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Federal Reserve Bank of Chicago
Credit Crunches and Credit Allocation
in a Model of Entrepreneurship
Marco Bassetto, Marco Cagetti, and
Mariacristina De Nardi
July 2013
WP 2013-06
Credit Crunches and Credit Allocation in a Model of
Entrepreneurship∗
Marco Bassetto†
Marco Cagetti‡
Mariacristina De Nardi§
Abstract
We study the effects of credit shocks in a model with heterogeneous entrepreneurs,
financing constraints, and a realistic firm size distribution. As entrepreneurial firms can
grow only slowly and rely heavily on retained earnings to expand the size of their business
in this set-up, we show that, by reducing entrepreneurial firm size and earnings, negative
shocks have a very persistent effect on real activity. In determining the speed of recovery
from an adverse economic shock, the most important factor is the extent to which the shock
erodes entrepreneurial wealth.
1
Introduction
The recent turmoil in financial markets has had deep consequences for the allocation of credit
within the economy. Access to credit is particularly important for nascent and growing firms,
∗
We are grateful to Matthias Doepke, Igor Livshits, Guido Lorenzoni, Nikolai Roussanov, and many seminars
participants for helpful comments. The views expressed herein are those of the authors and do not necessarily
reflect the views of the National Bureau of Economic Research, the Federal Reserve Bank of Chicago, the Board
of Governors, or the Federal Reserve System.
†
Federal Reserve Bank of Chicago and University College London.
‡
Board of Governors of the Federal Reserve System.
§
Federal Reserve Bank of Chicago, University College London, and NBER.
1
for which it is much more difficult to only rely on retained earnings as a source of financing.
In this paper, we study the effect of various types of financial shocks in a model with two nonfinancial sectors: a corporate sector, primarily composed of mature firms, and an entrepreneurial
sector, whose leverage is limited by their inability to fully commit to repay their debts. The
constraints generate a large, and realistic, dispersion in firm size, and limit the rate at which
entrepreneurial firms can grow. We build on the entrepreneurship model of Quadrini [43] and
Cagetti and De Nardi [13, 14], and introduce a financial intermediation sector that channels
resources from savers to users of capital. Both entrepreneurs and corporate firms require access
to intermediated funds. The reliance of entrepreneurs on intermediaries is one of the parameters used in our calibration, and is most associated with matching the ratio of the wealth of
entrepreneurs to that of workers. We calibrate directly the reliance of corporate firms on outside
funding to match data from the flow of funds.
Our main experiment considers the effects of an increase in the cost of channelling funds
through intermediaries, which increases the cost of borrowing and, in general equilibrium, also
depresses the rate of return earned by savers. This shock can be the result of either a negative
productivity shock in the financial intermediation sector, or the destruction of capital specific to
this sector (e.g., the loss in value of mortgage-backed securities). For the parameters that best
match our target moments, we find that entrepreneurial firms are affected to a deeper extent
than corporate firms. To the extent that entrepreneurial firms tend to be smaller, this is in line
with the empirical findings of Gertler and Gilchrist [21]. When intermediation costs return to
their steady-state levels, both entrepreneurs and corporate firms stage an initial rebound, but
the path to a full recovery is then slow. The wealth accumulation of the entrepreneurs is affected
in a very persistent way. Negative credit shocks reduce firm size, and, because entrepreneurial
firms can grow only slowly, limit the speed at which firms return to their previous scale when the
shocks subside. This slow transition is characterized by more capital misallocation and hence
lower output than in steady state.
An increase in intermediation costs also generates an endogenous tightening of borrowing constraints, as entrepreneurial activity becomes less profitable and the outside option of absconding
2
part of the capital becomes comparatively more attractive; this channel accounts for about 50%
of the drop in entrepreneurial firm size.
Government policy interacts with the financial disruption. We study two aspects of this interaction. First, the recession initiated by the financial shock creates a shortfall in the government
budget. If income taxes are raised to finance this shortfall, they constitute a new, independent
drain on entrepreneurial profits, which can be even bigger than the financial shock itself, and
leads to an even longer recovery. Second, we analyze the effects of government targeted intervention in the financial markets, that drives a wedge in the cost of funds across different classes of
borrowers. Our experiment is closest in spirit to the U.S. Treasury’s guarantee of money market
mutual funds (and implicitly of the underlying commercial paper): we consider a case in which
the government is able to completely and costlessly insulate the corporate sector from the shock.1
This guarantee is helpful in reducing the depth of the recession, but it does nothing to improve
the recovery, as it concentrates the shock onto the sector that is most vulnerable in the long run.
We contrast the effects of our baseline shock with alternative scenarios, such as a collateral
shock, that makes it harder for entrepreneurs to pledge future repayment of debt, similar to
Jermann and Quadrini [30], or a traditional TFP shock. We find that the response to these
shocks may be quite similar, to the extent that the balance sheet of entrepreneurs is hit in a
similar way; the evolution of this balance sheet is the key element that affects the speed of the
recovery. In our set-up all these shocks have a very persistent effect on real activity.
2
Related Works
Many works incorporate credit-market frictions in macroeconomic models but, rather than studying the direct effect of shocks to these frictions, they focus on how these frictions affect aggregate
investment and help generate and amplify business fluctuations. Among the earlier and most
influential contributions, Bernanke and Gertler [8] introduce agency problems such as costly
1
The government guarantee of money-market mutual funds was indeed costless ex-post for the United States
in the recent crisis; we choose a costless specification not because we believe that it was costless ex-ante, but to
show that this guarantee is not a panacea even in the best-case scenario.
3
state verification in a dynamic general equilibrium set-up, and Kiyotaki and Moore [34] further
illustrate the impact of collateral constraints and their interaction with asset prices and firms net
worth. In both papers, credit imperfections link investment decisions to the firms’ balance sheets
and generate a “financial accelerator” that amplifies and propagates shocks to the macroeconomy. The recent financial crisis has given further impetus to this literature, highlighting both
the many channels through which credit market imperfections can affect real activity, and the
possible effects of government interventions to improve the functioning of credit markets and
the flow of funds between borrowers and lenders. For a review of this literature, see Bernanke,
Gertler and Gilchrist [9] for earlier contributions and Gertler and Kiyotaki [22], Brunnermeier
and Sannikov [10] and Krishnamurthy [36] for more recent ones. Here, we only mention a few of
the papers most related to our work.
We model several types of financial frictions. Financial intermediation (and more in general
frictions in credit markets) introduce a wedge between the returns to lender and the cost of
capital to borrowers, a wedge related to the spread between liquid and easily intermediated
securities such as Treasuries and corporate bonds. These credit spreads vary over time and
their level and variation have been shown to be empirically correlated to and potentially key
to understand output fluctuations (for instance, Gilchrist, Sim and Zakrajsek [23], Christiano,
Motto and Rostagno [16], and Adrian and Shin [1]). Their role has been highlighted, among
others, by Hall [26], who show that in a simple representative-agent economy credit spreads
(including those for households) are powerful determinants of economic activity and can generate
fluctuations of the magnitude of those seen in the recent crisis, and by Curdia and Woodford [19],
who study how monetary policy rules should respond to shocks to credit spreads. We also find
that spreads have a significant impact on aggregate output during a credit crisis; by themselves,
spreads have a fairly short-lived effect in our model economy. It is a different source of frictions
that propagates the effect of spreads and generates a very persistent drop in output.
Among borrowers, we explicitly distinguish corporate and entrepreneurial firms; the latter potentially face different constraints and have reduced access to financial markets (see e.g.
Quadrini [42]). We model credit frictions to entrepreneurs as endogenous borrowing constraints
4
arising from imperfect enforceability of debt contracts (as in Kehoe and Levine [31] and Alvarez
and Jermann [5]). In this set-up, credit availability to entrepreneurs depends on their balance
sheet and their available collateral. This class of models has been shown useful to explain, for
instance, firm-size distribution (Akyol and Athreya [6], Monge [41]), firm dynamics (Albuquerque
and Hopenhayn [2]), macroeconomic fluctuations (Cooley, Marimon, and Quadrini [17], Jermann
and Quadrini [29]), and growth (Buera and Shin [12]). The presence of limited commitment slows
the growth of nascent firms and links it to the entrepreneurs’ cash flow. It is this channel that
propagates the initial financial shock in our model and is responsible for our main results. Our
paper is thus also closely related to Khan and Thomas [32], who examine the effect of capital
misallocation that result from a collateral requirement shock in a real business cycle model with
heterogeneous firms and capital rigidities.
The tightness of the borrowing constraints depends crucially on characteristics of the borrower
such as firm size, balance sheet, and personal wealth (Buera [11])). For this reason, we build a
model that quantitatively reproduces the high level of dispersion in these variables observed in
the data. Our work is thus related to the literature on wealth inequality and its determinants
(such as Quadrini and Rı́os-Rull [44] and Castaneda, Diaz-Gimenez and Rios-Rull [15]), and especially to the literature that identifies entrepreneurial wealth as a key force generating inequality
(Quadrini [42], Cagetti and De Nardi [13]). The interaction between frictions, entrepreneurship,
and inequality is crucial to understand the response to macroeconomic shocks (Jermann and
Quadrini [30]), the effect of certain government policies (Cagetti and De Nardi [14], Meh [40],
Kitao [33]), and asset pricing (Heaton and Lucas [27], Roussanov [45], Covas and Fujita [18]).
