The Cost of Debt∗
Jules H. van Binsbergen
Fuqua School of Business
Duke University†
John R. Graham
Fuqua School of Business
Duke University‡
and NBER
Jie Yang
Fuqua School of Business
Duke University§
This version: March 2007
AbstractWe use panel data from 1980 to 2005 to estimate cost functions for corporatedebt. We start with Graham’s (2000) debt benefit curves and assume thatfor financially unconstrained firms, the benefit curve intersects the cost curveat the actual level of debt, on average. Using this equilibrium condition,exogenous shifts of the benefit curves enable us to identify the marginal costcurve. We recover marginal cost functions that are positively sloped, and,by integrating to determine the area between the benefit and cost functions,we estimate that the net benefit of debt equals about 4% of asset value. Ourfindings are consistent across industries and years and are robust to accountingfor fixed adjustment costs of debt. We show that both the intercept andthe slope of the marginal cost curve of debt depend on firm characteristicssuch as asset collateral, book-to-market, sales, cash flows, cash holdings,personal taxes, wages, and whether the firm pays dividends. As such, ourframework provides a new parsimonious environment within which we canexamine implications from competing capital structure theories. Our approachalso allows us to make recommendations about firm-specific optimal debt ratiosand estimate the cost of being under or overlevered.
JEL classifications: G30,G32Keywords: Capital Structure, Cost of Debt
∗We thank Ravi Bansal, Jonathan Berk, Michael Brandt, Alon Brav, Hui Chen, Cam Harvey, Han Hong,Ralph Koijen, Mike Lemmon, Rich Mathews, Bertrand Melenberg, Anamarıa Pieschacon, Adriano Rampini,Michael Roberts, David Robinson, Ilya Strebulaev, George Tauchen, Toni Whited, and seminar participantsat Duke University for helpful comments.
†Durham, NC 27708. Phone: (919) 660-7636. Email: [email protected].‡Durham, NC 27708. Phone: (919) 660-7857. Email: [email protected].§Durham, NC 27708. Phone: (919) 660-2939. Email: [email protected].
1 Introduction
Hundreds of papers investigate corporate financial decisions and the factors influencing
capital structure. Much theoretical work characterizes the choice between debt and equity
in a trade-off context: firms choose their optimal debt ratio by balancing the benefits and
costs. Traditionally, tax savings that occur because interest is deductible while equity payout
is not have been modeled as a primary benefit of debt (Kraus and Litzenberger, 1973).
Other benefits of debt include committing managers to operate efficiently (Jensen, 1984) and
engaging lenders to monitor the firm (Jensen and Meckling, 1976). The costs of debt include
the cost of financial distress (Scott, 1976), personal taxes (Miller, 1977), debt overhang
(Myers, 1977), and agency conflicts between managers and investors or among different
groups of investors. For the most part, these theoretical predictions have been tested using
reduced form regressions that include proxy variables to measure the hypothesized effects.
The empirical results are somewhat mixed but a number of empirical regularities have been
documented. Large firms with tangible assets and few growth options tend to use a relatively
large amount of debt (Rajan and Zingales, 2003; Frank and Goyal, 2004). Firms with high
corporate tax rates also tend to have higher debt ratios and use more debt incrementally
(Graham, Lemmon, and Schallheim, 1998).
One reason that tax incentives receive a lot of attention in the literature (and in the
classroom) is because they are relatively easy to quantify and because the gross benefits seem
large (e.g., 35 cents per dollar of interest if the corporate income tax rate is 35 percent).
Tax incentives are sufficiently quantifiable that it is possible to simulate the entire benefit
function associated with interest tax deductibility and integrate under the curve to estimate
the gross tax benefits of debt (Graham, 2000). Therefore, at least in the tax dimension, we
are able to specify the firm-specific benefits of debt.
It has been much more elusive to quantify the costs of debt. Warner (1977) and Miller
(1977) observe that the traditional costs of debt (e.g., direct bankruptcy costs) appear to be
low relative to the tax benefits, implying that other, unobserved, or hard to quantify costs
are important. Several recent papers argue that once these other debt costs are considered,
the marginal costs roughly equal the marginal (tax) benefits of debt (e.g., Berk, Stanton and
Zechner, 2006; Carlson and Lazrak, 2006). Notwithstanding these theoretical arguments,
debt costs are generally hard to measure empirically. To date, the costs of debt have not
been explicitly quantified to the same degree as have the benefits.
In this paper, we explicitly map out the debt cost function. To do this, we need to address
issues related to the standard econometric difficulties associated with identifying demand and
supply curves. In our case, we start with Graham’s simulated marginal tax benefit curves
1
and the observed (equilibrium) debt choices. Observing variation in the marginal benefit
curve over time and in the cross section gives us an important advantage over the standard
demand and supply framework where only equilibrium points are observed. Whereas in the
latter framework one has to use as an instrumental variable that proxies for shifts of the
demand (supply) curve to identify the supply (demand) curve, we have the advantage of
observing the actual shifts of the marginal benefit curve. What remains is to purge from
these shifts potential correlation with cost curve shifts (econometric details are provided in
Section 2) by using a set of control variables that proxy for cost effects. Then, we use the
variation due to pure benefit shifts to identify the cost curve.
As just described, we use marginal benefit variation in both the cross section and in the
time series to determine marginal cost curves. However, our proposed method does critically
depend on the right choice of control variables. As such, omitted variables may induce a bias
in our estimates. To ensure that our results are not driven by such econometric issues we
repeat our analysis using as the sole instrument the exogenous tax regime shifts between 1980
and 2005. We show that this pseudo-natural experiment leads to estimates that are very
similar to those obtained in our main specification. Furthermore, our primary conclusions
hold when estimated from 1998 to 2005. During this period there were no exogenous tax
regime shifts, meaning that for this time period the time series approach is infeasible, and
therefore the identification of the cost curve is mainly based on cross-sectional marginal
benefit variation. Reassuringly, the cross-sectional approach also corroborates our main
results. This indicates that our results are robust to identifying the cost curve based on (i)
cross-sectional variation, (ii) time series variation, or (iii) a combination of the two.
Our analysis produces cost curves that are steeply and positively sloped, as expected.
We estimate different curves for each industry, and the slopes of these curves vary in ways
that make sense economically. We relate both the slope and the intercept of the cost curve
to firm characteristics such as whether the firm’s assets are collateralizable, book-to-market,
sales, cash flows, cash holdings and whether the firm pays dividends. We then compare our
findings to existing theories on the costs and benefits of debt. We also produce easy-to-
implement algorithms to allow researchers and practitioners to explicitly map out the debt
cost function by industry and by firm. This fills a big void in the current state of affairs by
providing both explicit quantification of the cost of debt and specific recommendations to
corporations in terms of optimal capital structure.
Our results are robust to the presence of fixed adjustment costs. Recently it has been
argued (e.g. Fischer, Heinkel and Zechner, 1989; Leary and Roberts, 2005; and Strebulaev,
2006) that fixed adjustment costs prevent firms from responding instantaneously to changing
2
conditions, leading to infrequent capital structure adjustments. With adjustment costs,
capital structure policy can be modeled as following an (s,S) rule, where an adjustment only
occurs if the ‘optimal’ capital structure falls outside a bandwidth with lower bound s and
upper bound S. We repeat our analysis by only including those firm-year observations in
which a substantial rebalancing of capital structure occurs. Our results appear the same on
this sample.
Armed with simulated debt benefit functions and estimated cost functions, we calculate
firm-specific optimal capital structure at the intersection of the curves. We also integrate the
area between the curves to estimate the net benefits of debt financing and the deadweight
costs to deviating from the optimum. We form subsamples based on the level of financial
constraint and financial distress. We assume that, on average, unconstrained and non-
distressed firms make optimal capital structure choices. Among these firms, we estimate that
the net benefit of debt financing equals 2.9-3.9% of book value for firms at the calculated
optimum leverage positions, on average, compared to a gross benefit of 10.1-10.2% of book
value. The net benefit of debt financing equals 0.2-1.7% of firm value for firms at the
observed leverage positions, on average, compared to a gross benefit of 9.0% of firm value.
This implies deadweight losses of about 2.2-2.6% of firm value due to costs of being away
from the optimum.
The rest of the paper proceeds as follows. In section 2, we explain the main intuition of
our instrumental variables approach. In section 3 we give an extensive data description. In
section 4, we report and discuss our results. Section 5 presents case examples of our analysis
for select firms. In section 6 we calculate the benefits and costs of debt and analyze the
costs of being under or overlevered. Section 7 discusses several robustness checks. Section 8
concludes.
2 Methodology of Estimating Marginal Cost Curves
Using the simulation techniques of Graham (2000), we create marginal tax benefit curves
of debt for a large panel of approximately 120,000 firm-years between 1980 and 2005. The
marginal benefit curve measures the marginal tax benefit for each dollar of incremental
interest deduction.1. The shape of these benefit curves varies by firm, but they are weakly
monotonic and typically horizontal for low levels of debt and become negatively sloped for
higher levels of debt (see Figure 1).
We know for each firm in each year the current level of debt. Henceforth, we will refer
1The mechanics of the marginal benefit curve simulations are described in section 3
3
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
x = interest/assets
MB(x)MC(x)
x*
y*
y =
MC
,MB
.
Figure 1: Capital structure equilibrium for a financially unconstrained firm. The figure shows the marginalbenefit curve of debt [MB(x)], the marginal cost curve of debt [MC(x)], and the equilibrium level of debt[x∗] where marginal cost and marginal benefit are equated. The equilibrium marginal benefit level at x∗
(which equals the cost level at x∗) is denoted by y∗.
to this current level of debt as the “equilibrium level of debt,” denoted by x∗i,t. That is,
we implicitly assume that for financially unconstrained firms, on average, the marginal cost
curve of debt (MC) intersects the marginal benefit curve of debt (MB) at the equilibrium
level. We refer to the observed corresponding marginal benefit level as the “equilibrium
benefit of debt,” denoted by y∗i,t. In equilibrium at xi,t = x∗i,t the following equality holds:
y∗i,t ≡ MCi,t
(x∗i,t
)= MBi,t
(x∗i,t
). (1)
The function fi,t, which is simulated, describes for firm i at time t the shape of the
marginal benefit curve of debt:
MBi,t = fi,t (xi,t) , (2)
where xi,t represents the level of debt, expressed as the ratio of interest over book value of
assets. Note that other measures of leverage, like the ratio of debt over the market value
of assets, can also be used. Figure 1 illustrates the equilibrium concept for a financially
unconstrained firm.
To recover the marginal cost function of debt from the equilibrium debt levels and the
equilibrium benefit levels, we need to identify ‘exogenous’ shifts of the marginal benefit
4
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42x = interest/assets
y =
MC
,MB
.
MB1(x)
MB2(x)
MB3(x)
MC(x)
Figure 2: Identifying the cost function using shifts in the marginal benefit function. The figure shows threemarginal benefit curves of debt, each intersected by the marginal cost curve of debt. The three curvescan represent the marginal benefit curves of the same firm at three different points in time. The curvescan alternatively represent the marginal benefit curves of three different firms at the same point in time.Empirically, we use both cross-sectional and time-series variation in the marginal benefit curve to identifythe marginal cost function of debt.
curve. In this context, the word exogenous implies that a shift of the marginal benefit curve
is uncorrelated with a shift in the marginal cost curve. In other words, we need to identify
shocks to the marginal benefit curve of debt while holding the marginal cost curve constant.
The exogenous benefit shifts may result from actual time series shifts of the marginal benefit
curve of firm i, for example after a tax regime shift. However, exogenous benefit shifts may
also result from cross-sectional variation in the location of the marginal benefit curve of debt
at some time t. If two otherwise similar firms have different marginal benefit curves, and
hence a different equilibrium level of debt, this provides information about the marginal cost
curve of debt that we exploit to estimate the marginal cost curve as illustrated in Figure 2.
To identify exogenous shocks to the marginal benefit curve, which we use as the
identifying instrumental variable, we can take either of two approaches: bottom-up or top-
down. The bottom-up approach is the direct way of finding an instrument by considering
variables that proxy for, or events that cause, exogenous marginal benefit shifts. One obvious
event is the tax regime changes mentioned earlier. The shifts of the marginal benefit curve
induced by such natural experiments can provide a clean instrument that has no or very
5
little correlation with shifts of the marginal cost curve. The advantage of this approach,
which we further address in the robustness section, is that the instrument is relatively clean.
The disadvantage of this approach, however, is that the exogenous variation of the benefit
curve is limited to the variation of the tax regime changes. In particular, this approach does
not exploit the fact that there is variation of the marginal benefit curve both in the time
series and in the cross section.
The top-down approach exploits the fact that, unlike the standard framework of
identifying demand and supply curves where only equilibrium points are observed, we observe
the entire simulated marginal benefit curve. In other words, apart from measurement errors
(which we assume to be idiosyncratic), we directly observe the cross-sectional and time series
variation (i.e., shifts) in the benefit curve, which we use to identify the cost function. What
then remains is to purge this variation from any cost effects. The result is an exogenous
benefit shifter.
To purge cost effects, we follow two steps. First, we compute for each firm in each year
the total potential tax benefit of debt, Ai,t, which is equal to the area under the marginal
tax benefit curve:
Ai,t =
∞∫
0
fi,t (xi,t) dxi,t. (3)
Empirically, this area provides an accurate description of the location of the marginal benefit
curve. If the marginal benefit curve shifts upward (downward), then the area under the curve
will increase (decrease). Henceforth, we will therefore interpret variation in this area measure
as variation (shifts) of the marginal benefit curve.2
We next purge the benefit measure Ai,t of potential cost effects. To accomplish this, we
include a set of control variables that are theorized to be correlated with the location of
the marginal cost curve of debt: proxies for a firm’s collateralizable assets (PPEi,t), sales
(LSALESi,t), book-to-market (BTMi,t), whether the firm pays dividends (DDIVi,t), the
firm’s cash flow (CFi,t), cash holdings (CASHi,t), and the personal tax penalty (PTPi,t)
that the firm faces. Define C as the set of cost control variables that drive the location of
the MC curve:
C ≡ {PPE, LSALES, BTM, DDIV,CF, CASH,PTP}. (4)
2Using other measures that proxy for shifts of the marginal benefit curve, such as the y-intercept of themarginal benefit curve, partitions of the area measure, or the coefficients of some polynomial approximationof each curve, leads to similar qualitative results to those we present below. For ease of exposition we focuson the area measure.
6
The purpose of our analysis is to estimate the marginal cost curve of debt, which we
assume to be linear in both interest-over-book (IOB), denoted by xi,t, and the cost control
variables, C.3 Under these assumptions, the marginal cost curve of debt is given by
MCi,t = a + bxi,t +∑c∈C
δcci,t + ξi,t. (5)
Define the error function gi,t as
gi,t = y∗i,t − a− bx∗i,t −∑c∈C
δcci,t. (6)
We then estimate the coefficients, in an exactly identified system of equations, using
generalized method of moments (GMM). The moments are obtained by interacting the
error function above with the following instruments: the constant term, the variation of
the marginal benefit curve Ai,t, and each of the control variables.
In equation (5) we assume that the control variables only cause parallel shifts of the
marginal cost curve of debt and that they do not change its slope. If we also allow the slope
of the marginal cost curve to depend on the control variables, the equation for the marginal
cost curve is given by
MCi,t = a + bxi,t +∑c∈C
δcci,t +∑c∈C
θcci,txi,t + ξi,t (7)
and the error function becomes
gi,t = y∗i,t − a− bx∗i,t −∑c∈C
δcci,t −∑c∈C
θcci,txi,t. (8)
In this setting, since we have to identify the coefficient on xi,t as well as the coefficients on
ci,txi,t for each c ∈ C, we construct additional instruments by taking the product of Ai,t and
each of the control variables. As we argue later in the paper, separately identifying intercept
and slope effects can be challenging. We therefore focus on the case where the intercept is
fixed across firms and only the slope is allowed to vary, conditional on the cost variables, C.
In this case the equation of the marginal cost curve is given by:
MCi,t = a + bxi,t +∑c∈C
θcci,txi,t + ξi,t (9)
3Note that the linearity of the marginal cost of debt implies that the total cost of debt is a quadraticfunction of xi,t and with a positive slope on xi,t in the marginal cost function, the total cost curve is convex.
7
and the error function is given by
gi,t = y∗i,t − a− bx∗i,t −∑c∈C
θcci,txi,t (10)
We estimate our coefficients by GMM for efficiency and correct standard errors. However,
to better explain the underlying intuition of our estimation, we now present the two-stage
least squares equivalent of equations 5 and 6.
First, we need to purge Ai,t of possible cost effects by running the following regression:
Ai,t = β0 +∑c∈C
βcci,t + εi,t (11)
By construction, the error term εi,t of this regression is orthogonal to the regressors (i.e., the
control variables). To the extent that the regressors span the information set that describes
the location of the marginal cost curve of debt, the error term εi,t can be interpreted as the
exogenous variation of the marginal benefit curve of debt that is not correlated with shifts
of the MC curve. We use this variation as the instrumental variable to identify the marginal
cost curve of debt. It is important to note that this variation of the marginal benefit curve
includes the tax regime shifts described earlier, and also includes other marginal benefit
shifters both in the time series and in the cross-section. The advantage of this approach is
that the exogenous variation (both time series and cross-sectional) in the benefit curve is large
and not limited to tax regime shifts. The disadvantage is that when purging the cost effects,
we may not have controlled for all possible cost variables. As in all model specifications, this
could possibly lead to an omitted variable bias. To ensure that our results are not driven
by such econometric issues, we also perform our analysis using the bottom-up approach
described above, in which we only use tax regime shifts as the instrument.
Armed with the error term εi,t from equation 11, we can then estimate the coefficients
through an instrumental variables (IV) analysis. This error term, which captures pure
benefit shifts, is the main identifying instrument. The first stage of the IV analysis involves
projecting firms’ equilibrium debt levels x∗i,t onto a constant, εi,t, and the control variables
in C:
x∗i,t = β0 + βεεi,t +∑c∈C
βcci,t + ηi,t, (12)
where ηi,t is the error term of the first-stage regression.4 The fitted values of this regression,
denoted by x∗i,t, represents the variation in the equilibrium debt level due to exogenous shifts
4Econometrically, given the presence of the control variables in the first stage, εi,t can be replaced in
8
of the marginal benefit curve, while holding the marginal cost curve fixed. In the second
stage, we regress y∗i,t on a constant, x∗i,t, and the control variables in C to obtain the slope
and the intercept of the marginal cost curve.
y∗i,t = a + bx∗i,t +∑c∈C
δcci,t + ξi,t, (13)
where ξi,t is the error term of the second-stage regression, which is uncorrelated with xi,t
by construction. Including the control variables in both stages of the analysis serves two
purposes. First, as mentioned in the previous paragraph, it allows us to control for shifts
in the location of the marginal cost curve. Second, it allows us to separately examine the
contribution of each control variable to the estimated functional form of the marginal cost
curve.
3 Data and Summary Statistics
3.1 Marginal benefit curves
Our marginal benefit curves are derived as in Graham (2000). Each point on these benefit
functions measures the present value tax benefit of a dollar of interest deduction. To
illustrate, ignore for this paragraph the dynamic features of the tax code such as tax loss
carryforwards and carrybacks and other complexities. The first point on the tax benefit
function measures the tax savings associated with deducting the first dollar of interest.
