Download On the impact of financial distress on capital structure

On the impact of financial distress on capital structure: The
role of leverage dynamics
Evangelos C. Charalambakis∗
Susanne K. Espenlaub†
Ian Garrett‡
∗
Corresponding author. Manchester Business School, University of Manchester, UK, email: [email protected]
†
Manchester Business School, University of Manchester, UK, email: [email protected]
‡
Manchester Business School, University of Manchester, email: [email protected]. We would like
to thank Michael Brennan, John Graham, participants at the 2008 FMA Conference in Dallas and seminar
participants at Manchester Business School for helpful comments.
1
On the impact of financial distress on capital structure: The role of
leverage dynamics
Abstract
This paper uses a research design that addresses the endogenous effect of financial
distress on debt ratios. Using a probability of financial distress derived from a hazard
model as a measure of financial distress, we find that leverage dynamics are crucial in
unraveling the true effect of financial distress on leverage. Our findings offer an explanation
for the prior conflicting evidence on the association between leverage and financial distress
and shed new light on the role of leverage dynamics in understanding capital structure
decisions. We then show that firms balance the tax benefit of debt and financial distress
costs when making financing decisions in a dynamic process.
2
1
Introduction
While the theoretical underpinnings of capital structure suggest a negative association between
financial distress costs and leverage, quantifying the impact of financial distress costs on debt
ratios is difficult. Early empirical studies of capital structure (e.g., Kim and Sorensen (1986)
and Titman and Wessels (1988)) use a firm’s operating risk, measured as either the coefficient
of variation or the standard deviation of earnings before interest and taxes (EBIT), to proxy
for financial distress costs. These studies find no evidence of a negative relationship between
financial distress costs and leverage. Several other studies that investigate the relationship
between leverage and financial distress costs do so incorporating firm size as an inverse proxy
for expected financial distress costs in their empirical specification (see, for example, ShyamSunder and Myers (1999), Fama and French (2002), and Flannery and Rangan (2006)). Even
if firm size is a suitable proxy for financial distress costs, it is subject to criticism as it is
likely to capture other firm characteristics, such as information asymmetry, access to public
debt markets and the extent to which firms’ assets are diversified.1 Recent studies have used
measures relating to the likelihood of financial distress, most notably Altman’s Z-score, or a
modified version of it (see, for example, Graham (2000) and Byoun (2008)). Studies using
Z-score typically find that a higher likelihood of financial distress, i.e., lower Z-score, leads to
higher debt ratios, a finding that seems puzzling. There is an additional concern that financial
distress costs are also endogenously related to debt ratios. Increasing leverage increases the
probability of financial distress while an increase in the probability of financial distress should
bring about decreases in the amount of debt a firm has in its capital structure. This issue
of endogeneity has, to our knowledge, not been considered in the existing literature. Taken
together prior studies that investigate the impact of financial distress on debt ratios have
used either relatively poor proxies for financial distress, or misspecified models ignoring that
financial distress is endogenous.
In this paper we properly address the endogenous association between financial distress
costs and debt ratios and provide new insights on how leverage dynamics affect corporate
1
Frank and Goyal (2003) argue that small firms are more likely to face information asymmetries as these
firms are more likely to be younger and therefore less well known. Fama and French (2002) argue that larger
firms have easier access to public debt markets as they find it more economical to produce the information
required for public securities. Titman and Wessels (1988) argue that larger firms tend to be more diversified.
3
financing decisions. As financial distress costs cannot easily be observed, we assume that
firms with a higher probability of financial distress are more likely to face higher financial
distress costs. We use a probability-based estimate of financial distress rather than the Zscore that previous studies tend to use to test the association between leverage and financial
distress costs. Specifically, we follow Shumway (2001) and estimate the probability of financial
distress using a hazard model with time-varying covariates. We use predetermined equity
market-driven variables to estimate the probability of financial distress, so that the estimated
probability of financial distress at time t is based on variables dated t − 1. An advantage
of using the estimated probability of financial distress is that, unlike Z-score, the estimated
probability of financial distress is based on a hazard model which accounts for how long
the firm has survived before moving into financial distress and treats the estimation of the
probability of financial distress as a dynamic multi-period problem that uses all available firmyear observations to estimate the probability. The Z-score is derived from a static bankruptcy
prediction model. Unlike hazard models, static bankruptcy prediction models (e.g. see,
Altman (1968) and Ohlson (1980)) are estimated only with each firm’s last observation. As
a result, static models produce inconsistent and biased estimates.2
We perform our tests in a) a static framework which assumes that there are no adjustment
costs when firms adjust toward their target capital structures and b) a dynamic framework in
which leverage dynamics enter in the model, allowing for costly adjustment. We formulate our
dynamic model using the first-differenced Arellano and Bond (1991) estimator and the twostep GMM-system estimator. These two econometric techniques are appropriate to estimate
our dynamic model because they enable us to treat leverage dynamics and the probability of
financial distress as endogenous variables. To test the effect of taxes on debt ratios we take into
consideration the endogeneity of corporate tax status documented by Graham et al. (1998).
