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Unformatted text preview: THE JOURNAL OF FINANCE • VOL. LIX, NO. 4 • AUGUST 2004 Tobin’s Q, Debt Overhang, and Investment
CHRISTOPHER A. HENNESSY∗
ABSTRACT
Incorporating debt in a dynamic real options framework, we show that underinvestment stems from truncation of equity’s horizon at default. Debt overhang distorts
both the level and composition of investment, with underinvestment being more severe for longlived assets. An empirical proxy for the shadow price of capital to equity
is derived. Use of this proxy yields a structural test for debt overhang and its mitigation through issuance of additional secured debt. Using measurement errorconsistent
GMM estimators, we find a statistically significant debt overhang effect regardless of
firms’ ability to issue additional secured debt. IN DYNAMIC INVESTMENT MODELS, the shadow price of capital, or marginal q, is a
sufficient statistic for investment.1 Since marginal q is unobservable, Tobin’s
average Q, the ratio of equity plus debt value to replacement cost of the capital
stock, is commonly used as an empirical proxy. Hayashi (1982) and Abel and
Eberly (1994) provide formal justifications for this practice, deriving conditions
under which average Q and marginal q are equal. A drawback of both models
is that they preclude any role for financial structure by assuming that the firm
is financed exclusively with equity.
Starting with the Abel and Eberly (1994) model of firstbest investment,
where marginal and average Q are equal, this paper analyzes the investment
policy of an equitymaximizing firm with longterm debt outstanding.2 In this
situation, levered equity’s marginal q does not ref lect the value of postdefault
investment returns accruing to existing lenders. However, such returns are
capitalized into the price of existing debt and thus included in the numerator
of average Q. This implies that marginal q is less than average Q for firms with
longterm debt. We show that levered marginal q is equal to average Q minus
the capitalnormalized value of existing lenders’ claim to recoveries in default.
A second expression relating levered and unlevered marginal q is also derived, facilitating analysis of the role played by asset life. The importance of
∗ Christopher A. Hennessy is at Walter A. Haas School of Business, University of California at
Berkeley. I am grateful to Jonathan Berk, Terry Hendershott, Amnon Levy, Ben Bernanke, Jose
Scheinkman, and especially my dissertation adviser Patrick Bolton. Thanks to Toni Whited and
Timothy Erickson for providing me with their data. The empirical section of this paper benefited
greatly from suggestions provided by an anonymous referee.
1
See Mussa (1977) and Abel (1983) for early treatments.
2
This is the objective function in Myers (1977). Recent numerical work includes Mello and
Parsons (1992); Mauer and Triantis (1994); Parrino and Weisbach (1999); Morellec (2001); Moyen
(2001); and Titman and Tsyplakov (2002). 1717 1718 The Journal of Finance asset life has thus far been neglected in the literature on agency costs of debt. We
show that levered marginal q equals unlevered marginal q minus the shadow
price of undepreciated capital at the time of default. For a firm investing in
multiple capital goods, the percentage of undepreciated capital remaining at
the time of default is higher for physical assets with low rates of depreciation.
This implies that overhang distorts the composition as well as the level of investment, with the underinvestment problem being more severe for longlived
assets.
In order to test the theory, an empirical proxy for the overhang correction
term is computed as the capitalnormalized value of total lender recoveries in
default. In the model, the optimal investment policy is shown to be linear in
average Q and the overhang correction term, with the latter predicted to have a
negative coefficient. Under the alternative hypothesis of firstbest investment,
the correction term has a coefficient of zero. Using the measurement errorconsistent generalized method of moments (GMMs) estimators of Erickson and
Whited (2002), we find that the overhang correction term is always statistically
significant.
The model also predicts that the absolute value of the coefficient on the overhang correction term will be smaller for firms that issue additional secured
debt in order to reduce the spillover benefit that new investment provides to
existing lenders. To test this hypothesis, we split the sample into two groups,
based on two alternative indicators for superior ability to issue new secured
debt: high bond ratings or high industryspecific recovery ratios. Regardless of
the sorting criterion, we fail to reject the null hypothesis that the coefficient on
the overhang correction does not depend on firm status.
The economic significance of the debt overhang effect varies systematically
with debt ratings. The term subtracted from average Q, the normalized value
of total default recoveries, is much larger for lowrated firms. For instance, the
mean ratio of the overhang correction term to average Q is 11% for firms below
investment grade and 0.8% for those above investment grade. Therefore, while
we find that the statistical significance of the overhang effect is not mitigated by
the issuance of future secured debt, the economic significance of the overhang
channel is relatively small for healthy firms.
In a related paper, Whited (1992) finds that an Euler equation without credit
constraints performs well for nondistressed firms, but is rejected for distressed
firms. The addition of a credit constraint improves the performance of the Euler
equation when applied to distressed firms. In our model, overhang and credit
constraints are linked, since overhang is most severe for firms that are unable to
issue additional secured debt. Whited’s finding of significant departures from
firstbest for distressed firms is consistent with our empirical results, since
distressed firms exhibit the largest wedge between levered equity’s marginal q
and average Q, with the latter being a sufficient statistic for investment under
firstbest.
