1. business and industrial
2. energy
3. oil
4. oil and gas prices

Carnegie-Rochester Conference Series on Public Policy 21 119941446
North-Holland
MONEY
IN A THEORY OF FINANCE
Robert
E. Lucas, Jr.*
The University
INTRODUCTION
I.
The
title
of
(1960) monograph
constructing
the
attainment
for
future
about
the problem
the reader
of
at
objective
it is easier
either
(1935)
regarded
must
as part
be something
did not see or did
to identify
this difficulty
exactly
this
to rapid
recent
progress
This
mutually
distinct)
lation
that
further
theoretical
This
revealed
paper
the Fisherian
review
of
economics.
*I
am
the
in Section
relationship
grateful
to
Allan
the contingent-
(1964)
and Oebreu
the
frameworks,
terms,
unity
and
Modigliani-Miller
discovered
but
within
all
differ-
three
have
and it was this reformuset
the
stage
II with a review of a simple
of real capital
A central
Kupferman,
re-
for each of the three pillars
theory,
theoretical
essential
within
by Arrow
in which
is largely
for
many
advances.
begins
model
and to
Theoretical
finance.
markets--was
in contingent-claim
their
theory,
entirely
statement,
of efficient
since been reformulated
of
introduced
theory--portfolio
and the theory
(and
theory
almost
framework
is not an historical
financial
modern
Theorem,
as monetary
in the
is now conducted
equilibrium
not ade-
it.
fails
in finance
of an adifficult
it was in 1960 to identify
general
of
"Suggestion."
today than
(1959).
Arthur
that the objective
of finance
search
ent
writers
there
Gurley/Shaw
is an old one, one that
Hicks's
is still
that
the
theory
claim
of
from
the
If
respects
due
J.R.
is an attempt
offer one way of dealing with
course,
and finance
since
suggests
that earlier
of
at the outset
of money
least
this
research
This paper
face.
is taken,
theory
theorists
genda
quately
essay
to remind
a unified
has challenged
That
this
of Chicago
of
feature
Nancy
Stokey
Meltzer,
theory
this model
in contingent-claim
to various
aspects
of this model
is that alI trading
for
an
Bennett
criticism
McCallum.
of
earlier
and Manuel
draft
Sanchez.
and
version
terms
of
financial
occurs
for
of
and a
in a
ccmments
by
centralized
sition
market,
of each agent
the market
over
goods
the fact
over other
curities
trading,
that,
I do
not
its market
of money,
III
Lucas
and Stokey
of market
market
in which
securities
a device
(1983),
money
which
in reality,
theoretical
is to
poor
has
say
preference,"
money
value
all
is to
has a relative
in centralized
model must
se-
place agents
How, as a matter
pricing
that
is
in
of modeling
from
the barter
testing.
agents
securities
in
model
that
to
the
and
system,
versions
Here a simplified
to the point where
and various
simple
by Clower
market
barter
operational
central
version
theory
reviewed
differ
are
in
re-
in important
to much
to the objectives
alternative
of the model
are fully
to
recent
em-
IV.
fiscal
of Section
one can begin to see what a full analysis
examples
goods
(1967).
of monetary
to the theory of finance,
under
to
if not continu-
modifications
subjected
been
in Section
securities
admits a theory of securi-
that have
equilibria
a
decentralized
formulas
peripheral
two different
Subsequent
regularly,
in
and
is ,assumed subject
so that pricing
These are reviewed
monetary
agents
(1982),
attend
are exchanged.
standard
fully
Section V turns to the question,
for constructing
between
all
(implicitly)
securities
close
though traditionally
they
formu-
introduced
Townsend
alternate
period,
alternative
model
(1982),
of the form suggested
this
interesting
for a monetary
with
of at least some goods
in a centralized
Yet
II.
of
in Lucas
trade
constraint
assumption
used
Each
agents
experience
now, but the monetary
in which
the purchase
the cash-in-advance
regimes.
the
his wealth,
any one claim
or of "liquidity
enough
and other
trading,
trade
have
question
situations.
in which
The
we
this
employs
kinds
theory
value,
in excess of its relative
a successful
believe
Section
pirical
The command
at least some of the time.
to answer
Section
by
number:
might this best be done?
lations
markets
he owns.
in some situations
goods
then
such situations,
ways
described
such a setting,
In
by a single
"liquid."
command
strategy,
present.
is fully described
is fully
capture
quired
agents
the point of a theory
If
ties
all
value of all the claims
claims are equally
ously,
with
"solved."
Section
of methods
and monetary
III
is studied
would
involve,
contains
con-
understood,
con-
VI
cluding comments.
II.
The theory
of finance,
THE THEORY OF FINANCE
as the term
10
is now generally
sists of various
specializations
tingent-claim
formulation
ating
time,
through
rizing
several
considering
to stochastic
of the main
results
(St), where
might
an economy
any consumption
full
history
this
setting
is known
of shocks
simplified
activity
as a function
of the good to be exchanged
t contingent
on the occurrence
here
to
two
leisure,
xt.
The
defined
over
each
individual
stances.
consumption
sequence
all
consumer's
time t.
a
possible
histories
shocks,
prior
st.
A commodity
I will confine
produced
st,
provides
ft
the
or good
in
denotes
or produced)
at date
attention
good,
of functions
for all dates,
to
to denote
the value of which
nonstorable,
[c+,,xt} of pairs
consumption
knowledge
the joint density
(or consumed
of the history
goods:
elements,
given stochastic
st is public
ct(st),
the quantity
and also for
version.
Use st = (~1 ,...,st)
up to and including
is idealized
of finance,
oper-
for summa-
to include monetary
in t and where
to all agents.
con-
for an economy
As background
to exogenously
of the vector
or production
(Sl,..., St)
shocks.
in the theory
subject
the realization
of the Arrow-Debreu
equilibrium
be extended
to state a highly
We consider
of
subject
how this theory
it will be useful
and applications
of a competitive
ct,
ct(st),
and
x+,(st),
a catalogue
under all possible
of
an
circum-
1
Consumers
will be taken to maximize
expected
utility:
m
z Bt I U(c&),
t=o
xt(st))ft(st)dst.
The shorthand
m
z
6
t
I U(ct,xt)f
t
ds
t
(2.1)
t=o
is taken
to mean
are assumed
the same thing
and will
be used
repeatedly
below.
Ct + gt + kt+1 = F(k$-x&
‘Here
and
elementary
provided
detail,
below
aspects
,
it
and
Firms
to have a technology:
would
phases
I
am simply
of
be
various
like
setting
models.
necessary
“defined
(2.2)
to
out
If
specify
over
a
a
the
all
notation
useful
for
discussing
mathematically-rigorous
commodity
possible
replacement.
11
space
histories”
technically-
exposition
and
functions
would
need
were
defined
elaboration
to
in
be
more
or
describing
the
consumption
produced
the
combinations
goods
gt,
of
and
when beginning-of-period
shock
history
different
is
consumers
st.
Questions
At
but
of government
the
to
possibility
levy
deficit
debt obligations
to formulate
quite
the
a definition
but
in general
traditions
Debreu,
finance,
the trading
different,
standard
of
scenario,
highly
financial
all agents
theory
and
are taken
of contingent
contingent
ct(st)
is
sequence
history
the
many
to con-
[gt) will be
has
Let
at t.
the
To admit
goods-denominated
to these agents,
to keep
scenarios,
to convene
shocks,
claims
one
In
on
so
that,
for
mt(st)ct(st)
and
the
and hence
in mind two
of
which
is closer
first,
at time 0, knowing
to trade 'in a complete
In this
on goods.
consumption
claim
st,
product
be
on consumers.*
initial,
theory.
leisure
of a contingent
shock
stream
and the other of which
monetary
of
the
consider
that government
it is useful
complementary
(ct,xt]
-nxt(st)
could
taxes
open
of equilibrium,
price
of
can
by government.
equilibrium
the
that
on subscripts
of consumers
possibilities
of sequences
nt(st)
one
by assuming
let 60 denote
f1,f2 ,... of future
the distributions
level
lump-sum
tax obligations
owed consumers
To describe
c+_, government
kt+I
are kt, labor is 1-xt, and
of the expenditure
the paper,
distortion-free,
contingent
of
stocks
formal
goods
stocks
it will economize
finance
here and throughout
denote
capital
many) of each.
kept simple,
ability
consumption
capital
this
and firms,
sider one ("representing"
et(st)
private
end-of-period
claim
xt(st)
example,
the
ct(st)
the
are both dated
the
present
ArrowSO
and
range
trading
and
is
to
the
price
functions
value
of
the
value
of
an
claim
entire
(ct] is3
m
z
I
&)ct(st)dst
t=o
Here
prices
are quoted
in an abstract
unit-of-account,
so a normalization
like no = 1 is permitted.
