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working paper
department
of economics
PRIVA TE AND PUBLIC SUPPL Y OF LIQUIDITY
Bengt Holmstrom
Jean Tirole
96-21
June 1996
massachusetts
institute of
technology
50 memorial drive
Cambridge, mass. 02139
PRIVA TE AND PUBLIC SUPPL Y OF LIQUIDITY
Bengt Holmstrom
Jean Tirole
96-21
June 1996
ittute
Private and Public Supply of Liquidity
Bengt Holmstrom*
and
Jean Tirole*"
First draft
:
This draft
We
September 21, 1995
:
June
17,
1996
thank Daron Acemoglu, Sudipto Bhattacharya,
Diamond, Mark
Olivier Blanchard,
Ricardo
Marquez, Rafael
Repullo, Jean-Charles Rochet, Julio Rotemberg, Andrei Shleifer, Jeremy Stein, Bob Wilson
and Mike Woodford for helpful discussions and comments. This research was supported by
a grant from the National Science Foundation.
Caballero, Peter
**
*"
Paris,
Gertler, Oliver Hart, Peter Howitt, Robert
Department of Economics, MIT.
IDEI and
and MJT.
GREMAQ
(CNRS
URA
947), Toulouse,
CERAS (CNRS URA
2036),
ABSTRACT
This paper addresses a basic, yet unresolved question:
Do
claims on private assets
provide sufficient liquidity for an efficient functioning of the productive sector?
State have a role in creating liquidity
and regulating
it
Or does
the
either through adjustments in the stock
of government securities or by other means?
In our model, firms can
meet future
liquidity
needs in three ways: by issuing
new
claims and diluting old ones, by obtaining a credit line from a financial intermediary, and
by holding claims on other firms.
When
there is
no aggregate uncertainty,
we show that these
instruments are sufficient for attaining the socially optimal (second-best) contract between
investors and firms. Such a contract imposes both a
constraint
on firms. Intermediaries coordinate the use of
scarce liquidity
When
may be wasted and
there
is
the social
liquidity.
optimum may not be
The government can improve liquidity, by
consumer income. Government bonds command a
claims.
The government should manage
(boosting the value of
liquidity
when
its
securities)
the shock
government supplied
leverage ratio and a liquidity
only aggregate uncertainty, the private sector
with regard to liquidity.
future
maximum
is
low.
when
Without intermediation,
attainable.
is
no longer
self-sufficient
issuing bonds that
commit
premium over
private
liquidity
the supply of liquidity
by loosening
liquidity
the aggregate liquidity shock is high and tightening
The paper
thus provides a microeconomic rationale for
liquidity as well as for an active
government policy.
Introduction
1.
This paper addresses a basic, yet unresolved question:
Do
private assets provide
sufficient liquidity for the efficient functioning of the productive sector?
have a role
in supplying additional liquidity
and regulating
it
Or does
the State
through adjustments in the stock
of government securities or by other means?
These questions presume a demand for
liquidity;
worry about supply. So why do firms demand
without demand there
is
no need
to
liquidity? In the standard theory of finance
(and in the Arrow-Debreu world of general equilibrium), firms can at any time issue claims
up
to the full value
of their expected returns. They have no reason to hold liquid reserves in
new
order to meet future financing needs, because they can just as well issue
funding needs arise.
As long
as they use their funds to finance positive net present value
projects, such firms will never encounter
The
first
liquidity, that is,
step in our analysis then
advance financing
model of moral hazard
in
claims as
any
is to
liquidity problems.
build a model in which there
is essential.
For
this
purpose
we
which the value of external claims are
is
a demand for
use an entrepreneurial
strictly less than the full
value of the firm for the standard reason that the entrepreneur must be given a
share of the firm in order to be motivated.
The wedge between
the full value and the external
value of the firm limits the firm's ability to raise funds to finance
positive net present value. In a
dynamic
minimum
all
projects that have
setting, this feature implies that liquidity
shocks
could force the firm to terminate a project mid-stream even though the project has a positive
continuation value.
either in the
To protect itself against
form of marketed
such risks, the firm wants to hold liquid reserves
assets that can
be readily sold or by arranging for credit
in
advance.
We study the determinants of the firm's liquidity demand in a simple,
hazard model. There are three periods. At date
sized project that pays off at date 2.
shock
is
a
random
The
1,
the firm raises funds to invest in a variablethe firm experiences a liquidity shock.
fraction of the date-0 investment
investment that must be
1
At date
made
dynamic moral
The
and represents the amount of additional
to continue the project.
1
If the necessary funds
can be raised,
It can be a cost overrun on the
can represent a shortfall in the date-1 revenue, which
could have been used to finance date-1 operating expenses. Or the shock might simply be
information about the firm's date-2 returns. The central feature in all these cases is that the
initial
liquidity
shock admits several interpretations.
investment. Alternatively,
it
1
the project proceeds, delivering a stochastic date-2 return that depends on the entrepreneur's
effort.
We
show
that the optimal date-0 contract
limits both the initial investment level
between the firm and the outside investors
and the amount that the firm
is
allowed to spend on
the liquidity shock, both constraints being proportional to the firm's initial assets. Because
the firm is credit constrained, the second-best solution trades off the benefits of a higher
initial
see
investment against the increased likelihood of having to terminate the project early and
go
it all
firm
to waste. This solution can
be implemented
in several
ways.
One
the necessary funds in advance, but add a liquidity covenant in
all
is to
give the
which the firm
promises to set aside a certain amount of funds to cover future liquidity needs. Alternatively,
2
intermediaries could fund future liquidity needs via a credit line.
Having established a demand for
liquidity,
embedding the model of an individual firm
number of such
its
firms.
Each firm
in
we move on
to study
its
supply by
a general equilibrium model with a large
(or intermediary) can issue arbitrary claims contingent
date-2 financial position and these claims can be freely traded in the market.
government can also supply
no other
the next.
assets that firms
4
liquidity
by
selling securities such as
and intermediaries can use
3
on
The
Treasury bonds. There are
to transfer wealth
from one period
Thus, a firm can meet liquidity needs in four ways: by issuing claims on
its
to
own
productive assets, by holding claims on other firms, by holding government issued claims,
or by using a credit line.
Our main
managing
interest is
in
understanding the government's role in supplying and
liquidity as a function of the severity
and nature of the liquidity shocks.
We
consider two polar cases, one in which the firms' liquidity shocks are independent, so that
there
is
no aggregate uncertainty, and the opposite case
shock affects the firm's net worth, which determines
2
Our theory
is
in
its
which the firms'
liquidity shocks
financing capacity.
too sparse to distinguish between different financial institutions.
we
When
use language (intermediary, bank, etc) that suggests an institutional interpretation,
should be interpreted as illustrative of many similar arrangements.
3
In contrast to
much of the literature, we do not restrict the
a spurious demand for publicly supplied
issue, in order to avoid
4
We can
set
of claims that firms can
liquidity.
allow other assets, such as real estate, as long as their value does not
the private sector's liquidity needs. See the conclusion.
this
fulfill
are identical.
we show
In the absence of aggregate uncertainty,
add useful liquidity beyond
any role
liquidity.
The
self-sufficiency of the private sector:
which
0.
is
deterministic,
government
must exceed
its
5
There
date-1 continuation value of the private sector,
date-0 value, else
it
shareholdings, or equivalently, by leveraging itself up with
However, even though the private sector
that individual firms will in general
be unable to
One might have
could not have invested at date
market solution
this
liquidity shocks
We
is in
that
could
sell
diluting
the aggregate,
would
when
we show
needs by holding only
suffice for each firm to
the liquidity shock hits.
liquidity.
Thus, scarce liquidity
is
wasted.
an optimal allocation can always be achieved by intermediaries.
Intermediaries hold corporate securities and simultaneously grant credit lines to firms.
take into account the fact that
some firms (namely, those with low
exhaust their credit lines at date
to firms that
1.
liquidity needs) will not
act as liquidity pools or insurers in preventing a
wasteful accumulation of liquidity by firms that end up being lucky at date
Note
that explains
may
that
why
strictly
it is
They
Intermediaries can therefore redistribute excess liquidity
do need extra funds. They
intermediation
its
debt.
satisfy their liquidity
it
by
1
general not efficient, because lucky firms with low
end up holding excess
show
it
new
is self-sufficient in
thought that
hold a share of the market portfolio, which
However,
do not
a simple intuition behind the
is
Therefore the private sector can raise sufficient funds at date
private market instruments.
securities
provided by private claims, nor does the government have
that
managing aggregate
in
that
1.
Thus,
dominate financial markets.
the anonymity of market claims, and not an informational handicap,
financial markets can
be inferior
to intermediation.
the credit line arrangement that yields a productive
present value investments at date
1.
By
optimum
The
is that it
critical feature
of
allows negative net
contrast, claimholders can dispose of negative value
claims in an anonymous financial market.
In the presence of pure aggregate uncertainty, the earlier argument for
private sector
is
self-sufficient breaks
down.
Now
there can
why
the
be no cross-subsidization,
because each firm faces trouble exactly when the other firms do. As the private sector
is
unable to provide insurance there will be a liquidity shortage whenever the reinvestment need
5
If issued,
government
securities will carry
3
no premium.
exceeds
This creates a potential demand for
value of corporate claims.
date-1
the
government-provided
liquidity.
We
show
improvement by issuing Treasury bonds, and
premium. The private sector
is
government can achieve a Pareto
the
that
that these
bonds can be sold
willing to purchase low-yielding securities because they serve
as an input into the production process. In our risk-neutral
rates
model
securities with different
of return co-exist in equilibrium.
It is
important to point out what the government can achieve that the private sector
cannot. In our model, individual investors can refuse to bring in
sector at date
1
,
that they
1
More
if this is unprofitable.
precisely,
promise to supply new funds
cannot at date
date
at a liquidity
new
we assume
at date 1:
funds to the corporate
that individual investors
For example they may pretend
have no new endowment. This assumption
is
at
both theoretically and
empirically reasonable. In practice individuals can borrow very limited amounts without
pledging assets as collateral (as in the case of a mortgage). Because the private sector has no
power
to audit
at date 1.
By
income and levy
contrast, the
taxes,
unable to check
it is
government has the power
who
to audit
is
lying about
incomes and impose non-
financial penalties (such as jail) to enforce tax payments. It can therefore,
consumers, commit new funds at date
l.
6
This
is
endowments
on behalf of the
what Treasury bonds issued
at date
achieve.
