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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
of Muth (1961).
~
Within
can alter
decisions.
--induced
real
rate
rate
clear,
this
models
of
a
incorporating
Sargent
and
the
balance
effect
extent
monetary
in
the
(2)
only
output
form
temporary
the
real
to which
store
(1976)
depends
the expected
monetary
disturbances
relevant
yields
depends on specification
--"
~
on
deflation
in
the
potentially
to agents'
movements in real
demand and supply
the
and bears
positively
rationally
yields
within
with
of value
anticipations
disturbance
commodity
be working
Barro
on money, i.e.,
(4) agents
by changing
by a temporary
the real
of return
we shall
resembling
of return,
framework,
output
However,
note,
(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
schedules.
.-,.
are
of
I
I
-2 -
I
The organization
we make the notion
I
of
I
section
I
three
commodity
balances.
case,
In this
do not have real
I
link
.income
between
I
monetary
I
permanent
I
theoretical
-Section
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
I
a rational
the model in which
is
monetary
money supply
we derive
movements in
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
f
= ~
(lb),
growth
(2a)
x
(2b)
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
p measuring
x
t
("1 -p)
= AX
t-
the
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
Specification
correlation
) + ~
t-2
t-l
by the authorities.
,
O<p<l
t
t
independent:
the
-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)
-(4)
-",here
-Bs(mt
ydt = Y -ad(pt
+ 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)
-
ySt = Y + as(pt -EPt+l)
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
(
and Barro.
f
Case2
real
present
yield
(
behavior
(
eliminated,
the jth
under
t+j
and output
is
the alternative
prediction
from (11) into
I
(13)
Ep t+j
I
(14)
y t = ]¥£t~T
(15)
Ey
t+j
I
I
(16)
Er
m ,t
of monetary
are
gradually
money is
(7) and (8),
the
= 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
of Lucas
money stock
7
Pt = ffi + S+a(~=p)(mt-ffi)
real
level
t
(12)
and the expected
for
result
specification
from a target
I
I
price
-j
= m
+ p (m -m)
Em
Substituting
prices
the characteristic
deviations
period
as the expected
= m = p
t
t
model reproduces
in which
(11)
I
I ,'
(lb)
on money is zero,
= Em
t+l
By contrast,
-
= 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
to fall,
raise
goods supply
to
additional
income.
I
and taking
a capital
for
on impact,
I
by the
current
I
anticipated
then
character,
because
Notice
that
is
this
level
rises
goods
must rise
eliminate
level
shown in
the solutions
money into
goods supplied
p-7l,
left
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
must rise,
shows the
current
equiproportionately
is
future
level
buy more goods in
excess supply.
the
for
and hoard
increase.
desired
anticipated
the price
future
goods demand and supply
the anticipated
as
him to
amount of
level
implies
that
additional
incipient
frame
level
substitute
money supply
the price
on impact
means that,
demand for
the price
above normal,
enables
real
market
The right
This
back down and thereby
price
to
deflation,
This
The
by examining
excess
an agent believes
total
exhibits
there.
I
gain
The goods market
I
balances
the market
nominal
clearing,
unchanged.
Therefore,
current
Carrying
future
money stock.
I
the
the price
supply
I
real
If
a given
Now if
remains
y.
2.
level.
and an incipient
he has incentive
I
I
in
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+a(l-l.)S
>..
(I=r)(mt-mt-l)
-
(2-- ) (mt mt-l )
+ B+a.(T-"1)\l-1.
+ ~(mt-
solution
rm,t
.=
real
expectations
are:
for
mt-l)]
output
-B+a1r=IrI.
is
I.
.Yt = y-H(l-l.)