In this
(nt,nXt),
2
See
Lucas
of government
3
Here
setting,
firms
choose
(ct +
gt,
l-xt,
kt+I),
given
k. and
to maximize
and
finance
and below,
Stokay
when
(1983)
all
for
taxes
a normative
analysis.
in a context
distort.
the normalization
/ds
t_ - I, all t,
12
is assumed.
similar
to this one,
-
m
(2.3)
~[~,(st)(ct(st)+gt(st))-nx,(st)(l-xt(st))~dst,
1
t=o
subject
Call the value of this maximized
to (2.2) for all t, st.
function
n.
period,
Consumers
they
outstanding
are
are
liable
government
for
endowed
taxes,
with
they
one
own
debt, so their budget
unit
of
the firms,
constraint
objective
labor-leisure
per
and they
the
hold
is:
m
rl$st)(ct(st) + e&H -
z
t=o
- nxt(st)(I-xt(st))]dst
Consumers
choose
(ct,xt},
(2.4)
< n + ,,oBo
given
(nt,nXt),
[et],",
and BO, to maximize
(2.1)
subject to (2.4).
This
scenario,
in which
at time 0, conflicts
in reality
trading
production
"large"
with
though
number
the
second,
t,
original
date,
Then
these
with
It also
pre-
equally
fully,
sheds
reinterpretation
superficial,
above
that
is much
scenario
some
of
a
that
and
activities.
is
are set
consumption
The next, alternative,
objection
sketched
that
will
(nt(st)
established
for goods
to these
and prices
the observation
concurrent
observation
a
with
light
a
deals
on
the
contingent-claim
closer
to traditional
theory.
all
dated
markets
agents
claims
Arrow-Oebreu,
prices
the price
or
permits
the sort
that
prior
this
securities.
in contingent
complication
than
quantities
superficially)
all the time,
observation
imagine
in the
very
believe
in general
of
trading
traded
rather
I
and monetary
First,
on
of traded
first
and
equilibrium
capital
goes
of goods
supposes,
all equilibrium
(though
of
time
shortly
above)
meet
at the beginning
exactly
0 market.
be
and,
T contingent
on the
character
utilizing
let
~Ot(~O,O~t)
in general,
simply
same
Then,
dropped,
at the time-t-market,
at t > 0 are
the
of every period
as
denote
use nt.T(st,tsT)
if st has occurred
history
redundant,
those
a notational
the
to denote
up to that
tsT from t+l through
for arbitrage
will
T.
en-
force
=
over
all
dates
and
~O,tbO’OST)
“t,rbtyST)
histories,
and
future
trades agreed to at t = 0.
13
trading
(2.5)
will
simply
reconfirm
In this
one
nomy,
"sequence
is free,
of prices
economy"
without
like ~~,~(s~,~s'),
or rationally
t market
the history
prices
as
being
formally
st be realized.
established
at each
other prices
terpretation
evidently
one to economize
assumed
as will
be
seen
Arrow-Debreu
it will
permits
to be traded
technology,
scenario
be useful
will
be used
The first-order
as
permit
still
follows,
the
formalism
to generate
of
for the consumer's
rein-
assumptions
further
equilibrium
rational
This
on the variety
Special
often
system with rational
conditions
light
drastically
to think of these equilibrium
of a competitive
in
be set later.
to keep this alternative-sequence
and, where possible,
the evolution
In what
date,
will
at any one date.
and shocks
below.
eco-
to think
That is, one thinks of certain
as to how certain
preferences,
an Arrow-Debreu
of equilibria,
(as of t = 0) to be set in the time-
expected
expectations
of securities
of
the analysis
T > t not as being set at time 0 but rather
being correctly
should
reinterpretation
affecting
of
the
timeless
conditions,
interpretation
conditions
on
economies,
but
in mind
as describing
expectations.
problem:
maximize
(2.1)
subject to (2.4) include:
0 =
2
Uc(ct,xt)ft
-Xnt,
0 =
2
Ux(ct,xt)ft
- x lVxt
all t, st
where the number x is the multiplier
The
first-order
conditions
,
(2.6)
, all t, st
associated
for
the
(2.7)
with (2.4).
firm's
problem:
maximize
subject to (2.2) include:
0 = nt - pt , all t, st
,
(2.8)
utFx(kt,l-xt,st),
0 = nxt
-
o=
Fk(ktJ-+&St
all t, st
(2.9)
and
I,I~
-
%-1 ’
all t 2 1, st-l,
14
(2.10)
(2.3)
where
the
functions
constraints
boundary
(2.2).
implicitly
are
In
(2.2)
define
are
addition,
or transversality
Equations
that
U+, = pt(st)
conditions
and
th e multipliers
under
"at infinity"
(2.6)-(2.10)
the set of stochastic
equilibria
for
and (2.7), equilibrium
this
economy.
prices
suitable
associated
the
certain
are also necessary.
together
with
processes
for quantities
Eliminating
boundary
conditions
and prices
multipliers
from
(2.6)
are given by:
U,(ct+)
“xt
with
restrictions,
(2.11)
T=U,(ct’xt)
and
(2.12)
Eliminating
prices
as well
from
(2.6)
(2.10), equilibrium
quantities
must
satisfy:
Ux(ct+)
m
Fx(ktJ-xt,st)
=
c Ct’xt
“&-1.xt_l)
6 I
where
Uc(ct,xt)Fk(kt,l-xt,st)F:_l
dst.
Equations
suitable
librium
(St} t:.
is the
interpretations
(2.12) to prices
Brock
=
f:_1 5 ft/ft-l
marginal
of
resource
and
intimate
connection
can
allocation
they are the
Much
(2.13)
(2.14)
conditions
(1982) for a useful
finance.
density
of
st
- (2.14)
(2.14)
conditional
,t-1
on
and their connections
The
.
(2.11)
-
are familiar.
(2.13)
boundary
:
(2.13)
,
together
sometimes
Capital
technology
given
t:o,
together
Asset
theory
15
the
Model
of
the
is a collection
and
the equishocks
of the system.
with an exposition
Pricing
of finance
(2.2)
to construct
Euler equations"
illustration
to the
the
be used
(ct.xt.kt+Q
"stochastic
of the existing
with
See
of their
theory
of
of obser-
vations
from
based
which
theory,
on these
they
are
in the remainder
these observations
theorems"
nature
category
on the
budget
value
the
of a claim
firm.
simply
consumers
are
same.
This
on
is
firm
the
between
"Ricardian
be
of the various
this
R,, with
consumer's
of
this
to divide
The
sequences
stream,
stream
and the
budget
of
the
the
form
of
n
value
The proof
(2.4):
if
government
can
consumer's
definition
(2.3) of the firm's value II. It is:
be
the
justly-celebrated
claims
budget
must
component
Theorem
receipts
gives
the arbi-
a power,
in appli-
of its proof.
of government
The
values
the
that
given the simplicity
from
in the
constraint
these
proof
fact
theorem"
R = (Rt(st)),
that "i"i = II .
of contingent
reasoning.4
derived
systems
side of (2.4) is II or ~i"i, and
the Modigliani-Miller
same
price
"equivalence
"iRi = R, each with
choices,
(1966)
Theorem.
equivalence
the
market
these
Hirshleifer's
(1958)
underlying
of
of the model
elements
be convenient
net receipts
RI,....
that may not be apparent,
The
main
of equilibrium
the right-hand
Ri can be arbitrary
application
it will
II~,...,~,,, it is evident
indifferent
Modigliani-Miller
cations,
the
observation
trage reasoning
the
Thus, the value II of (2.3) is the equi-
to the entire
can choose whether
if they
streams
sets.
streams
prices)
an
basic properties
consists
linearity
Should
to the receipts
(at equilibrium
section,
of results
rest
say, of
is
of this
of consumers'
librium
that
or on more
In reviewing
into three categories.
One important
claims
conditions
obtained.
finance
is another
constraint
constraint
facing
(2.4)
the
and
the
m
ToBo
=
Clearly,
for
the
debt
equilibrium
budget
prices
constraint
Let the time 0 deficit
noBo
B1(sl).