When
to issue
the
government issues
securities at a
premium and when firms are constrained
a single security (equity), a firm has an incentive to free-ride on the liquidity
provided by those firms that purchase government securities. The firm can buy their shares
instead of government securities.
by issuing multiple
liquidity services
We show that firms respond to the possibility of free riding
securities so as to price discriminate
much
then sold at a liquidity
(corporations) and those
premium
who
between investors
who
value
don't (consumers). Corporate debt
relative to equity.
However, these outcomes are not
socially efficient in that they
lead to distorted
reinvestments in an effort to economize on the use of government provided liquidity.
show
that
it is
more
efficient to
If
We
have the government issue state-contingent bonds, which
supply liquidity only as needed by the private sector. Such bonds have a high value
6
is
when
our model were one with overlapping generations, the government could commit
future consumers as well as current ones.
We
and a low value when liquidity needs are low.
liquidity needs are high
interpret state-
contingent bonds as a metaphor for an active government policy in which liquidity
tight
when
shock
is
the aggregate liquidity shock
made
the aggregate
unfavorable (high). Thus, the model offers a rationale, not only for government
management of
supplied liquidity, but also for the active
The paper
liquidity
when
favorable (low) and loose
is
is
demanded by a
embeds
single firm. Section 3
model without aggregate uncertainty and shows
demand
for and supply of
this
model
in a general equilibrium
that the private sector is self-sufficient
that intermediaries are used as liquidity pools. Section
analyzes the
by the government.
Section 2 sets up a partial equilibrium model of
organized as follows.
is
liquidity
government
and
4 studies aggregate uncertainty and
securities, including the optimal use
on
state-contingent bonds. Section 5 relates our results to the literatures
of
credit rationing,
intermediation and government debt. Section 6 concludes with remarks on the key features
of the model and suggestions for future research.
2.
Exogenous Liquidity Supply
The model.
2. 1
This section studies the investment decision of an individual firm.
There are three periods,
investors
There
(consumers).
t
is
=
0,1,2 and two types of agents, firms (entrepreneurs) and
one (universal) good used both for consumption and
investment. All agents are risk neutral with an additively separable
undiscounted consumption streams. For the
at
moment we assume
a zero rate of return and simply refer to
shortage of liquidity. In later sections
we
the endogenous supply of liquidity, that
it
utility
that the
function over
good can be stored
as "cash". This guarantees that there
we
is
no
will
drop
this
in
how
well financial assets can service future
is,
assumption as
are interested in
funding needs of firms.
The firm has access
initial
investment
investment
made
I
I
returns
to a stochastic constant-returns-to-scale technology,
which for an
The
scale of the
RI
if the project
succeeds and
if
it
fails.
can be varied freely, subject only to financial constraints. The investment
at date 0.
At date
1,
an additional, uncertain amount pi
>
of cash
is
is
needed to
finance cost overrruns or date-1 operating expenditures and thus to carry on with the project.
The
liquidity
shock p
is
distributed according to the cumulative distribution function F, with
a density function
If pi is not paid, the project terminates
f.
the project continues and
Investment
the probability
p
its
payoff
(l°
w)»
subject to moral hazard in that the firm (entrepreneur) privately chooses
is
that the project succeeds.
where Ph
If pi is paid,
realized at date 2.
is
firm behaves the probability of success
pL
and yields nothing.
-
Pl
— Ap >
proportional to the level of
is
Ph (high),
investment
its
firm can either "behave" or "shirk". If the
if
shirks the probability of success is
it
0. If the firm shirks, it
continuation decision. If the project
The timing of events
is
The
is
I.
enjoys a private benefit, BI
The firm makes
the decision on
p
>
0,
after the
abandoned, no decision on p needs to be made.
described in Figure
DateO
1.
Date 2
Datel
Continue
—
*
X
-*-
Liquidity shock
Investment
Financial
¥-
-K-
Moral
hazard
(pl)
contract
Outcome
(Rl or 0)
Abandon
Figure 1
The
wants to invest
If the firm
moment, we assume
shock are
endowment of
firm has a date-0
all
A
we
who pays
investment are distributed.
more funds than
It is
7
it
it
will need to raise I
-
at dates
A
investors.
from outside
will see, nothing
changes
if
A
I
amount
of the project, the contingencies
for the liquidity shocks, and finally
key constraint on the contract
has; there is
outcome and the
1
and
is
no
loss
liquidity
in
how
is that
that the investors will
which the project
is
the proceeds from the
the firm cannot pay out
limited liability.
The
assuming this. In the presence of a random date-1
shock must be thought of as being net of the date-1 revenue.
of generality
revenue stream, the liquidity
7
For the
easy to show that an optimal allocation has the following simple structure.
There
2.
only the entrepreneur observes
contract with the investors specifies the
contribute at date 0, the scale
continued at date-1,
A,
no endowments
that the initial investment level, the project
verifiable (as
the liquidity shock).
>
I
cash, A, and
in
firm invests
The
investors.
<
p
p,
all its
funds
project
with the balance of the investment,
initially
continued
is
p. Neither the investors
if
and only
if
nor the firm receive anything
f
project
R.
I,
8
A, paid by the
below a threshold
the liquidity shock falls
if the project fails
abandoned. If the project succeeds, investors are paid R;I and the firm
+ R =
-
I
is
or
is
paid RJ, where Rj
This allocation has three free parameters to be determined: the scale of the
the cut-off p, and the investors' share Rj.
To make
the analysis interesting,
present value if the firm
is diligent,
we
but not
will
assume
that the project has a positive net
if it shirks:
max fF(p)p H R-l-[V(p)dpl >0 >maxJF(p)p L R+B-l-j'pf(p)dp|.
(1)
P
Note
is
that the first
maximum
is
achieved by setting p
=
p
t
=
p HR. That
is,
net present value
maximized by continuing the project whenever the expected return exceeds the additional
need for funding.
We
We will
refer to p, as the first-best threshold.
turn to the second-best solution. If the firm continues,
it
must be given an
incentive to be diligent. This requires that
(Ap)Rf I
As
is
assume
-
Rb
BI.
(2)
standard in models with limited liability, the firm must be bribed to be diligent.
According
R
>
,
to (2), the
that this
minimum
minimum
is insufficient to
required by investors
is
is
bribe per unit of investment
is
Rf
= Rb =
B/Ap. 9
We
so high that the residual share that can be pledged to investors,
cover the expected cost of the investors' investment. If the return
zero, this assumption holds if
F(p)p
<l+[V(p)dp
for all p,
(3)
Jo
where
p
8
=
p H (R-Rb)
two-outcome world the investors' claim can either be interpreted as debt (the
if it cannot) or as equity (there is no debt and the
investors hold an equity share R/R).
In this
firm must pay back R^I and defaults
9
The minimum payment
shared by
efficiently.
all
to the entrepreneur
can more broadly be interpreted as a rent
employees of the firm. Without such
rents,
employees will not work as
is
the date-1 pledgeable per-unit return.
that
some equity
investors
is
needed
to
Note
that condition (3) is equivalent to the condition
implement the threshold
to outside
1
+
{V(p)dp.
that the investors' time preference is zero, the return they will require will also
Given
be zero as long as they
have more cash than demanded by the firms.
collectively
maintain this assumption throughout the paper.
,
most favorable
:
F(Po)Po<
cutoff p
that is
the investors' break-even constraint
F(p) p H (R-R f )I
With a zero
We
will
and for a given
rate of return,
is
>I-A+I [p
f(p)dp.
(4)
Jo
The
left-hand side represents the ex ante "pledgable expected income"
,
which must exceed
we
the investors' expected outlays found on the right-hand side. Given (3),
break-even constraint limits the firm's investment to a
investment capacity.
finite level,
which
Because investors break even, the firm's net
we
see that the
might term
its
equals the social
utility
surplus of the project, namely
=
U(p,I)
[F(p)p,-1- fpf(p)dp]
I
=
m(p)I,
(5)
Jo
where m(p), the term
in brackets in (5), represents the
investment.
For a given p
(4), that it is
optimal to set
,
marginal return on a unit of
the second-best solution therefore maximizes
R = R b The
.
f
I
firm's investment capacity
=
is
I,
initial
implying, by
then
k(p)A,
(6a)
where
k(p)^^
1
1
(6b)
+ ppf(p)dp-F(p)p
Jo
is
the equity multiplier.
multiplier can
be
In that case I-A
liquidity
<
Maximal leverage
is
achieved by setting
less than 1 if the expected liquidity
0.
(The
total
investment, that
is,
demand
at date
p=p
1 is
.
The
equity
sufficiently high.
the initial investment plus the expected
payments, will of course exceed the firm's
initial
cash A.)
Unless otherwise
—
specified,
(this will
It
it
we
assume
will
be the case
0.
denominator
if the
That
that
is,
the firm
in (6b) is less than
1
is
a net borrower at date
for p
=
p,).
remains to determine the optimal continuation threshold. Intuition might suggest that
would be optimal
p,).
>
I-A
that
to let the firm continue
Indeed, the first-best cut-off p,
However,
=
whenever continuation
is
p H R maximizes the per-unit profit of investing, m(p).
at p,, the equity multiplier k(p) is decreasing in p, indicating that
choose a lower treshold than the ex post efficient one. Substituting
one ought
(6) into (5)
through by F(p), one finds that the optimal (second-best) threshold,
expected unit cost of
<
ex post efficient (p
p*,
to
and dividing
minimizes the
expected investment:
total
p* minimizes
l+fVcpjdp
^
(7)'
*•
F(p)
It is
not difficult to
show
that the optimal threshold satisfies
p„(R-R b )
=
p
<
These bounds can be given a simple economic
by the
<
fact that if p
p
,
ex post. The upper bound
continuing
is
p*
<
p,
=
,0
p H R.
interpretation.
(8)
The lower bound
is
explained
both the firm and the investors prefer to continue with the project
is
explained by the fact that if p
negative, in which case an ex post Pareto
> p„
the net present value of
improvement could be achieved by
having investors compensate the firm (which always likes to continue ex post) for abandoning
the project. Since transfers from investors to the firm are not constrained
compatibility, both parties
Since k(p
)
would agree
to
abandon the project given such a
by incentive
liquidity shock.
represents the largest investment scale that the firm can achieve, while p x
maximizes the ex post surplus,
investment scale at date
we
see that the second-best solution trades off a larger
against fewer liquidations (more investment) at date
1
.