Lang, Ofek, and Stulz (1996) use average Q as a proxy for growth opportunities, with book leverage included as a regressor. Book leverage enters significantly only for lowQ firms. Although our evidence is consistent with their Tobin’s Q, Debt Overhang, and Investment 1719 findings, the mapping between their tests and the underlying theory is unclear since the leverage ratio is an imperfect proxy for the overhang correction.
In addition, it is impossible to determine whether the magnitude of the estimated coefficient is consistent with the overhang hypothesis. Using a structural approach, we find that the negative effect of debt on investment is actually somewhat stronger than that implied by the overhang channel working in
isolation.
The remainder of the paper is organized as follows. Section I presents the
basic model assuming that the senior debt contract prohibits issuance of additional secured debt. Section II extends the basic model, allowing for issuance
of additional secured debt. Section III includes the empirical tests. I. Basic Model
A. Contracting Framework
In the interest of transparency, we build directly upon the real options framework of Abel and Eberly (1994) and adopt their notation where possible. In contrast to their unlevered firm, consider a firm that has issued senior longterm
debt with a promise to pay an infinite stream of coupon payments, b. The assumption of a consol bond is motivated by our desire to model the agency costs
of debt, since debt maturing before a particular growth option becomes available is irrelevant to that investment decision. The optimal debt commitment
(b) is not derived since the objective of this paper is to determine the empirical implications of overhang for structural investment equations. The derived
structural investment equation holds for arbitrary b.
The firm has the option to default given limited liability, and there are no
deviations from absolute priority. Section I assumes that senior debt contains
a covenant specifying that future debt issuance must be subordinate instantaneous debt that does not affect the recovery claim of the senior lender. This
assumption is made for two reasons. First, as suggested by Myers (1977), eroding senior debt value with additional debt issuance is a device for mitigating
underinvestment. Second, provisions limiting future debt issuance are commonly included in debt covenants. Smith and Warner (1979) find that 90.8%
of their sampled covenants contain some restriction on future debt issuance.
The extended model presented in Section II allows a portion of incremental
investment to be financed with new secured debt.
The investment program maximizes equity value, with contractual commitment to firstbest ruled out. This is a reasonable assumption, given the difficulty
courts would have in determining whether particular investments are positive
NPV. Renegotiation of debt is also ruled out. With widely dispersed creditors,
the costs of renegotiation are prohibitive. Further, as discussed by Smith and
Warner (1979), public debt is subject to the Trust Indenture Act of 1939, which
places stringent conditions on restructurings. An interesting direction for future research, not explored here, is whether firms relying on bank or privately
placed debt avoid the overhang problem through renegotiation. 1720 The Journal of Finance Internal cash is the first source of funds, with additional investment financed
with capital infusions. As an abstraction, it is helpful to view the manager as
sole shareholder, with sufficient wealth to fund desired investment if it exceeds internal cash. The contributions may be considered to be equity or simply
viewed as the manager lending to himself. The two are economically equivalent.
We adopt the labeling convention of treating the manager’s value function as
equity.
B. Investment Problem
The firm is a pricetaker in both output and input markets. Let π represent
maximized instantaneous operating profits, which is a function of the capital
stock K and state ε . This specification allows for price, wage, and productivity
shocks. Letting F represent the production function, p the output price, w the
wage rate, and N variable labor inputs, maximized operating profits is
π ( K , ε ) ≡ max p(ε ) F ( K , N , ε ) − w(ε) N . (1) N The evolution of (K , ε ) is governed by
d K t = ( It − δ K t ) d t , (2) d εt = µ(εt ) d t + σ (εt ) d Wt . (3) The variables I and δ represent investment and the depreciation rate, respectively. Here W is a standard Wiener process, with the drift and volatility for ε
satisfying the necessary conditions for the existence of a unique solution to the
stochastic differential equation.3 The diffusion process for the state variable is
sufficiently general to allow for competitive dynamics that may affect the path
of ε.
Let c represent the total cost of changing the capital stock of the firm, with c
being a function of (I, K )
c( I , K ) = P ( I ) I + G ( I , K ) + ( I )a( K ). (4) The first term represents direct costs of investment, with the price at which
capital is purchased (P+ ) possibly exceeding that at which it is sold (P− ). The
function G represents the cost of adjusting plant and equipment and is smooth,
increasing in I on + , decreasing in I on − , decreasing in K , and strictly convex
in both arguments. The function is an indicator for nonzero investment, with
a(K ) representing fixed costs.
Smith and Warner (1979) find that 35.6% of their sample of debt covenants
place limits on the disposition of assets. In the model
no covenant restricting asset sales ⇒ I ∈
covenant restricting asset sales ⇒ I ∈
3 ≡
≡ ,
+. (5) We assume that stochastic integrals with respect to W are martingales. See Duffie (1996) and
Karatzas and Shreve (1988) for regularity conditions. Tobin’s Q, Debt Overhang, and Investment 1721 Let date zero represent the present for simplicity and T the stochastic default
time. One should think of the default threshold as being a contour in (K , ε) space.