4See
infinitely-lived
Bo,
[et) and
sets for consumers,
and quantities,
more frequently
be
financed
by
the
(1979)
household
for
references
device
used
appears
from the "stock"
Bi,
hence be
and hence
be
issue
as
of
new,
contingent
for
prmf
in the literform
no(gO - eo) plus retirement
Then, for all realizations
Barn
patterns
imply the same budget
same
in a "flow" form that can be derived
follows.
(2.15)
economically.
The government
ature
et)dst
-
any two debt-tax
gt,
(2.15) will
with
"equivalent"
.I-$gt
L
given
that satisfy
consistent
t=O
(2.15) as
of outstanding
one-period
debt
of s1
well
here.
16
as
a
that
does
not
rely
on
the
nB
1
must
hold,
1
,!, _I-Qgt
=
analogously
and subtracting
to
etMlst)
-
(2.15).
Integrating
new
states
that a current
debt.
The
literature
"flow
than does
that the latter
Notice
that
consequences
these
librium.
of
consider
goods
above,
is "lost" when
results
of
the
results
(2.6)-(2.10).
do
be clear
than does
not depend
system
is
involves
way.
of pricing
the
information
preferences.
for granted
the
They
the
involving
terms
equiof
the
existence
of
the technology
of contingent-goods
the remaining
detailed
are simply
manipulation
taking
but
in any
in competitive
claims,
and
in terms of
(Z j T T=t
prices
ntT
defined
In terms of the sequence economy
t.
in
but it should
more
similarly
be an arbitrary sequence
frequently
(2.15) is differenced.
or consumer
that
more
(2.15).
and contains
and quantities
the problem
this price, Q,(z) say, is
Q,(z)
The
=
time-0
normalization
i IntTzTd($)
T=t
prices
mt
on sequence
r_t
ntr
are
(2.18)
.
given
economy
prices
UC(CTJT)fT
= 6
U&+$
Since
spect
must be offset by net issues of
appears
in an essential
(zt)t10
at time
to s1
(2.17)
constraint"
hypothesis
category
prices
preferences
Let
respect
,
deficit
equivalence
conditions
equilibrium
and/or
the
= 0
(2.17)
fundamental
of technology
A second
first-order
the "stock
condition
on the nature
account
constraint"
is more
(2.17): a boundary
way
(2.16) with
from (2.15) gives:
no(go - eo) + xOBO - +Bldsl
which
(2.16)
by
(2.12).
the prices
Q,(z)
all t, Tzt., sT
the
(2.19)
.
on s t ,
integrating
operator
(2.19) into (2.18) gives the pricing
= zt +
using
’
fT/ft is the density of tS~ conditional
to this density
involves applying the
inserting
Similarly,
mtt = 1, (2.6) implies:
Tzf+l~‘-’
Etl+$$$
zT1 .
17
Et(.).
with
re-
Therefore,
formula:
(2.20)
The formula
(2.20) implies,
uc(ct+)(Qt(4-zt)
= 6EtlUc(ct+l,xt+l)Qt+l~z~l
If marginal
utility
linear or because
is near
one,
"dividend"
in turn,
Uc is roughly
consumption
as would
be
basis
for
Et(.)
is conditional
tests
the
duced
of specific
on
property
of
Perhaps
recently
crucially
follows
even
tests
reasoning
it has
on
from
not, the discount
the
prices that formed
Since
shock
the
history
in (2.22),
without
lasting
importance,
more
in which
underlying
the
operator
st,
a
vast
so these efficiency
stringency
stochastic
precedent
they
elements
the hypothesis,
to a relationship
measured
is a statistical
cations
not
(2.22).
A number
Fama
the
from
accuracy
of
observed
of studies
n
or
weaker
motivated
in
intro-
were
as opposed
into
by deterministic
easily
the
early
survey
(1965).
18
virtues
conditions
be made
original
a
(2.21) as
and its
it stands
into one, with
efficiency
literature
that
or
as a parame-
this idea in a variety
of
not
which
zero
can be parameterized
Hence,
do
under
whether
any value or treated
function
than
two
be measured,
time ,series.
can
these
narrow
can
have pursued
valuable,
that
the
Dividends
can be assigned
hypothesis
for
recognized
and the utility
appreciably
(1970)
been
(2.21).
factor
ter to be estimated,
See
a
if no
arguments.
(2.22)
5
of
empirical
of
of statistical
depend
arguments
and
to
is implicit
of
being added as an afterthought
More
is
factor
is short,
efficiency."5
components
all
degree
to the economic
theoretical
if the discount
unit
of securities
"market
predictions
a
utility
(2.22)
tests
research.
a class
trinsic
if the time
because
.
early
introduced
economic
case
(2.21)
either
does not vary much,
the
This is the famous Martingale
variety
constant,
zt is paid in t, (2.21) reduces
9, = Et(Qt+l)
.
impli-
hypothesis
of econo-
begins
with
Fama
metrically
sophisticated
It should
an
example
perhaps
of
stream
(zt}
ways.
There
for
of
is arbitrary
are many
all.
Finally,
and
similar
the
equivalence
nor
the
efficiency
solving
the
model
for
given the behavior
solutions
that
specified)
has
but
as
the
an
from
of
than
prices,
of
resolved,
See,
must
be
hold
in many
based
separately,
Et(.)
is
separately
on
the
firm's
and for each
type
for
in Mehra
and
example,
the
Prescott
the one-consumer,
Hall
exception
l1978),
of
(1983).
barter
model
Hall's
strongly
reviewed
category
consists
though
(and
reject
the
in this
Shiller
paper,
(1981),
of
for
much
is
as a solution for
marginal
of
one can exploit
the
homogeneous
the former
by dy-
solution
for the
(1982),
and
a method
Hansen
reported
their
for
an exchange
heterogeneous
tests
implications
section.
19
the
to
of methods
(again, with
of calculating
and
original
of finance
designed
solutions.
hence
accumulation,
with
as
results,
of equilibria
(2.20) as an operational
Grossman
of
For
of existence
allocations
allocations
fully
its usefulness
in practice.
quantities
the
systems
theories
In Lucas and Stokey
optimal
even
vacuous
(2.20) can be regarded
and capital
to view
not
that
from
for a class of models
section,
the question
security.
variables,
of the theory
monetary
theorem
the possibility
methods
price
require
follow
and characterizing
tested
and equilibrium
with
that
A third
policies,
in this
of
of
conditions
from
of view
to
an existence
not been
linearity
is typically
follow
ones.
the point
agents
for constructing
With
they
importance
behavior
an arbitrary
(1983).
implications
of alternative
has
the
marginal
in practice
and
discussed
on
on
economically-determined
simply
(which
production
together
namic programming
6
streams
return
kinds or even the verification
of, constructing,
of optimal
consumers)
are
and the formula
the
With
equivalence
of
of various
from
homogeneous
utilities).
behavior
essential
the one
given
of
based
internally-consistent
solutions
with
trivially
provided
model
(1972) provides
calculating
economy
theorems
equilibrium,
the existence
Bewley
broader
(2.22)
well
firm
based
They
the consequences
verifying
price
the
less interest
obviously
evaluate
as
for each
tests
of shocks
exist.
hypothesis
perhaps
could
is merely
The
of the set on which
consumers,
tests
(2.10).
systems
easily
to observed
specifications
many
(2.22)
hypotheses.
good.
Neither
such
the hypothesis
similar
be matched
can
with
conditions
that
conceptually
possible
Moreover,
first-order
of capital
be emphasized
a variety
conditioned.
6
ways.
and
in these
particular
is
consumers,
Singleton
papers,
as
versions
of
but with the environment
Mehra
and Prescott
adapted
for stationarity
test on United States
From
gained
restricted
(1983) uses
the
in rates
of
in restricting
view
its internal
data
on
sets
purely
of this
line
lateable,
of output,
such
negative
necessarily
having
Since
condition
there
will
application
of
models
I think
have
that
such as
with
conditions
effort
or
rich
program
has,
in a
that pursuit
to
obtain
the potential
that lead us to be interested
is
carrying
a research
it is clear
in the
that
condition
all models
is no doubt
first-order
adjunct
nothing
or solutions
to spell out each model
be rejected,
Yet
a useful
"false"
light on the questions
If a first-order
for a
prices.
testing,
that have solutions
without
paper by
version,
as the basis
one can view as rejected
possibilities.
is at best
hypothesis
to models
consistency.
any
inexhaustible
sense,
classical
as an implication,
verify
of growth
or simulated.
and rejected,
enough
based
of
attention
that can be characterized
this equality
A recent
of an exchange-economy
time series of output and securities
point
(2.22) is tested
to be deterministic.
simulations
simu-
for shedding
in monetary
theory
in
the first place.