Following Graham et al. (1998) we overcome the endogeneity problem by using a measure of
corporate tax rate that is based on earning before interest deductions (before-financing).
The results show that when leverage dynamics are excluded from the model, there is
a positive relationship between the probability of financial distress and leverage. However,
once we allow for leverage dynamics, the relationship between leverage and the probability
2
Shumway (2001) discusses this problem in detail.
4
of financial distress becomes negative and statistically significant, which reconciles with the
prediction of the tradeoff theory. We also find, regardless of whether dynamics are included
in the model, a positive relationship between corporate tax and leverage once we consider the
endogeneity of corporate tax status, consistent with the finding of Graham et al. (1998). The
only exception to this is for the effect of taxes on market leverage using the two-step ArellanoBond GMM estimator in our dynamic empirical model. Based on this GMM estimator, we
document that there is no association between market leverage and corporate taxes.
Our findings have important implications for capital structure. The assumption that firms
are optimally levered can lead to a misleading effect of financial distress on debt ratios. We
show how important leverage dynamics are in corporate financing decisions. It is leverage
dynamics in conjunction with the endogenous association between financial distress and debt
ratios that generates a negative relationship between financial distress and debt ratios. Importantly, and unlike other studies, only when using a measure of the probability of financial
distress and allowing for leverage dynamics do we find a negative relationship between financial distress and debt ratios. We then provide evidence that firms tradeoff between the tax
advantage to debt and financial distress costs when we consider the role of corporate refinancing, i.e., leverage dynamics. This paper suggests that we need to focus on leverage dynamics
to obtain a more comprehensive depiction of capital structure behavior.
The rest of the paper is organized as follows. Section 2 motivates our empirical approach
and describes the data. Section 3 presents and interprets the results while section 4 offers
concluding remarks.
2
2.1
Model Specification
Target adjustment model
Shyam-Sunder and Myers (1999), Flannery and Rangan (2006) and Huang and Ritter (2009),
among others, have used a target adjustment model to investigate corporate financing behavior. Following previous studies we use a partial adjustment formulation which is described by
5
the following equation:
∗
Levi,t = (1 − λ)Levi,t−1 + λLevi,t
+ ϵi,t
(1)
where Levi,t is actual leverage for firm i in year t, Levi,t−1 is actual leverage for firm i in year
∗ is target leverage for firm i in year t, λ is the speed of adjustment towards target
t − 1, Levi,t
leverage, and ϵi,t is an error term. The target is assumed to depend upon a vector of variables
∗ = β′ x
such that Levi,t
i,t−1 . Substituting in (1) gives the basis of our empirical model:
Levi,t = (1 − λ)Levi,t−1 + λ(β ′ xi,t−1 ) + ϵi,t
(2)
For (2) to be operational, we need to specify the variables that determine target leverage.
According to the tradeoff theory, target leverage is determined by trading off the tax benefit
of debt against financial distress costs. In addition to tax and distress variables, the other
variables we use in specifying the target are well-established in the literature (see, for example, Rajan and Zingales (1995) and Frank and Goyal (2009).) In particular, we specify the
following firm-specific factors:
1. Probability of Financial Distress (PROBFD)
Following Shumway (2001) we estimate the probability that a firm will enter financial distress using market-driven predictors.3 In particular, the probability of financial
distress is the fitted value from the multi-period logistic regression
Pi,t =
1
1+
′
e(−α+β xi,t−1 )
(3)
where Pi,t is the probability that firm i will enter either bankruptcy or liquidation at
time t and β ′ xi,t−1 = β1 REL SIZEi,t−1 + β2 EXRETi,t−1 + β3 σi,t−1 .The dependent
variable is a dummy equalling zero if the firm has not filed for bankruptcy or entered
liquidation. If the firm has entered liquidation or bankruptcy, then the dependent
3
Shumway (2001) also estimates the probability of bankruptcy using two additional accounting ratios, i.e,
profitability and leverage. However, as book leverage and profitability are both incorporated in the dynamic
panel data model we estimate, we choose not to include profitability and leverage in the estimation of the
probability of financial distress as this could bias our main empirical specification described by (2) and our
results.
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variable equals one only for its last firm-year observation. REL SIZE is a firm’s market
capitalization expressed relative to the total market capitalization of NYSE and AMEX
firms, EXRET is a firm’s past return in excess of the market and σi is firm i’s stock
return volatility. I calculate each firm’s σ for a given year by regressing each stock’s
monthly returns in year t − 1 on the value-weighted NYSE/AMEX index return in year
t − 1. The σ is the standard deviation of the residual of this regression. We expect there
to be a negative relationship between the probability of financial distress and leverage.