The firm
10
Note that p* does not depend on either p or p,, so how can (8) hold? The answer is
that program (7) gives the optimal cut-off only if (1) and (3) hold. We must have p* > p
else the firm would not be credit constrained at all and condition (3) would be violated. If
p* > p,, investment would not be profitable and condition (1) would be violated.
Note also that the first-order condition for (7) can be written
,
f'F(p)dp =
1.
Jo
A mean-preserving spread in the distribution of the liquidity shock therefore decreases
P*.
cannot freely choose both variables, because by (2)
it is
limited in
its
ability to transfer social
surplus to investors. Consequently, the firm distributes available funds so that
it is
credit
rationed both ex ante and ex post.
For future reference, we record the following
Lemma
optimal for the firm to adopt a cut-offpolicy in which liquidity needs are met
1: // is
<
if and only if p
p.
The firm's investment capacity
(i)
p=p
at
I
= k(p)A
at p
is
quasi-concave in p, with a
maximum
with a
maximum
.
The marginal return on investment m(p)
(ii)
result:
is
quasi-concave
in
p
,
=p r
The firm's expected output (F(p)p,k(p)A) and the value of external claims on
(Hi)
output (F(p)p k(p)A) are quasi-concave in p
optimum
p=p'
,
with a
maximum
this
at the second-best
.
Implementation of the optimal policy.
2 2
.
Suppose the decision
case, investors
liquidity needs
of the
initial
to continue the project is left to
would be willing
exceed p
investors
to inject
more cash
into the project if p
In the latter case, even if the firm
.
by issuing senior
when p
1
e (p
,
were allowed
securities at date 1,
because the maximal value of the firm's external claims
liquidity needs at date
be negotiated
is
it
at date 1. In that
<
p
,
but not
if
to dilute the claims
could not raise enough cash,
pj. Thus, to cover the firm's
p*) one must find a
way
for investors to
commit
sufficient funds at date 0.
One
credit in the
solution is to give the firm
amount
p*I to
be used for
consume funds, and always
permits.
11
11
I -
A
at date
and extend
liquidity needs at date 1.
prefers to continue,
it
will
it
an irrevocable line of
Given
that the firm
do so as long
cannot
as the credit line
This implements the optimal solution. [Equivalently, the investors can extend an
of credit be renegotiated for mutual advantage once p is realized? The
answer is no. If p < p*, then p < p H R and it is ex post efficient to continue so there is no
scope for renegotiation. Nor can both parties benefit from an increase in the line of credit
when
Could the
p*
<
p
<
line
pH R.
Even though
this increase raises total surplus, there is
10
no way
to
irrevocable credit line in the
amount (p* -p
) I
and grant the firm the right
to dilute outside
claims as needed to cover the liquidity shock.]
In practice, individuals do not grant credit lines, because they cannot
income or endowments. Ex
commitments would be
post, credit line
which case investors would claim
that they
commit
future
either unprofitable, in
have no funds, or be profitable,
in
which case
a commitment was unnecessary. Instead, credit lines are granted by intermediaries such as
banks, which can
that they
make commitments
have enough funds
to
meet
An
of
do so by
that they can
this
amount
is
liquidity needs
issuing shares that
alternative solution
is to
How
do
can be met? In the next section,
we
later credit needs.
own
intermediaries guarantee that their
show
(both in practice and in our model), assuming of course
This raises the question:
pay off only
give the firm 1(1 +p*)
-
A
at date 2.
demand
kept in liquid assets. In other words, investors
maintains a liquidity ratio equal to p7(l+p*), at least up to date
liquidity ratio is a
commonly observed
debt covenant.
As
and require that p*I
at date 1,
in
1.
that the firm
Indeed, a
minimum
the case of credit lines,
intermediaries are the natural party for overseeing the compliance of such a covenant.
worth stressing that the
partial equilibrium
model does not distinguish between a
It is
credit line
and the hoarding of liquid assets by the firm. But as the next section shows these two
methods of providing reserves are no longer equivalent once general equilibrium aspects
(namely, that the supply of liquid assets
Remark
1:
We assumed
that the liquidity
is
not unlimited) are brought into consideration.
shock
is
verifiable.
Nothing
is
altered if only the
firm observes the liquidity shock as long as the firm cannot use part of the credit line or
financial assets for
whenever p <p*.
in the firm.
A
If
consumption
p
>
p",
it
rational investor
because
it
Remark
2: If investors
has exceeded
its
at date
1.
Given the firm's reserves,
it
its
can continue
cannot continue, since no outsider can be induced to invest
would
infer that a firm that tries to raise
new funds does
reserves and therefore has experienced a shock p
>
p'
>
p
so
.
cannot control the firm's use of funds, one can show that the firm
does not want to distribute the funds between date-0 investment and date-1 investment in
accordance with the second-best solution. Either
distribute the surplus in
a manner that
the firm wants to invest less initially in
satisfies the investors.
11
order to be able to continue in more states at date
the firm wants to invest excessively
<
amount
full
1(1
+p*)
=
I*
To
p and there
is
a cash
illustrate the latter possibility,
in illiquid assets. Despite the lack
reinvestment, the project will often be continued, as the investors have an
left for
incentive to rescue the firm as long as p
initially that
Or
of the soft-budget constraint problem).
suppose that the firm invests the
of cash
.
on being bailed out by the investors when p
at date 0, relying partly
shortfall (a version
1
<
p
Of course,
.
money
they will not put any more
want
the investors might
to claim
into the venture, but this is not a credible
commitment. Anticipating a "soft budget constraint", the firm may overinvest. Indeed the
firm prefers investing
I*
rather than I if
F(p-)p H Rb I
FfcO
<
<
This condition can be satisfied by adjusting
We
summarize
Proposition
1.
A firm
(i)
fti)
F(Po)PhRJ*, or
F(p )(l+p-).
B
so that p
falls just
below
p'.
this section in:
In the second-best allocation:
with initial capital
The project
is
A
invests I
=
k(p')A where k(-)
is
given by (6b).
continued if and only if the liquidity shock falls below the cutoff p\ The
cutoff p' lies strictly between the (per-unit-of-invcstment) pledgeable expected
pH (R-B/Ap) and
(iii)
the expected return p,
Neither party
succeeds, the firm
(iv)
is
is
paid anything
=
return p
=
p„R.
if the project is terminated
or
fails.
If the project
paid (B/Ap)I and the investors (R-B/Ap)I.
This second-best allocation can be implemented by raising (I-A) in externalfundsfor the
initial
investment and extending the firm a line of credit in the amount p' I to be used for
reinvestment. Alternatively, the firm gets (1
+
p')l at date
with the convenant that
it
keeps
p'l in reserve for reinvestments.
3.
Endogenous Liquidity Supply without Aggregate Uncertainty.
3.1
The economy.
Next
we embed
our model
in
a general equilibrium framework. Our objective
analyze the endogenous supply of liquidity.
To
12
is to
focus on the problem of creating assets that
can meet the demand for liquidity at date
1,
we
drop the assumption that there
an
is
exogenously given storage technology. The single consumption good can no longer be stored
(there is
no longer cash), nor are there any other private
used to transfer wealth from one period to the next. The only private
across periods
is
by buying claims issued by
be
assets (like real estate) that can
firms. Later on,
we
way
to transfer wealth
will introduce
government
bonds.
There
is
a continuum of firms with unit mass. Each firm
endowed with
Because of constant returns to
stochastic technology described in section 2.
A
units of the
As
good
at date
and none
and
at dates 1
utility for
E[c
+
Consumers receive per-period endowments
required investments and taxes that
+
c,
consumption
endowed
do not care about the
is
cj.
that collectively are large
may be
is
no
2.
before, consumers and entrepreneurs are risk neutral and
timing of consumption. Their expected
the
scale, there is
assuming that firms have identical endowments; the representative firm
loss in
with
is
levied.
enough
Consumers cannot
to finance all
claims on their
sell
future endowments, because they can default with impunity.
Any
assets purchased
their collective
by the consumers must yield a zero expected return given
endowments exceed investment demand. By
may be
willing
a premium (a negative return) as long as those assets help them to meet
to purchase assets at
their liquidity needs.
entirely determined
contrast, firms
that
Thus, rates of return, to the extent they deviate from zero, will be
by the productive
sector. This is the
convenience afforded by a linear
preference structure.
In this section
Because there
is
we
will consider the case
a continuum of firms, there
is
where
liquidity shocks are independent.
no aggregate uncertainty and F(p) denotes
both the ex ante probability that a given firm faces a liquidity shock below p and the realized
fraction of firms with liquidity shock
below
p.
The independence assumption and
analysis in section 2 imply that the date-1 funds needed
the productive
optimum
is
the deterministic
D=
by the productive sector
the
to achieve
amount
[f'"pf(p)dp]I,
(9)
Jo
where
I is
the representative firm's investment.
The two ways of implementing
the productive
13
optimum discussed
in section 2,
an
irrevocable credit line or a liquidity requirement, both relied on an exogenously supplied
liquid asset, cash.
With cash no longer
finance their liquidity needs
additional claims at date
3.2
1
D
we
available,
are led to investigate whether firms can
by using available market instruments,
that is,
by
issuing
or by holding stakes in other firms.
Financial markets.
For the time being, assume
that there are
no intermediaries. There
market for claims issued by firms. The financial market
a given claim
independent of
is
who
holds
anonymous
is
is
in that the return
(senior) securities in the financial market.
Assuming
amount thus
maximum amount
market value (the
=
pH (R-Rb)I
The market value
to dilute their claims
investment.
Of
up
to the full
amount
its
by
selling
new
it
can raise)
is
Pol.
must
retain the stake
claim in order to behave. Since date-0 investors, those
cannot meet
1
that the firm is able to continue with the
pqI reflects the fact that the firm
securities, get nothing if the firm
on
it.
We first compute the maximum amount that a firm can raise at date
raised, its
only a financial
who bought
RJ
as an inside
the firm's initial
liquidity needs, they are willing (ex post)
some of
pqI in order to salvage
their initial
course, initial investors take the possibility of dilution into account in the
pricing of initial claims.
A
firm
is
unable to meet
its
liquidity needs
realized liquidity shock p falls in the interval (p ,p°].
by buying,
is,
at date 0,
can the firm assure
new
claims whenever the
Can a firm cover
the potential shortfall
by
issuing
claims issued by other firms and selling these claims at date 1? That
itself
enough
liquidity through the financial
market? The answer
is in
general negative.
