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Working Paper 84-8
INFORMATIONAL IMPLICATIONS OF INTEREST RATE RlJLES
Michael Dotsey
Federal Reserve Bank of Richmond
Robert G. King
University of Rochester
Federal Reserve Bank of Richmond
and
National Bureau of Economic Research
November 1983
revised September 1984
We have benefited
from the comments of Marvin Goodfriend
and presentation
of this paper at the Econometric
Society
meetings
in December 1983.
The
National
Science
Foundation
has supported
the second author's
participation
The views expressed
in this paper are not necessarily
in this research.
those of the NSF, of the NBER, or of the Federal Reserve Bank of Richmond.
Abstract
Returning
textbook
to
a topic
first
Keynesian
model,
this
Our analysis,
rules.
macro model
different
of
that
ial
market
and real
activity,
activity.
However,
of
the
either
of
these
by the monetary
is
system,
money stock
policies
rate
but
policy
it
control;
treated
faces
real
may be optimal,
given
expectations
frictions.
With
has
with
information
content
on the
can always
feedback
incomplete
choice
the
the
consequences
rule
in a
and money supply
a rational
can affect
a discrete
Depending
(1970)
and informational
money stock
authority
rate
within
targets
these
by Poole
interest
conducted
prices
chosen
when the
economic
peg and strict
I
interest
by an appropriately
compares
flexible
ion,
replicated
state
paper
by contrast,
incorporates
informat
prices
systematically
to economic
information
betweeen
-.-
parameters
informational
be
about
an interest
of
the
rate
the model,
constraints
faced
authority.
Michael Dotsey
Research
Department
Federal
Reserve
Bank of Richmond
Richmond, VA 23261
(804)-643-1250
(Ex. 3201)
Robert G. King
Department of Economics
University
of Rochester
Rochester,
NY 14627
(716)-275-3895
-
,
I
’
I.
Introduction
Policy
of
discussions
an appropriate
translated
to
context
this
monetary
the
for
policy
Poole’s
of
of
a search
rate
William
the
level
into
an interest
in central
been
(1970)
authority,
money stock
can be achieved
central
bank cannot
observe
policymakers
rate
to
counteract
Following
a poliry
shocks-for
should
this
of
is
analysis
analysis
of
2
the
the
line,
typically
of
output
policy,
Poole’s
authorities’
implications
of
money supply
observed
models
Poole’s
with
policy
to
(1970)
state
flexible
the
in the
rate
to
interest
shocks.
movements--i.e.,
standard
framework
work also
hinted
alternatives
nominal
rate
the
prices
economy,
interest
providing
interest
so that
when the
and nominal
interest
at a positive
rate
smoothing
and informational
are
in
equivalent,
of
real-
with
to
relevant
Second,
response
concern
adherence
known by the
are
contained
against”
In addition
is
means.
unobservable
of ‘Teaning
--
desirable.
expectations
of
been
instruments
results
policies
contemporaneous
effects
policy
economy
by either
has
But this
of
rate
selection
critics.
monetary
the
focus
rule.
two major
new information
contemporaneous
monetary
monetary
the
a policy
positive
In rational
t ions,
employ
the
this
yielded
and interest
demand management
fully
optimal
state
optimal
rate
on the
by monetarist
model
when the
centered
Recently,
interest
of
Keynesian
long
rate.
challenged
analysis
First,
controversy.
interest
an optimal
has
a textbook
banks have
dramatically
.l
fricaltered.
1
See, for example,
the discussion
of interest
rate smoothing
in the context
of a descriptive
analysis
of monetary policy
provided
by Poole (i975).
Goodfriend
(1984)
offers
a positive
theory of monetary policy
that incorporates
an interest
rate smoothing
objective.
2
Lucas (1972,
1973)
of informational
frictions
incorporate
economy-wide
and King (1983)--so
that
provided
initial
models that stressed
the importance
supply theory.
for aggregate
More recent
treatments
bond markets --Barro
( 19801, Grossman and Weiss ( 1982)
discussion
of monetary policy
choice
becomes feasible.
2
In these
models,
requires
the
a nominal
obtains
is
than
to
the
agents
nominal
interest
rate,
movements
paper
rules
rate,
Because
supply
fluctuations
(19821,
class
rule
with
than
interest
not
with
the
activity
literature
rate
rules
the
standard
alters
information
with
as
equivalence
real
activity
discussed
of
implications
of
by Poole,
in the
leaning
actively
against
expectational
feedback
information
and
level
.informational
it
nominal
equivalent
alters
channels
described
V>.
of
to a
the magnitude
analyzed
Section
content
the
to economic
is
mechanisms
(1970,
interest
targeting
targetting
conditions,
of
prices
expected
rate
as Poole
the
serves
contained
flexible
its
interest
such
response
informational
to economic
the
of
by a known policy
a policy
through
which
but rather
4
models
of
feedback
through
the
as adjusting
policy
rule,
more fundamental
policy
affected
rate.
interest
we define
expectations
of
is
postulated
the distribution
utilize
we consider
this
an even
Further,
expectations
in real
rather
rational
which
be arbitrarily
money supply
contemporaneous
concerned
which
cannot
Thus,
efficiently
in rational
catidit ions.
money
of
Specifically,
interest
3
analysis.
in the
is
rule
an underlying
system.
sort
private
frictions.