2. Corporate Tax Rate Before Financing (CTRBF)
CTRBF is a measure of the firm’s corporate tax rate, which reflects before-financing
decisions to address the endogeneity of corporate tax status associated with the debt
ratio. It is calculated as income tax expense plus (interest expense × the top statutory
tax rate), divided by earnings before interest and tax.4 Since we add back a proxy
for the interest tax shield, i.e., interest expense × the top statutory tax rate, to the
income tax expense in the numerator and we use before-financing taxable income in
the denominator CTRBF is exogenous to debt ratios.5 Based on the prediction of the
trade-off theory, we expect there to be a positive relationship between CTRBF and
leverage.
3. Firm Size (SIZE)
We define this as the natural logarithm of sales. Large firms are more profitable and
hence have more tax benefits of debt. As large firms have more stable profit streams,
they are less likely to go bankrupt. We therefore expect to see a positive relationship
between firm size and leverage.
4. Tangibility (TANG)
This is defined as fixed assets divided by total assets. If a firm has a large amount of
fixed (tangible) assets then these assets can serve as collateral to debtholders. If debt is
collateralized then the risk of the lender suffering agency costs of debt diminishes and
4
Following Sharpe and Nguyen (1995) and Graham et al. (1998) , CTRBF is set to zero if the numerator
is negative, and is set to one if the numerator is positive and the denominator is negative.
5
Interest expense divided by EBIT (interest coverage ratio) is inevitably a component of CTRBF. This
could bias our measure of corporate tax rate. However, when we performed a correlation test between CTRBF
and the interest coverage ratio, the correlation coefficient is low (0.04).
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the firm’s debt capacity increases. We therefore expect to see a positive relationship
between tangibility and leverage.
5. Profitability (PROF)
This is defined as earnings before interest, tax, depreciation and amortization (EBITDA)
divided by total assets. More profitable firms are more likely to have accumulated
retained earnings and thus have less incentive to issue debt.
6. Market to book (MTB)
This is defined as the market value of assets divided by book value of assets. Market to
book proxies for growth opportunities. Due to the agency costs of debt firms issue less
debt to protect their investment opportunities; see Myers (1977).
7. Industry Leverage (IND LEV)
This is defined as the industry median book leverage, based on four-digit SIC codes.
This factor accounts for industry effects on leverage. MacKay and Phillips (2005) and
Frank and Goyal (2009) find strong industry effects in the cross section of firms’ leverage.
With regard to the definition of Lev, we use a book measure of leverage and a marketbased measure to assess the robustness of our results. Book leverage is defined as book value
of debt divided by book value of debt plus stockholders’ equity. Market leverage is measured
as book value of debt divided by book value of debt plus market value of equity. We provide
more complete information about the definition of our variables in Appendix A.
2.2
Estimation of the target adjustment model
Allowing for a lagged dependent variable to appear on the right hand side in (2) creates
a dynamic panel data model. The error term ϵi,t in (2) consists of two components: an
unobserved firm-specific component ηi and the residual component ui,t . An OLS-estimated
coefficient on Levi,t−1 would be upward biased as ηi is correlated with ui,t . Including fixed
effects in (5) to control for unobserved heterogeneity will also induce a bias in the coefficient
on Levi,t−1 . This is because firm-specific effects are correlated with the lagged dependent
variable; see, for example, Nickell (1981) and Baltagi (2008). Expressing all variables as
8
deviations from their firm-specific time-series means (time-demeaned variables) removes the
time-invariant firm-specific effect. However, this simultaneously creates a correlation between
the time-demeaned lagged dependent variable and the time-demeaned error term, introducing
a bias in the dynamic panel data model.
To obtain unbiased coefficient estimates for a dynamic panel data model similar to that
described in (2) the econometric literature suggests various techniques. Anderson and Hsiao
(1981) first-difference the dynamic model to eliminate the fixed effects and then use the second lag of the dependent variable as an instrument for the first-differenced lagged dependent
variable. However, this technique cannot be applied to our case as it restricts the remaining
independent variables to be strictly exogenous. Therefore, we cannot address the endogeneity
of the probability of financial distress. Arellano and Bond (1991) first difference the dynamic
panel data model applying a generalized method of moments (GMM) framework to develop
valid instruments. In particular they use further lags of the endogenous variables as instruments for those independent variables that are endogenous, provided that the residuals have
no second-order autocorrelation. Arellano and Bover (1995) and Blundell and Bond (1998)
augment the Arellano-Bond estimator by using the lagged first differences of the exogenous
independent variables in a non-transformed (level) equation. They build a system of two
equations; the level equation as well as the first differenced one. This technique is widely
known as “GMM-system”. Both the Arellano- Bond estimator and the GMM-system estimator are appropriate for our empirical model because they consider the probability of financial
distress to be an endogenous variable.