To develop an
intuition for
why
firms' liquidity needs efficiently, let us
the financial market
assume
may be
unable to serve the
(for illustration only) that all external claims
are equity claims and that they are gathered in a single stock index (a mutual fund), which
firms can buy.
at date
1
,
is
The absence of aggregate shocks
deterministic.
with liquidity shock p
continue at date
1.
Suppose
continues
The
total
if
implies that S,
that the productive
and only
if
p
,
the value of the stock index
optimum of
< p\
section 2 obtains;
Then, a fraction F(p*) of firms will
value of external claims on the productive sector at date
14
a firm
1
(and
date 2)
is
v =F(p
*r -\)p
V,
(10)
t
I.
be diluted by the amount
In the absence of credit lines, these external claims need to
defined in (9), so, the value S, of the stock index at date
S,
D
1 is
=
V.-D
=
[F(p')p -fpf(p)dp]I=I-A.
(11)
Jo
a
Let us conduct the following thought experiment: Suppose that a fraction
of the stock index
index.
At date
1,
is
All firms have the
held by the firms themselves.
e [0,1)
same share
in the
each firm can then withstand liquidity shocks p satisfying
pI<p
For the right-hand side of (12)
to
be equal
I
+ oS r
to p*I for
(12)
<
some a
p* + f"pf(p)dp<[l + F(p-)]p
1,
one must have:
(13)
.
Jo
Recalling that p*
we
in
is
independent of the extent of moral hazard as measured by
conclude that for
B
large enough, that
which case firms are unable
index.
much
Intuitively,
capital
by
when
the firm's insider share
much by
small enough, condition (13)
for p
to withstand liquidity
diluting itself at date
the firm cannot raise
is
1.
Rb
is
little
is inefficient.
is
violated
large, an individual firm cannot raise
Concurrently, the stock index has a low value and
selling the stock index either.
is
not that the stock market
liquidity in the aggregate. Rather, the ex post distribution
The lucky
(see (7)),
shocks up to p* by holding the stock
Actually, as the next section demonstrates, the issue
delivers too
B
firms (those with liquidity shocks p
<
p
)
of liquid assets
hold shares in the stock
index, which they do not need. Meanwhile, other firms cannot withstand their larger liquidity
shocks because their share in the stock index
12
An example may be
parameters are such that p
helpful.
=
1.1
is
Suppose p
and p, =
15
confined to be the average share.
is
3.
12
uniformly distributed over [0,2] and the
Then
(7) implies p*
=
2.
The
initial
It is
claim
clear that the previous reasoning does not rely
More
(the stock index) that firms can purchase.
between the
threshold
is
total
p*
—
value
is
on there being a single financial
generally, S,
—
the difference
of external claims and the aggregate reinvestment cost when the
an upper bound on the combined value of all external date-0 claims on
the productive sector. Hence, in the aggregate, the value of the financial claims held
firms cannot exceed S,. Given that dilution cannot raise
(all
firms, if financial claims are uniformly distributed
exceeding p
1
+
more than p
among
1
by the
per firm, some firms
firms) cannot withstand shocks
S,.
To conclude, anonymous financial markets cannot in general implement the productive
optimum.
3.3
Intermediation.
When
the financial market fails to supply enough liquidity, the productive
optimum
can be implemented by introducing an intermediary that offers insurance against liquidity
needs by pooling firm risks. The optimal insurance arrangement entails subsidizing firms
with a high liquidity demand,
allowing them to draw on the market value of firms that
experience a low liquidity demand.
We first check that there is enough liquidity in the aggregate to implement the secondbest policy. Let all individual firms be pooled together into a single firm, an
conglomerate.
Assuming
that the
conglomerate follows the second-best policy, where
individual firms continue if and only if p
<
p*, the
conglomerate can be sold
of reinvestments) for the value F(p*)poI. The conglomerate needs to raise
its
liquidity needs. Since F(p*)poI
-
economy-wide
D=
S,,
which
is
positive, the
at date
1
(gross
D (see (9)) to cover
conglomerate can raise the
necessary funds to implement the second-best policy.
It
remains to show that an intermediary can make
value of the private sector. There are
investment level
is I
=
A/(.9). If
A =
many
full
use of the potential market
equivalent ways in which this can be done.
9, then I
=
10, with outside investors investing
the firm 9. Thus, the outside investors' stake in the stock index is worth
1
=
The
and
1. But p*-po
-9,
implying that there will be realizations of p such that firms will need up to 9 shares of the
stock index in order to continue. That is nine times as many shares as each can purchase at
date 0.
16
simplest
At date
the intermediary be a conglomerate as above."
is to let
0,
it
issues shares
These shares are claims on the intermediary's financial position
to investors.
The intermediary
uses the proceeds from
share issue to buy up
its
all
at date 2.
14
the external claims on
firms. Firms' securities are priced so that the intermediary breaks even
on each firm issue
(ex ante). Similarity, the shares of the intermediary are so priced that investors break even.
Assuming
now
will
that the intermediary succeeds in
sell for
The
portfolio.
arrangement
the
amount
S,, since its
its
shares
its
investment
zero, guaranteeing that the
is
financially feasible.
The intermediary proceeds
all
market value equals the value of
intermediary's net "cash flow" at date
is
the credit line
implementing the second-best policy,
is
to grant each firm a credit line equal to p*I. Attached to
the covenant that a firm cannot issue
or just a portion of
its
credit line at date 1.
return to this point below).
There
new claims
is
at date 1.
no charge for using
However, the firm has no use
A
firm can use
credit
(we
will
for excess credit, since the
enterpreneur cannot consume funds and any returns from market assets that the firm might
purchase
at date
entrepreneur
P
^
1
will
go
to the intermediary (except for the portion
if the project
succeeds). Given the credit line, a firm can continue
to the
whenever
P*-
The only remaining
1
RJ, which goes
meet
to
its
issue is whether the intermediary can raise
(deterministic) credit obligations
D. But
this follows
argued above, that the private sector can in the aggregate raise
A >
enough funds
at date
immediately from the
S,
+ D > D
fact,
(assuming
I -
0).
We
Remark
1:
liquidity
because the value of financial claims held by a firm cannot be contingent on a firm's
argued in section 3.1 that the financial market
idiosyncratic liquidity shock. Consequently, firms with
low
fails to
provide adequate
liquidity shocks
end up with
excessive liquidity, that could be efficiently redistributed to firms with higher liquidity
shocks. Such a redistribution however does not occur spontaneously at date
liquidity-rich firms
have no incentives
to enter negative
NPV
1,
since the
arrangements with liquidity-
In our model, the number of intermediaries is indeterminate. We will describe the
implementation of the second-best solution as if there were a single intermediary.
13
14
As in Jacklin (1987), it is important to avoid claims that can be redeemed at date 1,
since such claims can lead to "bank runs".
17
poor ones. One may wonder what
that
it is
an intermediary can do that the financial market
cannot do. Intermediation docs not dominate financial markets on informational grounds.
Rather, the critical feature of the credit line arrangement that yields a productive
that
is
allows negative
it
NPV
investments at date
dispose of negative value claims in an
Remark
anonymous
Because the private sector
2:
securities. If issued,
government
is
securities
15
By
l.
optimum
contrast, claimholders can
financial market.
no
self-sufficient there is
role for
government
must yield the market rate of interest, here equal
and they have no impact on the productive sector.
to zero,
Remark 3: Many
alternative arrangements involving intermediation are equivalent to the
described above. For instance, the intermediary could be
made
to
resemble a bank by
one
letting
firms issue shares directly to investors and having the intermediary hold only firm debt
(claims senior to equity).
amount of
credit used,
arrangement could
The intermediary could
rather than just an up-front fixed fee.
call for
a repayment of
course, only if the project succeeds)
the implied price for credit
is less
p
,
An
than pi, the
there
no
is
is
amount of
if
such fees are
the firm uses pi
therefore
we
We
(<
p*)
illustrate,
a credit
2 (which can be met, of
of credit at date
below par, as the expected repayment equals
1.
Note
(pp<)/p*)I,
credit used. In fact, because firms are fully diluted
must be imposed
common,
that
which
when p >
how
initial
how
surplus
is
is
indeed underpriced ex post.
redistributed
among
external claim
claims are priced, but they have no effect on real outcomes and
can proceed without pinning
summarize
to cover the intermediary's expected loss. In
suggesting that use of credit
Variations like these only influence
holders and
(p/p*) (R-R b)I at date
To
credit contract that charges an actuarially fair price for all realizations of p.
additional up-front fee
reality,
also charge the firm according to the
down
these contractual details.
16
this section in:
Proposition 2. In the absence of aggregate uncertainty:
(i)
The productive optimum cannot always be achieved through an (anonymous) financial
15
To
offset the date-1 loss, the intermediary receives either an upfront
commitment
fee
or securities in the firm at date 0.
16
Monitoring and control right considerations could be introduced to reduce contractual
ambiguity, but the implications of such embellishments must await further research.
18
Ex post,
market.
(li)
liquidity
may be
misallocated.
The productive optimum can be implcmcmcd
(if 1 -
A >
0)
by relying on private
intermediation of credit. Intermediaries act as insurers against liquidity shocks, crosssubsidizing firms. Intermediaries need not observe individual liquidity shocks in order to
implement the optimum.
fiii)
There
offered at
no
par
liquidity role for
government
(yielding zero interest)
securities. If issued,
and do not
such securities must be
affect real allocations.
Endogenous Liquidity Supply with Pure Aggregate Uncertainty
4.
4.
is
The demand for government bonds.
1
In the previous section liquidity shocks
extreme, the case where there
is
were independent.
We now
shift to the other
only aggregate uncertainty. All firms experience the same
liquidity shock.
It is
clear that in this case the private sector cannot
be
self-sufficient.
With pure
aggregate uncertainty, every firm needs to raise pi at the same time. Since a firm
at
most pj
t0 outsiders at date
1,
aggregate value of the private sector whenever p
the problem, because at best
which
it
demand
the aggregate
<
p
<
is
worth
for liquidity will exceed the
p\ Intermediation cannot overcome
can realize the net ex post value of the productive sector,
in this event is zero.
This creates a demand for government supplied liquidity. The government can meet
the
demand thanks
taxation.
and
sells
to
its
assumed
ability to
commit
future
Suppose the government issues one-period bonds
them
at par.
We
facility equivalent to cash.
can be achieved by having investors invest
)I
in the
amount
(p*-p )I at date 0,
are then back to the environment analyzed in section 2, with
government bonds providing a storage
firms to spend (p*-p
consumer endowments via
(1
+p*)I
-
A
in
The productive optimum
each firm at date 0, requiring
of this amount on the purchase of bonds.