!
to the
because
rate
of
in Poole’s
invariant
This
rate
specification
anchor
surprise
--
an interest
by King
in pre--
That
market
of
is,
prices.
our
5
_.
3
Sargent and Wallace
(1975)
introduced
the indeterminacy
of the price
level
that obtains
with an arbitrary
interest
rate rule under rational
expectations.
McCallum (1981b,
1984) discusses
some alternative
ways of resolving
this indeterminacy , which all amount to specificat
ion of a nominal anchor for the system by a
determinate
path for the money supply.
4
See King (19831,
Dotsey and King (19831,
and Canzoneri,
Henderson and Rogoff
(1983)
for alternative
discussions
of this irrelevance
result,
which requires
that agents observe
nominal interest
rates and that unanticipated
but accurately
perceived
money growth has no real effects.
5
agents
content
King (1982)
stresses
that
is a necessary
condition
of prices.
differential
for monetary
information
on the part of economic
policy
to affect
the information
1
3
Thus,
we conclude
variability
of
no reason
to
feedback
prefer
is
interest
activity.
But,
in contrast
interest
rate
an active
to economic
When the
that
real
that
such
money stock
‘interest
monetary
then
rule
rate
authority
interest
when there
either
are
The organization
informational
III,
the
matical
the
appendix.
expectation
particular
attention
based
II.
the
Poole,
an impact
on the
analysis
provides
our
to a money stock
rational
that
solution
rule
with
information,
so
paid
to
the
rate
rules.
Section
on this
paper
and related
Although
peg.
absorbs
the
paper
analysis
with
we consider
the
a strict
such
an
reminiscent
interest
rate
of
authority.
In Section
flexible
policy.
details
Poole
peg may be
as follows.
with
of
prices
and
In Section
presented
in a mathe-
how monetary policy
potentially
-real activity
in our model, with
informational
a brief
is
model
in our
hence,
or
no longer
money demand disturbances
on the monetary
of
scheme
policies,
constraints
and,
VI is
targeting
in a conculsion
the model,
format ion
rate
expectations
IV,
rate
rule
we employ
of
incomplete
money stock
remainder
In Section
influence8
interest
information
simple
frictions
we discuss
can have
non-activist
also
Thus,
shocks.
a strict
of
it
information,
V),
out
interest
and an unconditional
(1970,
we lay
or
two alternative
money supply
II,
rule
with
one must compare
and eliminates
optimal
to
policy
must operate
money supply
peg destroys
Section
targeting
conditions.
an optimal
feasible,
rate
implications
of
alternative
summary and presents
efforts.
’
a simple
aggregative
our
conclusions
The Model
In this
of
result8
of
these
paper,
concerning
results
also
we employ
interest
hold
rates
in other
model
and informational
more complicated
to
demonstrate
efficiency.
models
that
a set
But many
have
flexible
I
I
I
~
~
C
4
prices
and informational
frictions
(such
as King
(1983)
in the model
economy
that
and Dotsey
and King
(1983)).
There
for
our
are
two elements
SUbSeqUent
depend
on agents’
(1972)
and Barro
who are
of
prices,
these
previously
.
tial
is
the
authority
has no real
and,
Commodity
effects,
prospective
hence,
the
of
assumed
shocks
that
of
to
of
and demand
return
(1982).
the
as in Lucas
by two types
know only
of
agents,
role
is
to
neutral.
information
Taken
.7
unless
the
the
values
monetary
is,
feedback
--
of
current
prices
for
a
state
the
these
That
money growth
real
supply
Specifically,
on the
can alter
important
contemporaneous
current
information,
feedback
rate
determine
and King
as perceived
real
the
limitations
(1976)
commodity
information.6
(1-x)
is
particularly
populated
about
dictate
distribution
is
informed
underlying
superior
the
economy
endowment
fraction
by Barro
has
about
the
accurately
two elements
.
.
information,
prices
by their
discussed
monetary
economy
agents
but not
together,
Second,
current
First,
expectations
(1980).
The remaining
economy.
analysis.
rational
differentiated
fraction
of
policy
are
policy
the
state
of
the
With dif ferencontent
of
market
activity.
Demand and Supply
Supply
and demand at a given
and uninformed
agents.
date
In common with
t are
aggregates
other
intertemporal
of
the
actions
substitution
of
informed
models
6
By viewing
the information
structure
as exogenous,
we abstract
from equilibrium in the information
market as considered
by Edwards (1981).
The endogenously
determined
fraction
of informed
traders
would plausibly
respond
to policy,
an
effect
which is not considered
here.
7
Our basic results
do not require
that one group is fully
informed
or, even,
The key assumption
is that
that some agents are better
informed
than others.
agents
are differentially
informed
(see King (1982) and Dotsey and King (1983)).
The assumption
of fully
informed
agents yields,
however,
the simplest
analytical
solutions.
:
5
of
business
of
return
rate
of
of
expected
return
the
price
Informed
set
f luctat
level
price
I
all
r
In our
the
system
agents
are
limited
the
using
to
where
nominal
set
real
the
interest
logarithm
rate.
information
periods,
information
which
rate
the
Pt is
a complete
current
real
model
t and earlier
an information
rate,
log-linear
of
in date
on the
which
about
we denote
the
U = et,
t
).
