Are Firms Underleveraged? An Examination of the Effect of Leverage on Default Probabilities

Are Firms Underleveraged?
An Examination of the Effect of Leverage on
Default Probabilities


Carlos A. Molina*

* Molina is at the Pontificia Universidad Católica de Chile, Escuela de Administración.
This article is derived from my doctoral dissertation at the University of Texas at Austin.
I thank my advisors Andres Almazan and Sheridan Titman for their continued guidance
and support. I am specially indebted to the University of Texas at San Antonio and
Instituto de Estudios Superiores de Administración-IESA for their support during this
research. For helpful comments, I am grateful to Karan Bhanot, Alex Butler, David
Chapman, Jay Hartzell, Palani-Rajan Kadapakkam, Ayla Kayhan, Don Lien, Lalatendu
Misra, Thomas Moeller, Robert Parrino, Lorenzo Preve, Tom Shively, Laura Starks,
Sergey Tsyplakov, and seminar participants at the University of Texas at Austin, the
University of Texas at San Antonio, the Pontificia Universidad Católica de Chile,
Instituto de Estudios Superiores de Administración-IESA, Instituto de Empresa, the 2002
FMA meetings, and the 2002 SFA meetings. I thank John Graham for sharing his
marginal tax rates data. Valuable suggestions from Rick Green (the editor) and two
anonymous referees also significantly improved the paper. This paper previously
circulated under the title Capital Structure and Debt Rating Relationship: An Empirical
Analysis. All errors are my own.

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ABSTRACT

A commonly held view in corporate finance is that firms are less leveraged than
they should be, given the potentially large tax benefits of debt. In this paper, I study
the effect of firms’ leverage on default probabilities as represented by the firms’
ratings. Using an instrumental variable approach, I find that the leverage’s effect on
ratings is three times stronger than it is if the endogeneity of leverage is ignored.
This stronger effect results in a higher impact of leverage on the ex-ante costs of
financial distress, which can offset the current estimates of the tax benefits of debt.

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Ever since Modigliani and Miller (1963), a central question in corporate finance asks why, if
debt provides a large tax advantage, do firms not use debt more intensively?1 Graham (2000)
finds that by leveraging up to the point at which the marginal tax benefits begin to decline, a
typical firm could add 7.5 % to firm value, after netting out the personal tax penalty. So why
are firms not more leveraged?
According to the traditional trade-off theory of capital structure, the (ex-ante) costs of
financial distress should offset the benefits of the tax shields. The literature has made a
considerable effort to estimate the benefits and costs of debt. However, while Graham’s (2000)
estimate for the expected tax benefits of debt appears reasonable, current estimates of financial
distress costs (or indirect costs of bankruptcy) are less satisfactory because they measure the
costs ex-post on a sample of already distressed or defaulted firms.2 Hence, to be compared with
the potential benefits of debt, previous estimates of (ex-post) costs of financial distress must be
multiplied by the probability of encountering distress.
In this paper, I present an alternative measure of the ex-ante costs of financial distress. I
estimate the effect of an increase in a firm’s leverage on the default probability represented by
the firm’s rating. I then multiply previous estimates of ex-post costs of financial distress by the
estimated effect of leverage on the firm’s default probability, providing a measure of the ex-
ante costs of financial distress that is comparable to the current estimates of the tax benefits of
debt.
However, the estimation of the effect of leverage on default probabilities requires the
explicit consideration of the potential endogeneity of leverage. In particular, I consider a firm’s
rating as proxy for its default probability. I then argue that the endogeneity of leverage occurs
because leverage and ratings are jointly determined when affected by exogenous and
unobservable shocks to the firm’s fundamental risk.3 Ignoring the endogenous nature of

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leverage can lead to an underestimation of its effect on ratings, and consequently to an
underestimation of the costs of financial distress. In fact, my estimates suggest that the effect of
leverage on ratings is substantially stronger (up to three times) when I consider the
endogeneity. This larger estimate translates an increase in a firm’s leverage into an increase in
the firm’s ex-ante costs of financial distress, which largely offsets the tax benefits that, as
calculated in Graham (2000), the firm can obtain by leveraging up.
To see how ignoring the endogeneity can cause an underestimation of the impact of a
leverage increase on ratings, I consider the following situation. If a decrease in the firm’s
fundamental risk occurs, the firm’s prospects improve, which leads rating agencies to upgrade
the firm’s rating. Such a decrease in the firm’s risk simultaneously allows the firm to increase
its leverage, which in turn negatively affects the firm’s rating. Therefore, the total impact of a
risk reduction on ratings has two components: a rating upgrade directly from the firm’s risk
reduction, and a rating downgrade from the leverage increase induced by the risk reduction.
The rating upgrade from the risk reduction partly offsets the downgrade from the increased
leverage, making the total rating downgrade appear less significant than it really is.
To disentangle the direct effect of leverage on ratings, I use an instrumental variable
approach that accounts for the endogeneity of the leverage-rating relation. As instruments, I
use two variables that significantly affect leverage, yet seem reasonably unrelated to ratings.
These variables are the history of firms’ past market valuations (Baker and Wurgler (2002))
and the firms’ marginal tax rates (Graham (1996a, 1996b)). The instrumental variable
estimates for the effect of leverage on ratings are robust to the use of any of these instruments.
The stronger effect of leverage on ratings, which I obtain by instrumenting leverage, is
consistent with the actual variation of leverage ratios across rating categories. For instance, if
an average firm in my sample, rated BBB with a leverage ratio of 0.27, increases its leverage