17
Since government bonds, issued at par, lead to the productive optimum,
tells
Lemma
1
us that the introduction of these bonds raises total output and expected aggregate
17
Alternatively, an intermediary can offer each firm a credit line (p"-p
)I,
backed by the
purchase of an equal amount of government bonds. Firms can raise the missing PqI by issuing
new
shares.
19
investment (the date-0 investment plus the expected value of date-1 reinvestments). Note,
however, that the
to cover date-1
initial level
of investment
more of their resources
decreases as firms save
I
Thus, issuing government bonds crowds out productive
liquidity needs.
investments at date 0, but increases (expected) reinvestments at date
We
record these results
1.
in:
Proposition 3. In the presence of aggregate uncertainty:
The private sector
ft)
is
not self-sufficient.
Assuming that the net social cost of taxation
fti)
is
zero, the
government can ensure the
productive optimum by issuing a sufficient amount of bonds at the market rate of interest
(here, zero) in
ftii)
which case there
is
no demand for intermediation.
The introduction of government bonds reduces date-0 investments and increases date-1
reinvestments (reduces liquidations). Expected output, aggregate investment
firms
all increase.
The government's objective and
4.2
By
restricting attention to
made two
section 4.1
taxation.
18
>
1)
violated, the
is still
that there is
in the
no deadweight
loss of
deadweight loss of taxation. Second, that the
profit subject to the
government may want
per unit of expected return.
premia, there
First,
market rate of interest,
gain in productive efficiency brought about by the bond issue
government maximizes the firms'
is
premia.
securities that yield the
implicit assumptions.
Otherwise, the
assumption
liquidity
government
must be traded off against the change
(q
and the value of
We
refer to
to
consumers breaking even.
issue securities at a price
If either
q above par
premium. For small
q-1 as the liquidity
a demand for government securities, since the private sector uses them
as complementary inputs into the production process.
As
is
well known, credit rationing models raise
a welfare analysis.
A
government
producers') would redistribute
creates
18
more
all
that
aims
at
endowments
than one unit of output.
On
some
maximizing
difficult conceptual issues for
total surplus
to entrepreneurs as
the other hand, a
one unit of net worth
government
Or, more generally, the marginal deadweight loss of taxation
(consumers' plus
is
that
the
only represents
same
at all dates,
so the date-0 deadweight loss due to the income received by issuing government securities
is
equal to the date-1 (or date-2) deadweight loss associated with the reimbursement of the
public debt.
20
I
,
consumers might confiscate some or
conceptual issue
we
is
all
of the entrepreneurs'
not specific to our model and
lies
initial
beyond the limited scope of
this
this paper,
on the government's objective
investigate the effects of alternative assumptions
will not
wealth A. Because
function.
Instead,
we
simply assume that the government arranges for firms to bear the net cost
of supplying liquidity, leaving consumers as well off as without government intervention
(see,
however, the up-coming remark on seignorage). The net tax effect incorporates the
benefit of distributing the proceeds
from the bond issue
and the deadweight loss from taxing consumers
that at the social
Suppose
optimum
redeem the bonds
the marginal deadweight loss of taxation
deadweight loss were higher
that the marginal
government could then issue
interest).
to
strictly gain;
>
bonds
par
at
(at
We
conclude
1,
say.
The
zero rate of
made
(at least
that, for the
optimal
19
l.
The demand for government bonds.
4.3
Let us for the
moment
rule out cross-shareholdings and intermediation,
through the analysis of section 2. 1 to see
premium
threshold
>
q-1
(We
investment.
p
0.
For
where use
is
cannot partially liquidate
that a firm
will later discuss the case of partial liquidation at the firm level.)
made of
I
the fact that the
securities is
maximum
For a
)I
dilution at date
1
(14)
is
p
1,
so that (p-p
)
needed to reach the threshold p.
firm's net utility
is
now
=
m(p,q)k(p,q)A
The government cannot gain by reimbursing
deadweight loss of taxation
its
becomes
>I-A + (j'pf(p)dp)l+(q-l)(p-p
U,(p,q)
19
and run
firms respond to the presence of a liquidity
the investors' participation constraint
,
government
The
how
moment, assume
the
F(p)p
in
than at date
furthermore the firms would be
weakly) better off by the increased supply of liquidity.
apparent
at date 1. It is
must be time increasing.
at date
additional one-period
at date
The taxpayers would
debt policy, q
(or reducing date-0 taxes)
at date
is
public debt at date 2, because the
higher at date 2 than at date
21
(15).
1
by the same reasoning.
where
m(p,q)
is
= F(p)p,-l-J
pf(p)dp-(q-l)(p-p
„
)
fi
the modified margin on per-unit-of-investment profit, and
=
k(p,q)
-,
(17)
pf(p)dp + (q-l)(p-Po)-F(p)P
1+
Jo
is
the modified equity multiplier.
The
firm chooses the threshold p*(q) to minimize the
expected unit cost of effective investment:
—^
l+fpf(p)dp+(q-l)(p-p
p
*
(q)
minimizes
)
(18)
F(p)
>p
over p
.
As a
generalization of condition (8)
20
we
get
Po<P*(q) + -^rr<Pr
f(p
We next ask whether this allocation
(19)
(q))
remains an equilibrium when firms are allowed
we
to issue
and trade claims
to issue
a single security (equity), the equilibrium described above unravels because of free-
riding.
Suppose
in a financial market. First
that all firms issue shares at date 0.
argue
would not want
to
firms are constrained
Suppose a contrario
the financial market does not affect the equilibrium. Shares
investors
that, if
that the
must then trade
buy them. But then an individual firm could
needs more cheaply by buying shares rather than government bonds.
To
opening of
at par, else
satisfy its liquidity
see this, note that
the representative firm in the equilibrium without a financial market has an ex post value
equal to (p*(q)-p)I
>
when
the liquidity shock p falls in the interval (p ,P*(q)]- This value
20
The firm's optimal cut-off, p*(q), need not be monotone in q. The firm may respond
an increase in q by reducing its date-0 investment and raising the date-1 cut-off. On the
other hand, if q is high enough, shutting down all demand for bonds, the firm's date-0
to
investment will be higher than
if
q were equal to
22
1
(see Proposition 3).
stems from the excess amount of bonds
other firms, an individual firm can
it
by holding enough shares
holds. Hence,
accommodate shocks
in the
arbitrarily close to p*(q) without
paying any liquidity premium. Thus, the equilibrium without cross-shareholdings must
unravel once firms are allowed to buy each others' shares.
The
intuition
why
the government charges
the equilibrium breaks
down
Liquidity
is clear:
a premium. Each firm therefore wants
purchase government bonds.
Of course,
all
is
a public good
to free ride
on
firms that
firms cannot follow the free-rider strategy, since
then no firm would buy government bonds and there would be no protection at
liquidity shocks
4.4
An
above p
analysis
if
all
against
.
of the private sector's optimal policy.
This section derives the private sector's optimal policy
when
a premium. The next section will analyze the implementation of
the government charges
this policy, in particular the
private sector's response to the possibility of free-riding. Suppose the private sector buys
(p
—p
)I
bonds (where
I is
funds efficiently at date
p,
some firms must
sector
(p
can
resort
shock
is.
All firms can withstand the liquidity shock if p
shut down. Instead of shutting
to partial
~PoV(p ~Po) of firms
to continue is
1.
the investment level of the representative firm) and allocates the
liquidation
to continue
enough,
it
the
(we can assume
drawn randomly). Whether
If p is high
at
this is
may be better to
down
all
industry
<
p, but if p
>
firms, however, the private
level,
that the identity
allowing a
fraction
of firms that are allowed
optimal depends on
how
high the liquidity
return the bonds to the investors rather than
use the funds for reinvestment.
To determine
the private sector's optimal policy, let zl be the face value of the bonds
that the private sector
buys and
let
X(p,z) be the fraction of firms allowed to continue
the aggregate shock is p. Recalling that entrepreneurs get p H
Rb =
p,
-
p
when
per unit of
investment in case of continuation, an optimal strategy can be found by solving the following
program:
23
max
X(/>,z)(p,-p )f(p)dp,
I
Jo
I,X(0
a>
(i)
s.t.
X(p,z)p f(p)dp-l[^X(p,z)pf(p)dp + (q-l)
lJi
(20)
)
<
(ii)
X(p,z)
<
[l,— X.
min
P-P*
I
J
Letting 5 be the Lagrangian multiplier for the budget constraint, the optimal choice of
mil
X(p
,z) =
'['-.
.
z
is
3X(p,z)
U*z
3z
brackets in the integrand
some
p
<
[( Pl
is
<
p,
if
p
>p
(21)
we have
<
+ 5(p -p)]f(p)dp - 5(q-l) = 0.
)
is
p
+z
due
to (21). Also,
by
(22)
(21), the term in
>
non-negative. Therefore, (22) implies that 9X(5,z)/3z
values of p, as 5 and (q-1)
p
-p
lower integration bound
that the
<p
is
governed by the first-order condition:
r'
Note
p
-Pol
>
The choice of
if
X
>
X(p,z)
0. In particular,
<
1,
z
<
p
-
p
,
for
+
so that whenever z
p
=
implying that the private sector uses the option of
partial liquidation for these p-values.
The reason
the
private sector resorts to partial liquidation should be clear. If the
private sector bought enough bonds to allow
choice of
X would be unconstrained
all
firms to continue whenever p
(X would equal
or
1).
The
better to reduce z. Partial liquidation allows the private sector to
of bonds. Only when bonds carry no opportunity cost ex post (q
buy
full
=
p, the
first-order cost
reduction in z would then be zero, while the first-order benefit would be q-1
be
<
>
0;
of a
would
it
economize on the use
1) will the
private sector
coverage against adverse liquidity shocks.
We
summarize the
Proposition
negative)
4.
Ifq
is strictly
>
characteristics of the optimal solution in
1, that is, if the net
deadweight loss of taxation (which must be non-
positive, the private sector's optimal solution is characterized
24
by two
p and
thresholds,
CO Po
<
<
P
P
such that:
p,
<
Pi-
(ii)
The private sector buys zl
(Hi)
All firms continue if p
p
<
<
=
solution
is
government bonds.
p; the fraction
p; no firms continue if p
This
>
(p-Po)I
>
more
(p—Po)/(p—Po)
<
1
offirms continues
if p
<
p.
efficient,
privately
and
socially,
when firms
than
act
independently.