Rt ’ s-1
Commodity
supply
(1)
yt” = (1-A)a8
(2)
yz = -(l-h)od
and demand are
ErtlUt
specified
+ Aas ErtlIt
ErtlU.
--
In addition
commodity
We think
to
the
supply
of
g,
supply
government’s
intertemporal
effects
purchase
of
via
goods
demand.
The coefficient8
demand.
For a more detailed
on supply
bs,
to
private
Commodity market
description
by uninformed
agents
satisfy
see
Barro
- (l-~)fi’
+ esgt
EgtlUt
+ h6d Eg,l It + (1-h)~~
Eg&
+y
influences
on some current
level
of
of
the rate
disturbances.
government
influences
wealth
effects
of
effect
the
(1981)
or
return,
g,
and ct.
on private
government
(1984)).
which
(edgt),
on commodity
of
of
spending,
and demand effects
substitution
@d reflect
commodity
clearing
MS Eg,l It
productivity
less
and demand decisions
disturbance
depend
an unobservable
(egg,)
-
substitution
and demand also
as being
as
- Aod ErtlIt
+edgt
direct
level
expectation
to the
interest
and demand depend
t = P, + R, - Pt+ls
t and R is
t
shocks
and the
is
rational
Uninformed
t’
level
at date
supply
participants.
t and t+l
form their
containing
we denote
by market
between
agents
commodity
ions,
The term
i.e.,
commodity
supply
that
the
real
rate
of
return
and
purchase8
ct
is
demand.
requires
has
expected
a
6
(3)
where
ErtlUt
we have
B = BS + gd.
this
= x(EP,+~II,
defined
of
composite
into
the
also
supply
parameters
employs
the
0 = 0
fact
-EgtlUt)
s
- 13 , Q = us + ad,
that
we obtain
schedule,
d
(%
the
EgtlIt
= gt).
commodity
+ 1 Et,
P
and
Substituting
market-clearing
output
(4)
where
- EP,+~IU,)
(The derivation
expression
value
the
Cl-X)6
cJ+f3
+
+ gt
a
a
yt = y;
the
full
+ (1-A)
;
information
(gt
level
- *gthJt),
of
output
(y:)
is
S
(5)
Xn these
y:
express
G=
as(f3-8)
our
analysis.
8
= ;
g,
ions,
+ u(Bs
+ ;
Et’
we have
+ 8’)
used
the
and H = aSBd -
composite
parameters
8 d
8 a , which
are
G and H, defined
treated
as positive
as
in
8
Given the results
of Barro and King (1984),
a few words concerning
these
assumptions
are in order.
Barro and King show that in models where agents’
preferences
are time separable
and were commodities
are nonstorable
the parameter
Therefore,
output
G is positive
under standard
assumptions
but that H is zero.
will
never deviate
from its full
informat ion value regardless
of the degree
of confusion
about the actual
values
of m and g .
In order for misperceptions
one must do away with
of money and real disturbances
to have aneeffectton
output,
either
the time separability
or perishable
commodity assumptions.
However, the
resulting
models would be extremely
complicated.
We therefore
view the assumption of H greater
than zero as a convenient
device
for analyzing
the consequences
of misperceptions
on output.
In the context
of the subsequent
analysis,
all we
really
desire
is a reduced
form solution
in which misperceptions
of nominal
Since the underlying
structural
model plays only a
quantities
have real effects.
limited
role
in the results
obtained,
the above assumptions
have no qualitative
effect
on our results
and significantly
simplify
the analysis.
7
Money Demand &
Supply
The demand for
I
Sargent-Wallace
(6)
~
with
the
persisting
of
the
both
In this
driven
by the
to
to
is
t
used
by
an aggregate
velocity
shock
9
money.
rate
that
surprises
infinity.
we know that
rule.
the money supply
and feedback
to
rule
the
state
work of
one might
level
long-run
past
growth
Responses
with
to
path
of
interest
an interest
attention
McCallum
alternatively
We discus8
market
or
+ mt.
rate
in specifying
errors
in monetary
( 1981,
1983)
money and mt
rate
shocks
peg obtaining
feedback
control,
(ft)
are
when J,
to
i.e.,
+ fvvt-1.
this
III. Rational Expectation8
price
the
- ERt I It-l),
shocks
= fm mt,l
Commodity
is
We restrict
to velocity
f,
+ ft
the money supply.
term $(Rt
Based on prior
9
interest
Mt = Mo + nt
a random shock
(8)
the
form
(l-k)v,,l,
we specify
above,
+ JI(Rt - ERtlIt-1)
expression,
responses
rate
-
money demand and v
discussion
to
semi-logarithmic
(19801,
on the demand for
responses
MF = it
captured
is
of
the
economy.
(7)
is
logarithm
our
to have
- yRt - kvt
effects
Following
involves
taken
(1975) and Barro
Mz = P, + 6y,
Mz is
where
money is
possibility
the
authority
in greater
and King
as selecting
detail
later
( 19831,
an interest
in the
paper.
Solution
and monetary
and the
view
and Dotsey
nominal
equilibrium
interest
The first-order
moving average
was chosen for analytical
tractability
yield8
two equations
that
link
rate.
parameterization
of money demand disturbances
rather
than empirical
realism.
