A business cycle analysis of debt and equity financing.
Karabarbounis, Marios ; Macnamara, Patrick ; McCord, Roisin 等
The recent turmoil in financial markets has highlighted the need to
better understand the link between the real and the financial sectors.
For example, a widespread view holds that real shocks can propagate
themselves by adversely affecting credit markets (financial
accelerator). An informative way to establish such linkages is to look
at the co-movement between financial flows and macroeconomic conditions.
The magnitude and direction of this relationship can guide our thinking
regarding how strong these linkages are and the particular way in which
they manifest themselves.
This article takes a modest step in this direction. In particular,
we provide an introductory, yet comprehensive, business cycle analysis
of firm financing. We first document empirically the cyclical properties
of debt and equity issuance. We then build a simple two-period model to
analyze the optimal capital structure as well as the response of firm
financing to exogenous shocks such as a productivity shock. Finally, we
examine how well a fully dynamic, reasonably calibrated,
heterogeneous-firm model replicates the business cycle properties of
debt and equity issuance.
We document empirical patterns of firm financing based on Compustat
for the period 1980-2013. We find that firms issue more debt during
expansions. In contrast, the cyclical properties of equity issuance
depend on the exact definition of equity. If we define equity issuance
using the sale of stock net of equity repurchases (following Jermann and
Quadrini [2012]), we find a countercyclical equity issuance (or a
procyclical equity payout). If we follow Covas and Den Haan (2011) and
define equity issuance based on the change in the book value of equity,
we find equity issuance to be weakly procyclical. Equity financing
through mergers explains much of the discrepancy between the two
measures. Stock compensation also explains the discrepancy but to a
smaller degree. Moreover, regardless of the measure used, the
countercyclicality of net equity issuance is driven by a strongly
procyclical dividend payout and not countercyclical gross equity
issuance. The data also reveal a substantial degree of heterogeneity in
firms' financial decisions. Compared to large firms, the debt
issuance of small firms tends to be less procyclical while equity
issuance tends to be more procyclical.
To build intuition, we analyze the firm's optimal capital
structure within a simple two-period model. Each period, firms receive
an idiosyncratic productivity shock. The firm chooses how much to invest
and how it will finance this decision. Financing can take the form of a
one-period bond (debt) and external equity. The firm chooses debt
issuance to balance the tax benefits of debt with the expected
bankruptcy costs of default. External equity is also assumed to be
costly. We show how the policy functions for investment, debt, and
equity vary with internal equity, the costs of issuing equity, and
idiosyncratic productivity.
Our fully dynamic model incorporates many of the elements outlined
in the two-period model. Firms experience both aggregate and
idiosyncratic productivity shocks. Nevertheless, we keep the analysis
simple and assume a partial equilibrium framework. The model is
calibrated to match several cross-sectional moments as calculated from
Compustat. We then examine how well our model can explain the cyclical
properties of debt and equity issuance. As in the data, firms issue more
debt in response to a positive productivity shock. Higher productivity
implies that firms desire to invest more, which makes default more
costly and, hence, borrowing easier. Moreover, equity issuance is
countercyclical. This is driven by large firms issuing more dividends
during expansions. The model also captures the firm-size relationship in
firm financing. Specifically, the model is able to match the empirical
observation that net equity issuance of small firms is procyclical,
while debt issuance is less procyclical than for larger firms.
This article contributes to the literature on firm financing in two
ways. First, we highlight how equity financing through mergers and stock
compensation can account for the different measures of net equity
issuance used in the literature. In particular, we show that if one
excludes mergers and stock compensation, the measures used by Covas and
Den Haan (2011) and Jermann and Quadrini (2012) (change in book value of
equity and net sale of stock, respectively) lead to the same conclusion.
Moreover, we show that a countercyclical net equity issuance in the data
is driven by dividend payouts falling during recessions, not gross
equity issuance increasing during recessions. Although such a
distinction is crucial for understanding how firm financing varies over
the cycle, it is not stressed in the literature. Second, we test these
predictions within a quantitative model of firm financing with
heterogeneous firms. Although this is certainly not the first
quantitative article of firm financing, our article makes several novel
contributions. For example, we build intuition regarding the
determinants of firm financing using a simple two-period model.
Moreover, using our heterogeneous-firm model we can test if the model
captures the empirical firm-size relationship and especially the
decomposition of equity financing into gross equity issuance and payout
components.
1. RELATED LITERATURE
Our analysis borrows many elements from the work of Covas and Den
Haan (2011), who look at disaggregated data from Compustat and document
the cyclical properties of firm finance for different firm sizes. Their
finding is that debt and (net) equity issuance is procyclical as long as
the very large firms are excluded. Hence, Covas and Den Haan (2011)
stress the importance of incorporating heterogeneity in quantitative
models of firm financing. (1) Jermann and Quadrini (2012) document the
cyclical properties of financial flows using aggregate data from the
flow of funds accounts. The authors find a procyclical debt issuance but
a countercyclical net equity issuance. Their article also examines the
macroeconomic effects of financial shocks by constructing a shock series
for the financial shock and then feeding the shock into a real business
cycle model. Beganau and Salomao (2014) also document financial flows
from Compustat. Following the equity definition of Jermann and Quadrini
(2012), Beganau and Salomao (2014) also find net equity issuance is
countercyclical.
Although the focus on the cyclicality of financial flows has been
relatively new, there is ample work on the cross-sectional determinants
of capital structure and firm dynamics. Rajan and Zingales (1995)
investigate the relationship between leverage and firms'
characteristics for a set of countries. They report that most of the
empirical regularities found in the United States (such as the positive
relationship between firm size and leverage) are also true for other
countries. Cooley and Quadrini (2001) introduce financial frictions in a
model of industry dynamics and study the relationship between firm
financing and firm size and age. Hennessey and Whited (2007) build a
structural model of firm financing and estimate the magnitude of
external financing costs. Recently, Katagiri (2014) builds a general
equilibrium model of firm financing to study the distribution of
leverage.
2. EMPIRICAL ANALYSIS
In this section, we describe several empirical patterns regarding
firm financing. We first explain how we construct the variables used in
the analysis. We next present aggregate statistics both in the
cross-section of firms and along the business cycle. The main findings
emerging from the analysis are the following. First, debt issuance is
strongly procyclical. Second, the cyclicality of equity issuance depends
on the specific measure used. However, smaller firms seem to issue more
equity in expansions relative to larger firms, independent of the
measure. Third, there is widespread heterogeneity in firm financing
decisions.
Data Construction
To construct our variables we use annual data from Compustat.
Compustat contains financial information on publicly held companies.
Following the literature on firm financing, we focus on the period
between 1980 and 2013. Jermann and Quadrini (2012) document that during
this period there was a break in macroeconomic volatility as well as
significant changes in U.S. financial markets. We exclude financial
firms and utilities as these industries are more heavily regulated. (2)
One important concern is whether we include firms affected by a merger
or an acquisition. For this purpose, we separately report results for
two cases. In the first case, we follow Covas and Den Haan (2011) and
drop all firm-year observations that are affected by a "major"
merger or acquisition. By "major" we mean that the merger or
acquisition causes the firm's sales to increase by more than 50
percent. In the second case, we drop all observations affected by any
kind of merger. After imposing these restrictions and dropping all
observations affected by a major merger, we are left with an unbalanced
panel of 19,101 firms and a total of 168,295 firm-year observations.
When we also drop observations affected by any merger, we are left with
18,486 firms and 141,379 observations.
Variable Definitions
The literature uses two different methods to measure equity
issuance. Fama and French (2005) and Covas and Den Haan (2011) use
changes in the book value of equity (reported on the firm's balance
sheet) to measure equity issuance. Jermann and Quadrini (2012) use the
"net sale of stock" (from the statement of cash flows) in the
construction of equity issuance. To clarify the difference between these
two measures, it is useful to define a company's accounting
identity:
[A.sub.i,t] = [SE.sub.i,t] + [RE.sub.i,t] + [L.sub.i,t].
For firm i at date t, assets [A.sub.i,t] must equal equity plus
liabilities [L.sub.i,t] (all variables are book values). Total equity
includes retained earnings [RE.sub.i,t], which is the portion of the
company's net income it has retained rather than distributed to
shareholders as dividends. Therefore, [SE.sub.i,t] is the company's
total equity net of retained earnings. This part of the firm's
balance sheet reflects equity that the firm has obtained from
"external" sources such as sale of common stock.