The
last inequality in part (i)
follows because h represents the marginal value of firm
wealth and therefore must be greater than
1.
The
private sector's solution
is
better than the
solution that individual firms could obtain (as described in section 4.2), because partial
liquidation
socially
feasible at the industry level, but not at the firm level.
is
more
efficient,
The outcome
also
because consumers are as well off whether firms act alone or
collectively. In both cases all the social surplus goes to the entrepreneurs.
partial liquidation
is
been feasible
at the firm level, the analysis
21
Note
that
had
of section 4.3 would have
coincided with that of this section, with the convention that X(p,z) would have denoted the
fraction of the individual firm's investment that
is
not liquidated
when
the aggregate shock
is p.
Implementing the optimal policy:
4.5
We now
There are two
First,
liquidation
21
It is
is
A
rationale for multiple securities.
turn to the implementation of the optimal policy derived in section 4.4.
distinct issues for implementation.
the private sector's optimal policy involves partial liquidation.
infeasible at the firm level,
worth noting
it
must be performed
that the established social value
If partial
at the industry level. Financial
of the private optimum depends on
the government's objective function. If the government, instead of letting all the surplus
to the entrepreneurs,
surplus),
it
may
chose to maximize
its
net revenue from selling bonds (that
is,
go
consumer
well be that restrictions on private arrangements would lead to a higher
The private sector's optimal policy just described has two effects. On one hand
makes bonds more valuable to firms, increasing their demand; on the other hand, it allows
firms to bypass the government's mark-up, reducing the demand for bonds. This situation
is reminiscent of a government trying to maximize seignorage in a monetary model.
Seignorage may be higher if private liquidity creation by way of intermediation and crosssocial utility.
it
shareholdings
is restricted.
25
markets in general cannot implement the partial liquidation policy described
4
since the private sector as a
iii),
government bonds. There
intermediary
is
is
whole would need
to
buy
more than (p-p
strictly
Note
thus a need for intermediation.
in Proposition
that the role
)I
of the
here to implement the partial liquidation policy while economizing on
expensive government bonds; by contrast in the absence of aggregate liquidity shock, liquid
claims
commanded no premium and
properly
among heterogenous
firms.
intermediation no longer plays a role
We
the private sector's.
When
22
since the individual firm's
case the solution
for multiple securities
is
program coincides with
conclude that under a pure aggregate shock intermediation
is
the issuing
a clientele one. Free-riding
is
is infeasible.
Second, and more interestingly, whether intermediation
in either
to dispatch liquidity
partial liquidation is feasible at the firm level,
necessary only when partial liquidation at the firm level
an issue and
was
the role of intermediaries
is
used or not, free-riding
is
of multiple securities. The rationale
may
arise because firms that
buy
costly
Treasury securities provide socially valuable liquidity to other firms that invest in them. The
purchasers of Treasury securities however cannot internalize the value of this liquidity service
if
they also want to
must be sold
at
sell
who have no
shares to consumers,
liquidity needs.
par to consumers, which precludes charging a liquidity premium to corporate
purchasers of shares. Because the industry needs outside funding,
optimum
we
conclude that the
derived in section 4.4 cannot be achieved if firms issue a single security. In
contrast, the use of multiple securities allows the issuer to price discriminate
who
Indeed shares
value liquidity services differently
(this
point
is
among
investors
highly reminiscent of Gorton-Pennacchi
(1990)).
To
illustrate
the rationale for multiple securities without needing to introduce
intermediaries, let us allow partial liquidation at the firm level. Let us construct an industry
equilibrium that yields the same allocation as that obtained from program (20) as described
in Proposition 4. In this equilibrium, all firms invest I (the level
They
4
all
pledge not to finance liquidity shocks exceeding p
'type- 1 firms", purchase
other firms.
22
strictly
At date
Of course, when
(p-p )I Treasury
.
A
securities at price
given in Proposition 4).
fraction
q and
a of
the firms,
hold no shares in
they issue a) equity, sold at par, and b) short-term (maturing at
idiosyncratic and aggregate shocks coexist, intermediation again is
preferred by firms as scarce liquidity
is
26
wasted by financial markets.
1
-p
date 1) debt with face value (p
) I
with the covenants that a) they must fully
at price q',
dilute their equity before selling Treasury securities to finance liquidity needs
can
up
sell
shock
is
to (p-p )I
.
p, before servicing the short-term debt.
shock p belongs
The remaining
it
23
Covenant
worth
no liquidation
value of short-term
in
all
the short-term debt of type-1 firms. Let
any type of firm when
claims
debt
a(p-p)I/(l-a) >(p-p
Type-2 firms can continue
p
I),
in type-1 firms.
the
(23)
p< p.
Suppose
\p
l to
The aggregate
new
that
p
<p <
I
p.
is
when p
X2 of
E
Then
the
equal
to
selling these debt claims
withstand their liquidity shock, pi.
to operate a fraction
X 2 pI=X2 p
they can pledge
when
).
and thus type-2 firms can, by
)I,
other hand, type-2 firms are partially liquidated
is,
1
a be given by
by a representative type-2 firm
held
diluting their initial investors (to obtain
That
at date
1-a of the firms, the "type-2 firms", do not purchase
fraction
a(p-p) = (l-a)(p-p
is
(p-p)I
to the interval [p ,p].
Treasury securities, but buy
There
a) implies that equity in type-1
becomes valueless when the aggregate shock exceeds
that the short-term debt is
Covenant b) implies
liquidity
that they
Treasury securities to finance their liquidity need when the aggregate
firms carries no liquidity premium, as
p
and b)
and by
On
the
[p,p]. while type-1 firms are not.
their assets,
where
+ _^_(p-p)I.
1-or
investors and further use the return on short-term debt
(type-1 and type-2 firms) fraction
X of
assets that are not
liquidated is therefore
X
-
or+O-oOX, = a+(l-«)
|—
-
—
l_l-ap-p J
P-Po
P-Po
23
The debt
expositional
contract
is
contingent on the realization of the aggregate shock for
convenience only.
Alternatively,
type-1
firms
can
substitute
a class of
nondilutable long-term (maturing at date 2) senior claim for the short-term debt and dispense
with writing a covenant that is contingent on the aggregate shock.
27
and coincides with the fraction specified
demand
for Treasury securities
is
the
same
Note
in Proposition 4.
also that the aggregate
as in the intermediated case
from Proposition
4ii),
as (23) implies that
a(p-Po)
I
= (P -
Po)
L
Last, the price of short-term senior debt, q', is set so that firms are indifferent
We thus conclude that the optimal policy
a type-1 and a type-2 firm.
when
issuing of multiple corporate securities
When
liquidation
partial
the firm
at
is
between being
implemented by the
partial liquidation at the firm level is feasible.
level
is
infeasible,
the optimal policy must be
implemented through intermediaries, and these intermediaries must similarly issue multiple
securities in order to price discriminate
4 6
.
State-contingent bonds.
While
partial liquidation reduces the
the private sector given that the
socially
better
and avoid free-riding.
most
deadweight loss of taxation and
government issues non-contingent bonds,
efficient solution. In this section
we show how
outcome by issuing state-contingent bonds.
optimum when general
We
the
is efficient
it is
for
not the
government can achieve a
begin by characterizing the social
state-contingent transfers between consumers and producers are
allowed.
A
by
social plan is defined
the initial level of investment
(i)
I
per firm,
and
(ii)
a
state-contingent continuation policy X(p) e [0,1] that determines the fraction of firms that
continue
when
The
the aggregate liquidity shock is p.
social
program
exception that the transfers
the social
program
is
identical to the
program studied
are not constrained by an
initial
in section 4.4, with the
purchase of bonds. Formally,
solves:
max
X(p)(p,-p )f(p)dp,
I
f
<D
s.t.
(i)
Iqf X(p)(p -p)f(p)dp
Jo
(ii)
<
X(p) <1.
28
>
I-A,
(24)
Letting 5 be the Lagiangian multiplier (again, 5
of entrepreneurial wealth), the solution to
where p*
is
>
program
this
ri1
if
P
[0
if
p
1,
because
it is
the
shadow value
is
^ P#
> p\
,
defined by
^-TT-
<
In contrast to the solution in section 4.4, the social
firms continue, or no firm continues.
program does not have
only as needed.
satisfies
<
p
The
24
social
the holder an
specifies either that all
for the difference
is that
the social
hoard liquidity (by buying bonds); rather, transfers are provided
Furthermore, since
<
p*
to
The explanation
optimum
25 >
5,
q
>
1,
we
see that the socially optimal cut-off p*
p,.
optimum
amount x(p)
X*(p) can
be implemented using state-contingent bonds, which pay
as a function of the aggregate shock p. In particular, let the
bonds
have the following date-1 payoff:
if
P
if
p
x(p) = 1°'
lX*(p)(p-p
-PoJ),
<P
or p
>
p*,
<p<p*.
Let the date-0 price of these bonds be set so that
r\'(p)q(p-P()f(p)dp.
Note
that priced
this
way, bond revenues exactly compensate the consumers for the
deadweight loss of taxation when the policy X*(p)
It is
social
is
followed.
straightforward to check that with these payoffs and price, firms can replicate the
optimum,
if
they so desire, by buying
I
bonds, where
I is
the socially optimal level
of investment. This amount of bonds enables a firm to continue exactly when the social plan
calls for continuation. Also, the firm's
budget constraint coincides with the social budget
constraint so that the firm can attract the required funds
24
if
at date 0.
would become relevant only if investors or entrepreneurs were
the government could not use state-contingent transfers.
Partial liquidation
averse or
from investors
29
risk
Can
the firm
do
better
by deviating from the
a better plan for the firm. In this plan,
let I
socially optimal plan?
be the date-0 investment
amount of state-contingent bonds the firm purchases, and
To be
feasible, the plan
ex ante constraint
I
must
satisfy both
be the
X(p) be the continuation policy.
an ex ante and an ex post budget constraint. The
-Iz
f"X(p)(p -p)f(p)dp
rX'(p)(q-l)(p-p )f(p)dp
>
I
-A.
(26)
Jo
post constraint
is
<
X(p)
<
min{l,z X*(p)}.
(27)
Substituting the ex post constraint into the ex ante constraint,
be feasible for a
level, let zl
is
is
Jo
The ex
let
Suppose there
social planner to replicate the firm's plan.
it is
Given
immediate
that
it
would
that the social objective
function coincides with the firm's, the firm's plan cannot be better than the social optimum.
Hence, the firm prefers the socially optimal plan.
