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Working Paper 9602
AGENCY COSTS, NET WORTH, AND BUSINESS FLUCTUATIONS:
A COMPUTABLE GENERAL EQUILIBRIUM ANALYSIS
by Charles T. Carlstrom and Timothy S. Fuerst
Charles T. Carlstrom is an economist at the Federal Reserve
Bank of Cleveland, and Timothy S. Fuerst is an associate
professor of economics at Bowling Green State University
and a consultant at the Federal Reserve Bank of Cleveland.
Working papers of the Federal Reserve Bank of Cleveland
are preliminary materials circulated to stimulate discussion
and critical comment. The views stated herein are those of
the authors and not necessarily those of the Federal Reserve
Bank of Cleveland or of the Board of Governors of the
Federal Reserve System.
Working papers are now available electronically through the
Cleveland Fed's home page on the World Wide Web:
http://www .clev .frb.org.
May 1996
i
Abstract
This paper develops a computable general equilibrium model in which endogenous
agency costs can potentially alter business cycle dynamics. The model resembles the
influential theoretical work of Bemanke and Gertler ( 1989), from whom we borrow our
title. The model is calibrated to match key features of U.S. aggregate activity. Two
sources of shocks are considered: shocks to the distribution of wealth and shocks to
aggregate productivity. We reach two conclusions. First, "debt-deflations" can have a
significant and persistent effect on real activity. In the case of large monitoring costs, a
relatively small wealth redistribution (corresponding to a one-time annual surprise
inflation of 1.0 percent) leads to a 0.5 percent increase in investment spending. Second,
the agency-cost model naturally delivers a hump-shaped investment response to a
productivity shock. This is because households delay their investment decisions until
agency costs are at their lowest, a point in time several periods after the initial shock.
I
1. Introduction
At least since Irving Fisher's (1933) "debt-deflation" explanation of the Great
Depression, many economists have viewed financial factors, such as borrower net worth, as
important elements of business cycle fluctuations.
like this.
To engage in investment opportunities, entrepreneurs must partially rely on
external finance.
involved.
The familiar story goes something
This borrowing is typically limited because of the agency costs
An aggregate shock that transfers wealth from entrepreneurs to lenders will
lower aggregate investment because this wealth redistribution will increase the need for
external finance and thus lead to greater agency costs.
These shocks can then be
propagated forward because the lower level of investment today tends to lead to lower
levels of capital, output, and net worth tomorrow.
A seminal contribution to this line of research was made by Bemanke and Gertler
(1989) (hereafter denoted as BG).
BG developed a general equilibrium model in which
agency costs arise endogenously.
This is a nontrivial exercise because these agency
problems arise only in a setting in which the Modigliani-Miller theorem does not hold.
We borrow our title from BG because, in this paper, we build on their work by
constructing a calibrated,
computable general equilibrium model
quantitatively the effects that BG analyze qualitatively.
that can capture
Our study thus also builds on
Fuerst (1995), which provided a first attempt at quantitatively modeling the BG
environment.
We view this paper as a preliminary step in a larger research program that
will quantitatively investigate the role of agency costs in general equilibrium business
cycle models.
The BG model is a natural place to begin this line of research because it
is both well known and quite influential within the profession.
An important innovation in the current paper is to model the entrepreneurs as long
1
I
lived. 1 BG ignore this issue by analyzing a Diamond-type (1965) overlapping generations
model in which entrepreneurs make investment decisions in only one period.
Although
Fuerst (1995) assumes that households are infinitely lived, he follows BG by assuming
that entrepreneurs live for only a single period.
is
potentially
difficult
because
the
Allowing for long-lived entrepreneurs
contracting
problem
between
lenders
and
entrepreneurs then takes on the characteristics of a repeated game with moral hazard. 2
We ignore much of this difficulty by assuming that there is enough interperiod anonymity
so that financial contracts can depend only on an entrepreneur's level of net worth, and
not on his entire past history of debt repayment (although history of course plays a role
in that it affects the current level of net worth).
Even with this simplification, we still have the problem of heterogeneity.
point
in
time,
there
will
be
a
great
deal
of
net-worth
heterogeneity
At any
across
entrepreneurs, and keeping track of the net-worth distribution and of how it affects the
aggregate economy is in general quite difficult.
However, by assuming a linear
investment and linear monitoring technology, we are able to exploit an aggregation
result:
Only the first moment of the distribution of entrepreneurial net worth has any
effect on the aggregate economy. Keeping track of the mean is quite easy, and amounts to
simply adding an additional state variable to the dynamic program.
The paper reaches two main conclusions.
First, debt-deflations can have a
significant and persistent effect on real activity.
In the case of large monitoring
costs, a relatively small wealth redistribution (corresponding to a one-time annual 1
percent surprise inflation) leads to a 0.5 percent increase in investment spending.
iThe importance of long-lived entrepreneurs was also suggested by Gertler (1995) in
his comments on Fuerst (1995).
2 See
Gertler (1992) for a theoretical analysis of an agency-cost model in which
entrepreneurs write two-period contracts.
2
I
Second, the agency-cost model naturally delivers a hump-shaped investment response to a
productivity shock.
This is because households delay their investment decisions until
agency costs are at their lowest--a point in time several periods after the initial
shock.
This second conclusion is related to the first.
The hump-shaped investment
response occurs because the productivity shock increases the return to internal funds,
which in turn redistributes wealth from households to entrepreneurs.
The investment
response thus mirrors the hump-shaped behavior of entrepreneurial net worth.
A related attempt to model long-lived entrepreneurs is provided by Kiyotaki and
Moore (1995).
There are two distinct differences between the current paper and theirs.
First, the underlying contracting environment in Kiyotaki and Moore is quite different.
They build on the work of Hart and Moore (1994), which analyzes the contracting problem
in an environment with ex post renegotiation and the inalienability of human capital.
One
implication of the
Kiyotaki-Moore
contract
is
that borrowing
is
so tightly
constrained by the level of net worth that default never occurs in equilibrium.
In
contrast, we follow BG and adopt the costly state verification model of Townsend (1979).
Here, lending exceeds net worth, so that default is an equilibrium phenomenon.
A second
difference between this paper and Kiyotaki and Moore is that we attempt to quantify the
effects of agency costs in an otherwise standard real business cycle (RBC) model.
Section 2 of the paper develops the optimal financial contract in a partial
equilibrium setting and demonstrates the aggregation result that is so important in the
sequel.
Section 3 lays out the complete general equilibrium environment.
discusses calibration, and sections 5 and 6 present our numerical results.
in section 7.
3
l
Section 4
We conclude
I
2. The Financial Contract
In this
setting.
section,
This
investment goods.
we consider the financial
financial
contract in a partial equilibrium
contract generates an upwardly
sloped supply curve
for
In the next section, we will embed this supply curve into an otherwise
standard RBC model.
We are able to separate consideration of the contract from the rest
of the general equilibrium model because the contract is only one period in length--it is
negotiated at the beginning of a period and resolved by the end of that same period.
General equilibrium issues affect the contract through the level of entrepreneurial net
worth, n
> 0, and through the aggregate price of capital, q > 0. For the purposes of
this section, we will take n and q parametrically.
The contract consists of two parties:
an entrepreneur with net worth n
lender with resources that he may wish to lend to the entrepreneur.
> 0, and a
Both are assumed to
have risk-neutral preferences over end-of-period consumption. 3
The entrepreneur has access to a stochastic technology that contemporaneously
transforms i consumption goods into roi units of capital.
The random variable ro is i.i.d.
across time and across entrepreneurs, with distribution <1>, density cj>, a non-negative
support, and a mean of unity.