3
3.1
The Model
Demographics
A young person faces a constant probability of aging during each period (1 − πy ), and an old
person faces a constant probability of dying during each period (1 − πo ). When an old person
dies, his offspring enters the model, carrying the assets bequeathed to him by the parent.
5
3.2
Preferences
The household’s flow of utility from consumption is given by
c1−σ
t
.
1−σ
The households discount the
future at rate β and are perfectly altruistic toward their descendants.
3.3
Technology
Each person possesses two types of ability, which we take to be exogenous, stochastic, positively
autocorrelated, and stochastically independent of each other. Entrepreneurial ability (θt ) is
the capacity to invest capital and labor more or less productively using one’s own production
function. Working ability (yt ) is the capacity to produce income out of labor by working for
others.
The entrepreneurs can borrow, invest capital, hire labor, and run a technology whose return
depends on their own entrepreneurial ability: those with higher ability levels have higher average
and marginal returns from capital and labor. When the entrepreneur invests kt production is
given by
f (kt , nt ) = θt (ktγ (1 + nt )(1−γ) )ν
where ν, γ ∈ [0, 1], and n is hired labor (n ≥ 0). We normalize the labor of the entrepreneur to
1. Entrepreneurs thus face decreasing returns from investment, as their managerial skills become
gradually stretched over larger and larger projects (as in Lucas [39]). While entrepreneurial ability is exogenously given, the entrepreneurial rate of return from investing in capital is endogenous
and is a function of the size of the project that the entrepreneur implements.
There is no within-period uncertainty regarding the returns of the entrepreneurial project.
The ability θt is observable and known by all at the beginning of the period. We therefore abstract
from problems arising from partial observability, costly state verification, and from diversification
of entrepreneurial risk.
In addition to entrepreneurs, there is also a non-entrepreneurial sector, represented by a
standard Cobb-Douglas production function:
F (Ktc , Lct ) = A(Ktc )α (Lct )1−α
6
(1)
where Ktc and Lct are the total capital and labor inputs in the non-entrepreneurial sector and A
is a constant. In both sectors, capital depreciates at a rate δ.
3.4
Credit
External financing to both entrepreneurs and non-entrepreneurial firms is provided by competitive financial intermediaries. The intermediaries borrow funds from workers (and possibly
entrepreneurs, though in equilibrium almost all entrepreneurs will be credit constrained and will
invest all their wealth in their own firm).
Intermediation is costly. For each unit of capital, it requires φt units of the consumption good
as an intermediate input.
Financial intermediaries operate competitively. At any time t, they take as given the interest
rate required by savers (it ) and the interest rate paid by borrowers (rt ). Given the technology,
an equilibrium with a positive and finite supply of intermediation requires
rt = it + φt .
(2)
For the non-entrepreneurial sector, we assume that it must finance a given fraction ξt of
its capital through external borrowing. This constraint can be justified by an agency problem
between shareholders and managers.
The entrepreneurial demand for borrowed funds arises endogenously in the model. As in
Kehoe and Levine [31], entrepreneurs are subject to borrowing constraints that are endogenously determined in equilibrium and stem from the assumptions that contracts are imperfectly
enforceable.
In particular, as in Cagetti and De Nardi [13], we assume that the entrepreneurs who borrow
either can invest the money and repay their debt at the end of the period or can run away without
investing it and be workers for one period. In the latter case, they retain a fraction f of their
working capital kt (which includes own assets and borrowed money) and their creditors seize the
rest. We assume that labor services are paid at the end of the period, hence entrepreneurs are
not constrained in the amount of labor that they hire.
7
3.5
Government and taxation
The government is infinitely lived. It levies taxes, pays a pension pt to each retiree, provides
a certain level gt of public purchases (which do not enter the households’ utility function),
repays existing debt with interest, and issues new debt. In steady state, tax revenues from
income, consumption, and estate taxes are equal to government purchases, pension payments,
and interest payments on the debt.
We model progressive taxation of total income as in Cagetti and De Nardi [14], and use their
parameter estimates.
Total income taxes paid by each household are given by
Tti (Yt ) = τ i (Yt )Yt + τts Yt ,
where i indicates occupational choice (e or w). τts represents an additional flat rate that is allowed
to adjust to meet the government budget constraint. The government also levies a sales tax on
consumption, at rate τ c . Estates larger than a given value e are taxed at rate τ b on the amount
in excess of e.
As a first pass, we abstract from the tax implications of corporate finance decisions by assuming that corporate income taxes are zero and that capital gains are taxed as regular income.2
3.6
The corporate firms’ problem
In each period t, a corporate firm starts with resources AC
t , which include undepreciated capital
from last period, retained earnings, and last period’s equity issuance. The firm uses AC
t and new
debt (external) financing Bt to purchase capital for operation in period t (KtC ), subject to the
minimum external finance constraint
Bt ≥ ξKtC .
(3)
Residual internal funds can be invested with financial intermediaries at the rate it .
Since corporate firms will always be owned by savers (workers), their objective function is to
maximize the discounted sum of profits, using the interest rate it as a discount factor.
2
These two assumptions tend to offset each other.
8
Formally, the problem a firm faces as of period t is described recursively as follows:
Jt (AC
t ) =
max
C
KtC ,LC
t ,Bt ,At+1
AC
t+1
C
C
C
C
F (KtC , LC
t ) + (At + Bt − Kt )(1 + it ) − wt Lt − (1 + rt )Bt − δKt −
(4)
1
Jt+1 (AC
+
t+1 ),
1 + it+1
subject to
KtC ≤ AC
t + Bt
(5)
and (3). In equation (4), Jt represents the cum-dividend value of the firm’s equity in terms of
C
C
period-t goods. In period t, the firm’s profits are given by F (KtC , LC
t ) + (At + Bt − Kt )(1 +
C
C
C
it ) − wt LC
t − (1 + rt )Bt − At+1 − δKt . Of these profits, the firm retains At+1 to finance future
operations, and it pays out the rest as dividends (with negative dividends corresponding to new
equity issuance).
It is straightforward to verify that the firms’ problem is homogeneous of degree 1 in AC
t .
This implies that the size distribution of corporate firms is irrelevant, and we can work with
one representative (competitive) firm. It also implies that the firm’s value is proportional to
C
ˆ C
its initial internal funds: Jt (AC
t ) ≡ Jt At . Using ˆ to denote the optimal choice rescaled by At
and denoting by ω1t and ω2t the Lagrange multipliers on (5) and (3) respectively, the first-order
conditions that will hold if the corporate sector is active yield:
FK (K̂tC , L̂C
t ) − δ = 1 + it + ω1t + ξω2t ,
FL (K̂tC , L̂C
t ) = wt ,
(6)
rt − it = ω1t + ω2t ,
and
1=
Jˆt+1
.
1 + it+1
(7)
For t > 0, the envelope condition yields
Jˆt = 1 + it + ω1t
From these equations, for period t > 1 we obtain
FK (K̂tC , L̂C
t ) = δ + (1 − ξ)it + ξrt .
9
(8)
In the initial period, the internal funds of the corporate sector (AC
1 ) are exogenously given.
Depending on its value and factor prices, the corporate firms’
= r1
FK (K̂1C , L̂C
∈ [(1 − ξ)i1 + ξr1 , r1 ]
1)−δ
= (1 − ξ)i1 + ξr1
optimization problem yields
if K̂1 >
1
1−ξ
if K̂1 =
1
1−ξ
if K̂1 <
1
.
1−ξ
(9)
Given our assumptions, the timing of dividend payments does not matter. Whether dividends
are kept by the firm as retained earnings, or distributed and invested by firm owners, they yield
the same rate of return it . For this reason, we assume that the corporate sector has enough
retained earnings so that K̂1 < 1/(1 − ξ) even when faced with the unexpected shocks described
below.3 In this case, equation (9) coincides with equation (8), and we obtain Jˆ1 = 1 + i1 . A
corollary of this result is that firm owners will not have unexpected capital gains (or losses)
when the shock occurs. This allows us to only keep track of their total assets invested with
third parties, without distinguishing between firm stock, funds invested with intermediaries, and
government debt.
3.7
Households
Each young individual starts the period with assets at , entrepreneurial ability θt , and worker
ability yt , and chooses whether to be an entrepreneur or a worker during the current period.
An old entrepreneur that is still able to run a business can decide to keep the activity going
or retire, while a retiree cannot start a new entrepreneurial activity.
The young’s problem
The value function of a young person is
Vt (at , yt , θt ) = max{Vte (at , yt , θt ), Vtw (at , yt , θt )},
3
(10)
In a stochastic model, corporate firms would find it optimal to accumulate financial asset and to ensure that
the condition above is satisfied, since a shortfall in resources would require costly debt financing.