Note
that the
partial liquidation if
government need not be concerned by the
bond
possibility
of free-riding and
yields are state contingent, because firms holding
have excess liquidity when p
>
p
,
bonds do not
and therefore other firms cannot free-ride by holding
their shares.
Remark on seignorage. Suppose
issuing
government
that the
government aims
at
maximizing net revenue from
of taxation. Let us compute an upper bound
securities, ignoring costs
on the government's net revenue. Let U( = m(p )k(p )A) denote the "autarky
entrepreneur with assets A, that
is
is
the utility she gets
a lower bound on entrepreneurial
max
utility.
when holding no
utility"
R
of an
reserves. Clearly,
U
Consider the following program:
R
I.MO
,
s.t.
(i)
lf° X(p)(p -p )f(p)dp
1
>
U,
Jo
(28)
(ii)
-R-I fX(p)(p -p)f(p)dp >I-A,
Jo
JO
(iii)
<
X(p) <1.
30
Constraint
(ii)
must break even. Substituting constraint
reflects the fact that investors
(which obviously holds with equality) into the objective function,
is
the dual of
program
That
(24).
optimum has
the social
is,
we
the
(ii)
see that program (28)
same
characterization
whether the government maximizes entrepreneurial welfare subject to a deadweight loss of
taxation or maximizes seignorage.
An
4.7
interpretation
The economic
amount
fixed
of state-contingent bonds.
rationale for using state-contingent
most
will provide excess liquidity in
will cash in the
bonds
that they
bonds
Bonds
is clear.
states at date 1.
that
Firms (or intermediaries)
do not need for reinvestment, forcing the government
consumers and implement a wealth transfer
that is unnecessary
pay a
and socially costly
to tax
(in the
deadweight-loss-of-taxation interpretation). While partial liquidation reduces the tax burden,
it still
leaves slack and also distorts investment and liquidation decisions.
attacks the root cause of the
problem
exactly as needed and eliminates
Of
is
solution that
a state-contingent bond, which dispenses liquidity
wasteful transfers of wealth.
course, this solution works ideally only in our idealized model. In reality, state-
contingent bonds are not used.
there
all
is
The
The most obvious reason why such bonds
no aggregate, measurable
be provided more
liquidity.
state that
unequivocally identifies times
There are other shocks than
measured variables, and these shocks may
realizations of the aggregate measures.
call
are not used
is that
when firms should
liquidity shocks that
move
publicly
for very different transfers for similar
Macroeconomic policy
is
not a mechanical exercise,
because new, unforeseen contingencies keep appearing. Rather than limiting government
policy to bonds that are contingent on a few, foreseeable, and verifiable variables, a
discretionary policy
may be more
desirable (at least if one ignores the political
government policy). Thus, we want
to
view the use of state-contingent bonds as a metaphor
for an active
government policy rather than as a serious policy instrument
The value of
state-contingent bonds
shows
that,
in its
own
right.
besides creating liquidity, the government
has a potential role in actively managing liquidity. Note that this
contracts could be indexed on
economy of
is
true even if private
government actions or on the aggregate shock.
In our model, optimal liquidity
management entails increasing the value ofgovernment
31
bonds
in times
when
at date 1, this is
It
liquidity
25
needs are high. Since
we
have assumed that bonds mature
accompanied by a corresponding, immediate increase (decrease)
may seem odd
in taxes.
that taxes are being raised in adverse liquidity states (recessions), as
consumers might simultaneously be experiencing negative demand shocks. But
Our
underscores the importance of multiple shocks, as discussed above.
specific result is
clearly sensitive to the assumption that there is a single liquidity shock with
experiencing no shocks at
all.
this just
consumers
an adverse demand shock that requires
If consumers experience
resources to be shifted to consumption, then taxation and the value of bonds should be
reduced rather than increased, notwithstanding negative liquidity shocks. This does not negate
the general logic that state-contingent
bonds are of value,
improve the allocation of resources through wealth
that
is,
an active policy can
transfers.
We cannot associate state-contingent bonds with monetary or fiscal policies,
model does not distinguish between nominal and
drawn between the
real effects
monetary
Note
where
is
policies.
fiscal
will either
first that
we
be accompanied by a
it
A
related:
imposes an inflation
further parallel
same
is that, in
when
and
liquidity is tight, fiscal policy
that this is also true in reality, since loose
consumers
tight budget, forcing
therefore adjust to immediately, with the
linear taxes).
fiscal
only have a single instrument, corresponding to a case
Some might argue
they do in our model), or
But certain analogies can be
of state-contingent bonds and the alleged effects of
and monetary policies are inversely
loose and conversely.
real claims.
since our
tax,
to
money
pay up immediately
(as
which consumers might anticipate and
effect as tightening the budget (barring non-
the model, liquidity
is tight
when
the value of
bonds are low.
Note
1,
also that, if
one imagined a second generation of entrepreneurs entering
at date
facing liquidity shocks at date 2, and producing at date 3, then tighter liquidity (lower
bond
prices) at date
1
would decrease
their date
1
investments, and increase their date-2
reinvestments (by Proposition 3), as the cost of carrying liquidity into date 2 would
relatively
less
expensive.
In
other words,
reinvestments (of date-0 entrepreneurs) and
tighter
initial
moving aggregate investment unambigously down
25
Note
that
we
liquidity
at
date
1
become
reduces
both
investments (of date-1 entrepreneurs),
at date 1.
Again,
this
conforms with
are not rationalizing continuous government intervention, but rather
intervention in severe circumstances.
32
standard views on policy effects. Furthermore, in a model with
study bonds with longer maturities.
more
periods,
With long-term bonds, wealth
one could also
transfers
between
consumers and producers would be accomplished by early redemptions (purchases) of these
bonds (adding
liquidity) or
We do
liquidity).
not suggest that these parallels can be used to draw strong conclusions about
real policies as
Nevertheless,
by issuing new bonds (tightening
our model says nothing specifically about monetary or
we
find
it
fiscal interventions.
reassuring that one can associate alleged features of real policies
with the abstract state-contingent outcomes in the model. Also, the model gives
some
guidance for government interventions intended to accomplish wealth transfers between the
producers and consumers in response to unforeseen, aggregate real shocks.
As an
illustration,
consider the recent collapse of the Soviet Union. In several
made
accommodate
European countries no attempt was
initially
wants
stubborn stance on exchange rates as an active policy,
to interpret the central banks'
money was made very
tight).
The
result
to
was a massive reduction
as interest rates soared and asset values plunged.
this
shock
(or, if
in entrepreneurial
one
wealth
Our analysis supports those who argued
that
the governments should have responded with policy measures that transferred wealth back
to entrepreneurs,
by bringing
down. According
interest rates
to received
wisdom (and
validated by the subsequent events), a reduction in interest rates required a devaluation of the
currencies or abandoning fixed exchange rates. In the logic of our model, and
reality, too,
believe in
such an exchange rate policy should be seen as part of an insurance policy in
which the government plays a
5.
we
central role.
Relationship to the literature
Several papers have relevance for our work, although they do not address in a unified
way
the main questions
we
are interested in, namely corporate liquidity needs, the partial
self-sufficiency
of the private sector,
management by
the government. Let us take
and
the
foundations
up these themes
33
for
liquidity
in order.
supply and
Corporate liquidity needs
By now,
there is a very large literature on credit rationing,
making the point
that
investment will be constrained by the firm's net worth (for a survey, see for instance,
Most of
Bernanke-Gertler-Gilchrist (1994)).
demand
this
literature
does not deal with liquidity
as such, but rather with the structure of optimal financial contracts, including the
decision to liquidate assets in case of financial hardship. Obviously, decisions to liquidate are
closely related to decisions to
However, the
make
result that firms face
a liquidity covenant in the optimal financial contract
On
of our knowledge new.
to the best
further investments, as illustrated in Hart (1995).
the other hand, the result that investors
firms with extra cash (or a credit line) ex ante,
also Hart (1995)),
by using a
who show
that
is
reminiscent of Hart and
which
is
Moore
(1989) (see
been exploited
in recent
not investigated).
as productive inputs as well as
fact that real assets serve a dual purpose,
collateral for debt, has
must provide
a given class of financial contracts can be improved upon
similar arrangement (the optimality of
The
is
papers by Kiyotaki and
Moore
(1993) and
Shleifer and Vishny (1992). Both models are broadly concerned with the general equilibrium
implications of wealth constrained financing.
features with our model.
may
try to
It
The
latter
model, in particular, shares some
has two firms, each facing an idiosyncratic
demand shock. Firms
piggy-back on each others' investment decisions to generate future income in hard
times, not directly through security purchases, as
we have
it,
but rather through the ability
to sell assets to the other firm ex post. If the firms' liquidity shocks are not perfectly
correlated (so that they are not in default simultaneously), then
a
liquidity
shock but not the other,
no other informed purchaser of
albeit imperfect,
Self-sufficiency
it
can
its assets.
way of enhancing
sell its assets for
In effect, the
when one firm experiences
a higher value than
if
there
were
model describes a market mediated,
firm liquidity.
and intermediation
The study of the demand
Diamond and Dybvig
(1983).
26
for
consumer
liquidity
was originated by Bryant (1980) and
Diamond and Dybvig demonstrate
that intermediaries can
provide limited insurance by subsidizing consumers with high liquidity needs. Jacklin (1987),
however shows
that the associated cross-subsidy is infeasible in the
presence of financial
markets, as those consumers with low liquidity needs can pretend to have high liquidity
26
See also Ramakrishnan and Thakor (1984) and Williamson (1986).
34
needs, pocket the subsidy and reinvest
the
it
in financial markets.
27
Thus, financial markets
Diamond-Dybvig framework both reduce welfare and make intermediation
misuse credit
The main reason
lines.
Our
results
for the difference in conclusions
how
on
the
government should manage
liquidity
Diamond and Dybvig.
contingent on the macroeconomic shock (the
made
28
macroeconomic shock.
our firms cannot
own
use other than
In our model,
obtained in section 4,
In their model,
while bank contracts with depositors cannot be
depositors)
that
by B.
are also quite different from those in
policy can be
is
Entrepreneurs cannot divert corporate funds for their
in the limited fashion captured
By
useless.
improvements despite the existence of
contrast, in our model, intermediaries bring strict
financial markets.
in
government
number of withdrawing
made
contingent on this
government policies do not use more aggregate
information than private contracts.