Additional points on the function measure the tax savings from deducting a second dollar
of interest, a third dollar, etc. Based on the current statutory federal tax schedule, each of
these initial interest deductions would be worth $0.35 for a profitable firm, where 0.35 is the
corporate marginal income tax rate. At some point, all taxable income would be shielded
by interest deductions, and incremental deductions would be worthless. Therefore, ignoring
the complexities of the tax code, a static tax benefit function would be a step function that
has an initial value of 0.35 and eventually drops to 0.0.
The dynamic and complex features of the tax code have a tendency to stretch out and
smooth the benefit function. First, consider dynamic features of the tax code, such as
tax loss carryforwards. At the point at which all current taxable income is shielded by
current interest deductions, an extra dollar of interest leads to a loss today, and this loss is
equation (12) by Ai,t. We have presented equation (11) merely to convey the intuition that εi,t captures theexogenous variation of the marginal benefit curve, as this residual is by construction orthogonal to the costcontrol variables.
9
carried forward to shield profits in future years. For example, for a loss firm that will soon
become profitable, an extra dollar of interest today effectively shields income next year, and
saves the firm $0.35 one year from today. Therefore, the present value tax savings from an
incremental dollar of interest today is worth the present value of $0.35 today, or about $0.33.
Once carryforwards are considered, therefore, rather than stepping straight down to zero at
the point of surplus interest deductions, the benefit function is sloped smoothly downward,
reaching zero more gradually. Other features of the tax code that we consider, including tax
loss carrybacks, the alternative minimum tax, and investment tax credits also smooth the
tax benefit function (see Graham and Smith, 1999 for details).
Second, consider an uncertain world in which the probability of profitability is between
zero and one. Say, for example, that there is a one-half chance that a firm will be profitable
and a one-half chance that it will be unprofitable. In this case, even with a simple, static
tax code, the expected tax benefit is $0.175 for one dollar of interest deduction. Therefore,
we simulate tax benefit functions so that the tax benefit of interest deductions at any given
point is conditional on the probability that the firm will be taxable.
More specifically, we calculate one point on a tax benefit function for one firm in one year
as follows. (Recall that each point on the function represents the expected corporate marginal
tax rate (MTR) for that level of income and deduction.) The first step for a given firm-year
involves calculating the historic mean and variance of the change in taxable income for each
firm. The second step uses this historic information to forecast future income many years
into the future, to allow for full effects of the tax carryforward feature of the tax code (e.g.,
in 2005, tax losses can be carried forward 20 years into the future, so we forecast 20 years
into the future when simulating the 2005 benefit curves). These forecasts are generated with
random draws from a normal distribution, with mean and variance equal to that gathered
in the first step; therefore, many different forecasts of the future can be generated for each
firm. In particular, we produce 50 forecasts of the future for each firm in each year.
The third step calculates the present value tax liability along each of the 50 income paths
generated in the second step, accounting for the tax-loss carryback and carryforward features
of the tax code. The fourth step adds $1 to current year income and recalculates the present
value tax liability along each path. The incremental tax liability calculated in the fourth
step, minus that calculated in the third step, is the present value tax liability from earning
an extra dollar today; in other words, the economic MTR. A separate marginal tax rate is
calculated along each of the forecasted income paths to capture the different tax situations
a firm might experience in different future scenarios. The idea is to mimic the different
planning scenarios that a manager might consider. The fifth step averages across the MTRs
10
from the 50 different scenarios to calculate the expected economic marginal tax rate for a
given firm-year.
These five steps produce the expected marginal tax rate for a single firm-year, for a
given level of interest deduction. To calculate the entire benefit function (for a given firm
in a given year), we replicate the entire process for 17 different levels of interest deductions.
Expressed as a proportion of the actual interest that a firm deducted in a given firm-year,
these 17 levels are 0%, 20%, 40%, 60%, 80%, 100%, 120%, 160%, 200%, 300%, 400%, ...,
1000%. To clarify, 100% represents the actual level of deductions taken, so this point on the
benefit function represents that firm’s actual marginal tax rate in a given year, considering
the present value effects of the dynamic tax code. The marginal tax benefit function is
completed by “connecting the dots” created by the 17 discrete levels of interest deduction.
Also, note that the area under the benefit function up to the 100% point represents the gross
tax benefit of debt for a given firm in a given year, ignoring all costs.
These steps are replicated for each firm for each year, to produce a panel of firm-year tax
benefit functions for each year from 1980 to 2005. The benefit functions in this panel vary
across firms. They can also vary through time for a given firm as the tax code or a firm’s
circumstances change.
3.2 Corporate financial statement data
We obtain corporate financial statement data from Standard & Poor’s COMPUSTAT
database from 1980 to 2005. Merging the tax benefit functions with COMPUSTAT based on
the eight digit firm CUSIP leaves 119,199 firm-year observations.5 For each firm, we create
empirical measures of the control variables described in the previous section, which includes
plant, property and equipment over total book assets (PPE), log of net sales (LSALES), book
equity to market equity (BTM), indicator for a dividend paying firm (DDIV), cash flow over
total book assets (CF), cash holdings over total book assets (CASH), and personal tax
penalty (PTP) as calculated in Graham (1999). We measure financial distress by Altman’s
(1968) Z-score (ZSCORE). Firms are defined to be non-distressed if they have Z-scores
above the median. We measure financial constraint according to four definitions offered in
the literature: (i) firms with no or limited leverage adjustments, (ii) the Kaplan and Zingales
(1997) index (KZ), (iii) the Cleary (1999) index (CL), and (iv) the Whited and Wu (2005)
index (WW). We discuss the four measures in the next subsection. Appendix A provides a
5To avoid issues involving changes in firm CUSIP across time, we track firms across time usingCOMPUSTAT’s GVKEY variable, which is created for this purpose. However, merging by firm CUSIPwithin each year will not be affected by this issue.
11
detailed description on the construction of each variable.
We normalize equilibrium interest expense by total book assets, which hereafter we refer
to as interest-over-book (IOB). Note that PPE, CF, and CASH are normalized by total book
assets. For the construction of LSALES, we chain net sales revenue to 2000 dollars to adjust
for inflation before taking logarithms. We further remove all firms with non-positive book
values, common equity, capital, and sales, or negative dividends. Such firms have either
unreliable COMPUSTAT data or are typically distressed or severely unprofitable and are
likely to be constrained with respect to accessing financial markets. Within our framework
they can therefore be considered as potentially being “out of equilibrium.” Further,
we remove firms that were involved in substantial M&A activity, defined as acquisitions
amounting to over 15 percent of firm total assets. Finally, we remove outliers defined as
firm-year observations that are in the first and 99th percentile tails for (i) the area under the
marginal benefits curve (A), (ii) the normalized observed interest-over-book (IOB) expenses
(x∗), (iii) the book to market ratio (BTM), (iv) the financial distress measure (ZSCORE),
and (v) the four financial constraint measures (long term debt issuance or reduction, KZ,
CL, and WW). 6 We also windorsize the personal tax penalty at the first and 99th percentile
levels. This results in a sample of 102,896 firm-years. Table 1 provides an overview of
the sample construction. Table 2 provides the summary statistics and Table 3 shows the
correlations between the variables in each of the samples.
3.3 Financial constraints measures
One important assumption underlying our framework is that firms are able and willing to
adjust capital structure. If firms are not able to adjust their capital structures because they
are financially constrained or financially distressed (i.e., out of equilibrium) they should
be excluded from our estimation procedure. Moreover, recent research on dynamic capital
structure highlights that firms may not continuously adjust their leverage ratios due to non-
negligible adjustment costs (Leary and Roberts, 2005; Kurshev and Strebulaev, 2006; etc.).
Therefore, when a firm does not adjust capital structure it is not clear whether the firm is
acting optimally, is acting passively due to adjustment costs, or is acting suboptimally due
to being constrained in financial markets. Conversely, if a company makes a (substantial)
capital structure adjustment, we can deduce that transactions costs were not sufficient to
prevent capital structure adjustments.
6Removing the outliers of the other control variables (PPE, LSALES, DDIV, CF and CASH) does notchange the distribution of the sample much.
12
To address these issues, we also perform our analysis for those firm-year observations in
which a substantial capital structure adjustment takes place, i.e., those firm-year observations
in which there is substantial long term debt and/or an equity issuance or repurchase
(LTDEIR). In our sample the median level of long term debt issuance/reduction among all
firm-year observations is, respectively, 6.8/3.3 percent of book value. These numbers increase
to respectively 16.0/9.1 percent when we consider debt issuances/reductions above the 75th
percentile. For equity issuances/repurchases, the median is 0.7/0.9 percent, respectively
and 3.3/3.1 percent respectively at the 75th percentile. We define a firm to be financially
unconstrained if it has long term debt or equity adjustment (LTDEIR) above the median
issuance or reduction. Even when we tighten the definition by including only firms above
the 75th percentile, our main results do not change.
3.4 Data description of the subsamples
To explore industry effects, we estimate the marginal cost curve by industry. Additionally,
we perform our empirical analysis for four subsets of our primary sample. These subsets are
based on two criteria. The first criterion is based on the firms’ degree of financial distress,
which we measure by ZSCORE. The second criterion is based on the firms’ long term debt
and equity issuance and repurchases (LTDEIR), as explained in the previous section. The
amount of LTDEIR reflects the firm’s ability to adjust its capital structure and can be
interpreted as a measure of financial constraint. The four samples are then given by:
A : All firms
B : Financially non-distressed firms: ZSCORE above median
C : Financially unconstrained firms: LTDEIR above median
D : Financially unconstrained and non-distressed firms as defined in samples B and C
The analysis of unconstrained firms helps to highlight those firms that can “freely”
optimize their capital structure. Because we assume in our estimation procedure that, on
average, the cost curve of debt intersects the marginal benefit curve of debt at the actual level
of debt, our estimation is most accurate for those firms that have the flexibility to actively
optimize over the amount of debt. If the firm is constrained, it may be (temporarily) “out
of equilibrium.” Figure 3 plots the histograms of the area under the marginal benefits curve
for each subsample. The majority of the firms have areas under the marginal benefit curve
that are less than 0.5 percent of book value in a single year, which corresponds to around 5.1
percent of the firm’s book value in perpetuity. The low benefit for these firms arises either
13
0.0
5.1
.15
.2.2
5P
erce
nt
0 .01 .02 .03 .04 .05 .06 .07 .08 .09 .1 .11 .12Area Under Curve
Sample A
0.0
5.1
.15
.2.2
5P
erce
nt
0 .01 .02 .03 .04 .05 .06 .07 .08 .09 .1 .11 .12Area Under Curve
Sample B
0.0
5.1
.15
.2.2
5P
erce
nt
0 .01 .02 .03 .04 .05 .06 .07 .08 .09 .1 .11 .12Area Under Curve
Sample C
0.0
5.1
.15
.2.2
5P
erce
nt
0 .01 .02 .03 .04 .05 .06 .07 .08 .09 .1 .11 .12Area Under Curve
Sample D
Figure 3: Histogram of the area under the curve. This figure shows the relative frequency distribution ofthe area under the marginal benefits curve for samples: i) A, all firms, ii) B, non-distressed firms, iii) C,financially unconstrained firms, iv) D, non-distressed and unconstrained firms. Small bins indicate firms withdeclining marginal benefits or constantly low marginal benefits. Large bins indicate firms with consistentlyhigh marginal benefits.
from benefit functions that are relatively flat but at a low benefit level, or that are steeply
downward sloping. Firms in the 0.5 and above bin are typically firms that have constant
marginal tax rates at the highest tax rate. These are firms we would expect to load heavily
on debt in equilibrium unless their marginal cost curve is especially steep. As we move from
Sample A to Sample D, the distribution of the area under the marginal benefits curve shifts
to the right. This indicates that the firms in Sample D tend to be more profitable and thus
have higher total potential benefits to debt through interest deductions. Table 2 compares
the summary statistics of the four samples.
14
4 Results
4.1 Marginal Cost Curves with Fixed Intercept
We estimate the coefficients in equation 9 for the four subsamples A-D, which are reported
in the first four columns of Table 4. These estimates allow the slope of the marginal cost
curve to depend on the control variables, but assume that the intercept is the same for all
firms. We allow for intercept variation in the next section. The slope of the marginal cost
curve determines the convexity of the total cost curve and measures the increase in marginal
cost that results from a one-unit increase in the interest-over-book ratio. When the intercept
of the marginal cost curve is fixed, a larger slope on the marginal cost curve implies higher
marginal cost for all values of leverage.
Within our framework, the capital structure decision follows from a tradeoff between the
tax benefits of debt and the costs of debt. It is important to stress that, in our framework,
the marginal benefit curve only measures the tax benefits of debt. As a consequence, the
other benefits of debt, such as committing managers to operate efficiently (Jensen, 1984)
and engaging lenders to monitor the firm (Jensen and Meckling, 1976), are included in
our framework as negative costs, and therefore are reflected in our estimated marginal cost
curves. Our cost curves also include the traditional costs of debt, such as the cost of financial
distress (Scott, 1976), personal taxes (Miller, 1977), debt overhang (Myers, 1977), agency
conflicts between managers and investors or between different groups of investors, and any
other cost that firms consider in their optimal debt choice.
We interpret the cost coefficients embedded in the cost of debt functions, and compare
the implications from these coefficients to the capital structure regularities documented
elsewhere. For example, the literature has documented that large firms with tangible assets
and few growth options tend to use relatively large amounts of debt (Frank and Goyal, 2004).
As we will show, the effects of individual cost variables on the cost of debt function are
consistent with debt usage implications in the existing capital structure literature, which we
find very reassuring. There are a great many unanswered questions in the capital structure
literature in terms of interpreting individual coefficients, and by no means do we believe
that our procedure helps to solve every puzzle. Rather, our procedure quantifies just how
large the influence of individual variables must be on the cost of debt to explain capital
structure regularities. Table i summarizes the effect of the control variables on the cost of
debt function, and summarizes the standard capital structure result (as presented in Frank
and Goyal (1994) and elsewhere).
We begin by interpreting the effect of collateralizable assets on the cost of debt function.
15
Control Variable Cost of Debt LeveragePPE – +LSALES + +/-BTM – +DDIV + –CF + –CASH + –PTP + –
Table i: The influence of each of the control variables on (i) the cost of debt following from Table 4, and (ii)the leverage of the firm, as documented by the literature.
The -0.470 coefficient in Table 4, sample D shows that the cost of debt decreases in the
proportion of a firm’s assets made up by property, plant, and equipment (PPE, normalized
by the book value of assets). This is consistent with the common capital structure finding
that high PPE leads to increased use of debt (see Table i). Note that all control variables
are standardized (i.e., have mean zero and standard deviation of one) so that the results
have a one standard deviation interpretation. In terms of economic magnitude, the -0.470
coefficient indicates that a one standard deviation change in PPE would lead to a 0.470
reduction in the slope of the marginal cost function of debt.
The 0.405 coefficient on LSALES indicates that, on average, large firms face a higher
cost of debt. This result is somewhat surprising but is consistent with some recent literature
that indicates that large firms use less debt (Faulkender and Petersen, 2004; Kurshev and
Strebulaev, 2006). Other research (as summarized in Frank and Goyal, 2004) documents a
positive relation between size and debt usage. In Table 5 we show that the benefits of debt
also increase with firm size. Therefore, the net effect of size on the use of debt depends on
whether the cost or benefit effect dominates.7 The differing firm size implications documented
in various capital structure papers imply that the influences of size on the costs versus benefits
of debt dominate in different settings and samples.
Firms with growth opportunities (i.e., a low book-to-market (BTM)) on average face a
higher cost of debt (coefficient of -0.518). This is consistent with the common finding that
for growth firms the opportunity cost of debt is high because debt can restrict a firm’s ability
to exercise future growth opportunities due to debt overhang (Myers, 1977). The inflexibility
7For recent work on the relation between size and capital structure, see Kurshev and Strebulaev (2006).They argue that fixed costs of external financing lead to infrequent restructuring and create a wedge betweensmall and large firms. Small firms choose higher leverage at the moment of refinancing to compensate forless frequent rebalancing.
16
arising from debt covenants could also restrict a firm’s ability to optimally invest and exercise
growth options.
Dividend paying firms (DDIV) face a higher cost of debt, as indicated by the 1.066
coefficient in Sample D on Table 4. All else equal, committing to pay dividends reduces the
availability of cash flows to service debt, given the extreme stickiness of dividend payments
(e.g., Brav et al., 2005), thereby increasing debt costs. This result and interpretation
are consistent with the negative relation between dividend-paying status and debt ratios
documented in Frank and Goyal (2004) and elsewhere (see Table i).8
Large cash holdings (CASH) and cash flows (CF) indicate a higher cost of debt according
to the estimates of 1.837 and 1.504, respectively, in Sample D of Table 4. Interpreting these
results is somewhat ambiguous. It may just be that firms that face higher costs of debt, for
whatever reason, find it optimal to hold more cash, which shows up in the cost function.
Or that profitable (high CF) firms use less debt on average, which is consistent with the
implication of higher costs in our estimated cost of debt function.
Finally, using Graham’s (1999) method to quantify the personal tax penalty, we include
this measure in our analysis as one of the cost control variables.9 The 0.915 coefficient
indicates that the cost of debt increases as personal taxes on interest income increase. This
result is consistent with high personal taxes on interest income leading to less debt usage,
as documented by Graham (1999).
As summarized in Table i, in every instance the relation between the control variables
and the cost of debt function are consistent with the relations between these same variables
and debt ratios, as documented in the extant literature. This is reassuring and implies that
our methodology, though technical, is not producing spurious relations in the cost of debt
function. Moreover, our approach allows us to explicitly quantify the effect of each variable
on the implicit cost of debt function that we estimate. At the same time, our approach does
not resolve certain existing capital structure puzzles or debates, such as why profitable firms
use less debt.
It is important to note that we measure the cost of debt as perceived by the firm and
therefore reflected in its chosen debt policy. This cost of debt could, but does not have to,
coincide with the cost of debt perceived by debt markets.
8There is also a pecking-order interpretation of the positive relation between dividend-paying status andthe cost of debt. For companies that are on the margin between issuing either debt or equity (like Sample D,by construction), those that pay dividends may have lower information asymmetry costs and therefore userelatively more equity (and less debt). Therefore, the positive coefficient on dividends might indicate that,relative to equity, debt is less attractive in dividend-paying firms.
9Graham (1999) shows that when measuring the tax benefits of debt, a specification that adjusts forpersonal tax penalty statistically dominates specifications that do not.
17
4.2 Marginal Costs with Fixed Slope
In the previous section we assumed that only the slope of the marginal cost curve depends
on the control variables, but that these variables do not influence the intercept. As an
alternative experiment we assume that the slope of the marginal cost curve is fixed across
firms but that the intercept of the marginal cost curve depends on the control variables. The
results are presented in the last four columns of Table 4. We find that the qualitative results
are identical to the ones described in the previous section. That is, small, non-dividend
paying firms with high collateralizable assets, few growth options, and low cash face a lower
cost of debt.
4.3 Marginal Costs with Varying Slopes and Intercepts
In the previous two sections we assumed that either the intercept or the slope of the cost curve
is the same for all firms. In this section we explore the possibility that both the slope and
the intercept vary with the control variables. In equation 7 we include the control variables
and the interaction terms between the interest-over-book (IOB) and the control variables.
Econometrically this is challenging because the information contained in our instruments may
not be sufficient to identify the slope and intercept effects separately. Indeed our estimation
results indicate that when we include the interaction terms, the statistical significance of our
results decreases, specifically when we move from samples A through D with progressively
smaller sample sizes.
