Reorganization or Liquidation:
Bankruptcy Choice and Firm Dynamics∗
Dean Corbae
Pablo D’Erasmo
University of Wisconsin - Madison
FRB Philadelphia and
and NBER
University of Maryland
This Version: March 5, 2014
Abstract
In this paper, we ask how bankruptcy law affects the financial decisions of corporations and
its implications for firm dynamics. According to US law, firms have two bankruptcy options:
Chapter 7 liquidation and Chapter 11 reorganization. Under Chapter 7, the proceeds from
liquidating corporate assets are used to repay debt and bankruptcy costs and limited liability
exempts corporate shareholders for the excess losses. In the other case, when firms reorganize
under Chapter 11, bankruptcy law determines the negotiation rules over the fraction of debt
that is repaid, the reorganized corporation retains its assets and continues to operate. We
extend the basic firm dynamics model with endogenous entry and exit and costly equity finance
to include both bankruptcy options. We find that changes to the law can have significant
consequences for borrowing costs, capital structure, and firm dynamics.
∗
Preliminary and Incomplete. We thank Vincenzo Quadrini for helpful comments.
1
1
Introduction
According to (p.524) Aghion, Hart, and Moore [2] Western bankruptcy procedures “are thought
either to cause the liquidation of healthy firms (as in Chapter 7 of the U.S. Bankruptcy Code)
or to be inefficient and biased toward reorganization under incumbent management (as in
Chapter 11 in the United States).” They add there is no “consensus about how to improve these
procedures.” To asses the implications of bankruptcy procedures for firm value and industry
dynamics, we propose a structural corporate finance model which includes both options (as in
the data) and consider counterfactuals without these procedures.
Under US bankruptcy law, firms have two bankruptcy options: Chapter 7 liquidation and
Chapter 11 reorganization. Under Chapter 7, the proceeds of liquidating the corporation’s
assets are used to repay debt and cover bankruptcy costs. Limited liability exempts corporate
shareholders from liability for the corporation’s debt beyond liquidation value. When firms
reorganize under Chapter 11, on the other hand, bankruptcy law determines the negotiation
rules over the fraction of debt that is repaid, the reorganized corporation retains its assets and
continues to operate.
There are several studies which document heterogeneity among firms which choose Chapter
7 and Chapter 11 bankruptcy. One of the more recent papers is by Bris, Welch and Zhu [5]
who provide a comprehensive study of the costs of Chapter 7 versus Chapter 11 in a sample
of 300 public and private firms in Arizona and New York from 1995-2001. Reorganization by
Chapter 11 comprises 80% of their sample. Chapter 11 firms are substantially larger in terms
of assets, have a larger fraction of secured debt, and have roughly similar debt to asset ratios
to Chapter 7 (see their Table 1). Importantly, their paper documents substantial differences in
recovery rates. In particular, the median (mean) recovery rate (as a percentage of the initial
claim) is 0% (5.4%) for Chapter 7 while it is 79.2% (69.4%) for Chapter 11. Further, the
fraction of firms which have 0% recovery is 79% for Chapter 7 and 0% for Chapter 11.
As Bris, et. al. [5] point out, whether a corporation files for Chapter 7 or Chapter 11 is
endogenous and self-selection can contaminate the estimation of bankruptcy costs. In particular, if firms self-select, then it could be misleading to compare the cost of procedures, without
controlling for endogeneity of chapter choice. The authors carefully attempt to control for the
self-selection into bankruptcy chapter (Chapter 7 or Chapter 11) in their regressions.
To understand the determinants of corporate bankruptcy choices and complement empirical
studies like Bris, et. al. [5], we extend the basic structural corporate finance models of Cooley
and Quadrini [7], Gomes [11], and Hennessy and Whited [13] to incorporate a nontrivial
bankruptcy choice.1 We compare firm dynamics and productivity between a model where
both bankruptcy options are available to counterfactuals without both options to evaluate
1
Other closely related papers include Arellano, Bai and Zhang [3], Broadie, Chernov, and Sundaresan [?],
D’Erasmo and Moscoso Boedo [8], Eraslan [10], Khan, Senga, and Thomas [15], Meh and Terajima [16].
2
possible inefficiencies of such policies. Adding a nontrivial bankruptcy choice to an environment
where cash flows can turn negative (due to fixed costs as in Hopenhayn [14]) has important
implications beyond the selection issues raised above. For instance, it implies that liquidation
arises in equilibrium for a subset of firms in our model, while it does not in Cooley and
Quadrini [7] nor Hennessy and Whited [13]. It even shows up methodologically since with
liquidation costs which depend on the amount of collateral, here we must expand the state
space and cannot simply use net worth. Interestingly, we find that a change in bankruptcy
laws (getting rid of one of the bankruptcy options) can have a significant impact on interest
rates, equilibrium capital structure, and welfare. Since we cons
2
Bankruptcy Facts from Compustat
Given the fact that the vast majority of empirical corporate finance papers use data from
Compustat, we organize bankruptcy facts using Compustat data from 1980-2012. This is
obviously a different sample than that in Bris, et. al. [5]. Certain of our facts are similar
to those in Bris, et. al. [5] (e.g. the fraction of Chapter 11 bankruptcies relative to the
total number of bankruptcies) while other facts differ (firms are more highly levered in their
sample). We note, however, that there can be substantial differences in reported bankruptcy
facts across datasets. For instance, bankruptcy statistics on all business filings from the U.S.
Courts (http://www.uscourts.gov/Statistics/BankruptcyStatistics.aspx) suggest that the Bris,
et. al. [5] sample as well as ours overstates the proportion of Chapter 11 business bankruptcies.
For instance, in the U.S. Courts dataset (which includes smaller firms), the fraction of Chapter
11 business bankruptcies to total business bankruptcies was roughly 25% for the year ending
in December 2013.
Besides simply comparing characteristics of firms in the state of bankruptcy as in [5] or the
U.S. Courts, here we also compare characteristics of firms that are not bankrupt to those which
are bankrupt. Table 1 displays a summary of some key differences between Chapter 7, Chapter
11 and Non-Bankrupt firm variables which have analogues in our model (see Appendix A1 for
a detailed description of the data). Since there can be substantial differences between the
median and mean of these variables, the table provides both. In Figures 1 and 2 we graph the
conditional distributions of some of the key variables in the model. Further, we test whether
the means differ between Chapter 7, Chapter 11, and Non-bankrupt.
3
Table 1: Balance Sheet and Corporate Bankruptcies 1980-2012
Moment
Frequency of Exit (%)
Fraction of Exit by Ch 7 (%)
Frequency of (all) Bankruptcy (%)
Fraction of Chapter 11 Bankruptcy (%)
0.71
59.23
0.87
80.82
Non-Bankrupt
Chapter 11
Chapter 7
Avg. Median
Avg.
Median
Avg.
Median
Capital (millions 1983$)
356.46
29.00
370.13∗,∗∗∗ 112.66
80.71∗∗
22.94
∗∗∗
∗∗
Cash (millions 1983$)
50.97
8.13
50.82
11.30
11.37
3.41
366.55
46.97
409.83∗∗∗
128.05
92.34∗∗
34.29
Assets (millions 1983$)
Op. Income (EBITDA) / Assets (%)
10.88
16.31
-22.27∗
0.06
-22.70∗∗
-3.63
∗
∗∗
40.95
26.98
62.59
45.58
61.83
46.63
Net Debt / Assets (%)
61.11
39.83
78.49∗
59.22
80.29∗∗
61.70
Total Debt / Assets (%)
∗
∗∗
Frac. Firms with Negative Net Debt (%) 26.26
17.49
18.37
45.71
43.79
50.75∗
50.79
46.93
45.46
Secured Debt / Total Debt (%)
Interest Coverage (EBITDA/Interest)
13.74
4.54
-1.21∗
0.25
-7.15∗∗
-0.35
17.35
2.01
21.37
5.54
16.13
2.97
Equity Issuance / Assets (%)
Fraction Firms Issuing Equity (%)
48.00
44.45
40.00
1.14
0.41
-6.24∗
-5.78
-6.90∗∗
-4.98
Net Investment / Assets (%)
9.24
3.42
5.74∗,∗∗∗
1.63
12.66
2.51
Dividend / Assets (%)
Z-score
4.02
3.27
0.46∗,∗∗∗
0.77
1.37∗∗
1.35
∗
∗∗
0.88
0.00
1.54
0.19
1.51
0.21
DD Prob. of Default (%)
Note: See appendix A1 for a detailed definition of variables and the construction of bankruptcy and exit
indicators. Medians (and means) reported in the table correspond to the time series average of the
cross-sectional median (mean) obtained for every year in our sample. Test for differences in means at 5%
level of significance: ∗ means Chapter 11 different from Non-bankrupt, ∗∗ means Chapter 7 different from
Non-bankrupt, ∗∗∗ means Chapter 11 different from Chapter 7.