10
where Vte (at , yt , θt ) is the value function of a young individual who manages an entrepreneurial
activity during the current period. The term Vtw (at , yt , θt ) is the value function if he chooses to
be a worker during the current period.
The young entrepreneur’s problem can be written as
Vte (at , yt , θt ) =
max
ct ,kt ,nt ,at+1
{u(ct ) + βπy Et Vt+1 (at+1 , yt+1 , θt+1 ) + β(1 − πy )Et Wt+1 (at+1 , θt+1 )} (11)
subject to
Yte = θ(ktγ (1 + nt )(1−γ) )ν − δkt − (kt − at )(rt Ikt >at + it Ikt <at ) − wt nt
(12)
at+1 = Yte − Tte (Yte ) + at − (1 + τtc )ct
(13)
u(ct ) + βπy Et Vt+1 (at+1 , yt+1 , θt+1 ) + β(1 − πy )Et Wt+1 (at+1 , θt+1 ) ≥ Vtw (f · kt , yt , θt )
(14)
at ≥ 0
(15)
nt ≥ 0
(16)
kt ≥ 0.
(17)
The term Yte represents the entrepreneur’s total profits. The expected value of the value function is taken with respect to (yt+1 , θt+1 ), conditional on (yt , θt ). Eq. (14) determines the maximum
amount that an entrepreneur with given state variables can borrow. The term Wt (at+1 , θt+1 ) is
the value function of the old entrepreneur at the beginning of the period, before deciding whether
to stay in business or retire. We have
r
Vtw (at , yt , θt ) = max {u(ct ) + βπy Et Vt+1 (at+1 , yt+1 , θt+1 ) + β(1 − πy )Wt+1
(at+1 )}
ct ,at+1
(18)
subject to eq. (15) and
Ytw = wt yt + it at
(19)
at+1 = (1 + it )at − Ttw (Ytw ) − (1 + τtc )ct ,
(20)
where wt is the equilibrium wage rate.
11
The old’s problem
Since the old entrepreneur can choose to continue the entrepreneurial activity or retire, his state
variables are his current assets at and his entrepreneurial ability level θt .4 His value function is
given by
Wt (at , θt ) = max{Wte (at , θt ), Wtr (at )},
(21)
where Wte (at , θt ) is the value function for the old entrepreneur who stays in business, and Wtr (at )
is the value function of the old retired person. Define the inherited assets, net of estate taxes, as
b
ant+1 = at+1 − τt+1
· max(0, at+1 − et+1 ). We have
Wte (at , θt ) =
max
ct ,kt ,nt ,at+1
{u(ct ) + βπo Et Wt+1 (at+1 , θt+1 ) + β(1 − πo )Et Vt+1 (ant+1 , yt+1 , θt+1 )} (22)
subject to eq. (12), eq. (13), eq. (15), eq. (16), eq. (17) and
u(ct ) + βπo Et Wt+1 (at+1 , θt+1 ) + β(1 − πo )Et Vt+1 (ant+1 , yt+1 , θt+1 ) ≥ Wtr (f · kt ).
(23)
The child of an entrepreneur is born with ability level (θt+1 , yt+1 ). The expected value of the
child’s value function with respect to yt+1 is computed using the invariant distribution of yt ,
while the one with respect to θt+1 is conditional on the parent’s θt and evolves according to the
same Markov process that each person faces for θt while alive. This is justified by the assumption
that the child of an entrepreneur inherits the parent’s firm.
A retired person (who is not an entrepreneur) receives pensions and social security payments
(pt ) and consumes his assets. His value function is
r
(at+1 ) + β(1 − πo )Et Vt+1 (ant+1 , yt+1 , θt+1 )}
Wtr (at ) = max {u(ct ) + βπo Wt+1
ct ,at+1
(24)
subject to eq. (15) and
at+1 = (1 + it )at + pt − Ttw (pt + it at ) − (1 + τtc )ct .
(25)
The expected value of the child’s value function is taken with respect to the invariant distribution
of yt and θt .
4
We assume that the option of continuing is only open to entrepreneurs that have not lost their entrepreneurial
skill. We rule out the possibility that an old person with θt = 0 chooses not to retire to preserve the future option
of starting a new business should θt revert to the higher level.
12
3.8
Equilibrium definition
Let xt = (at , yt , θt , zt ) be the state vector, where z distinguishes young workers, young entrepreneurs, old entrepreneurs, and old retired. From the decision rules that solve the maximization problem and the exogenous Markov process for income and entrepreneurial ability, we can
derive a transition function Mt (xt , ·), which provides the probability distribution of xt+1 (the
state next period) conditional on the current state xt .
An equilibrium is given by the following elements at any time t:
interest rates rt , it , a wage rate wt ,
taxes (T w (.), T e (.),τ c , τts , τ b ), a bequest exemption level e, and social security payments pt ,
allocations ct (x), and at (x), occupational choices,
entrepreneurial labor hiring nt (x), and investments kt (x),
and a distribution of people over the state variables x : m (x),
t
t
such that, given it , rt , wt , and government taxes and transfer schedules:
• The functions ct , at , nt and kt solve the maximization problems described above.
• The amounts of labor and capital employed by the corporate sector satisfy (6) and (8).
• Financial intermediaries break even, that is, equation (2) holds.
• The value of corporate firms is given by (7).
• The labor market clears, that is, the total labor supplied by the workers equals the total
labor employed in the non-entrepreneurial sector and total labor hired by the entrepreneurs.
• The capital markets clear. Total household savings (inclusive of capital owned indirectly
through the stock of corporate firms) are equal to the capital employed for production by
the corporate sector and by the entrepreneurs, government debt, and the capital used by
financial intermediaries as an intermediate input.
• The government budget constraint balances in present value: total taxes collected plus
new debt issues equal government purchases, transfers, and repayment of previously issued
13
government debt (with interest):
Z
(T x (Yx )+τ c c(x)+Io (x)τ b (1−πo )·max(0, at+1 (xt )−et ))dmt (x) = pt πr +gt +(1+it )Dt −Dt+1 .
The integral is over all of the population, Io is an indicator function that is equal to one
if the person is old and zero otherwise, and πr is the fraction of retired people in the
population. In steady state Dt = D̄.
• The government present-value budget constraint holds, i.e.,
lim Dt
t→∞
t−1
Y
1
= 0.
1
+
i
s
s=2
• The distribution of people mt is induced by the transition matrix of the system as follows
m0t+1 = Mt (xt , ·)0 m(t)0 .
In steady state mt = m∗ is the invariant distribution for the economy and debt, prices, and
government policies are constant and the individual’s decision rules are time-independent.
4
Calibration
In this section, we describe the parameters taken from the literature or estimated outside of the
model (table 1), and the moments we use to calibrate the remaining parameters (tables 2 and
3).
4.1
Non-calibrated parameters
The coefficient of relative risk aversion σ, the capital share in the non-entrepreneurial CobbDouglas production function α, and the depreciation rate δ are set to values commonly used
in the literature (for instance, respectively, Attanasio et al. [7], Stokey and Rebelo [46], and
Gollin [24]).
The probabilities of aging and of dying are such that the average length of working life is 45
years and that of retirement is 11 years.
14
Parameter
Value
Source(s)
Preferences, technology, and demographics
σ
1.5
Attanasio et al. [7]
δ
.06
Stokey and Rebelo [46]
α
.33
Gollin [24]
A
1
normalization
φ
.015
Baa-Treasury spread
ξ
.33
Flow of funds
πy
.98
average working life: 45 years
πo
.91
average retirement life: 11 years
Labor income process and social security payments
y, Py
see appendix in Cagetti and De Nardi [14]
Huggett [28], Lillard et al. [38]
p
40% average yearly income
Kotlikoff et al. [35]
Public expenditure, government debt, and taxes
g
18.7% GDP
NIPA
D
see text
Altig et al. [3]
τc
11%
Altig et al. [3]
bw
.32
Cagetti and De Nardi [14]
be
.26
Cagetti and De Nardi [14]
sw
.22
Cagetti and De Nardi [14]
pw
.76
Cagetti and De Nardi [14]
pe
1.4
Cagetti and De Nardi [14]
se
.42
Cagetti and De Nardi [14]
Table 1: Fixed parameters and their sources.
15
We assume that the logarithm of the workers’ income is an AR(1) process and approximate
it as a 5 point Markov chain using Tauchen and Hussey’s [47] method. The autocorrelation
coefficient and the variance of the error term for the AR(1) process are chosen to obtain a
correlation coefficient of .95 (among others, Lillard et al. [38]) and a Gini coefficient for earnings
of .38 (Huggett [28] and De Nardi [20]).
The social security replacement rate is 40% of average gross income (see Kotlikoff, Smetters
and Walliser [35]). The steady-state ratio of government spending to GDP is set to 18.7%, and
the tax rate on consumption is 11%. All of these parameter choices are discussed in Cagetti and
De Nardi [14].