Flannery and Rangan (2006) use the fixed effects instrumental variables (IV) approach
by instrumenting lagged book (market) leverage with lagged market (book) leverage for the
dynamic book and market leverage regressions, respectively. Huang and Ritter (2009) use
the long differencing technique to estimate a partial adjustment model of capital structure.
However, both of these estimation methods are not suitable for the empirical specification
described in (2) as they assume that apart from the lagged dependent variable all the other
independent variables are strictly exogenous.
We first use the two-step Arellano and Bond GMM first-difference estimator for our dy-
9
namic panel data model. We therefore estimate a first-differenced version of (2),
∆Levi,t = λ(β ′ ∆xi,t−1 ) − λ∆Levi,t−1 + ϵi,t − ϵi,t−1
(4)
We also estimate (2) using the two-step GMM-system technique. Our dynamic panel data
model is estimated in both levels and first-differences. Based on the GMM-system method
level equations are simultaneously estimated using lagged first differenced regressors as instruments. The GMM-system estimator increases the number of instruments and imposes
additional moment restrictions, which can dramatically improve efficiency. We use the approach of Windmeijer (2005) to correct for the finite sample bias associated with the two-step
first-differenced GMM and the two-step GMM-system estimators.
2.3
Data
Our sample initially comprises active and inactive non-financial (SIC codes 6000–6999 are
excluded) and non-utility (SIC codes 4900–4949 are excluded) firms traded on NYSE, AMEX
and NASDAQ over the period 1963–2006. The accounting and market data are obtained
from the CRSP/Compustat Merged Database. We obtain data on the top statutory tax rates
from the Office of Tax Policy Research at the University of Michigan. We exclude firms with
missing data for any variable. We restrict the sample to firms with available data for at least
five consecutive years over the period 1963–2006 because of the use of the Arellano-Bond firstdifferenced GMM estimator and the GMM-system estimator. To estimate the probability of
financial distress we need to identify which of the inactive firms were financially distressed.
All inactive listed firms that entered any type of bankruptcy or liquidation are considered
financially distressed. We identify from our sample 195 financially distressed firms between
1963–2006. The final sample consists of 6,901 firms with 98,583 firm-year observations.
All the variables are winsorized at the upper and lower 0.5 tails except the corporate tax
rate before-financing, market leverage, size and probability of financial distress.6 Following
Sharpe and Nguyen (1995) and Graham et al. (1998) , we censor CTRBF to be bounded
between zero and one. Table I presents some descriptive statistics for the variables. Prof6
We did not winsorize market leverage and size because descriptive statistics indicate that they are normally
distributed, although the results remain unaltered if we also winsorize these two variables.
10
itability and the probability of financial distress (PROF and PROBFD, respectively) are the
most volatile variables.
3
Results
3.1
A Static Model
As a benchmark, we begin by estimating a static version of the model by setting λ = 1 in (2).
The static model we estimate is
Levi,t = β0 + β1 P ROBF Di,t−1 + β2 CT RBFi,t−1 + β3 SIZEi,t−1
+β4 T AN Gi,t−1 + β5 P ROFi,t−1 + β6 M T Bi,t−1
(5)
+β7 IN D LEVi,t−1 + ϵi,t−1
We estimate the static model using Tobit and fixed effects regression models.7 In particular
we use a double-censored Tobit estimator as the dependent variable is restricted to the range
zero to one. We also use a Fixed effects estimator to control for unobserved sources of firm
heterogeneity that are relatively constant over time.8 Finally we perform regressions with
clustered standard errors to account for cross-sectional and time-series dependence. Table II
shows the regression results for book leverage. Size, tangibility, profitability, growth opportunities and median industry leverage are all significant and have the expected signs. The
results are also robust to the method of estimation, so we will discuss the results as a whole.
The results indicate that the coefficient on PROBFD is significantly positive, suggesting that
as the probability of financial distress increases, so does leverage. This seems counter-intuitive
and is inconsistent with the prediction of the tradeoff theory. On the other hand, we find
a positive and significant association between corporate tax rate before-financing (CTRBF)
and book leverage, consistent with the findings of Graham et al. (1998) and with the trade-off
theory. To examine whether the results reported in Table II are due to the use of book leverage, Table III reports regression results for (5) with market leverage replacing book leverage
as the dependent variable. As for book leverage, there is a significantly positive relationship
7
For the fixed effects regressions, ϵi,t = ηi + υi,t in (5) where ηi are the fixed effects.
We also estimated random-effects regressions. However, a Hausman specification test suggests that the
fixed effects specification is most appropriate in estimating the static model.
8
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between PROBFD and market leverage. We also document a positive association between
CTRBF and market leverage, as we would expect. The effect of size, tangibility, profitability,
growth opportunities and median industry leverage is the same as with the book leverage
regressions. In the next section we explore whether the static model is misspecified leading
to a positive bias on the coefficient of the probability of financial distress.