Note that, like I, the stopping time T is not chosen at date zero, but is chosen
optimally based on current information.4 Letting S denote the value of equity
(stock), we have
T S ( K 0 , ε0 ) ≡ max E
I ∈ ,T e−rt [π ( K t , εt ) − c( It , K t ) − b] d t . (6) 0 The Bellman equation for this problem is5
r S ( K , ε ) = max π ( K , ε ) − c( I , K ) − b +
I∈ 1
E [d S ].
dt (7) Applying Ito’s lemma, the Bellman equation may be written as
r S ( K , ε ) = max π ( K , ε ) − c( I , K ) − b + ( I − δ K ) S K
I∈ + µ(ε ) Sε + 1 σ 2 (ε ) Sεε .
2 (8) The key variable determining investment is the shadow price of capital to
equity, which is denoted q. More formally
q ( K , ε ) ≡ S K ( K , ε). (9) Ignoring terms on the right side of the Bellman equation not involving I, the
manager’s instantaneous problem is
max I q ( K , ε ) − c( I , K ).
I∈ (10) Assume first that investment is perfectly reversible (P+ = P− ), with no fixed
costs of adjustment (a = 0), and no covenant restriction on asset sales. Under
these three assumptions, the function c is smooth and optimal instantaneous
investment equates the marginal cost of investment with marginal q
c I ( I ∗ , K ) = q ( K , ε ). (11) Abel and Eberly’s (1994) characterization of the investment rule in the presence of fixed costs of adjustment and irreversibilities carries over to our setting,
with the exception that the relevant shadow price in our model is the shadow
price of capital to equity. In the interest of avoiding redundancy, we refer readers to their paper, noting that fixed costs of adjustment and irreversibilities
generate a region where optimal investment is zero and insensitive to perturbations in the shadow price of capital. It is sufficient to note that the optimal
investment rule for the basic model presented in this section satisfies
I ∗ c I ( I ∗ , K ) = I ∗ q ( K , ε ).
4
5 Formally, investment and stopping time are adapted to the natural filtration.
Verification is standard (see Fleming and Soner (1993)). (12) 1722 The Journal of Finance The optimality condition (12) also holds if senior debt includes a covenant prohibiting asset sales. In this case, when the shadow price of capital is sufficiently
low, the nonnegativity constraint binds and I∗ = 0.
C. Derivation of Marginal q
Proposition 1 contains a simple expression for q that is useful in interpreting
the nature of the underinvestment problem.
PROPOSITION 1: The shadow price of capital to equity is
T q ( K 0 , ε0 ) = E e−(r +δ)t [π K ( K t , εt ) − c K ( It , K t )] d t . 0 Proof: See Appendix A.
Marginal q is simply the discounted value of the effect of a unit of installed
capital on cash f low to equity prior to the expected default date. The discount
rate is r + δ due to exponential depreciation. Lemma 1 in Abel and Eberly (1994)
is the analog under firstbest. The only difference between their expression for
the shadow price of capital to the unlevered firm and that in Proposition 1
is that their upper limit of integration is infinity. Therefore, underinvestment
relative to firstbest is due to truncation of equity’s horizon.
It is generally argued that the underinvestment problem is more severe for
firms in distress. In the model, distress corresponds to short horizons (low T in
expectation). More formally, underinvestment is more severe in distress due to
the smooth pasting condition (q = 0) that is satisfied along the optimal default
contour.6 For reasonable specifications of the adjustment cost function, the optimal investment rule when q approaches zero entails negative investment if
allowed. Here one sees an obvious role for debt covenants.7
Note that underinvestment is properly treated as distinct from the asset substitution problem, first discussed in Jensen and Meckling (1976). It is possible
to extend the model and permit endogenous risk choice by including σ as a
control. The Bellman equation (8) is separable in (I, σ ), so that the characterization of the optimal investment level remains correct when σ is a control. High
volatility is optimal when equity is convex in ε , which is necessarily the case
near the default contour, indicating that the optimal policy for distressed firms
entails paying the maximum dividend allowed by the debt covenant, since q
approaches zero, and speculating with any remaining funds.
In the event of default, the lender(s) take over an unlevered firm and implement firstbest. The value function for the unlevered firm is denoted V .
Following Leland (1994), it is assumed that a fraction α ∈ [0, 1] is lost during
the reorganization process. Absent issuance of additional collateralized debt,
6 See Dumas (1991) for a discussion of smooth pasting conditions.
See Morellec (2001) for analysis of the relation between covenants, liquidity in secondary asset
markets, and underinvestment.
7 Tobin’s Q, Debt Overhang, and Investment 1723 the value of the senior debt, denoted D, is equal to the value of coupon payments
plus total recoveries in default:
T D ( K 0 , ε0 ) = E e−rt b d t + e−rT (1 − α )V ( K T , εT ) . (13) 0 It is convenient to split the senior debt value into two pieces, the value of the
coupons and the value of total recoveries in default (R):
T D ( K 0 , ε0 ) = E e−rt b d t + R ( K 0 , ε0 ), (14) 0 R ( K 0 , ε0 ) ≡ (1 − α ) E [e−rT V ( K T , εT )]. (15) Average Q is equal to the ratio of the market value of the firm to the current
capital stock:
Q ( K 0 , ε0 ) ≡ S ( K 0 , ε0 ) + D ( K 0 , ε 0 )
.