I
8
(9)
Pt = -Rt
+ Ept+l IUt + A(EP,+~$
Cl-X)B
+
(10)
t
-
Given
the
-
%
structure
solutions
+ 6[;
of
the
S
Ii
G
1
Rt = --(p
v+JI
ypf
+
1
+ ; et
Eg&)
(gt-
a
- EP~+~&)
gt + (1-A);
(gt
a
- EgtlUt)
+ 7
E&
- it + WRt I Itml - fmmtvl - fvvtBl - m,)
Wk)vt-1
the
economy,
following
undetermined
coefficients
can be postulated:
+ "lit
(11)
Rt=$
(12)
Pt = ?T +*lHt
0
0
+ @2mt-l
+ @ft-1
+- Opt
+ yt
+ n2mt-l
+ r3vtBl
+ r4mt + r5vt
+ Qgt
+ 0 7 E:t'
+ n6gt
+ R7Etj
--
The details
frequently
of
the
the
case
solution
in this
and most simply
solve
the
of
dependences
have
the
following
method
for
prices
class
the
are
of
part
spelled
rational
of
the
and interest
intuitive
out
equilibrium
rates
ERtlItBl
= $. + 41it
(14)
EP& I,,1
= x0 + nlMt
=Yn+M
trend
absence
the
rate
of
of
nominal
constant
+ r2mt-l
solution
of
one can
that
I
first
involves
These
t-l'
solutons
rate
rnt-1
fm
1+y mt-l
fv+(l-k)
-
Vt-l
l+Y
+ "3Vt-l
+
Vt-l’
l+v
.
has an unconditional
(the
in
and
(1)
= n -
fv+(l-k)
expansion
terms
models,
on elements
+ (b2mt-1 + 03~t-l
t + $
interest
monetary
As is
form
(13)
is,
appendix.
expectations
f
That
in the
real
(2)).
rate
of
mean n equal
interest
The price
level
is
zero
depends
to
the
due to
the
one-to-one
9
on the
trend
money stock
expansion
(via
inteasity
of
stock
the
an expected
inverse
which
is
raise
(fmmt-1)
own serial
fv)
but
Expectations
price
-of
works
Following
Lucas
like
information
rates.
Given
that
induced
solely
balances
of
and lower
the net
by k)
expected
high
the
influence
of
of
the
interest
of
vt
influence
money supply
monetary
inflation,
values
nominal
and policy
rate
the
money
rate
via
1 involves
(governed
by
disturbances.
Agents
and Barro
from available
departures
by g,
level
on the
Temporarily
by Y).
a temporary
(1973)
as extracting
on cash
(governed
Uninformed
positively
Similarly,
effect.
correlation
otherwise
and depends
effect
governed
the
deflation
its
(Mt)
of
- EgtlUt,
output
we focus
(1976,
19801,
signals
contained
from its
on this
we view
full
uninformed
in prices
information
expectation;
--
which
agents
and interest
value
are
takes
the
form
(15)
Egt IU, = bp Spt + bR SRt
--
bdme
are
Spt and S
Rt
By observing
rate
given
10
by (10)
the
signals
price
agents
contained
level
receive
in the
as expressed
the
The conventional
way to derive
be to use the undetermined
coefficients
provided
by the nominal interest
rate
following
price
in
(9)
level
and interest
and the
effective
nominal
rate.
10
interest
signals.
these signals,
as in Lucas and Barro,
would
representation
(111,
so that the signal
Here,
would be $4mt + 45~t + $6gt + (P7ct.
we employ an alternative
solution
strategy
developed
by Hercowitz
(1980) which
culls
“ef feet ive signals”
from prices
and interest
rates
by using the fact that
in equilibrium,
agents know the influence
of their
own expectations
on prices.
This strategy
frequently
leads to sharper
intuition
and more readily
obtainable
so lut ions .
10
Spt = Ar2mt + lr3vt
(16)
(17)
SRt = &
There
are
level
signal
= “2mt
the
$,
- kvt
Cmt
two important
is
facts
influenced
+ n v , so long
3 t
interest
rate
as agents
is
But,
aEt
S
1 g,
about
+ +
of
by any finite
and learn
when JI is
subsequent
signals.
informed
Second,
zero.
Et)}.
these
expectations
“rescale”
our
‘t
to notice
altered
disturbances.
In interpreting
+
by the
not
1
+-
G+(l-X)H
a
(
as X is not
can simply
fundamental
e-w
+ a
the
value
the
it
the
the
will
provided
policy
rate
be useful
to
depending
can accurately
infer
(18)
where
bi
EgtlUt
and bi
Monetary
IV.
In this
policies
neous
response
m
= 0).
+ b;
two underlying
g,.
Thus,
in this
shocks
g,
and
lost.
discuss
et,
Then,
of
nominal
agents
case,
S;Zr = g,,
regression
coefficients.
and Expectations
section,
we explore
Money -Stock
to
of
population
Policies
interest
in money demand ( fv
(f
Sit
on expectations
& Strict
on the
the value
= b;
are
only
of
is
expectation
information
in the case where there are no nominal shocks.
indicating
the absence
with the two signals
Sit and S*Rt (the asterisk
disturbances),
by
parameter
combination
interest
price
EP,+lII,
information
of
the
agents,
same linear
infinite
analysis,
First,
= 0).
and,
the
hence,
Rule.
effects
Further,
some alternative
monetary
on output.