3.2
Enter Leverage Dynamics
Several studies have documented that leverage dynamics are important in explaining capital
structure empirically (see, for example, Leary and Roberts, 2005, Flannery and Rangan, 2006,
and Byoun, 2008). To examine the effects of leverage dynamics on the results of the previous
section, we relax the restriction that λ = 1 in (2). The model we estimate is
Levi,t = β0 + β1 Levi,t−1 + β2 CT RBFi,t−1 + β3 P ROBF Di,t−1 + β4 SIZEi,t−1
+β5 T AN Gi,t−1 + β6 P ROFi,t−1 + β7 M T Bi,t−1
(6)
+β8 IN D LEVi,t−1 + ηi + υi,t
As mentioned earlier we estimate our dynamic panel data model using the two-step Arellano and Bond (A-B) first-differenced GMM estimator and the two-step GMM-system estimator.
Tables IV and V report the results for the dynamic panel data model for book and market
leverage, respectively. The estimated coefficient on lagged leverage is positive and statistically significant. The magnitude of this coefficient indicates that firms adjust rapidly toward
their target capital structures. The GMM system estimator for book and market debt ratio
produces lower speed of adjustment (36% and 27%, respectively) than that of the A-B GMM
estimator for book and market debt ratio (45% and 34%, respectively). The most striking
result, however, is the change in sign on the probability of financial distress, PROBFD using
both the two-step GMM estimation methods. The presence of lagged leverage in the model
now generates a significant negative relationship between financial distress and leverage. Using the two-step GMM-system estimator we find that the impact of CTRBF on leverage is
positive and significant, in line with the prediction of the tradeoff theory. While we document
a positive association between corporate tax rate and book leverage using the two-step A-B
12
GMM estimator, there is no association between the corporate tax rate and market leverage.
In the dynamic model, irrespective of whether we use book leverage or market leverage, an
increase in the probability of financial distress leads to a decrease in leverage, which is as we
would expect. With respect to the GMM-system estimates, all the remaining firm-specific
variables enter significantly and with the expected sign. While there is a negative sign on
profitability and growth opportunities and a positive sign on industry leverage when we use
the two-step A-B GMM estimator, there is no evidence on the effect of size and tangibility
on leverage.
We also report in Tables IV and V the AR(2) test statistic, that examines the null hypothesis of no second-order serial correlation in the error term, is statistically insignificant.
Therefore, unlike Flannery and Rangan (2006), we show that there is no second-order correlation of υit in the dynamic empirical specification using either the Arellano-Bond GMM
estimator or the GMM-system estimator.
Overall, our results shed new light on the role of leverage dynamics in corporate financing
decisions. Our evidence shows that accounting for leverage dynamics as well as addressing
properly the endogeneity of financial distress, allows us to uncover a negative relationship
between distress and leverage, something which the existing literature has not been able to
unravel. The positive effect of taxes on debt ratios and the negative effect of financial distress
on debt ratios documented in Tables IV and V show that firms trade-off the tax benefit of
debt against financial distress costs when determining their financing policy.
4
Summary and conclusions
In this paper we thoroughly estimate the impact of financial distress costs on debt ratios
addressing properly the endogenous association between financial distress and leverage. In
contrast to previous studies, we use the estimated probability of financial distress derived from
a hazard model based on equity market-driven variables as a measure of financial distress.
To measure the tax impact on capital structure we use a before-financing measure of the
corporate tax rate to overcome the endogenous association between corporate tax rates and
debt ratios. We use a static and a dynamic model of capital structure to quantify the effect
of financial distress costs on debt ratios investigating the role that leverage dynamics play.
13
The static model assumes that firms adjust immediately toward their target capital structures
whereas the dynamic model includes leverage dynamics allowing for costly adjustment. We
estimate the dynamic model using the two-step first-differenced GMM estimator and the twostep GMM-system estimator, which enable us to account for the endogenous effect of financial
distress on debt ratios. When there are no leverage dynamics in the model, we find that an
increase in the probability of financial distress increases leverage. This result is inconsistent
with what theory of capital structure suggests. Using a dynamic model that accounts for
leverage dynamics we find that leverage decreases with the probability of financial distress as
predicted by the trade-off theory. We find a positive relationship between the before-financing
corporate tax rate and leverage irrespective of whether we allow for leverage dynamics in the
regression model. When we use the first-differenced GMM estimator for our dynamic empirical
specification there is no association between corporate tax rates and market leverage.
Our results show that only when accounting leverage dynamics and considering the endogeneity of financial distress do we provide evidence that firms with higher probability of
financial distress issue less debt, in line with the tradeoff theory. This finding provides new
evidence on how leverage dynamics affects corporate financing decisions. Leverage dynamics enables us to understand the endogenous association between financial distress and debt
ratios and therefore to estimate properly the effect of the probability of financial distress on
leverage. Having thoroughly examined the association between debt ratios and financial distress costs, we show that firms tradeoff between the tax benefit of debt and financial distress
costs taking into account that firms rebalance their capital structures over time. This paper
suggests that the role of leverage dynamics is important in order to understand how firms
make their financing decisions.