Chapter 7 in Table 1 corresponds to values for the final observation of a firm that exits
via a Chapter 7 bankruptcy. Chapter 11 refers to an observation in the initial period of a
Chapter 11 bankruptcy. Non-bankrupt identifies annual observations of firms that are not in
the state of bankruptcy (i.e. firms which never declare bankruptcy as well as observations of
firms before they declare bankruptcy excluding the above). To be consistent with the way that
the U.S. Bureau of the Census uses to construct its exit statistics, a deleted firm (i.e. a firm
that disappears from our sample) is counted as a firm that exits if its deletion code is not 01,
02, 04, 07, 09 or 10 . For example, this means that firms which are acquired or go from public
to private are not counted as exiting. In the Appendix, we provide more information about
the frequencies of those events.
4
Figure 1: Distribution of Debt/Assets and EBITDA/Assets
Distribution Debt / Assets
Non−Bankrupt
Chapter 11
Chapter 7
debt/assets
3
2
1
0
1
5
10
25 median 75
90
percentiles distribution Debt/Assets
95
99
95
99
Distribution EBITDA / Assets
Non−Bankrupt
Chapter 11
Chapter 7
EBITDA/assets
1
0
−1
−2
−3
1
5
10
25 median 75
90
percentiles distribution EBITDA/Assets
Table 1 documents that exit rates (fraction of deletions to all firms in a given year) are
small (0.7%) in our sample and 60% of exits are by Chapter 7 liquidation. The fraction of all
firms declaring bankruptcy is also small (0.87%) in our sample and 81% of bankruptcies are
by Chapter 11 (as in [5]).
Since firms in our model choose physical capital and net debt (total debt minus cash),
we examine differences in size measured by total assets (capital plus cash) as well as its
composition. Chapter 11 firms are bigger than Non-bankrupt firms which in turn are bigger
than Chapter 7 firms. In all cases, the differences in mean are statistically significant.
Earnings before interest, taxes, depreciation, and amortization (EBITDA) measures a firm’s
profitability. Negative values generally indicate a firm has fundamental profitability issues,
while a positive value does not necessarily mean it is profitable since it generally ignores
changes in working capital as well as the other terms described above. The median and mean
ratio of EBITDA to assets is in general negative for both Chapter 11 and Chapter 7 firms, while
it is positive for Non-bankrupt firms. The differences in mean between bankrupt and Nonbankrupt are statistically significant, while there are not statistically significant differences
across bankruptcy type. These statistics accord well with the idea that bankrupt firms have
5
profitability problems.
We provide several measures of leverage. Net debt is measured as debt minus cash, where
negative values imply that the firm is liquid. We find that both median and mean net debt or
total debt to assets are highest for Chapter 11 and lowest for Non-bankrupt firms. Statistical
significance of differences in mean leverage exist only between bankrupt and Non-bankrupt,
but not across bankruptcy type. The time average of the fraction of firms with negative net
debt (i.e. liquid firms) is highest for Non-bankrupt and similar for bankrupt firms. There is
a statistically significant difference in means between bankrupt and Non-bankrupt. The ratio
of secured to total debt is highest for Chapter 11 and lowest for nonbankrupt firms. There
is only a statistically significant difference in means between Chapter 11 and Non-bankrupt.
Interest coverage is measured as the ratio of EBITDA to interest expenses. It is generally
thought that a ratio less than one is not sustainable for long. Here we see that both mean
and median interest coverage is positive and large for nonbankrupt firms while it is in general
negative for bankrupt firms. There are insignificant statistical differences in mean between the
two bankruptcy choices, but the differences are statistically significant between bankrupt and
Non-bankrupt.
While equity issuance is highest for Chapter 11, all means are insignificant statistically. The
time average of the fraction of firms issuing equity in any given period is lower for bankrupt
firms than Non-bankrupts, but the differences are not statistically significant.
Median and average net investment (gross investment minus depreciation) is positive for
Nonbankrupt firms and negative for bankrupt firms. The differences between bankrupt and
Non-bankrupt are statistically significant, but insignificant between bankruptcy types. Median
dividend payouts are highest for nonbankrupt firms and lowest for Chapter 11 firms. In terms
of means, there is a statistically significant difference between Chapter 11 and other types of
firms.
We also consider two well accepted measures of corporate default probabilities from the
finance literature: “z-scores” and “distance-to-default (DD)”. The Altman [1] z-score is a linear
combination of five common firm level ratios: working capital to assets, retained earnings
to assets, earnings before interest and taxes, market value of equity to book value of total
liabilities, and sales to total assets. While simplistic, Altman’s z-score is widely used by
practitioner’s as a predictor of default within the next two years with values greater than 2.9
safe while values less than 1 indicative of distress. Table 1 documents that both the median
and average z-score for nonbankrupt firms exceeds 3, while z-scores for both Chapter 7 and 11
are generally below 1. All differences in mean are statistically significant. The DD measure
is based upon an estimate of the asset value and volatility of a firm using an option pricing
model, along with the observed book value of debt and market value of equity. To compute
estimates of asset value and volatility we use an iterative procedure as in Duffie, et. al. [9]
6
(see Appendix for a full description of the construction of DD). Table 1 documents that the
average DD is at least double for firms we classify as bankrupt than nonbankrupts, but in
general all DD measures are relatively low.
Figure 2: Distribution of Net. Investment/Assets and z-scores
Distribution Net Inv. / Assets
Net Inv./assets
0.3
Non−Bankrupt
Chapter 11
Chapter 7
0.2
0.1
0
−0.1
−0.2
−0.3
1
5
10
25 median 75
90
percentiles distribution Net Inv./Assets
95
99
95
99
Distribution z−scores
20
Non−Bankrupt
Chapter 11
Chapter 7
z−scores
15
10
5
0
−5
1
5
10
25 median 75
90
percentiles distribution z−scores
In summary, nonbankrupt firms: (i) are similar in size to Ch 11 while bigger than Ch 7; (ii)
are profitable while bankrupt firms are not; (iii) have lower leverage than bankrupt firms; (iv)
have lower interest expenses relative to their cash flow; (v) do not have statistically significant
differences in equity issuance; (vi) have positive net investment as opposed to negative net
investment for bankrupt firms; (vii) have higher dividend payouts than bankrupt firms; and
(viii) have lower likelihoods of default as measured by practitioner’s “models” of default.
Further, in terms of statistical significance, there is resounding support for differences between
bankrupt and Non-bankrupt firms but less so between firms which choose Chapter 11 versus
Chapter 7. This latter result could be due to the small sample size of bankrupt firms.
7
3
Environment
We consider a discrete time, general equilibrium model where heterogeneous firms produce
a homogeneous good and issue short term defaultable debt and costly equity to undertake
investment and dividend choices. Since firms can choose chapter 7 or chapter 13 bankruptcy,
competitive lenders must attempt to predict default decisions of the firms they are lending
to when determining the price of debt. There is a representative household which maximizes
lieftime utility and whose income comes from wages and dividends on the shares that the household holds in every firm. We will focus our attention on a stationary equilibrium characterized
by a measure of firms endogenously distributed across capital and net debt.
