
-(I-e)
a+B \: t

I

I

in

as follows:

t+j+l

m + ~(m
l-ep

)

(

+

t

(m -rn~
t')

+-

are taken

-m)'
~

-m) ; ~
l-ep

=

B
B + a(l-p)

Y

't' ej m + pj+l(m
-m)\\
j=O
t
'I)
(1-0)-L(m
1-0p

t

+ y

+ y

y

to be identical,

then

since

goods markets

are assumed to clear,
individual
money hoarding
must be zero each period.
Within the context
of this model the possibility
of individual
"current
account imbalance"
can be rationalized
by taking
(3) and (4) as the
representative
agent's
demand and supply functions.

I

If real balances are excluded
from the supply function,
then
agents have incentive
to allow current
good supply to respond to
anticipated
deflation
only if money can be hoarded or dishoarded
to take
advantage of an anticipated
capital
gain or loss.
In this case, goods
market equilibrium
must allow a voluntary
transfer
of money balances
from,
one subset of agents to another for good supply to be affected
by anticipated
deflation.
Note that this requires
a reverse transfer
to occur in the future,
before a full
long run equilibrium
is reached.
However, it is beyond the
scope of this paper to pursue this line of thought further.

I

I

,,

I

I

I

.'

-

-".c.

-19

II

9 The new long run level
Suppose mt-mt-l

I

rot

So

+ -1-:(m

1-A

-m

t

).

I

(X)

,E 8
J=O

a+13j=O

= m

t-l

I

j

(~)

a+13

(X) j

t-1

1-A

t

-m

-(~)

,

either
least

t-1

13+ a(l-A)

Aj+1

t

once in either

-m

(I-A)

(2-)

1-A

t

1
+ -(m
1-A

-m

A A(1-8)
(H)~(mt-mt-1)}

+

A(1-8»

-1-8),

new

t

(m -m

t

))

.8

~I'

t-l

=

~
a+13

)

t-1

Aj+2
) --(m
1-A

t

-m
)~~
t-1

~

) (mt-mt-l)
+!

that in the period of unanticipated
money growth there
output to rise since we assume complete contemporaneous

11 The results for output hold throu~hout
p -Ep or m -p is in the supply function
t

Al[the

+ y

-HA
13+ a(l-A) (mt-mt-l)

is no tendency for
information.

~

tI

A

=

-(m

(X) j
E 8 1m
J=O \' t-1

-H

I

t

)

) -13

t-l

H (~
c;+"B"\l-A (mt-mt-1)

(1

-m

j!o(-!B)jEmt+j+l)

=

--~(H)

1
---(m
1-A

+

~

I

m is

t+j

= --1L- m -(1-8),
a+13 t

I

and

Em

~
m

+ -L(m

y t = ~~t

~

are summarized as follows:

S
= -E

(l-e)

l~(m -m
) = fii-m
1\ t t-l
t-1

1 ) + ...=

t-1

=

t

I

I

t-

10 For example, the difference
between
series in m -m 1 starting
at t+l].
t t-

p

sum of changes.

> 0, then

The derivations
I

is found as an infinite

--t

t-1

infinite

-

t 1 + A(mt -mt 1 ) + A2 (m -m

-ro

ffi = m

II

..Remember
~

.

C;;"

"""

:'ti"jt; 1~
1ft,..;;;,.,
,..)
')~~
;;'.:"

I

I

"';"

t

t

function.

I
I
~

.~

this section so long as
and they each appear at

I
I

-.-21-

I

I

BIBLIOGRAPHY

Barro, R.J.,
Journal

I

"Rational Expectations and the Role of Monetary Policy,"
of Monetary

I

Friedman,
M.,
University

,

Muth,

I
I
I
I
I
I
I

July-August

1976,1-32.

March 1978.

1968,876-880.

A Theory of the Consumption
Press, 1957.

paper,

October

of Economic Theory,
"An

Political

I

paper,

Function,

Equilibrium
Economy,

J., "Rational
Econometrica,

4,

April

Model
83,

Princeton

of Money," unpublished

1978.

Lucas, R.E., "Expectations and the Neutrality

I

iI

working

King, R.G., "Asset Markets and the Neutrality
working

I

January

Clower, R., "The Optimal Growth Rate of Money," Journal of Political
Economy,

II

2,

, "A Capital Market in an Equilibrium Business Cycle Model,ll
unpublished

I

Economics,

1972,

of

December

the

of Money," Journal

103-124.
Business

Cycle,"

Journal

of

1975,1113-1144.

Expectations
and the Theory
29, July 1961, 315-335.

of Price

Sargent,
T.J. and N. Wallace,
"Rational
Expectations,
Instrument,
and the Optimal Money Supply Rule,"
Economy, 83, April
1975,241-254.

Movements,"

the Optimal Monetary
Journal
of Political