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of Finance 43, 1–21.
Windmeijer, F., 2005, ”A Finite Sample Correction for the Variance of Linear Efficient TwoStep GMM Estimators,” Journal of Econometrics 126, 25–51.
17
Table I
Summary Statistics
The table presents the summary statistics of the variables used in the study. We exclude
firm-years in which the firm has missing data. The sample contains 6,901 firms and 98,583
firm-year observations from 1963–2006. We censor the corporate tax rate before-financing
(CTRBF) to be bounded between zero and one. All the remaining variables except market
leverage, size and the probability of financial distress are winsorized at the 0.5th and 99.5 th
percentiles. Book leverage is book value of debt divided by book value of debt plus book value
of stockholders’ equity. Market leverage is book value of debt divided by book value of debt
plus market value of equity. Lagged book leverage is the book leverage in year t-1. Lagged
market leverage is market leverage in year t − 1. The before-financing tax rate, CTRBF, is
measured as total income tax plus interest expense multiplied by the top statutory tax rate,
all divided by earnings before interest and tax (EBIT). PROBFD is the estimated probability
of financial distress. SIZE is defined as the natural logarithm of net sales. TANG is the ratio
of fixed assets to total assets. PROF is measured as earnings before tax,interest, depreciation
and amortization divided by total assets. MTB is the market value of assets divided by
the book value of assets. IND LEV is the median industry book leverage based on the SIC
four-digit code.
Variable
Book Leveraget−1
Market Leveraget−1
PROBFDt−1
CTRBFt−1
SIZEt−1
TANGt−1
PROFt−1
MTBt−1
IND LEVt−1
Mean
0.3264
0.2648
0.0036
0.3832
5.2759
0.3187
0.0045
1.7476
0.2963
Median
0.3006
0.2081
0.0024
0.3826
5.2912
0.2733
0.0430
1.2683
0.2998
18
Std.dev
0.2748
0.2398
0.0040
0.2801
2.1632
0.2172
0.1896
1.5796
0.1624
Min
0.0000
0.0000
0.0001
0.0000
-6.9078
0.0016
-1.7743
0.4883
0.0011
Max
1.9163
0.9985
0.1127
1.0000
12.5918
0.9267
0.2885
15.5373
0.7974
Table II
Tobit Fixed Effects and Clustered Regressions, Book Leverage
This table contains results from a static model of capital structure using censored Tobit,
Fixed effects and clustered regressions. The dependent variable is book leverage which is
book value of debt divided by book value of debt plus book value of stockholders’ equity. The
sample consists of 98,583 observations from 1963–2006. PROBFD is the estimated probability
of financial distress. The before-financing tax rate, CTRBF, is measured as total income tax
plus interest expense multiplied by the top statutory tax rate, all divided by earnings before
interest and tax (EBIT). SIZE is defined as the natural logarithm of net sales. TANG is
the ratio of fixed assets to total assets. PROF is measured as earnings before tax,interest,
depreciation and amortization divided by total assets. MTB is the market value of assets
divided by the book value of assets. IND LEV is the median industry book leverage based on
the SIC four-digit code. The regression is estimated using a Tobit model censoring at zero at
the lower end and one at the upper end with robust standard errors, a Fixed effects(FE) and
a clustered model. The estimated model is: Levi,t = α + β1 P ROBF Di,t−1 + β2 CT RBFi,t−1 +
β3 SIZEi,t−1 + β4 T AN Gi,t−1 + β5 P ROFi,t−1 + β6 M arket to booki,t−1 + β7 IN D LEVi,t−1 + ϵit .