3.1
Firms and Technology
Competitive firms produce a homogeneous good that can be consumed by households or can
be used as capital. Firm j maximizes the expected discounted value of dividends
E0
∞
X
(1 + r)−t djt
(1)
t=0
where djt denotes dividends in period t and (1 + r)−1 is the discount rate of the firm.2 Firms
have access to a decreasing returns to scale production technology
ν
α 1−α
, α ∈ (0, 1), ν ∈ (0, 1)
njt
yjt = zjt kjt
(2)
where zjt ∈ Z ≡ {z 1 , . . . , z n }, is an idiosyncratic productivity shock, i.i.d. across firms, that
follows a first order Markov Process with transition matrix G(zjt+1 |zjt ), njt ∈ R+ is labor
input, and kjt ∈ K ⊂ R+ is capital input. There is a fixed cost of production cf , measured in
units of output. Firms must pay this fixed cost in order to produce. Active firms own their
capital and decide the optimal level of gross investment igjt = kjt+1 − (1 − δ)kjt = injt + δkjt
where injt is net investment.
In any given period, firm j’s operating income (EBITDA) are given by
πjt = yjt − wt njt − cf
(3)
where wt is the competitively determined real wage. Inputs can be financed from three sources:
(i) one period non-contingent debt bjt+1 ∈ B ⊂ R at discounted price qjt ; (ii) current cash
flow and internal savings; and (iii) external equity at cost λ per unit of funds raised (so firms
will never find it optimal to simultaneously pay dividends and issue equity). Taxable income
2
Since there are no aggregate shocks in this model, to conserve on notation here we define the objective using a
constant discount rate, which is consistent in equilibrium.
8
is Υjt = πjt − δkjt −
1
qjt
bjt+1
− 1 (1+r)
(i.e. operating profits less economic depreciation less
discounted interest expense) and corporate taxes are
Tjtc = I{Υjt ≥0} τc · Υjt
(4)
where I{·} is the indicator function that takes value one if the condition in brackets holds and
zero otherwise.3
The after-tax net cash flow to equity holders is given by
djt =
(
(1 − τd )ejt
if ejt ≥ 0
ejt − λ(ejt ) if ejt < 0
(5)
where
ejt = πjt − Tjtc − ijt − bjt + qjt bjt+1 .
(6)
In particular, firms pay dividends if ejt ≥ 0 which incurs dividend taxes τd . If ejt < 0, firms pay
external finance costs λ(ejt ), assumed to be a quadratic function. Note that provided
taxable
income is positive, the tax benefit of a unit of debt is given by (1−τd )·τc q1jt − 1 /(1+r) > 0.
Firms can enter by paying a cost κ. After paying this cost, which is financed by either equity
or debt issue, firms observe their initial level of productivity zj0 drawn from the stationary
distribution G(z) derived from G(zjt+1 |zjt ).
3.2
Financial Markets
Firms finance operations either through debt or equity. Equity issuance costs are a quadratic
function λ(ejt ) of the amount of equity issued and we normalize the number of shares per firm
to 1. A share is a divisible claim on the dividends of the firm.
Competitive lenders have access to one period risk free discount bonds at after-tax price qtB .
Loans mature each period and their price qjt depends on how much the firm borrows bjt+1 as
well as other characteristics like firm capital holdings kjt+1 (since this affects liquidation value)
and current productivity zjt . Debt is non-contingent in the sense that it does not depend on
future zjt+1 .4
A firm can choose to exit (without default) at any point in time. In this case, the firm
liquidates its assets (we assume at par) and pays its debts in full. Alternatively, firms are
allowed to default on their debt triggering a bankruptcy procedure. To resemble the actual
3
As in Strebulaev and Whited [17] we assume the firm takes the present value of the interest tax deduction in the
period in which it issues debt. This allows us to avoid adding another state variable. Further, for simplicity, unlike
Hennessy and Whited [13] we assume there are no loss limitations (i.e. τc+ = τc− = τc ).
4
Our use of equilibrium price menus which depend on agent characteristics in the presence of default in a quantitative model is similar to that in Chatterjee, et. al. [6] and Hennessy and Whited [13].
9
law, we allow for two default options:
1. Chapter 7 liquidation: Firm j liquidates its assets at firesale discount s < 1 which it
uses to pay debts, incurs a bankruptcy cost c7 , and exits. Shareholders obtain (pre-tax):
max{skjt − bjt − c7 , 0}. Lenders obtain: min{bjt , max{skjt − c7 , 0}}.
2. Chapter 11 reorganization: Firm j and lenders renegotiate the defaulted debt, bargain over the repayment fraction φjt (where the firm’s bargaining weight is given by θ),
the firm pays bankruptcy cost c11 , reduces its debt to φjt bjt (where φjt ∈ [0, 1]), faces
equity finance costs λ11 (ejt ), debt finance costs λb11 ≤ 1, and continues operating (i.e.
does not exit).
When making a loan to a firm, lenders take into account that in the case of default they
can recover up to a fraction of the original loan. As described above, the recovery rate of a
loan depends on the bankruptcy procedure chosen by the firm. In the case of a Chapter 7
liquidation, when making a loan of size bjt in period t, lenders can expect to recover in period
t + 1, min bjt+1 , max{skjt+1 − c7 , 0}} where s is the scrap price of the firm’s capital (which
serves as collateral).5 If the firm chooses to reorganize (i.e., Chapter 11), the recovery rate in
period t + 1 will be φjt+1 , that is lenders will recover the fraction of the debt that they agree
upon the reorganization process. We assume the negotiation over recovery rate solves a Nash
Bargaining problem where the firm’s weight is θ and the lender’s weight is 1 − θ.
3.3
Households
In any period t, households choose a stream of consumption Ct , shares {Sjt+1 }j of incumbent
and entrant firms, and risk free bonds Bt+1 to maximize the expected present discounted value
of utility given by
max E0
"∞
X
#
β t U (Ct )
t=0
(7)
subject to
Ct +
Z
pjt Sjt+1 dj + qtB Bt+1 = wt +
Z
(pjt + djt ) Sjt dj + Bt + Tth
(8)
where pjt is the after dividend stock price of firm j, qtB is the after-tax price of the risk free
discount bond, and Tth are lump sum taxes/transfers for households. The marginal income
tax τi applied to wage and interest earnings is rebated back to households in Tth . It should
be understood that the stock price of a firm which exits is taken to be zero and that since
preferences do not include leisure, households supply their unit of labor inelastically.
5
Hennesy and Whited [12] make a similar assumption. Stromberg [18] finds that asset fire sales and resales to
management can lead to low salvage values and striking inefficiencies in the Chapter 7 procedure.
10
3.4
Timing
In this section, we describe the timing of the model. At the beginning of period t:
1. Productivity zjt is realized. The state space for incumbent firm j is given by {zjt , kjt , bjt }.
2. Exit or Continuation decision for incumbent firms.
• If the firm chooses to exit, it chooses whether to exit by Chapter 7 liquidation
incurring costs (c7 , s) and paying “final dividends” djt = (1−τi ) max{skjt −bjt −c7 , 0}
or by repaying debt in full and paying “final dividends” djt = (1 − τi ) (kjt − bjt ) if
kjt ≥ bjt and djt = (1 + λ)(kjt − bjt ) otherwise.
• If the firm chooses to continue, it chooses whether to repay debt in full or to start a
Chapter 11 reorganization process.
– If firm j chooses to repay its debt in full, it pays back the lenders bjt and chooses
the amount of capital kjt+1 for the following period. The firm has access to
internal funds, debt bjt+1 at price q(kjt+1 , bjt+1 , zjt ) and equity issuance cost λ.
– If the firm chooses to reorganize, it bargains with lenders over a recovery rate φjt
and incurs costs c11 . Once the firm and lenders agree on a recovery rate, the firm
repays φjt bjt and chooses an amount of capital kjt+1 for the following period.
The firm has access to internal funds, debt bjt+1 at price λb11 q(kjt+1 , bjt+1 , zjt )
and equity issuance with costs λ11 (ejt ).
3. Entry decision. Potential entrants decide whether to start a firm or not. If they enter,
they pay the entry cost κ and choose their initial level of capital by issuing equity at cost
λE (ejt ) or debt. The initial productivity shock is drawn from G(z).