Agency issues are introduced into the environment by
assuming that ro is privately observed by the entrepreneur.
Others can privately observe
ro only at a monitoring cost of J.d capital units, i.e., the attempt to monitor the project
results in the destruction of 11i units of capital.
This informational asymmetry creates
a moral hazard problem because, absent monitoring, the entrepreneur may wish to misreport
3Jn the next section, risk-averse households will be the source of loanable funds
to the entrepreneurs.
However, in terms of the financial contract, they will be
effectively risk neutral because
1) there will be no aggregate uncertainty over the
duration of the contract, and 2) they will carry out their lending through a capital
mutual fund (CMF). By funding a large number of entrepreneurs, the CMF will take
advantage of the law of large numbers to eliminate idiosyncratic entrepreneurial
uncertainty and guarantee a sure return to the households.
4
I
the true value of ro.
The optimal contract will be structured in such a way that the
entrepreneur will always truthfully report the ro realization.
Note that the capital
production and monitoring technologies each exhibit constant returns to scale.
This
assumed linearity is the source of the aggregation result below.
To make the asymmetric information problem relevant, assume that net worth is
sufficiently small so that entrepreneurs would like to receive some external financing
from firms.
Gale and Hellwig (1985) and Williamson (1987a) have demonstrated that in
environments of this type, the optimal contract between lenders and entrepreneurs is
risky debt. 4
The contract will be characterized by an interest rate rk.
An entrepreneur
who borrows (i-n) consumption goods agrees to repay (1 +rk)(i-n) capital goods to the
lender.
The entrepreneur will default if the realization of ro is "low," i.e., if ro
(1 +rk)(i-n)/i
= ro.
<
The lender will monitor the project outcome only if the entrepreneur
defaults, in which case it will confiscate all the returns from the project.
Note that
the contract is completely defined by the pair (i,ro), and that it is convenient to
consider the optimization problem over these two arguments.
Once the optimal (i,ro) have
been found, one can then back out the implied lending rate of interest, (1 +rk) = roi/(in).
Under the contract (with q denoting the end-of-period price of capital), expected
entrepreneurial consumption is given by
00
J
q[ roict>(dro) - (1-ct>)(l +rk)(i-n)].
-
(I)
Using the definition of ro, this can be simplified to
4In addition, we must assume that a commitment device exists, and that stochastic
monitoring is impossible. See, for example, Townsend (1979) and Prescott and Townsend
( 1984). In contrast, BG allow for the possibility of stochastic monitoring so that the
optimal contract cannot be interpreted as risky debt. Recent work by Boyd and Smith
(1994) suggests that (in a quantitative sense) there is little loss of generality in
restricting the contract to pure strategies.
5
I
00
qif(ro) = qi{J(J)<t>(dro) - [1-<D(ro)]ro},
-
(1)
where f(ro) is interpreted as the fraction of the expected net capital output received by
the entrepreneur.
Similarly, the expected consumption of the lender on such a contract
is given by
-
(1)
q[Jroi<l>(dro)- <1>1-1i + (1-<l>)(l+rk)(i-n)],
0
or
-
(1)
qig(ro)
=qi{J ro<l>(dro) - <l>(ro)!l
+ [1-<l>(ro)]ro},
0
where g(ro) is interpreted as the fraction of the expected net capital output received by
the lender.
Note that
f(ro) + g(ro) = 1 - <I>(ro)!l.
so that on average, <l>(ro)!l of the produced capital is destroyed by monitoring, and the
remainder is split between the entrepreneur [f(ro)] and lender [g(ro)].
The optimal contract is given by the (i,ro) pair that maximizes the entrepreneur's
expected return subject to the lender being indifferent between loaning the funds and
retaining them. 5 More precisely, the optimal contract is given by the solution to
max qif(ro), subject to qig(ro) 2: (i-n).
An additional constraint guarantees the participation of the entrepreneurs,
namely,
5W e are assuming that the economic rents generated by the contract flow to the
entrepreneur--an assumption that is quite plausible given that entry into lending is more
likely than entry into entrepreneurial activity.
Also, since these loans are
intraperiod, the opportunity cost of the funds is simply (i-n).
6
I
qif(ro)
~
n, which will always be satisfied below.
It is also straightforward to show
that the entrepreneur will always want to invest all of his net worth in his own project.
The first-order conditions to the problem include
q{l-<I>(ro)~
i
+
=
cj)(ro)~[f(ro)tr(ro)]}
=
1
(1)
{11[1-qg(ro)]}n.
(2)
Equation (1) defines an implicit function ro(q), with ro increasing in q.
Substituting
this function into (2), we have the implicit function i(q,n), which represents the amount
of consumption goods placed into the capital technology.
then given by ls(q,n)
=
The expected capital output is
i{q,n){l-~<l>[ro(q)]}, which can be interpreted as the investment
(or new-capital) supply function.
Since ( 1) pins down ro uniquely, the linearity of (2)
implies that this supply function aggregates:
aggregate investment (summing Is across
all entrepreneurs) depends only on the economywide price of capital q and aggregate net
worth (summing n across all entrepreneurs).
It is this aggregation result that we
exploit below.
Before proceeding to the general equilibrium model, it is instructive to review
some of the comparative statics of the contracting problem.
show that l~(q,n) > 0 and l~(q,n) > 0 (see the appendix).
capital supply curve (I~
The positive slope to the
> 0) is isomorphic to models that assume some increasing cost to
adjusting the capital stock.
problem.
It is straightforward to
Here, this positive slope is a natural result of the agency
For a given level of net worth, increases in capital production are possible
only with a greater reliance on external funds, and these external funds are subject to
greater agency costs.
As for net worth, it can be viewed as a supply-curve shifter
because increases in net worth lower agency costs and thus boost the level of capital
production for a given price of capital (I~ > 0).
7
i
I
l
I
Another variable that will be useful below is the expected return to internal
funds.
This is given by qf(ro)i/n
=
qf(ro)/[1-qg(ro)].
(Intuitively, net worth of size n
is leveraged into a project of size i, entrepreneurs keep share f(ro) of the capital
produced, and capital is priced at q consumption goods.)
economic
rents
on the contract flow
Because we assume that all
to the entrepreneur,
this
return is strictly
increasing in q.
3. The General Equilibrium Model
The goal of this section is to embed the contracting problem of section 2 into an
otherwise standard RBC model.
The standard model assumes that new capital is created at
the end of the period using consumption goods,
with a nonstochastic one-to-one
transformation rate (implying an investment supply curve that is perfectly elastic at
unity).
This newly produced capital then comes "on line" in the next period.
Below, we
will utilize this same timing, but replace the one-to-one transformation assumption with
the contracting problem outlined in section 2.
In particular, if a household wishes to
purchase capital, it must fund entrepreneurial projects, and these projects are subject
to agency problems.
Figure 1 summarizes the sequence of events in a given period.
We
will now tum to the specifics of the model.
The model economy consists of a continuum of agents with unit mass. The agents are
of two types:
households (fraction 1-TJ) and entrepreneurs (fraction TJ).
As discussed in
the previous section, the entrepreneurs are involved in producing the investment good.
Entrepreneurs receive their external financing from households via intermediaries that we
will refer to as capital mutual funds (CMFs).
The economy is also populated with
numerous firms producing the single consumption good. We follow BG and assume that these
8
I
consumption-producing firms are not subject to any agency problems, so that we need not
be specific about how they are financed.
Because their activities are somewhat standard,
we will first discuss the behavior of households and firms.
We will then tum to the
entrepreneurs and the CMFs.
Households are infinitely lived, with preferences given by
00
Eo
L ptU(ct,l-Lt},
t=O
where E denotes the expectation operator conditional on time-0 information, P e (0,1) is
0
the personal discount factor, ct is time-t consumption, Lt is time-t labor, and the
leisure endowment is normalized to unity.