Under this
rates
of
(J, = 0)
all
policy,
nor
policy
feedback
errors
there
is
neither
contempora-
to unpredictable
(mt)
are
eliminated
changes
11
Contemporaneous
(1970)
to
puts
forwar,d
interest
rates
-An Interest
rate.
system
and the
surprise
(1981,
Under a peg,
money supply
signal
expected
movements
has
feasible
under
provides
a nominal
the
authority
context,
the
in the
taught
rational
selects
feasible
to
the
rate
to occur
such
a policy
rate
as long
system
among a class
interest
a policy
to
expectations,
anchor
the
are
of
targets
(such
feasible
with
of
RE =n+Tm
Clearly,
there
feedback
parameters
11
is
+T
m t-l
fv)
case
of
a
the
demanded
eliminated
at
the
from
the
economic
rate
conditions,
in response
of
interest
as (i>
targeting
but
to
rate
interest
targeting
responses
to mt,l
--
is
authority
analysis
rate
McCal lum
shocks.
the monetary
as Mt in our
permitting
> and (ii)
rules.
In our
and vt-1
take
v
v t-l’
an equivalence
(fm,
by
Specifically,
interest
form
(19)
depicted
limiting
balances
disturbances
response
(7).
$ = CD)-
nominal
(ERJ It-l)
interest
us that
(i.e.,
of
We define
level
peg is
is
Poole
11
SRt destroyed.
Rate Target.
its
1983)
rates
any quantity
This
$ in equation
rate
previously,
money supply
fluctuations.
parameter
interest
As discussed
contemporaneous
supplies
Interest
as adjusting
that
An interest
to
Rates.
economic
the
Rate Peg.
authority
&
of
response
pegged
Interest
the hypothesis
value
contemporaneous
-to
can stabilize
finite
a nonzero,
monetary
Response
between
the
and specification
specification
of
the
of
interest
money supply
rate
target
For a more detailed
discussion
of the determinacy
properties
of various
pegs
see McCallum (1981)
and (1983)
and Dotsey and King (19831.
In general
the
resolution
of indeterminacy
involves
the
specification
of an underlying
money
stock rule.
12
parameters
and is
(r
m’
T ).12
v
therefore
supply
rule
effects
of
(41,
on the
information
contexts
section,
can alter
the
paper,
perceptions
the
our
implies
level
in ERt I I,,1
a change
of
are
specific
characteristics
of
present
of
specific
in which
the various
general
we focus
about
on the
ion
Ext if+
on a case
agents
Sqt>’
informat
analysis
a single
S t = <s lt’---’
12
which
content
informati&ial
--
of
purpose,
(20)
fv
targeted
the
interest
prices
our results
cases
each
a general
problem
we want to distinguish
the
comparison
For this
or
m
rate
in
discussion
such
likely
the money
and decide
and formulate
in
are
of
of
which
the
a means
a general
setting
to arise.
and Policy.
To make our
in
so,
Placing
policies.
other
the
we will
of
In this
our
to compare
doing
Information
for
we wish
policy
f
policies,
Before
suggest
policy
monetary
optimal.
comparing
will
altering
(7).
the various
rule
is
rule
is,
to moving
equivalent
the money supply
Given
That
set
the
in which
xt,
Xt’ St are
it
AtB1 = uX + bxs(St
to
the
is
itself
of
information
jointly
normally
follows
-
a foundation
above.
specific
agents
ways in which
building
discussed
economic
which
two different
economy,
policies
comparable
a vector
A
--then
t-l
of
monetary
variable
have
If
state
between
problem
are
not
forming
directly
variables
addressed
or
rational
observable.
signals
distributed--conditionally
that
us),
form of an interest
rate target
as
One can also view a more restricted
f(ER II,,1
- ER 1.
In the present
case where only the past history
of velocity
shot k s 1s impor Eant this type of response
would be equivalent
to feedback
on a
velocity
shock.
13
where
-1
ps = E(St ’At-l ) and bxs =u xs c as for
px = E(xt IA&,
uxs = ExtSt IAtB1 and us9 = EStS;
St
1 At-1
The conditional
l
variance
of
xt
given
.
1s
(21)
uxx -
ux; z,s’ uxs.
2
oxx = Ex, IAt-l.
where
Throughout
conditional
state”
on a specified
of
value
the
we use
our discussion,
agent
the magnitude
information
or economy
set,
under
of
the variance
as our measure
That
study.
is,
of
the
of
x
t’
“informational
when there
is
a lower
of
(22)
E(x
- Ex&A~)~IA~,
t
-
-where
At- is
tional
the
about
the
out 1 ined
effects
above.
two basic
covariance
the
informational
then,
x
the
of
we say
set,
structure
econometrics
information
increases,
fixed,
policy
is
that
there
is
That
structure
statistical
lowering
a reduction
the
to
the
alter
Then it
state.
from
discussion,
way is
fixed.
and practice,
obtained
can alter
structure
covariance
training
subsequent
and simplest
from elementary
t
our
ways that
the
include
of
In the
The first
of
information
a better
informa-
state.
As a result
the
current
is,
let
the
informational
in the
sort
of
we use
that
intuition
informat
list
easy
ion
of
subset
of
we know that
state.
number of
signals
of
signals
set
the
intuition
the
signal
discuss
economy.
while
the
model
to
holding
effect
available
the
That
our
“regression”
state
to determine
information
and a proper
theory,
the
the
is
much of
on
to
agents
vector
S ;
t
conditional
variance
with
covariance
is,
worsens
the
the
informational
14
state.