In addition, in this case, slope and intercept effects may offset each other. Only when
the coefficient signs of a certain control variable is the same for both the slope (interaction
term) and the intercept is the resulting effect of that control variable on the marginal cost
curve monotone. When the slope and intercept coefficients are of opposing signs, the effect is
ambiguous, leading to a higher cost curve in one region and potentially a lower cost curve in
another (e.g., higher intercept but flatter slope). This is not surprising and can be understood
in the following way. When we fix the slope across all firms and only allow the intercept
to vary with the control variables, as in section 4.2, changes in the control variables lead
to parallel shifts of the cost curve. When we fix the intercept, as in section 4.1, variation
in the control variables implies pivoting the marginal cost curve around the intercept point.
However if we let both the intercept and the slope vary, the procedure can pivot around
some center point of the curve.
18
4.4 Marginal Costs By Industry
The estimation results of the coefficients in equation 9 by industry are given in Table 6. These
estimates allow the slope of the marginal cost curve to vary with the control variables while
keeping the intercept fixed within an industry. We estimate the coefficients in equation 9
for (i) all firms, (ii) all firms excluding utilities, finance, and public administration10 (iii)
by industry as categorized by the two-digit Standard Industry Classification (SIC). The
classification of the industries is documented in Appendix B. We find steep, positive, and
highly significant slopes for the full sample as well as in each industry. The slope is
particularly steep for the utilities industry and flat for the finance, insurance and real estate
industry. At the same time, the intercept is particularly low for utilities and high for finance,
insurance, and real estate.
4.5 Interpreting Recent Capital Structure Theories
In this section we investigate recent research that proposes effects that may influence the cost
of debt function. In each case, these theories lead to control variables that greatly reduce
sample size, so they are not included in the main analysis discussed earlier.
4.5.1 Wages
Recent work by Berk, Stanton and Zechner (2006) suggests that ex post the true costs of
bankruptcy are born by the employees of the firm. As a consequence, the firm needs to
compensate employees ex ante if it makes riskier capital structure decisions. If a firm wants
to take on additional debt, part of the cost of debt will therefore be the higher wages that
employees require as compensation for bankruptcy risk. The authors argue that employees
self-select, implying that risk-averse employees will find employment with firms that take on
low leverage. As a consequence, changing leverage is more costly for firms with risk averse
employees. The theory suggests that we should include wages per employee as a control
variable in our analysis. We use log of labor expenses divided by number of employees
(LWAGE) as our COMPUSTAT proxy for wages.
Table 7 shows the estimation results when log wages per employee (LWAGE) is included
as a control variable. We do find that high wages are correlated with high costs of debt,
consistent with Berk, Stanton, and Zechner (2006). This result is significant and leaves the
results on other control variables largely unaffected. Note that our sample size drops from
25,977 to 2,211 in Sample D due to a lack of wage data in the COMPUSTAT database.
10Excluding these industries is common practice in the capital structure literature.
19
4.5.2 Macroeconomic Influences
Chen (2006) and Almeida and Philippon (2006) propose that bankruptcies are concentrated
in bad times, i.e., periods when consumers’ marginal utilities are high. This leads investors
to demand higher credit risk premia during bad times due to higher default rates and higher
default losses. This naturally suggests that credit spreads should play a significant role in
the time variation of the cost of debt from the viewpoint of financial markets. As noted
before, the cost of debt as perceived by the firm could, but does not have to, coincide with
the costs perceived by the markets.
Table 8 gives the results for the analysis when we include the Moody’s Baa-Aaa spread
as a control variable. When the spread is high, indicative of bad times with high volatility,
we expect the cost of debt to be high. Thus, we expect a positive sign on our credit spread
variable. We see that this is indeed true for the financially non-distressed samples (B and
D). However, we find the opposite for samples A and C. Financially distressed firms may be
forced to take on additional debt to continue operations in distressed times. As such, these
firms may be “out of equilibrium” and less suitable for our analysis. Therefore we rely more
heavily on the results in samples B and D.
The examples presented in the last two sections illustrate that our framework can be
used to analyze implications from various capital structure theories. After the tax benefits
of debt have been modeled, the control variables in the cost curve can be used to assess the
importance of other factors that affect capital structure decisions.
5 Applications Using Marginal Cost of Debt Functions
Using the fixed intercept results from the left side of Table 4, Sample D, the marginal cost
function for any particular firm can be determined by:
MCi,t = 0.190 + 4.192IOBi,t − 0.470PPEi,t ∗ IOBi,t + 0.405LSALESi,t ∗ IOBi,t
− 0.518BTMi,t ∗ IOBi,t + 1.066DDIVi,t ∗ IOBi,t + 1.837CFi,t ∗ IOBi,t
+ 1.504CASHi,t ∗ IOBi,t + 0.915PTPi,t ∗ IOBi,t
(14)
and, when using the fixed slope results from the right side of Table 4, Sample D, given by:
MCi,t = 0.120 + 5.086IOBi,t − 0.019PPEi,t + 0.015LSALESi,t − 0.029BTMi,t
+ 0.047DDIVi,t + 0.112CFi,t + 0.044CASHi,t + 0.035PTPi,t
(15)
20
where each of the control variables are standardized based on Sample A to have a mean
of zero and a standard deviation of one. The mean and standard deviation for each of the
control variables for Sample A is reported in Table 2.11
5.1 Case Studies of Optimal Debt Usage
Once the cost and benefit functions have been estimated, they can be used to draw inference
on optimal capital structure. We illustrate with three specific cases. The following three firms
are chosen based on name recognition and span of industries: i) Bed, Bath, and Beyond,
in the retail industry, ii) Columbia Broadcasting System (CBS), in the communications
industry, and iii) Morgan Stanley, in the financial services industry. Figure 4 displays the
marginal benefit and marginal cost curves for the three firms, respectively. We estimate the
marginal cost curve using the estimated coefficients from the analysis run on Sample D, as
reported in Table 4, where we assume that the intercept is fixed across firms and the slope
depends on the control variables (see equation (15).12 For these three cases we see that each
of these firms are indeed close to its ‘equilibrium’ because the marginal cost curve and the
marginal benefit curves intersect close to the actual amount of debt the firm uses.
Table ii compares the decile rankings of specific financial ratios for the three firms. All
three firms are large with relatively high total book assets and market equity. However, the
three firms differ substantially in terms of decile ranking for the other control variables.
In 2005, Bed, Bath, and Beyond does not pay dividends, has moderate asset
collaterizability, and relatively high growth opportunities, cash holdings, and sales. The
firm seems to minimize its payment obligations. Given the firm’s high growth opportunities,
cash holdings, sales, and income, the firms capital structure decision is consistent with our
cost/benefit analysis.
We examine CBS, Inc. just before it disappears from the Compustat database in 1994,
after merging with Westinghouse Electronic Corporation. In 1994, CBS has moderate
collateral, cash holdings, and debt to equity ratio, and high growth opportunities, dividend
payments, sales, and cash flow. The growth opportunities, dividend payments and cash
flow indicate a high marginal cost of debt. Our analysis suggests that CBS is about 20%
overlevered and should use less debt as defined by interest payment obligations. However,
their recommended or ‘optimal’ debt is still within 20% of the observed debt level.
11The control variables are not re-standardized by sample to prevent selection bias when analyzing acrosssamples.
12The qualitative results are similar for the case in which we fix the slope and let the intercept vary withthe control variables
21
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5Bed, Bath, and Beyond, 2005
Interest−Over−Book−Value
MB
/ M
C R
ates
MB CurveMC CurveActual
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5CBS, 1994
Interest−Over−Book−ValueM
B /
MC
Rat
es
MB CurveMC CurveActual
0 0.01 0.02 0.03 0.04 0.05 0.060
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5Morgan Stanley, 2004
Interest−Over−Book−Value
MB
/ M
C R
ates
MB CurveMC CurveActual
Figure 4: Marginal benefit and marginal cost curves for i) Bed, Bath, and Beyond in 2005, ii) CBS in 1994,and iii) Morgan Stanley in 2004. The vertical line reflects the actual debt in terms of interest of book valueobserved empirically.
Morgan Stanley in 2004 had low capital, dividend obligations, sales, and cash flow,
moderate growth opportunities, and high cash holdings and debt to equity ratio. The
fact that Morgan Stanley is a financial firm complicates what really should be classified
as debt and equity. Nonetheless, using our marginal cost curve derived from the sample D
population, we use the coefficients to calculate the marginal cost function for more general
firms. Morgan Stanley seems to be close to its optimal ratio of interest payments over book
value.
These cases illustrate that our analysis can be used not only to interpret capital structure
theories, but our analysis provides a benchmark against which companies can compare their
capital structure decisions. Our analysis identifies the intersection of each firm’s marginal
benefit and marginal cost curves, where the costs are backed out of debt choices made by
22
Table ii: Key financial characteristics of the three firms studied in our case analysis. TA is the total assetsexpressed in thousands of 2000 dollars, MCAP represents the market capitalization expressed in thousands of2000 dollars, BTM is the book equity to market equity ratio, PPE stands for plants, property, and equipmentover total book assets, DIVIDENDS is the total dividend payout in thousands of dollars over total bookassets, SALES is firm sales over total book assets, CASH is cash holdings over total book assets, CF isincome over total book value and D/E is the debt to equity ratio.
BBB, 2005 CBS, 1994 Morgan Stanley, 2004Ranking Value Ranking Value Ranking Value
TA ($thousand) 8 3000 9 2393 10 708624MCAP ($thousand) 9 9396 10 4420 10 50095PPE 6 0.218 5 0.241 1 0.008BTM 2 0.214 1 0.069 6 0.515DIVIDENDS 1 0 8 0.013 6 0.001SALES 9 1.718 9 1.718 1 0.051CASH 8 0.193 5 0.047 8 0.248CF 10 0.202 9 0.162 2 0.007D/E 1 0 5 0.183 10 8.940
other, similar firms.
6 Quantifying the Cost and Benefit of Debt
As just illustrated, using both the marginal benefit and marginal cost functions, we can
compute the ‘optimal’ or ‘equilibrium’ capital structure for a firm as the intersection between
the two curves. This allows us to infer whether a firm is over-, under-, or optimally leveraged.
We define over- and under-leverage as follows.
First, for each firm, we normalize the current interest-over-book value (IOB) to one;
this has the interpretation that a firm is at 100% of its observed IOB. The ‘optimal’ or
‘equilibrium’ level of debt is calculated as the intersection between the marginal benefit and
marginal cost curves. This ‘equilibrium’ level is then normalized by the observed level, i.e.,
‘equilibrium’ capital structure is expressed as a proportion of the observed. For example, a
firm that has an equilibrium factor of 0.8 should, according to our model, optimally have
80% of the observed IOB. Suppose the normalized equilibrium level of debt equals e, then
the percentage of underleverage/overleverage is given by:
Underleverage = 1− 1/e when e > 1 (16)
Overleverage = 1/e− 1 when e < 1 (17)
23
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
x = interest/assets
MB(x)MC(x)
x*
y*
xo
DWo = Cost of being overleveraged
y =
MC
,MB
.
Figure 5: The costs of being overleveraged. The figure shows the marginal benefit curve of debt [MB(x)],the marginal cost curve of debt [MC(x)], and the equilibrium level of debt [x∗] where marginal cost andmarginal benefit are equated. The marginal benefit level at x∗ (which equals the cost level at x∗) is denotedby y∗. The actual level of debt, denoted by [xo], exceeds the equilibrium level of debt [x∗]. The shaded areaindicates the deadweight loss of being over-leveraged.
Using our example of a firm with equilibrium factor of 0.8, this implies this firm is
overleveraged by 25%. We can also say this firm is 25% “out of equilibrium.” Equipped
with these definitions, we can use our benefit and cost functions to quantify the gross and
net benefits of debt and the costs of being “out of equilibrium.” Note that we use the
statement in a relative sense: the observed debt usage “relative to the optimum implied by
the coefficients of our empirical model.”
6.1 Gross and net benefits of debt
The observed (equilibrium) gross benefits of debt, GBDo (GBDe), is the area under the
marginal benefits curve up to the observed (equilibrium) level of interest over book value
(IOB). The observed (equilibrium) cost of debt, CDo (CDe), is the area under the marginal
cost curve up to the observed (equilibrium) level of IOB. The observed (equilibrium) net
benefits of debt, NBDo (NBDe), is the difference between the gross benefit of debt and the
cost of debt.
Tables 9 and 10 report the unconditional and conditional summary statistics for the gross
benefit of debt, cost of debt, and net benefit of debt. Values are reported for firms both at
the observed level of interest-over-book values (IOB) as well as at the equilibrium implied
24
by the results in Table 4. We see that although the gross benefits of debt are similar for
observed debt levels and equilibrium debt levels, the costs to debt are lower at equilibrium
levels. This results in a higher net benefit of debt for firms at the equilibrium implied by
our analysis, relative to their observed levels. On average, the net benefits of debt at the
implied equilibrium is 3.8% of firm value, and only 0.2% of firm value at observed debt
levels. This suggests that our analysis indeed is able to help firms choose a more optimal
capital structure. Th This result is consistent for both over- and under-leveraged firms. The
difference between the equilibrium and observed net benefits increases as firms move further
out of equilibrium and is on average 5.23% of firm value for firms that are further than 80%
or more from the equilibrium.
6.2 The cost of being underlevered or overlevered
Our analysis allows us to answer the question: how costly is it for firms to be out of
equilibrium? The cost of being ‘overlevered’ can provide insight on the potential cost of
financial distress, while the cost of being ‘underlevered’ can shed light on the cost of financial
constraints. Figure 5 depicts the cost of being overleveraged. The cost of being overleveraged,
DWo, is the loss due to additional costs from having interest over book value (IOB) above
the equilibrium. This is because overleveraged firms pay higher costs relative to the benefits
received. On the other hand, the cost of being underleveraged, DWu, is the deadweight loss
from lower benefits due to having IOB below the equilibrium; the deadweight loss comes
from leaving money on the table in the form of unused benefits relative to cost of debt. The
cost of being out of equilibrium, DWt, combines DWo and DWu into one measure.
Tables 9 and 10 also report the costs of being “out of equilibrium” as value of the
deadweight losses mentioned above. Table 9 show that on average the cost of being out of
equilibrium is 2.2-2.6% of firm value. However, we see that the costs for overleveraged firms
(on average, 3.3-4.0% of firm value) are much higher than those for underleveraged firms (on
average, 1.2-1.3% of firm value). This suggests that it is much more costly for firms to be
overleveraged than underleveraged. This gives insight as to why firms might be conservative
in their debt usage (Graham, 2000). If a firm is incorrect in the analysis of its optimal capital
structure, it is less costly to err on the side of having too little debt than too much debt.
Table 10, panel A show that, sensibly, costs of being out of equilibrium increases as firms
are further away from the equilibrium. We see that a vast majority of overleveraged firm
are more than 80% away from the equilibrium. This suggests that deadweight costs of being
out of equilibrium has a heavy impact.
25
7 Robustness checks
7.1 Different financial constraint measures
As discussed previously, our estimation procedure depends on the assumption that, on
average, firms optimize over their capital structure decisions. In this section we explore
how excluding firms based on a variety of financial constraint or financial distress measures
affects our results. Previously, we used long-term debt issuance or reduction as a measure
of financial constraint. As an additional robustness check, we also identify unconstrained
firms based on (i) the financial constraints measure derived by Kaplan and Zingales (1997)
as estimated by Lamont, Polk, and Saa-Requejo (2001), hereafter referred to as KZ, (ii)
the Cleary (1999) index, hereafter called CL, and (iii) the Whited and Wu (2005) index,
hereafter called WW.
Kaplan and Zingales (1997) categorize the 49 low dividend paying firms of Fazzari,
Hubbard, and Petersen (1988) into five degrees of financial constraint and estimate an
ordered logit model to obtain the probability of a firm falling into any one of the five financial
constraint categories, with financial slack being the lowest state and financial constraint the
highest state. Lamont, Polk, and Saa-Requejo (2001) report the coefficients for the KZ index
that uses only variables available on COMPUSTAT. We use these coefficients to construct our
KZ index. Following the approach of Kaplan and Zingales (1997), Cleary (1999) calculates a
more general financial constraint measure by grouping firms into categories based on whether
they increase or decrease dividend payments. Using this classification procedure, Cleary
(1999) performs discriminant analysis to obtain a measure for financial constraint. We
reproduce this procedure over Cleary’s (1999) sample period of 1987 to 1994 to obtain the
coefficients for our CL index. Finally, in a recent paper, Whited and Wu (2005) argue
that the KZ measure is inconsistent with the intuitive behavior of financially constrained
firms. They derive an alternative measure of financial constraint by formulating the dynamic
optimization problem of a firm that faces the constraint that the distributions of the firm
(e.g., dividends) need to exceed a certain lower bound. They parameterize the Lagrange
multiplier on this constraint and estimate its coefficients with GMM. Effectively, the WW
index indicates that a firm is financially constrained if its sales growth is considerably lower
than its industry’s sales growth. In other words, a highly constrained firm is a slow growing
firm in a fast growing industry. A fully unconstrained firm is a fast growing firm in a slow
growing industry.
26
The formula for the KZ index is given by
KZi,t = −1.002CFi,t + 3.139LTDi,t − 39.367TDIVi,t − 1.314CASHi,t + 0.282Qi,t, (18)
the CL index is given by
CLi,t = 0.176CURi,t−1 − 0.0003FCi,t−1 + 0.008SLi,t−1 − 2.802NI%i,t−1
+0.018SGi,t−1 + 4.372DEBTi,t−1,(19)
and the WW index is given by
WWi,t = −0.091CFi,t − 0.062DDIVi,t + 0.021LTDi,t − 0.044LTAi,t
+0.102ISGi,t − 0.035SGi,t,(20)
where CF is cash flows, LTD is long-term debt, TDIV is total dividends over assets, Q is
Tobin’s Q, DDIV is a dummy variable that equals 1 when a firm pays dividends and 0
otherwise, ISG is industry sales growth, SG is the firm’s sales growth, CUR is the firm’s
current ratio, FC is the fixed charge coverage, NI% is the firms net income margin, DEBT
is the firm’s debt ratio, and SL is the ratio of slack over net fixed assets.
In this section we explore these other financial constraint measures. In particular, in
addition to the four samples described above, we also perform our analysis using the following
samples:
E : KZ below median and ZSCORE above median
F : CL below median and ZSCORE above median
G : WW below median and ZSCORE above median
H : LTDEIR above 3rd quartile and ZSCORE above median
I : KZ below 1st quartile and ZSCORE above median
J : CL below first quartile and ZSCORE above median
K : WW below first quartile and ZSCORE above median
Table 1 summarizes the sample size for each of the 11 samples. The estimation results
given in Tables 11 and 12 indicate that our findings are robust to the different samples and
our main qualitative results are broadly unaffected.
27
7.2 Alternative Instrumental Variables
Thus far, we have used the area measure Ai,t to summarize the variation in the marginal
benefit curve of debt. If the marginal benefit curve was a simple linear function with a
constant slope, summarizing the variation would be an easy task because the y-intercept, or
the x-intercept, of each function would suffice. However, not only is the functional form of
the benefit curves non-linear, the shape is potentially different for each firm for each year. In
other words, the variation of the marginal benefit curves is caused by more than just parallel
shifts. As a consequence, the challenge is to summarize this changing functional form of the
benefit curve, which, empirically, we achieve through the area measure.
To more fully represent the various shapes of the marginal benefit function, we
could include the y-intercept of the marginal benefit curve as an additional instrument.
Alternatively, we could include several variables that represent the area for different
partitions of benefit function, to more explicitly capture its shape over different ranges.