Under the first definition, equity issuance is the annual change in
[SE.sub.i,t] minus cash dividends distributed to shareholders
[d.sub.i,t]. We subtract cash dividends from our definition because,
effectively, they represent one of two ways firms can distribute funds
to shareholders: They can buy back stock, which would decrease
[SE.sub.i,t], or they can issue dividends, which would decrease
[RE.sub.i,t] instead. Therefore, in our first definition, the equity
issuance of firm i at date t is
[DELTA][E.sub.i,t](1) [equivalent to] [DELTA][SE.sub.i,t] -
[d.sub.i,t], (1)
where [DELTA][SE.sub.i,t] [equivalent to] [SE.sub.i,t] -
[SE.sub.i,t-1] is the annual change in [SE.sub.i,t]. This corresponds to
one of the primary definitions of equity issuance in Covas and Den Haan
(2011). Our second definition of equity issuance is defined as follows:
[DELTA][E.sub.i,t](2) [equivalent to] [DELTA]S[S.sub.i,t] -
[d.sub.i,t]; (2)
[DELTA]S[S.sub.i,t] is the net sale of stock, which is defined as
the gross revenue from the sale of stocks minus stock repurchases. This
corresponds to the definition of equity issuance utilized by Jermann and
Quadrini (2012).
Ideally these two measures would be equivalent, as the net sale of
stock [DELTA]S[S.sub.i,t] affects [SE.sub.i,t]. Nevertheless, the two
definitions lead to different conclusions about the cyclicality of
equity issuance. This discrepancy has to do with the way firms choose to
issue equity. Apart from equity offerings to the public, equity issuance
can take place through mergers, warrants, employee options, grants, and
benefit plans among others. Hence, as Fama and French (2005) note, the
net sale of stock measure captures only a few of the ways in which firms
can raise outside equity. Take, for example, a merger or an acquisition.
Suppose a firm acquires another firm by issuing equity to the
shareholders of the target firm. This transaction will change the book
value of equity. However, it will not alter the sale of stock measure
because no actual revenue is raised by the transaction. Moreover,
suppose a firm were to compensate its employees with a stock. Again, if
equity is measured using the book value of equity, equity issuance will
increase. This is because employee compensation will decrease retained
earnings and thus increase [SE.sub.i,t], the company's equity net
of retained earnings. Meanwhile, as before, the sale of stock measure
will not record the equity issuance because no actual revenue is raised.
In the data, a situation in which no firms issue equity (on net)
will look the same as a situation in which some firms issue equity while
others reduce equity. To uncover such heterogeneity, we break up our
first definition of equity issuance into a "gross equity
issuance" and "gross equity payouts" component. (3) In
particular, we define gross equity issuance [E.sup.I.sub.i,t] to be
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (3)
Similarly, we define gross equity payouts [E.sup.P.sub.i,t] to be
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (4)
Note that [DELTA][E.sub.i,t](1) = [E.sup.I.sub.i,t] -
[E.sup.P.sub.i,t] by construction. By looking at gross flows, we can
separately identify firms that raise equity and firms that reduce
equity.
Moreover, we also consider several other variables of interest. In
particular, [w.sub.S] will denote employee stock compensation;
[DELTA][RE.sub.i,t] [equivalent to] [RE.sub.i,t] - [RE.sub.i,t-1] is the
change in retained earnings. A firm's net debt issuance
[DELTA][D.sub.i,t] [equivalent to] [D.sub.i,t] - [D.sub.i,t-1] is
defined to be the change in the firm's book value of debt between
period t - 1 and t. A firm's net change in sales [DELTA][S.sub.i,t]
[equivalent to] [S.sub.i,t] - [S.sub.i,t-1] is defined to be the change
in the firm's nominal sales between t and t - 1. Finally,
[I.sub.i,t] is the firm's investment while [K.sub.i,t] is the
firm's capital stock.
Construction of Group Aggregates
To uncover any underlying heterogeneity in the financing decisions
of firms, we sort firms by size. At each date t, we sort firms into four
possible groups based on their size (more on the construction of these
groups later). Then, for every date t, we aggregate each firm-level
variable across all the firms in each bin. To be precise, let
[X.sub.i,t] be a variable of interest for firm i at date t. For example,
this might be [DELTA][D.sub.i,t], the net debt issuance of a particular
firm. Let [G.sub.j,t] denote the set of firms in group j at date t.
Then, we can construct the group aggregate [X.sub.j,t] as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)
The numerator is the sum of [X.sub.i,t] across all firms in group j
at date t. Therefore, if [X.sub.i,t] is [DELTA][D.sub.i,t], then the
numerator of (5) is the net amount of debt issued by all firms in group
j at date t. Meanwhile, the denominator of (5) is the total amount of
capital in group j at date t. The denominator is used to normalize the
resulting aggregate variable and capital is chosen because it is
acyclical. Following this procedure, we obtain a time series for the
aggregate variable X for each group. Note, however, that the composition
of firms in each group varies over time. Not only may a firm transition
between groups over time, but the groups may include newly listed firms.
To construct the firm groups, we sort firms based on the previous
period's book value of their assets. At each date, we sort firms
into four groups. The first group consists of firms with assets below
the median ([0, 50]). The second group consists of firms between the
50th and 75th percentile ([50, 75]), and the third group consists of
firms between the 75th and 99th percentile ([75, 99]). And finally, the
last group consists of firms in the top 1 percent ([99, 100]). As the
book value of assets tends to grow over time, we have to be careful in
how we determine the asset boundaries for these size groups. Define
[A.sub.50,t], [A.sub.75,t], and [A.sub.99,t] to be the asset boundaries
between the four size bins. In other words, a firm with assets
[A.sub.i,t] < [A.sub.50,t] will be in the [0, 50] group at date t +
1. Following Covas and Den Haan (2011), we construct [A.sub.50,t],
[A.sub.75,t], and [A.sub.99,t] by fitting a (log) linear trend through
the asset values that correspond to the 50th, 75th, and 99th percentiles
at each time t.
Cross-Sectional Analysis
We begin our analysis by looking at group aggregates for the whole
period between 1980 and 2013 (Table 1). Each variable is expressed as a
percentage of the group capital stock. In the top panel we exclude major
mergers from the sample while in the lower panel we exclude all mergers.
Looking at the top panel, we see that relative to their size, small
firms tend to issue more debt and equity than large firms. Debt issuance
decreases monotonically from 14.1 percent of the group's capital
stock in the [0, 50] bin to 2.9 percent for firms in the top 1 percent.
Equity issuance [DELTA]E(1) decreases from 64.9 percent of capital for
firms in the [0, 50] bin to -3.9 percent for firms in the top 1 percent.
For our second measure, [DELTA]E(2), these numbers are 44.4 percent and
-6.4 percent, respectively. Nevertheless, the two measures of equity do
differ in a significant way. [DELTA]E(2), which is based on the net sale
of stock, underestimates the amount of equity that firms raise. While
the measures differ across all size groups, they are significantly
different for smaller firms.
As noted earlier, mergers financed through the issuance of stock
may also explain part of the difference between the two equity measures.
To investigate how much mergers and acquisitions explain the difference,
we repeat our earlier analysis, but we exclude all mergers from the
sample. The bottom panel of Table 1 reports the results when all mergers
are excluded. While the same results hold as before, firms on average
issue less debt than before (1.8 percent versus 5.0 percent). Firms also
issue less equity under both definitions (-3.9 percent and -6.2 percent
versus -1.7 percent and -6.0 percent, respectively). Overall, the
difference between the two equity measures falls by almost half.
Moreover, stock compensation (which is not reflected in [DELTA]E(2))
does explain some of the remaining discrepancy between the two measures.
(4) In fact, for small firms it is a major explanation for the
discrepancy between the two measures. Still, after accounting for
mergers and stock compensation, significant differences remain.
[FIGURE 1 OMITTED]
Figure 1 shows how our equity measures, [DELTA]E(1) and
[DELTA]E(2), differ between 1980 and 2013. Similar to Table 1, we plot
the difference [DELTA]E(1) - [DELTA]E(2) for three different cases: (i)
if no major mergers are included, (ii) if no mergers at all are
included, and (iii) if no mergers at all are included and we subtract
from the difference equity issuance related to stock compensation. The
left panel of Figure 1 shows the differences for firms in the [0, 50]
size group, while the right panel shows the differences for all firms.
This figure highlights how the differences between these two measures
have grown since the late 1990s. Moreover, it also demonstrates the
importance that mergers and acquisitions have had on equity financing,
especially in the late 1990s. [DELTA]E(1) can capture these effects
while [DELTA]E(2) cannot. However, in the period after 2007, mergers
seem to account for only a small part of the discrepancy. Nevertheless,
during that period, stock compensation seems to account for a larger
fraction of the difference. As seen in Figure 1, this is especially true
for firms in the [0, 50] size group.
Finally, from Table 1 (both top and bottom panels) it is readily
apparent that small firms grow faster (in terms of sales growth) and
invest at a higher rate. Moreover, excluding the top 1 percent, smaller
firms have lower growth in retained earnings and [DELTA]RE is even
negative for firms in the [0, 50] size group. These results are
consistent with the findings of Covas and Den Haan (2011).