***, ** and * denote significance at the 1, 5 and 10 percent levels, respectively.
Constant
PROBFDt−1
CTRBFt−1
SIZEt−1
TANGt−1
PROFt−1
MTBt−1
IND LEVt−1
Number of observations
Dependent Variable=Book leverage
Censored Tobit
FE
Clustered
∗∗∗
-0.0873
-0.0040
-0.0473∗∗∗
(-22.57)
(-0.61)
(-3.51)
6.4291∗∗∗
3.3649∗∗∗ 6.9202∗∗∗
(26.85)
(14.82)
(6.82)
0.1233∗∗∗
0.0509∗∗∗ 0.1134∗∗∗
(42.11)
(18.94)
(8.92)
0.0256∗∗∗
0.0319∗∗∗ 0.0235∗∗∗
(55.63)
32.57
(11.08)
∗∗∗
∗∗∗
0.1204
0.1100
0.0953∗∗∗
(31.44)
(14.62)
(8.22)
∗∗∗
∗∗∗
-0.2402
-0.2329
-0.2812∗∗∗
(-50.13)
(-47.79)
(-11.14)
-0.0180∗∗∗
-0.0051∗∗∗ -0.0107∗∗∗
(-32.35)
(-8.66)
(-5.45)
0.6290∗∗∗
0.3810∗∗∗ 0.6011∗∗∗
(118.30)
(52.92)
(34.52)
98,583
98,583
98,583
19
Table III
Tobit Fixed Effects and Clustered Regressions, Market Leverage
This table contains results from a static model of capital structure. The dependent variable is market leverage which is book value of debt divided by book value of debt plus market
value of equity. The sample consists of 98,583 observations from 1963–2006. PROBFD is
the estimated probability of financial distress. The before-financing tax rate, CTRBF, is
measured as total income tax plus interest expense multiplied by the top statutory tax rate,
all divided by earnings before interest and tax (EBIT). SIZE is defined as the natural logarithm of net sales. TANG is the ratio of fixed assets to total assets. PROF is measured
as earnings before tax,interest, depreciation and amortization divided by total assets. MTB
is the market value of assets divided by the book value of assets. IND LEV is the median
industry book leverage based on the SIC four-digit code. The regression is estimated using a
Tobit model censoring at zero at the lower end and one at the upper end with robust standard errors and a Fixed effects(FE) model and a clustered model. The estimated model is
Levi,t = α+β1 P ROBF Di,t−1 +β2 CT RBFi,t−1 +β3 SIZEi,t−1 +β4 T AN Gi,t−1 +β5 P ROFi,t−1 +
β6 M arket to booki,t−1 + β7 IN D LEVi,t−1 + ϵit . ***, ** and * denote significance at the 1, 5
and 10 percent levels respectively.
Constant
PROBFDt−1
CTRBFt−1
SIZEt−1
TANGt−1
PROFt−1
MTBt−1
IND LEVt−1
Number of observations
Dependent Variable=Market leverage
Censored Tobit
FE
Clustered
∗∗∗
∗∗∗
-0.0304
-0.0142
0.0200∗
(-8.81)
(-2.93)
(1.85)
7.1987∗∗∗
3.1057 ∗∗∗ 6.7723∗∗∗
(33.90)
(18.43)
(8.94)
0.1050∗∗∗
0.0415∗∗∗
0.0821∗∗∗
(40.21)
(20.79)
(10.52)
0.0197∗∗∗
0.0287∗∗∗
0.0157∗∗∗
(48.13)
(39.46)
(11.28)
∗∗∗
∗∗∗
0.0898
0.1439
0.0690∗∗∗
(26.36)
(25.77)
(6.05)
∗∗∗
∗∗∗
-0.1786
-0.1261
-0.1577∗∗∗
(-41.72)
(-34.85)
(-7.09)
-0.0489∗∗∗
-0.0209 ∗∗∗ -0.0397∗∗∗
(-94.69)
(-47.74)
(-12.17)
0.5761∗∗∗
0.3215∗∗∗
0.5315∗∗∗
(121.84)
(60.15)
(28.33)
98,583
98,583
98,583
20
Table IV
Two-step GMM Estimation Results, Book Leverage
This table presents the results from a dynamic model of capital structure. We use firm-year
observations with available data for at least five consecutive years. The dependent variable
is book leverage which is book value of debt divided by book value of debt plus book value
of stockholders’ equity. Lagged book leverage is the book leverage in year t-1. PROBFD
is the estimated probability of financial distress. The before-financing tax rate, CTRBF, is
measured as total income tax plus interest expense multiplied by the top statutory tax rate, all
divided by earnings before interest and tax (EBIT). SIZE is defined as the natural logarithm
of net sales. TANG is the ratio of fixed assets to total assets. PROF is measured as earnings
before tax,interest, depreciation and amortization divided by total assets. MTB is the market
value of assets divided by the book value of assets. IND LEV is the median industry book
leverage based on the SIC four-digit code. The dynamic panel data model we estimate is of the
following form: Levi,t = α + β1 Levi,t−1 + β2 P ROBF Di,t−1 + β3 CT RBFi,t−1 + β4 SIZEi,t−1 +
β5 T AN Gi,t−1 +β6 P ROFi,t−1 +β7 M arket to booki,t−1 +β8 IN D LEVi,t−1 +ηi +ηt +υi,t . We also
include year dummies (not reported). The model is estimated using the two-step ArellanoBond GMM estimator and the two-step GMM-system estimator, which treat PROBFD as
an endogenous variable. For the two-step GMM estimation methods we apply Windmeijer’s
correction to the standard errors. ***, ** and * denote significance at the 1, 5 and 10 percent
levels respectively.