Yet another alternative is to approximate the marginal benefit curve in each year and for
each firm by a polynomial expansion (Taylor or Chebyshev polynomials) and include the
coefficients on these polynomials as the instruments. Our main conclusions are robust to
using these different instruments.
7.3 Time Series Analysis - Tax Regime Shifts
So far we have used both cross-sectional and time series variation of the marginal benefit
curves to estimate the marginal cost curve of debt. To purge potential variation of cost
effects from the benefit functions, we included a set of control variables that are theorized
to be correlated with the marginal cost curve. After purging the cost effects, we are left
with ”exogenous” variation of the marginal benefit curve, which we use as the identifying
instrument to recover the marginal cost curve. Even though we believe that we have
controlled for the most important cost effects in our analysis (i.e., those used in the capital
structure literature), there is no way to ensure that all relevant cost control variables are
included. Failing to include cost control variables could lead to an omitted variables bias.
To rigorously address this issue, we repeat our analysis in this section, using as the sole
identifying instrument the corporate tax regime shifts over the period 1980-2005 (the bottom-
up approach mentioned in the introduction). The tax regime shifts should be correlated with
the benefit function but not the cost function, thereby permitting identification of the cost
curve.
Tax regime changes lead to changes both in the level of the statutory corporate tax rates
28
.1.2
.3.4
.5T
ax R
ate
1980 1985 1990 1995 2000 2005Year
0 to 25 25 to 50 50 to 75 75 to 100
100 to 335 335 to 1000 1000 to 1405 1405 to 10000
10000 to 15000 15000 to 18333 18333+
Eleven Income Brackets in Thousands $Corporate Tax Rates Across Years
Figure 6: Corporate federal income tax rates for the eleven statutory tax brackets.
as well as the income level applicable to each tax bracket. To incorporate both shifts, we
create eleven non-overlapping brackets across all years in the sample period.13 For example
in 1980 the lowest tax bracket is from $0 to $25,000, but changes to $0 to $50,000 in 1988.
This results in two brackets in every year: one from $0 to $25,000 and one from $25,000 to
$50,000. Figure 6 plots the marginal tax for the eleven income brackets. Appendix C lists
the corporate tax rates for all eleven brackets in detail.
Time variation in the tax regimes can be considered a ‘cleaner’ instrument that is unlikely
to be correlated with cost effects. The disadvantage is that this approach uses much less
information to uncover the marginal cost curve of debt: it does not use the cross-sectional
variation in marginal benefit curves and therefore does not use the fact that we “observe”
the whole marginal benefit curve of debt, as opposed to just the equilibrium points where
the marginal cost and marginal benefit curves intersect.
Table 13 reports the coefficient estimates based on using tax regime shifts as an
instrument. The bottom-up analysis, which only uses the exogenous tax regime shifts as
13To address the possibility that the results from the time series analysis are largely driven by the rateshifts in the lower tax brackets, the entire analysis is repeated using only the top tax bracket. The resultsare similar to the results using all eleven brackets.
29
the identifying instrument, leads to similar regression results, for both the slope of the
marginal cost curve and the dependence of the intercept on the cost control variables. This
corroborates our earlier approach and results. The marginal cost curve is still steep with
a slope of the same order of magnitude as in our earlier analysis. Further, the signs and
magnitudes of the coefficients of the cost control variables, which influence the intercept and
the slope of the cost curve, respectively, are the same as well.
Finally, we also perform our main analysis based on data between 1998 and 2005. During
this period there were no exogenous tax regime shifts, meaning that for this sample, the time
series approach described above is not possible. The identification of the cost curve during
this period is mainly based on cross-sectional information, and it also leads to highly similar
results.14 This indicates that it does not seem to matter whether we identify the cost curve
based on (i) cross-sectional information, (ii) time series information, or (iii) a combination
of the two. We consider this to be a very reassuring corroboration of our findings.
8 Conclusion
We use panel data from 1980 to 2005 to estimate cost curves for corporate debt. We simulate
debt tax benefit curves and assume that for financially unconstrained firms, the benefit curve
intersects the cost curve at the actual level of debt, on average. Using this equilibrium
condition, exogenous shifts to the benefit curves enable us to identify the marginal cost
function. We recover marginal cost curves that are steeply positively sloped. Both the
slope and the intercept of these curves depend on firm characteristics such as collateral,
sales, book-to-market, cash flows, cash holdings, personal tax penalty, and whether the firm
pays dividends. We perform a multitude of robustness checks and find that our findings
are robust across industries and years. Our results are also robust to accounting for fixed
adjustment costs of debt. As such, our framework provides a new parsimonious environment
to estimate and evaluate competing capital structure theories. We also provide firm specific
recommendations of optimal debt policy against which firms’ actual debt choices can be
benchmarked.
14This point was further confirmed by including year dummies in our analysis.
30
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32
Appendix A
Detailed description on the construction of the control variables using in the analysis andvariables included in the summary statistics reported in Table 2. Numbers in parenthesesindicate the corresponding COMPUSTAT annual industrial data items.
PPE = Net Plants, Property, and Equipment (8)Total Book Assets (6)
LSALES = log (Net Sales (12))
BTM = Total Common Equity (60)Fiscal Year Close Price (199) *Common Shares Outstanding (54)
DDIV =
1 if Common Dividends (21) > 0
0 if Common Dividends (21) = 0
CF = EBIT (18) + Depreciation (14)Total Book Assets (6)
CASH = Cash and Short Term Investments (1)Total Book Assets (6)
HHI = H− 1N
1− 1N
where H =N∑i
s2i and si = market share of firm i
LWAGE = log (WAGE) = log(
Labor and Related Expenses (42)Number of Employees (29)
)
CS = Moody’s Baa Rate−Moody’s Aaa Rate (Source : Economagic)
ZSCORE = 3.3*Pretax Income (170) + 1.0*Net Sales (12) + 1.4*Retained Earnings (36) + 1.2*Working Capital (179)Total Book Assets (6)
TLC = Net Carryloss Forward (52)Net Sales (12)
PTP = τp − (1− τ c)τe for τ c = observed marginal tax rate and τe = [d + (1− d)gα]τp
where d is the dividend payout ratio, g is 0.4 before 1987 and 1.0 after (although gτp is never greater than
0.28), α is 0.25, and τp is 47.4% for 1980-1981, 40.7% for 1982-1986, 33.1% for 1987, 28.7% for 1988-1992,
and 29.6% for 1993 and onwards.
33
Appendix B
Firms are classified by their two-digit SIC codes into industries. The following table describes
the industries and the corresponding two-digit SIC codes we use in our analysis.
Agriculture, Forestry, and Fishing 01-09
Mining 10-14
Construction 15-17
Manufacturing 20-39
Transportation 40-47
Communication 48
Utilities 49
Wholesale Trade 50-51
Retail Trade 52-59
Finance, Insurance, and Real Estate 60-67
Services 70-89
Public Administration 91-99
34
Appendix C
Corporate tax rates over the period 1980 to 2005. Both the corporate tax rates as well as
their corresponding income tax brackets change during this period. To resolve this issue,
eleven non-overlapping income tax brackets are created that exist for all years.
Year Income Tax Bracket in Thousands $$
0 25 50 75 100 335 1000 1405 10000 15000 18333+to to to to to to to to to to25 50 75 100 335 1000 1405 10000 15000 18333
1980 0.170 0.200 0.300 0.400 0.460 0.460 0.510 0.460 0.460 0.460 0.460
1981 0.170 0.200 0.300 0.400 0.460 0.460 0.510 0.460 0.460 0.460 0.460
1982 0.160 0.190 0.300 0.400 0.460 0.460 0.510 0.460 0.460 0.460 0.460
1983 0.150 0.180 0.300 0.400 0.460 0.460 0.510 0.460 0.460 0.460 0.460
1984 0.150 0.180 0.300 0.400 0.460 0.460 0.510 0.460 0.460 0.460 0.460
1985 0.150 0.180 0.300 0.400 0.460 0.460 0.510 0.460 0.460 0.460 0.460
1986 0.150 0.180 0.300 0.400 0.460 0.460 0.510 0.460 0.460 0.460 0.460
1987 0.150 0.165 0.275 0.370 0.425 0.400 0.425 0.400 0.400 0.400 0.400
1988 0.150 0.150 0.250 0.340 0.390 0.340 0.340 0.340 0.340 0.340 0.340
1989 0.150 0.150 0.250 0.340 0.390 0.340 0.340 0.340 0.340 0.340 0.340
1990 0.150 0.150 0.250 0.340 0.390 0.340 0.340 0.340 0.340 0.340 0.340
1991 0.150 0.150 0.250 0.340 0.390 0.340 0.340 0.340 0.340 0.340 0.340
1992 0.150 0.150 0.250 0.340 0.390 0.340 0.340 0.340 0.340 0.340 0.340
1993 0.150 0.150 0.250 0.340 0.390 0.340 0.340 0.340 0.350 0.380 0.350
1994 0.150 0.150 0.250 0.340 0.390 0.340 0.340 0.340 0.350 0.380 0.350
1995 0.150 0.150 0.250 0.340 0.390 0.340 0.340 0.340 0.350 0.380 0.350
1996 0.150 0.150 0.250 0.340 0.390 0.340 0.340 0.340 0.350 0.380 0.350
1997 0.150 0.150 0.250 0.340 0.390 0.340 0.340 0.340 0.350 0.380 0.350
1998 0.150 0.150 0.250 0.340 0.390 0.340 0.340 0.340 0.350 0.380 0.350
1999 0.150 0.150 0.250 0.340 0.390 0.340 0.340 0.340 0.350 0.380 0.350
2000 0.150 0.150 0.250 0.340 0.390 0.340 0.340 0.340 0.350 0.380 0.350
2001 0.150 0.150 0.250 0.340 0.390 0.340 0.340 0.340 0.350 0.380 0.350
2002 0.150 0.150 0.250 0.340 0.390 0.340 0.340 0.340 0.350 0.380 0.350
2003 0.150 0.150 0.250 0.340 0.390 0.340 0.340 0.340 0.350 0.380 0.350
2004 0.150 0.150 0.250 0.340 0.390 0.340 0.340 0.340 0.350 0.380 0.350
2005 0.150 0.150 0.250 0.340 0.390 0.340 0.340 0.340 0.350 0.380 0.350
35
Table 1: Sample construction. y∗i,t is the ‘equilibrium’ marginal benefit level, x∗i,t is the observed or‘equilibrium’ interest payments over book value (IOB), A is the area under the marginal benefit curve, andC is the set of control (cost) variables. C ≡ {PPE, LSALES, BTM,DDIV, CF,CASH, PTP}. ZSCOREis a measure of financial distress. LTDEIR is the long term debt and/or equity issuance or repurchase usedto measure for financial constraint. KZ, CL, and WW are financial constraint measures as defined by Kaplanand Zingales (1997), Cleary (1999), and Whited and Wu (2005) indices respectively.
Sample No. Obs
All firm-year obs. with marginal benefit (MB) curves and COMPUSTAT data in 1980-2005 119,199
Non M&A firm-years with positive book value, common equity, capital, and sales 108,789
Sample without outliers 102,896
Sample with non-missing (y∗i,t, x∗i,t, Ai,t, Ci,t) variables: Sample A 80,039
Sample of firm-years without financial distress: Sample B 39,112ZSCORE above median
Sample of financially unconstrained firm-years: Sample C 57,310LTDEIR above median
Sample of financially unconstrained and non-distressed firm-years: Sample D 26,725LTDEIR above median and ZSCORE above median
For robustness checks:
Sample of financially unconstrained and non-distressed firm-years: Sample E 23,147KZ below median and ZSCORE above median
Sample of financially unconstrained and non-distressed firms: Sample F 20,542CL below median and ZSCORE above median
Sample of financially unconstrained and non-distressed firms: Sample G 20,668WW below median and ZSCORE above median
Sample of financially unconstrained and non-distressed firms: Sample H 13,843LTDEIR above third quartile and ZSCORE above median
Sample of financially unconstrained and non-distressed firms: Sample I 11,077KZ below first quartile and ZSCORE above median
Sample of financially unconstrained and non-distressed firms: Sample J 11,183CL below first quartile and ZSCORE above median
Sample of financially unconstrained and non-distressed firms: Sample K 9,176WW below first quartile and ZSCORE above median
36
Table 2: Summary statistics for the samples used in the analysis. HCR is the historical credit rankings basedon the S&P long term domestic issuer credit ratings. PPE is property, plant, and equipment over total bookvalues, LSALES is log of net sales expressed in 2000 dollars, BTM is book equity to market equity, DDIVis an indicator for dividend paying firms, CF is net cashflow over total book values, CASH is cash holdingsover total book values, PTP is the personal tax penalty on interest as measured in Graham (1999), and HHIis the normalized Herfindahl-Hirschman index for industry concentration based on the 3-digit SIC. ZSCOREis a measure of financial distress. UNFC is an indicator for financially unconstrained firms, defined as firmsthat adjust capital structure either through debt or equity issuance or repurchase. KZ, CL, and WW arefinancial constraint measures as defined by the Kaplan and Zingales (1997), Cleary (1999), and Whited andWu (2005) indices, respectively. TLC is total tax loss carryforwards normalized by total sales. WAGE istotal labor compensation normalized by total employees.
Sample A: All Firms
No. Obs Mean Std. Dev Min Max
Area Under Curve 80039 0.032 0.026 0.000 0.137Interest Over Book Value 80039 0.032 0.024 0.000 0.133HCR 15537 4.063 1.289 1 10PPE 80039 0.327 0.244 0.000 1.000LSALES 80039 5.014 2.367 -7.028 12.582BTM 80039 0.789 0.643 0.034 4.674DDIV 80039 0.430 0.495 0 1CF 80039 0.051 0.161 -4.847 3.121CASH 80039 0.133 0.172 -0.010 1.000PTP 80039 0.249 0.091 -0.171 0.451HHI 79711 0.188 0.153 0.000 1.000ZSCORE 73435 1.602 2.053 -13.7 5.595UNFC 80039 0.964 0.186 0 1CL 59176 1.935 86.078 -627.915 13843KZ 72529 -13.069 1280.381 -335562 1198WW 70372 -0.222 0.367 -21.715 50.016TLC 58852 2.686 106.326 0.000 15571WAGE 9102 53.442 398.182 0.000 20358
Sample B: Financially Non-distressed FirmsZSCORE above medianNo. Obs Mean Std. Dev Min Max
Area Under Curve 39112 0.041 0.027 0.000 0.137Interest Over Book Value 39112 0.028 0.022 0.000 0.133HCR 5838 3.771 1.250 1 10PPE 39112 0.281 0.173 0.000 0.953LSALES 39112 5.544 1.916 -5.606 12.582BTM 39112 0.768 0.595 0.035 4.639DDIV 39112 0.518 0.500 0 1CF 39112 0.109 0.071 -0.902 1.219CASH 39112 0.131 0.151 -0.002 0.992PTP 39112 0.259 0.088 -0.171 0.451HHI 38939 0.200 0.154 0.000 1.000ZSCORE 39112 2.850 0.772 1.801 5.60UNFC 39112 0.970 0.171 0 1CL 31465 -0.130 1.571 -207.099 17.033KZ 36499 -17.489 1800.499 -335562 25.312WW 37791 -0.233 0.202 -20.285 14.331TLC 32576 0.024 0.340 0.000 50.598WAGE 3665 38.786 285.333 0.003 14500
37
Sample C: Financially Unconstrained FirmsLTDEIR above medianNo. Obs Mean Std. Dev Min Max
Area Under Curve 57310 0.033 0.026 0.000 0.137Interest Over Book Value 57310 0.034 0.024 0.000 0.133HCR 12246 4.123 1.262 1 10PPE 57310 0.338 0.246 0.000 1.000LSALES 57310 5.104 2.333 -7.028 12.582BTM 57310 0.728 0.608 0.034 4.674DDIV 57310 0.403 0.490 0 1CF 57310 0.050 0.165 -4.847 1.898CASH 57310 0.128 0.170 -0.010 0.999PTP 57310 0.249 0.088 -0.171 0.451HHI 57063 0.186 0.152 0.000 1.000ZSCORE 53009 1.499 2.08 -13.69 5.59UNFC 57310 1.000 0.00 1 1CL 43179 2.285 98.65 -628 13843KZ 51522 -6.525 106.72 -14708 1198WW 50302 -0.226 0.389 -21.7 50.0TLC 41161 2.930 118.618 0.000 15571WAGE 6256 52.888 414.916 0.000 20357
Sample D: Financially Unconstrained and Non-distressedLTDEIR above median and ZSCORE above median
No. Obs Mean Std. Dev Min Max
Area Under Curve 26725 0.042 0.027 0.000 0.137Interest Over Book Value 26725 0.030 0.022 0.000 0.132HCR 4592 3.799 1.236 1 10PPE 26725 0.285 0.174 0.000 0.953LSALES 26725 5.668 1.873 -2.577 12.582BTM 26725 0.703 0.558 0.035 4.598DDIV 26725 0.490 0.500 0 1CF 26725 0.113 0.070 -0.902 1.219CASH 26725 0.125 0.149 -0.002 0.985PTP 26725 0.258 0.084 -0.171 0.451HHI 26598 0.198 0.153 0.000 0.993ZSCORE 26725 2.817 0.763 1.801 5.59UNFC 26725 1.000 0.000 1 1CL 21870 -0.103 1.648 -207.1 17.0KZ 24678 -5.574 62.77 -7213 21.8WW 25656 -0.238 0.222 -20.3 14.3TLC 21870 0.023 0.368 0.000 50.6WAGE 2355 37.006 194 0.003 9393
38
Table 3: Correlation between control variables used in the analysis. PPE is plant, property, and equipmentover total book values, LSALES is log of net sales expressed in 2000 dollars, BTM is book equity to marketequity, DDIV is an indicator for dividend paying firms, CF is net cashflow over total book values, CASH iscash holdings over total book values, and PTP is the personal tax penalty as measured in Graham (1999).KZ, CL, and WW are financial constraint measures as defined by the Kaplan Zingales (1997), Cleary (1999),and Whited Wu (2005) indices, respectively. ZSCORE is a measure of financial distress.
Sample A: All Firms
PPE LSALES BTM DDIV CF CASH
LSALES 0.1048BTM 0.0482 -0.1166DDIV 0.1560 0.5074 -0.0707CF 0.1413 0.3497 -0.0654 0.2579CASH -0.3442 -0.3085 -0.1504 -0.1707 -0.1638PTP -0.0266 -0.1698 0.0902 -0.1891 0.0011 -0.0029
Sample B: Financially Non-distressed FirmsZSCORE above median
PPE LSALES BTM DDIV CF CASH
LSALES 0.2405BTM -0.0196 -0.2072DDIV 0.2478 0.4157 -0.0949CF 0.2059 0.0397 -0.4281 0.1138CASH -0.3067 -0.2507 -0.1579 -0.1158 0.2176PTP -0.0260 -0.1835 0.1359 -0.1745 -0.0339 0.0009
Sample C: Financially Unconstrained FirmsLTDEIR above median
PPE LSALES BTM DDIV CF CASH
LSALES 0.0795BTM 0.0854 -0.0827DDIV 0.1451 0.5098 -0.0535CF 0.1388 0.3717 -0.0391 0.2436CASH -0.3537 -0.2948 -0.1922 -0.1934 -0.1968PTP -0.0077 -0.1845 0.0869 -0.2029 -0.0013 -0.0027
Sample D: Financially Unconstrained and Non-distressedLTDEIR above median and ZSCORE above median
PPE LSALES BTM DDIV CF CASH
LSALES 0.2095BTM 0.0172 -0.1972DDIV 0.2310 0.4207 -0.0798CF 0.1780 0.0261 -0.4213 0.0760CASH -0.3217 -0.2108 -0.1899 -0.1502 0.2335PTP -0.0194 -0.2134 0.1326 -0.1945 -0.0511 0.0148
39
Tab
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publ
icad
min
istr
atio
nfo
rsa
mpl
esA
thro
ugh
D.T
heer
ror
func
tion
sar
ede
fined
acco
rdin
gto
equa
tion
s6
and
10w
here
y∗ i,
tis
the
‘equ
ilibr
ium
’m
argi
nalbe
nefit
/cos
tle
vel,
x∗ i,
tis
the
obse
rved
or‘e
quili
briu
m’in
tere
stex
pens
esov
erbo
okva
lue
(IO
B)
and
Cis
the
set
ofco
stco
ntro
lva
riab
les.