Business Cycle Analysis
We next turn to the business cycle analysis of debt and equity
issuance. In Table 2, we report the correlation of various group
aggregates with real corporate gross domestic product (GDP). To compute
these correlations, both GDP and the group aggregates are de-trended
with an H-P filter. (5) First consider the top panel of Table 2, which
includes results for the case when only major mergers are excluded from
the sample. Consistent with Covas and Den Haan (2011) and Jermann and
Quadrini (2012), debt issuance is strongly procyclical. The cyclicality
is stronger for larger firms. The correlation between debt issuance and
corporate GDP increases from 0.536 for the [0, 50] size group to 0.755
for the [75, 99] size group. The correlation falls to 0.547 for firms in
the top 1 percent. However, note that there is a relatively small number
of firms in this group. (6)
Overall, equity issuance, as measured by [DELTA]E(1), is acyclical.
However, according to this measure, equity issuance tends to be
procyclical and statistically significant for firms in the [0, 50] size
group. The cyclicality of equity issuance monotonically decreases across
size groups and becomes essentially uncorrelated with output for the top
1 percent. In particular, the correlation decreases from 0.345 for firms
in the [0, 50] size group to 0.044 for firms in the top 1 percent. These
results are consistent with Covas and Den Haan (2011). In contrast, if
we measure equity issuance using the net sale of stock ([DELTA]E(2)),
then equity issuance becomes strongly countercyclical. This is
consistent with Jermann and Quadrini (2012). However, even according to
this measure, equity issuance of the smallest firms tends to be
procyclical (although statistically insignificant) with a correlation of
0.243. Meanwhile, [DELTA]E(2) is significantly countercyclical for firms
in the [75, 99] size group with correlation equal to -0.617. This
pattern of financing across firm size is consistent with the net sale of
stock measure reported in Covas and Den Haan (2011).
In Table 2, we also report how the cyclicality of [DELTA]E(1)
breaks into a gross equity issuance and gross equity payouts component,
both defined in (3) and (4). For smaller firms, gross equity issuance is
driving the (pro)cyclicality of net equity issuance. But for all other
firm sizes, procyclical gross equity issuance is associated with a more
procyclical gross equity payout. Both statistics may explain the weak
cyclicality of net equity issuance [DELTA]E(1). This decomposition can
also shed some light on the discrepancy between our net equity measures
[DELTA]E(1) and [DELTA]E(2). Since [DELTA]E(2) underestimates gross
equity issuance, it is mostly affected by a countercyclical gross equity
payout.
Similar to our cross-sectional analysis, we trace the discrepancy
in the cyclical behavior of [DELTA]E(1) and [DELTA]E(2) to mergers and
stock compensation. In the bottom panel of Table 2, we report the
business cycle correlations when we exclude all mergers from the sample.
In this case, debt issuance is slightly less correlated with GDP but is
still strongly procyclical (0.661 versus 0.785). However, according to
[DELTA]E(1), equity issuance for all firms now becomes significantly
countercyclical (at the 10 percent level) and significantly
countercyclical for the top 25 percent. For example, the correlation for
firms in the [75, 99] size group is -0.419 when we exclude all mergers
versus 0.016 when we do not. Nevertheless, for the smallest firms,
equity issuance according to [DELTA]E(1) is still procyclical, but it is
not significant. Moreover, gross equity issuance is now statistically
insignificant for all size groups. For all firms, gross equity payouts
is still significantly procyclical. Therefore, the procyclical nature of
merger activity (7) appears to play an important role in explaining the
differences in the cyclicality between [DELTA]E(1) and [DELTA]E(2).
Another candidate to explain the discrepancy in the cyclicality of
the two measures is stock compensation. Table 2 includes information on
the cyclicality of stock compensation by firms. As mentioned earlier,
this type of equity issuance is captured by [DELTA]E(1) but not by
[DELTA]E(2). Therefore, it could help explain the discrepancy between
the two measures. However, as we see from Table 2, stock compensation is
itself acyclical. Therefore, while it does explain some of the
difference in levels between the two measures (especially for small
firms), it does not help explain the different cyclicalities.
3. OPTIMAL CAPITAL STRUCTURE: A TWO-PERIOD MODEL
In this section we outline a simple two-period model to explain how
the firm chooses its capital structure. Firms are perfectly competitive
and produce a single homogeneous good. Capital is the only input in the
firm's production function, zf(k), and z is the firm's
productivity. Productivity follows an AR(1) process. We denote by
F(z'|z) and f(z'|z) the cumulative distribution and
probability density functions for next period's productivity
z', conditional on the current-period productivity z.
Budget Constraint
The firm enters the first period with an initial level of capital,
k, and a required debt payment, b. Given k and b in the first period,
the firm (i) produces zf(k), (ii) chooses investment i = k' - (1
-[delta])k, (iii) issues dividends d (or raises external equity if d
< 0), and (iv) issues new debt, q(z, k', b')b' The
firm borrows using a defaultable one-period noncontingent bond. It
promises to pay b' tomorrow and in return the firm receives q(z,
k', b')b' today, where q is the price of the bond. Later
in this section we discuss how this price is determined. To facilitate
the analysis, we follow Gourio (2013) by assuming that the firm receives
a tax subsidy from the government proportional to the amount borrowed.
In other words, for every dollar the firm raises in the bond market, the
government gives the firm a subsidy of [tau]. (8)
The firm chooses dividends d, tomorrow's capital k', and
debt b' subject to the following budget constraint:
d + k' = e(z, k, b) + (1 + [tau])q(z, k',
b')b', (6)
where e(z, k, b) [equivalent to] zf(k) + (1 - [delta])k - b is
defined to be internal equity. Therefore, when choosing tomorrow's
capital stock, the firm has access to three sources of funding: (i)
internal equity e, (ii) debt qb', which is supplemented by the tax
subsidy, and (iii) external equity (when d < 0).
As discussed in Fazzari, Hubbard, and Petersen (1988), there are
many reasons why external equity is costly, including taxes and
flotation costs. Thus, we assume that issuing equity is costly and
specify the cost [LAMBDA](d) as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (7)
When d < 0, the firm is issuing external equity and the cost is
assumed to be proportional to the amount of funds raised. Moreover, note
that [LAMBDA](d) does not appear in (6). Therefore, when d < 0, -d is
the amount of funds actually received by the firm. However, shareholders
actually pay -d + [LAMBDA](d) = -(1 + [[lambda].sub.0])d, of which only
-d goes to the firm.
Default Decision
We also allow firms to default on their debt obligations. In
particular, in period 2, the firm chooses whether it will pay b' or
declare bankruptcy. If the firm does not default, it receives
[V.sup.ND](z', k', b') = z' f(k') + (1 -
[delta])k' - b'. (8)
In this case, the firm's shareholders receive output and the
undepreciated capital minus the debt payment. However, if the firm
defaults, we assume that the firm can hide and keep a fraction [theta]
of its assets. Therefore, in this case, the firm receives
[V.sup.D](z',k') = 6 [z'f(k ') + (1 -
S)k'] * (9)
Due to bankruptcy costs, lenders will only recover a fraction 1 -
[psi] of the total remaining assets in the case of default. In other
words, the lender recovers (1 - [psi])(1 - [theta]) [z'f (k')
+ (1 - [delta])k'] when the firm defaults.
Given (8) and (9), the firm will default tomorrow when [V.sup.ND]
(z', k', [b'.sup.D](z', k'). This implicitly
defines a productivity threshold [z.sup.*](k', b') such that
the firm will default if and only if [z'.sup.*](k, b'). This
threshold is defined to be the value of productivity, [z.sup.*], such
that the firm is indifferent between defaulting and not defaulting:
[V.sup.ND]([z.sup.*], k', [b'.sup.D]([z.sup.*], k').
Using (8) and (9), we can then obtain the following functional form for
[z.sup.*](k', b'):
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (10)
Consequently, default is only possible when b' > (1 -
[theta])(1 - [delta])k'. Moreover, when b' is above this
threshold, [z.sup.*] depends negatively on k' and positively on
b'. The more firms invest, the more output and capital the firm
will have next period. This will make default more costly. Consequently,
the default threshold decreases (i.e., [partial
derivative][z.sup.*]/[partial derivative]k' < 0). In contrast,
the more debt the firm issues, the more attractive default will be next
period. In this case, the default threshold will increase (i.e.,
[partial derivative][z.sup.*]/[partial derivative]b' > 0).
Bond Price
We assume there are households willing to lend their savings to
firms. The price that lenders charge, q(z, k', b'), takes into
account the probability that a firm will default, which depends on the
firm's choices for k' and b'. Specifically, it is assumed
that q is set to guarantee the lender an expected return equal to the
risk-free rate r. Hence, q will be given by
q(z, k', b') = [1/[1 + r]] [1 - F([z.sup.*](k',
b')|z) + [R(z, k', b')/b']], (11)
where
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
is the unconditional expected recovery value of the bond in the
case of default. Therefore, the price of debt is composed of two terms.
With probability 1 - F([z.sup*]|z), the firm will not default and the
lender receives b'. However, when the firm does default, the lender
receives a fraction (1 - [psi])(1 - [theta]) of total assets.
Firm's Problem
We can now write the firm's problem as a dynamic programming
problem. Define V(z, k, b) as the value of a firm with productivity z,
capital k, and debt b. This value function is given by
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (12)
subject to the budget constraint in (6), which is repeated here:
d + k' = e(z, k, b) + (1 + [tau])q(z, k',
b')b'.