III.
Insofar
as the
the main features
to illustrate
model
model
the
theory
markets
section
and
those
suggested
least
are carried
some
trades
in centralized
below,
trading,
seems to
in the Introduction
once,
advance constraint
money can be used to effect
section
theory.
at time
0, or
succeeds
advantage
as the main
Whether
out
repeatedly,
cannot
me consistent
I will
from
centralized
This
trades
and no
the
cash-in-
markets,
interpretation,
with the many earlier
20
all
the idea that at
that other securities,
effect.
in this
trading,
interpret
(1967) as capturing
away
purchases
difficulty
trading
over any other.
following,
by Clower
in capturing
it is surely well-suited
with all agents simultaneously
security can enjoy a "liquidity"
In this
preceding
with monetary
as occurring
occur in centralized
OF FINANCE
theory of finance,
I identified
that
is viewed
of
of the modern
what
in integrating
MONEY IN A THEORY
so that
equally
valued
elaborated
applications
on
of this
The present
constraint.'
applying
only,
the
treatment
cash-in-advance
permitting
the possibility
holding of money without
As
tween
in Section
the
terms
of
securities--the
full
trading
say
day,
production
workers
from
of current
selling
contact
with
a particular
with
firm
think
sellers
‘See
Kohn
(1980),
at tomorrow's
The
and
advance
securities
those
on
The
types.
that
it
See
do
not
By
I view
see
any
this
way
does
the
question
fiat
of each
is concluded,
out in the remainder
scattered,
to a specific
of
its specific
and/or
with
location,
purchasing
for in advance,
structure
goods
location.
evidence
sellers
at
each
Equivalently,
assumed
invoices,
of
lo-
under
here,
one may
or trade
credit,
In either case, the relein the competitive
constraint
Younes
with
shoppers
market.
finance
is
(1973);
that
for
of
at
traced
Foley
and
to
securities
Robertson
Hellwig
judging
not
particular
as closed
in
the
same
and
timing
by
general
which
involve
(1940)
(1975);
Lucas
of
Clover-type
at
the
21
utilizing
example,
agents
are
Comparison
of
the
of
between
the
Grossman
always
their
equilibrium
cash-inand
engaged
results
depend
in
with
critically
conventions.
of
these
out
approach
present
synchronously
of
For
some
time.
Samuelson
working
ways
markets.
which
(195.9)
equilibrium
description
alternate
many
incomplete
introduced
a useful
traders
of
characteristics
rules
the
one
models
the
trading
all
only
with
agents
within
(1980)
that
pursuing
all
models
issues
Wallace
questions
and
is made
that
is
examine
clear
assumed
monetary
paper
situations
never
makes
the
this
(1982)
intergenerational
f i nance.
I
of
e
and
markets
study
but
above
nature
in
Rotemberg
trading
analyzing
which
to
of
together
in
in
(1982).
adopted
and
cited
the
Townsend
idea
Grandmont
decentralized
constraint
(1982)
the
also
of trade
spatially
going
issuing
securities
Think
trading
then taking place.
determination
where
See
convention
centralized
Weiss
,
(1980)
and
are
buyers
transactions
be-
inter-
the beginning
to go to
information
in general.
fashion.
firm
obliged
exchange
in these
(1956).
(1982);
that
by
II
is carried
labor,
presented
and the
vant price and quantity
Tsiang
of
similarly
the indicated
expectations
and
buyers
is simply
to be cleared
firms
to a particular
other
rational
of
Section
and labor have been contracted
contracts
cation,
I mean
labor
the
it is easier to think
securities
goods
against
back and forth
period.
I think of as a decentralized
in
goods
sequence-economy
currency--at
After
a.m.
its
each
in
substitute
to shift
(1983)
consumption
consumption
of money,
on future
of
can
and
meeting
considered
claims
9:00-9:15
Insofar as goods
such
range
"decentralized'
BY
losing
the introduction
and exchange
the day, in what
against
scenario
of markets,
and contingent
Lucas and Stokey
a subset
be convenient
Arrow-Debreu
a sequence
currency
substituting
To motivate
pretation.
follow
to
that consumers
II, it will
timeless
will
constraint
time.
provide
framework
recent
will
prove
implications
used
in
context
the
for
theory
of
developments.
approaches
the
another
used
here.
of
I
do
not
most
useful
for
theories
of
both
mean
to
suggest
market,
with only the actual execution
In
thought
the
of
economic
much
as executed
activity
analytical
as arrived
of
complete-markets
in this
as occurring
simplicity
circumstances
way,
so that
the buyer
either
if purchased
at all, must
different
times
period
of
in
somewhat,
shocks
s2t
until
securities
is known
prior
issued
to a portfolio
any
period
be
is
acquired
assumed
in
securi-
Such goods,
in advance:
at
to
take
at
t, the information
public
in goods
closed.
structure
and
let the
prior
to all
(sit, s2t), where
trading
labor,
agents
of partia;
the density
(st-', sit), and fZt z ft/fi the conditional
place
As before,
knowledge
Hence,
on the basis
to denote
a subset
in earlier
St, be the pair
trading
t
decisions
exchanged
later.
to the last section.
decision
Use ft as before
goods
t's shock,
for
of much
is lost, and
so that the latter
known prior to any securities
to
trading
in
trading
Let period
as
be
or earlier.
(sI,...,st_I)
and publicly
where
mation.
=
think
section,
of
to be discharged
and
relative
st-I
t trading.
sit is realized
themselves
a given
within
thought
claims
can
of all economic
be paid for with currency
securities
one may
way, nothing
to the seller,
as payment
market of that morning,
is complicated
history
to accept
all exchange
In this
be
is unknown
or to issue trade credit
trading
while
market.
goods"--will
is unwilling
With
II,
by thinking
ties trading
the securities
taking place elsewhere.
Section
in a decentralized
centralized
goods--"cash
where
of
is gained,
at in a single,
consumption
of trades
model
in t and
but
unknown
must
commit
current
infor-
of st, fl the density
density
of
given
(St-'.
cIt, and credit
goods,
of
s2t,
sit)'
Let preferences
distinguish
between
cash goods,
c2t, as follows:
m
et~U(cIt,c2t,xt)f20ftds20dst
I:
(3.1)
t=o
The technology
is assumed unchanged
from Section
II:
= F(kt,l-xt,st).
c1t + c2t + gt + kt+1
It remains
objective
to formulate
function
nario sketched
households
1,2,... under
budget
firm
constraints
in a way
of
consistent
the
with
household
the
and
trading
the
sce-
above.
It is most
and
the
of the
(3.2)
convenient,
at 9:00
a.m.
as in Section
at t=O,
all contingencies
II, to begin
reviewing
s20, sI,s2,...,
22
the
by picturing
possibilities
for
firms
t=O,
with sIo being known and k0
Let us begin with the firm.
being given.
In terms
firms wishes
of
c2t(st)+gt(st)),
expression
price
the
un-normalized,
to choose
labor
(2.3).
of goods
unit-of-account
history-contingent
input
and capital
[l-xt(st)}.
For the monetary
in t and Wt(st)
prices
(rt,mxt),
plans for total output
economy,
[kt+l(st)}
let pt(st)
be the dollar
to maximize
be the dollar
spot wage.
the
(clt(st) +
Then,
spot
net dollar
inflow in t is
Pt(c1t + c2t + gt) - Wt(l-xt).
These
dollar
curities
labor
receipts
trading
bought)
balances,
are
in period
in t for
or
for
Jqt+ldsl
This
distribution
with
as dividends
is true whether
which
is carried
payment
on
(st-l,slt).
due
at
Since
of st but not of sl,t+l,
Then,
, t+1 *
mize:
for
goods
into
t+l
t+l.
of
se-
are sold
(or
as overnight
At
this
point,
Let qt(st-l ,slt) be the price at 0 of a claim to one
t, contingent
is a function
t+l.
currency,
credit,
(st,sl t+l) is known.
dollar'at
available
in time-0
this net-receipts
each dollar
dollars,
the firm's
is valued
expression
at time 0 at
objective
is to maxi-
m
z /Jqt+ldsl,t+l[pt(clt
t=o
- wt(l-xt)lds20dst
subject
the
firm
to
be
[nt,nXt) or at the dollar
Iqt+ldsl
must hold.