4. Households choose shares and bonds, which given earnings and taxes determines their
consumption. If the household chooses to purchase the stock of an entrant, then Sjt+1 =
Sjt and djt = −kjt+1 + q(kjt+1 , bjt+1 )bjt+1 − κ − λE (−kjt+1 + q(kjt+1 , bjt+1 )bjt+1 − κ).
4
Equilibrium
We consider only stationary equilibria of the model. In what follows we use the notation that
xt = x and xt+1 = x′ . Rather than refer to a given firm by its name j, it will be named by
its place in the cross-sectional distribution of firms Γ(z, k, b). To save on notation, we avoid
making the dependence of decision rules on prices explicit.
11
4.1
Recursive Representation of the Firm’s Problem
An incumbent firm starts the period with capital k, debt b and productivity z. Then, it decides
to operate the technology or exit. The value of the firm V (z, k, b) is defined as follows:
V (z, k, b) = max V x (z, k, b)
x∈{0,1}
(9)
where x = 0 denotes the decision to stay in the market and x = 1 corresponds to the exit
value.
A firm which chooses to stay (x = 0) still must choose whether it wants to reorganize via
Chapter 11 or not (ξ ∈ {0, 11}):
V 0 (z, k, b) = max Vξ0 (z, k, b)
ξ∈{0,11}
(10)
If the firm chooses to pay in full (ξ = 0):
V00 (z, k, b) =
max
′
n≥0,k ≥0,b′
n
o
d + (1 + r)−1 Ez ′ |z [V (z ′ , k′ , b′ )]
(11)
s.t.
e = π − T c (k, z, k′ , b′ ) − (k′ − (1 − δ)k) − b + q(b′ , k′ , z)b′
(
(1 − τd )e if e ≥ 0
d=
e − λ(e) if e < 0
We denote the optimal labor, capital, debt, and dividend decision rules by n = hn0 (z, k, b),
k′ = hk0 (z, k, b), b′ = hb0 (z, k, b), and d = hd0 (z, k, b), respectively.
If the firm chooses to reorganize under Chapter 11 bankruptcy (ξ = 11), we can define
payoffs taking as given the recovery rate φ(z, k, b) which will be determined by Nash bargaining
in subsection 4.4 below as:
0
V11
(z, k, b) =
max
′
n
o
−1
′ ′ ′
′ |z [V (z , k , b )]
d
+
(1
+
r)
E
z
′
n≥0,k ≥0,b
(12)
s.t.
e = π − T c (k, z, k ′ , b′ ) − (k′ − (1 − δ)k) − φ(z, k, b)b + λb11 q(k′ , b′ , z)b′ − c11
(
(1 − τd )e if e ≥ 0
d=
e − λ11 (e) if e < 0
We allow the external finance costs λb11 and λ11 (e) to differ for a firm under reorganization.
We denote the optimal labor, capital, debt, and dividend decision rules by n = hn11 (z, k, b),
k′ = hk11 (z, k, b), b′ = hb11 (z, k, b), and d = hd11 (z, k, b) respectively.
Alternatively, if the firm chooses to exit (x = 1), it still must choose whether it wants to
12
declare Chapter 7 bankruptcy or repay its debt (χ ∈ {0, 7}):
V 1 (z, k, b) = max Vχ1 (z, k, b)
(13)
χ∈{0,7}
where V01 (z, k, b) denotes the value of exit without default and V71 (z, k, b) the value of Chapter
7 liquidation. In the event of exiting without default, the dividend policy implies
V01 (z, k, b)
=
(
(1 − τi )(k − b)
if k ≥ b
k − b − λ(k − b) if k < b
.
(14)
That is, if the firm wishes to exit without using the limited liability benefit that Chapter 7
provides in the event of k < b, it must pay off its debt by an equity infusion.6 In the event of
default, the policy implies
V71 (z, k, b) = (1 − τi ) max{sk − b − c7 , 0}.
4.2
(15)
Entrants
In order to draw an initial productivity z0 , potential entrants must pay κ. New firms are
created with an initial value of equity raised by issuing new shares and debt. The value of a
potential entrant is given by:
o
n
X
′
−1
′ ′
)
d
+
(1
+
r)
V
(z
,
k
,
0)G(z
VE = max
E
′
′
(16)
′
′
′
′
dE = −kE
+ q(kE
, b′E )b′E − κ − λE (−kE
+ q(kE
, b′E )b′E − κ).
(17)
k ≥0,b
z′
where
′ and b′ .
We denote the optimal capital and borrowing decision rules by kE
E
4.3
Lender’s Problem
Lenders pool risky corporate loans and borrow from households in the risk free market at price
q B . The profit on a loan of size b′ has two important components. First, the probability of
default Λ(b′ , k′ , z) given by:
Λ(b′ , k′ , z) =
{z ′ ∈D
6
7
X
(k ′ ,b′ )}∪{z ′ ∈D
Obviously, this won’t happen in equilibrium.
13
G(z ′ |z),
11
(k ′ ,b′ )}
(18)
where D7 (k, b) and D11 (k, b) denote the Chapter 7 and Chapter 11 default sets respectively
defined as:
z ∈ Z : x(z, k, b) = 1 & χ(z, k, b) = 7 ,
D11 (k, b) = z ∈ Z : x(z, k, b) = 0 & ξ(z, k, b) = 11 .
D7 (k, b) =
The second important component of a lender’s profit is the expected recovery rate. If the
firm chooses to file for Chapter 7 bankruptcy the lender recovers min b′ , max{sk′ − c7 , 0}}. If
the firm chooses to reorganize under Chapter 11 the lender will recover φ(z ′ , k′ , b′ )b′ which is
the solution to a bargaining game between the firm and the lender. Thus, we can write the
lender’s profit function as follows:
Ω(b′ , k′ , z) = −q(b′ , k′ , z)b′ + q B [1 − Λ(b′ , k′ , z)]b′
X
min b′ , max{sk′ − c7 , 0}}G(z ′ |z)
+q B
(19)
z ′ ∈D7 (k ′ ,b′ )
+q B
X
φ(k′ , b′ , z ′ )b′ G(z ′ |z).
z ′ ∈D11 (k ′ ,b′ )
4.4
Reorganization
Upon reaching a bargaining agreement, the value of defaulted debt is reduced to a fraction ϕ
of the unpaid debt b. The value of an agreement of size ϕ to the firm is:
n
o
−1
′ ′ ′
′
d
+
(1
+
r)
E
[V
(k
,
b
,
z
)]
V R (z, k, b; ϕ) = max
z |z
′ ′
n,b ,k
s.t.
e = π − T c (k, z, k′ , b′ ) − (k′ − (1 − δ)k) − φb + λb11 q(k′ , b′ , z)b′ − c11
(
(1 − τd )e if e ≥ 0
d=
e − λ11 (e) if e < 0
After the repayment of a fraction ϕ of debt, the firm chooses the optimal level of investment,
can issue debt or equity which may cost a different amount during renegotiation, and continues
operating.
Since either the borrower or lender in the renegotiation phase of Chapter 11 have a right
to declare Chapter 7 bankruptcy, we assume that the threat points are equal to the payoffs
14
associated with Chapter 7 liquidation.7 In that case, the surplus for the firm is
W R (z, k, b; ϕ) = V R (z, k, b; ϕ) − (1 − τi ) max{sk − b − c7 , 0}.
(20)
Since the value of an agreement for the lender is ϕb (i.e., the recovery on defaulted debt), the
surplus for the lender is:
W L (z, k, b; ϕ) = ϕb − min b, max{sk − c7 , 0}}.
(21)
The recovery rate is then the solution to the following Nash Bargaining problem:
φ(z, k, b) ≡ arg max [W R (z, k, b; ϕ)]θ [W L (z, k, b; ϕ)]1−θ
ϕ∈[0,1]
(22)
s.t.
W R (z, k, b; ϕ) ≥ 0,
W L (z, k, b; ϕ) ≥ 0.