K0 (16) The relationship between average Q and equity’s marginal q is given in Proposition 2.8
PROPOSITION 2: If π is homogeneous degree one in K ; c is homogeneous degree one
in (I, K ); and the ﬁrm is prohibited from issuing additional secured debt, then
the shadow price of capital to equity is equal to average Q, less the normalized
current market value of total default recoveries (R):
q ( K 0 , ε0 ) = Q ( K 0 , ε0 ) − R ( K 0 , ε0 )
.
K0 Proof: See Appendix A.
Note that in the absence of debt, we arrive at Lemma 2 from Abel and Eberly
(1994), which states that for the unlevered firm q = Q under linear homogeneity. The intuition behind Proposition 2 is as follows. The manager of the levered
firm takes into account only those benefits accruing prior to default. Average
Q overstates marginal q by incorporating postdefault returns to investment
through its inclusion of the portion of senior debt value attributable to recoveries in default. Postdefault investment returns must be netted out in order to
determine the shadow price of capital to equity.
Corollary 1, which might initially seem counterintuitive, follows directly from
the preceding argument.
COROLLARY 1: If the ﬁrm is prohibited from issuing additional secured debt,
then for a given coupon on existing (sunk) debt, larger bankruptcy costs imply a
smaller wedge between average Q(K , ε ) and levered marginal q(K , ε ). When all
value is lost in bankruptcy (α = 1), Q(K , ε ) = q(k, ε ).
If π and c are homogeneous degree ρ , then q = ρ (Q − R/K ). Although treated in Abel and Eberly
(1994), the assumption seems dubious for ρ = 1.
8 1724 The Journal of Finance Proof: Consider two firms indexed by h and l with αh > αl at the same point
in (K , ε) space with the same coupon commitment b. The S and q functions are
identical, as is the stopping policy T . Therefore, Rh (K , ε ) < Rl (K , ε ). If αh = 1,
then Rh (K , ε ) = 0. The result follows from Proposition 2. Q.E.D.
The intuition for Corollary 1 is as follows. The wedge between average Q
and marginal q stems from value left on the table for the senior lender. When
bankruptcy costs are high, recoveries in default are low, resulting in a smaller
wedge. Note that Corollary 1 is based on the assumption that the benefits from
issuing the senior debt are already sunk. Section II considers an alternative
setting in which the firm is able to issue new secured debt in order to finance
a portion of incremental investment.
Drawing inferences about investment incentives from average Q is particularly misleading near the default date. This is because the smoothpasting
condition for endogenous default demands q(KT , εT ) = 0. However,
Q ( K T , εT ) = D ( K T , εT )
(1 − α )V ( K T , εT )
=
,
KT
KT (17) which is strictly positive if α < 1. Intuitively, investment near default produces
benefits accruing almost entirely to lenders, which are capitalized into debt
value and average Q.
D. Role of Asset Life
Given that overhang is due to truncation of equity’s horizon, intuition suggests that the underinvestment problem is more severe for longlived assets. We
confirm this intuition by contrasting the investment decisions of levered and
unlevered firms. Consider a pricetaking firm with Cobb–Douglas production
technology under constant returns to scale. The price process is stochastic and
adjustment costs are independent of K .
Summarizing the assumptions:
F ( K , N ) = N θ K 1−θ ,
θ ∈ (0, 1),
π ( K , p) ≡ max pF ( K , N ) − wN ,
N (18) d pt = σ pt dW t ,
cK ( I , K ) ≡ 0 for all ( I , K ). Under these assumptions, the profit function is linear in K . In particular,9
π ( K , p) = hpζ K ,
9 h ≡ (1 − θ )θ θ/(1−θ ) w−θ/(1−θ ) > 0, See Abel and Eberly (1994, p. 1378) for a derivation. ζ ≡ 1/(1 − θ ) > 1. (19) Tobin’s Q, Debt Overhang, and Investment 1725 We now relate the shadow price of capital to the levered firm (ql ), with that of
the unlevered firm (qu ). Abel and Eberly (1994) show that
∞ qu ( pt ) = h
0 ζ hpt ζ e−(r +δ)s Et pt +s d s = r + δ − 1 ζ (ζ − 1)σ 2
2 . (20) Applying Proposition 1, it follows that
T ql ( p0 ) = E ζ e−(r +δ)t hpt d t . (21) 0 Combining (20) and (21), it follows that
ql ( p0 ) = qu ( p0 ) − E e−rT (e−δ T )qu ( pT ) . (22) Expression (22) clarifies the source of underinvestment. The equitymaximizing
manager does not incorporate postdefault returns into his computation of the
shadow price. At the default date T , the value to the unlevered firm of the undepreciated portion of a machine purchased at date zero is equal to e−δT qu (pT ).