Clearly,
claims
Iqt+ldsl
as
price
prices
between
[qt,pt,Wt),
contracting
in
the proportionality
one may
conditions
claims
think of firms as trading
to dollars.
Similarly,
- pt as a future price at 0 for goods
expectation
at
(3.5)
interchangeably
or trading
advance
(3.4)
* Wt = VTxt
in advance
Jqt+ldsl,t+l
pt(st)
indifferent
, t+1 * Pt = ““t
Iqt+ldsl,t+l
view
= vn
to (3.2).
For
goods
(3.3)
+ C2t + gt)
rationally
I t+l as the price at 0 of one
23
held
at 0 about
dollar
at
t+1,
one may
in t, or
prices
real
in t,
contingent
view
and
on
(St-1,qt).
The household,
cash and on trade
in contrast,
credit
is not
indifferent
between
as it is, by convention,
obliged
purchasing
for
to acquire
cash
in advance:
t-1
pt(st)clt(st)
5 M&s ‘Sit)
where
Mt(st-',slt)
in t and
ptclt
is currency
is cash
holdings
goods
to cover cash goods spending
relevant
way (suggested
to me by Edwin Burmeister
demand
To develop
to this spending
sources
of dollars
as of 9:00
of dollars
at t+l include
The time-0
price
is Jqt+ldsl,t+l
*
in t, ptc2t,
later.
on
The
third, qt+l
These
sl,t+l)
time-0
to securities
trading
debt,
that
if
text),
equation
(1983)
individual
committing
himself
$_I
the
agents
for
agent
to
money
know
equilibrium
(5.16)
a
t+l and its uses of dollars.
wages
earned
items,
accrued
Mt+l
first
of
during
on
for
(s~~,s~),
for goods
in t, ptet,
items
t, Wt(l-
over unspent,
contingent
cash
two
derived
apply to all times
at 0), i
government
Svennson
an
is one
the household's
in t and carried
two
for taxes
the
consider
at t+l include payment
the firm, with value
summing up and collecting
See
of these
of
and uses
owns
6
in period
(I assume)
acquisitions
price
the household
Though
This formulation
and Robert Flood) of introducing
and
spending
bought
(possibly
in
is Iqt+ldsl,t+l;
t+l
or
of
the
.
sources
nominated
a.m.
Uses of dollars
on trade
contingent
(3.6)
is to say that money
in advance of the realization
held for cash good purchases
credit
trading
This constraint
decision.
budget constraint,
Sources
Mt - ptc1t.
t.
for cash balances.8
the household's
xt) and dollars
during
of the shock szt, which
of information
precautionary
at the close of securities
purchases
must hold for all realizations
must be acquired
(3.6)
sZt
and
These
UK,
initial
In addition,
.
initial
holdings
considerations
cash
(prior
of dollar
motivate,
de-
after
terms, the budget constraint:
a
useful
would,
in
holdings,
at
the
resource
below,
(say),
BO.
t=0,1,2,...
at G of
development
this
it
same
al location
in
which
the
is
the
time
case
as
wil
of
be
Set-up,
I
Sit
not
decomposition
24
scme
aspects
willing
(as
to
Marianne
(as
opposed
be
affected.
of
St
into
of
pay
to
Baxter
to
later,
This
(s,~,s~~)
this
formulation.
observe
szt
before
pointed
out
to
assumed
in
as
is
clear
is
from
immaterial.
me)
the
the
m
E
+ c2t + et) - Wt(l-xt) - Mtl
~uqt+lsl,t+llpt(xlt
t=o
+ qtMtlds20ds
The
Lagrangean
associated
straints
with
(3.6).
t
< VII + M + B.
for
(3.7)
the
and
(3.7)
.
consumer's
problem
multipliers
pt(st)
involves
associated
a
multiplier
with
the
con-
It is:
m
L =
L @t ,U(ct,xt)f20ftds20dst
t=o
+
Bol + z ht[Mt-Ptcltld~20dst
t=o
m
+x[un + M
The first-order
conditions
t
t
- xptlqt+ldsl,t+l
0 = 6 Ut(ct.xt)f20f
t
include,
then,
(3.8)
- XptJqt+ldsl,t+l,
all t,st,s20,
0 = 6 Ux(ct+)f20f
problem
- utpt,
all t,st,s20,
0 = stu2(ct+)f20ft
.
for the household's
t
(3.9)
- xWt+.+ldsl,t+ls
(3.10)
all t,st,s20,
0 = XJq t+1ds2 tds1 t+1 - Xqt + /+ds2 1'
,
,
,
(3.11)
all t,st-1,slt,s20,
M+_ L ptclt, with equality
all t,st,s20
if pt > 0,
(3.12)
.
25
x
Here
(3.11)
reflecting
sets to zero the derivative
of L with
the fact that Mt is a function
The firm's first-order
0 = ptFx(kt,l-xt,st)
conditions
- Wt
,
to Mt.
t
include
(3.13)
)dst-lqtdsltpt_l,
(3.14)
all t 2 1, s~,s~~
together
with
suitable
librium condition
As
obtain
in Section
tution,
transversality
II, one may
An
conditions.
is given by the technology
eliminate
additional
equi-
(3.2).
multipliers
from
familiar
relationships
among
marginal
of transformation,
and relative
prices.
Thus,
various,
its form
t), not (~20,s~).
, all t,st,s20
P t Fk (kt J-xt,s
' = "qt+l.dsl,t+l
respect
of (s~O,S~-~,S~
(3.8)-(3.14)
rates
from
to
of
substi-
(3.9).
(3.10).
and (3.13),
ux+q
-)
2 Ct'xt
analogous
between
(3.15)
to (2.11) and (2.13), and from (3.9) and (3.14):
u2(ct_1,xt_l)
analogous
Wt
= p
t
= Fx(kt,l-xt,st)
to
These
(2.14).
credit
(3.16)
= 6 J u2(ct,xt)Fk(kt&xt&f:_ldst,
goods
margins
at different
between
dates
credit
goods
are not disturbed
and
leisure
and
by the addition
of money.
The
monetary
margin
between
considerations.
U2(CtJt)
cash
and credit
first
is, of course,
affected
by
From (3.8) and (3.9),
++ldsl,t+l
U1(ct.xt) = Wt+ldsl,t+l
Consider
goods
the case in which
+ ut
all uncertainty
26
(3.17)
in t is resolved
prior
to
securities
Xt'
Then
trading,
so
that
st = sit
and
Ixtdszt
= xt
for
any
variable
(3.11) gives:
= iqt - Xlqt+ldst+l
9
and (3.17) becomes
where
rt
U2(cyxt)
Iqt+ldst+l
U1(ct'xt)=
qt
is the nominal
benefit
to
holding
nominal
bond
rate
cash
price,
= (l+r
t )-
latter
(3.18)
,
of interest.
is determined
so the
1
Here
the marginal-transactions
simultaneously
measures
with
the
exactly
the
one-period
relative
price
of
cash and credit goods.
More
nominal
generally,
interest
in the
presence
rate at t is given
of
a precautionary
motive
in terms of the time-0
~2~'
bond prices
the
qt
by
-1 = %+ldSZtdSl,t+l
(l+r t 1
Then
dividing
(3.8) and
to szt, and substituting
(l+r
Roughly
t
)-
1
=
Section
for Iutds2t
by pt, integrating
both with
respect
from (3.11);
(3.20)
.
IPt -1’Jl(ct,xt)f2tds2t
nominal
speaking,
exactly.
(3.9) through
% -l’J2(ct.xt)f2tds2t
marginal-transactions
money-holding
(3.19)
.
%
decision
Further
interest
benefit
must
uses
of
be
rates
holding
made
must
cash
before
of these marginal
be
in
these
conditions
equated
to
an
situations
benefits
will
can
expected
where
be
the
known
be considered
in
IV and V.
In addition
households
and
to these first-order
the government
(3.7), the government
must
conditions,
hold
budget constraint
27
is
the budget constraints
in equilibrium.
Using
(3.3)
of
and
m
M + BO =
i :04t(qt-iqt+ldsl,t+l)
t=o
Ptfqt+ldsl,t+l(gt-3t))d520dst
-
or:
initial
fiscal
government
surpluses,
liabilities
et - gt, plus
i + BO must equal
the present
(3.21)
the present
value of
value of seigniorage
profits,
:'t(qt - Iqt+ldsl,t+l).