We set the steady-state financial intermediation cost to obtain a 1.5% spread between the
interest rate paid by borrowers and that received by lenders. This is calibrated to the historical
average of the spread between Baa-rated companies and Treasuries. In our model, both public
and private debt is risk free, and the spread is entirely due to the special liquidity role of
Treasuries, that are assumed not to require any intermediation. For this reason, we choose to
match our private borrowing rate to an empirical counterpart that features low default risk but
is also unlikely to carry any liquidity premium (see Krishnamurthy-Vissing Jorgensen [37] for
more discussion). As a comparison with other securities, the average spread between AAArated corporate bonds and Treasuries is about 1.25% and that between BBB-rated bonds and
Treasuries is about 2.2%.
The parameter ξ, the constraint on debt financing, is the average ratio of total corporate
debt to the value of corporate tangible assets, a ratio equal to about .34 in the Flow of Funds
Accounts. Corporate debt includes commercial paper, corporate bonds, mortgages, and other
loans; tangible assets include equipment and software (at replacement cost), structures (at market
value), and inventories. The ratio has generally been increasing since the beginning of the data
in 1950, from below .25 during the 1950’s to values near or above .5 in recent years. This ratio
jumped to .58 immediately after the financial crisis, as the crash in commercial real estate prices
sharply reduced the value of tangible assets, but since 2009 the ratio has been trending down
towards pre-recession norms.
16
We use Gouveia and Strauss’s [25] parametrization of the average tax rate:
i
τ i (Yt ) = bi − bi (si Ytp + 1)
−
1
pi
,
(26)
We estimate the relation separately for entrepreneurs and workers, using nonlinear least on
1989 PSID data. Our measure of total monetary income includes all forms of labor income,
capital income, transfers, and income from entrepreneurial activities. Total federal taxes paid
is the variable computed in the PSID (in our case, V18862 in the 1990 file). The dependent
variable in the regression, average tax rate, is the ratio of (PSID-estimated) federal taxes paid to
total monetary income. To obtain a representative sample, we exclude the poverty and Latino
samples. To obtain the appropriate tax rate for our model (in which the lowest income level is
positive), we also drop all observations with income smaller than $1,000 or negative taxes paid.
We define as entrepreneurs those who declare themselves to be self-employed and own or have a
financial interest in a business activity. The resulting sample of entrepreneurs has very similar
characteristics to those from the SCF. Our estimates would be very similar if we were to assume
a somewhat smaller or larger cutoff for the amount of business income received during the period.
For the other parameters, we take a ratio of government expenditures to GDP of 18.7% (NIPA
data), a consumption tax of about 11% (Altig et al. [4]), and a level of government debt that,
given the equilibrium interest rate, yields an average ratio of total interest payments to GDP of
3% (Altig et al. [3]).
4.2
Calibration targets
In previous work (Cagetti and De Nardi [14]), we have discussed the relevant empirical counterpart to concept of entrepreneur in this model. Our entrepreneurs are the self-employed business
owners that actively manage their own firm(s). We identify them in the Survey of Consumer
Finances (SCF) with those that declare that they are self-employed, that they own a business,
and that they actively manage it.
We assume that the worker’s income ability process is independent from the entrepreneurial
ability process (Cagetti and De Nardi [13] discuss how the results change with a different correlation coefficient between the two processes). We consider only two values of entrepreneurial
17
Target
Moment
Target
Model
Capital-output ratio
2.9-3.0
3.0
Percentage of Entrepreneurs
7.5-7.6
7.7
Percentage of Exiting Entrepreneurs
22-24
22.4
Percentage of Workers Entering Entrepreneurship
2.0-3.0
2.4
Median Net Worth of Entrepreneurs to Workers
5.3-6.5
6.2
7-13
11.9
57.4-64.6
58.8
Revenue from Estate and Gift Taxes (as % of output)
0.2-0.3
0.27
Percentage of Estates Paying Estate Taxes
1.5-2.0
1.9
Percentage of People at Zero Wealth
Percentage of Entrepreneurs Hiring on the Labor Market
Table 2: Target values.
Calibrated
Parameter
Value
β
.91
θ
{0, 1.16 }
Pθ
see text
ν
.88
γ
.80
f
75%
τb
16%
e
120
Table 3: Calibrated parameters.
18
ability: zero (no entrepreneurial ability) and a positive number. This implies that Pθ is a twoby-two matrix. Since its rows have to sum to one, this gives us two parameters to calibrate.
We also have to choose values for ν, the degree of decreasing returns to scale to entrepreneurial
ability, γ, the share of income going to entrepreneurial working capital, f , the fraction of working
capital the entrepreneur can keep in case he defaults, the estate tax rate, and its corresponding
exemption level.
In total, we calibrate nine parameters. We use the first seven parameters to target the
following moments: the capital-output ratio, the fraction of entrepreneurs in the population, the
fraction of entrepreneurs exiting entrepreneurship during each period, the fraction of workers
becoming entrepreneurs during each period,5 the ratio of median net worth of entrepreneurs
to that of workers, the fraction of people with zero wealth, and the fraction of entrepreneurs
hiring workers on the labor market. We choose the other two parameters to match the revenue
from estate and gift taxes and the fraction of the estates that pay estate taxes. Table 2 reports
the target values from the data and the values generated from our model; Table 3 reports the
parameter values used in our calibration.
For the capital output ratio, we use the Federal Reserve Board Flow of Funds Accounts. We
define capital as tangible assets excluding consumer durables and excluding federal and state
and local governments assets. The measure thus includes equipment and software, structures,
both residential and nonresidential, and inventories. Equipment and software is measured at
replacement cost; structures are measured at market value (except nonresidential structures
owned by the financial sector, for which market value information is not recorded). With this
definition, the ratio for the available years (1960-2009) is 2.96. Excluding the data after year
2000, which have experienced first a large increase and then a boost in house values, the ratio is
slightly smaller, about 2.89.
5
Both in the model and in the data, entry and exit rates refer only to people that were in the model (or
survey) in both periods and transitioned from one occupation to the other; they do not include people that die
while running an enterprise, nor people that start their enterprise at the beginning of their economic life. For
this reason, entry, exit, and the steady-state fraction of entrepreneurs are not linked by the identity that would
hold in an economy with infinitely-lived agents.
19
The fraction of entrepreneurs in the population, the probability of entering and exiting entrepreneurship6 , the ratio of the median wealth of an entrepreneur to that of a non-entrepreneur
and the fraction of entrepreneurs hiring workers are computed from the 1989 Survey of Consumer Finances (other waves gives similar results). We compute the transition matrix between
entrepreneurship and non-entrepreneurship by looking at households who are present in two
consecutive surveys.
The fraction of the population at zero wealth, also computed from the SCF, is somewhat
sensitive to the exact cutoff point (whether exactly zero, or some positive but small amount such
as $100). This fraction varies from roughly 7% to 13%. The percentage of entrepreneurs hiring
workers (besides themselves and, possibly, their spouse) is also computed from the SCF.
We do not use the statutory exemption and tax schedule to model the estate tax. As explained
in Cagetti and De Nardi [14] and in the references therein, these can differ substantially from the
statutory one. We thus calibrate the exemption level and the (flat) tax rate above the exemption
to match the percentage of estates that pay an estate tax (2%) and the total amount of revenues
of estate and gift taxes (about .2-.3% of GDP).
5
A Discussion of the Steady State, the Fit of the Model
and its Mechanisms
As we have shown in our previous work, our model of entrepreneurship, although simple, matches
very well the wealth distributions of both entrepreneurs and workers. In presence of borrowing
constraints, this is very important to determine the response to financial shocks for both the
whole distribution of entrepreneurs and for the important macroeconomic aggregates. Figures 1
and 2 compare the distribution of net worth for workers and entrepreneurs generated by the
6
Both in the model and in the data, entry and exit rates refer only to people who were in the model (or
survey) in both periods and transitioned from one occupation to the other; they do not include people who die
while running an enterprise, nor people who start their enterprise at the beginning of their economic life. For this
reason, entry, exit, and the steady-state fraction of entrepreneurs are not linked by the identity that would hold
in an economy with infinitely lived agents.
20
0.08
0.07
Fraction of people
0.06
0.05
0.04
0.03
0.02
0.01
0
0
1000
2000
3000
4000
Positive wealth, in thousands of dollars
5000
Figure 1: Distribution of wealth, conditional on wealth being positive, for the whole population.
Dash-dot line: data; solid line: model.
model and in the actual SCF data and confirms that the model generates the long upper tail of
the wealth distribution that is observed in the data for the whole population, and also the large
wealth holdings concentrated in the hands of a few entrepreneurs.