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by 0.08, its rating is downgraded by one category. This leverage’s increase corresponds to the
actual difference in leverage between BBB and BB firms. This correspondence with the actual
variations of leverage ratios adds to the trade-off between the ex-ante costs of financial distress
and the tax benefits of debt described in this paper, contributing to explain why firms use the
amount of leverage that they do.
I also investigate whether the effect of leverage on ratings is present across all firms with
the same intensity. Graham and Rogers (2002) and Leland (1998) show that risk management
activities impact firms’ debt choice and can cause a firm engaged in risk management to
respond differently to a change in its fundamental risk. Korajczyk and Levy (2003) find that
only unconstrained firms are able to adjust their capital structures to time their issue choice.
Baker, Stein, and Wurgler (2003) provide a rationale for why endogeneity might be less severe
when firms are financially constrained (or equity dependent).
I examine these issues by separating firms according to their level of hedging activity and
financial constraints. Consistent with previous arguments, I find that the impact of leverage on
ratings is stronger when firms do not hedge and when firms are unconstrained. Moreover, I
find that the effect of endogeneity is weakened when firms are engaged in risk management
activities or are financially constrained.
The approach followed in this paper to address the underleverage question is similar to
the approach that has been used to deal with other puzzles in corporate finance in which
endogeneity can be central. For example, Chevalier (2004), Lamont and Polk (2001), Campa
and Kedia (2002), and Graham, Lemmon, and Wolf (2002) argue that to a large extent
selection bias can explain the previously documented diversification discount. Himmelberg,
Hubbard, and Palia (1999) conclude that the effect of managerial ownership on firm
performance is not apparent when the endogeneity in this relationship is considered. Goyal,

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Lehn, and Racic (2002) use a focused sample of defense firms to infer a causal relation
between a firm’s growth opportunities and its debt policy, taking into account that they may be
jointly determined. Johnson (2003) uses a simultaneous equation approach to find that shorter
debt maturity attenuates the negative effect of growth opportunities on leverage.
The paper is organized as follows. Section I proposes an empirical framework to estimate
the impact of leverage on default probabilities. Section II describes the data sample and the
variables I use. Section III reports the results for the econometric implementation proposed.
Section IV presents an estimation of the ex-ante costs of financial distress to address the
underleverage question. Section V presents the robustness checks. Section VI examines the
leverage impact on ratings when firms engage in hedging activities and when firms are
financially constrained. Section VII concludes.
I. Empirical Framework
A. The Leverage-Rating Relation
Although it is widely accepted that a firm’s leverage affects its bond ratings (and its
probability of default), the empirical relation between these two variables has not been
carefully examined, in that previous research on ratings has neglected the fact that leverage is
an endogenous variable and has not suggested any source of exogenous variation that allows
the true impact of leverage on ratings to be identified.4
To see how ignoring the leverage endogeneity can cause underestimation of the impact of
a leverage increase on ratings (risk of default), and therefore on the ex-ante financial distress
costs, consider the following situation. Suppose that leverage and ratings are jointly affected by
exogenous and unobservable shocks to the firm’s fundamental risk. These shocks are
unobservable to outsiders (specifically, to the econometrician) but can capture at least part of

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what the rating agencies call their subjective judgment. In this case, if I try to estimate the
effect of leverage on ratings by using a reduced form estimation—which ignores the source of
variation that is producing the change in ratings and leverage—the estimation will be biased.
The bias will depend on the interaction of the firm’s fundamental risk with the firm’s leverage
and rating. However, it is reasonable to argue that the impact of leverage on ratings is likely to
be underestimated by the reduced form regression.
To understand why a negative bias is likely to occur, I consider the following. First, a
change in a firm’s risk negatively affects the amount of debt that the firm can support,5 and a
change in leverage induced by a risk adjustment negatively affects the firm’s rating
(Ederington and Yawitz (1987)). Second, the change in a firm’s risk also affects debt ratings
directly, because rating agencies use ratings to represent the fundamental risk of the firm.
Therefore, risk affects ratings both directly and through leverage (see Figure 1). Thus, I can
argue that a decrease in the firm’s fundamental risk has two components that offset each other:
a rating upgrade directly from the firm’s risk reduction and a rating downgrade from the
leverage increase (induced by the risk reduction). Therefore, if I want to disentangle the direct
impact of a leverage change on the firm’s rating, I must first take into account the reason for
the leverage increase.
[Insert Figure 1 here]
In a different context, the literature on contingent claims models of firms’ capital
structures (Leland (1994), Leland and Toft (1996), Leland (1998), and Titman and Tsyplakov
(2003)) predicts optimal levels of leverage by maximizing the firm’s value with respect to
leverage. These models measure risk as the assets’ volatility and, except for Leland (1998),
consider risk as exogenously given. Leland (1998) analyzes the interaction between the capital
structure and risk level choices, allowing firms to choose risk endogenously; a firm may impact