The firm's objective is to choose next period's capital
stock k', debt b', and dividends d in order to maximize its
lifetime valuation.
Characterizing the Solution
In this subsection we explain what determines the firm's
optimal capital structure. To do so, it is useful to first re-write the
firm's value function defined in (12). Specifically, using the bond
price function defined in (11), the firm's value function can be
re-written as (9)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (13)
subject to the budget constraint in (6). Recall that e(z, k, b)
[equivalent to] zf(k) + (1 - [delta])k - b is defined to be internal
equity. Let T(z, k', b') = [tau]q(z, k', b')b'
denote the total value of the tax subsidy. This term reflects the tax
benefit of debt issuance. Similarly, B(z, k', b') is defined
to be the expected bankruptcy costs and is given by
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
As before, firms will choose k', b', and d to maximize
the firm's lifetime valuation. As is clear from (13), the effect of
marginal changes in k' and b' on T(z, k', b') and
B(z, k', b') will play a key role in determining the
firm's optimal capital structure. To ease the exposition of the
firm's problem, we will first consider the case where issuing
equity is costless (i.e., [[lambda].sub.0] = 0) and describe how the
optimal policies for k', b', and d are determined. We then
allow for costly equity ([[lambda].sub.0] > 0) and analyze how the
firm's optimal choices change.
Costless Equity Issuance
We first assume that [[lambda].sub.0] = 0, which implies that
[LAMBDA](d) = 0 for all d. In this case, the first order conditions for
k' and b' become
[tau] [[partial derivative]q/[partial derivative]k'] -
[[partial derivative]B/[partial derivative]k'] +
[[E[z'f'(k')|z] + 1 - [delta]]/[1 + r]] = 1 (14)
[tau][q + [[partial derivative]q/[partial
derivative]b']b'] = [partial derivative]B/[partial
derivative]b'. (15)
When [tau] = [psi] = 0, the first-order condition for k' in
(14) reduces to the familiar expression that the expected marginal
product of capital equals interest plus depreciation (i.e.,
E[z'f'(k')|z] = r + [delta]). Therefore, the firm invests
the first-best amount of k'. Moreover, when [tau] = [psi] = 0, both
sides of (15) are always zero. Therefore, the Modigliani-Miller theorem
(10) applies and the optimal capital structure is indeterminate. In this
case, there is no benefit or cost from issuing debt.
However, when [tau] > 0 and [psi] > 0, the Modigliani-Miller
theorem no longer applies. As seen in (14), the tax subsidy and
bankruptcy costs now affect the firm's investment decision. By
affecting the net tax benefit, [tau]qb' - B, a marginal change in
k' now has an additional benefit or cost. Consequently, whether the
optimal k' is above or below the first-best level of k'
depends on how a marginal change in k' affects the net tax benefit.
Under our benchmark parameterization, [tau] [[partial
derivative](qb')/[partial derivative]k'] > [[partial
derivative]B/[partial derivative]k'] > we imply that k' can
be higher than the first-best level of k'. Moreover, when [tau]
> 0 and [psi] > 0, debt is beneficial to the firm because it
increases the tax subsidy it receives. At the same time, more debt makes
default more likely and increases the expected costs of bankruptcy.
Consequently, as seen in (15), firms choose b' to equate the
marginal tax benefits of debt with marginal bankruptcy costs.
The left panel of Figure 2 provides a visual characterization of
the optimal capital structure. Since external equity is costless,
internal and external equity are perfect substitutes. Hence, internal
equity does not have any effect on the optimal value for k' and
b', which are both horizontal lines. In what follows, we denote by
[k.sup.*] and [b.sup.*] the firm's optimal choice of k' and
b' when [[lambda].sub.0] = 0. Given that k' = [k.sup.*] and
b' = [b.sup.*] for any value of e, it follows from the firm's
budget constraint in (6) that the optimal dividend policy is then just a
straight line (with a slope of 1). Firms with low (or even negative)
internal equity are able to choose k' = [k.sup.*] because they can
issue equity costlessly. Firms with large amounts of internal equity
choose k' = [k.sup.*] and also choose to issue a positive dividend.
Costly Equity Issuance
Now we assume that external equity is costly (i.e.,
[[lambda].sub.0] > 0). In this case, the first-order conditions for
b' become
([tau] + [I.sub.d<0][[lambda].sub.0](1 + [tau])) [q + [[partial
derivative]q/[partial derivative]b'] b' = [partial
derivative]B/[partial derivative]b'. (16)
This condition will only hold when d [not equal to] 0. In the case
of costly external equity, the marginal cost of an additional unit of
debt is the same. Nevertheless, there is potentially an additional
benefit of debt. In particular, an additional unit of debt allows the
firm to substitute away from costly external equity. As seen in (16), a
marginal increase in b' means that the firm is able to raise (1 +
[tau]) [q + [[partial derivative]q/[partial derivative]b'] b']
in extra funds through the debt market (and through an additional tax
subsidy). For each unit of extra funds raised, the firm is able to save
on the external equity cost [[lambda].sub.0]. (11)
Similarly, the first-order condition for k' is now given by
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (17)
This condition only holds with equality when d [not equal to] 0. In
the case of costly external equity, the marginal benefit of additional
investment is the same. However, there is now potentially an additional
cost associated with increasing k'. When the firm is already
relying on external equity (d < 0), the additional unit of k'
must be financed with expensive external equity. Since a higher k'
tends to lower the price on existing debt, the firm only needs to raise
1 - (1 + [tau]) [[partial derivative]q/[partial
derivative]k']b' of external equity. For every unit of
additional external equity the firm raises, it must pay the cost
[[lambda].sub.0].
The right panel of Figure 2 plots the policy functions for k',
b', and d as a function of internal equity when external equity is
costly. Examination of Figure 2 reveals that firms now behave
differently depending on how much internal equity they have (their
initial size). There are three regions of interest: (1) firms with low
levels of internal equity, (2) firms with medium levels of internal
equity, and (3) firms with high levels of internal equity.
First consider firms with low (but not necessarily negative) levels
of internal equity. From Figure 2, it can be seen that k' <
[k.sup.*], b' < [b.sup.*], and d < 0. Because these firms
start out with low levels of internal equity, they need to issue equity
to reach even low levels of k'. Consequently, it is still
beneficial to issue even a small amount of external equity to increase
their investment. However, because of the cost, they do not issue as
much as they would when [[lambda].sub.0] = 0. Nevertheless, even though
they choose b' < [b.sup.*], it is the case that b'/k'
> [b.sup.*]/[k.sup.*]. Because of the high cost of external equity,
they still do substitute toward more debt relative to a lower level of
k'. As internal equity increases they substitute external with
internal equity while maintaining the same amount of investment and debt
issuance.
[FIGURE 2 OMITTED]
Now consider firms with medium levels of internal equity. These
firms choose k' < [k.sup.*] and b' < [b.sup.*], but also
d = 0. Intuitively, the first-order conditions for b' and k'
in (16) and (17) do not hold with equality. Because they have more
internal equity, they avoid issuing costly external equity. Instead,
they rely only on internal funds and debt to finance investment.
However, firms in this region will use any additional internal equity to
increase their investment (while maintaining d = 0). As a result, both
k' and b' are increasing with e. Moreover, as firms obtain
more internal equity, b'/k' is decreasing toward
[b.sup.*]/[k.sup.*].
Finally, consider firms with high levels of internal equity. These
firms have so much internal equity that they are able to choose k'
= [k.sup.*] and b' = [b.sup.*] without having to raise external
equity. When external equity was costless, they chose d > 0. Costly
external equity has no effect on them because they were not raising
external equity anyway. Hence, their behavior coincides with the case of
costless external equity where investment and debt issuance are constant
and the firms are issuing positive dividends.
Cyclicality of Debt and Equity Issuance
Here we use our stylized framework to analyze the effects of
productivity changes (z) on investment, debt, and equity issuance
(k', b', and d, respectively). Figure 3 plots the policy
functions for k', b', and d as a function of internal equity
when external equity is costly. We plot the policy functions when
productivity is low (z = [z.sub.L]) and when productivity is high (z =
[Z.sub.H]). A higher value of productivity will affect the firm's
capital structure in two ways. First, internal equity e(z, k, b) = zf
(k) + (1 - [delta])k - b will increase. Second, if shocks are
autocorrelated (which is true in our simple example), a higher z in the
first period will imply a higher expected z' in the next period.
Using Figure 3, we can distinguish between the two since we plot how the
policy functions change for a given amount of internal equity.
Looking at Figure 3, we see that higher productivity shifts k'
upward since the marginal benefit of investing increases (see Equation
[14]). This means that a fraction of previously unconstrained firms will
find themselves constrained since the same amount of e will not be
enough to sustain the larger amount of investment. Debt issuance b'
will also increase. As firms invest more, the default threshold
decreases for any given b' > (1 - [theta])(1 - [delta])k'
(i.e., [partial derivative][z.sup.*]/[partial derivative]k' <
0). This increases the borrowing capacity of the firm and lowers the
marginal bankruptcy costs for each individual b'. Since the tax
benefit of debt is [tau]qb', the higher borrowing capacity also
increases the marginal benefit of issuing debt. Both effects cause
b' to increase for a given level of internal equity. The increase
in debt issuance is not uniform across firm sizes though. Smaller firms
issue less debt than larger firms.