As shown in (22), it is this term that creates underinvestment relative to firstbest. Note that in addition to the expected horizon (T ), the depreciation rate
(δ ) is an important determinant of the difference between the shadow price of
capital for unlevered and levered firms.
II. Extended Model with Secured Debt
Myers (1977) noted that firms can mitigate the overhang problem if incremental investment is (partially) financed with new secured debt. In our neoclassical capital accumulation framework, issuance of new secured debt mitigates
overhang by allowing equity to capture a portion of postdefault returns by
pledging collateral to new lenders.10 After modeling this effect, the objective is
to determine how secured loans affect the relationship between marginal q and
average Q.
Assume that for each new unit of capital purchased, the senior debt covenant
allows the firm to raise a fixed amount λ through zero coupon secured debt.
The parameter λ is interpreted as a measure of the firm’s ability to issue new
secured debt. In the model, the entire value of new secured debt is derived
from the underlying pledged collateral. We assume that the new debt carries
no coupon payments in order to highlight the role of pledged collateral. In
particular, the value of pledged collateral accounts for the entire increase in
NPV to equity, constituting a transfer from senior lenders.
Each new secured loan gives the respective lender rights to some fraction (γt )
of the particular piece of capital that her funds partially financed. Senior debt
retains rights over existing capital and the unsecured portion (1 − γt ) of new
10 Deviations from absolute priority in favor of equity would serve a similar purpose. 1726 The Journal of Finance capital. Since all debt is secured by some asset, disinvestment is prohibited. In
the event of default, total reorganized firm value is allocated in proportion to
the percentage of physical capital over which individual lenders have rights.
For instance, if a particular lender has rights over a fraction γt of a machine
purchased at time t and default occurs at time T > t, then the value recovered
by this lender is
γt e−δ(T −t )
KT (1 − α )V ( K T , εT ). (23) Lemma 1, proved by Abel and Eberly (1994), is a useful result utilized below.
LEMMA 1: If π is homogeneous degree one in K and c is homogeneous degree one
in (I, K ), then unlevered ﬁrm value is linear in K and may be represented as
V ( K , ε) = v(ε) K .
Using Lemma 1, the expression given in (23) simplifies to
γt (1 − α )e−δ(T −t ) v(εT ). (24) Since secured debt is priced at λ, it must be the case that for all t < T :
λ = γt (1 − α ) Et [e−(r +δ)(T −t ) v(εT )]. (25) The pricing identity (25) is utilized in the derivation of marginal q presented
in Appendix A.
The equity value function in the extended model is
T S ( K 0 , ε0 ) ≡ max E
I ∈ ,T e−rt [π ( K t , εt ) − c( It , K t ) + λ It − b] d t . (26) 0 Note that the only change in the objective function is the term λIt , which represents the amount raised with new secured debt. Following the same steps as
in Section I, it follows that the optimal investment policy satisfies
I ∗ c I ( I ∗ , K ) − λ = I ∗ q ( K , ε). (27) Outside of corner solutions, at which I∗ = 0, the optimality condition is
c I ( I ∗ , K ) = q ( K , ε ) + λ. (28) Proposition 3 is useful in interpreting condition (28).
PROPOSITION 3: In the extended model with the ﬁrm being allowed to issue additional secured debt, the shadow price of capital to equity is
T q ( K 0 , ε0 ) = E e−(r +δ)t [π K ( K t , εt ) − c K ( It , K t )] d t . 0 Proof: See Appendix A.
Note that the shadow price of capital to equity is the same as that presented
in Section I. This is not surprising, given that the secured debt does not change Tobin’s Q, Debt Overhang, and Investment 1727 the cash f low rights of equity, nor the value of its claim in default, which is
zero. Rather, the secured debt has simply redistributed some of the recovery
claim value to new lenders. This transfer is captured by equity when new debt
is issued. Condition (28) shows that the ability to collateralize new debt serves
as a subsidy to investment. The effect is equivalent to reducing the purchase
price of capital from P+ to P+ − λ, with the optimality condition indicating that
investment is strictly increasing in λ, excluding corner solutions.
Despite the fact that the shadow price of capital to equity is unchanged,
Proposition 4 demonstrates that the mapping between marginal q and average
Q is changed when the firm is allowed to issue new secured debt.
PROPOSITION 4: If π is homogeneous degree one in K ; c is homogeneous degree one
in (I, K ); and the ﬁrm raises λ per unit of new capital with pledged collateral, then
the shadow price of capital to equity is equal to average Q, less the normalized
current market value of total default recoveries, plus the normalized value of
future pledged collateral:
R ( K 0 , ε0 )
q ( K 0 , ε0 ) = Q ( K 0 , ε 0 ) −
+
K0 T λE e−rt It d t 0 . K0 Proof: See Appendix A.
Proposition 2 assumes that senior debt recovers all value in default, implying
that the entire normalized recovery claim value (R/K ) must be subtracted from
Q in order to compute equity’s marginal q. In contrast, when the firm is able to
issue new secured debt, the value of existing debt includes R minus the value
pledged to new lenders. In order to derive equity’s marginal q, only this net
value must be subtracted from average Q. To illustrate this more formally, note
that the value of senior debt in the context of the extended model is
T D ( K 0 , ε0 ) = E T e−rt b d t + R ( K 0 , ε0 ) − λ E0 0 e−rt It d t . (29) 0 Comparison of (14) and (29) reveals that in both the basic and extended models,
the wedge between average Q and levered marginal q is attributable to the
portion of senior debt value coming from recoveries in default.