-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
original
I
real
balances
operation
period
but
"0, II at output
I
to
limit
I
excess
the
rise
demand for
of
level
y.
current
the
current
cannot
I
rise
I
reduce
-
further
current
end of the
in
yield
periods
and this
in
a
the
fraction
worksII
in money implies
real
illustrated
run equilibrium,
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
on money.
increase
level.
by the
means that
goods in
must rise
and eliminate
the
on impact
incipient
goods.
money stock.
be the
j
shock is
implies
Therefore
Suppose the price
I
yield
of the period
this
real
on a one-to-one
of the model is
determination
rise,
the
Specifically,
monetary
to increase
Suppose the price
the
money as captured
in prices
and the real
a current
run and continues
discussion
in
In the new long
back to
run level.
changes
of a positive
case,
movement,
only
movements in case 2.
are reflected
in the future.
brought
money
current
that
through
a movement in
the
to output
The effect
operating
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
then
Emt+j
-Pt
= 0
I
(30b)
Emt+j
-Pt
= pj(mt-m)
(30c)
Em
-p
=--
I
I
t+j
t
AJ.+1 (m-m
I-A
t
t-l
monetary
The expected
is 13
(30a)
measured
transitory
or consumption.
I
I
)
specification,
accommodate
output
balances
-m
t-l
t
)
real
movements
behavior
I
I
-14
I
I
I
The consequence
make a large
class
with
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
held
only
to be permanent.16If
agents
,
and lengthy
horizons,
monetary
movement cannot
response
in
the future,
(
to real
II
then
a given
periods,
a factor
a reduction
in
In our view,
interpretation
of section
while
with
the
the
along
III
for
is
current
that
to
take
supply.
advantage
of
consumption
budget constraint.
as a medium of
balances
that
temporary
a countervailing,
renders
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
invite,
these lines.
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
it
suppose
in
utility
lifetime
current
might
flow
anticipated
necessitates
the purchase
balances
real
to an anticipated
the services
a reduction
essentially
interpretation
The
specifications
current
marginal
who suffers
these periods.
current
specification
schedules.
balances
an unchanged
with
in order
of production,
in real
as it
satisfy
an individual
to future
is
in the
alternative
then
response
For example,
in measur,ed real
in
a real
held
reduction
transactions
to changes
associated
wealth,
these
as an asset,
becomes plausible
costs
relate
be optimal,
flow decisions.
transactions
for
it
only
demand and supply
have diminishing
to
When money is
exchange,
to
purely
,
I
is
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
II
the real
rational
independence
II
the
II
return
on money,
supply
schedules.
present
nonneutrality
alternative
the
of
It
assumed to be that
II
distinction
retains
a critical
classical
invariance
from perceived
variations
manner on the specification
framework
enters
is
store-of-value
monetary
that
incorporates
important
yield
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
of an asset
between
its
single
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
the
magnitudes
in a basic
of value,
marginal
II
II
in
transitory
which
stores
relevant
-real
effect,
of real
that
expectations.
In the
II
demonstrates
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
t
I
I
).
=
,E 8
J=O
a+13j=O
t-l
I
a+13
I
,
1-A
t
-m
-(~)
=
H (~
c;+"B"\l-A (mt-mt-1)
-H
A
is no tendency for
information.
either
least
(1
-m
t
)
-(m
t-1
) -13
t-l
13+ a(l-A)
Aj+1
(2-)
1-A
+ y
(X) j
E 8 1m
J=O \' t-1
t
1
+ -(m
1-A
-m
A A(1-8)
(H)~(mt-mt-1)}
+
A(1-8»
-1-8),
t
once in either
Al[the
new
t
(m -m
t
t-1
))
.8
~I'
t-l
=
~
a+13
)
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
-m
(I-A)
j!o(-!B)jEmt+j+l)
13+-HAa(l-A) (mt-mt-l)
=
~
1
---(m
1-A
+
t-1
+ -L(m
--~(H)
m is
Em
~m
~
I
and
t+j
= --1L- m -(1-8),
a+13 t
I
tI
j
(~)
(X) j
y t = ~~t
~
are summarized as follows:
(X)
(l-e)
l-~(m -m
) = fii-m
1\ t t-l
t-1
1 ) + ...=
t-1
S
= -E
= m
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
@FedFRASER