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its risk by engaging in risk management practices. In contrast, my approach empirically
estimates the impact of leverage on ratings (probability of default), considering the firm’s
unobservable fundamental risk to be endogenous.6 I contribute to an explanation of the
observed leverage levels without explicitly calculating an optimal level of leverage. In any
case, the effect of a leverage increase on the probabilities of default proposed in this paper can
be related to the relation between leverage and risk of default predicted in this strand of the
literature.
B. Modeling the Effect of Leverage on Ratings
I consider a firm’s rating as proxy for its default probability, and then examine the
following model to measure the leverage’s impact on ratings:





Rat = ? + ? Lev + ? X + ? u + ?
(1)
i
1
1
i
2
i
1
3
i
i
1

Lev = ? + ? X + ? X
+ ? u + ? .

(2)
i
2
4
i
1
5
2i
6
i
2i
In this model u is the unobservable fundamental risk that creates the endogeneity
i
problem. Equation (1), the rating equation, models the rating setting behavior by rating
agencies. The equation examines the determinants of the rating ( Rat ), including the firm’s
i
leverage ( Lev ), the unobserved firm’s fundamental risk ( u ), and other factors described
i
i
below.
Equation (2) is the firm’s leverage equation. It relates the firm’s leverage to its exogenous
determinants and the unobserved firm’s fundamental risk ( u ). I include in X a common set
i
1
of determinants for leverage and rating, such as size, profitability, income volatility,
uniqueness, asset tangibility, and industry dummies. In X , I consider the determinants of
2
leverage that do not affect rating directly and can be used as instruments of leverage to identify
the rating equation.

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To estimate ? , the coefficient that captures the true impact of leverage on ratings, I must
1
include the unobserved firm’s fundamental risk ( u ). If I ignore it, the estimation of ? is
i
1
inconsistent, because the firm’s leverage and fundamental risk are related, cov(Lev , u ) ? 0 . In
i
i
fact, if I assume that risk negatively affects leverage ( ? < 0 in equation (2)), then
6
cov(Lev , u ) < 0 . Consequently, if I omit u from the estimation, the coefficient ? is biased
i
i
i
1
downwards (in absolute value).
Intuitively, the model captures the same economic effect referred to above. A decrease in
the firm’s fundamental risk, u , improves the firm’s prospects, leading rating agencies to
i
improve the firm’s rating, Rat . Such a decrease in the firm’s risk (through equation (2) and
i
given 0
? < ) simultaneously allows the firm to increase its leverage, Lev , which in turn
6
i
negatively affects the firm’s rating and diminishes the importance of the coefficient ? .
1
Instrumental variables can correct the econometric problem and provide a consistent
estimator for ? . To do so, I must instrument leverage with any of its determinants (in X )
1
2
that are not correlated with the unobserved factor u (i.e., cov(Lev , u ) ? 0 ). In what follows, I
i
i
i
consider two main instruments for leverage.
The first instrument is the history of past market valuations, measured by the history of
market-to-book ratios. Baker and Wurgler (2002) show the strong influence of firms’ past
market valuations on their leverage. Firms with past high valuations (high market-to-book
ratios) issue equity when funds are needed, and firms with low past valuations (low market-to-
book ratios) issue debt to raise funds.

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My second instrument for leverage is the firm’s marginal tax rate from Graham (1996a,
1996b). As Graham (1996a) shows, high-tax-rate firms issue more debt than do their low-tax-
rate counterparts.
The two instruments proposed here make significant contributions to the leverage
equation (see Section III.A and Table III) and exhibit low univariate correlations with ratings
(0.19 and 0.12, respectively). In addition, there are no obvious reasons why the proposed
leverage’s instruments affect the rating determination process by agencies. Rating agencies’
reports do not refer to these instruments when explaining the rating criteria.7 The relation
between the proposed instruments and leverage ratios, and the fact that rating agencies pay
little or no attention to past market valuations or taxes, make these candidates good instruments
for leverage.
Following Kaplan and Urwitz (1979), I use an ordered probit model for the estimation of
the rating equation (1), which allows me to take into account the ordinal characteristic of a
rating dependent variable. I estimate the ordered probit model with instrumental variables in a
two-stage process by following Smith and Blundell (1986) and Nelson and Olsen (1978). To
avoid concerns in the estimation of a nonlinear limited dependent variable model with
endogenous variables like the one described here, I alternatively use the yields of the firms’
bonds—instead of ratings—as the dependent variable in equation (1). Altman’s Z-scores
(Altman (1968)) and firms’ interest coverage ratios (Kaplan and Urwitz (1979) and Ederington,
Yawitz, and Roberts (1987)) are other alternatives that can be considered proxies of firms’
default risks and constitute robustness checks to firms’ ratings. The main advantage of using
cardinal variables is that the model to estimate is transformed into a linear one. However, I use
debt ratings as the base case because they are more easily translatable into default probabilities.

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