4.5
Household’s problem
The first order conditions for the household’s problem (7)-(8) are given by
Bt+1 : qtB U ′ (Ct ) = βEt U ′ (Ct+1 )
Sjt+1 , ∀j : pjt U ′ (Ct ) = βEt U ′ (Ct+1 ) (pjt+1 + djt+1 )
In a steady state this implies
qtB = β
(23)
pjt = βEt [pjt+1 + djt+1 ]
(24)
To characterize stock prices, consider the case of an incumbent firm and let p(z, k, b) =
V (z, k, b) − d(z, k, b) as well as (1 + r)−1 = β. Then it is straightforward to show that (24) is
equivalent to (9) or
p(z, k, b)
=
βEz ′ |z p(z ′ , k′ , b′ ) + d(z ′ , k′ , b′ )
(25)
⇐⇒ V (z, k, b) − d(z, k, b) = (1 + r)−1 Ez ′ |z V (z ′ , k′ , b′ )
In the case of purchasing a stock of an entrant, SE = S ′ = S, in which case pj Sjt+1 and pj Sjt
7
See “Conversion or Dismissal” in http://www.uscourts.gov/FederalCourts/Bankruptcy/BankruptcyBasics/Chapter11.aspx
15
cancel and the initial equity injection given by dE in (17) is accounted for in the household’s
budget set (8).
4.6
Cross-Sectional Distribution
Let K0 ⊂ K, B0 ⊂ B and Z0 ⊂ Z. Further, let x(z, k, b) = arg maxx∈{0,1} V x (z, k, b) and
ξ(k, b, z) = arg maxξ∈{0,11} Vξ0 (z, k, b). The law of motion for the cross-sectional distribution of
firms is given by:
Γ′ (K0 , B0 , Z0 ; M, w) =
Z
X
K0 ,B0 Z
0
(Z
X
K,B Z
h
(1 − x(z, k, b)) I{ξ(k,b,z)=0} I{k′ =hk (z,k,b),b′ =hb (z,k,b)}
+I{ξ(k,b,z)=11} I{k′ =hk
b
′
11 (z,k,b),b =h11 (z,k,b)}
+M
X
0
i
′
0
)
G(z |z)Γ(dk, db, z) dk ′ db′
I{kE′ ,b′E } G(z).
(26)
Z0
4.7
Definition of Equilibrium
∗ , Λ∗ , Γ∗ , M ∗ , C ∗ , B ′∗ , S ′∗ , T ∗
A stationary Markov Equilibrium is a list V ∗ , w∗ , r ∗ , q B∗ , q ∗ , φ∗ , p∗ , D7∗ , D11
such that:
1. Given w, r, q, φ, the value function V ∗ is consistent with the firm’s optimization problem
in (11)-(15).
2. Given V, w, r, q, the recovery rate φ∗ (k, b, z) solves the bargaining problem (22).
3. The probability of default Λ∗ in (18) and the sets Di∗ for i = 7, 11 are consistent with
firm decision rules.
4. The equilibrium loan price schedule is such that lenders earn zero profits in expected
value on each contract. That is, at q ∗ (b′ , k′ , z), Ω∗ (b′ , k′ , z) = 0 in (19).
5. The cost of creating a firm is such that VE∗ = 0 in (16).
6. Γ∗ (z, k, b) and M ∗ in (26) is a stationary measure of firms consistent with firm decision
rules and the law of motion for the stochastic variables.
7. Given (w, q B , p) and taxes/tansfers T h , households solve (7)-(8) and (q B∗ , p∗ , r ∗ ) are
consistent with (23)-(25).
16
8. Labor, bond and stock markets clear at w∗ , q B∗ , p∗ or:
Z
Z
hn (z, k, b)dΓ(z, k, b) = 1
hb (z, k, b)dΓ(z, k, b) = B ′∗
S ′∗ = 1
9. Taxes/Transfers satisfy the government budget constraint:
T
h
d
= T +T
B
7
i
+T +T +
Z
K×B
X
(1 − x(k, b, z))T c (k, z)Γ(dk, db, z) − T L (27)
z
where dividend taxes T d are
Z
X
d
(1 − x(k, b, z))I{e(k,b,z)≥0} e(k, b, z)Γ(dk, db, z),
T = τd
K×B
z
taxes on interest earnings T B are
T B = τi qeB
at pre-tax bond price qeB ,
1
−
1
B ′,
qeB
taxes to cover bankruptcy cost of liquidated firms T 7 are
7
T =
Z
K×B
X
8
x(k, b, z)I{ζ=7} max{c7 , sk}Γ(dk, db, z),
z
income taxes on the final distribution by exiting firms T i are
i
T =τ
i
Z
K×B
X
z
x(k, b, z) I{ζ=0} (k − b) + I{ζ=7} max{sk − b − c7 , 0} Γ(dk, db, z),
and taxes necessary to cover ex-post losses associated with bankruptcy T L are
T L = qB
Z
K×B
X
{−Λ(z, k, b)b + min b, max{sk − c7 , 0}} + φ(z, k, b)b}Γ(dk, db, z).
z
8
Note that in general, bankruptcy costs for liquidated firms need to be recovered by taxes only for those firms
that go bankrupt and have sk − b − c7 < 0. However, since this condition always holds in equilibrium we omitted
the corresponding indicator function.
17
Of course, by Walras’ law the household budget constraint (8) implies the goods market
clearing condition is satisfied and aggregate consumption is given by
C = Y − CF − I + Λ + X − BC − E
(28)
where aggregate output is
Y =
Z
K×B
X
(1 − x(k, b, z))z(kα n1−α )ν Γ(dk, db, z),
z
aggregate operating costs are
Z
CF =
K×B
X
(1 − x(k, b, z))cf Γ(dk, db, z),
z
aggregate investment is
I=
Z
K×B
X
z
(1 − x(k, b, z)) k′ − (1 − δ)k Γ(dk, db, z),
aggregate equity issuance costs are
Λ=
Z
K×B
X
(1 − x(k, b, z))I{e(k,b,z)<0} e(k, b, z)(I{ζ=0} λ + I{ζ=11} λe11 )Γ(dk, db, z),
z
final distributions from exiting firms are
X=
Z
K×B
X
z
x(k, b, z) I{ζ=0} (k − b) + I{ζ=7} max{sk − b − c7 , 0} Γ(dk, db, z),
aggregate bankruptcy costs are
BC =
Z
K×B
X
z
(1 − x(k, b, z))I{ζ=11} c11 + x(k, b, z)I{ζ=7} max{c7 , sk} Γ(dk, db, z),
and entrants’ investment and costs are
′
′
′
E = M {kE
+ κ + λE (−kE
+ q(kE
, b′E )b′E − κ)}.
5
Calibration
A summary of the model implied definitions for key variables we observe in the data is given
in Table 2.
18
Table 2: Model Definitions
Variable
Book Value Assets
Capital
Net Debt
Total Debt
Operating Income
Taxable Income
Equity Issuance
Dividends
Gross Investment
Net Investment
Secured Debt
Unsecured Debt
Market Value Assets
Model Expression
k + I{b<0} (−b)
k
b
I{b≥0} b
π =P zk α− cf
π − δk − 1q − 1 b′ /(1 + r)
π − 1q − 1 b′ − T
I{e<0} e
I{d≥0} (1 − τ d )d
ig = k′ − (1 − δ)k
in = ig − δk
I{b≥0} min{sk, b}
I{b≥0} max{0, b − sk}
V (k, b, z) + qb′
We parameterize equity issuance costs as a quadratic function. For the nonbankrupt case
this is:
λ(x) = λ0 + λ1 x + λ2 x2
(29)
E
The function under Chapter 11 and entry is given by λ11
n and λn .
Our model has 21 parameters which appear in Table 3. Those above the line are chosen
outside the model, while those below the line are chosen to match moments within the model.