GM
Mm
omen
tsar
eob
tain
edby
inte
ract
ing
the
erro
rfu
ncti
onw
ith
the
follo
win
gin
stru
men
ts:
the
cons
tant
term
,the
vari
atio
nof
the
mar
gina
lben
efit
curv
eA
i,t,a
ndea
chof
the
cont
rolv
aria
bles
.T
hese
tof
cont
rolv
aria
bles
,C,i
nclu
des{P
PE
,LS
AL
ES,B
TM
,DD
IV,C
F,C
AS
H,P
TP}w
here
PP
Eis
plan
t,pr
oper
ty,a
ndeq
uipm
ent
over
tota
lboo
kva
lues
,LSA
LE
Sis
log
ofne
tsa
les,
BT
Mis
book
equi
tyto
mar
ket
equi
ty,D
DIV
isan
indi
cato
rfo
rdi
vide
ndpa
ying
firm
,C
Fis
net
cash
flow
over
tota
lbo
okva
lues
,C
ASH
isca
shho
ldin
gsov
erto
talbo
okva
lues
,an
dP
TP
isth
epe
rson
alta
xpe
nalty
asm
easu
red
inG
raha
m(1
999)
.T
heco
ntro
lva
riab
les
are
stan
dard
ized
toha
vem
ean
zero
and
stan
dard
devi
atio
non
eba
sed
onSa
mpl
eA
(and
are
not
re-s
tand
ardi
zed
acro
sssa
mpl
es).
Rob
ust
GM
Mst
anda
rder
rors
are
repo
rted
inth
epa
rent
hese
s.Si
gnifi
canc
eat
the
10%
leve
lis
indi
cate
dby
*,5%
leve
lby
**,an
d1%
leve
lby
***.
(9)
MC
i,t
=a
+bx
i,t+P c∈C
θcc i
,tx
i,t+
ξi,
t(5
)M
Ci,
t=
a+
bxi,
t+P c∈C
δcc i
,t+
ξi,
t
Sam
ple
ASam
ple
BSam
ple
CSam
ple
DSam
ple
ASam
ple
BSam
ple
CSam
ple
D
Const
ant
0.0
17
***
0.2
02
***
-0.0
20
***
0.1
90
***
-0.0
12
***
0.1
34
***
-0.0
55
***
0.1
20
***
(0.0
05)
(0.0
03)
(0.0
06)
(0.0
04)
(0.0
05)
(0.0
04)
(0.0
07)
(0.0
05)
IOB
8.8
14
***
3.8
71
***
9.5
73
***
4.1
92
***
8.6
10
***
4.8
52
***
9.4
75
***
5.0
86
***
(0.1
56)
(0.1
25)
(0.2
02)
(0.1
57)
(0.1
41)
(0.1
00)
(0.1
93)
(0.1
28)
PP
E*IO
B-0
.731
***
-0.3
71
***
-0.8
52
***
-0.4
70
***
(0.0
31)
(0.0
40)
(0.0
37)
(0.0
46)
LSA
LE
S*IO
B0.6
61
***
0.3
29
***
0.8
60
***
0.4
05
***
(0.0
45)
(0.0
38)
(0.0
55)
(0.0
45)
BT
M*IO
B-0
.544
***
-0.4
53
***
-0.6
28
***
-0.5
18
***
(0.0
29)
(0.0
32)
(0.0
35)
(0.0
39)
DD
IV*IO
B1.8
30
***
1.2
11
***
1.6
58
***
1.0
66
***
(0.0
41)
(0.0
30)
(0.0
48)
(0.0
34)
CF*IO
B2.2
97
***
2.0
88
***
2.3
94
***
1.8
37
***
(0.0
78)
(0.1
81)
(0.0
86)
(0.2
06)
CA
SH
*IO
B2.4
98
***
1.4
16
***
2.6
99
***
1.5
04
***
(0.0
91)
(0.0
71)
(0.1
15)
(0.0
89)
PT
P*IO
B0.6
85
***
1.0
67
***
0.4
86
***
0.9
15
***
(0.0
31)
(0.0
27)
(0.0
39)
(0.0
31)
PP
E-0
.024
***
-0.0
13
***
-0.0
29
***
-0.0
19
***
(0.0
01)
(0.0
01)
(0.0
01)
(0.0
02)
LSA
LE
S0.0
18
***
0.0
11
***
0.0
26
***
0.0
15
***
(0.0
01)
(0.0
01)
(0.0
02)
(0.0
01)
BT
M-0
.020
***
-0.0
24
***
-0.0
26
***
-0.0
29
***
(0.0
01)
(0.0
01)
(0.0
01)
(0.0
02)
DD
IV0.0
81
***
0.0
51
***
0.0
78
***
0.0
47
***
(0.0
01)
(0.0
01)
(0.0
01)
(0.0
01)
CF
0.1
03
***
0.1
15
***
0.1
04
***
0.1
12
***
(0.0
02)
(0.0
05)
(0.0
03)
(0.0
05)
CA
SH
0.0
79
***
0.0
43
***
0.0
87
***
0.0
44
***
(0.0
02)
(0.0
01)
(0.0
02)
(0.0
02)
PT
P0.0
24
***
0.0
38
***
0.0
16
***
0.0
35
***
(0.0
01)
(0.0
01)
(0.0
01)
(0.0
01)
No.
Obs.
69569
37978
50345
25977
69569
37978
50345
25977
40
Table 5: Regressing area under the marginal benefits curve on the set of cost control variables. The setof control variables, C, includes {PPE,LSALES,BTM, DDIV, CASHFLOW,CASH,PTP} where PPEis plant, property, and equipment over total book values, LSALES is log of sales expressed in 2000 dollars,BTM is book equity to market equity, DDIV is an indicator for dividend paying firms, CF is net cashflowover total book values, CASH is cash holdings over total book values, and PTP is the personal tax penalty.Standard errors are reported in the parentheses. Significance at the 10% level is indicated by *, 5% level by**, and 1% level by ***.
Sample A Sample B Sample C Sample D
Panel A: Ai,t = α +P
c∈Cβcci,t + νi,t
PPE -0.0009 *** -0.0003 ** -0.0014 *** -0.0003 *(0.0001) (0.0001) (0.0001) (0.0002)
LSALES 0.0031 *** 0.0031 *** 0.0025 *** 0.0022 ***(0.0001) (0.0001) (0.0001) (0.0002)
BTM -0.0025 *** -0.0034 *** -0.0024 *** -0.0035 ***(0.0001) (0.0001) (0.0001) (0.0002)
DDIV 0.0049 *** 0.0039 *** 0.0053 *** 0.0043 ***(0.0001) (0.0001) (0.0001) (0.0002)
CF 0.0048 *** 0.0050 *** 0.0054 *** 0.0051 ***(0.0001) (0.0002) (0.0002) (0.0002)
CASH -0.0032 *** -0.0050 *** -0.0032 *** -0.0051 ***(0.0001) (0.0001) (0.0001) (0.0002)
PTP 0.0089 *** 0.0111 *** 0.0088 *** 0.0111 ***(0.0001) (0.0002) (0.0001) (0.0002)
Constant 0.0324 *** 0.0406 *** 0.0332 *** 0.0420 ***(0.0001) (0.0001) (0.0001) (0.0001)
No. Obs. 80039 39112 57310 26725R2 0.2446 0.2632 0.2468 0.2548
41
Tab
le6:
Mar
gina
lco
stof
debt
byin
dust
ry.
GM
Mes
tim
atio
nof
the
coeffi
cien
tsin
equa
tion
9(s
eebe
low
)by
indu
stry
.T
heer
ror
func
tion
isde
fined
ineq
uati
on10
whe
rey∗ i,
tis
the
‘equ
ilibr
ium
’m
argi
nal
bene
fit/c
ost
leve
l,x∗ i,
tis
the
obse
rved
or‘e
quili
briu
m’
inte
rest
expe
nses
over
book
valu
e(I
OB
)an
dC
isth
ese
tof
cost
cont
rol
vari
able
s.G
MM
mom
ents
are
obta
ined
byin
tera
ctin
gth
eer
ror
func
tion
wit
hth
efo
llow
ing
inst
rum
ents
:th
eco
nsta
ntte
rm,
the
vari
atio
nof
the
mar
gina
lbe
nefit
curv
eA
i,t,
and
each
ofth
eco
ntro
lva
riab
les.
The
set
ofco
ntro
lva
riab
les,
C,
incl
udes
{PP
E,L
SA
LE
S,B
TM
,DD
IV,C
F,C
AS
H,P
TP}w
here
PP
Eis
plan
t,pr
oper
ty,a
ndeq
uipm
ent
over
tota
lboo
kva
lues
,LSA
LE
Sis
log
ofne
tsa
les,
BT
Mis
book
equi
tyto
mar
keteq
uity
,DD
IVis
anin
dica
tor
for
divi
dend
payi
ngfir
m,C
Fis
netca
shflo
wov
erto
talb
ook
valu
es,C
ASH
isca
shho
ldin
gsov
erto
talbo
okva
lues
,an
dP
TP
ispe
rson
aliz
edta
xpe
nalty
asm
easu
red
inG
raha
m(1
999)
.T
heco
ntro
lva
riab
les
are
stan
dard
ized
toha
vem
ean
zero
and
stan
dard
devi
atio
non
efo
rea
chin
dust
ry.
Rob
ust
GM
Mst
anda
rder
rors
are
repo
rted
inth
epa
rent
hese
s.Si
gnifi
canc
eat
the
10%
leve
lis
indi
cate
dby
*,5%
leve
lby
**,an
d1%
leve
lby
***.
(9)
MC
i,t
=a
+bx
i,t+P c∈C
θcc i
,tx
i,t+
ξi,
t
Const
ant
IOB
PP
ELSA
LE
SB
TM
DD
IVC
FC
ASH
PT
PN
o.
Obs
*IO
B*IO
B*IO
B*IO
B*IO
B*IO
B*IO
BSam
ple
A:A
llFir
ms
All
Indust
ries
0.0
32
***
8.3
73
***
-0.5
07
***
0.6
97
***
-0.5
17
***
1.8
12
***
2.1
78
***
2.2
57
***
0.7
11
***
80039
(0.0
04)
(0.1
32)
(0.0
28)
(0.0
40)
(0.0
27)
(0.0
36)
(0.0
73)
(0.0
83)
(0.0
29)
All
Indust
ries
Exce
pt
Uti
liti
es,
0.0
17
***
8.8
14
***
-0.7
31
***
0.6
61
***
-0.5
44
***
1.8
30
***
2.2
97
***
2.4
98
***
0.6
85
***
69569
Fin
ance
,&
Public
Adm
in.
(0.0
05)
(0.1
56)
(0.0
31)
(0.0
45)
(0.0
29)
(0.0
41)
(0.0
78)
(0.0
91)
(0.0
31)
Min
ing
&C
onst
ruct
ion
-0.0
09
8.4
57
***
0.3
26
***
1.2
31
***
-0.5
00
***
1.2
73
***
2.4
66
***
2.3
98
***
0.4
98
***
6003
(0.0
11)
(0.4
41)
(0.1
26)
(0.2
05)
(0.1
08)
(0.1
40)
(0.2
79)
(0.2
96)
(0.1
20)
Uti
liti
es-0
.097
***
13.2
37***
-0.0
17
-0.1
88
-0.5
45
***
2.2
61
***
1.4
24
***
1.3
76
***
0.9
55
***
4013
(0.0
32)
(0.9
76)
(0.1
51)
(0.1
22)
(0.1
37)
(0.1
71)
(0.2
62)
(0.2
73)
(0.1
27)
Manufa
cturi
ng
0.0
14
11.1
29***
-0.0
30
0.6
54
***
-0.5
69
***
2.0
18
***
3.4
71
***
4.1
45
***
0.6
33
***
39888
(0.0
09)
(0.3
59)
(0.0
48)
(0.0
70)
(0.0
47)
(0.0
68)
(0.1
71)
(0.2
01)
(0.0
49)
Whole
sale
&R
etail
Tra
de
-0.0
45
***
7.7
52
***
-0.7
28
***
0.9
48
***
-0.6
30
***
1.1
51
***
1.1
05
***
0.3
93
***
0.8
12
***
9364
(0.0
17)
(0.3
85)
(0.0
63)
(0.0
85)
(0.0
62)
(0.0
73)
(0.1
28)
(0.1
09)
(0.0
61)
Tra
nsp
ort
ati
on,W
are
housi
ng,
-0.0
48
*8.8
90
***
-0.5
02
***
0.1
75
-0.4
52
***
2.1
65
***
2.1
43
***
0.5
36
***
0.5
87
***
3692
&C
om
munic
ati
on
(0.0
27)
(0.6
95)
(0.1
55)
(0.1
62)
(0.1
21)
(0.1
84)
(0.2
11)
(0.2
07)
(0.1
39)
Fin
ance
,In
sura
nce
,&
Rea
lE
state
0.1
73
***
4.0
67
***
-0.4
12
***
0.3
83
***
-0.2
84
***
0.8
76
***
1.4
82
***
0.7
97
***
0.5
30
***
5928
(0.0
06)
(0.1
66)
(0.0
55)
(0.1
01)
(0.0
57)
(0.0
77)
(0.1
98)
(0.1
41)
(0.0
72)
Ser
vic
es&
Lei
sure
-0.0
64
***
10.0
54***
-1.1
36
***
1.0
97
***
-0.3
98
***
1.0
43
***
1.7
03
***
3.7
11
***
0.5
50
***
10287
(0.0
13)
(0.4
06)
(0.0
79)
(0.1
06)
(0.0
72)
(0.0
81)
(0.1
35)
(0.2
35)
(0.0
72)
Sam
ple
D:Fin
anci
ally
Unco
nst
rain
edand
Non-d
istr
esse
d:
LT
DE
IRabove
med
ian
and
ZSC
OR
Eabove
med
ian
All
Indust
ries
0.1
91
***
4.1
16
***
-0.4
71
***
0.4
46
***
-0.5
14
***
1.0
83
***
1.7
11
***
1.4
82
***
1.0
16
***
26725
(0.0
04)
(0.1
50)
(0.0
47)
(0.0
45)
(0.0
38)
(0.0
34)
(0.1
92)
(0.0
84)
(0.0
34)
All
Indust
ries
Exce
pt
Uti
liti
es,
0.1
90
***
4.1
92
***
-0.4
70
***
0.4
05
***
-0.5
18
***
1.0
66
***
1.8
37
***
1.5
04
***
0.9
15
***
25977
Fin
ance
,&
Public
Adm
in.
(0.0
04)
(0.1
57)
(0.0
46)
(0.0
45)
(0.0
39)
(0.0
34)
(0.2
06)
(0.0
89)
(0.0
31)
Min
ing
&C
onst
ruct
ion
0.1
38
***
6.8
72
***
1.2
28
**
0.3
97
-0.7
07
**
0.6
14
**
1.8
83
**
1.3
74
**
0.5
34
*648
(0.0
23)
(1.3
13)
(0.5
76)
(0.5
45)
(0.2
89)
(0.2
97)
(0.8
71)
(0.6
31)
(0.2
89)
Uti
liti
es0.1
06
**
7.3
26
***
0.4
49
0.0
46
-1.0
31
**
1.4
48
***
-0.9
37
1.6
77
***
2.8
68
***
171
(0.0
53)
(1.6
20)
(0.4
91)
(0.5
45)
(0.5
21)
(0.4
82)
(0.8
41)
(0.5
03)
(0.6
02)
Manufa
cturi
ng
0.1
97
***
5.2
85
***
0.1
49
**
0.4
05
***
-0.4
77
***
1.0
62
***
2.8
65
***
2.7
86
***
0.9
32
***
16489
(0.0
05)
(0.2
97)
(0.0
60)
(0.0
61)
(0.0
65)
(0.0
47)
(0.4
41)
(0.1
59)
(0.0
39)
Whole
sale
&R
etail
Tra
de
0.0
75
***
5.2
08
***
-0.6
01
***
0.7
78
***
-0.6
01
***
0.7
77
***
1.0
13
***
0.1
40
0.7
82
***
4981
(0.0
14)
(0.3
09)
(0.0
71)
(0.0
89)
(0.0
68)
(0.0
65)
(0.1
57)
(0.0
95)
(0.0
63)
Tra
nsp
ort
ati
on,W
are
housi
ng,
0.1
66
***
3.0
70
***
-0.8
00
***
0.7
98
**
-0.5
90
***
0.5
70
***
1.8
08
***
0.1
25
1.0
14
***
712
&C
om
munic
ati
on
(0.0
21)
(0.5
25)
(0.2
50)
(0.3
33)
(0.1
85)
(0.1
96)
(0.5
27)
(0.2
01)
(0.1
73)
Fin
ance
,In
sura
nce
,&
Rea
lE
state
0.2
55
***
1.7
47
***
-0.7
25
***
0.5
27
*-0
.236
0.7
99
***
0.2
11
0.9
65
***
2.0
36
***
482
(0.0
15)
(0.6
11)
(0.2
63)
(0.2
78)
(0.2
18)
(0.2
17)
(0.4
71)
(0.2
55)
(0.4
09)
Ser
vic
es&
Lei
sure
0.1
56
***
5.1
01
***
-0.4
12
***
0.8
61
***
-0.5
14
***
0.5
02
***
0.5
21
*2.4
51
***
0.8
29
***
3068
(0.0
13)
(0.4
73)
(0.1
25)
(0.1
22)
(0.1
08)
(0.0
77)
(0.2
78)
(0.2
43)
(0.0
98)
42
Tab
le7:
Wag
esan
dla
bor
com
pens
atio
nfo
rco
rpor
ate
capi
tal
stru
ctur
ech
oice
s.G
MM
esti
mat
ion
ofth
eco
effici
ents
ineq
uati
ons
5an
d9
for
all
indu
stri
esfo
rsa
mpl
esA
thro
ugh
D.
The
erro
rfu
ncti
ons
are
defin
edac
cord
ing
toeq
uati
ons
6an
d10
whe
rey∗ i,
tis
the
‘equ
ilibr
ium
’m
argi
nal
bene
fit/c
ost
leve
l,x∗ i,
tis
the
obse
rved
or‘e
quili
briu
m’
inte
rest
expe
nses
over
book
valu
e(I
OB
)an
dC
isth
ese
tof
cost
cont
rol
vari
able
s.G
MM
mom
ents
are
obta
ined
byin
tera
ctin
gth
eer
ror
func
tion
wit
hth
efo
llow
ing
inst
rum
ents
:th
eco
nsta
ntte
rm,t
heva
riat
ion
ofth
em
argi
nalb
enefi
tcu
rve
Ai,
t,
and
each
ofth
eco
ntro
lva
riab
les.