Viewing
(18)
in that
intution,
The second
I
the
on the
of
alteration
I
of
x
t’
informational
variables
can effect
structure
fixed
accords
informational
case
state
the
to determine
our
basic
population
there
to specify
number of
with
to a Larger
In this
One needs
state.
with
lead
the
slc~--.lsqt.
in covariance
a prediction
In models
are
not
covar iance
where
agents
directly
In this
while
Monetary
section,
is
is
ef feet
about
state
by altering
an ambigious
precise
the
variance.
nature
on the
conditional
signals,
by considering
interest
rate
target.
interest
rate
peg.
or monetary
the
lowest
Thus,
E(g,
the
policy
economy.
our
- Egt lu,)21ut
interventions
interventions
affect
affect
the
feedback
feasible
policy
or,
we compare
a money stock
the
number of
signals.
preceeding
discussion,
we define
as the one
that
monetary
equivalently
rule
policies.
an optimal
to an unconditional
Policy
will
l
policy
some alternative
an optimal
variance
objective
all
variables
Policies
Specifically
conditional
some policy
Then,
Monetary
Following
perceptions
almost
we consider
We start
Optimal
form rational
observable,
structure,
Alternative
v.
of
policy
this
- ExtlAt)‘IAt.
E(xt
that
I
I
regression,
independent
structure
effect
variance
fewer
way that
covariance
the
as a population
, the
of
be to
produces
optimal
the
highest
policy
is
gt given
the
find
policy
the
the
interest
informational
that
information
that
optimal
which
set
minimizes
of
rate
state
produces
uninformed
the
agents.
w
15
From our
infer
discussion
in Section
*
from S* and S
Rt
Pt
g,
effectively
alter
g,
even
in the
is
now given
(23)
the
It
is
now easy
to show that
of
content
nominal
of
prices
b
P
Egt I Ut = bp .Spt + bR SRT = bp(S&
*
P
optimal
ting
for
and b
R
influence
a full
of
*
of
m
a feedback
policy
can
allowing
agents
to
infer
expectation
of
gt
+ Ar2mt + ~~~~~ >
set
will
agents
- mt - k,>
so that
be identical
will
optimal
price
We stress
information
to equation
be able
feedback
in the
solution.
b ,AIT - bR f 0 and
P 2
is
infer
able
this
as in the
g,
with
accurately
to negate
and interest
that
(X+0),
to
(18)
rate
the
with
contamina-
signals,
can only
occur
analysis
of
allowing
in the
King
(1982)
(1980).
values
for
and T
t!le values
*
V
of
f
m
derivations
*
= (pv results
and fv are
>.
Further,
in a full
equivalence
in contrast
to unpredictable
any considerat
of
to
Poole,
movements
ion
of
these
relative
the optimal
current
variances.
= -
--
and fz
yda’
an optimal
at
two policies,
in the
l+y
fz
information
of $m and $v when fm and fv are
fundamental
However,
is,
shocks
differential
appendix
= 0;
nominal
are
(23)
In essence,
The optimal
t
That
information
and Weiss
(see
equation
= b*
R’
feedback.
presence
fm and fv
parameters
- bRk = 0 then
=b
correctly
by
feedback
bp is
could
The conditional
shocks.
+ bR(st
If
agents
l
information
presence
we saw that
III,
=
targeting
interest
scheme
opt irnal levels.
as in
policy
-
y6as
Poole’s
does
rate,
(1-k)
with
*
*
where $m and 0,
solution,
their
k(l+Y)
not
This
(1970)
involve
nor
does
reflects
analysis.
responses
it
involve
I
I
-An Interest
Rate Peg Versus
Suppose,
rule
of
the
unavailable
produces
the
this
stress,
interest
rates
t ion
Since
.
the
This
stock
rule
value
n.
policies
a policy
.of
perceived
These
possessed
of
Poole
the
signals
-_
number of
pegging
a signal.
with
the
rational
for
is
unaffected
to
by finite
interest
rates
and King
and observe
by responses
produced
are
the
the
rule.
shocks
only
of
to
output
(1983)
the
interest
or
the
are
at
its
a strict
informa-
since
structure
under
is,
a peg,
completely
to
two policies
nontrivial,
money
unconditional
ones-given
the
and correspond
covariance
under
between
feasible
these
is
That
Furthermore,
and velocity
rate
authority
by each
and (ii)
a choice
interest
The comparison
the money stock
arise
both
a feedback
shocks
As Dotsey
rule.
no consequence
authori&y
policies
(1970).
(i>
no longer
are
follow
on lagged
responds
in money caused
by the monetary
state
no longer
agents
to
in Pt and Rt is
contemporaneously
and have
the monetary
alternative
with
unable
prices.
informational
is
that
movements
Therefore,
the
compared
embodied
because
occurs
and a policy
of
information
is
information
result
leaves
information
because
as a pure money stock
perfectly
content
perhaps
authority
same solution
rate.
are
Rule
the monetary
discussed,
of JI, we find
values
that
however,
type
a Money -Stock
a peg,
of
the
limited
passive
in terms
the
money supply
absorbed
the
expected
of
peg alters
the model
interest
when
rate
disturbances
by changes
in the
money stock.