In our calibration the entrepreneurial sector employs about 57% of the capital, a little over the
one reported by the Small Business Administration (which is about 50%).7 It also employs 33%
of the efficiency units of labor in the economy; in the data, the Small Business Administration
that they employ almost 50% of the workers in the economy; in the data larger (corporate) firms
tend to pay more, which helps in closing this gap. Table 4 displays the distribution of labor
hiring by entrepreneurial firms. The first line is computed from the 2007 SCF data, which is
the last survey year before the crisis (the numbers from previous years are very similar). The
question asked in the SCF is how many workers the entrepreneurs hire in their firm (we exclude
the entrepreneur and his or her spouse). To compare it with the model, we assume that the
average employee of the entrepreneurial firm (up to the 95% quantile) lies at either the 33rd
7
The figures from the Small Business Administration refer to independent businesses having fewer than 500
employees. This definition is a reasonable, but not perfect match with our entrepreneurs.
21
Fraction of people
0.08
0.06
0.04
0.02
0
0
1000 2000 3000 4000 5000
Positive wealth, in thousands of dollars
Figure 2: Distribution of wealth, conditional on wealth being positive, for the entrepreneurs.
Dash-dot line: data; solid line: model.
Labor hiring
25%
50%
75%
90%
95%
2007 SCF data, number of workers
0
1
5
18
49
Model, number of 33rd percentile workers
0
0.6
5.0
15
27
Model, number of median workers
0
0.4
2.9
8.8
16
Table 4: Workers hiring in the SCF data and in the model.
quantile (second line) or the median of the efficiency distribution (third line) and that it works
full time. Given that part the employees in the SCF data will be part time, we conclude that
the distribution of hiring by entrepreneurial firms in the model matches the one in the data
reasonably well.
To better understand the workings of the model, the left hand side panel of Figure 3 reports
maximum investment as a function of one’s net worth (expressed in terms of multiples of average
income) for a young entrepreneur of median worker ability. Until the entrepreneur owns enough
assets, he keeps being a worker and does not enter entrepreneurship. For this reason, both
investment and leverage are reported as being zero until the entry point. The solid line refers to
22
the benchmark economy, while the crossed line refers to an economy in which the enforcement
frictions become tighter (f = 0.80, up from 0.75). The picture shows that tighter borrowing
constraints do not shift the amount of resources that one needs to hold to find it profitable to
enter entrepreneurship: the tightening of the constraint discourages entry, but at the same time
it induces a lower interest rate, which has a countervailing effect. Even though entry occurs
at similar wealth levels, tighter borrowing constraints result in smaller investment and leverage
and slow business growth. In the aggregate economy, slower-growing firms result in less capital
accumulation and less inequality. The capital-output ratio in steady state drops from 3.0 to 2.9,
the Gini coeeficient drops from 0.81 to 0.79, and the share of net worth held by the richest 1%
drops from 28.4% to 26.4%.
Figure 3: Left panel: Investment as a function of one’s net worth (in multiples of average income)
and workers’ ability. Right panel: Borrowing as a function of one’s assets. baseline model. Right
panel: baseline model and model with tighter borrowing constraints
23
In the data, entrepreneurs are much richer than workers, and their saving rate does not
quickly decline with wealth. To match these facts, the calibration implies borrowing limits that
are tight compared to the optimal firm size, hence the growth process of entrepreneurial firms is
slow. This plays an important role for the response of the economy to various shocks, to which
we now turn.
6
Computing Transitions: The shocks and their effects
Throughout the experiments below, a shock hits the economy unexpectedly in year 2 and lasts
for 3 years. After year 4, the exogenous parameters return to their steady state level.
The sequence of events within a period is as follows:
• Idiosyncratic shocks and the unexpected aggregate shock are realized. All agents have
perfect foresight about aggregates from this period onwards.
• Capital markets open; entering entrepreneurs liquidate their positions in corporate stock
and government debt to invest in their own business, and borrow from intermediaries;
workers and retirees (both from the previous period as well as exiting entrepreneurs) absorb these positions and lend to the intermediaries. Corporate firms raise funds from
intermediaries according to their constraint (3) and deposit any internal funds in excess.8
• Corporate firms and entrepreneurs hire workers and production takes place.
• Wages, taxes, and dividends are paid, loans are repaid, and the government issues new
debt.
• Households consume and government spending occurs.
8
We assume that the interest rate on government debt is also reset at this stage, even though debt is issued
at the end of the previous period. Results are very similar if we assume that the rate of return on government
debt is predetermined; in this case, the government would not benefit from the drop in i2 and taxes would have
to be slightly higher to balance the budget.
24
For each experiment, we isolate the effects of taxes and interest-rate changes by proceeding as
follows. First, we keep lending rates, taxes, and government debt fixed at the initial steady state
level, and we let government expenditure adjust to balance the government budget constraint.
Second, we let lending rates clear the capital market in a closed economy, while we still keep
taxes and government debt fixed at the initial steady state level, with government spending acting
again as a residual. Finally, we consider an experiment where government spending is fixed, and
both taxes and interest rates adjust. In particular, we increase the proportional component of
the tax schedule (τts ) after the end of the financial shock, in years 5 through 13, to balance
the present-value budget constraint of the government. We are interested in this comparison
to understand the way in which taxes affect entrepreneurial incentives; a meaningful welfare
comparison between cuts in government spending and increases in tax rates is not possible in
our model, since by assumption government spending is wasted.
6.1
Negative technology shock in the intermediation sector.
We consider the effect of a shock that unexpectedly increases φ from 1.5% to 3.5% for three
years.9
This is a way of capturing either of two alternative shocks:
• More monitoring is necessary to ensure loan performance due to the financial turmoil.
• φ stands in as payments to a factor that is fixed in the short run and that is temporarily
depleted. As an example, suppose that banks face capital requirements and that some
initial losses wipe some of the capital out, constraining the banks’ ability to offer additional
intermediation services. In this case, the increase in φ would reflect the additional reward
for the scarcer banking capital.10
9
For a comparison, the spread between Baa corporate bonds and Treasuries jumped to more than 5% after
the recent crisis, and decreased only gradually over the course of 2009.
10
To spell out completely this story, we should explain what prevents capital from immediately flowing back
into the banking sector.
25
100
100
99.5
99
99.8
98.5
Average Firm Size
Entrepreneurs
99.6
99.4
99.2
99
98
97.5
97
96.5
96
98.8
95.5
98.6
95
98.4
94.5
5
10
15
20
25
30
35
Time
5
10
15
20
25
30
35
Time
Figure 4: Number of entrepreneurs (left) and average size of entrepreneurial firms (right) in
response to a shock to φ. Steady state = 100. Solid line: fixed lending rate, government
spending adjusts. Dashed line: general equilibrium, government spending adjusts. Dotted line:
general equilibrium, taxes adjust.
Figure 4 shows the effect of the financial intermediation shock on the number of entrepreneurs
and their average firm size. The fraction of entrepreneurs drops, particularly when taxes adjust,
but this margin is not very persistent: when intermediation costs and taxes are back to normal,
entrepreneurs quickly reenter the market. This is because the minimum firm size that makes entry
profitable is small, and potential entrepreneurs can save to reach that point quickly. Average firm
size also drops; this effect is bigger and much more persistent. The intermediation cost reduces
the entrepreneurs’ cash flow and their ability to retain earnings to foster their business’ growth.
Since both the wealth distribution and the distribution of assets across firms that we match is
very spread out, our model implies a very gradual growth of firms, with almost no entrepreneur
attaining sufficient wealth that borrowing constraints cease to bind. It follows that any negative
shock has almost a permanent effect on each entrepreneur, and its aggregate impact vanishes
fully only when each entrepreneur loses his ability and closes the firm. As soon as the shock is
over, firm growth resumes, but at a slow pace dictated by the tight borrowing limits.
The alternative ways in which taxes, spending, and interest rates adjust across the three
experiments reveal some differences. Consider first the cases in which taxes are held fixed, and
26
0.06
0.055
Interest rate
0.05
0.045
0.04
0.035
0.03
0.025
5
10
15
20
25
30
35
Time
Figure 5: Evolution of interest rates in response to a shock to φ when government spending
adjusts: experiment with a fixed lending rate (solid = lending rate, dotted = borrowing rate)
and general equilibrium (dashed = lending rate, dash-dotted = borrowing rate).
government spending acts as a residual. Figure 5 plots the borrowing and lending rates for the
case in which the lending rate is held fixed (a small open economy) and that in which the capital
market clears. During the periods of the shock, borrowing rates spike higher when savers have
the opportunity of earning a fixed rate abroad. As a consequence, in Figure 4, average firm size
drops more when lending rates are held constant (solid line) than when the effect of the shock
is spread between borrowers and savers, as in general equilibrium (dashed line). The difference
between partial and general equilibrium reverses after the shock is over. The shock triggers a
reduction in aggregate capital; in general equilibrium, the resulting higher interest rates impair
the entrepreneurs’ ability to rebuild their balance sheet and lead to a slower recovery in firm size.
The differences between the solid and dashed lines in Figure 4 are minor compared to the
differences between either of those lines and the dotted line, which represents the case in which the
government balances its budget by increasing taxes rather than cutting government spending. To
balance the budget, the government needs an increase in the tax rate of about 1.5% for 10 years.