A flow version
observation
playing
that
of (3.21),
condition
analogous
(3.21)
the role of M for t > 0.
must
That
to (2.17), can be derived
hold
for
all
t,
st,
from the
with
Mt_l
is, for all t, st:
m
qt(Mt_l+Bt) =
-P,
Now
updating
z I(‘$(q, - fqT+ldsl,r+l)
T=t
(fqT+ldsl,T+l(gT(3.22)
from
sl,t+l, and subtracting
t to
gT)!ds2td(tst)
.
t+l,
integrating
(3.22)
with
respect
to
s2t
and
from (3.22) gives:
(3.23)
- ‘I&
= ~8t+l%+lds2tdsl,t+l
That
is, a current
fiscal
deficit,
+ qt(Mt-Mt_l)
exclusive
of debt
service,
must
be fi-
nanced by net issues of new debt or by issues of money.
For
prior
the
case,
discussed
to the close of securities
interest
rate is defined
trading
in (3.18)
Bt+l%+l
1
(l+r )- p (g -9 ) = I
t
t t t
qt
in which
above,
all uncertainty
(that is, sit z st), the nominal
and (3.23) becomes:
dst+l
28
is resolved
- Bt + Mt - M
t-1
*
If, in addition,
one-period
government
-1
1
(l+r t )- p t (gt -e t ) = (l+rt)
general,
In
tures
gt
with
that
Bt+l - Bt + Mt - Mt_l
the government
depend
on
debt is uncontingent,
assumed
involve
szt
.
to buy on trade
the
implicit
credit,
expendi-
issue of s2t-contingent
"bonds."
IMPLICATIONS FOR THE THEORY OF FINANCE
IV.
The incorporation
as
carried
theorems"
out
of
in
private
The
applications.
The
so
that
also
equivalence
sequences
If
satisfying
(3.21),
then
the
second
policy.
follows
from
question
does not alter budget
Notice
the
that
policy-change
general,
As
the
of
this
same
that
[Mt)
Theory
and
on which
its
they
complications.
public
finance
Government
if
requires
policy
taxes,
and money
policy
(gt,e;,Mt)
modi-
consists
supply:
in this
is another
sense,
policy
equilibrium
is associated
with
the
the
of
given
prices
theorem,
the
policy
of
this
proof
change
in
sets.
argument
as well
Mt paths
and/or prices,
"equivalence
version
at
equivalence
involves
the
systems
for a given
and
barter
observation
different
quantities
with
price
expenditures,
holds,
on
Modigliani-Miller
as follows.
is an equilibrium
(3.21)
effect
of monetary
theorem
setting,
in particular
no
equilibrium
of government
there
into the real theory of finance
has
the
i.e.,
of
by the addition
Ricardian
(gtrat.Mt).
elements
section
finance:
in a monetary
contingent
last
linearity
rest is not altered
fication
of monetary
the
will
as
does
(et},
be associated
and the seigniorage
not
(gt)
go
being
with
through
held
different
if
fixed.
the
In
equilibrium
term
m
I:
t=o
IMtht
on the right-side
tax.
theorem
operations.
real
into
Jqt+ldsI ,t+P2&
of (3.21) will
One way to interpret
valence
of
-
or
trading
is
The path
government
withdrawn
as
not represent
this monetary
"irrelevance
an
[Mt) matters,
consumption,
from
the
is of no independent
the proceeds
amendment
theorem"
in this economy,
but the route
system,
importance.
29
changes
from a lump-sum
to the Ricardian
about
as does the path
by which
money
in
or
(et),
equi-
open-market
in
(gt)
is injected
securities
Though
minor,
these
for barter
economies
announcements
what
the second
change
as
term
be
taxes,
in the
to
future
processes and,
but
policy
second,
and fiscal processes
fore
be
changes
the
arbitrary
to goods-in-general)
value,
goods of the remaining
and, using
or
is that something
In the barter
One
are,
other
system,
could
first,
than
analyzing
the
must
system,
it could
catalogue
futility
changes
in
changes
in
of
policy
in monetary
II also require
a monetary
claims
to
economy.
credit
Let {ztl as be-
goods
be the price
significant
(and
hence,
in terms
in
of time-t
Then
c Ip,lqT+ldsl,t+l.zrds(t’T)
T=t
(3.10),
m
Q,(Z)
= zt +
z
r=t+1
which
exactly
Et(.)
is
within
for
of
1~~1 rzt.
,-1
Q,(z) = btNt+ldsl,t+l
deficit
(3.21)
of Section
and let Q,(z)
terms
simply
In a rational-expectations
changes.
of
theorem
being
of each other.
formulas
sequence
deficits,
In the monetary
terms
impossibility
independently
technically
(3.21).
lessons
in
are
in the current
of
that
main
or reinterpretation
an
right
policy
the
The securities-pricing
modification
by a change
[gt) or [et).
monetary
economy
reading of the equivalence
that government
sum on the
is either
assess
monetary
terms so as to maintain
possibilities,
trying
a
do not matter.
is "announced"
"something"
well
for
a popular
to the effect
in subsequent
various
reverse
of future
equilibrium,
this
modifications
they completely
no
replicates
longer
period
Ct J
The
2 Ct'xt
(2.20)
useful
t.)
U2kTPT)
u(
with
because
z,ft4$)
UC
(4.1)
replaced
uncertainty
analogues
to
(2.21)
by
U2.
(The
is resolved
and
(2.22)
at
then
notation
two
points
follow
from
(4.1) as from (2.?0).
The
marginal
marginal
utility
WltJlt
utility
U2
of
credit
of goods-in-general
+ c2t’xt)
absence
in the monetary
of a precautionary
can
be
interpreted
V is defined
if the function
as
the
by:
g wlyc2yq
so (4.1) and (2.20) are very close.
ties differ
goods
The arguments
and real cases,
motive
of these marginal
however.
(sit : St), clt =
30
For example,
M+
Pt
utiliin the
in equilibrium,
and
U2(cyxt)
so that both real balances
consumption.
Clearly
a separable
Mt
= V2(pt’ clt+c*&
= v2(cltJlt+c2yxt)
and leisure
one would
function
of clt
affect the marginal
utility
not wish to impose the hypothesis
and
clt + c2t.
so this
of total
that V is
is not an inessential
amendment.
Perhaps
in general
an equity
ble
at
more
fundamentally,
be claims
share
the
to streams
beginning
let
function
of st,
of
the
including
period
function
information
the
t.
events
in
We
of the stochastic
Since
of real goods.
(Z,) be an arbitrary
curities-trading
trading,
in a monetary
economy
For example,
in the firm has title to a stream of dollar
general,
of
securities
the dollars
after
dollar
~2~ that
wish
to
find
(st-l,slt)
receipts
and
the
at
time
m
T=t
while
only as of securities-trading
(4.2)
~-1pr-16~U2(cr,x,)f20fT
from (3.8) and (3.10).
qt =
Substituting
Apt -’ ‘Jl(ct,xt)f20ftds2t
.
these values
Rt(Z) =
into (4.2) gives:
UP, -1U2(cr,x,)Zrlst-1,sltl
E ,r-t
T=t
E[pt +J1(ct.xt)I
st-l,sltl
From the interest-rate
definition
(3.20),
31
a
.
qt-l 1q,+lZlds2td(ts~)dsl,,+1
=
as
securities--
From (3.9),
IqT+ldsl,T+l
of se-
Rt(Z),
t
In
Zt is a
time ~+l,
RtU) = .z
paya-
earned.
that
price
Zt+l(st+l),...
available
are
at the time
dollar
not
the owner of
receipts,
assume
are unknown
available
stream Zt(st),
ZT become
these
stream,
will
(4.3) is equivalent
(4.3)
to
at
E[U2(cT,xr)
1 S%ltl
; B'-~ (l+r t )- 1
r=t
Elpt +J2(ct,xt)I
In general,
will
2
T
Rt(Z) =
not
be the case
as given
that
it is clear
by
(4.4).
ties-pricing
that
The
if zt
Q,(z)
in a monetary
in (4.1)
as given
natural
to
the
is identified
by
deflations
world
(4.4)
st-lJltl
(4.1) will
do not
pricing
Pt
nominal
real
, it
‘Rto
match
reduce
of
zt
p+
with
securi-
securities
in a
barter world.
Obviously,
duces
the predictions
into it elements
observations
"barter"
do
model
applications
not
from which
amount
to
to a monetary
of financial
to the good judgment
cations
aside.
is not
could
The
that
it be otherwise?)
testable
Viewed
the
introducing
affect
successful
from monetary
theorists
so these
application
of
a
empirical
complications
in leaving such compli-
monetary
complications
the predictions
of the
as done
theory
(how
but to show that they do so in a fully operational,
of
constructed
IMPLICATIONS
as examples
such
testing
shocks
of
they
abstracted,
of
On the contrary,
that abstracts
if one intro-
way.