External equity issuance will increase (or dividend payout will
decrease) in response to an increase in productivity. Firms with low
amounts of internal equity e will increase their equity issuance to
sustain a larger amount of investment. Since equity issuance is costly,
they will change their issuance by only a small amount. Firms with a
medium level of e will not issue equity or distribute any dividends.
However, the set of (constrained) firms that do not distribute any
dividends will increase. Similarly, firms with a high level of e will
decrease the amount of dividends that they pay out.
Hence, for a given amount of internal equity our simple model
predicts a procyclical debt and equity issuance. Of course, as stated
before, e will also increase if z increases. A larger internal equity
will represent a movement along the policy functions. This can
potentially increase debt issuance but decrease external equity issuance
(or increase dividend payout). So while debt issuance is definitely
procyclical, equity issuance might be procyclical or countercyclical
depending on how strong the opposing effects are. Based on Figure 3 it
seems that for smaller firms the equity issuance is more likely to be
countercyclical but for larger firms it is more likely to be
procyclical.
[FIGURE 3 OMITTED]
4. FULL MODEL
Utilizing the basic ingredients of our stylized two-period model in
Section 3, we now build a fully dynamic model with heterogeneous firms
and aggregate productivity shocks. Nevertheless, to keep the analysis
simple, we assume a partial equilibrium framework.
Entrepreneurs and Firms
The economy is populated by a continuum of entrepreneurs. Each
entrepreneur operates a firm. Entrepreneurs, and thus the firms they
operate, differ with respect to their idiosyncratic productivity z.
Firms are perfectly competitive and produce a single homogeneous good.
Capital k and labor l are inputs into the firm's production
function, y = Az[([k.sup.[alpha]][l.sup.1-[alpha]]).sup.[gamma]], where
A is aggregate productivity. We assume that [gamma] [member of] (0,1),
implying that there are decreasing returns to scale at the firm level.
With the assumption of perfect competition, diminishing returns to scale
enable heterogeneity to exist in equilibrium. Assuming a competitive
labor market, the firm's profits can be denoted by
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (18)
where w is the real wage. Since this is a partial equilibrium
analysis, the wage w is normalized to 1.
We assume that both ln z and ln A follow an AR(1) process:
ln z' = [[rho].sub.z] ln z + [[epsilon].sup.z] ln A' =
[[rho].sub.a] ln A + [[epsilon].sup.A],
where [[epsilon].sup.z] ~ N(0, [[sigma].sup.z.sub.[epsilon]]) and
[[epsilon].sup.A] ~ N(0, [[sigma].sup.A.sub.[epsilon]]). Since z is an
idiosyncratic shock, [[epsilon].sup.z] is assumed to be independent of
[[epsilon].sup.A]. We denote by F(z'|z) and f(z'|z) the
cumulative distribution and probability density functions for next
period's productivity z', conditional on the current
productivity z. Similarly, let p(A'|A) denote the probability
density function for A', conditional on current aggregate
productivity A.
Every period firms choose how much capital to invest for next
period k'. Investment is subject to a capital adjustment cost g(k,
k'). We will assume that this function takes the form g(k,k')
= [phi][([k'.sup.2]/k]. This will guarantee a gradual transition of
firms toward their optimal size. Firms issue bonds b', which are
priced at q(A, z, k', b'). This price will be determined
endogenously based on the investment and debt issuance decisions of the
firm as well as the idiosyncratic and aggregate shocks. As in Section 3,
firms receive a tax subsidy from the government, [tau]q(A, z, k',
b')b'. Firms also have the option of distributing dividends (d
> 0) or issuing equity (d < 0). As in Section 3, we assume that
external equity is costly. However, now we specify the cost [LAMBDA](A,
d) as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Following Covas and Den Haan (2012), we assume that equity issuance
costs are lower during expansions. This assumption will be critical to
match the procyclicality of equity issuance in the data.
After the firm chooses k', b', and d, it may exit next
period. We assume there are two reasons a firm may exit. First, a
constant fraction p will exogenously be forced to exit. In this case, it
is assumed that the entire firm value is destroyed. This implies that
the firm will default and both the entrepreneur and lender will recover
nothing. Second, depending on tomorrow's realization of A' and
z', some entrepreneurs will endogenously default on their debt
obligations. In this case, we assume that the firm is liquidated but
that the entrepreneur lives on to found a new firm (a start-up). We
discuss this default decision in the next subsection in more detail.
Default Decision
In deciding whether or not to default, the entrepreneur compares
the value of "not defaulting" to the value of
"defaulting." We define [V.sup.ND] (A, z, k, b) to be the
value of not defaulting for a firm with state (A, z, k, b). Similarly,
we define [V.sup.D (A, z, k) to be the firm's value of default.
These value functions will be defined below. Given these value
functions, the firm's total value V(A, z, k, b) is defined to be
V(A, z, k, b) = max {[V.sup.ND](A, z, k, b), [V.sup.D](A, z, k)}.
(19)
If [V.sup.ND](A, z, k, b) [greater than or equal to] [V.sup.D](A,
z, k), the firm pays back its debt b and continues its operations.
Otherwise, the firm chooses not to pay back its debt b and defaults.
The value of not defaulting, [V.sup.ND](A, z, k, b), is then
defined to be
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (20)
s.t. d = [pi](A, z, k) + (1 - [delta])k - b + (1 + [tau])q(A, z,
k', b')b' - k' - g(k, k'). (21)
If the firm does not default, it chooses how much to invest
(k'), how much debt it will issue (b'), and if it will
distribute dividends (d > 0) or issue equity (d < 0). It makes
these decisions subject to the budget constraint in (21). As noted
earlier, the firm must also pay an equity issuance cost ([LAMBDA](A, d)
> 0) if it issues equity (d < 0). Next period, with probability r,
the entrepreneur receives the exogenous exit shock and receives nothing.
With probability 1 - [eta], however, the firm does not exogenously exit.
In this case, depending on tomorrow's realization of A' and
z', the firm can decide tomorrow whether to default or continue
operating.
If the firm defaults, it shuts down its operations and is
liquidated. Nevertheless, the entrepreneur can hide a fraction [theta]
of the firm's undepreciated capital. Moreover, the entrepreneur can
start a new firm next period. Hence, the owner can transfer his
idiosyncratic productivity to a different project while eliminating his
debt obligations. Given these assumptions, the value of defaulting,
[V.sup.D](A, z, k) is assumed to be
[V.sup.D](A, z, k) = {[theta](1 - [delta])k + [1/[1 + r]] E
[[V.sup.s](A', z')|A, z]}, (22)
where [V.sup.s](A', z') is the value of a start-up
tomorrow with aggregate productivity A' and idiosyncratic
productivity z'. This value function will be defined later.
In general, we can define a threshold [z.sup.*](A, k, b) such that
firms with capital k, debt b, and idiosyncratic productivity lower than
[z.sup.*](A, k, b) will default. This threshold is defined to be the
value of idiosyncratic productivity [z.sup.*] such that the firm is just
indifferent between defaulting and not defaulting:
[V.sup.ND](A, [z.sup.*], k, b) = [V.sup.D (A, [z.sup.*], k). (23)
Consequently, this default threshold will depend on the aggregate
level of productivity (A) as well as the firm's individual levels
of capital (k) and debt (b). The default threshold [z.sup.*] increases
if debt b is large and decreases if capital k is large or if the economy
is booming (A is high).
Bond Price
The firm issues bonds that are purchased by risk-neutral
households. Households lend q(A, z, k', b')b' to firms
today, and in return the firm promises to pay b' next period. Given
that the default is possible, the price q(A, z, k', b') is set
to guarantee the lender an expected return equal to the risk-free rate
r. Consequently, the bond price will be given by
q(A, z, k', b') = [[1 - [eta]]/[1 + r]] [l -
F([z.sup.*](A', k', b')|z) + [R(A, z, k',
b')/b']], (24)
where
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
is the unconditional recovery value of the bond. With probability
[eta], the firm receives an exogenous exit shock and the lender receives
nothing. However, with probability (1 - [eta]), the firm does not
receive an exit shock. In this case, the firm does not default with
probability 1 - F([z.sup.*]|z) and the lender receives b'. However,
if the firm defaults, then the lender receives fraction (1 - [psi])(1 -
[theta]) of its undepreciated capital. The parameter [theta] controls
how much of the capital stock the entrepreneur can hide while [psi]
reflects the bankruptcy costs.
Entry
As noted earlier, there are two reasons firms exit in this model.