To compare
variance
of
two policies,
g t in a way that
rate.
We start
of
price
the
these
by calculating
level.
we find
highlights
the
Then we revise
the
expectat
this
it
useful
signalling
ion
of
expectation
to decompose
role
of
gt conditional
using
the
the
the
conditional
interest
on observation
information
contained
17
in the
interest
receive
informat
(24)
where
‘RR
tions
for
= [o
Rt
/
gp ‘pp’
),a
gP
The second
contained
the
thereby
of
lowering
comparison
(1970,
= var(Spt),
the
extent
Spt>.
to which
agents
interest
rate.
in the
-a(u
- $1
PP
side
of
right-hand
it
is
The second
revise
term
their
expecta-
The analogous
formula
term in
to
(24)
see
the
price
which
no longer
the
first
of
the
neither
depends
V).
right-hand
Thus,
prediction
that
the
term in
peg destroys
(25)
a signal,
standpoint
it
However,
contains
in format ion
error.
From this
the economy.
the
also
any nominal
and improving
reduces
disturbances,
the
economy.
the
peg nor
on relative
of
side
PP
and (25).
of
-l
nonnegative.
the
state
signal,
)
-
is
of
easy
‘gP”RP
u
(25)
the variance
and (25)
-
gR
informational
parameters
Section
uPP
the
state
In general,
and on the
(24)
the second
informational
the
= (ugg
worsen
the variance
= [‘RP”PPISPt
--
in S
cannot
Pt
peg reduces
agents
- ES~~IS,,>
and uRP = cov(SRt,
contained
right-hand
out
+ a(Spt
Spt),
term on the
By examining
wiping
because
is
3
EgtlUt)L]
E[(gt-
as arising
Formally,
>
ref lects
on information
the variance
procedure
- uR;/uppL
= cov$,
side
this
‘Pt ’ ERt lsPt
/u,,mY,,
right-hand
based
(25)
sequent ially.
SRt = EgtlSpt
gR - ugP %P
=var(S
on the
ion
EgtlSpt,
EgtlSpt
a = {a
(One can view
rate.
the
magnitudes
model,
For example,
the money stock
of
a conclusion
as the variance
rule
is
the variance
which
of
real
is
Instead
dominant.
of
the
reminiscent
shocks
is
disturbances
of
smaller
Poole
18
((32 +
E
0)
pegging
of
v.
added
interest
gt and full
communicate
the
the
information
the money stock
rate
would
information
contained
allow
solution
in the
the
price
would
interest
level
However,
obtain.
rate
to accurately
wouLd imply
as o2 + 00,
E
a dominance
rule.
Summary and Conclusions
This
paper
in rational
the
expectations
Overall,
our
monetary
policy
real
explores
effects
models
analysis
of
with
suggests
in terms
of
systematic
implications
informational
flexible
that
there
interest
rate
actions
prices
to
be gained
Yet,
rules.
interest
rate
and informational
little
is
framed
of
in those
it
does
by Poole
it
represents
simply
(1970)
is
not
a perceived
and more importantly,
we find
of
the
real
activity,
identical
either
via
to the
a strict
effects
This
Suppose
that
finding
only
by the monetary
would
state
not
rule
characterize
the
potentially
operates
of
choice
First,
observable
actual
be a desirable
prices,
but only
feedback
rules.
Finally,
rate
state
behavior
of
response
of
of
sector.
avenue
the
Then,
a money supply
pegging
elements.
in a situation
distribution
in a manner
we find
it
latter
authority
of
policy,
of .further
is
that
rule,
based
rate
there
on
at a level
policy
appears
in the
U.S.
incomplete
research.
observable
appears
interest
that
information.
economy
feedback
the
This
the monetary
Second,
the
incomplete
rewarding
state
of
because
peg may be a dominant
in a situation
private
the variety
neutral.
of
interest
and a policy
is
of
activity
can affect
the aggregate
between
and hence,
real
targets
a potentially
and the
elements,
on the
or
of
rate
contnet
out
terms.
determinant
action
interest
money supply
suggests
authority
conditional
that
rule
a subset
be a nontrivial
observable
of
authority
third
monetary
information
money stock
when the monetary
an important
frictions.
by discussing
we have three ma-jor finding
of our analysis.
More specifically,
we find that
contemporaneous
response
as in some earlier
analyses,
discussed
policies
to
and could
information.
19
Append ix
As shown in the
two conditions
(Al)
text,
+ EPt+l IU, + X(EPt+l
+ v
Rt = &{P,
(gt
+ Q
- kvt
Using
(11)
(Al)
and (A2)
and (12)
elements
of
and money market
gives
the
following
:
P, = -Rt
(A21
in the goods
equilibrium
I
t-l
’
(l-k)vt,l
and the
namely
-
EgtIUt)+ d Et
(gt -
gt + (1-9~
-
we can solve
- Egt
0-B
g,
1% - EPt+$Ut) + 7
- Mt + ~JER~IItml
undetermined
for
Egt.l U,)
the
solutions
coefficients
These
Mt, rntel -and vtWl.
Et1
- fmmtBl - f/t-l
coefficients
undetermined
+a;
- mt )
postulated
attached
solutions
to
in
the
are
-.-
lTo = Y
4.