19
Table 3: Parameter Values
Parameter
Value
Pre-Tax Risk Free Rate
q̃ B 1.02−1
depreciation rate
δ
0.150
capital share
α
0.330
returns to scale
ν
0.850
Corporate Tax Rate
τc
0.350
Dividend Tax Rate
τd
0.060
Income Tax Rate
τi
0.200
11
Debt Cost in Chapter 11
λb
1.000
autocorrelation z
ρz
0.684
0.118
Std. Dev. Shock
σǫ
Fixed Cost Production
cf
0.330
Chapter 7 cost
c7
0.099
Price capital after liquidation s
0.739
Chapter 11 cost
c11 0.078
0.519
Firm’s Bargaining Power
θ
New shares cost
λ2 0.065
New Shares cost in Ch 11
λ11
0.401
2
E
New Shares cost entrant
λ1
0.350
Avg. Firm productivity
µz 1.340
Adjustment Cost
ψ
0.203
Entry cost
κ
1.984
Note: Parameters below the line are set to target moments in Table 4.
11
E
E
We set λ0 = λ11
0 = λ1 = λ1 = 0 and λ0 = λ2 = 0.
Note that once we set the pre-tax risk-free rate, together with income tax τi the equilibrium
conditions determine β, r and q B . More specifically, β = q B = (1 + r)−1 = q̃ B ∗ (1.0 + τi ) − τi .
We use Tauchen’s procedure to discretize
log(z ′ ) = ρ log(z) + ǫ, ǫ ∼ N (0, σǫ )
into a eleven state markov process {z1 , ..., z11 }.
Given these parameter values, the moments we find in the model are given in Table 4.
20
Table 4: Comparison of Data and Model Moments
Frequency of all bankruptcy %
Entry/Exit Rate
Fraction of Exit by Chapter 7 %
Recovery Rate in Chapter 7 %
Fraction of Bankruptcy by Chapter 11 %
Recovery Rate in Chapter 11 %
Debt / Assets non-Bankrupt %
Debt / Assets Chapter 11 %
Net Investment / Assets non-bankrupt %
Net Investment / Assets Ch 11 %
Avg. Number workers (000s)
Equity Issuance / Assets non-Bankrupt %
Equity Issuance / Assets Chapter 11 %
Net Debt / Assets non-Bankrupt %
Net Debt / Assets Chapter 11 %
Interest Rate Non-Bankrupt %
Interest Rate Chapter 11 %
Avg Size (k) / Prod. z Non-Bankrupt
Avg Size (k) / Prod. z Ch 11
Avg Size (k) / Prod. z Ch 7
6
6.1
Data
0.87
0.71
59.23
0.8
80.82
86.9
61.11
78.49
1.14
-6.24
1.85
17.35
21.37
40.95
62.59
Model
0.59
0.86
55.53
9.24
39.12
90.08
32.44
102.59
1.46
-16.18
1.74
1.51
38.86
20.05
102.59
2.75
9.65
4.97 / 1.369
5.11 / 1.147
0.645 / 1.018
Results
Positive Analysis
We begin by describing decision rules concerning exit and bankruptcy choice. Figure 3 presents
the exit and default decision rules across capital, debt and productivity. The left panels present
exit (top), reorganization (i.e. whether to repay in full or go to Chapter 11, middle), and
liquidation (i.e. whether to exit by full repayment or go into Chapter 7 bankruptcy, bottom)
decision rules respectively for a firm with low productivity (z = zL ). The next two columns
present the same decision rules for firms with median and high productivity (z = zM and
z = zH ). The blank regions in the middle and bottom panels occur when the decision rule
is not relevant. More specifically, in states where a firm chooses to exit x(k, b, z) = 1 the
decision rule for reorganization is not shown. Similarly, in states where a firm chooses to stay
x(k, b, z) = 0 the decision rule for liquidation is not shown.
21
Figure 3: Exit and Default Decision Rules
As evident in Figure 3 firms with low productivity: (i) low debt and high capital choose
to exit; (ii) high debt and low capital choose Chapter 7; and (iii) high debt and high capital
choose Chapter 11.
We next describe recovery rates and the price of debt. As evident in Figure 4, for a given
level of capital, the higher a firm’s debt the less lenders recover and for a given level of debt,
the higher a firm’s capital the more lenders recover.9 Thus, firms with high debt to assets face
higher interest rates.
9
We note that at high debt and capital levels, the recovery rate is 100% since at those levels the participation
constraint of the firm (20) is violated.
22
Figure 4: Recovery Rates and Debt Price Schedule
Recovery Rate φ(k, b, zM )
60
1
capital (k)
0.8
40
0.6
0.4
20
0.2
0
−10
0
10
20
30
40
0
debt (b)
Price Function q(k ′ , b′ , zM )
Future capital (k′)
60
1
0.8
40
0.6
0.4
20
0.2
0
−10
0
10
20
Future debt (b′)
30
40
0
Debt dynamics are illustrated in Figure 5. Firms with: (i) low productivity, some cash
and low capital choose to accumulate debt (since they start with negative debt, the change is
negative due to the denominator); (ii) medium productivity, low debt and high capital choose
to accumulate debt since they face low interest rates due to their high level of collateral while
those with low capital choose equity issuance to finance investment since they face high interest
rates, and finally those with significant debt choose to retain earnings (i.e. pay down their
debt); and (iii) high productivity and low debt choose to accumulate debt to finance positive
net investment.
23
Figure 5: Change in Debt Non-Bankrupt
Growth Debt b0,0(k,b,z )/b−1
L
capital (k)
60
1
0.5
40
0
20
0
−5
−0.5
−1
0
5
10
15
20
25
debt (b)
0,0
Growth Debt b (k,b,zM)/b−1
30
35
40
capital (k)
60
1
0.5
40
0
20
0
−5
−0.5
−1
0
5
10
15
20
25
debt (b)
0,0
Growth Debt b (k,b,zH)/b−1
30
35
40
capital (k)
60
1
0.5
40
0
20
0
−5
−0.5
−1
0
5
10
15
20
debt (b)
25
30
35
40
Dividend distribution (e > 0) and equity issuance (e < 0) is illustrated in Figure 6. Firms
with: (i) low productivity who do not exit choose to pay some dividends; (ii) medium productivity, low debt and high capital choose to pay some dividends while those with low capital
choose equity issuance to finance investment since they face high interest rates, and finally
those with significant debt choose to retain earnings (i.e. pay down their debt); and (iii) high
productivity choose a similar policy to (ii).
24
Figure 6: Net cash flow over Assets Non-Bankrupt
0,0
capital (k)
Dividend Policy e
0.4
40
0.2
20
0
0
−5
capital (k)
(zL)
60
0
5
10
15
20
25
debt (b)
0,0
Dividend Policy e (zM)
30
35
40
−0.2
60
0.4
40
0.2
20
0
0
−5
0
5
10
15
20
25
debt (b)
Dividend Policy e0,0(z )
30
35
40
−0.2
capital (k)
H
60
0.4
40
0.2
20
0
0
−5
0
5
10
15
20
debt (b)
25
30
35
40
−0.2
The equilibrium conditional distributions of firms are illustrated in Figure 7. It is evident
that firms with low productivity are amassed on lower capital and debt levels while those with
high productivity are amassed on higher capital and debt levels.
25
Figure 7: Distribution of Firms (conditional on z)
Conditional Distribution (k,b,z )
L
capital (k)
60
0.01
40
0.005
20
0
−5
0
5
10
15
20
25
debt (b)
Conditional Distribution (k,b,z )
30
35
40
0
M
capital (k)
60
0.01
40
0.005
20
0
−5
0
5
10
15
20
25
debt (b)
Conditional Distribution (k,b,zH)
30
35
40
capital (k)
60
0.01
40
0.005
20
0
−5
6.2
0
0
5
10
15
20
debt (b)
25
30
35
40
0
Normative Analysis
Our counterfactual is to ask, what are the equilibrium consequences of removing the Chapter
11 option? This is accomplished in the prior model by simply setting c11 = ∞. Effectively this
means that “punishment” is harsher. The new moments associated with this counterfactual
are given by Table 5.