First, a fraction [eta] of firms will exogenously exit. The
entrepreneurs of these firms are assumed to be replaced by
"new" entrants. Therefore, while a constant fraction of
entrepreneurs exit each period, a constant mass of entrepreneurs are
born each period. These new entrepreneurs are assumed to draw their
initial idiosyncratic productivity from the invariant distribution for
z. Second, some of the remaining firms will endogenously choose to
default. The entrepreneurs of these firms, however, are able to
continue. In particular, these entrepreneurs can start a new firm
(start-up) in the next period.
Therefore, in every period, firms will be destroyed and created at
the same time. Because firms are assumed to be born with no capital, a
start-up will have zero profits in the first period. Then, a start-up
firm will choose how much to invest (k'). This investment can be
financed by raising equity (d < 0) or by issuing debt (b'). Let
[V.sup.s](A, z) denote the value of a start-up with aggregate
productivity A and idiosyncratic productivity z. This value is defined
to be
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (25)
Therefore, the problem of a start-up is very similar to the problem
of a continuing firm. However, a start-up begins its life with no debt
and no assets. Because the start-up has no initial capital, it is
assumed that it does not pay any capital adjustment costs.
Timing
The timing of the economy can be described as follows.
1. All entrepreneurs/firms receive productivity draws A and z.
2. A fraction q of firms are exogenously destroyed.
3. Surviving firms with state {z, A, k, b} decide to default if z
< [z.sup.*] (A, k, b). Firms that default exit.
4. Firms that did not default, as well as new start-ups, make
investment and firm financing (debt and equity) decisions.
5. QUANTITATIVE ANALYSIS
In this section we quantitatively characterize our model of firm
financing. We calibrate our model either using parameters commonly used
in the literature or targeting specific moments computed in the data. We
compare the model's predictions for the same set of statistics
computed from Compustat in Section 2.
Calibration
All parameter values are reported in Table 3. The model is computed
at an annual frequency. We normalize the wage rate to 1 and set an
annual risk-free rate of 4 percent. The depreciation rate is set at 10
percent, a value commonly employed in the literature. The capital share
equals [alpha] = 0.36 and, based on Gomes and Schmid (2010), the
decreasing returns to scale parameter is [gamma] = 0.65. The firms'
exit rate [eta] is set to 0.04 based on Cooley and Quadrini (2001).
Bankruptcy cost equals [psi] = 0.25 based on Arellano, Bai, and Zhang
(2012). Following Covas and Den Haan (2012), we assume that equity
issuance costs are lower during expansions and set[ [lambda].sub.0] =
0.75 and [[lambda].sub.1] = 20.
The persistence of idiosyncratic productivity [[rho].sub.z] = 0.55
is based on Clementi and Palazzo (2014). Although the authors provide an
estimate for [[sigma].sup.z.sub.[epsilon]], we choose to use this
parameter to match a specific moment (see below). We also borrow their
estimates to calibrate the persistence and standard deviation of the
aggregate productivity process. In particular,[ [rho].sub.a] is set to
0.68 and [[sigma].sup.A.sub.[epsilon]] is chosen to be 0.016.
The remaining parameters, {[tau], [theta], [phi],
[[sigma].sup.z.sub.[epsilon]]}, are chosen to match specific model
moments. In particular, a higher tax benefit [tau] will encourage firms
to issue more debt and increase their leverage ratio. Therefore, to
match the mean leverage ratio observed in Compustat, [tau] is set to
0.02. Conditional on the value of [psi], a larger value of [theta]
induces more firms to default since they can hide and keep a larger
fraction of their assets. Thus, to match the mean default rate in the
economy, [theta] is set to 0.93. The adjustment cost parameter 0 affects
how fast firms grow. Hence, to match the average cross-sectional growth
rate of sales, [phi] is set to 0.10. Finally, a larger dispersion in
idiosyncratic productivity will lead to a larger dispersion in the
growth of sales. With a value of [[sigma].sup.z.sub.[epsilon]] = 0.18,
the model matches the cross-sectional standard deviation of sales
growth.
Steady-State Results
We start by characterizing the steady state of the economy. In the
steady state, aggregate productivity is constant in every period (A =
1). Based on our policy functions, we simulate a panel of firms and
track their behavior over time. We use the stationary distribution to
construct several statistics and compare them to the ones computed from
Compustat. Table 4 gives a summary of the results.
In Compustat the distribution of leverage across firms is found to
be highly skewed to the right. Excluding firms at the top 1 percent of
the distribution, the average leverage ratio is 27 percent. Our model
economy is able to match this statistic by targeting the tax credit
[tau]. In contrast, leverage ratios are more dispersed in the data than
our model. The standard deviation of leverage in Compustat is 0.37, much
higher than the model's result of 0.15. A reason for this failure
is the relatively low value for the persistence of idiosyncratic
productivity [[rho].sub.z]. If idiosyncratic shocks are not very
persistent then even unproductive firms can easily get access to credit.
Indeed, we have experimented with higher values of [[rho].sub.z] and
found that the standard deviation of leverage increases. Moreover, the
model can perform well with respect to sales growth. The mean of sales
growth in the model is 0.12, very close to the value computed in the
data (0.11). This statistic was targeted using the adjustment cost
parameter [phi]. The model can also capture the dispersion in sales
growth rates (0.45 in the model versus 0.51 in the data). To match this
moment, we used the dispersion of idiosyncratic productivity shocks
[[sigma].sup.z.sub.[epsilon]].
We next compare the behavior of small versus large firms. Using
data from Compustat and consistent with Rajan and Zingales (1995) and
Cooley and Quadrini (2001), we find a positive relationship between
leverage and total assets. However, the differences seem to be minor as
firms with assets smaller than the median have a leverage equal to 0.27
while firms with assets larger than the median have a leverage equal to
0.28. In our model, these numbers are 0.30 and 0.23, respectively. In
Section 3, we saw that as firms obtain more internal equity, the ratio
[b'/k'] decreases. Smaller firms (with lower internal equity)
substitute more toward debt to avoid using costly external equity.
Moreover, due to decreasing returns to scale, the model replicates
qualitatively the empirical observation that smaller firms grow faster.
In the model, sales growth is 0.21 for small firms and 0.04 for large
firms. In Compustat, these numbers are 0.12 and 0.10, respectively. In
general the model captures the basic features of the data with some
success.
Business Cycle Results
We now allow the economy to experience aggregate productivity
shocks. To avoid further computational complexity we assume that the
prices do not adjust in response to productivity changes. If we allowed
for a general equilibrium framework, we would have to keep track of the
distribution of firms over debt, capital, and equity, which would
greatly increase the state space.
Table 5 reports the correlation between debt and equity issuance
with aggregate output. To facilitate the comparison with the data, we
include information from the top panel of Table 2 that excludes only
major mergers from the sample. In Section 2, we showed that mergers are
an important way that firms raise equity. The model replicates the
positive correlation between debt issuance and aggregate output (0.868
in the model versus 0.785 in the data). As explained in Figure 3, a
higher productivity increases k', allowing the firm to issue more
debt. Table 5 also reports how the cyclicality differs among small and
large firms. In Section 2, we documented that the cyclicality is
stronger for larger firms (excluding the top 1 percent). Our model
replicates this pattern and can match very closely the cyclicality of
firms in the [75, 99] bin (0.737 in the model versus 0.755 in the data).
In response to an increase in productivity, a small firm may
disproportionately increase b' by disproportionately decreasing
external equity issuance. In contrast, large firms that issue a small
amount of external equity will increase b' in a relatively
proportional manner. (12) As a result, we find the correlation between
debt issuance and output (productivity) to be much higher in the case of
large firms. A similar nonlinearity occurs for the largest firms when
they start distributing dividends, which explains why the correlation
decreases for that group.
The model also generates a countercyclical equity issuance. In
Section 2, we documented that equity issuance can be weakly procyclical
or countercyclical depending on the way we measure equity. Moreover, we
have shown that much of the procyclicality is due to raising equity
through mergers and that the cyclicality becomes negative if we just
consider net sale of stock. In the model, net equity issuance [DELTA]E
is strongly countercyclical. Similar to the data, we break net equity
issuance [DELTA]E into a gross equity issuance [E.sup.I] and a gross
equity payout [E.sup.P] component, with [DELTA]E = [E.sup.I] -
[E.sup.P]. Our decomposition reveals that the strong countercyclicality
of net equity issuance is driven by a strongly procyclical gross
dividend payout. In the model, smaller firms prefer to raise more gross
equity than paying out gross dividends during expansions. This leads to
a procyclical equity finance for firms in the [0, 50] bin, similar to
what we observe in the data. Nevertheless, the procyclicality of equity
issuance for small firms relies on our assumption (among others) of
countercyclical equity issuance costs. Overall, the model is consistent
with the empirical patterns we see in equity financing.
6. CONCLUSION
This article provides an introductory, yet comprehensive, business
cycle analysis of firm financing. We first document several empirical
patterns of debt and equity issuance based on data from Compustat. While
we find that debt issuance is strongly procyclical, the cyclicality of
net equity issuance depends on the exact definition used. If we define
equity using the net sale of stock (following Jermann and Quadrini
[2012]), we find net equity issuance to be countercyclical.