The government imbalance does not have a large impact on the depth of the initial recession, but
it causes a prolonged slump once the fiscal adjustment takes place. Taxes deprive entrepreneurs
27
100
102
101
99
Value added across sectors
Value added across sectors
99.5
98.5
98
97.5
97
100
99
98
97
96
96.5
95
96
94
5
10
15
20
25
30
35
Time
5
10
15
20
25
30
35
Time
Figure 6: Value added in the corporate sector (solid) and entrepreneurial sector (dashed), in
response to a shock to φ. Left panel: general equilibrium with government spending adjusting.
Right panel: general equilibrium with taxes adjusting. Steady state = 100.
of resources to grow their firms, redistributing to government debt holders (workers), and they
also drive a further wedge between savers and borrowers, since they hit capital as well as labor
income. The tax increase is a new hit to the entrepreneurs’ cash flow and results in a slow but
persistent erosion of firm size, with a cumulative effect that is more than twice as large compared
to the case of cuts in government spending. The recovery from the double shock of an increase
in the intermediation cost and the subsequent response in taxes is thus delayed and starts from
a weaker position.
Figure 6 compares value added in the entrepreneurial vs. the corporate sector of the economy.
Since both sectors use capital intermediated by the financial sector, their value added drops when
the cost of accessing the intermediaries’ services increases. For our calibration, entrepreneurs are
more reliant on financial intermediation, and the drop in their value added is twice as large than
it is for the corporate sector. In period 5 the borrowing-cost shock is over and the effect reverses.
In this period, the value added in the entrepreneurial sector grows faster than in the corporate
sector; nonetheless, entrepreneurs do not recover fully, while the corporate sector stages a full
recovery. The difference across the two sectors is due to the nature of the credit frictions faced by
the two types of firms. Entrepreneurs are primarily constrained by their net worth, which can only
28
be rebuilt slowly, whereas corporate firms curtail their investment only because of the additional
cost of borrowing in equation (8), a period-by-period cost that returns almost to normal as
soon as intermediation costs revert to their steady state level. From period 5, the behavior
of the economy in the left and right panels of Figure 6 diverge. When (wasteful) government
spending acts as the residual (left panel), no further shock perturbs the entrepreneurs’ wealth
accumulation, and the economy immediately starts on a path of slow convergence back to the
steady state. In contrast, when taxes adjust, their effect on the entrepreneurs’ balance sheet
tightens the constraint on entrepreneurial firm size, and results in a reallocation of resources
from entrepreneurs to corporate firms.
Due to computational limitations related to the endogenous borrowing constraints, our model
features an inelastic labor supply, and thus it cannot capture the decline in labor occurring during
the downturn. However, we can analyze the relative allocation of labor across the two sectors,
which we show in Figure 7. This picture mirrors what we observed for output: the recession
caused by the financial shock shrinks the share of employment at entrepreneurial firms, in line
with Gertler and Gilchist’s [21] observation that small firms are more sensitive to the business
cycle. The share of employment at entrepreneurial firms stages a partial recovery when financial
conditions return to normal, in period 5. From there, it continues on a path of gradual increase
if government spending absorbs the impact of the shock on the government budget, whereas it
drops anew and more markedly if taxes go up instead.
Having analyzed the forces that drive the behavior of our economy, we now turn to their
aggregate implications. Figure 8 plots aggregate GDP. The increase in intermediation costs
(an intermediate input in our economy) depresses TFP and output during the financial shock.
This is particularly true when lending rates are fixed, since in this case capital moves out of the
economy.11 In general equilibrium, the output drop on impact is mostly driven by the TFP effect
of the shock: the drop in output is close to 3%, with 0.3% being due to the misallocation of
factors. As the net worth of entrepreneurs is eroded, the misallocation becomes a more prominent
force; after the shock is over, the entire difference between the solid line and the steady state is
11
National output declines much less, since the capital invested abroad continues to earn a rate of return.
29
99
Relative Employment
98
97
96
95
94
93
92
91
5
10
15
20
25
30
35
Time
Figure 7: Employment in the entrepreneurial sector, relative to the corporate sector, in response
to a shock to φ. Dashed line: general equilibrium, government spending adjusts. Dotted line:
general equilibrium, taxes adjust. Steady state = 100.
due to this misallocation, whereas in general equilibrium (dashed and dotted line) the decrease
in capital accumulation plays a role. When taxes hit the entrepreneurs’ ability to accumulate
wealth and grow their own business the economy fares much worse. This second dip would be
less pronounced, the longer the transition period over which taxes are raised; but, of course, in
this case the policy response to the shock would have even more persistent effects.
Figure 9 plots aggregate consumption and investment.12 As in most business-cycle models,
investment bears the brunt of the shock on impact. Nonetheless, consumption drops too. Unlike
a pure tightening of borrowing constraints, a shock to financial intermediation entails real output
costs, that reduce total available resources from the outset. In general equilibrium, the behavior
of aggregate investment contributes to a slow recovery: after the initial drop in the periods of the
shock, investment never overshoots its steady-state level. When government spending adjusts,
12
We do not plot aggregate investment for the case of fixed lending rates. In this case, the shock triggers a
large capital outflow, and the drop in domestic investment happens on a much bigger scale, reversing itself after
the intermediation shock is over. We do not view these international flows as realistic, but we are interested in
this experiment purely as a way to isolate the effects of interest-rate movements on the economic incentives of
the actors of our economy.
30
100
99.5
99
98.5
GDP
98
97.5
97
96.5
96
95.5
95
5
10
15
20
25
30
35
Time
Figure 8: GDP in response to a shock to φ. Solid line: fixed lending rate, government spending
adjusts. Dashed line: general equilibrium, government spending adjusts. Dotted line: general
equilibrium, taxes adjust. Steady state = 100.
investment merely returns close to steady state; when taxes further depress wealth accumulation,
investment remains 2% below its steady state several years after taxes have returned to their
steady-state level.
It has often been remarked that, during the crisis, credit standards were extremely tight and
that businesses found it difficult to access credit at any price (see for example the Quarterly
Senior Loan Officer Opinion Survey conducted by the Federal Reserve Board). A similar effect
arises in our model: the increase in intermediation costs is accompanied by an endogenous
tightening of the constraints, because entrepreneurship becomes less profitable and thus the
temptation of terminating the business and absconding part of the capital becomes stronger. To
illustrate this mechanism, we run an alternative experiment, where intermediation costs increase
by the same amount and duration (2% for three years), but borrowing constraints are held fixed
exogenously at their steady-state values. Figure 10 compares the effect of the intermediation
shock for exogenous and endogenous borrowing constraints, when the government spending acts
as a residual. It shows that the adjustments of the extensive margin are almost exclusively driven
by the tightening of the borrowing limits, that forces potential entrepreneurs to accumulate more
31
100
100
99.5
98
99
Investment
Consumption
96
98.5
98
94
92
97.5
90
97
88
96.5
5
10
15
20
25
30
35
Time
5
10
15
20
25
30
35
Time
Figure 9: Aggregate consumption (left panel) and investment (right panel) in response to a
shock to φ. Solid line: fixed lending rate, government spending adjusts. Dashed line: general
equilibrium, government spending adjusts. Dotted line: general equilibrium, taxes adjust. Steady
state = 100.
wealth before entry becomes worthwhile. The profit loss from the intermediation shock leads to
smaller firms even with fixed borrowing constraints, but the drop in average firm size is about half
as large. After the shock, the speed of recovery is similar, but the level from which the economy
has to recover is much lower with endogenous borrowing constraints, so that it takes longer to
return to the same level of output. The behavior of GDP with endogenous vs. fixed borrowing
limits (Figure 11) mirrors the one for the average size of firms, but quantitatively the tightening
of borrowing constraints has a more muted impact in the periods of the shock. When the shock
is active, both entrepreneurs and corporate firms are subject to it, and holding borrowing limits
fixed only benefits entrepreneurs. After the shock is over, the gap between the two lines widens,
because the persistent effect of the shock is dictated by the evolution of entrepreneurial wealth,
which is less severely impacted when borrowing constraints are held fixed.
Figures 12 and 13 compares the behavior of entrepreneurial firms and GDP with endogenous
vs. fixed borrowing constraints in the case in which the government raises taxes to balance its
budget. The differences are here starker, because an increase in taxes drains the profitability of
entrepreneurs and generates its own credit crunch if borrowing constraints are allowed to adjust
32
100
99.8
100
99.6
99.4
Average Firm Size
Entrepreneurs
99.8
99.6
99.4
99.2
99.2
99
98.8
98.6
98.4
98.2
99
98
5
10
15
20
25
30
35
5
10
15
Time
20
25
30
35
Time
Figure 10: Number of entrepreneurs (left) and average size of entrepreneurial firms (right) in
response to a shock to φ with borrowing constraints held fixed (solid line) and allowed to vary
endogenously (dashed line). Steady state = 100. General equilibrium, government spending
adjusts.