In the course of any given period, households
sell their labor input to consumption-producing firms at a wage rate of wt' rent their
previously accumulated capital holdings to these firms at rental rate rt, purchase
consumption from these firms at a price of unity (i.e., consumption is the numeraire},
and purchase new capital goods at a price of qt.
Capital goods are purchased in a
competitive capital market that opens at the end of the period--a market that potentially
involves households purchasing capital from other households, from entrepreneurs, or from
CMFs.
In equilibrium, however, the capital purchases are entirely from the CMFs.
Household choices are summarized in the labor supply curve
and in the dynamic capital-demand relationship
where 3 is the rate of depreciation on capital.
Each household also owns an equal equity
share in each of the firms.
The firms in this economy produce the consumption good utilizing a standard
9
I
constant-returns-to-scale production function.
In the aggregate,
this
technology
is
given by
where Yt denotes aggregate output of the consumption good, et denotes the stochastic
productivity parameter, Kt denotes the aggregate capital stock, Ht denotes the aggregate
supply of household labor, and H~ denotes the aggregate supply of entrepreneurial labor.
Competition in the factor market implies that wage and rental rates are equal to their
respective marginal products:
=
rt
8ll (t), wt
the wage rate for entrepreneurial labor.
=
el 2(t), and xt
=
8tF 3(t), where xt is
The assumption of entrepreneurial labor income
is necessary because it ensures that each entrepreneur always has a nonzero level of net
worth.
This is important because the financial contracting problem is not well defined
for zero levels of net worth.
Below, we will assume that this source of net worth is
quite small but nonzero.
Entrepreneurs maximize the intertemporal objective
where c~ denotes time-t consumption and T is the stochastic death date.
The expectation
is taken over the aggregate productivity shocks (8t)' the idiosyncratic technology shocks
(rot)'
and the idiosyncratic lifetime of the entrepreneur (T).
all uncorrelated with one another.
These three shocks are
There is a law of large numbers at work here, so that
only the aggregate productivity shock has any aggregate consequences.
The moral hazard problem implies that the return to entrepreneurial savings is
greater than the return to household savings.
10
In the steady state, the latter is given
I
by 11~.
Since the entrepreneurs have linear preferences, this implies that they will
postpone consumption and accumulate capital throughout their lifetime, with the goal of a
consumption binge on the eve of their death. 6
This uncertain lifetime and desire to
postpone consumption is discussed more fully below.
Let zt denote the capital holdings of a typical entrepreneur at the beginning of
period t.
To raise internal funds, the entrepreneur rents this capital and inelastically
supplies his unit endowment of labor to firms.
After these transactions are finished,
the net worth of the entrepreneur is given by
The entrepreneur uses this net worth as the basis for the loan agreement that he will
enter into with the lender.
aspects
of the
financial
As noted in the introduction, we sidestep any repeated game
contract by assuming
that there
is enough intertemporal
anonymity among entrepreneurs so that the contract can be based on entrepreneurial net
worth, but not on past contractual outcomes.
Since the entrepreneurs use the borrowed funds to produce capital, the lenders in
this economy are ultimately the households that wish to purchase capital.
As in Diamond
(1984) and Williamson (1986), there is a clear role for CMFs to intermediate these
purchases between households and entrepreneurs.
By providing resources to an infinite
number of entrepreneurs, the CMF can ensure a certain return
to
the household, i.e., an
expenditure of qt consumption goods guarantees one capital good.
The law of large
numbers, and the assumption that there is no aggregate uncertainty over the duration of
the contract, implies that the CMF will be, as assumed in section 2, risk neutral.
CMF is thus a type of cooperative by which capital can be efficiently purchased.
The
A
6 More precisely, this desire to postpone consumption holds for the nonstochastic
steady state and for small perturbations around it.
11
I
household that turns over qt consumption goods to the CMF receives in return one capital
good.
The CMF takes the funds provided to it by households and uses them to provide
loans to entrepreneurs and to purchase capital from the entrepreneurs who die at the end
of the period.
This leads us back to entrepreneurial lifetime.
At the end of each period,
fraction y of entrepreneurs "die," where death entails selling all of their accumulated
capital to CMFs, consuming the proceeds, and exiting the .economy.
At the beginning of
the next period, these expired entrepreneurs are replaced by new entrepreneurs (endowed
with zero capital), so that the population of entrepreneurs remains fixed.
If we let Zt
denote the aggregate entrepreneurial capital stock, then we have
This equation is quite intuitive.
entrepreneurial net worth.
The first term in braces
is time-t aggregate
The second term in braces is the investment-to-net-worth
ratio and thus represents the method by which a given level of net worth is leveraged up
into a larger project size.
Finally, the entrepreneur keeps share f(rot) of the project
outcome, and only fraction (1-y) of these entrepreneurs live on into the next period.
The previous equation also makes clear why we need to assume that entrepreneurs
die.
In the steady state, a unit of entrepreneurial capital is transformed into q/p
units of net worth.
The financial contract then transforms this net worth back into
(q/p)[f/(1-qg)] > 1 units of capital.' Zt thus roughly evolves according to
'This discussion also highlights the entrepreneur's desire to postpone consumption
until his death. lntertemporally, one unit of consumption becomes (1/q)(q/p) = liP units
of consumption goods in the next period. The entrepreneur then transforms this net worth
into (1/p)q[f/(1-qg)] consumption goods at the end of the same period. Since this total
return is greater than (1/p), the entrepreneur will always postpone his consumption.
That is, the entrepreneur postpones his consumption because the internal return is
greater than the opportunity cost of unity.
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zt+ 1 = (1-y)[f/(1-qg)J(qtp)zt > (1-y)Zr
Absent the death rate y, entrepreneurs would accumulate capital until they are totally
self-financed (i
=
n) and agency costs disappear.
Thus, the death rate y ensures that
even though individual entrepreneurs would always like to accumulate more capital, in the
aggregate they never actually achieve net worth levels that allow aggregate equilibrium
investment to be entirely internally financed.
This last statement makes clear that some
assumption analogous to our death assumption is needed in agency models with long-lived
entrepreneurs.
Agency costs imply that the return to internal funds is greater than the
return to external funds,
so that absent some ad hoc assumption on behavior,
entrepreneurs will quickly accumulate a large share of the capital stock. 8
To close the model, we need only state the market-clearing conditions.
four markets in this economy:
There are
two labor markets, a consumption-goods market, and a
capital-goods market. The respective clearing conditions are given by
H = (1-11)L
t
t
e
Ht
= ..,
where the consumption-goods relationship sums household consumption, entrepreneurial
consumption, and aggregate investment.
A recursive competitive equilibrium is defined by
decision rules for Kt+ 1, Zt+ 1, Ht, qt, nt, it, rot' and ct' where these decision rules are
BKiyotaki and Moore's (1995) assumption of nontradable output ("bruised fruit")
provides entrepreneurs with the incentive to accumulate capital, and their strict
borrowing constraint implies that some of the capital stock will always be held by nonentrepreneurs in equilibrium.
13
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stationary functions of (Kt,Zt,8t) and satisfy the following Euler equations:
UL (t)/Uc(t)
=
(3)
8tF2(Kt'Ht'TJ)
qtUc(t) = PEtUc(t+ 1)[qt+ 1(1-S) +8t+ 1F 1(Kt+ 1,Ht+ 1'TJ)]
Kt + 1
=
(1-S)Kt + TJit[l - <l>(rot)f.l]
0-TJ)ct + TJ'YqtV<ffit) + 11it
qt
= v {1-<I>(rot)J.L
=
yt.