V.
models
world.
theory
criticism
of financial
virtue
to show
the original
serious
theory
testify
here
of any theory will be altered
as
that
or prototypes
sketched
first-order
and
FOR THE THEORY OF MONEY
in
conditions
characterized,
to the system.
This
of monetary
III
Section
as
in
given
section
theories,
is
whether
assumed
uses
not
their
behavior
simple
our interest
so
much
solutions
for
examples
in
in direct
can
the
be
various
to address
this
issue.
Constructive
III
Section
proofs
are even
exchange
economies
(1982).
With
that equilibria
equilibrium
production
as illustrated
by Bewley
(1972) and Heller
(1982)
prices
but without
obtained,
istence
exist
less well-developed
below.
are
easily
capital,
Townsend
allocations
exploiting
is not
the
(1974) to sketch
link
available
between
in monetary
32
as discussed
obtained,
less trivial
as
a quite
in
results
III.
general
Lucas
can be
proof
work
of ex-
The device used by Brock
optimally-planned
systems,
in
For pure
(1982) has built on earlier
for a model close to that in Section
of
for models
than for barter systems.
and
in general,
equilibria
because
of
the "wedge"
which
substitution
in
the inflation
cash
and
tax introduces
credit
goods
between
and
their
the marginal
unit
marginal
rate of
rate
of
transformation.
In this
excluding
section,
capital
C1t
where
C2t
+
the model
goods,
+ gt
follow
(Stdit
a Markov
process
III will
that the shocks
. ..)
with transition
is, the joint density
density
5 s'Ist = SI
ft(sI,...,st)
p(s',s)
given by
.
(5.2)
takes the form:
ft(st) = ft-I(st-')p(st,st_l)
Finally,
the money-supply
the current
process
(5.3)
is assumed
given by a fixed function
(5.4)
these
additional
assumptions,
and J, such that the allocations
balances
m of
state:
Mt = m(sJ Mt_l .
Under
by (1)
to the form
(5.1)
of St, and (3) assuming
= Pr{st+I
be specialized
the technology
9
other variables
Is' p(u,s)du
That
Cl-Xt)St
=
Et is a component
St =
of Section
(2) restricting
e(st) = Mt/pt
with
an
equilibrium
rate
function
equilibrium
satisfy
in this
rt = r(st)
I will
ct = (clt,c2t)
(3.14)-(3.16)
for all
stationary
sense
similar
recursive
and
first
= c(st),
will
seek
functions
t, st.
Associated
be a nominal
expressions
for
interestall
other
prices.
As a useful
intermediate
step, define
the functions
v(s) and w(s)
v(s) = S(S)U2(C(S)J(S))
(5.5)
v(s) + w(s) = s(s)uI(c(s),x(s))
(5.6)
and
SO that from
c,x
xt = x(st) and real
(3.8) and (3.9):
33
by
V(St) =
++ldsl,t+lMt
(5.7)
stf*Oft
and
V(St) + et)
We are headed
=
~~~t+ldsl,t+lMt+~tMt
(5.8)
Btf*Oft
for a functional
equation
in this function
From (3.9) and (3.10), an additional
equilibrium
v(s).
condition
is:
U2(c(s),x(s)
j= c
(5.9)
From (5.4), (3.12) and the definition
u(s) > cl(s)
For given
with equality
s = St, then,
"equations"
in the
of w(s) and c(s),
if w(s) > 0
(5.1), (5.5),
six
"unknowns"
.
(5.10)
(5.6). (5.9). and>(5.10)
provide
c~(s),c~(s),
x(s),o(s),w(s),
Alternatively,
for given v(s) and (5,s) we can think of solving
for cl,c2,x,$,
and w as functions
where
for
the
constraint
(c1,c2,x)
as
given by (5.6).
the condition
tained
from
(5.10)
functions
is binding,
of
Ul(c,x)
= U,(c,x)
(5.6).
and denote
w(s) = h(v(s),c,g)
(5.1),(5.5),
(v(s),s),
For values where
(5.5) or
solved uniquely,
of (v,c,g) or of (v(s),s).
b(s)
equals
and
are
solved
Let us assume
the solution
for
for w in particular
and
w(s)
(5.1),(5.9),
static
Then
J, is ob-
by
an equilibrium.
Next, note that from (5.7),
v(st_l) =
i+QtdsltMt_l
(5.12)
,t-lft-l
From (3.11). integrated
with respect
to sit.
34
is
and
system can be
(5.11)
= h(v(s),s)
This is the first step toward constructing
(5.9) are solved
(c~,c~,x).
that this
v(s).
this system
For s-values
cl(s),
(5.10) is slack, w(s)=O,
and
five
xlqtdslt
= mt+ldsltds2tdsl
, t+l
tt
= j- s-v(st)ds,
+
tt
,r =w(s,)dst
the
second
equality
(5.13)
%
%
where
J+dSltdS2t
+
follows
from
(5.7)
and
(5.8).
Inserting
from
(5.13) into (5.12):
%-1
= BJ"Mt
V(S&
Since
this
nitions
derivation
holds
for all states
(5.11),
= BJ-
w
p(s',s)ds'
in the
ditional
St-l, we have,
using
the defi-
(5.15)
goods
(5.15)
.
(5.15) becomes:
v(s) = aJ v
Equation
(5.14)
*
of m(s) and p(s',s),
I,(S)
Using
ft
-ft-l dst
(v(st)+w(st))
arises
market
dollar
p(s',s)ds'
from
the marginal
in state
on credit
balancing
s, deciding
whether
The utility
goods.
.
(5.16)
undertaken
or not
by an agent
to spend
of this marginal
an ad-
expenditure
is
1
Pt
The utility
u
2
(c
x ) =
t' t
foregone
That
is, a dollar
(5.16)
is
.
is, from (5.15),
V(St+l)+W(St+l)
& EC
t
%+A
for spending
j$v(st)
t
s ) = sE[ 1
pt+l Ul(ct+l’xt+l
t
spent on credit goods
a
functional
equation
today involves
a dollar
unavailable
Since m is a given function,
on cash goods tomorrow.
in
35
the
single
unknown
equation
function
v(s).
Solving
it is the second step toward constructing
Third
constraint
and
(3.21).
the function
side
finally,
of
Given
m(s),
(3.21)
an equilibrium
initial
values
and the functions
is
determined.
must
an equilibrium.
satisfy
the government
SO of St, the transitions
c,x,$,w
and v just
Substituting
from
solved,
(5.7)
and
budget
p(s',s),
the right
(5.8)
into
(3.21) gives
x(M + Bo) =
L a j(w(s,)-v(s,)
t=o
From (5.7), the multiplier
lv(so)f20ds20
A = Molqlds20dsll
Policies
(gt,et],
cations
only
satisfy
(5.17).
The
Bo,
if the
just
the simplest,
is constant.
and
implied
construction
begin with
m(s))
A is
l+ro J ( )f ds
= T
v so 20 20
M,
(5.17)
~Jf20ftds20dst.
m(st)
values
sketched
consider
(5.18)
-
are associated
of w,v,$
can
be
and
with
equilibrium
A, calculated
illustrated
the deterministic
allo-
as above,
by examples.
case where
To
s (and hence
Then (5.15) becomes
mv = a(v + w)
so that (5.5) and (5.6) give
t$(c*x) _ m
(5.19)
.m-B
(provided
and
m t a).
Then,
(5.1) are solved
with
for
(s,g) constant
(c,x) as functions
are equal
to cl, and the equilibrium
clU2(c,x)
and
(i - l)cllJ2(c,x)
.
values
as well
as m, (5.17).
of (z,c,g)
of v and w are,
The constant
nominal
(5.9),
Real balances
.
$
respectively,
rate of interest
r
is, from (3.18) and (5.19), given by
(l+r)
-1
This completes
this
deterministic
w,v,g,e
=i
(5.20)
.
the first
case.
two steps
For
the
in constructing
third,
insert
the
an equilibrium
constant
and JI into (5.17) and use (5.18) and (5.20) to get:
36
values
for
of
M + B.
9-e=!!!