100
99.5
GDP
99
98.5
98
97.5
97
5
10
15
20
25
30
35
Time
Figure 11: GDP in response to a shock to φ with borrowing constraints held fixed (solid line)
and allowed to vary endogenously (dashed line). Steady state = 100. General equilibrium,
government spending adjusts.
33
100
100
99.8
99
Average Firm Size
Entrepreneurs
99.6
99.4
99.2
99
98
97
96
98.8
98.6
95
98.4
5
10
15
20
25
30
35
Time
5
10
15
20
25
30
35
Time
Figure 12: Number of entrepreneurs (left) and average size of entrepreneurial firms (right) in
response to a shock to φ with borrowing constraints held fixed (solid line) and allowed to vary
endogenously (dashed line). Steady state = 100. General equilibrium, taxes adjust.
endogenously.
6.2
Negative technology shock in the intermediation sector, only for
entrepreneurs.
In the wake of the financial crisis of 2008, the government took several actions aimed at restoring
calm in several financial markets. Among the actions that were most successful ex-post was a
blanket guarantee of money-market mutual funds, and thus, indirectly, of the commercial paper
of corporate industrial firms that those funds purchased. More in general, companies with direct
access to markets seemed better able to cope than those that were forced to go through the
banking sector.13
In this section, we consider the same shock to φ as in the previous section, but we assume
that the government neutralizes its impact on the corporate sector; we do so by varying ξt to
hold ξt φt constant throughout. We take the best-case scenario in which this policy comes at no
13
For instance, data from the Flow of Funds accounts show that bond issuance for large corporations recovered
quickly after the financial crisis, while bank lending remained subdued for several years.
34
100
99.5
99
GDP
98.5
98
97.5
97
96.5
5
10
15
20
25
30
35
Time
Figure 13: GDP in response to a shock to φ with borrowing constraints held fixed (solid line)
and allowed to vary endogenously (dashed line). Steady state = 100. General equilibrium, taxes
adjust.
cost, in the way this happened with the money market guarantee ex-post.14
Figure 14 studies the differences between this experiment and the case of a pure shock to φ for
the entrepreneurial sector, in the case of general equilibrium and fixed taxes (with government
spending adjusting as a residual). Since corporate firms are insulated from the shock in this new
experiment, entrepreneurs face stiffer competition in the factor markets, which thins their ranks
and leads them to shrink their firm size more. The recovery is affected by two opposite forces.
The greater hit taken by entrepreneurs slows the return to the steady state. However, aggregate
investment (Figure 15) drops less when only one sector is hit by the shock, and the additional
capital is beneficial to the recovery. The first force dominates in the short run, but about 5 years
after the shock the two experiments become quite similar.
Figure 16 displays the value added in the two sectors in response to the shock to φ and
the contemporaneous offset through ξ. When the corporate sector is completely insulated, its
size actually expands during the financial disruption, as it poaches workers and capital from the
14
We could easily add a cost to this guarantee, in which case taxes would have to go up more during the
transition, and would exacerbate the persistence of the drop in output.
35
100
100
99.5
Average Firm Size
Entrepreneurs
99.8
99.6
99.4
99.2
99
98.5
98
99
97.5
98.8
5
10
15
20
25
30
35
5
10
15
Time
20
25
30
35
Time
Figure 14: Number of entrepreneurs (left) and average size of entrepreneurial firms (right) in
response to a shock to φ (solid line), and to φ and ξ simultaneously (dashed line). Steady state
= 100. General equilibrium, government spending adjusts.
100
98
Investment
96
94
92
90
88
5
10
15
20
25
30
35
Time
Figure 15: Aggregate investment in response to a shock to φ (solid line), and to φ and ξ simultaneously (dashed line). Steady state = 100. General equilibrium, government spending
adjusts.
36
Value added across sectors
101
100
99
98
97
96
95
5
10
15
20
25
30
35
Time
Figure 16: Value added in the corporate sector (solid) and entrepreneurial sector (dashed), in
response to a shock to φ and ξ simultaneously. General equilibrium with government spending
adjusting.
entrepreneurs.
Figure 17 shows how all of these effects combine to determine aggregate GDP. Even in
the best-case scenario in which the government intervention entails no cost, it is successful at
reducing the severity of the recession, but it has almost no impact on the recovery. By helping
the corporate sector, the government exacerbates the misallocation of resources due to financial
frictions.
6.3
A shock to required collateral.
Here, we consider a shock that increases the collateral that the entrepreneurs need to secure their
loans. Specifically, we raise the fraction of capital than can be absconded (f ) from 75% to 80%.
We calibrate this shock to have an effect on aggregate output during the credit crunch that is of
similar magnitude of the drop that we obtained considering a shock to φ, for the cases of general
equilibrium. This can be seen in Figure 18.15
15
For brevity, we present only the case in which government spending adjusts to restore budget balance. The
conclusions that we draw for this case apply also to the case in which taxes adjust instead.
37
100
99.5
GDP
99
98.5
98
97.5
97
5
10
15
20
25
30
35
Time
Figure 17: GDP in response to a shock to φ (solid line), and to φ and ξ simultaneously (dashed
line). Steady state = 100. General equilibrium, government spending adjusts.
100
99.5
GDP
99
98.5
98
97.5
97
5
10
15
20
25
30
35
Time
Figure 18: GDP in response to a shock to f (solid line) and φ (dashed line). Steady state = 100.
General equilibrium, government spending adjusts.
38
100
100
99
98
Average Firm Size
Entrepreneurs
99.5
99
98.5
97
96
95
98
94
5
10
15
20
25
30
35
93
5
Time
10
15
20
25
30
35
Time
Figure 19: Number of entrepreneurs (left) and average size of entrepreneurial firms (right) in
response to a shock to f (solid line) and φ (dashed line). Steady state = 100. General equilibrium,
government spending adjusts.
Since this shock only affects the entrepreneurial sector, matching the output drop in impact
requires a much deeper contraction in the number of entrepreneurs and firm size when f increases
than the baseline case in which borrowing costs increase for both entrepreneurs and corporate
firms. This can be seen in Figure 19. It might seem surprising that the deeper contraction
in entrepreneurial firms does not bear bigger implications for the entrepreneurs wealth in the
recovery phase. The reason for this result is that a shock to f hits only the marginal profits of
the firm: it forces entrepreneurs to shrink their scale, but it has no effect on their profits for a
given scale of operations. In contrast, an increase in φ raises the rental rate of capital paid by
entrepreneurs; this effect applies to all of the capital that they rent, and has a negative effect on
their profits even conditioning on their scale of operations.
6.4
A TFP shock.
We finally contrast a credit shock to a TFP shock that hits both the corporate sector and the
entrepreneurial sector. In this case, total factor productivity drops by 2.5% for 3 years, and
subsequently reverts to steady state. Once again, the magnitude of the TFP drop is chosen so
as to obtain a similar GDP drop on impact in general equilibrium. As Figures 20 and 21 show,
39
100
99.5
99
GDP
98.5
98
97.5
97
96.5
5
10
15
20
25
30
35
Time
Figure 20: GDP in response to a shock to TFP (solid line) and φ (dashed line). Steady state =
100. General equilibrium, government spending adjusts.
the evolution of the economy under this shock is fairly similar to that of a shock to φ.
7
Conclusion
From the experiments that we ran, we learn three lessons. First, and foremost, we find that it
is not the source of the disturbance that determines our economy’s speed of recovery, but rather
the way in which the shock affects the profitability of credit-constrained entrepreneurs. Recovery
is comparatively slowest in the case of an increase in borrowing rates from which the corporate
sector is shielded (our experiment of Section 6.2). Among our experiments, this one has the
shallowest recession, and yet during the recovery output is at a similar level as that of the others,
in which the economy needs to make up for deeper drops. When losses are concentrated in the
entrepreneurial sector, it takes more time for entrepreneurs to rebuild their balance sheet.
Second, the way public finances adjust in response to the shortfalls caused by a recession is
important. Income taxes are a further drain on the cash flow available for successful business
owners to grow and represent a further significant drag on the economy. From an efficiency perspective, entrepreneurship subsidies would contribute to increase output. It should be noted that
40
100
99.8
100
99.6
99.8
Average Firm Size
Entrepreneurs
99.4
99.6
99.4
99.2
99.2
99
98.8
98.6
99
98.4
98.8
98.2
98
98.6
5
10
15
20
25
30
35
5
10
15
Time
20
25
30
35
Time
Figure 21: Number of entrepreneurs (left) and average size of entrepreneurial firms (right) in
response to a shock to TFP (solid line) and φ (dashed line). Steady state = 100. General
equilibrium, government spending adjusts.
this does not necessarily imply that subsidizing entrepreneurs is an optimal policy. Even if it were
easy to identify the exact counterpart to credit-constrained, highly productive entrepreneurs, this
policy would require taxing workers, who are on average far poorer in our economy, as in the
data, to subsidize comparatively richer business owners, raising equity considerations.