26
Table 5: Counterfactual No Chapter 11
Frequency of all bankruptcy %
Entry/Exit Rate
Fraction of Exit by Chapter 7 %
Recovery Rate in Chapter 7 %
Fraction of Bankruptcy by Chapter 11 %
Recovery Rate in Chapter 11 %
Debt / Assets non-Bankrupt %
Debt / Assets Chapter 11 %
Net Investment / Assets non-bankrupt %
Net Investment / Assets Ch 11 %
Avg. Number workers (000s)
Equity Issuance / Assets non-Bankrupt %
Equity Issuance / Assets Chapter 11 %
Net Debt / Assets non-Bankrupt %
Net Debt / Assets Chapter 11 %
Interest Rate Non-Bankrupt %
Interest Rate Chapter 11 %
Avg Size (k) / Prod. z Non-Bankrupt
Avg Size (k) / Prod. z Ch 11
Avg Size (k) / Prod. z Ch 7
Equilibrium wage
Aggregate Consumption
Aggregate Output
Measured TFP (= Y /K α )
Data
0.87
0.71
59.23
0.8
80.82
86.9
61.11
78.49
1.14
-6.24
1.85
17.35
21.37
40.95
62.59
Benchmark
Only Ch 7
Model
c11 = ∞
0.59
0.16
0.86
0.80
55.53
20.06
9.24
2.39
39.12
90.08
32.44
39.76
102.59
1.46
1.76
-16.18
1.74
1.73
1.51
1.710
38.86
22.46
32.85
102.59
2.75
2.50
9.65
4.97 / 1.369 4.95 / 1.370
5.11 / 1.147
0.645 / 1.018 0.039 / 0.984
1.000
1.010
1.235
1.244
1.752
1.755
1.235
1.236
Stronger punishment, ceteris paribus, should lead to a lower frequency of bankruptcy and
less entry which is evident in Table 5. Harsher punishment, however, does have equilibrium
effects on interest rates and wages. As evident in Table 5 interest rates drop and in response
there is a rise in leverage which is evident in Figure 8. As evident in Figure 8, firms that used
to reorganize with median productivity now exit by Ch 7. While the decision rule changes,
this does not translate into an increase in the equilibrium fraction of Chapter 7 defaults (or
frequency of bankruptcy) since that region of the cross sectional distribution is not realized
in equilibrium. We observe that the equilibrium wage rate increases since there is an increase
in the mass of firms demanding workers. Aggregate output rises two tenths of one percent
and productivity rises one tenth of one percent. Finally, aggregate consumption rises by seven
tenths of one percent.
27
Figure 8: Comparison Debt to Asset Distribution
Distribution Debt / Assets
Benchmark
No Chapter 11
Fraction of Firms
0.2
0.15
0.1
0.05
0
0
0.5
1
1.5
Debt/Assets
Note: 1.5 debt to asset ratio includes all firms with debt to asset ratios ≥ 1.5.
28
Figure 9: Exit and Default Decision Rules c11 = ∞ case
7
Conclusion
We extend a standard model of firm dynamics to incorporate Chapter 7 and Chapter 11
bankruptcy choices. We find that bankruptcy law can have important implications for corporate capital structure and firm dynamics. If Chapter 11 is eliminated, there are significant
changes in capital structure (debt-to-capital ratios), the firm size distribution, and borrowing
costs. We also find that this reform increases average productivity and welfare by seven tenths
of one percent.
29
References
[1] Altman, E. (1968) “Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy”, The Journal of Finance, vol. 23, p. 589-609.
[2] Aghion, P., O. Hart, and J. Moore (1992) “The Economics of Bankruptcy Reform ”,
Journal of Law, Economics, and Organization, vol. 8, p. 523-546.
[3] Arellano, C., Y. Bai, and J. Zhang (2012) “Firm Dynamics and Financial Development”,
Journal of Monetary Economics, vol. 59, p. 533-549.
[4] Bharath, S. and T. Shumway (2009) ”Forecasting Default with the Merton Distance-toDefault Model”, Review of Financial Studies, vol. 21, p.1339-1369.
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31
Appendix
Appendix A1:
Data
We use data from Compustat North America Fundamental Annual.10 Our choice of firm
identifier is GVKEY. The sample period for the fundamentals data ranges from 1980 to 2012.
Our year variable is extracted from the variable DATADATE. We exclude financial firms with
SIC codes between 6000 and 6999, utility firms with SIC codes between 4900 and 4999, and
firms with SIC codes greater than 9000 (residual categories). Observations are deleted if they
do not have a positive book value of assets or if gross capital stock or sales are either zero,
negative, or missing. We censorize the top and bottom 2% of every variable as in Henessy and
Whited [13]. The final sample is an unbalanced panel with more than 12,000 firms and 117,746
firm/year observations. All nominal variables are deflated using the CPI index (normalized to
100 in 1983). See Tables 6 and 7.
Identifying Exit and Bankruptcies
We document firm exit, Chapter 11 bankruptcy and Chapter 7 bankruptcy using different
sources. We code a firm/year observation as being in Chapter 11 bankruptcy whenever the
footnote to total assets reports codes “TL” (Company in bankruptcy or liquidation) or “AG”
(reflects adoption of fresh-start accounting upon emerging from Chapter 11 bankruptcy). To
complement Compustat and dates from the footnote of Total Assets, we use dates provided
for firms with assets worth 100 million or more (in 1980 US$) available in the UCLA-LoPucki
Bankruptcy Research Database (BRD). If the firm/year observation corresponds to the last
period of the firm in our sample and the firm is identified as going into Chapter 11 bankruptcy
we keep the Chapter 11 identifier only if the variable DLRSN (Research Company Reason for
Deletion) is equal to codes 01 (Acquisition or merger), 04 (Reverse Acquisition), 07 (Other, no
longer files with SEC among other possible reasons, but pricing continues), 09 (now a private
company) and 10 (Other, no longer files with SEC among other possible reasons). We also
code as Chapter 11 bankruptcy observations which in their final period have DLRSN equal to
code 02 (Bankruptcy). We code a firm/year observation as Chapter 7 if it is the last period
in our sample and the variable DLRSN (Research Company Reason for Deletion) is equal to
code 03 (Liquidation). The classification into Chapter 11 and Chapter 7 bankruptcy during
the last period of the firm in the sample is the same used by Duffie, Saita and Wang [9]. To
be consistent with the definition of Chapter 11 bankruptcy, a deleted firm (i.e. a firm that
disappears from our sample) is counted as a firm that exits if the variable DLRSN is not equal
to codes 01, 02, 04, 07, 09 or 10 (i.e. those identified as continuing firms due to mergers or
because they go private for example). This is consistent with the definition of exit that the
10
All variable names correspond to the Wharton Research Data Services (WRDS) version of Compustat.
32
Table 6: Variables
Variable
GVKEY
DATADATE
Company Name
DLDTE
DLRSN
NAICS
SIC
AT
PPEGT
SPPE
CAPXV
DP
IB
SSTK
DLTT
DLC
DVP
DVC
PRSTKC
CHE
SALE
CEQ
PRCC F
CSHO
ACT
LCT
OIBDP
XINT
INVT
RECT
BAST
PPENT
DM
DD1
LT
GP
DT
TFVA
TFVL
EBIT
EBITDA
Item (old definition)
Description
Firm Identifier
Data Date
Research Company Deletion Date
Research Co Reason for Deletion
6
7
107
30
14
18
108
9
34
19
21
115
1
12
60
199
25
4
5
13
15
3
2
104
8
241
book assets
Property, Plant and Equipment - Total (Gross)
Sale of Property
Capital Expend Property, Plant and Equiment
Depreciation and Amortization
Income Before Extraordinaty Items
Sale of Common and Preferred Stock (equity issuance)
Long-Term Debt - Total
Debt in Current Liabilities
Dividends - Preferred/Preference
Dividends Common/Ordinary
Purchase of Common and Preferred Stock
Cash and Short-Term Investments
Sales
Common/Ordinary Equity - Total
Price Close - Annual Fiscal
Common Shares Outstanding
Current Assets - Total
Current Liabilities - Total
Operating Income Before Depreciation
Interest and Related Expense - Total
Inventories - Total
Receivables Total
Short Term Borrowings
Property, Plant and Equipment - Total (Net)
Debt - Mortgages and Other Secured = Secured Debt
Long Term Debt Due in one Year
Total Liabilities
Gross Profits
Total Debt Including Current
Total Fair Value Assets
Total Fair Value Liabilities
Earnings before Interest and Taxes
Earnings before Interest
Source: Compustat - Fundamental (WRDS).