III. Empirical Testing
A. Structural Investment Equation
Following a number of authors, empirical estimation is based upon the following linear homogeneous quadratic adjustment cost function:11
c( I j t , K j t ) = I j t + 1
ηK jt
2 I
K 2 −δ . (30) jt 11
See Summers (1981), Poterba and Summers (1983), Chirinko (1987), and Whited (1992), for
example. 1728 The Journal of Finance Under this adjustment cost function, the optimality condition from the extended
model (28) simplifies to
I
K = δ−
jt 1
η + λj
1
+ qjt.
η
η (31) Although we assume a smooth adjustment cost function for the purpose of
estimation, the derivations of q presented above allow for a wedge between
the buy and sell prices of capital, fixed costs of adjustment, and prohibitions on
asset sales. Data limitations preclude estimation of the nonlinear investmentq
relationships implied by these frictions. See Abel and Eberly (2001) and Barnett
and Sakellaris (1998) for empirical tests of the theory under the assumption
that the manager implements firstbest.
Estimation is based on the optimality condition (31). Substituting in the q
expression from Proposition 4 yields
I
K 1
η = δ−
jt 1 +
η
Now define the parameter jt + T λ j Et
t R
K jt e−r (s−t ) Is d s + ujt. Kt (32) as follows:
T λ j Et
jt 1
1
1
Q jt + λ j −
η
η
η e−r (s−t ) Is d s t ≡ ∈ [0, 1]. R jt Therefore, jt is a measure of the relative importance of collateral pledged to
future lenders. For instance, if the firm cannot secure any future loans, jt =
0. Conversely, if future secured lenders capture all postdefault returns, then
jt = 1. Using this definition, we may rewrite the regression equation (32) as
I
K = δ−
jt 1
η + 1
1
1
λ j + Q jt −
η
η
η R
K +
jt jt η R
K + ujt. (33) jt Suppose firms can be classified into “high” and “low” groups according to their
ability to collateralize future loans, with H > L and λH > λL . Sorting in this
way and letting HIGH be an indicator function, the regression equation (33)
becomes:
I
K = δ−
jt − 1 λL
+
η
η 1−
η L +
R
K 1
Q jt +
η
+
jt λ H − λL
η
H −
η L HIGH j t
HIGH × R
K + ujt.
jt (34) Tobin’s Q, Debt Overhang, and Investment 1729 Equation (34) serves as the theoretical basis for the empirical specification. The
sorting of firmyears into high and low categories is based on two measures of
ability to issue future secured debt. The first sorting criterion is whether the
S&P debt rating is at/below BB+ or above BB+, which is the traditional cutoff
for determining “investment grade” status. Firms with debt obligations below
investment grade are more likely to face binding debt covenant prohibitions on
future debt issuance. The second sorting criterion is whether the firm belongs
to an industry that has historically enjoyed a recovery ratio on defaulted debt
above the median value in our sample. Recovery ratios by threedigit SIC code
are taken from Altman and Kishore (1996), who compute averages over the
period 1971–1995. Firms in industries with recovery ratios at or above the
sample median of 41.5% are categorized as having HIGH status.
B. Estimation Procedure
Caballero (1997) documents poor performance of the standard Q theory in explaining aggregate and firmlevel investment. Frequently, the coefficients on Q
are insignificant, while measures of liquidity enter positively and significantly.
A possible explanation is that average Q is necessarily measured with error.
Using measurement errorconsistent GMM estimators, Erickson and Whited
(2001) find that most common approaches generate poor proxies for true Q.
Therefore, in moving from theory to data, our major concern is dealing with
the lack of a clean measure of the shadow price of capital to the firm, which is
equal to average Q under the stated homogeneity assumptions.
For the purpose of empirical testing, we depart from ordinary least squares
(OLS) and employ the measurement errorconsistent GMM estimator presented
in Erickson and Whited (2002). Using this estimator, Erickson and Whited
(2000) find that many stylized facts in the empirical investment literature potentially result from measurement error in Q. In particular, they find that
cash f low becomes insignificant, while the point estimates of the Qcoefficient
roughly triple in magnitude relative to the OLS baseline estimation. We describe how their GMM estimator is applied to our model below.