+ ~<rot)f.l[f(rot)tf(rot)]}
(5)
(6)
(7)
{11[1-qtg(rot)]}nt
(8)
8tF 3(Kt,Ht'TJ) + (Zt/T))[qt(l-S) + 8tF 1(Kt,Ht'T))]
(9)
it
nt
=
=
(4)
zt + 1
In the appendix,
=
(10)
(1-y)f(rot)llir
we demonstrate that if we hold net worth constant,
then
equilibrium conditions (3)-(8) are isomorphic to a standard RBC model with costs of
adjusting the capital stock. 9
It is in this sense that the agency- cost model can be seen
as a particular way of endogenizing adjustment costs.
One unique characteristic of these
adjustment costs is that they are affected by the level of net worth--Increases in net
worth lower agency costs and thus make it easier to expand the capital stock.
The
remaining two Euler equations (9)-(10) track the dynamic behavior of this net worth
9There are a few inconsequential differences between this model with net worth held
constant and an adjustment-cost model (such as entrepreneurial labor and entrepreneurial
capital). With J.1 = 0, (7) implies that q = 1, so that the model further collapses to the
standard RBC model with no adjustment costs.
14
I
variable.
4. Calibration
The model is parameterized at the nonstochastic steady state to roughly match
empirical counterparts.
Household preferences are given by U(c,l-L)
is set equal to 2.807, so that L
real rate of interest.
=
The value of
.3.
T)
We set
= ln(c) +
P=
v(l-L), where the constant v
.99, thus implying a 4 percent annual
is simply a normalization.
The consumption production technology is assumed to be Cobb-Douglas with a capital
share of .36, a household labor share of .6399, and an entrepreneurial labor share of
.0001.
Recall that this last share needs to be positive to ensure that each entrepreneur
always has at least some net worth.
=
We set it arbitrarily small so that the model with J.L
0 essentially collapses to the standard RBC model.
set to 8
=
The capital depreciation rate is
.02.
As for the monitoring technology, there is a great deal of controversy within the
empirical literature on this number.
direct costs of bankruptcy.
One perspective is that it should entail only the
For example, Warner (1977) examines the railroad industry
and comes up with a bankruptcy cost estimate of about 4 percent.
However, in our view,
this parameter should also include indirect costs of financial distress, such as lost
sales and lost profits, because these costs can be viewed as deadweight losses from
keeping capital idle for some period of time.
One study that includes indirect costs
estimates the sum of direct and indirect bankruptcy costs at about 20 percent of total
firm assets (Altman [1984]).
In our model, bankruptcy can be viewed as the entrepreneur being closed and his
15
I
assets being liquidated.
This suggests that another measure of bankruptcy costs could be
obtained by comparing the value of the firm as a going concern with the liquidation value
of the firm (absent any other direct or indirect costs of bankruptcy).
Using data from
Chapter 11 proceedings, Alderson and Betker (1995) estimate the internal and external
value of the firm (where the former is the firm's value as a going concern, and the
latter
is
the
value
if its
assets were
liquidated).
Using
these estimates,
they
calculate that liquidation costs are equal to approximately 36 percent of firm assets.
Because of our uncertainty about which measure of agency costs is more appropriate,
we provide some sensitivity analysis by presenting results for
J..l.
=
J..l.
=
.2 and
J..l.
=
.3. We use
.3 instead of Alderson and Betker's .36 because the authors admit that, since the
figure was calculated by investment bankers hired by the firm in Chapter 11, it is
probably an overestimate.
As for the distribution <D, we assume that it is lognormal with a mean of unity and a
standard deviation of cr.
An important characteristic of this distribution is that the
bankruptcy probability, <D, is convex in the loan repayment rate, ro.
In contrast, Fuerst
(1995) assumes that <D is uniform, implying that <D is linear in ro.
Our assumption of
convexity is important:
Since both the entrepreneur and CMF wish to avoid costly
bankruptcy' this implies that the greater is the convexity of <D, the less will ro vary in
response to shocks.
We are thus left with two parameters: cr andy. We choose these to uniquely match
two measures of default risk.
The first is the model's bankruptcy rate, <D(rot).
The
second is the model's risk premium, which we set to match the risk premium in the data.
Since a loan of one consumption good implies a risky return of 1 +r~ capital goods, or
qt(l +r~) consumption goods, the model's risk premium is given by [qt(l +r~)-1].
Fisher (1994) reports a quarterly bankruptcy rate of .974 percent (using the Dun &
16
I
Bradstreet data set for 1984-1990), and an average annual risk premium of 157 basis
points (measured as the average spread between the commercial bank lending rate and the
commercial paper rate from 1967-1988).
the last two identifying restrictions.
.053.
J..l.,
Matching these two empirical measures provides
For example, for
J..1.
= .2, we set cr = .211 and y =
These imply an internal financing percentage of n/i = 39.0 percent.
For a higher
we need to decrease cr to match the risk premium, and to increase y to match the
default rate. Hence, for
J..l.
= .3, we set cr = .088 andy= .122. These imply n/i = 17.2
percent.
5. Simulation
We are now ready to tum to a numerical analysis of the model.
familiar.
The methods are
The equilibrium conditions (3)-(10) are linearized about the steady state, and
linear decision rules are then computed using the method of undetermined coefficients.
Figures 2 through 4 report the results of two experiments for the two values of
bankruptcy costs (J..I. = .2 and
J..l.
= .3).
For both sets of experiments, we compute the
impulse responses for the model with agency costs (J..I. > 0) and for a model without agency
costs (J..I. = 0).
The latter is essentially the standard RBC model. 10 The steady states of
the two models differ, since the capital stock is slightly higher in the RBC model than
in the agency-cost model.
For this reason, we report the behavior of all variables
relative to their steady-state values.
First,
tothe presence of entrepreneurs does alter the RBC model slightly.
entrepreneurs receive a small wage and capital income. Second, shocks to entrepreneurial
capital and hence to household wealth can potentially affect RBC dynamics. However,
entrepreneurial capital and the entrepreneurial labor share are so small that the
difference between our model with J..1. = 0 and the RBC model of say, King, Plosser, and
Rebelo (1988), is almost imperceptible.
17
•
I
5a. A Wealth Shock
The first experiment we consider is a one-time shock to the distribution of wealth
in the two economies.
This shock will be a one-time transfer of capital from households
(lenders) to entrepreneurs (borrowers). This experiment is useful for considering the
effects of various shocks to the economy that might redistribute wealth from households
to
For example,
entrepreneurs.
in Irving
Fisher's debt-deflation story,
increases in the price level shift wealth from lenders to borrowers.
be the standard productivity shock in RBC models.
effect of such a productivity shock.)
surprise
Another shock might
(The next section will consider the
Since productivity shocks will also (indirectly)
cause a wealth redistribution, it is instructive to examine a pure wealth shock in order
to help understand the second, more complicated experiment.
Figure 2 presents the economy's response to a one-time redistribution of capital
from
households
to
entrepreneurs.
The
redistribution
entrepreneurial net worth increases by .01 in period five.
is
such
that
aggregate
In both cases, this amounts
to a redistribution of approximately .1 percent of steady-state capital. 11
This trivial
reduction in household capital is actually a relatively large increase in entrepreneurial
net worth.
For the
~
=
.2 case, net worth increases by 14 percent, while in the
~
=
.3
case, it increases by 29 percent.
In the frictionless RBC model, the source of investment financing is irrelevant, so
that the decline in the need for external finance has no effect on the aggregate economy.
As for direct wealth effects, they are so small as to be imperceptible.
Hence, we do not
report the RBC model.
Matters are much different in the economy with agency costs.