33
Table 7: Derived Variables
Variable
PPEGT + CHE
SSTK / (PPEGT + CHE)
CAPXV-SPPE
CAPXV-SPPE-DP
(CAPXV-SPPE-DP) / (PPEGT + CHE)
DVP+DVC+PRSTKC
Item (old definition)
7+1
108 / (7 +1 )
30-107
30-107-18
(30-107-18) / (7 + 1)
19+21+115
14+18
(19+21+115) / (7 + 1)
34+9
34+9-1
Description
Total Assets = Capital + Cash
Equity Issuance / Total Assets
gross investment
net investment
Net Investment / Total Assets
Dividends = total cash distributions
Cash Flow
dividends / Assets
(DVP+DVC+PRSTKC) / (PPEGT + CHE)
Total debt
DLTT+DLC
DLTT+DLC-CHE
Net Debt = Total Debt - Cash
Negative Net Debt
DLTT+DLC-CHE¡0
EBITDA/XINT
Interest Coverage Ratio (EBITDA)
Source: Compustat - Fundamental (WRDS).
U.S. Bureau of the Census uses to construct its exit statistics. Table 8 provides summary
statistics about the frequency of each of the above codes. Using this information, we have
173,617 nonbankrupt firm/year observations, 1,319 Chapter 11 firm/year observations, and
315 Chapter 7 firm/year observations.
In Table 1 we include tests of the differences between means. To do so, for each variable
of interest xt (i.e. variables listed in Table 1), we run the following regressions:
xit = a0 + a1 dch11
+ a2 dch7
it
it + bt + uit
(A.1.1)
Table 8: Bankruptcy, Deletion and Exit Statistics
Moment
Frequency of Deletion (%)
Frequency of Deletion by Exit (%)
Frequency of Deletion by M & A (%)
Frequency of Deletion by going private (%)
Fraction of Deletion by Exit as Ch 7 (%)
Frequency of (all) Bankruptcy (%)
Fraction of Chapter 11 Bankruptcy (%)
Note: Deletion corresponds to the fraction of firms that disappear from
M& A refers to mergers and acquisitions. Source: Compustat -
34
6.59
0.71
3.35
0.21
59.23
0.87
80.82
our sample in any given period.
Fundamental (WRDS).
where dch11
is a dummy variable that takes value 1 if the firm/year observation corresponds to
it
the start of a Chapter 11 bankruptcy and zero otherwise; dch7
it is a dummy variable that takes
value 1 if the firm/year observation corresponds to a Chapter 7 bankruptcy and zero otherwise;
and bt corresponds to a full set of year fixed effects. A significant coefficient a1 reflects that
average xt is significantly different for firms in Chapter 11 bankruptcy than that of Nonbankrupt firms. Similarly, a significant coefficient a2 reflects that average xt is significantly
different for firms in Chapter 7 bankruptcy than that of Non-bankrupt firms. To test whether
a1 is significantly different than a2 we perform an F-test. A significant test implies that average
xt for firms in Chapter 11 is significantly different than that of firms in Chapter 7 bankruptcy.
Z-scores and Distance to Default
The Altman z-score is a commonly used measure of the level of distress of corporations
(see Altman [1] for the seminal paper on the subject). The basic idea is to construct an index
based on observable variables that helps to predict whether a firm is close to bankruptcy or
not. More specifically, the z−score is defined as follows:
z = 1.2x1 + 1.4x2 + 3.3x3 + 0.6x4 + 0.999x5 ,
where x1 is the working capital to total assets ratio (measured as current assets minus current
liabilities over assets), x2 is retained earnings over assets, x3 corresponds to the earnings before
interest and taxes over assets, x4 is the market value of equity over the book value of total
liabilities and x5 is sales over total assets. The coefficients are determined using a multiple
discriminant statistical method. Once the z-score is constructed the rule of thumb is to define
all firms having a z-score greater than 2.99 as “non-distressed” firms, while those firms having
a z-score below 1.81 as “distressed” firms. The area between 1.81 and 2.99 is defined as the
“zone of ignorance”.
In order to construct a default probability based on the distance to default model, we
follow Duffie et. al [9]. The default probability is constructed using the number of standard
deviations of asset growth by which a firm’s market value of assets exceeds a liability measure.
That is, for a given firm, the 1-year horizon distance to default is defined as
Dt =
2)
ln(Vt /Lt ) + (µA − 1/2σA
σA
where Vt is the market value of the firm’s assets at time t and Lt is the liability measure
(calculated as short term book debt plus 1/2 of long-term book debt), µA is the mean rate
of asset growth and σA the standard deviation of asset growth. The market value of the
firm is estimated following the theory of Merton (1974) and Black and Scholes (1973). More
specifically, we let Wt denote the market value of equity which is equal to an option on the value
of a firm’s assets, currently valued at Vt , with strike price of Lt and one-year to expiration.
35
We obtain the asset value Vt and the volatility of asset growth by solving the following system
of equations iteratively:
Wt = Vt Φ(d1 ) − Lt er Φ(d2 ),
σa = Std.Dev.(ln(Vt ) − ln(Vt−1 ),
2)
ln(Vt /Lt ) + (r + 1/2σA
,
d1 =
σA
d2 = d1 − σA ,
where Φ(·) is the standard normal cdf, Std. Dev. denotes standard deviation and r is the
risk-free rate (that we take to be the real 1-year T-bill rate). The initial guess for Vt is the
sum of Wt (measured as end-of-period real stock price times number of shares outstanding)
and the book value of total debt (sum of short term and long term book debt). Once Vt and
σA are estimated, we compute Dt . The corresponding default probability is
pD
t = Φ(−Dt ).
Appendix A2:
Computational Algorithm
In this section, we describe our computational algorithm.
1. Set grids for k ∈ K, b ∈ B and z ∈ Z.
2. Guess initial wage rate w0 , price schedule q 0 (k′ , b′ , z), recovery rate schedule φ0 (k′ , b′ , z).
3. Solve Firm Problem: Given the bond price schedule, recovery schedule and wage rate,
solve the firm problem to obtain capital, debt, exit and bankruptcy decision rules as well
as value functions.
4. Obtain Recovery Schedule: Using the value functions obtained in point 3, solve the
renegotiation problem to obtain φ1 (k′ , b′ , z).
5. Obtain Bond Price Schedule: Using the exit and bankruptcy decision rules obtain a
price function that is consistent with them. Let it be q 1 (k′ , b′ , z).
6. If ||φ1 (k, b, z) − φ0 (k, b, z)|| < ǫφ and ||q 1 (k′ , b′ , z) − q 0 (k′ , b′ , z)|| < ǫq , for small ǫφ and
ǫq , then we have obtained the equilibrium price and recovery schedule (for a given price
w0 ), continue to the next step. If not, update the price and recovery schedule and return
to point 3.
7. Free Entry Condition: Evaluate the free entry condition V E at w0 . If it holds with
equality, continue. If it does not, proceed as follows:
• If V E is positive, increase w0 and return to point 3.
36
• If V E is negative, reduce w0 and return to point 3.
8. Labor Market Clearing:
• Set M = 1 and compute the stationary distribution associated with the set of decision rules obtained above and this mass of entrants. Denote this distribution
Γ̂(k, b, z; M = 1).
• Calculate labor demand Γ̂(k, b, z; M = 1), that is
N̂ (M = 1) =
Z
n(z, k, b)dΓ̂(z, k, b; M = 1).
• Set M 0 to satisfy the labor market clearing condition. That is set M 0 as follows
M 0 = 1/N̂ (M = 1)
• The equilibrium prices and distribution are: w∗ = w0 , M ∗ = M 0 , Γ∗ = M ∗ Γ̂(k, b, z; M =
1), q ∗ = q 0 ,φ∗ = φ0 .
• Aggregates and Taxes: Compute aggregate consumption and taxes.
37