IT1 = 1
41 = 0
= 0
f
(A31
f
=2 -g
$2 --TYy
fv+( 1-k)
=3 =
and are
l+y
independent
responses
to
fv+( 1-k)
$3 = -
of
the
policy
1+y
parameter
$,
which
simply
controls
policy
shocks.
To study incomplete
informat ion, we note that
#
interest
rates are equivalent
to observing
signals
(A41
Spe = Xr2mt + An3vt
(A51
SRt = -m
e-xf3
+ 7
g,
the
price
level
and
+ $,
and
where
the
t
- kvt
+
1
term has been
Y+JI
6G+(1ix)H
omitted
gt+,d$
since
it
c
is
t
merely
a scaling
factor.
‘PC
’ I
The solutions
straight
andS’
Rt
forward
=B
for
bi and bi
to obtain,
G+(l-A)H
a
+ -E
a
gt
a
-a/6[0-X8as
- (G+(I-~1~1.
expressions
for tl andn3and
2
kb* = 0.
R
in the
by employing
S
.
regression
g
t
We find
that
The solutions
for
t
solving
the
EgtlUe
= Egt lUt
= b;
and S&
Sbt + b;
843
= - a
Sit
1
gt + act
b* = aaS/[(@-Afi)aS(5+(1-X)H)]
P
f,* and fv* are found by using
restrictions
b*hn
~2
20
are
and b* =
R
the
- b* = 0 and b*X= R
P 3
21
Barro,
References
Expectations
and the Role of
R. .I., “Rational
2, January 1976, l-32.
-of Monetary Economics,
"A Capital
Econome;ricia
, 48,
Market in an Equilibrium
September 1980, 1393-1417.
Monetary
Business
Policy,”
Cycle
Journal
Model,”
Preferences
and Intertemporal
and R. G. King, “Time-separable
Substitut ion Models of Business
Fluctuations,”
NBER working paper 888,
May 1982, forthcoming
Quarterly
Journal of Economics,
November 1984.
Canzoneri,
M., D. Henderson and K. Rogoff,
“The Information
Rates and the Effectiveness
of Monetary Policy
Rules,”
November 1982.
-of Monetary Economics,
Content of Interest
quarterly
Journal
Instruments
and Policy
Rules in a Rational
Dotsey,
M. and R. G. King, "Monetary
Expectat ions Environment ,” Journal of Monetary Economics,
12, September
1983,
357-382.
Edwards, M., “Informational
Equilibrium
in a Monetary Theory
University
of Rochester
working paper, May 1981.
of
the
Business
Goodfr iend, M. S.. , "Rat ional Expectat ions,
Interest
Rates Smoothing,
Optimality
of a Non-Trend-Stationary
Money Supply Rule,” FRB of
working paper,
July 1983.
Grossman, S.-J.
and L. Weiss,
Business Cycle,”
Journal
“Heterogeneous
Information
of Political
Economy, 90,
Hercowit 2, 2. , “Money and the
University
of Rochester,
Dispersion
1980.
King,
R. G.,
Political
-of
Lucas,
of
Relative
"Monetary
Policy
and the Information
Economy, 90, April
1982, 247-249.
“Interest
Rates,
Aggregate
Monitary Economics,
12, August
R. E., “Expectations
Theory,
4, April
1972.
and the
Prices
Content
of
Rat ional
716-746.
,” Ph.D.
of
Money,”
Prices
Journal
“Some International
Evidence
on Output-Inflation
Econom;c Review,
63, June 1973, X6-334.
McCallum, B. T., “Rational
An Overview,"
Journal
716-746.
Expectations
and Macroeconomic
of Money L Credit and Banking,
and the
Richmond
and the Theory of the
August 1982, 699-727.
Information
and Monetary
1983, 199-234.
Neutrality
Cycle,”
dissertation
,I’ Journal
Policy,”
of
Journal
Economic
Tradeoffs
Stabilization
November 1981
“Price
Level Determinacy
with an Interest
Eipec t at ions, ” Journal
of
Monetary
Economics,
-
-of
,” American
Policy:
(pt -21,
Rate Policy
Rule and
7, November 1981 (pt.
21,
22
“Some Issues
minacy,
an:
University,
Poole,
W. W.,
Model,”
Economil
Concerning
the Real Bill Doctrine,”
September 1983.
Interest
Rate Pegging,
Price Level Deterpreliminary
working paper, Carnegie
Mellon
in a Simple
Choice of Monetary Instruments
Journal -of Economics,
May 1970, 197-216.
“Optimal
Quarterly
“The Making of Monetary Policy:
June 1975, 253-265.
Inquiry,
Description
Stochastic
Macro
and Analysis,”
Sargent,
T. J. and N. Wallace,
“Rational
Expectations,
the Monetary Instrument,
and the Optimal !4oney Supply Rule ,I’ Journal of Political
Economy, 83, April
1975, 241-254.
Weiss,
L., “The
Journal
of
Role of
Political
Active ?lonetary
Policy
in a Rat ional
Economy, 88, April
1980, 221-233.
“Interest
Rate Policies
Foutfdation
Discussion
Paper
Woglom, G., “Rational
Model,” Quarterly
Expectations
Journal of
Expectations
Model ,”
and Informat ional Efficiency
,I’ Cowles
April
1981.
No. 589, Yale University,
and Monetary Policy
Economics,
February
in a Simple
1979, 91-105.
-_
Macroeconomic
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