The
set
ofco
ntro
lva
riab
les,
C,
incl
udes{P
PE
,LS
AL
ES,B
TM
,DD
IV,C
F,C
AS
H,P
TP}
whe
reP
PE
ispl
ant,
prop
erty
,an
deq
uipm
ent
over
tota
lbo
okva
lues
,LSA
LE
Sis
log
ofne
tsa
les,
BT
Mis
book
equi
tyto
mar
ket
equi
ty,D
DIV
isan
indi
cato
rfo
rdi
vide
ndpa
ying
firm
,C
Fis
net
cash
flow
over
tota
lbo
okva
lues
,C
ASH
isca
shho
ldin
gsov
erto
talbo
okva
lues
,an
dP
TP
isth
epe
rson
alta
xpe
nalty
asm
easu
red
inG
raha
m(1
999)
.T
heco
ntro
lva
riab
les
are
stan
dard
ized
toha
vem
ean
zero
and
stan
dard
devi
atio
non
eba
sed
onSa
mpl
eA
(and
are
not
re-s
tand
ardi
zed
acro
sssa
mpl
es).
Rob
ust
GM
Mst
anda
rder
rors
are
repo
rted
inth
epa
rent
hese
s.Si
gnifi
canc
eat
the
10%
leve
lis
indi
cate
dby
*,5%
leve
lby
**,an
d1%
leve
lby
***.
(9)
MC
i,t
=a
+bx
i,t+P c∈C
θcc i
,tx
i,t+
ξi,
t(5
)M
Ci,
t=
a+
bxi,
t+P c∈C
δcc i
,t+
ξi,
t
Sam
ple
ASam
ple
BSam
ple
CSam
ple
DSam
ple
ASam
ple
BSam
ple
CSam
ple
D
Const
ant
0.0
49
***
0.2
47
***
-0.0
79
***
0.1
99
***
0.0
16
0.1
88
***
-0.0
60
**
0.1
63
***
(0.0
15)
(0.0
09)
(0.0
30)
(0.0
15)
(0.0
15)
(0.0
10)
(0.0
24)
(0.0
15)
IOB
7.3
84
***
2.6
05
***
10.2
07***
3.7
74
***
7.1
51
***
3.2
22
***
8.6
47
***
3.7
36
***
(0.4
68)
(0.2
71)
(0.8
35)
(0.4
25)
(0.4
10)
(0.2
45)
(0.6
35)
(0.3
43)
PP
E*IO
B-0
.725
***
-0.2
17
***
-1.0
39
***
-0.3
91
***
(0.0
94)
(0.0
84)
(0.1
39)
(0.1
10)
LSA
LE
S*IO
B0.8
44
***
0.7
38
***
1.0
20
***
0.9
10
***
(0.1
29)
(0.1
02)
(0.1
88)
(0.1
41)
BT
M*IO
B-0
.846
***
-0.4
63
***
-1.1
76
***
-0.5
93
***
(0.1
02)
(0.0
93)
(0.1
54)
(0.1
31)
DD
IV*IO
B2.4
34
***
1.3
75
***
2.6
77
***
1.3
61
***
(0.1
36)
(0.0
92)
(0.2
05)
(0.1
26)
CF*IO
B1.4
02
***
0.7
11
***
1.4
33
***
0.6
09
**
(0.2
28)
(0.2
03)
(0.2
85)
(0.2
46)
CA
SH
*IO
B0.7
81
***
0.4
10
***
0.3
25
0.0
91
(0.2
08)
(0.1
30)
(0.3
01)
(0.1
86)
PT
P*IO
B1.3
22
***
1.5
50
***
0.8
88
***
1.2
19
***
(0.0
93)
(0.0
90)
(0.1
36)
(0.1
13)
LW
AG
E*IO
B0.6
88
***
0.3
50
***
0.9
82
***
0.5
76
***
(0.1
04)
(0.0
92)
(0.1
60)
(0.1
35)
PP
E-0
.021
***
-0.0
05
**
-0.0
30
***
-0.0
11
***
(0.0
03)
(0.0
03)
(0.0
04)
(0.0
03)
LSA
LE
S-0
.001
0.0
15
***
0.0
03
0.0
20
***
(0.0
04)
(0.0
02)
(0.0
05)
(0.0
04)
BT
M-0
.027
***
-0.0
21
***
-0.0
40
***
-0.0
31
***
(0.0
04)
(0.0
04)
(0.0
05)
(0.0
06)
DD
IV0.1
11
***
0.0
61
***
0.1
13
***
0.0
58
***
(0.0
05)
(0.0
03)
(0.0
07)
(0.0
04)
CF
0.1
03
***
0.0
61
***
0.1
06
***
0.0
56
***
(0.0
07)
(0.0
10)
(0.0
10)
(0.0
14)
CA
SH
0.0
45
***
0.0
22
***
0.0
35
***
0.0
17
***
(0.0
05)
(0.0
04)
(0.0
07)
(0.0
05)
PT
P0.0
38
***
0.0
47
***
0.0
30
***
0.0
42
***
(0.0
03)
(0.0
03)
(0.0
04)
(0.0
04)
LW
AG
E0.0
21
***
0.0
00
0.0
22
***
0.0
03
(0.0
04)
(0.0
02)
(0.0
05)
(0.0
03)
No.
Obs.
6413
3462
4447
2211
6413
3462
4447
2211
43
Tab
le8:
Mac
roec
onom
icin
fluen
ce.
GM
Mes
tim
atio
nof
the
coeffi
cien
tsin
equa
tion
s5
and
9fo
ral
lin
dust
ries
for
sam
ples
Ath
roug
hD
.T
heer
ror
func
tion
sar
ede
fined
acco
rdin
gto
equa
tion
s6
and
10,w
here
y∗ i,
tis
the
‘equ
ilibr
ium
’m
argi
nalbe
nefit
/cos
tle
vel,
x∗ i,
tis
the
obse
rved
or‘e
quili
briu
m’
inte
rest
expe
nses
over
book
valu
e(I
OB
)an
dC
isth
ese
tof
cost
cont
rolv
aria
bles
.G
MM
mom
ents
are
obta
ined
byin
tera
ctin
gth
eer
ror
func
tion
wit
hth
efo
llow
ing
inst
rum
ents
:th
eco
nsta
ntte
rm,th
eva
riat
ion
ofth
em
argi
nalbe
nefit
curv
eA
i,t,an
dea
chof
the
cont
rolva
riab
les.
The
set
ofco
ntro
lva
riab
les,
C,in
clud
es{P
PE
,LS
AL
ES,B
TM
,DD
IV,C
F,C
AS
H,P
TP
,CS}
whe
reP
PE
ispl
ant,
prop
erty
,an
deq
uipm
ent
over
tota
lbo
okva
lues
,LSA
LE
Sis
log
ofne
tsa
les,
BT
Mis
book
equi
tyto
mar
ket
equi
ty,D
DIV
isan
indi
cato
rfo
rdi
vide
ndpa
ying
firm
,CF
isne
tca
shflo
wov
erto
talb
ook
valu
es,C
ASH
isca
shho
ldin
gsov
erto
talbo
okva
lues
,P
TP
isth
epe
rson
alta
xpe
nalty
asm
easu
red
inG
raha
m(1
999)
,an
dC
Sis
Moo
dy’s
Baa
rate
min
usM
oody
’sA
aara
te.
The
cont
rol
vari
able
sar
est
anda
rdiz
edto
have
mea
nze
roan
dst
anda
rdde
viat
ion
one
base
don
Sam
ple
A(a
ndar
eno
tre
-sta
ndar
dize
dac
ross
sam
ples
).R
obus
tG
MM
stan
dard
erro
rsar
ere
port
edin
the
pare
nthe
ses.
Sign
ifica
nce
atth
e10
%le
velis
indi
cate
dby
*,5%
leve
lby
**,an
d1%
leve
lby
***.
(9)
MC
i,t
=a
+bx
i,t+P c∈C
θcc i
,tx
i,t+
ξi,
t(5
)M
Ci,
t=
a+
bxi,
t+P c∈C
δcc i
,t+
ξi,
t
Sam
ple
ASam
ple
BSam
ple
CSam
ple
DSam
ple
ASam
ple
BSam
ple
CSam
ple
D
Const
ant
0.0
13
***
0.2
06
***
-0.0
28
***
0.1
92
***
-0.0
30
***
0.1
38
***
-0.0
89
***
0.1
19
***
(0.0
05)
(0.0
03)
(0.0
06)
(0.0
04)
(0.0
05)
(0.0
04)
(0.0
08)
(0.0
05)
IOB
8.9
51
***
3.7
20
***
9.8
59
***
4.1
09
***
9.1
59
***
4.7
35
***
10.4
34***
5.1
25
***
(0.1
64)
(0.1
28)
(0.2
15)
(0.1
64)
(0.1
66)
(0.1
08)
(0.2
38)
(0.1
44)
PP
E*IO
B-0
.731
***
-0.3
76
***
-0.8
49
***
-0.4
72
***
(0.0
32)
(0.0
39)
(0.0
38)
(0.0
45)
LSA
LE
S*IO
B0.6
32
***
0.3
59
***
0.8
05
***
0.4
19
***
(0.0
45)
(0.0
37)
(0.0
56)
(0.0
44)
BT
M*IO
B-0
.514
***
-0.4
92
***
-0.5
68
***
-0.5
38
***
(0.0
29)
(0.0
32)
(0.0
36)
(0.0
39)
DD
IV*IO
B1.9
44
***
1.0
94
***
1.8
68
***
1.0
11
***
(0.0
46)
(0.0
33)
(0.0
55)
(0.0
39)
CF*IO
B2.3
11
***
2.0
94
***
2.4
21
***
1.8
40
***
(0.0
78)
(0.1
81)
(0.0
87)
(0.2
06)
CA
SH
*IO
B2.5
17
***
1.3
92
***
2.7
50
***
1.4
87
***
(0.0
92)
(0.0
70)
(0.1
19)
(0.0
89)
PT
P*IO
B0.8
79
***
0.8
59
***
0.8
64
***
0.8
13
***
(0.0
39)
(0.0
34)
(0.0
47)
(0.0
40)
CS*IO
B-0
.287
***
0.2
96
***
-0.5
65
***
0.1
48
***
(0.0
41)
(0.0
33)
(0.0
50)
(0.0
40)
PP
E-0
.025
***
-0.0
14
***
-0.0
30
***
-0.0
19
***
(0.0
01)
(0.0
01)
(0.0
01)
(0.0
02)
LSA
LE
S0.0
15
***
0.0
11
***
0.0
22
***
0.0
15
***
(0.0
01)
(0.0
01)
(0.0
02)
(0.0
01)
BT
M-0
.018
***
-0.0
25
***
-0.0
23
***
-0.0
29
***
(0.0
01)
(0.0
01)
(0.0
02)
(0.0
02)
DD
IV0.0
91
***
0.0
49
***
0.0
92
***
0.0
47
***
(0.0
02)
(0.0
01)
(0.0
02)
(0.0
01)
CF
0.1
05
***
0.1
15
***
0.1
09
***
0.1
13
***
(0.0
02)
(0.0
05)
(0.0
03)
(0.0
05)
CA
SH
0.0
83
***
0.0
42
***
0.0
94
***
0.0
45
***
(0.0
02)
(0.0
01)
(0.0
03)
(0.0
02)
PT
P0.0
36
***
0.0
35
***
0.0
37
***
0.0
36
***
(0.0
01)
(0.0
01)
(0.0
02)
(0.0
02)
CS
-0.0
23
***
0.0
05
***
-0.0
40
***
-0.0
02
(0.0
02)
(0.0
01)
(0.0
02)
(0.0
02)
No.
Obs.
69569
37978
50345
25977
69569
37978
50345
25977
44
Tab
le9:
Sum
mar
yst
atis
tics
for
bene
fitan
dco
stof
debt
.M
easu
res
are
base
don
the
mar
gina
lco
stcu
rves
esti
mat
edfr
omeq
uati
ons
(9)
and
(5)
for
sam
ple
Dfo
ral
lin
dust
ries
exce
ptut
iliti
es,
finan
ce,
and
publ
icad
min
stra
tion
.T
heob
serv
edgr
oss
bene
fits
ofde
bt,
GB
Do,
isth
ear
eaun
der
the
mar
gina
lben
efits
curv
eup
toth
eob
serv
edle
velo
fint
eres
tov
erbo
okva
lue
(IO
B).
The
obse
rved
cost
ofde
bt,C
Do
isth
ear
eaun
der
the
mar
gina
lcos
tcu
rve
upto
the
obse
rved
leve
lof
IOB
.T
heob
serv
edne
tbe
nefit
sof
debt
,N
BD
o,is
the
area
unde
rth
em
argi
nalbe
nefit
scu
rve
min
usth
ear
eaun
der
the
mar
gina
lco
stcu
rve
upto
the
obse
rved
IOB
.E
quili
briu
mis
defin
edas
the
inte
rsec
tion
ofth
em
argi
nal
bene
fitan
dco
stcu
rves
.T
heob
serv
edgr
oss
bene
fits
ofde
bt,G
BD
e,is
the
area
unde
rth
em
argi
nalbe
nefit
scu
rve
upto
the
equi
libri
umle
velof
IOB
.T
heeq
uilib
rium
cost
ofde
bt,C
De
isth
ear
eaun
der
the
mar
gina
lcos
tcu
rve
upto
the
equi
libri
umle
velo
fIO
B.T
heeq
uilib
rium
net
bene
fits
ofde
bt,N
BD
e,i
sth
ear
eaun
der
the
mar
gina
lbe
nefit
scu
rve
min
usth
ear
eaun
der
the
mar
gina
lcos
tcu
rve
upto
the
equi
libri
umIO
B.T
heco
stof
bein
gov
erle
vera
ged,
DW
o,i
sth
ede
adw
eigh
tlo
ssfr
omad
diti
onal
cost
sdu
eto
havi
ngIO
Bab
ove
the
equi
libri
um.
The
cost
ofbe
ing
unde
rlev
erag
ed,D
Wu,is
the
dead
wei
ght
loss
from
low
erbe
nefit
sdu
eto
havi
ngIO
Bbe
low
the
equi
libri
um.
The
cost
ofbe
ing
out
ofeq
uilib
rium
,D
Wt,co
mbi
nes
DW
oan
dD
Wu
into
one
mea
sure
.
Analy
sis
Base
don
(9)
MC
i,t
=a
+bx
i,t+P c∈C
θcc i
,tx
i,t+
ξi,
t
NM
ean
Std
.D
ev.
1%
10%
25%
Med
ian
75%
90%
99%
Obse
rved
gro
ssben
efits
ofdeb
t(G
BD
o)
85356
0.0
895
0.0
860
0.0
000
0.0
028
0.0
231
0.0
680
0.1
294
0.2
050
0.3
807
Obse
rved
cost
sofdeb
t(C
Do)
69569
0.0
874
0.0
838
0.0
000
0.0
125
0.0
312
0.0
650
0.1
170
0.1
888
0.3
986
Obse
rved
net
ben
efits
ofdeb
t(N
BD
o)
69569
0.0
024
0.0
572
-0.2
179
-0.0
593
-0.0
099
0.0
142
0.0
295
0.0
510
0.0
966
Equilib
rium
gro
ssben
efits
ofdeb
t(G
BD
e)
69569
0.1
014
0.0
919
0.0
000
0.0
000
0.0
126
0.0
939
0.1
548
0.2
126
0.3
707
Equilib
rium
cost
sofdeb
t(C
De)
69569
0.0
728
0.0
622
0.0
000
0.0
000
0.0
105
0.0
705
0.1
124
0.1
505
0.2
465
Equilib
rium
net
ben
efits
ofdeb
t(N
BD
o)
69569
0.0
285
0.0
384
0.0
000
0.0
000
0.0
017
0.0
224
0.0
411
0.0
623
0.1
316
Cost
ofbei
ng
out
ofeq
uilib
rium
(DW
t)
69569
0.0
262
0.0
506
0.0
000
0.0
003
0.0
023
0.0
093
0.0
270
0.0
713
0.2
451
Cost
ofover
lever
agin
g(D
Wo)
35521
0.0
401
0.0
612
0.0
000
0.0
004
0.0
036
0.0
178
0.0
524
0.1
086
0.2
847
Cost
ofunder
lever
agin
g(D
Wu)
34048
0.0
117
0.0
304
0.0
000
0.0
002
0.0
017
0.0
061
0.0
134
0.0
247
0.0
999
Analy
sis
Base
don
(5)
MC
i,t
=a
+bx
i,t+P c∈C
δcc i
,t+
ξi,
t
NM
ean
Std
.D
ev.
1%
10%
25%
Med
ian
75%
90%
99%
Obse
rved
gro
ssben
efits
ofdeb
t(G
BD
o)
85356
0.0
895
0.0
860
0.0
000
0.0
028
0.0
231
0.0
680
0.1
294
0.2
050
0.3
807
Obse
rved
cost
sofdeb
t(C
Do)
69569
0.0
729
0.0
854
-0.0
535
0.0
036
0.0
196
0.0
509
0.1
002
0.1
733
0.3
923
Obse
rved
net
ben
efits
ofdeb
t(N
BD
o)
69569
0.0
169
0.0
581
-0.1
993
-0.0
303
0.0
007
0.0
179
0.0
420
0.0
698
0.1
484
Equilib
rium
gro
ssben
efits
ofdeb
t(G
BD
e)
69569
0.1
022
0.0
831
0.0
000
0.0
000
0.0
259
0.0
954
0.1
574
0.2
162
0.3
223
Equilib
rium
cost
sofdeb
t(C
De)
69171
0.0
636
0.0
643
-0.0
676
0.0
000
0.0
113
0.0
652
0.1
025
0.1
501
0.1
949
Equilib
rium
net
ben
efits
ofdeb
t(N
BD
o)
69171
0.0
392
0.0
465
0.0
000
0.0
000
0.0
087
0.0
288
0.0
562
0.0
868
0.1
839
Cost
ofbei
ng
out
ofeq
uilib
rium
(DW
t)
69171
0.0
224
0.0
448
0.0
000
0.0
002
0.0
017
0.0
076
0.0
229
0.0
561
0.2
247
Cost
ofover
lever
agin
g(D
Wo)
32556
0.0
327
0.0
563
0.0
000
0.0
003
0.0
018
0.0
103
0.0
378
0.0
916
0.2
761
Cost
ofunder
lever
agin
g(D
Wu)
36615
0.0
133
0.0
281
0.0
000
0.0
002
0.0
015
0.0
063
0.0
161
0.0
313
0.0
964
45
Tab
le10
:C
ondi
tion
alsu
mm
ary
stat
isti
csfo
rbe
nefit
and
cost
mea
sure
sba
sed
onth
em
argi
nalco
stcu
rves
esti
mat
edfr
omeq
uati
ons
(9)
and
(5)
for
sam
ple
Dfo
ral
lin
dust
ries
exce
ptut
iliti
es,fi
nanc
e,an
dpu
blic
adm
inst
rati
on.
Pan
elA
grou
psob
serv
atio
nsba
sed
onho
wfa
ra
firm
-yea
rob
serv
atio
nac
tual
lyob
serv
edis
from
the
equi
libri
umfo
ri)
all
obse
rvat
ions
,ii)
over
leve
rage
dfir
m-y
ears
,an
diii
)un
derl
ever
aged
firm
-yea
rs.
Pan
elB
grou
psob
serv
atio
nsba
sed
onho
wfa
rth
eeq
uilib
rium
IOB
ofa
firm
-yea
rob
serv
atio
nis
from
the
obse
rved
actu
alIO
B.