Here, increases in
liThe wealth redistribution is equal to .0986 percent of capital for the ~ =
case, and to .0989 percent for the ~ = .3 case.
18
.2
I
entrepreneurial net worth lower the need for external financing and thus reduce the
agency costs of investment.
This increase in net worth shifts the investment supply
curve to the right (as discussed in section 2), thus boosting investment and lowering the
equilibrium price
of capital.
This
increased
investment entails
lower household
consumption, which in tum motivates households to increase their labor input, which
raises output.
For the J.l = .3 (J.l = .2) case, investment increases by 12.1 percent (6.3
percent), consumption declines by 1.14 percent (.60 percent), labor increases by 3.2
percent (1.7 percent), and output increases by 1.75 percent (.9 percent).
=
when agency costs are relatively large (J.l
Notice that
.3), the percentage changes in these
macroeconomic variables are nearly twice that of the lower agency-cost case (J.l
=
After
state
the
initial
shock,
the
economy
slowly
returns
to
the
steady
.2). 12
as
entrepreneurial deaths and bankruptcies return entrepreneurial capital to its steadystate value.
One prediction of the model that is potentially counterfactual is the decline in
aggregate consumption following a wealth shock.
Although the figures refer to household
consumption and not aggregate consumption (household plus entrepreneurial consumption),
aggregate
consumption
behaves
similarly.
This
consumption is procyclical, it is only 1.5 percent (for J.1
is
=
because
while
entrepreneurial
.3) of aggregate consumption.
This is not a monetary economy, and we present no theory for why loan contracts
12The conclusion that the effects of a wealth shock are nearly twice as large in the
J.l = .3 case is sensitive to the nature of the shocks being considered. If we considered
a shock such that net worth increased by 10 percent in both economies, the implications
would be almost identical in either economy. The reason, of course, is that steady-state
net worth is slightly more than twice as large in the case with low monitoring costs.
The decision to model the shock as an absolute (versus percentage) change in net worth
was arbitrary. However, we chose this convention because we believe that most potential
shocks to the economy would come closer to redistributing an absolute amount of net worth
(and hence a given fraction of total capital) versus a given percentage change in net
worth.
19
I
would not be nominally indexed.
However, it is instructive to translate how surprise
inflation (price) shocks translate into wealth shocks, and hence output shocks, in a
nonindexed economy.
The typical loan size is (i-n), so that if loans were nominal and
nonindexed, a one-time surprise inflation of 1 percent annually (.25 percent quarterly)
would correspond to an increase in aggregate net worth of (.0025)ll(i-n)[q(l-8) +r].
the fl
=
.2 case, net worth increases by .0003, while for the fl
=
For
.3 case, it increases by
Hence, for the case of large monitoring costs, a one-time surprise annual
.0004.
inflation of 1 percent will lead to an increase in investment of .5 percent and an
increase in output of .07 percent.
The dynamics after such a shock would be identical
(though scaled down) to those shown in figure 2. Thus, although this is a one-time shock
to prices, output remains above trend for several quarters as entrepreneurial capital
takes time to return to its steady state.
5b. A Productivity Shock
The second experiment we consider is a shock to aggregate productivity.
To be
precise, the technology process is assumed to follow
where vt is a serially uncorrelated shock, p is the autocorrelation coefficient, and the
nonstochastic steady state of 8 is unity.
methodology, we set p
=
.95. The shock is v
Following the typical RBC calibration
=
.01. Although this is a one-time shock,
because technology is autocorrelated, productivity will stay above trend for several
quarters.
The results for the low- and high-agency-cost cases are presented in figures 3 and
4, respectively.
Each figure contains the dynamics of three different models.
20
The first
I
model sets agency costs to zero and is thus the standard RBC model.
The second model
holds net worth in the relevant agency-cost model constant and is thus isomorphic to a
standard cost-of-adjustment model (see the appendix). The third model is an economy with
agency costs.
The RBC dynamics are familiar.
There is a spike in investment, hours, and output
as productivity increases, then each series slowly returns to normal as productivity
starts declining back to its steady state.
As Cogley and Nason (1993, 1995) demonstrate,
the dynamics of investment, hours, and output are all inherited from the autocorrelation
structure of the technology shock.
Capital adds little propagation to these variables in
and of itself.
The cost-of-adjustment model resembles the RBC model except that the initial
impulse for investment, hours, and output is muted.
Initial investment increases by much
less as the rise in the price of capital serves to choke off investment demand.
muted response of investment amplifies the initial increase in consumption.
This
The increase
in consumption shifts back the labor supply curve, thus muting the responses of both
hours and output.
After the initial impulse, investment, hours, and output all start
returning to their steady state.
The dynamics closely resemble those of the RBC model,
with a little added persistence.
In the agency-cost model, the dynamics in the early periods are quite different
because of the behavior of net worth.
On impact, net worth increases slightly as the
technology shock boosts entrepreneurs' wage and rental income.
capital
is
initially fixed,
limiting
net worth's rise.
However, entrepreneurial
Subsequently,
the
share of
entrepreneurial capital picks up rapidly as the increased demand for capital pushes up
the price of capital, thus sharply driving up the return to internal funds [qf/(1-qg)] _13
t3Recall from section 2 that this return is increasing in the price of capital.
21
I
Mirroring the price of capital, this return stays high for several quarters after the
shock, leading to a hump-shaped path for entrepreneurial capital and thus net worth.
For
J.l = .3 (J.l = .2), entrepreneurial net worth peaks after six (ten) quarters at a value of
4.5 percent (3.5 percent) above steady state.
To see the importance that net worth plays in the dynamics of the agency-cost
model, compare the impulse response functions for the agency-cost model and the
adjustment-cost model.
For the case of J.l
=
.3, three quarters after the initial
productivity increase, investment is 4. 7 percent above steady state with variable net
worth, but only 3.4 percent above steady state when net worth is held constant.
Similarly, output is 1.64 percent above normal with variable net worth, but only 1.45
percent above normal for constant net worth.
The important difference between the agency-cost model and either the adjustmentcost or the standard RBC model is the hump-shaped response function for investment. The
hump shape in investment leads to a "reverse hump" in consumption after its initial
increase.
The decline in consumption (after its initial increase) raises household labor
supply, which, when coupled with the increase in labor demand (due to the technology
shock), results in a hump-shaped response for hours worked.
For the model with large
monitoring costs, this hump is pronounced enough to lead to a hump shape in output as
well.
To
better understand the
model's
investment behavior,
figure
5 presents a
supply/demand analysis of the market for investment goods (or new capital).l 4
Initially,
t4The demand curve for household capital is given by taking a linear approximation
of equation (4), where future consumption is set to its steady-state value and current
consumption is given by subtracting investment demand from household income. The supply
curve is given by taking a linear approximation of
s
111 (q,n) - [Zt + 1 - (1-3)Zt],
where the second term is deducted because it represents the entrepreneurs' net capital
acquisitions (which are not handled through the CMF).
22
I
(t
=
0), the economy is in the steady state.
the investment demand curve.
to normal as time progresses.
coefficient, p. 15
At t
=
1, the technology shock shifts out
Subsequently, investment demand starts moving slowly back
This movement is largely driven by the autocorrelation
The productivity shock increases the return to internal funds, thereby
causing entrepreneurial capital and hence net worth to rise.
By boosting entrepreneurial
net worth, the productivity shock shifts the investment supply function to the right.
This continues for several periods as net worth continues to grow.
It is this dynamic
behavior that generates the hump in the investment response and that can lead to a
similar hump in hours and output.