*
With
1 - p-6)
-
6
That
monetary
=
BO
6g + r* A
is, tax receipts
real
vention
level
taxes
.
must
debt.
that
interest
(MO = i and m = 1), the price
policy
at $-I i and (5.21) implies:
66
original
-
Mo
a noninflationary
is constant
(5.21)
-
equal
(That
and
government
purchases
e and g are discounted
government
spending
plus
service
by B reflects
are carried
of the
the con-
out on credit,
and
is due in cash.)
Treating
arbitrary
MO
as
a
open-market
debt is initially
free
parameter
operation
"monetized,"
amounts
before
pursuing
MO = i + B
to
permitting
an
the policy m.
initial,
Thus,
if all
, (5.21) gives
g - e = @(m-l)
so
that
real
seigniorage
maximum
deficits
revenues
seigniorage
In general,
fining
the equilibrium
cally
shocks,
constant
(ct,gt).
k.
from
with
s2t
of s2t,
shock
Then c,x,$
=
-
financed
by
real
e + J, (i - l),
the
and with
government
From
and fiscal
with given m,g,M,MO
[St1 be
with
deficits
(5.16)
That
identimonetary
is, in each
are traded, real shocks
or surpluses
in this
and w are functions
and
determining
at 8.
and B, or
system.
independent
sit
et constant
securities
policies
(5.21) may be read as de-
of the monetary-fiscal
shocks
is realized,
k + h(k,s2)
m(s
1)
interest
g
Equation
(ct,gt),
The value of k is implicit
The nominal
perpetually
(5.21) that monetary
let the
is concluded.
k = BE{
be
MO -c -,
way.
"free parameter"
(necessitating
trading
can
tax rate e consistent
example,
independent
a monetary
realized
and
some other
a second
e
As
in an unrestricted
distributed,
period
-
for given m.
it is clear
be set
As
g
b(m-1).
revenue
cannot
as fixing
of
case,
on trade
v(s)
credit),
: k for
of k and the real shocks
in
(5.22)
1 .
rate is, from (3.20),(5.5),
37
and (5.6):
are
some
s2t =
11 + r(s,)l
k
= k + Ih(k,sl)p2(s2)ds2
Applying
(5.22) to the numerator
(1 + r)
-1
As a variation
pendence
but
Nominal
I1 +
which
varies
to (5.20).
that
again,
interest
(5.23)
on this
assume
Then
and cancelling:
= a+-~)
which may be compared
trading.
’
last example,
shocks
all
v(s)
retain
are
is constant
at
the assumptions
realized
prior
a value
to
of indesecurities
k satisfying
(5.22).
is now given by
r(s)l-1=
with
k
htk
+
g)
5
,
the real shock
(
,
(f,,g).
The formula
comparable
to (5.20)
is, in this case.
[l + r(s)]-' = BE($) vw
Inserting
this information
[I +
must
be constant
-
with
coincidentally,
the
for this case.
With
tically
makes
required
circumstances.
MO
9t - e
- r(st) +
m
respect
conclusion
taxes
the
determined,
the
into (5.20) one finds that the magnitude
M + B.
r(s,)l
value
(5.24)
Since
to St.
is that,
this condition
in general,
fixed at e and government
fact
that
equality
A compensating
interest
(3.20)
tax
rates
impossible
or open-market
will
hold only
no equilibrium
spending
vary
with
gt stochasreal
to maintain
policy
exists
shocks
under
is required
all
for
internal consistency.
These
(5.16)
three
examples
it is clear
that,
all
involve
in general,
serially
v(st) will
38
independent
vary with
shocks.
From
st due solely to
the
extent
sponding
st conveys
that
Equation
(5.25)
real
nominal
from other
is consistent
the
with
variables:
the
fact
pages
that
any
kind
rational-expectations
from the financial
from
about
future
for the one-period
Jv(s)p2(s2's1)ds2
-1
111
= f(v(s) + w(s))p2(s2,sl)ds2
[l+r(s
and
information
expression
"general"
of
corre-
rate is:
(5.25)
of
interest
single-equation
and,
rates
vacuity
and the transition
and
familiar
in the case of interest
The content
of any newspaper.
both r(st)
interest
’
co-movements
models
The
shocks.
nominal
rates,
in (5.25) must come
function
p(st+I,st)
are,
at least in part, observable.
The
plete
examples
analysis
for
pricing
must
await
theory
the
another
on
This
paper
in this
which
as
the
enterprise
securities
well
as
centralized
iS
was motivated
theories
valued
I think
money.
the
will
sense
exchanges,
higher
that
than
this
in situations
Ultimately,
however,
ent objectives,
and
identify
strong
forces
theory.
The real capital
two
distinct
however
goods
are
directed
idea that
model
the
traded
in Sections
theoretical
sense
theory
of
these
("money")
grounds
in most
in
markets
outside
market
at
success
"efficient"
is present
and monetary
alone.
writing
on
III-V.
have
"unity"
quite
may
differ-
be, one can
to pull apart these two bodies of
theory
reviewed
toward
increasing
39
and that
conditions
at least one security
forms,
that will continue
directions:
in a single
where
desirable
research
in centralized
it was proposed
financial
familiar
case,
stochastic
and by the
to be on efficient
in various
One way of developing
reproduce
to that
under
analysis
that an operational
will
to earlier
capturing
and priced
it "ought"
however,
implications
That
economy.
REMARKS
and finance
other
its
a com-
inadequate.
by reference
in which
constitute
and of
a theory
predictions
CONCLUDING
involve
idea,
(5.16)
specialized
is plainly
of money
are traded
such
when
to make
theory
VI.
"unifying"
that
theory
do not
in a monetary
They do suggest,
(5.16),
deterministic
conventional
certainly
equation
allocation
can be extended
for which
through
functional
occasion.
be based
from
its scope
of
worked
and resource
can
results
just
in Section
II can be modified
generality
in its
in
assumptions
about
technology,
needed
to
demography,
permit
the
empirical
failures
cate that
increased
of first-order
ficiency
of the
generality
monetary
theory,
duction
necessarily
of monetary
renders
solution
optimality
methods
inapplicable
to produce
The
models
indi-
success
in the sense
descendants
is not difficult
simulatable
the associated
exploit
and requires
III and V of this paper outline
models,
of the ef-
to obtain,
and
an objective
central
direction.
The
in the opposite
with
that
specificity
methods.
work in this direction.
pulls
elements,
the
consumer"
the modern
Such generality
of designing
toward
solution
"representative
can pass
Fruitful
or
constructive
is required
that
tests of Finance.
I expect much additional
preferences
of
simplest
conditions
The objective
and
application
the
intro-
"wedge" of inefficiency,
links
between
new analytical
one possible
to
equilibrium
approaches.
approach
and
Sections
and pursue
it to the
point where one can begin to get some idea of its potential.
If
I am
economics
right
that
is not, even
the case that
there
in applications
in finance,
is much
will
to be gained
the reduction
the more
the theory
of
"goods"
finance
as
had
"debt"
and
corporate
capital
indifference
curves
budget
Miller
to
showed to be spurious
Postulating
other "goods"
debt
necessary
of
preferences
is no more
a
particular
and flexibility
some of
by
this
its
of money
approach
axioms
as
the
by
would
that
over
still
tangency
picture
If
are claims.
preferences
textbooks
"real
points
be
of
Modigliani
convention,
and
beyond
whether
questions
as applied
so,
the merits
capable
it
I have
for
is
that money
is
of the power
also
else) will
revealed
approach
be judged
of giving
reliable
that lead us to be interested
in mone-
JO
seems
point,
of a particular
of anything
with
a demand
in this paper,
some aspects
in doing
it
this
together
it is, exactly,
to illustrate
and,
balances"
than postulating
To get
Ultimately,
than
to the study of de-
assets
unique
about what
(as to the theory
answers to the substantive
demands
to postulate
for
corporation.
specifically
its limitations.
to the theory
less
of
on
or demands
I have tried
one way to do this.
in the
of this framework
in 1958.
The Clower
to.
is not
financial
lines,
evident
(This
to which
structure
The power
so clearly
is the ability
content
surely
on the best recent work
(and no less) useful
to think more
gives one access
attributes
"equity,"
"explaining"
the
I think,
remained
interaction.
of view,
of the study of asset
fundamental
and monetary
to monetary'theory.
as it is an observation
to permit
financial
it is nevertheless
by close
point
applied
The source of this power,
for
between
one of "unity,"
be as usefully
mands
such
relationship
of the contingent-claim
so much a prediction
area.)
the
ideally,
tary
theory
in the first
place.
This
just begun.
41
is an inquiry
that
has clearly
only
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