Alternatively, if we define equity issuance using the change in the book
value of equity (following Covas and Den Haan [2011]), we find net
equity issuance to be weakly procyclical. Nevertheless, we find that
equity financing through mergers and, to a lesser extent, stock
compensation can explain much of the discrepancy between the two
measures. Moreover, regardless of the measure used, the
countercyclicality of net equity issuance is driven by a strongly
procyclical gross payout to equity and not countercyclical gross equity
issuance. Overall, these empirical findings should be useful in
evaluating theoretical models, which stress the role of the financial
sector in propagating aggregate fluctuations. Of particular interest,
perhaps, is the heterogeneous behavior of firm financing and the role of
mergers and acquisitions.
To help build intuition, we analyze the firm's optimal capital
structure within a simple two-period model. Then, to determine how well
our framework can match the cyclical properties of firm financing, we
build a fully dynamic quantitative model. The model features
heterogeneous firms that endogenously choose their capital structure by
balancing the tax benefits against the bankruptcy costs of debt issuance
and the expenses associated with equity issuance. The model generates a
procyclical debt and countercyclical net equity issuance. Moreover, the
model can match the firm-size relationship regarding debt and especially
equity issuance. Overall, the model is useful for illustrating the
important mechanisms involved. While firms issue more debt to finance
more investment, the model highlights that equity issuance provides
conflicting motives for the firm. On the one hand, firms would like to
issue more equity (which may be costly) to finance more investment. On
the other hand, firms would like to pay out more dividends in good
times. For most firms the second effect dominates in our model. However,
to generate procyclical net equity issuance for small firms, we assume
that equity issuance costs are lower during expansions.
APPENDIX A: DATA SOURCES
We obtain annual data from Compustat between 1980 and 2013. We
exclude financial firms (SIC 6000-6999) and utilities (SIC 4900-4999).
We drop any firm-year observations if we do not have any information on
assets, capital stock, debt, or both equity measures. We drop
observations that violate the accounting identity by more than 10
percent. We drop firms affected by 1988 accounting change (GM, GE, Ford,
Chrysler). (13) We only include firms reporting in USD. One important
concern is whether we include firms affected by a merger or an
acquisition. For this purpose, we separately report our results for two
cases. In the first case, we follow Covas and Den Haan (2011) and drop
all firm-year observations that are affected by a "major"
merger or acquisition. By "major" we mean that the merger or
acquisition causes the resulting firm's sales to increase by more
than 50 percent. In the second case, we drop all observations affected
by any kind of merger. To identify whether a firm was involved in a
merger, we use the footnote code on sales. Compustat assigns the
footnote code AB if the data reflects a major merger or acquisition.
Meanwhile, footnote code AA reflects other acquisitions.
SE is defined as the book value of stockholder's equity (data
item #216) minus retained earnings (data item #36). [DELTA]E(1) is
defined to be the annual change in SE minus cash dividends (data item
#127). The net sale of stock is defined to be the funds received from
the issuance of common and preferred stocks (data item #108) minus
equity repurchases (data item #115). [DELTA]E(2) is defined to be the
net sale of stock minus cash dividends. RE is the balance sheet item for
retained earnings (data item #36). ws is stock compensation (data item
#398). Sales is given by data item #12, which represents gross sales
(i.e., the amount of actual billings to the customers). Total assets is
the book value of assets (data item #6). We define debt as the sum of
debt in current liabilities (data item #34) and long-term debt (data
item #9). The capital stock K is (net) property, plant, and equipment
(data item #8). Investment I equals capital expenditures on property,
plant, and equipment (data item #30).
And finally, we obtain real corporate GDP from the Bureau of
Economic Analysis's National Income and Product Accounts.
Particularly, we use Table 1.14, which reports the gross value added of
domestic non-financial corporate business, in billions of chained (2009)
dollars.
APPENDIX B: SIMPLIFIED VALUE FUNCTION
In (12), the firm's problem was given by
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
subject to the budget constraint, which is
d + k' = e(z, k, b) + (1 + [tau])q(z, k',
b')b'.
Using the definitions of [V.sup.ND](Z, k', b') and
[V.sup.D](z', k') in (8) and (9), we can re-write the
firm's value function as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
When we substitute for d using the firm's budget constraint,
this becomes
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Moreover, in (11), the bond price was defined to be
q(z, k', b') = [1/[1 + r]][1 - F([z.sup.*](k',
b')|z) + [R(z, k', b')/b']],
where
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Therefore, using that qb'(1 + r) = [1 - F([z.sup.*])] b'
+ R, we arrive at (13):
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
REFERENCES
Arellano, Cristina, Yan Bai, and Jing Zhang. 2012. "Firm
Dynamics and Financial Development." Journal of Monetary Economics
59 (6): 533-49.
Begenau, Juliane, and Juliana Salomao. 2014. "Firm Financing
over the Business Cycle." Working Paper, Stanford University.
Bernanke, Ben S., John Y. Campbell, and Toni M. Whited. 1990.
"U.S. Corporate Leverage: Developments in 1987 and 1988."
Brookings Papers on Economic Activity 21 (1): 255-86.
Clementi, Gian Luca, and Berardino Palazzo. 2014. "Entry,
Exit, Firm Dynamics and Aggregate Fluctuations." Working Paper, New
York University.
Cooley, Thomas F., and Vincenzo Quadrini. 2001. "Financial
Markets and Firm Dynamics." American Economic Review 91 (December):
1,286-310.
Covas, Francisco, and Wouter J. Den Haan. 2011. "The Cyclical
Behavior of Debt and Equity Finance." American Economic Review 101
(April): 877-99.
Covas, Francisco, and Wouter J. Den Haan. 2012. "The Role of
Debt and Equity Finance over the Business Cycle." Economic Journal
122 (December): 1,262-86.
Eisfeldt, Andrea L., and Adriano A. Rampini. 2006. "Capital
Reallocation and Liquidity." Journal of Monetary Economics 53
(April): 369-99.
Fama, Eugene F., and Kenneth R. French. 2005. "Financing
Decisions: Who Issues Stock?" Journal of Financial Economics 76
(June): 549-82.
Fazzari, Steven M., R. Glenn Hubbard, and Bruce C. Petersen. 1988.
"Financing Constraints and Corporate Investment." Brookings
Papers on Economic Activity 1988 (1): 141-195.
Gomes, Joao F., and Lukas Schmid. 2010. "Levered
Returns." Journal of Finance 65 (April): 467-94.
Gourio, Francois. 2013. "Credit Risk and Disaster Risk."
American Economic Journal: Macroeconomics 5 (July): 1-34.
Hennessey, Christopher A., and Toni M. Whited. 2007. "How
Costly is External Financing? Evidence from a Structural
Estimation." Journal of Finance 62 (August): 1,705-45.
Jermann, Urban, and Vincenzo Quadrini. 2012. "Macroeconomic
Effects of Financial Shocks." American Economic Review 102
(February): 238-71.
Katagiri, Mitsuru. 2014. "A Macroeconomic Approach to
Corporate Capital Structure." Journal of Monetary Economics 66:
79-94.
Modigliani, Franco, and Meron H. Miller. 1958. "The Cost of
Capital, Corporation Finance and the Theory of Investment."
American Economic Review 48 (June): 261-97.
Rajan, Raghuram G., and Luigi Zingales. 1995. "What Do We Know
about Capital Structure? Some Evidence from International Data."
Journal of Finance 50 (December): 1,421-60.
For very helpful suggestions we thank Kartik Athreya, Arantxa
Jarque, Marisa Reed, and Alex Wolman. Any opinions expressed are those
of the authors and do not necessarily reflect those of the Federal
Reserve Bank of Richmond or the Federal Reserve System. E-mail:
[email protected];
[email protected].
(1) In a related article, Covas and Den Haan (2012) build a
quantitative model of debt and equity finance. Our model in Section 4
uses many of their modeling assumptions.
(2) For more details on the construction of our data, see Appendix
A.
(3) We can similarly break up the second definition of equity.
However, as discussed earlier, the second definition of equity tends to
understate equity issuance.
(4) However, note that our data for stock compensation only begins
in 2001.
(5) Throughout this article, we use a smoothing parameter of 100 to
de-trend annual data.
(6) There are, on average, 31 firms in the top 1 percent every
year.
(7) Eisfeldt and Rampini (2006) document that capital reallocation
due to acquisitions is procyclical.
(8) We are assuming that the tax subsidy takes place at issuance.
However, in reality, the implicit tax subsidy takes place when the
firm's earnings are taxed, as interest payments can be deducted
from corporate taxable income.
(9) The readers can find the exact derivation of this expression in
Appendix B.
(10) See Modigliani and Miller (1958).
(11) We should note that in the infinite-horizon version of this
model, issuing debt will be associated with one more cost. In
particular, the firm might want to issue less debt in case it ends up
receiving a bad draw tomorrow and issuing costly equity to avoid
default. This is a precautionary savings mechanism for the firm. In our
two-period version there are only positive payments to shareholders in
the second period.