This does not occur in either the standard RBC model
(where the supply curve is completely elastic at unity) or a cost-of-adjustment model
(where the supply curve remains stationary). 16
The model's hump-shaped impulse response is of particular interest given the recent
work of Cogley and Nason (1995). Their study documents that 1) a hump-shaped response
of output to a transient shock is consistent with U.S. time series, and 2) standard RBC
models are unable to deliver their hump-shaped behavior (a notable exception is the
labor-hoarding model of Burnside, Eichenbaum, and Rebelo [1993]).
In the agency-cost
model, this hump shape is a natural outcome of the dynamic behavior of net worth in
I 5In equilibrium, the investment demand curve actually remains nearly stationary for
several quarters following the initial shock, as the decline in tomorrow's consumption
increases investment demand next quarter.
It shifts back in figure 5 because future
consumption is set to its steady state.
16In
the adjustment-cost model, the supply curve remains stationary when adjustment
costs are assumed to be a function of investment only. If instead these costs depend on
the investment-capital ratio, then the supply curve also shifts out as capital begins to
grow. This, however, does not lead to a hump-shaped investment response, since households
internalize the effect and increase their initial investment in anticipation.
With
agency costs, investment supply shifts out as net worth grows, but since net worth is
exogenous from the household's standpoint, this shift is not internalized.
23
I
response to a technology shock.
6. Sensitivity Analysis
To better understand the model,
it is important to conduct some sensitivity
analysis.
The above discussion suggests a convenient way of characterizing the model's
outcome.
The power of agency costs in this model can be conveniently captured by
analyzing the investment supply function.
In particular, in table 1, we conduct
sensitivity analysis on 1) the size of the supply curve shift (given the price of
capital) in response to a shock to the entrepreneur's net worth, and 2) the magnitude of
the net worth change in response to a technology shock.
To be consistent with our impulse response functions, we report the semi-elasticity
of investment supply tomorrow with respect to a change in net worth, and the semielasticity of net worth tomorrow with respect to a change in technology today.
In
addition, we report the total effect, that is, the elasticity of tomorrow's investment
supply with respect to a shock to today' s technology.
The first two rows are the two calibrated experiments with low and high agency
costs.
These elasticities show what our previous impulse response functions indicated.
A given change in net worth has a much larger effect on investment supply for large
agency costs (a semi-elasticity of 24.8) versus small agency costs (a semi-elasticity of
8.1). 17
The other important ingredient needed to understand the technology-shock case is
how much net worth increases with respect to a percentage change in technology.
actually
slightly
higher
with
small
agency
costs,
indicating
that
the
This is
important
17The response of investment with large agency costs is three times bigger than with
small agency costs. In equilibrium, figure 5 illustrated that the effect was just under
twice as big. The difference is that table 1 takes the price of capital as a given, and
in equilibrium, the price of capital rises more with large agency costs to help choke off
the increase in investment.
24
I
difference between the two simulations is the effect of net worth on investment supply.
The third row illustrates the importance that the size of monitoring costs has on
the model, everything else held constant.
That is, we report the results for J..l = .2
given the distribution obtained when calibrating for J..l = .3.
alone has little effect.
Investment supply's response to a change in net worth- falls
slightly, from 24.8 to 23.5.
Similarly, the response of net worth to technology is
slightly smaller (.069 versus .061).
The total change in investment supply in response
to a technology shock declines from 1. 71 to 1.44.
the calibrated J..l
=
Lowering monitoring costs
This is in sharp contrast to
.2 case, where the comparable elasticity is . 77. 18
Notice that the only parameter which is different between the two J..l =
.2
experiments is that the noncalibrated low-monitoring-cost experiment has a smaller
variance.
Thus, the large differences between the two calibrated economies is not the
difference in monitoring costs, per se, but the increased standard deviation of ro that is
necessary to match the economy's risk premium when monitoring costs are small. The risk
premium in the calibrated economy · falls from 157 basis points to 108 basis points for the
low-monitoring-cost, noncalibrated economy.
Therefore, this analysis also illustrates
the significant role that the risk premium plays in our calibration exercise.
Row 4 of the table shows the importance that the estimated bankruptcy rate of .974
percent has on our calibration by demonstrating the effect of calibrating to a higher
bankruptcy rate of 1.5 percent.
Although monitoring costs are assumed to be relatively
!Sif monitoring costs were zero, investment would be perfectly elastic at unity so
that changes in net worth would have no effect on investment supply. This elasticity
increases, everything else held constant, as monitoring costs decline.
Therefore, the
difference between the calibrated J..l = .3 experiment and the noncalibrated J..l = .2
experiment will be a little larger than indicated by the semi-elasticity of investment
with respect to net worth. Similarly, when calibrating for J..l = .2, the increased variance
of ro causes the price elasticity to decline, so that the effect between the two
calibrated agency-cost experiments is a littlt: closer than indicated.
25
I
small (J.L
=
.2), the dynamic effects of agency costs are larger now than when agency costs
were high (J.L
=
.3) but the bankruptcy rate was .974 percent.
A one percent change in
productivity will have a 1. 9 percent change in investment supply next period.
This is in
contrast to the 1. 7 percent change that occurs when we calibrate with high monitoring
costs. 19
This apparent effect is muted somewhat by the increased price elasticity of
investment supply when bankruptcy probabilities are high.
Perusing
table
1 indicates
that a statistic which appears to be useful for
predicting the dynamic effects of agency costs is the internal financing ratio, defined
as net worth divided by investment.
The larger the share of investment that is financed
internally, the smaller is the impact of agency costs on the economy.
makes intuitive sense:
agency costs,
This, of course,
A firm that is entirely internally financed would suffer no
since no moral hazard problems would arise.
This relationship is
especially tight given the linearity of investment with respect to net worth.
From equation (2), the internal financing percentage in the model is simply [1qg( ffi)].
Therefore, the higher the fraction of net capital output that goes to the lender
[g(w)], the lower is the fraction of investment that is financed internally and the
bigger is the impact that agency costs will have on the dynamics of the model.
From the
definition of f( ffi), the fraction of net capital output that goes to the entrepreneur,
given both the distribution of w and the probability of bankruptcy, is not affected by
monitoring costs (J.L).
Therefore, the parameter
changes expected monitoring costs.
J.L
affects g(ro) only to the extent that
J.L
Because the probability of bankruptcy is so small,
19Jn fact, the hump in output for the model with low agency costs and high
bankruptcy probabilities is more pronounced than in our calibrated economy with high
agency costs. There is reason to believe that our estimated bankruptcy probability is on
the low side, since the estimated sample does not include nonincorporated businesses
(either individually owned or partnerships). These companies tend to have much larger
bankruptcy probabilities.
26
l
I
changing monitoring costs alone has a relatively minor impact on the dynamics of the
model.
Yet the more uncertain the shock in the investment production process, the larger
is the fraction of net capital output entrepreneurs must (on average) receive.
due to the option value of the optimal debt contract for entrepreneurs.
expected return increases as the variance of ro rises.
This is
Entrepreneurs'
A higher return leads to a larger
steady-state level of net worth and to a reduced need for external finance.
This
explains why increasing the variance lowers the impact of agency costs.
The model appears to suggest that countries with a larger share of internally
financed investment would be less affected by agency costs.
In contrast, differences in
the risk premium may be an extremely poor indicator of the impact of agency costs, since
the risk premium is positively related to the variance of the shock process.
Aggregate measures of internal financing, however, may not indicate the importance
of agency costs. We could have calibrated the model by matching an empirical measure of
the internal financing percentage.
We chose not to follow this route because the model
makes no clear prediction on this percentage.
Remember, there are two different types of
firms in our model--investment firms and consumption-producing firms.
Although there is
a clear prediction for this ratio for the investment firms, the form of capital financing
for the consumption-producing firms is indeterminate.