Let z be the vector of explanatory variables, excluding Q. In addition to the
explanatory variables generated directly by the theory (see (34)), we estimate
separate cash f low coefficients for firms with debt above and below investment
grade. Letting CF A and CF B denote cash f low for firms above and below investment grade, respectively, we have:
z ≡ HIGH , R
R
, HIGH ×
K
K , C F A, C F B . (35) There are two motivations for adding cash f low in this way. First, some would
argue that liquidity is an important determinant of investment, with the effect being most pronounced for weak firms. Second, adding these regressors
was necessary to ensure a reasonable degree of confidence in satisfying the
identifying assumptions required to use the GMM estimators.12
12 Interacting cash f low and a size dummy, as in Erickson and Whited (2000), produced weak
evidence for model identification. 1730 The Journal of Finance Let B represent the vector of regression coefficients on z and β the true
coefficient on unobserved Q, which, according to the model, is the reciprocal of
η. Then the regression equation (34) for firm j may be written as
I
K ≡ ij = zj B + βQ j + uj . (36) j The true value of Q is unobserved, with x denoting the noisy proxy, which is
represented as
x j = constant + Q j + j. (37) Now let ω denote the residual from the projection of Q on z:
ω j ≡ Q j − z j mQ , m Q ≡ [ E (z j z j )]−1 E [z j Q j ]. (38) The following assumptions are made:
A1 : E [u j ] = 0, independent of (z j , Q j ). A2 : (u j , A3 : E [ j ] = 0, independent of (u j , z j , Q j ). A4 : β = 0. A5 : E ω3 = 0.
j j, z j , Q j ) ∼ i.i.d. for all j . A1 and A2 are standard. Given the numerous approximations that are necessarily made in constructing any measure of Q, it is important to note that A3
is satisfied for classical measurement error, implying the GMM estimator is
robust, while the presence of such measurement error causes OLS to produce
downwardbiased Q coefficients and contaminated coefficients on other regressors.13 A test for satisfaction of the identifying conditions A4 and A5 is provided
below.
The endogeneity of leverage creates possible concern regarding the satisfaction of A1 and A3. First, due to agency costs, firms with good growth options can
be expected to issue less debt. Coupling good growth options with low leverage
leads to high investment. However, if the data reveal that such firms do invest
more, it is precisely because they anticipated the ex post incentive compatible
investment policy for equity, as given by (34). That is, causation works from
leverage to investment, and not vice versa. Therefore, there is no a priori reason to assume that the endogenous choice of leverage causes violation of the
stated independence assumptions.
A second more troubling concern is the issuance of debt in order to fund
contemporaneous investment. This may lead to violation of A1. As a robustness
check, we estimate all specifications using current R/K and then lagged R/K .
The tradeoff here is that using lagged R/K cuts one year from the sample.
13 See Greene (1997, p. 440) for a discussion. Tobin’s Q, Debt Overhang, and Investment 1731 Anticipating, results do not vary with the lag structure. As a final check, we
conduct a GMM J test of the overidentifying restrictions to detect violations of
the stated assumptions needed to ensure consistency.
We now move on to discussion of the moment conditions exploited in the
estimation process. Let
mi ≡ [ E (z j z j )]−1 E [z j i j ] (39) mx ≡ [ E (z j z j )]−1 E [z j x j ]. 2
There are three secondorder moment conditions, with four unknowns: β , E(ωj ),
E(u2 ), and E( j2 )
j E (i j − z j mi )2 = β 2 E ω2 + E u2 ,
j
j
E (i j − z j mi )(x j − z j mx ) = β E ω2 ,
j
E ( x j − z j m x )2 = E ω 2 + E
j (40)
2
j . We have the following thirdorder moment conditions:
E (i j − z j mi )2 (x j − z j mx ) = β 2 E ω3 ,
j
E (i j − z j mi )(x j − z j mx )2 = β E ω3 .
j (41) 3
The two additional moment conditions give us only one more unknown, E[ωj ].
Under A4 and A5, (40) and (41) represent a system of five equations in five
unknowns based on moment conditions up to the thirdorder. Proceeding in
similar fashion, it is possible to show that using higher order moment conditions
produces overidentified systems, offering alternative parameter estimates, and
serving as the basis for overidentification tests.
This procedure produces a parameter estimate for each year of crosssectional
data. However, it is asymptotically more efficient to minimize a quadratic in
the vector of unknown parameters, where the matrix of the quadratic form
is the inverse of the asymptotic covariance matrix. This is referred to as the
classical minimum distance estimator. Following Erickson and Whited (2000),
we present classical minimum distance parameter estimates, beginning with
those based on product moments up to the thirdorder (GMM3) and continuing
up to those based on product moments up to the fifthorder (GMM5). C. Data
In order to clarify the exact role played by the overhang correction, we use the
Erickson and Whited (2000) data, which are drawn from a sample of 3,869 manufacturing firms in SIC’s 20003999. Firms with missing data, potential coding
errors, or mergers accounting for more than 15% of book value are deleted. This
results in a balanced panel of 737 firms over the period 1992 to 1995. Since bond
ratings are needed in order to impute the value of R/K and to sort firms into 1732 The Journal of Finance
Table I Descriptive Statistics
The full sample consists of the 278 firms with bond ratings included in Erickson and Whited (2000)
data during the period 1992 to 1995. Data are normalized by the estimated replacement value of the
capital stock. Investment is total reported spending on plant, property, and equipment, excluding
spending on acquisitions. Average Q is the estimated market value of the capital stock, exclusive
of inventories, normalized by the replacement value of the capital stock. Details regarding the
required imputations for computing Q are provided in Whited (1992). Cash f low is equal to income
plus depreciation. The recovery claim is the imputed market value of total lender recoveries in
default. Details on the imputation are provided in Appendix B.