Finally, in an environment with endogenous borrowing constraints, financial shocks that
increase interest costs have two effects. The interest rate increase represents a direct drain on
firms’ profits. The indirect effect is that higher borrowing rates trigger a tightening of credit
limits. Hence, for a given contraction in credit, financial shocks that affect borrowing rates have
potentially more severe implications than pure credit rationing.
References
[1] Tobias Adrian and Hyun Song Shin. Financial Intermediation and Monetary Economics.
Staff Report 398, Federal Reserve Bank of New York, Oct 2009.
[2] Rui Albuquerque and Hugo A. Hopenhayn. Optimal Dynamic Lending Contracts with
Imperfect Enforceability. Review of Economic Studies, 71(2):285–315, Apr 2004.
41
[3] David Altig, Alan J. Auerbach, Laurence J. Kotlikoff, Kent A. Smetters, and Jan Walliser.
Simulating Fundamental Tax Reform in the United States. American Economic Review,
91(3):574–595, June 2001.
[4] David Altig, Alan J. Auerbach, Laurence J. Kotlikoff, Kent A. Smetters, and Jan Walliser.
Simulating Fundamental Tax Reform in the United States. American Economic Review,
91(3):574–595, June 2001.
[5] Fernando Alvarez and Urban Jermann. Efficiency, Equilibrium, and Asset Pricing with Risk
of Default. Econometrica, 68(4):775–797, 2000.
[6] Kartik Athreya and Ahmet Akyol. Self-Employment Rates and Business Size: The Roles of
Occupational Choice and Credit Market Frictions. Annals of Finance, 5(3-4):495–519, Jun
2009.
[7] Orazio P. Attanasio, James Banks, Costas Meghir, and Guglielmo Weber. Humps and
Bumps in Lifetime Consumption. Journal of Business and Economic Statistics, 17(1):22–
35, January 1999.
[8] Ben S. Bernanke and Mark Gertler. Agency Costs, Net Worth, and Business Fluctuations.
American Economic Review, 79(1):14–31, Mar 1989.
[9] Ben S. Bernanke, Mark Gertler, and Simon Gilchrist. The Financial Accelerator in a Quantitative Business Cycle Framework. In John Taylor and Michael Woodford, editors, Handbook
of Macroeconomics, volume 1C, pages 1341–1393. Elsevier, 1999.
[10] Markus Brunnermeier and Yuliy Sannikov. A Macroeconomic Model with a Financial Sector.
Mimeo, Princeton University, 2010.
[11] Francisco Buera. A Dynamic Model of Entrepreneurship with Borrowing Constraints: Theory and Evidence. Annals of Finance, 5(3-4):443–464, Jun 2009.
[12] Francisco Buera and Yongseok Shin. Financial Frictions and the Persistence of History: A
Quantitative Exploration. Mimeo, UCLA.
42
[13] Marco Cagetti and Mariacristina De Nardi. Entrepreneurship, Frictions, and Wealth. Journal of Political Economy, 114(5):835–870, October 2006.
[14] Marco Cagetti and Mariacristina De Nardi. Estate Taxation, Entrepreneurship, and Wealth.
American Economic Review, 99(1):85–111, 2009.
[15] Ana Castañeda, Javier Dı́az-Giménez, and José-Victor Rı́os-Rull. Accounting for the U.S.
Earnings and Wealth Inequality. Journal of Political Economy, 111(4):818–857, Aug 2003.
[16] Lawrence Christiano, Roberto Motto, and Massimo Rostagno. Financial Factors in Economic Fluctuations. Working Paper 1192, European Central Bank, May 2010.
[17] Thomas Cooley, Ramon Marimon, and Vincenzo Quadrini. Aggregate Consequences of
Limited Contract Enforceability. Journal of Political Economy, 112(4):817–847, Aug 2004.
[18] Francisco Covas and Shigeru Fujita. Private Risk Premium and Aggregate Uncertainty in
the Model of Uninsurable Investment Risk. Working Paper 07-30, Federal Reserve Bank of
Philadelphia, 2007.
[19] Vasco Curdia and Michael Woodford. Credit Spreads and Monetary Policy. Staff Report
385, Federal Reserve Bank of New York, Aug 2009.
[20] Mariacristina De Nardi. Wealth Inequality and Intergenerational Links. Review of Economic
Studies, 71(3):743–768, July 2004.
[21] Mark Gertler and Simon Gilchrist. Monetary Policy, Business Cycles, and the Behaviour of
Small Manufacturing Firms. The QuarterLy Journal of Economics, 109(2):309–340, 1994.
[22] Mark Gertler and Nobuhiro Kiyotaki. Financial Intermediation and Credit Policy in Business Cycle Analysis. In Benjamin M. Friedman and Michael Woodford, editors, Handbook
of Monetary Economics. Elsevier, Forthcoming.
[23] Simon Gilchrist, Jae Sim, and Egon Zakrajsek. Uncertainty, Financial Frictions, and Investment Dynamics. Mimeo, Boston University, 2010.
43
[24] Douglas Gollin. Getting Income Shares Right. Journal of Political Economy, 110(2):458–
474, April 2002.
[25] Miguel Gouveia and Robert P. Strauss. Effective Federal Individual Income Tax Functions:
An Exploratory Empirical Analysis. National Tax Journal, 47(2):317–339, June 1994.
[26] Robert E. Hall. The High Sensitivity of Economic Activity to Financial Frictions. Mimeo,
Stanford University, 2009.
[27] John Heaton and Deborah Lucas. Portfolio Choice and Asset Prices: The Importance of
Entrepreneurial Risk. Journal of Finance, 55(3):1163–1198, Jun 2000.
[28] Mark Huggett. Wealth Distribution in Life-cycle Economies. Journal of Monetary Economics, 38(3):469–494, December 1996.
[29] Urban Jermann and Vincenzo Quadrini. Macroeconomic Effects of Financial Shocks. Discussion Paper 7451, CEPR, 2009.
[30] Urban J. Jermann and Vincenzo Quadrini. Stock market boom and the productivity gains
of the 1990s. Journal of Monetary Economics, 54(2):413–432, 2007.
[31] Timothy J. Kehoe and David K. Levine. Debt-constrained Asset Markets. Review of Economic Studies, 60(4):865–888, October 1993.
[32] Aubhik Khan and Julia Thomas. Credit Shocks and Aggregate Fluctuations in an Economy
with Production Heterogeneity. Mimeo, Ohio State University, 2011.
[33] Sagiri Kitao. Entrepreneurship, Taxation, and Capital Investment. Review of Economic
Dynamics, 11(1):44–69, Jan 2008.
[34] Nobuhiro Kiyotaki and John Moore.
Credit Cycles.
105(2):211–248, Apr 1997.
44
Journal of Political Economy,
[35] Laurence J. Kotlikoff, Kent A. Smetters, and Jan Walliser. Privatizing Social Security in
the United States: Comparing the Options. Review of Economic Dynamics, 2(3):532–574,
July 1999.
[36] Arvind Krishnamurthy. Amplification Mechanisms in Liquidity Crises. American Economic
Journal: Macroeconomics, Forthcoming 2010.
[37] Arvind Krishnamurthy and Annette Vissing-Jorgensen. The Demand for Treasury Debt.
Working Paper 12881, NBER, 2007.
[38] Lee A. Lillard and Robert J. Willis. Dynamic Aspects of Earning Mobility. Econometrica,
46(5):985–1012, September 1978.
[39] Robert E. Lucas, Jr. On the Size Distribution of Business Firms. The Bell Journal of
Economics, 9(2):508–523, 1978.
[40] Césaire Meh. Entrepreneurship, Wealth Inequality, and Taxation. Review of Economic
Dynamics, 8(3):688–719, Jul 2005.
[41] Alexander Monge. Entrepreneurship and Firm Heterogeneity under Limited Commitment.
Annals of Finance, 5(3-4):465–494, 2009.
[42] Vincenzo Quadrini. The Importance of Entrepreneurship for Wealth Concentration and
Mobility. Review of Income and Wealth, 45(1):1–19, Mar 1999.
[43] Vincenzo Quadrini. Entrepreneurship, Saving, and Social Mobility. Review of Economic
Dynamics, 3(1):1–40, 2000.
[44] Vincenzo Quadrini and José-Victor Rı́os-Rull. Models of the Distribution of Wealth. Federal
Reserve Bank of Minneapolis Quarterly Review, 21(2):1–21, Spring 1997.
[45] Nikolai Roussanov. Diversification and Its Discontents: Idiosyncratic and Entrepreneurial
Risk in the Quest for Social Status. Journal of Finance, Forthcoming 2010.
45
[46] Nancy L. Stokey and Sergio Rebelo. Growth Effects of Flat-Rate Taxes. Journal of Political
Economy, 103(3):519–550, June 1995.
[47] George Tauchen and Robert Hussey. Quadrature-Based Methods for Obtaining Approximate
Solutions to Nonlinear Asset Pricing Models. Econometrica, 59(2):371–396, March 1991.
46
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