Modigliani-Miller theorem.
27
This indeterminacy is just the
I
7. Conclusion
The principal contribution of this paper is to demonstrate a tractable way of
modeling and quantifying the role of agency costs in the business cycle.
quantitative
conclusions
warrant
restatement.
significant and persistent effect on real activity.
First,
debt-deflations
can
Two
have
a
In the case of large monitoring
costs, a relatively small wealth redistribution (corresponding to an annual 1.0 percent
surprise inflation) leads to a 0.5 percent increase in investment spending.
Second, the
agency-cost model naturally delivers a hump-shaped investment response to a productivity
shock.
This is because households delay investment decisions until agency costs are at
their lowest--a point in time several periods after the initial shock.
Another contribution of the paper is to demonstrate the linkages between explicit
models of agency costs and adjustment-cost models which assume that there are increasing
costs to producing capital.
Holding net worth fixed, this paper's agency-cost model
closely resembles an adjustment-cost model in that both deliver an upwardly sloped
capital supply curve.
The paper thus delivers an endogenous model of capital adjustment
As part of this endogeneity, the model also demonstrates how the capital supply
costs.
curve is shifted by movements in entrepreneurial net worth.
There are several natural extensions of the current work.
easily amenable to considering other shocks to the economy.
First, the model is
For example, Fisher (1994)
and Fuerst (1994, 1995) examine the effect of monetary shocks in related agency-cost
models.
Similarly,
Williamson ( 1987b) considers shocks to the variance of the
entrepreneur's technology in an overlapping generations model.
assumptions can deliver differing models of agency costs.
Second, a wide variety of
In this paper, agency costs
arise in the creation of new capital and thus affect the investment supply curve.
One
obvious alternative is to construct a model in which agency costs arise in the
28
I
consumption sector, and thus affect the investment demand curve.
Finally, several
authors have stressed that only a subset of firms are constrained by agency issues, while
many other firms are so large that these agency issues are relatively unimportant (for a
recent survey and discussion, see Bernanke, Gertler, and Gilchrist [1994]).
An
interesting extension of this work would be to construct a model that captures these
types of asymmetries.
29
I
APPENDIX
In this appendix, we demonstrate how the agency-cost model developed in the paper
is isomorphic to a model in which there are costs
to
adjusting the capital stock.
A
standard cost-of-adjustment model (Hayashi [1982]) assumes that capital evolves according
to
where
\jf
> 0 is increasing and concave.
Maximizing lifetime utility subject
to
this
constraint yields
(Al)
(A2)
where qt corresponds to the price of installed capital (or Tobin's q).
corresponds to equation (4) in the agency-cost model.
Equation (Al)
Equation (A2) represents the
supply curve for newly installed capital, It = S(qt)' with dS/dqt > 0.
In the agency-
cost model, we have a supply curve for new capital given by ls(qt,nt) = i(qt,nt){lJl <1>[ ffi (qt)]} . Analogous to the adjustment-cost model, we have I~
> 0. In contrast to the
adjustment-cost model, we also have that the supply curve is shifted by net worth.
Specifically, increases in net worth shift the supply curve to the right, I~
effect is a central issue in the agency-cost model.
> 0.
This
Note in particular that if net worth
is held constant, the agency-cost model is isomorphic to the adjustment-cost model.
It is a straightforward application of comparative statics to show that I~
I~ > 0.
Define the Lagrangean
30
> 0 and
I
L(i,ro,A.)
=qif(ro)
+
A.[qig(ro) - i
+
n].
We then have the following comparative statics:
dro/dn
where
1::!.
= o,
2
= -Lit..
Lroro > 0 is the second-order condition. Since ro does not vary with n, it is
now obvious that I~
Cl>(ro)J..L-g(ro)].
>
0.
As for I~, the optimal contract also maximizes if(ro) = i[l-
An increase in q relaxes the constraint on the lender's return, so that
if(ro) must be increasing in q.
Since ig(ro) is increasing in q, we then have that i[l-
Cl>( ro )J..L] = Is is also increasing in q.
31
I
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337-348.
Williamson, Stephen, "Costly Monitoring, Financial Intermediation, and Equilibrium
Credit Rationing," Journal of Monetary Economics (18), 1986, 159-179 .
...-----..--=---.--or---:' "Costly Monitoring, Optimal Contracts, and Equilibrium Credit
Rationing," Quanerly Journal of Economics (102), 1987a, 135-145.
. "Financial Intermediation, Business Failures, and Real
Business Cycles," Journal of Political Economy (95), 1987b, 1196-1216.
--~-....-~~--:--~
33
I
FIGURE 1:
The Sequence of Events in a Given Time Period
1. The current aggregate productivity shock is realized (8t).
2. Firms hire labor and rent capital from households and entrepreneurs.
These inputs are
used to produce the consumption good, Yt = 8tF{Kt,Ht,H~).
3. Households decide how much of their labor and capital income to consume immediately,
and how much to use to purchase the investment good. For each unit of investment that
the household wishes to purchase, it gives qt consumption goods to the capital mutual
fund (CMF).
4. The CMFs use the resources obtained from households to provide loans to an infinite
number of entrepreneurs utilizing the optimal financial contract derived in section 2.
5. Entrepreneurs borrow resources from the CMF and place the resources into their
capital-creation technology.
6. The idiosyncratic technology shock of each entrepreneur is realized, c), where j
indexes the infinite number of entrepreneurs. If c) ~ ffi, the loan from the CMF is repaid; otherwise, the entrepreneur declares bankruptcy and is monitored by the CMF.
7. Fraction y of the entrepreneurs receive news that they are to die. They sell their
capital holdings (if any) to the CMF, consume the proceeds, and exit the economy. At the
beginning of the next period, a new batch of entrepreneurs is born that will replace
those who have expired.
I
Figure 2: Wealth Shock
Entrepreneurial net worth
gr------~~------~------------~--------------------------~-----------------------------,
'r,
i!
~
)
~
0
"'{,1-~
.
... _,_.I
0
.
-~
··."·· ... ,.
Je-m"=
··~.. ~:-:-:.:::::.:;.:::.a:-.::.,..!f" ...,....--a-...- ...-....--·--·-e-... ·-·•····
10
20
40
30
'I
G··· mu = .3
··-~
50
60
quarters
Investment
..
0
......
.
""
·a
,----------.,
·..'c....
"·· ......,_ ...,_ ... •... ., ·· .. B· ... .., .....
:.:::.~..:-fr.. :o,.,.
...,_ .... -
I
-·--·--·-e-·. . -··-···-tl-··· eG ...
mu
.2
mu
.3
~·~
~~o------------~.~o------------~zo~------------J~-o--------------.~o~-----------~;,0:=:=:=:=:=~~.80
quorters
Price of capital
8r---------------------------------------------------------~----------------------------,
a
D .... e-···
~--o-·,
.,· ..-o- ...,.0'.
!
-~·-~·:.:·::~ ~··..:..f3·.:,:··~·.:.;.··@r·~o~o~·8w·-G-·-o- ·4--·4·-·•---~-&--G--~-···-·+·-&-·-&-
A-~
-:,.·CY'
""'
'I
/.~
"'
,;'
.,
"'"'
0
oO
l
10
20
30
40
50
60
I
Figure 2: (cont.}
Consumption
g,---------------~--------------~----------------------------------------------~---------------,
':I
'I / D
. <5 _,·
e-
mu
0··
mu
.3
~L------~----~~----~----~~----~====~
0
,0
.30
40
60
~0
:£0
0
•I•.I•Jrters
Household labor
0~--------------------------------------------------------------------------~
0
0
"'0
0
0
"'
0
E~
D
o
to
20
•a
eo
~~--------------~--------------~--------------~--------------~--------------~--------------~
~(l
o
~o
lurJrters
Output
0~------------------------------~----------------------------------------------~---------------,
Q
"'
0
0
0
0
0
G-·--·;
.,
~o~--------------~,o~------------~20~------------~~~------------~.o~------------~5~0--------------~.o·
quarters
Source: Authors' calculations.