The
cuto
ffsfo
llow
thos
eof
the
mar
gina
lben
efit
curv
es.
The
obse
rved
gros
sbe
nefit
sof
debt
,GB
Do,i
sth
ear
eaun
der
the
mar
gina
lben
efits
curv
eup
toth
eob
serv
edle
velo
fin
tere
stov
erbo
okva
lue
(IO
B).
The
obse
rved
cost
ofde
bt,
CD
ois
the
area
unde
rth
em
argi
nal
cost
curv
eup
toth
eob
serv
edle
vel
ofIO
B.
The
obse
rved
net
bene
fits
ofde
bt,
NB
Do,
isth
ear
eaun
der
the
mar
gina
lbe
nefit
scu
rve
min
usth
ear
eaun
der
the
mar
gina
lco
stcu
rve
upto
the
obse
rved
IOB
.E
quili
briu
mis
defin
edas
the
inte
rsec
tion
ofth
em
argi
nalbe
nefit
and
cost
curv
es.
The
obse
rved
gros
sbe
nefit
sof
debt
,G
BD
e,is
the
area
unde
rth
em
argi
nalbe
nefit
scu
rve
upto
the
equi
libri
umle
velof
IOB
.T
heeq
uilib
rium
cost
ofde
bt,C
De
isth
ear
eaun
der
the
mar
gina
lco
stcu
rve
upto
the
equi
libri
umle
velo
fIO
B.T
heeq
uilib
rium
net
bene
fits
ofde
bt,N
BD
e,i
sth
ear
eaun
der
the
mar
gina
lben
efits
curv
em
inus
the
area
unde
rth
em
argi
nal
cost
curv
eup
toth
eeq
uilib
rium
IOB
.T
heco
stof
bein
gov
erle
vera
ged,
DW
o,is
the
dead
wei
ght
loss
from
addi
tion
alco
sts
due
toha
ving
IOB
abov
eth
eeq
uilib
rium
.T
heco
stof
bein
gun
derl
ever
aged
,D
Wu,is
the
dead
wei
ght
loss
from
low
erbe
nefit
sdu
eto
havi
ngIO
Bbe
low
the
equi
libri
um.
The
cost
ofbe
ing
out
ofeq
uilib
rium
,D
Wt,co
mbi
nes
DW
oan
dD
Wu
into
one
mea
sure
.
Panel
A:G
roupin
gby
per
centa
ge
ofobse
rved
IOB
from
equilib
rium
IOB
Analy
sis
Base
don
(9)
MC
i,t
=a
+bx
i,t+P c∈C
θcc i
,tx
i,t+
ξi,
tA
naly
sis
Base
don
(5)
MC
i,t
=a
+bx
i,t+P c∈C
δcc i
,t+
ξi,
t
NG
BD
oC
Do
NB
Do
GB
De
CD
eN
BD
eD
Wt
NG
BD
oC
Do
NB
Do
GB
De
CD
eN
BD
eD
Wt
All
Obse
rvati
ons
Wit
hin
5%
ofeq
uilib
rium
2897
0.1
453
0.1
065
0.0
388
0.1
471
0.1
070
0.0
400
0.0
012
3281
0.1
354
0.0
856
0.0
498
0.1
358
0.0
859
0.0
499
0.0
001
Bet
wee
n5%
-10%
from
equilib
rium
3035
0.1
396
0.1
010
0.0
386
0.1
428
0.1
023
0.0
405
0.0
019
3346
0.1
323
0.0
829
0.0
494
0.1
338
0.0
840
0.0
498
0.0
004
Bet
wee
n10%
-20%
from
equilib
rium
6052
0.1
388
0.1
009
0.0
379
0.1
466
0.1
054
0.0
412
0.0
033
6744
0.1
315
0.0
829
0.0
486
0.1
364
0.0
862
0.0
502
0.0
016
Bet
wee
n20%
-40%
from
equilib
rium
11551
0.1
255
0.0
906
0.0
348
0.1
477
0.1
067
0.0
411
0.0
062
12977
0.1
177
0.0
728
0.0
448
0.1
369
0.0
867
0.0
502
0.0
054
Bet
wee
n40%
-60%
from
equilib
rium
10884
0.1
001
0.0
728
0.0
273
0.1
445
0.1
037
0.0
408
0.0
134
11967
0.0
930
0.0
574
0.0
357
0.1
323
0.0
828
0.0
495
0.0
139
Bet
wee
n60%
-80%
from
equilib
rium
8231
0.0
701
0.0
528
0.0
173
0.1
345
0.0
965
0.0
380
0.0
207
9222
0.0
636
0.0
408
0.0
228
0.1
175
0.0
713
0.0
462
0.0
234
More
than
80%
from
equilib
rium
26919
0.0
536
0.0
959
-0.0
423
0.0
341
0.0
242
0.0
099
0.0
521
21634
0.0
575
0.0
904
-0.0
329
0.0
394
0.0
222
0.0
172
0.0
501
Over
lever
aged
Obse
rvati
ons
NG
BD
oC
Do
NB
Do
GB
De
CD
eN
BD
eD
Wo
NG
BD
oC
Do
NB
Do
GB
De
CD
eN
BD
eD
Wo
Wit
hin
5%
ofeq
uilib
rium
1234
0.1
455
0.1
080
0.0
376
0.1
431
0.1
045
0.0
386
0.0
011
1550
0.1
351
0.0
867
0.0
484
0.1
320
0.0
835
0.0
485
0.0
001
Bet
wee
n5%
-10%
from
equilib
rium
1320
0.1
460
0.1
095
0.0
366
0.1
384
0.0
996
0.0
388
0.0
022
1488
0.1
395
0.0
914
0.0
481
0.1
305
0.0
820
0.0
485
0.0
004
Bet
wee
n10%
-20%
from
equilib
rium
2458
0.1
567
0.1
199
0.0
368
0.1
415
0.0
999
0.0
415
0.0
047
2805
0.1
481
0.1
003
0.0
478
0.1
306
0.0
809
0.0
497
0.0
018
Bet
wee
n20%
-40%
from
equilib
rium
3476
0.1
715
0.1
398
0.0
317
0.1
379
0.0
998
0.0
381
0.0
064
4088
0.1
543
0.1
130
0.0
413
0.1
228
0.0
762
0.0
466
0.0
053
Bet
wee
n40%
-60%
from
equilib
rium
2666
0.1
763
0.1
551
0.0
212
0.1
265
0.0
909
0.0
356
0.0
144
3097
0.1
570
0.1
270
0.0
299
0.1
118
0.0
678
0.0
440
0.0
141
Bet
wee
n60%
-80%
from
equilib
rium
1597
0.1
834
0.1
705
0.0
129
0.1
175
0.0
846
0.0
329
0.0
200
2035
0.1
540
0.1
360
0.0
180
0.0
977
0.0
592
0.0
386
0.0
205
More
than
80%
from
equilib
rium
22770
0.0
605
0.1
118
-0.0
513
0.0
222
0.0
158
0.0
065
0.0
578
17493
0.0
679
0.1
112
-0.0
433
0.0
275
0.0
165
0.0
111
0.0
543
Under
lever
aged
Obse
rvati
ons
NG
BD
oC
Do
NB
Do
GB
De
CD
eN
BD
eD
Wu
NG
BD
oC
Do
NB
Do
GB
De
CD
eN
BD
eD
Wu
Wit
hin
5%
ofeq
uilib
rium
1663
0.1
451
0.1
054
0.0
397
0.1
500
0.1
089
0.0
411
0.0
014
1731
0.1
357
0.0
847
0.0
510
0.1
391
0.0
880
0.0
511
0.0
001
Bet
wee
n5%
-10%
from
equilib
rium
1715
0.1
347
0.0
944
0.0
402
0.1
463
0.1
044
0.0
418
0.0
016
1858
0.1
265
0.0
761
0.0
504
0.1
364
0.0
855
0.0
509
0.0
005
Bet
wee
n10%
-20%
from
equilib
rium
3594
0.1
265
0.0
879
0.0
385
0.1
501
0.1
092
0.0
410
0.0
024
3939
0.1
197
0.0
705
0.0
492
0.1
405
0.0
899
0.0
506
0.0
014
Bet
wee
n20%
-40%
from
equilib
rium
8075
0.1
056
0.0
694
0.0
362
0.1
520
0.1
096
0.0
423
0.0
062
8889
0.1
008
0.0
544
0.0
464
0.1
434
0.0
915
0.0
519
0.0
055
Bet
wee
n40%
-60%
from
equilib
rium
8218
0.0
754
0.0
461
0.0
293
0.1
503
0.1
079
0.0
424
0.0
131
8870
0.0
707
0.0
330
0.0
377
0.1
395
0.0
880
0.0
515
0.0
138
Bet
wee
n60%
-80%
from
equilib
rium
6634
0.0
428
0.0
244
0.0
184
0.1
386
0.0
994
0.0
392
0.0
209
7187
0.0
380
0.0
138
0.0
241
0.1
231
0.0
747
0.0
484
0.0
242
More
than
80%
from
equilib
rium
4149
0.0
159
0.0
087
0.0
073
0.0
993
0.0
708
0.0
285
0.0
213
4141
0.0
135
0.0
027
0.0
108
0.0
896
0.0
464
0.0
432
0.0
324
46
Panel
B:G
roupin
gby
per
centa
ge
ofeq
uilib
rium
IOB
from
obse
rved
IOB
Analy
sis
Base
don
(9)
MC
i,t
=a
+bx
i,t+P c∈C
θcc i
,tx
i,t+
ξi,
tA
naly
sis
Base
don
(5)
MC
i,t
=a
+bx
i,t+P c∈C
δcc i
,t+
ξi,
t
Over
lever
aged
Obse
rvati
ons
NG
BD
oC
Do
NB
Do
GB
De
CD
eN
BD
eD
Wo
NG
BD
oC
Do
NB
Do
GB
De
CD
eN
BD
eD
Wo
Wit
hin
5%
ofobse
rved
1308
0.1
454
0.1
078
0.0
376
0.1
433
0.1
041
0.0
392
0.0
015
1619
0.1
351
0.0
867
0.0
484
0.1
319
0.0
833
0.0
485
0.0
001
Bet
wee
n80%
-95%
ofobse
rved
4807
0.1
574
0.1
215
0.0
359
0.1
415
0.1
012
0.0
403
0.0
043
5461
0.1
483
0.1
014
0.0
469
0.1
310
0.0
821
0.0
489
0.0
020
Bet
wee
n60%
-80%
ofobse
rved
5688
0.1
754
0.1
512
0.0
242
0.1
294
0.0
934
0.0
360
0.0
119
6695
0.1
556
0.1
226
0.0
330
0.1
141
0.0
698
0.0
443
0.0
113
Bet
wee
n40%
-60%
ofobse
rved
4194
0.1
738
0.1
772
-0.0
034
0.1
000
0.0
713
0.0
287
0.0
321
5419
0.1
385
0.1
385
-0.0
001
0.0
788
0.0
468
0.0
319
0.0
320
Bet
wee
n20%
-40%
ofobse
rved
2884
0.1
308
0.1
696
-0.0
388
0.0
568
0.0
390
0.0
178
0.0
566
4103
0.0
916
0.1
349
-0.0
433
0.0
365
0.0
214
0.0
150
0.0
584
Les
sth
an
20%
ofobse
rved
16640
0.0
267
0.0
884
-0.0
618
0.0
018
0.0
014
0.0
004
0.0
622
9259
0.0
274
0.0
874
-0.0
600
0.0
027
0.0
018
0.0
009
0.0
609
Under
lever
aged
Obse
rvati
ons
NG
BD
oC
Do
NB
Do
GB
De
CD
eN
BD
eD
Wu
NG
BD
oC
Do
NB
Do
GB
De
CD
eN
BD
eD
Wu
Wit
hin
5%
ofobse
rved
1589
0.1
448
0.1
053
0.0
395
0.1
495
0.1
086
0.0
409
0.0
014
1621
0.1
361
0.0
849
0.0
511
0.1
393
0.0
881
0.0
512
0.0
001
Bet
wee
n105%
-120%
ofobse
rved
3992
0.1
302
0.0
911
0.0
390
0.1
466
0.1
055
0.0
411
0.0
021
4448
0.1
232
0.0
737
0.0
496
0.1
375
0.0
871
0.0
504
0.0
008
Bet
wee
n120%
-160%
ofobse
rved
8279
0.1
102
0.0
734
0.0
368
0.1
512
0.1
092
0.0
420
0.0
052
9078
0.1
049
0.0
578
0.0
471
0.1
428
0.0
913
0.0
515
0.0
044
Bet
wee
n160%
-200%
ofobse
rved
5232
0.0
860
0.0
539
0.0
321
0.1
520
0.1
098
0.0
422
0.0
101
5678
0.0
811
0.0
404
0.0
408
0.1
424
0.0
911
0.0
512
0.0
105
Bet
wee
n200%
-300%
ofobse
rved
6329
0.0
635
0.0
377
0.0
258
0.1
490
0.1
067
0.0
423
0.0
165
6852
0.0
579
0.0
242
0.0
337
0.1
351
0.0
833
0.0
518
0.0
181
Bet
wee
n300%
-400%
ofobse
rved
2762
0.0
437
0.0
250
0.0
187
0.1
455
0.1
045
0.0
409
0.0
222
3061
0.0
374
0.0
135
0.0
239
0.1
257
0.0
767
0.0
490
0.0
251
Bet
wee
n400%
-500%
ofobse
rved
1716
0.0
283
0.0
155
0.0
128
0.1
207
0.0
859
0.0
347
0.0
219
1726
0.0
254
0.0
082
0.0
173
0.1
110
0.0
661
0.0
448
0.0
276
Bet
wee
n500%
-600%
ofobse
rved
1503
0.0
167
0.0
091
0.0
076
0.0
863
0.0
611
0.0
252
0.0
176
1249
0.0
186
0.0
046
0.0
141
0.1
012
0.0
551
0.0
461
0.0
321
Bet
wee
n600%
-700%
ofobse
rved
921
0.0
179
0.0
098
0.0
082
0.1
078
0.0
754
0.0
324
0.0
242
915
0.0
133
0.0
019
0.0
114
0.0
856
0.0
406
0.0
450
0.0
336
Bet
wee
n700%
-800%
ofobse
rved
691
0.0
165
0.0
091
0.0
075
0.1
098
0.0
783
0.0
315
0.0
240
760
0.0
112
0.0
021
0.0
091
0.0
825
0.0
418
0.0
407
0.0
316
Bet
wee
n800%
-900%
ofobse
rved
599
0.0
127
0.0
067
0.0
060
0.1
047
0.0
739
0.0
309
0.0
249
659
0.0
103
0.0
005
0.0
098
0.0
867
0.0
387
0.0
480
0.0
382
More
than
900%
ofobse
rved
435
0.0
125
0.0
068
0.0
056
0.1
024
0.0
785
0.0
238
0.0
182
568
0.0
088
0.0
029
0.0
059
0.0
821
0.0
509
0.0
312
0.0
253
47
Tab
le11
:A
naly
sis
onqu
alifi
ed50
perc
ent
offin
anci
ally
unco
nstr
aine
dfir
ms
usin
gfo
urfin
anci
alco
nstr
aint
mea
sure
s:(i
)lo
ngte
rmde
btor
equi
tyis
suan
ceor
repu
rcha
se,(
ii)K
Zin
dex,
(iii)
CL
inde
x,(i
v)W
Win
dex.
GM
Mes
tim
atio
nof
the
coeffi
cien
tsin
equa
tion
s5
and
9fo
ral
lind
ustr
ies
exce
ptut
iliti
es,fi
nanc
e,an
dpu
blic
adm
inst
rati
onfo
rsa
mpl
esD
thro
ugh
G.T
heer
ror
func
tion
sar
ede
fined
acco
rdin
gto
equa
tion
s6
and
10w
here
y∗ i,
tis
the
‘equ
ilibr
ium
’mar
gina
lben
efit/
cost
leve
l,x∗ i,
tis
the
obse
rved
or‘e
quili
briu
m’i
nter
est
expe
nses
over
book
valu
e(I
OB
)an
dC
isth
ese
tof
cost
cont
rol
vari
able
s.G
MM
mom
ents
are
obta
ined
byin
tera
ctin
gth
eer
rorfu
ncti
onw
ith
the
follo
win
gin
stru
men
ts:
the
cons
tant
term
,the
vari
atio
nof
the
mar
gina
lbe
nefit
curv
eA
i,t,a
ndea
chof
the
cont
rolv
aria
bles
.T
hese
tof
cont
rolv
aria
bles
,C,i
nclu
des{P
PE
,LS
AL
ES,B
TM
,DD
IV,C
F,C
AS
H,P
TP}w
here
PP
Eis
plan
t,pr
oper
ty,a
ndeq
uipm
ent
over
tota
lboo
kva
lues
,LSA
LE
Sis
log
ofne
tsa
les,
BT
Mis
book
equi
tyto
mar
ket
equi
ty,D
DIV
isan
indi
cato
rfo
rdi
vide
ndpa
ying
firm
,CF
isne
tca
shflo
wov
erto
talb
ook
valu
es,C
ASH
isca
shho
ldin
gsov
erto
talb
ook
valu
es,a
ndP
TP
isth
epe
rson
alta
xpe
nalty
asm
easu
red
inG
raha
m(1
999)
.T
heco
ntro
lva
riab
les
are
stan
dard
ized
toha
vem
ean
zero
and
stan
dard
devi
atio
non
eba
sed
onSa
mpl
eA
(and
are
not
re-s
tand
ardi
zed
acro
sssa
mpl
es).
Rob
ust
GM
Mst
anda
rder
rors
are
repo
rted
inth
epa
rent
hese
s.Si
gnifi
canc
eat
the
10%
leve
lis
indi
cate
dby
*,5%
leve
lby
**,an
d1%
leve
lby
***.
(9)
MC
i,t
=a
+bx
i,t+P c∈C
θcc i
,tx
i,t+
ξi,
t(5
)M
Ci,
t=
a+
bxi,
t+P c∈C
δcc i
,t+
ξi,
t
Sam
ple
DSam
ple
ESam
ple
FSam
ple
GSam
ple
DSam
ple
ESam
ple
FSam
ple
G
Const
ant
0.1
90
***
0.2
73
***
0.2
35
***
0.2
61
***
0.1
20
***
0.2
37
***
0.2
02
***
0.1
93
***
(0.0
04)
(0.0
02)
(0.0
03)
(0.0
03)
(0.0
05)
(0.0
03)
(0.0
04)
(0.0
04)
IOB
4.1
92
***
2.6
15
***
3.7
68
***
2.2
63
***
5.0
86
***
3.3
01
***
3.9
21
***
3.8
23
***
(0.1
57)
(0.1
13)
(0.1
38)
(0.1
24)
(0.1
28)
(0.0
90)
(0.1
11)
(0.1
10)
PP
E*IO
B-0
.470
***
0.3
79
***
-0.1
84
***
-0.2
07
***
(0.0
46)
(0.0
59)
(0.0
52)
(0.0
40)
LSA
LE
S*IO
B0.4
05
***
0.1
36
***
0.1
53
***
0.1
58
***
(0.0
45)
(0.0
44)
(0.0
55)
(0.0
46)
BT
M*IO
B-0
.518
***
-0.2
43
***
-0.5
36
***
-0.2
55
***
(0.0
39)
(0.0
45)
(0.0
52)
(0.0
48)
DD
IV*IO
B1.0
66
***
0.8
85
***
1.2
67
***
0.9
52
***
(0.0
34)
(0.0
39)
(0.0
43)
(0.0
30)
CF*IO
B1.8
37
***
1.2
36
***
0.9
24
***
2.0
43
***
(0.2
06)
(0.1
46)
(0.1
53)
(0.2
15)
CA
SH
*IO
B1.5
04
***
0.7
48
***
0.9
25
***
0.6
61
***
(0.0
89)
(0.0
54)
(0.0
76)
(0.0
71)
PT
P*IO
B0.9
15
***
1.3
76
***
1.4
34
***
1.0
86
***
(0.0
31)
(0.0
37)
(0.0
48)
(0.0
32)
PP
E-0
.019
***
0.0
12
***
-0.0
06
***
-0.0
08
***
(0.0
02)
(0.0
01)
(0.0
01)
(0.0
01)
LSA
LE
S0.0
15
***
0.0
07
***
0.0
08
***
0.0
00
(0.0
01)
(0.0
01)
(0.0
01)
(0.0
01)
BT
M-0
.029
***
-0.0
15
***
-0.0
23
***
-0.0
20
***
(0.0
02)
(0.0
02)
(0.0
02)
(0.0
02)
DD
IV0.0
47
***
0.0
33
***
0.0
43
***
0.0
37
***
(0.0
01)
(0.0
01)
(0.0
01)
(0.0
01)
CF
0.1
12
***
0.0
51
***
0.0
63
***
0.0
92
***
(0.0
05)
(0.0
04)
(0.0
04)
(0.0
05)
CA
SH
0.0
44
***
0.0
22
***
0.0
24
***
0.0
23
***
(0.0
02)
(0.0
01)
(0.0
01)
(0.0
01)
PT
P0.0
35
***
0.0
43
***
0.0
43
***
0.0
36
***
(0.0
01)
(0.0
01)
(0.0
01)
(0.0
01)
No.