(12) To understand these properties better we refer the reader to
Figure 3. Although in our fully dynamic model we include quadratic
capital adjustment costs and quadratic equity issuance costs, the basic
properties of the policy functions remain intact.
(13) See Bernake, Campbell, and Whited (1990) for details.
Table 1 Summary Statistics
Size Class (Percent)
No Major [0, 50] [50, 75] [75, 99] [99, 100] [0, 100]
Mergers
[DELTA]D 10.1 8.6 5.4 2.7 4.7
[DELTA]E(1) 69.0 8.6 -3.0 -5.3 -3.0
[DELTA]E(2) 40.6 -1.5 -9.9 -10.0 -9.4
[DELTA]E(i)- 28.4 10.0 6.9 4.7 6.3
[DELTA]E(2)
[w.sub.S] 7.9 2.6 0.9 0.3 0.8
[E.sup.I] 79.8 18.0 6.9 4.7 6.9
[E.sup.P] 10.8 9.4 10.0 10.0 10.0
[DELTA]RE -35.7 3.6 4.5 3.4 4.0
I 4.6 1.9 0.7 1.1 0.9
[DELTA]S 42.1 28.3 14.5 14.3 15.0
Size Class (Percent)
No Mergers [0, 50] [50, 75] [75, 99] [99, 100] [99, 100]
At All
[DELTA]D 4.0 0.7 1.7 0.9 1.5
[DELTA]E(1) 76.8 3.6 -5.8 -7.4 -5.6
[DELTA]E(2) 53.3 -1.7 -9.5 -10.7 -9.3
[DELTA]E(i)- 23.4 5.3 3.7 3.3 3.7
[DELTA]E(2)
[w.sub.S] 8.7 2.6 0.8 0.4 0.8
[E.sup.I] 87.8 14.1 3.6 2.4 4.0
[E.sup.P] 11.0 10.5 9.4 9.9 9.6
[DELTA]RE -49.9 4.1 4.5 6.1 4.8
I 4.8 1.5 0.3 0.5 0.5
[DELTA]S 30.7 15.2 9.4 10.6 9.9
Notes: This table reports the average of various group aggregates
between 2001 and 2013. Each variable is expressed as a percentage
of the group capital stock. [DELTA]D is net debt issuance.
[DELTA]E(1) is the first measure of net equity issuance and is
defined in (1). Similarly, [DELTA]E(2) is the second measure of
equity issuance and is defined in (2). [w.sub.S] is stock
compensation. [E.sup.I] is gross equity issuance and is defined in
(3). [E.sup.P] is gross equity payouts and is defined in (4).
[DELTA]RE is the net change in retained earnings. I is investment.
[DELTA]S is the net change in sales. Note that we only have data on
stock compensation between 2001 and 2013.
Table 2 Business Cycle Correlations of Debt and Equity
Issuance
Size Class (Percent)
No Major [0, 50] [50, 75] [75, 99] [99, 100] [0, 100]
Mergers
[DELTA]D 0.536 0.611 0.755 0.547 0.785
(0.001) (0.000) (0.000) (0.001) (0.000)
[DELTA]E(1) 0.345 0.191 0.016 0.044 0.096
(0.046) (0.280) (0.927) (0.804) (0.589)
[DELTA]E(2) 0.243 -0.250 -0.617 -0.312 -0.509
(0.166) (0.155) (0.000) (0.072) (0.002)
[w.sub.S] 0.010 -0.050 0.066 0.022 0.341
[E.sup.I] (0.973) (0.859) (0.816) (0.937) (0.214)
0.353 0.268 0.306 0.250 0.363
(0.041) (0.125) (0.079) (0.153) (0.035)
[E.sup.P] 0.069 0.279 0.654 0.314 0.588
(0.697) (0.110) (0.000) (0.071) (0.000)
Size Class (Percent)
No Mergers [0, 50] [50, 75] [75, 99] [99, 100] [0, 100]
At All
[DELTA]D 0.646 0.590 0.661 0.418 0.661
(0.000) (0.000) (0.000) (0.014) (0.000)
[DELTA]E(1) 0.264 -0.168 -0.419 -0.303 -0.322
(0.132) (0.343) (0.014) (0.082) (0.064)
[DELTA]E(2) 0.230 -0.312 -0.687 -0.193 -0.506
(0.191) (0.072) (0.000) (0.274) (0.002)
[w.sub.S] 0.035 0.027 0.009 -0.005 0.225
[E.sup.I] (0.901) (0.924) (0.975) (0.985) (0.421)
0.283 -0.040 0.033 -0.113 0.100
(0.105) (0.824) (0.852) (0.524) (0.573)
[E.sup.P] 0.240 0.273 0.627 0.314 0.586
(0.172) (0.119) (0.000) (0.071) (0.000)
Notes: This table reports correlations of group aggregates with
real corporate GDP. All variables are de-trended with an H-P
filter. The p-values for each correlation are shown in parentheses.
Coefficients that are significant at the 5 percent level are shown
in bold. [DELTA]D is net debt issuance. [DELTA]E(1) is the first
measure of net equity issuance and is defined in (1). Similarly,
[DELTA]E(2) is the second measure of equity issuance and is defined
in (2). [w.sub.S] is stock compensation. [E.sup.I] is gross equity
issuance and is defined in (3). [E.sup.P] is gross equity payouts
and is defined in (4). Note that we only have data on stock
compensation between 2001 and 2013.
Table 3 Parameter Values
Parameter Description Value
r Real interest rate 0.04
[delta] Depreciation rate 0.10
[alpha] Capital share 0.36
[gamma] Returns to scale 0.65
[eta] Exit rate 0.04
[psi] Bankruptcy cost 0.25
[[lambda].sub.0] Equity issuance cost 0.75
[[lambda].sub.1] Equity issuance cost 20
[[rho].sub.z] Persistence of z 0.55
[[rho].sub.a] Persistence of A 0.68
[[sigma].sup.z. Standard deviation of 0.18
sub.[epsilon]] [[epsilon].sup.z]
[[sigma].sup.A. Standard deviation of 0.016
sub.[epsilon]] [[epsilon].sup.A]
[tau] Tax credit 0.07
[theta] Hidden fraction 0.93
[phi] Capital adjustment cost 0.10
Parameter Target
r Standard
[delta] Standard
[alpha] Standard
[gamma] Gomes and Schmid (2010)
[eta] Cooley and Quadrini (2001)
[psi] Arellano, Bai, and Zhang (2012)
[[lambda].sub.0] Covas and Den Hann (2012)
[[lambda].sub.1] Covas and Den Hann (2012)
[[rho].sub.z] Clementi and Palazzo (2014)
[[rho].sub.a] Clementi and Palazzo (2014)
[[sigma].sup.z. S.D. of sales growth
sub.[epsilon]]
[[sigma].sup.A. Clementi and Palazzo (2014)
sub.[epsilon]]
[tau] Mean leverage
[theta] Mean default
[phi] Mean of sales growth
Notes: This table reports the parameter values used in the
quantitative model. Each parameter is calibrated either based on
the literature or targeting a specific moment.
Table 4 Steady-State Results
Data-Compustat
Statistic Small Firms Large Firms All
Mean (Leverage) 0.27 0.28 0.27
S.D. (Leverage) -- -- 0.34
Mean (Sales Growth) 0.12 0.10 0.11
S.D. (Sales Growth) -- -- 0.51
Model
Statistic Small Firms Large Firms All
Mean (Leverage) 0.30 0.23 0.27
S.D. (Leverage) -- -- 0.15
Mean (Sales Growth) 0.21 0.04 0.12
S.D. (Sales Growth) -- -- 0.45
Notes: This table shows the steady-state results for the mean and
standard deviation of leverage and sales growth respectively.
Statistics on leverage and sales growth are calculated from the
data (Compustat).
Table 5 Business Cycle Results
Size Class (Percent)
Data [0, 50] [50, 75] [75, 99] [99, 100] [0, 100]
[DELTA]D 0.536 0.611 0.755 0.547 0.785
[DELTA]E(1) 0.345 0.191 0.016 0.044 0.096
[DELTA]E(2) 0.243 -0.250 -0.617 -0.312 -0.509
[E.sup.I] 0.353 0.268 0.306 0.250 0.363
[E.sup.P] 0.069 0.279 0.654 0.314 0.588
Size Class (Percent)
Model [0, 50] [50, 75] [75, 99] [99, 100] [0, 100]
[DELTA]D 0.260 0.244 0.737 0.277 0.868
[DELTA]E(1) 0.447 -0.326 -0.714 -0.942 -0.764
[DELTA]E(2) 0.528 0.445 0.356 -- 0.386
[E.sup.I] 0.287 0.335 0.715 0.942 0.759
[E.sup.P]
Notes: This table reports the model-generated business cycle
properties of debt and equity issuance. This table also reports
empirical statistics as calculated in Section 2. For simplicity
we report empirical measures that exclude only major mergers from
our sample. For the empirical section, we show coefficients that
are significant at the 5 percent level in bold.