Book Leveraget−1
PROBFDt−1
CTRBFt−1
SIZEt−1
TANGt−1
PROFt−1
MTBt−1
IND LEVt−1
Number of observations
AR(1)
AR(2)
Dependent Variable=Book leverage
A-B GMM Estimator GMM-system Estimator
0.5509 ∗∗∗
0.6364 ∗∗∗
(17.73)
(29.48)
∗∗∗
-4.6159
-4.0340∗∗∗
(-6.87)
(-6.59)
0.1110 ∗∗∗
0.1663 ∗∗∗
(5.14)
(11.93)
0.0053
0.0084∗∗∗
(0.59)
(7.53)
0.0650
0.0685∗∗∗
(1.25)
(7.70)
∗∗∗
-0.3341
-0.2711∗∗∗
(-5.64)
(-11.37)
-0.0106∗∗∗
-0.0215∗∗∗
(-2.89)
(-13.86)
0.0441∗∗
0.1052∗∗∗
(2.04)
(6.45)
84,594
91,495
-16.87∗∗∗
-17.36∗∗∗
1.32
1.46
21
Table V
Two-step GMM Estimation Results, Market Leverage
This table presents the results from a dynamic model of capital structure. We use firmyear observations with available data for at least five consecutive years. The dependent
variable is market leverage which is book value of debt divided by book value of debt plus
market value of equity. PROBFD is the estimated probability of financial distress. The
before-financing tax rate, CTRBF, is measured as total income tax plus interest expense
multiplied by the top statutory tax rate, all divided by earnings before interest and tax
(EBIT). SIZE is defined as the natural logarithm of net sales. TANG is the ratio of fixed
assets to total assets. PROF is measured as earnings before tax,interest, depreciation and
amortization divided by total assets. MTB is the market value of assets divided by the
book value of assets. IND LEV is the median industry book leverage based on the SIC
four-digit code. The The dynamic panel data model we estimate is of the following form:
Levi,t = α + β1 Levi,t−1 + β2 CT RBFi,t−1 + β3 P ROBF Di,t−1 + β4 SIZEi,t−1 + β5 T AN Gi,t−1 +
β6 P ROFi,t−1 + β7 M arket to booki,t−1 + β8 IN D LEVi,t−1 + ηi + ηt + υi,t . We also include year
dummies (not reported). The model is estimated using the two-step Arellano-Bond GMM
estimator and the two-step GMM-system estimator, which treat PROBFD as an endogenous
variable. For the two-step GMM estimation methods we apply Windmeijer’s correction to the
standard errors. ***, ** and * denote significance at the 1, 5 and 10 percent levels respectively.
Market Leveraget−1
PROBFDt−1
CTRBFt−1
SIZEt−1
TANGt−1
PROFt−1
MTBt−1
IND LEVt−1
Number of observations
AR(1)
AR(2)
Dependent Variable=Market leverage
A-B GMM Estimator GMM-system Estimator
0.6606∗∗∗
0.7264∗∗∗
(33.64)
(64.19)
∗∗∗
-3.0821
-3.5281∗∗∗
(-5.57)
(-7.84)
0.0139
0.0661∗∗∗
(0.79)
(7.81)
0.0082
0.0019∗∗∗
(1.17)
(2.96)
0.0428
0.0299∗∗∗
(1.10)
(5.75)
-0.0838∗∗
-0.1906∗∗∗
(-2.39)
(-16.56)
∗∗∗
-0.0304
-0.0271∗∗∗
(-11.58)
(-20.79)
0.0673∗∗∗
0.0988∗∗∗
(3.63)
(7.31)
84,594
91,495
-38.96∗∗∗
-42.09∗∗∗
-1.25
-1.47
22
Appendix A
Table A1
Definition of Variables
This appendix defines the variables used in the study. All numbers in parentheses refer to the
Compustat code of each accounting item.
Variable Name
Total Debt
Book Leverage
Total debt
Book Leverage
Market value of equity
Market Leverage
EBIT
Variable definition
Debt in Current Liabilities (34) + Long–term Debt (9)
Total Debt
Total Debt + Stockholders’ Equity (216)
Debt in current liabilities (34) + Long–term debt (9)
Total debt
Total debt + Stockholders’ equity (216)
Stock Price (199) ∗ Shares outstanding (54)
Total debt
Total debt + Market value of equity (mcap)
Pretax income (170) + Interest expense (15)
PROBFD
(Income tax (16) + (Interest expense ∗ Top Statutory Tax Rate))
EBIT
Estimated probability of financial distress from a hazard model
Working Capital
Current assets(4) − Current liabilities(5)
Size
Natural logarithm of net sales, where net sales are deflated by the GDP
CTRBF
Tangibility
Profitability
Market to book
Ind LEV
Property, plant and equipment (8)
Book value of assets (6)
Operating income before depreciation (13)
Book value of assets
Book value of assets − Common equity (60) + Market value of equity
Book value of assets
the median industry book leverage, based on the SIC four-digit code
23