Obs.
25977
22387
19942
20176
25977
22387
19942
20176
48
Tab
le12
:A
naly
sis
onqu
alifi
ed25
perc
ent
offin
anci
ally
unco
nstr
aine
dfir
ms
usin
gfo
urfin
anci
alco
nstr
aint
mea
sure
s:(i
)lo
ngte
rmde
btor
equi
tyis
suan
ceor
repu
rcha
se,(
ii)K
Zin
dex,
(iii)
CL
inde
x,(i
v)W
Win
dex.
GM
Mes
tim
atio
nof
the
coeffi
cien
tsin
equa
tion
s5
and
9fo
ral
lind
ustr
ies
exce
ptut
iliti
es,fi
nanc
e,an
dpu
blic
adm
inis
trat
ion
for
sam
ples
Hth
roug
hK
.The
erro
rfu
ncti
ons
are
defin
edac
cord
ing
toeq
uati
ons
6an
d10
whe
rey∗ i,
tis
the
‘equ
ilibr
ium
’mar
gina
lben
efit/
cost
leve
l,x∗ i,
tis
the
obse
rved
or‘e
quili
briu
m’i
nter
est
expe
nses
over
book
valu
e(I
OB
)an
dC
isth
ese
tof
cost
cont
rol
vari
able
s.G
MM
mom
ents
are
obta
ined
byin
tera
ctin
gth
eer
rorfu
ncti
onw
ith
the
follo
win
gin
stru
men
ts:
the
cons
tant
term
,the
vari
atio
nof
the
mar
gina
lbe
nefit
curv
eA
i,t,a
ndea
chof
the
cont
rolv
aria
bles
.T
hese
tof
cont
rolv
aria
bles
,C,i
nclu
des{P
PE
,LS
AL
ES,B
TM
,DD
IV,C
F,C
AS
H,P
TP}w
here
PP
Eis
plan
t,pr
oper
ty,a
ndeq
uipm
ent
over
tota
lboo
kva
lues
,LSA
LE
Sis
log
ofne
tsa
les,
BT
Mis
book
equi
tyto
mar
ket
equi
ty,D
DIV
isan
indi
cato
rfo
rdi
vide
ndpa
ying
firm
,CF
isne
tca
shflo
wov
erto
talb
ook
valu
es,C
ASH
isca
shho
ldin
gsov
erto
talb
ook
valu
es,a
ndP
TP
isth
epe
rson
alta
xpe
nalty
asm
easu
red
inG
raha
m(1
999)
.T
heco
ntro
lva
riab
les
are
stan
dard
ized
toha
vem
ean
zero
and
stan
dard
devi
atio
non
eba
sed
onSa
mpl
eA
(and
are
not
re-s
tand
ardi
zed
acro
sssa
mpl
es).
Rob
ust
GM
Mst
anda
rder
rors
are
repo
rted
inth
epa
rent
hese
s.Si
gnifi
canc
eat
the
10%
leve
lis
indi
cate
dby
*,5%
leve
lby
**,an
d1%
leve
lby
***.
(9)
MC
i,t
=a
+bx
i,t+P c∈C
θcc i
,tx
i,t+
ξi,
t(5
)M
Ci,
t=
a+
bxi,
t+P c∈C
δcc i
,t+
ξi,
t
Sam
ple
HSam
ple
ISam
ple
JSam
ple
KSam
ple
HSam
ple
ISam
ple
JSam
ple
K
Const
ant
0.1
89
***
0.2
99
***
0.2
75
***
0.2
77
***
0.1
20
***
0.2
82
***
0.2
43
***
0.2
15
***
(0.0
05)
(0.0
02)
(0.0
03)
(0.0
04)
(0.0
07)
(0.0
04)
(0.0
04)
(0.0
07)
IOB
4.2
86
***
2.8
08
***
2.7
13
***
1.9
89
***
4.9
94
***
2.6
90
***
2.9
45
***
3.5
71
***
(0.1
96)
(0.1
70)
(0.1
65)
(0.1
85)
(0.1
78)
(0.1
11)
(0.1
20)
(0.1
55)
PP
E*IO
B-0
.465
***
1.0
57
***
-0.0
65
-0.0
84
(0.0
58)
(0.1
14)
(0.0
68)
(0.0
52)
LSA
LE
S*IO
B0.4
24
***
-0.0
53
0.3
85
***
0.2
20
***
(0.0
62)
(0.0
70)
(0.0
80)
(0.0
68)
BT
M*IO
B-0
.590
***
-0.1
50
*-0
.531
***
0.1
68
**
(0.0
51)
(0.0
83)
(0.0
77)
(0.0
74)
DD
IV*IO
B0.9
48
***
0.8
52
***
1.2
01
***
0.8
16
***
(0.0
45)
(0.0
59)
(0.0
61)
(0.0
55)
CF*IO
B1.2
38
***
0.7
88
***
0.4
66
***
2.0
73
***
(0.2
20)
(0.1
69)
(0.1
68)
(0.2
04)
CA
SH
*IO
B1.6
54
***
0.4
83
***
0.5
16
***
0.4
54
***
(0.1
18)
(0.0
63)
(0.0
82)
(0.1
06)
PT
P*IO
B0.9
29
***
1.5
49
***
1.9
65
***
1.2
43
***
(0.0
45)
(0.0
64)
(0.0
99)
(0.0
45)
PP
E-0
.020
***
0.0
24
***
-0.0
02
-0.0
04
***
(0.0
02)
(0.0
02)
(0.0
02)
(0.0
01)
LSA
LE
S0.0
17
***
0.0
04
***
0.0
10
***
0.0
04
***
(0.0
02)
(0.0
01)
(0.0
01)
(0.0
02)
BT
M-0
.035
***
-0.0
13
***
-0.0
23
***
-0.0
06
**
(0.0
02)
(0.0
02)
(0.0
02)
(0.0
03)
DD
IV0.0
44
***
0.0
32
***
0.0
39
***
0.0
29
***
(0.0
01)
(0.0
01)
(0.0
01)
(0.0
02)
CF
0.0
92
***
0.0
29
***
0.0
39
***
0.0
80
***
(0.0
07)
(0.0
04)
(0.0
05)
(0.0
06)
CA
SH
0.0
46
***
0.0
14
***
0.0
15
***
0.0
16
***
(0.0
02)
(0.0
01)
(0.0
02)
(0.0
02)
PT
P0.0
38
***
0.0
44
***
0.0
48
***
0.0
38
***
(0.0
02)
(0.0
01)
(0.0
02)
(0.0
02)
No.
Obs.
13455
10610
10815
8985
13455
10610
10815
8985
49
Tab
le13
:T
ime
seri
esan
alys
isus
ing
tax
regi
me
shift
s.G
MM
esti
mat
ion
ofth
eco
effici
ents
ineq
uati
ons
5an
d9
for
all
indu
stri
esex
cept
utili
ties
,fin
ance
,an
dpu
blic
adm
inis
trat
ion
for
sam
ples
Ath
roug
hD
.T
heer
ror
func
tion
sar
ede
fined
acco
rdin
gto
equa
tion
s6
and
10w
here
y∗ i,
tis
the
‘equ
ilibr
ium
’m
argi
nal
bene
fit/c
ost
leve
l,x∗ i,
tis
the
obse
rved
or‘e
quili
briu
m’
inte
rest
expe
nses
over
book
valu
e(I
OB
)an
dC
isth
ese
tof
cost
cont
rol
vari
able
s.G
MM
mom
ents
are
obta
ined
byin
tera
ctin
gth
eer
ror
func
tion
wit
hth
efo
llow
ing
inst
rum
ents
:th
eco
nsta
ntte
rm,
the
vari
atio
nof
the
corp
orat
eta
xra
tes
from
elev
enta
xbr
acke
tsac
ross
tim
e,an
dea
chof
the
cont
rol
vari
able
s.T
hese
tof
cont
rol
vari
able
s,C
,in
clud
es{P
PE
,LS
AL
ES,B
TM
,DD
IV,C
F,C
AS
H,P
TP}
whe
reP
PE
ispl
ant,
prop
erty
,an
deq
uipm
ent
over
tota
lbo
okva
lues
,LSA
LE
Sis
log
ofne
tsa
les,
BT
Mis
book
equi
tyto
mar
ket
equi
ty,D
DIV
isan
indi
cato
rfo
rdi
vide
ndpa
ying
firm
,CF
isne
tca
shflo
wov
erto
talb
ook
valu
es,C
ASH
isca
shho
ldin
gsov
erto
talb
ook
valu
es,a
ndP
TP
isth
epe
rson
alta
xpe
nalty
asm
easu
red
inG
raha
m(1
999)
.T
heco
ntro
lvar
iabl
esar
est
anda
rdiz
edto
have
mea
nze
roan
dst
anda
rdde
viat
ion
one
base
don
Sam
ple
A(a
ndar
eno
tre
-sta
ndar
dize
dac
ross
sam
ples
).R
obus
tG
MM
stan
dard
erro
rsar
ere
port
edin
the
pare
nthe
ses.
Sign
ifica
nce
atth
e10
%le
velis
indi
cate
dby
*,5%
leve
lby
**,an
d1%
leve
lby
***.
(9)
MC
i,t
=a
+bx
i,t+P c∈C
θcc i
,tx
i,t+
ξi,
t(5
)M
Ci,
t=
a+
bxi,
t+P c∈C
δcc i
,t+
ξi,
t
Sam
ple
ASam
ple
BSam
ple
CSam
ple
DSam
ple
ASam
ple
BSam
ple
CSam
ple
D
Const
ant
0.1
93
***
0.2
50
***
0.1
90
***
0.2
42
***
0.1
60
***
0.1
70
***
0.1
72
***
0.1
72
***
(0.0
04)
(0.0
05)
(0.0
04)
(0.0
05)
(0.0
04)
(0.0
06)
(0.0
04)
(0.0
07)
IOB
2.8
02
***
1.8
44
***
2.6
29
***
2.1
14
***
3.2
20
***
3.7
38
***
2.6
67
***
3.5
28
***
(0.1
43)
(0.1
82)
(0.1
46)
(0.1
85)
(0.1
27)
(0.1
91)
(0.1
29)
(0.2
03)
PP
E*IO
B-0
.516
***
-0.4
15
***
-0.5
38
***
-0.5
16
***
(0.0
21)
(0.0
41)
(0.0
22)
(0.0
45)
LSA
LE
S*IO
B0.9
85
***
0.4
97
***
1.0
93
***
0.5
84
***
(0.0
29)
(0.0
39)
(0.0
30)
(0.0
42)
BT
M*IO
B-0
.438
***
-0.5
13
***
-0.4
41
***
-0.5
43
***
(0.0
17)
(0.0
29)
(0.0
19)
(0.0
33)
DD
IV*IO
B1.6
87
***
1.3
85
***
1.4
33
***
1.1
79
***
(0.0
28)
(0.0
32)
(0.0
28)
(0.0
32)
CF*IO
B2.0
88
***
3.4
03
***
1.9
69
***
3.0
25
***
(0.0
58)
(0.1
81)
(0.0
59)
(0.1
90)
CA
SH
*IO
B0.9
82
***
1.7
16
***
0.7
98
***
1.8
19
***
(0.0
71)
(0.1
02)
(0.0
72)
(0.1
09)
PT
P*IO
B1.0
53
***
1.2
05
***
0.9
76
***
1.0
64
***
(0.0
23)
(0.0
31)
(0.0
25)
(0.0
34)
PP
E-0
.016
***
-0.0
11
***
-0.0
17
***
-0.0
14
***
(0.0
01)
(0.0
01)
(0.0
01)
(0.0
01)
LSA
LE
S0.0
27
***
0.0
12
***
0.0
32
***
0.0
16
***
(0.0
01)
(0.0
01)
(0.0
01)
(0.0
01)
BT
M-0
.013
***
-0.0
22
***
-0.0
14
***
-0.0
25
***
(0.0
01)
(0.0
01)
(0.0
01)
(0.0
01)
DD
IV0.0
59
***
0.0
47
***
0.0
52
***
0.0
42
***
(0.0
01)
(0.0
01)
(0.0
01)
(0.0
01)
CF
0.0
75
***
0.1
05
***
0.0
71
***
0.0
96
***
(0.0
02)
(0.0
05)
(0.0
02)
(0.0
05)
CA
SH
0.0
32
***
0.0
34
***
0.0
26
***
0.0
32
***
(0.0
01)
(0.0
02)
(0.0
01)
(0.0
02)
PT
P0.0
39
***
0.0
41
***
0.0
40
***
0.0
40
***
(0.0
01)
(0.0
01)
(0.0
01)
(0.0
01)
No.
Obs.
69569
37978
50345
25977
69569
37978
50345
25977
50
Tab
le14
:Si
ngle
vari
ate
anal
ysis
.G
MM
esti
mat
ion
ofth
eco
effici
ents
ineq
uati
ons
5an
d9
usin
gon
eco
ntro
lat
ati
me
for
alli
ndus
trie
sex
cept
utili
ties
,fin
ance
,an
dpu
blic
adm
inis
trat
ion
for
sam
ple
D.
The
erro
rfu
ncti
ons
are
defin
edac
cord
ing
toeq
uati
ons
6an
d10
,w
here
y∗ i,
tis
the
‘equ
ilibr
ium
’m
argi
nalbe
nefit
/cos
tle
vel,
x∗ i,
tis
the
obse
rved
or‘e
quili
briu
m’in
tere
stex
pens
esov
erbo
okva
lue
(IO
B)
and
Cis
the
set
ofco
stco
ntro
lva
riab
les.
GM
Mm
omen
tsar
eob
tain
edby
inte
ract
ing
the
erro
rfu
ncti
onw
ith
the
follo
win
gin
stru
men
ts:
the
cons
tant
term
,the
vari
atio
nof
the
mar
gina
lben
efit
curv
eA
i,t,a
ndea
chof
the
cont
rolv
aria
bles
.T
hese
tof
cont
rolv
aria
bles
,C,i
nclu
des{P
PE
,LS
AL
ES,B
TM
,DD
IV,C
F,C
AS
H,P
TP}w
here
PP
Eis
plan
t,pr
oper
ty,an
deq
uipm
ent
over
tota
lbo
okva
lues
,LSA
LE
Sis
log
ofne
tsa
les,
BT
Mis
book
equi
tyto
mar
ket
equi
ty,SA
LE
Sis
net
sale
sov
erto
talbo
okva
lues
,D
DIV
isan
indi
cato
rfo
rdi
vide
ndpa
ying
firm
,C
Fis
net
cash
flow
over
tota
lbo
okva
lues
,C
ASH
isca
shho
ldin
gsov
erto
talbo
okva
lues
,and
PT
Pis
the
pers
onal
tax
pena
lty
asm
easu
red
inG
raha
m(1
999)
.T
heco
ntro
lvar
iabl
esar
est
anda
rdiz
edto
have
mea
nze
roan
dst
anda
rdde
viat
ion
one
base
don
Sam
ple
A(a
ndar
eno
tre
-sta
ndar
dize
dac
ross
sam
ples
).R
obus
tG
MM
stan
dard
erro
rsar
ere
port
edin
the
pare
nthe
ses.
Sign
ifica
nce
atth
e10
%le
velis
indi
cate
dby
*,5%
leve
lby
**,an
d1%
leve
lby
***.
(9)
MC
i,t
=a
+bx
i,t+P c∈C
θcc i
,tx
i,t+
ξi,
t(5
)M
Ci,
t=
a+
bxi,
t+P c∈C
δcc i
,t+
ξi,
t
No
PP
ELSA
LE
SB
TM
DD
IVC
FC
ASH
PT
PP
PE
LSA
LE
SB
TM
DD
IVC
FC
ASH
PT
PC
ontr
ols
Const
ant
0.0
81
***
0.0
78
***
0.0
85
***
0.1
24
***
0.1
05
***
0.1
24
***
0.0
93
***
0.0
80
***
0.0
70
***
0.0
82
***
0.1
20
***
0.0
99
***
0.0
64
***
0.0
39
***
0.0
80
***
(0.0
06)
(0.0
06)
(0.0
06)
(0.0
05)
(0.0
05)
(0.0
06)
(0.0
05)
(0.0
06)
(0.0
06)
(0.0
06)
(0.0
05)
(0.0
05)
(0.0
05)
(0.0
07)
(0.0
06)
IOB
8.1
84
***
8.2
20
***
7.8
09
***
7.0
40
***
7.2
73
***
5.9
75
***
8.6
23
***
8.2
13
***
8.4
19
***
7.8
63
***
6.8
54
***
7.2
68
***
6.6
26
***
9.8
68
***
8.2
25
***
(0.1
80)
(0.1
82)
(0.1
70)
(0.1
43)
(0.1
51)
(0.2
53)
(0.1
88)
(0.1
81)
(0.1
91)
(0.1
71)
(0.1
39)
(0.1
50)
(0.1
33)
(0.2
37)
(0.1
82)
PP
E*IO
B-0
.373
***
(0.0
57)
LSA
LE
S*IO
B0.8
62
***
(0.0
50)
BT
M*IO
B-1
.158
***
(0.0
41)
DD
IV*IO
B1.2
48
***
(0.0
37)
CF*IO
B2.8
65
***
(0.3
41)
CA
SH
*IO
B2.7
38
***
(0.1
16)
PT
P*IO
B0.1
73
***
(0.0
48)
PP
E-0
.021
***
(0.0
02)
LSA
LE
S0.0
29
***
(0.0
02)
BT
M-0
.070
***
(0.0
02)
DD
IV0.0
49
***
(0.0
01)
CF
0.1
83
***
(0.0
07)
CA
SH
0.1
05
***
(0.0
03)
PT
P0.0
01
(0.0
02)
No.
Obs.
29674
29670
29670
28184
29671
29645
29671
27354
29670
29670
28184
29671
29645
29671
27354
51