Boyd and
constructs a
Prescott (1986), in a related effort to understand the role of intermediation,
model
which financial markets cannot duplicate the services provided by
in
intermediaries. Their
model
the efficent organization
is
not about the provision of liquidity as such, but rather about
of monitoring. Financial markets are inefficient relative to
intermediation, because financial contracts are assumed to be contingent on whether projects
are evaluated and also on the outcome of the evaluation. Intermediaries, on the other hand,
can offer contracts before an evaluation
made, avoiding the problem of premature
is
information revelation. This seems to be an ad hoc limitation in favor of intermediation.
Bhattacharya and Gale (1987) look at a variation of the Diamond-Dybvig model that
is
closer in structure to ours. In their
model there are several banks (corresponding
which experience idiosyncratic, "sectoral"
firms),
aggregate.
The paper
to
our
liquidity shocks that cancel out in the
characterizes the socially optimal
mechanism
for sharing risks across
banks, noting that this mechanism cannot be implemented through an interbank lending
market.
Whether a market
in
bank shares or some other
institution could
27
Diamond (1995) shows that intermediaries have a role
consumers have imperfect access to financial markets.
28
as
The subsequent literature on bank runs
we do in
shock on the the short term
at date 1
interest rate
to play as long as
some
most part assumes independent shocks,
macroeconomic uncertainty through a date-1
between date 1 and date 2, and shows that depositors
for the
section 3. Hellwig (1994) introduces
who withdraw
implement the
must bear some of the aggregate
35
risk.
social
optimum
is left
The
open.
authors suggest that a central bank might be the right
institution for carrying out interbank risk sharing.
Government supplied
The
first
of investment
liquidity
paper to argue that government debt can improve the intertemporal allocation
by Diamond (1965). In an overlapping generations model he showed
is
government debt can crowd out private investment, which
may be excessive.
at par.
in
in the
In his model, government bonds provide
Another difference
is that in
Diamond
no
that
absence of government debt
liquidity services
and are sold
public debt crowds out private investment while
our paper public debt boosts private investment by providing aggregate liquidity. Models
of crossgenerational insurance (Fisher (1983), Pagano (1988) and Gale (1990)), and of
asynchronized investment opportunities (Woodford (1990)) are expressely concerned with the
role of
government debt as a medium of transfer across periods. Woodford's paper
is
most
closely related to ours. In one version of his model, he assumes that individuals periodically
receive investment opportunities, which they cannot take advantage of without storing wealth
from one period
in
a stationary
to the next.
state, the
government debt
possibility
that
is
Government debt
is
a vehicle for storing wealth.
He shows
optimal level of government debt should be positive.
thus the
same
The
that
role of
However, Woodford does not consider the
as in our paper.
a private market in claims on output could accompUsh the same as
government debt.
It
appears that
it
could, because there are no agency costs that would limit
the sales of such private claims.
In a related vein, Williamson (1992) demonstrates the benefits of fiat
model
in
which adverse selection prevents entrepreneurs from pledging
income. 29 Fiat money plays the role of a store of value (which
government
securities in
our model, and
may have
of overlapping generations). Williamson's focus
government
securities (in the
form of
Indeed, Williamson concludes that
that there exists
29
On
fiat
an equilibrium with
the counterpart of
from ours; he argues
is
one
in favor
of
money) and against the trading of private claims.
money has no value
fiat
a
their entire future
value because Williamson's model
is distinct
in
money
if private
that Pareto
claims are traded, and
dominates the purely private
the adverse selection problem and related issues, see also Banerjee-Maskin (1991)
and the references
see,
fiat
is
money
Williamson (1992). For other models on money and government debt,
for instance, Bewley (1980) and Levine (1991).
in
36
Our conclusions
equilibrium as long as agents are prevented from trading private claims.
are
rather different.
Finally,
literature
should be evident that our work has
it
on incomplete markets. Markets
in
some
points of contact with the
our model are incomplete because individuals
cannot borrow against future income and because the value of a firm's claimholdings cannot
be contingent on
liquidity shock.
its
The
latter
intermediaries even though the intermediaries
while the former problem
that can
be used
to
is
partly resolved
problem
do not observe individual
by the government, which
to
incomplete market
6.
creates a
literature,
which
source of incompleteness
is
new
asset
fact that the
securities is related to a general
states that generically
an incomplete market and make everyone better off (Elul (1995)).
literature, the
liquidity shocks,
improve the allocation of investment across periods. The
government can improve on private outcomes by issuing new
result in the
effectively dealt with through
is
one can add an
Of
asset
course, unlike this
spelled out in our model.
Concluding remarks.
Rather than summarize our
may
raise
results,
and indicate directions
in
we wish
to address
some
questions that our paper
which the analysis could be extended. 30
First,
the
questions.
What do we mean by
literature. In
liquidity? Liquidity has
models with adverse
information about an asset.
been given various interpretations
selection, liquidity is related to the degree of
Assets about which there
is
in the
asymmetric
a great deal of asymmetric
information are less liquid than assets which everyone knows equally well. Firms can address
this illiquidity
problem
different informational
in various
demands on buyers. This
Pennacchi (1990), where debt
therefore a firm
30
ways. For instance, firms can issue claims that place
may be
is
shown
to
is illustrated in
be informationally
less
the
paper by Gorton and
demanding than equity and
able to raise funds at a lower cost of capital by issuing both.
We are grateful to Peter Diamond,
Peter Howitt and Andrei Shleifer for raising
31
many
of these questions.
31
which the
government can influence the liquidity of bank liabilities by guaranteeing some of the bank
debt through deposit insurance. In his model, liquidity coincides with reserves. His paper
does not address why the government would like to supply liquidity, nor why it would want
to influence liquidity by changing reserve requirements. But his paper, unlike ours, gives one
In a related vein, Stein (1995) presents an adverse selection
37
model
in
In our
model of moral hazard,
assets are not illiquid because people
assessments about their value. Rather, claims on firms
fall
by entrepreneurs, and outsider claims, held by
claims, held
completely illiquid in the sense that
into
categories: insider
investors. Insider claims are
entrepreneur were to
if the
two
have different
sell
these claims in the
market, the value of them (as well as of the external claims) would drop. External claims,
on the other hand, are
have assumed
that the value
therefore, insiders
and can be sold
entirely liquid
at
no discount
at all times.
Because
we
of insider claims exceeds the value of the firm's investment (and
must chip
in
some of
their initial
endowment
to raise funds), there is a
potential shortage of liquid assets.
Why do we need an agency model? This
paragraphs. Without an agency problem,
all
question
assets
is
largely answered
would be
fully liquid.
by the previous
Firms could
sell
claims up to the value of their investments at any point in time and could therefore undertake
all socially
productive investments.
It is
the inability to transfer all the social surplus to
external investors that constrains the firm's financing opportunities.
firm
is
credit constrained both ex ante
As we have shown,
and ex post. Therefore, ex post financing
is
the
not
forthcoming without ex ante commitments. Such commitments require assets that allow the
firm to hoard liquidity (and pay for
it
in advance).
This
is
what creates a demand for
liquid
assets.
What
if there
were other real private assets
in the
model? The assumption
are no other private assets than the investment projects themselves
would be easy
to introduce assets like real estate,
from one period
to the next. If there
need for government
securities,
minimum amount of government
p
)I), real
assets
not eliminate
this
32
it.
but
which could be used
were enough of those
if the
securities
was a
assets, they
that there
simplification. It
to transfer wealth
would obviate the
aggregate value of the assets
fell
below the
needed to achieve a productive optimum
((/?* -
would merely reduce the demand for government bonds, but they would
Similarity, if the liquidation value of firms
were positive rather than zero,
would reduce the demand for government bonds.
interpretation of the transmission
mechanism of monetary
32
policy.
Real estate would in general carry a liquidity premium for the same reason
government bonds do in our model. We derive liquidity premia in a simplified setting in
Holmstrom-Tirole (1996). It should also be noted that real estate prices are likely to move
procyclically, making it a worse instrument than government provided insurance.
38
investment-capital
the
75
intervention
is
ratio
realistic?
The model
implies
government
that
needed only when the aggregate demand for liquidity exceeds the value of the
private sector. This seems grossly at odds with the empirical fact that the market value of
the corporate sector
is
large relative to investment. Part of the explanation has to
interpretation of investment.
all
As we
do with the
already pointed out, in our model reinvestments include
the cash outlays (wages and working capital, for instance) needed to continue the firm,
not just investments in physical capital. This figure
is
surely an order of magnitude larger
than measured aggregate investment.
Nevertheless,
as p
<
driven
p
,
that
down
is,
it
remains true that the private sector can continue on
its
own
as long
as long as the value of the initial claimholders' investment has not been
to zero.
Only when
their investment has lost all its value
step in. This is an unrealistic feature of the model. It is driven
feature that external claims are fully liquid.
To
the extent that
need the government
by the equally
new
unrealistic
issues of equity and debt
are costly, because of difficulties in valuing these claims correctly, the private sector will run
into reinvestment
problems before the
Similarly, the holdings of
initial
claimholders have lost
monitors Qzrge shareholder, bank, venture
33
be diluted without generating further incentive problems. Thus,
where the private
all
we
of their investment.
capitalist,...)
cannot
think of p as the point
sector hits a serious debt capacity constraint.
Let us finally suggest some extensions of our model. Currently, the link between the
producer and the consumer sector
is
very simple and uninteresting.
desirable to study a general equilibrium extension that could highlight
It
would be highly
how consumer and
producer shocks would affect the overall economy and feed back on each sector. This might
give a more realistic picture of the need for transferring wealth in one direction or the other
and therefore on
also
want
to
how
the government should
manage
liquidity. In this context,
one would
be more careful about the deadweight losses caused by taxation and the role
played by individual time preferences and risk aversion.
Another important extension would introduce more periods into the model, perhaps
by overlapping firms as
earlier indicated. In such
an extension, the government could issue
long-term as well as short-term bonds, which would raise questions about managing the
33
It is
straightforward to add monitors into our model, along the lines of Holmstrdm-
Tirole (1994).
39
maturity structure of government debt.
While intermediaries play a role
in
our model,
it is
merely conduits for forming contracts that are unavailable
anonymous claims on corporate income are
a rather passive one. They are
in
a financial market in which
traded. In reality, intermediaries play a
active role, monitoring investments and liquidity needs. This role
a multi-period analysis, since one would have to worry about
liquidity. In the present
more
would probably emerge
how
in
firms use their excess
model, excess liquidity was never misused by firms, since they had
no use for the extra funds.
40
MIT LIBRARIES
3 9080
428 2534
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