I
Figure 3: Productivity Shock (mu = .2)
Entrepreneurial net worth
or---------------~~~--~-----------------------------------------------------------------------,
Jl
,
/
"'
....
0
I
' ....
d
I
.,
' ·.·,
I
,'
-·_.
.........
' /
·-·--· -·- ·-·-·-
&--~·····0·····-et·····O·····~·····O·••••-B·····0······0·····0·····D·····e·
"<>,
·:-
..
-':..:::.. -::::-~-..
..... _~
···0·····-&·····0·····of)••••·B
-.
---6·-...a.---&.
····e···:~..':":'A-·.:8':.::·!''''
e- mu = .2
G.... n at ss
~
mu = 0
.,._
···El·
~L_----~----~----~----~----~~==~--~~0
0
20
30
4.0
60
0
~0
I
q•,art'l?rs
Investment
,,
~r-------~---------------------------------------------------------------------------------------,
r\
eg
8-··
mu = .2
n at ss
~
mu = 0
~L---------------------------~----======~
ao
10
20
JO
40
50
flO
•1•Jarters
Price of capital
0
0
~-
fl
0
I
0
0
i
;
0
i
0
0
I
I
~
g
I
I
I
0
I
~
I
I
0
~
\
"
\
'\
.. ·o ..
\,
I
0
0
0
0
.G
.
.,
. ·o
D
~
·o.
e,.__.....L. -· -·- ~...:. '....... --.- ....... -.- .,_ ..._ ~-:~:.::: ~~~-~:·;.;.:.~t··...
... -o- ~
9 ...
-.J
'8.-
- ..... -o-- --o- --o- -..- .. -
e..
-o- -o--
~-
-e- -
mu = .2
n at ss
::.~
fr- mu = 0
~L..._______________.________________~--------------~----------------~------------~=;::::::::::::~
~0
10
20
.so
q•.1orters
40
50
__j
60
I
Figure 3: (cont.)
Consumption
8r---------------~--------------------------------------------------------------~--------------~
:/'
"
0
·-. 0
····-o ..
/1
·o
/I
e-
~
0
0
mu
= .2
.. "•fi.
G-··· n at ss
f
~
mu = 0
~ 0~--~~1·--------~,0~------------~,0~-------------t.30;-------------~.o;-----------~~5~o:::::::::::___-t6o
•J•Jorters
Household labor
~~--------------------------------------~
·1uorters
Output
0~--------------------------------------~
0
0
quorters
Source: Authors' calculations.
I
Figure 4: Productivity Shock (mu = .3)
Entrepreneurial net worth
or---------------~-------------------------------------------------------------------------------,
I'
_......,_
........
I
"-
'a...
J
'a.._
I
I
I
;;
I
,..
_.... _... _..
.....
"",
....... . .....
~
.....
...
.....
. _ . .,_ ·l!l--.' .............
,.__A.~·-···<9·····0·····~·-···0······E>· · O· · ·<>·· · D· · ·<> · · 0····:-::::.~:;::;.:-::::::::::.:::-o-. ::::
0
0
·<T··
e-
mu =
.3
G-··· n at 55
fr- mu = 0
.... :.~
r-...,
~L-----~----~~----~----~~----~====~
0
10
20
.30
40
50
60
-<-
0
q•Jorters
Investment
<D
0
.,
0
;;
g
e-
mu = .3
G
n at ss
fr- mu = 0
.··:.:.;.;
~L-------------------~------~----~====~0
0
10
~0
20
40
50
60
'luorters
Price of capital
gr-----------------------------------------------------------------------------------------------------,
0
0
0
"'
r
"
0
0
0
0
"
I
I
0
·,.
I
I
. o.
I
0
g
'\
·.,.
··o.
\
I
··o.
\
0
0
,._..J_,._____"' ,~---- ---
'
·o
e····o ...... D·-···o. ····o·-···e······
...... -
-
---- ,_ ---~~=-~=-_.;:t~
~---~-~-
......----
mu = .3
G-··· n at ss
fr- mu = 0
:-:-~
__
m~--------------~--~~~-~~~-~~~=-~~~-~o-~~::-~~------~--------------~--------------~;:::::::::::~
_j60
~0
10
20
30
40
50
1.1UOrters
I
Figure 4: (cont.)
Consumption
8~------------~------------~------------~--------------~---------------------------,
~~-~····0···:;·::!:~--;~-.:.~ ::--~ ~~~-~
f
I
"'
0
0
,.. 7
_,..
.
~
····o
._..____
····o · ··o
-......,.
j/
0
0
~~
·G.D
't
····e .. ··o .... ._
'.
.......... ' -
····ll .......... IJ ...
11
""5-.-·--
~
8- mu = .3
8-··· n at ss
fr- mu = 0
i
--
-· ··o.
8L--L;·---~~-----~~-----~--------~----------~====~~
o
1o
20
Jo
•o
5o
6o
~
•Juarters
Household labor
~~------------~------------~---------------------------------------------------------,
A
1\
I '\
0
0
"'
0
0
8- mu = .3
n at ss
&- mu = 0
0
0
0
...
D
10
oO
20
30
40
50
60
quarters
Output
0~--------------------------~----------------------------~--------------------------~
0
0
~
"'g
8- mu
g
=
.3
G-··· n at ss
fr- mu = 0
•J•unters
Source: Authors' calculations.
I
Table 1: Sensitivity Analysis
Simulation
High J.1 calibration
Low Jl calibration
Parameters
J.1=.3, cr=0.088,
'Y= 0.122,
n/i = 0.172
Steady State
Kss = 9.77, Tlna = .034,
4>= 0.00974,
risk premium=.0157
Comparative Statics
l.,(t+1)= 24.8,
ne(t+1)= 0.069,
le(t+1) = 1. 71,
1
E = 11.5
J.L=.2, 0=0.211,
Kss = 9.85, rrna = .07,
4>= 0.00974,
risk premium=.0157
ln(t+1)= 8.1,
n9(t+l) = 0.087,
le(t+1) = 0.767,
1
E =9.3
Kss = 9.89, rrnss = .035,
4>= 0.00974,
risk premium=.0108
ln{t+1)=23.5,
ne(t+1)= 0.061,
le(t+ 1) = 1.44,
1
E = 15.3
Kss = 9.81, Tlnss = .026,
4>= 0.015,
risk premium=.0157
In {t+ 1) = 33.8,
ne(t+1)= 0.057,
le(t+1) = 1.91,
1
E = 15.8
'Y= 0.053,
n/i = 0.39
Sensitivity analysis of
agency costs/the risk
premium
'Y= 0.085,
Sensitivity analysis of
steady-state bankruptcy
probability
'Y= 0.137,
=
J.1=.2, CJ=0.088,
n/i = 0.178
Jl=.2, CJ=0.072,
nli= 0.132
=
Note: I investment, n net worth, CJ
co - log normally distributed
. nss
n I 1=-
i..
s
d1n['(t+1)
I • (t + 1) -- ---:-=--dn(t + 1)
I' (t + 1) = () In[' (t + 1)
9
ne
£1
d In9(t)
(t+ 1)= dn(t+1)
d1n9(t)
ain['(t)
aIn q(t)
Source: Authors' calculations.
=standard deviation of co
@FedFRASER