25th
Percentile Median 75th
Percentile Average Standard Deviation Full Sample
Normalized investment
Average Q
Normalized cash f low
Normalized recovery claim 0.060
0.725
0.080
0.004 0.100
1.505
0.120
0.008 0.150
2.895
0.170
0.026 0.120
2.254
0.136
0.029 0.100
2.283
0.080
0.063 Above Investment Grade
Normalized investment
Average Q
Normalized cash f low
Normalized recovery claim 0.070
0.840
0.090
0.003 0.110
1.750
0.120
0.006 0.160
3.115
0.170
0.012 0.125
2.478
0.136
0.012 0.098
2.386
0.067
0.021 Below Investment Grade
Normalized investment
Average Q
Normalized cash f low
Normalized recovery claim 0.035
0.540
0.070
0.027 0.070
0.955
0.115
0.049 0.120
1.705
0.170
0.096 0.096
1.491
0.134
0.088 0.094
1.679
0.114
0.108 Variable high and low categories, we drop those firms for which ratings are not available
for all 4 years, leaving us with a balanced panel of 278 firms. Details regarding
the method used to compute average Q may be found in Whited (1992). The
imputation of R/K is discussed in Appendix B.
Table I reports descriptive statistics. From the sample of 1,112 firmyear
observations, 252 (22.7%) are below investment grade. Firms below investment
grade exhibit much lower investment and Q values, and slightly lower cash
f low. Of particular interest is the fact that the normalized recovery claim (R/K )
is much larger for firms below investment grade. The median value of R/K
is equal to 0.049 for firms below investment grade, but only 0.006 for firms
above investment grade. The mean (median) ratio of R/K to average Q is 11%
(6%) for firms below investment grade. By way of contrast, the mean (median)
ratio of the R/K to average Q is only 0.8% (0.6%) for those above investment
grade.
D. Estimation Results
The theory is tested using four variants of the vector of regressors listed in
(35). Models 1 and 2 use bond ratings above investment grade as the basis Tobin’s Q, Debt Overhang, and Investment 1733 Table II pValues from Identification Tests
The null hypothesis is that the true Q coefficient is zero and/or that the residuals from a projection
of true Q on the other regressors, excluding measured Q, are not skewed. The model is identified if
the null is false. Model 1 uses the following regressors: Q; dummy for bond rating above investment
grade; separate cash f low variables for firms above and below investment grade; R/K , which is the
imputed market value of lenders’ recovery claim in default normalized by the capital stock; and
R/K interacted with the indicator for bond rating above investment grade. Model 2 is identical
to Model 1, with the exception that the lagged value of R/K is used instead of the current value.
Model 3 uses the following regressors: Q; dummy for recovery ratio at/or above sample median of
41.5%; separate cash f low variables for firms above and below investment grade; R/K ; and R/K
interacted with the indicator for recovery ratio above the sample median. Model 4 is identical to
Model 3, with the exception that the lagged value of R/K is used instead of the current value. The
sample consists of the 278 firms with bond ratings included in Erickson and Whited (2000) data
during the period 1992 to 1995.
1992
Model 1
Model 2
Model 3
Model 4 1993 1994 1995 0.077
NA
0.039
NA 0.066
0.061
0.087
0.078 0.090
0.091
0.127
0.125 0.035
0.031
0.028
0.026 for categorizing a firmyear as having HIGH status. The difference between
Models 1 and 2 is that the former uses contemporaneous R/K , while the latter
uses lagged R/K as a robustness check. Models 3 and 4 use industryspecific
recovery ratios as the basis for categorizing a firm as having HIGH status, with
the former using contemporaneous R/K and the latter using lagged R/K as a
robustness check.
Recall that the models are identified only if the coefficient on true Q is nonzero
and the residuals from a projection of true Q on the vector of other regressors
are skewed. Table II reports pvalues from identification tests, where the null
3
hypothesis is that β = 0 and/or E[ωj ] = 0. There is reasonable basis for rejecting
the null for all model variants. For Models 1 and 2, the null is rejected at the 10%
level in each year. The case for identification is somewhat weaker for Models
3 and 4, with the pvalues below 10% for all years other than 1994, where the
pvalues are just under 13%.
Table III reports parameter estimates for Model 1. For the purpose of contrast, we report parameter estimates from OLS in addition to those from GMM3
to GMM5. Consistent with the results in Erickson and Whited (2000), the
Qcoefficients generated using GMM are more than three times the magnitude
of the point estimates from OLS. The existence of debt overhang is supported
by the negative coefficient on R/K , which is always statistically significant.
Erickson and Whited document that ttests on perfectly measured regressors
tend to overreject in finite samples. The high degree of significance suggests
that this is not an important concern. The coefficient on R/K is also economically significant. To see this, note that if L = 0, the structural model indicates that the coefficients on average Q and R/K are equal to η−1 and −η−1 , 1734 The Journal of Finance
Table III Test of Overhang Effect by Bond Rating Using the Current Value
of the Normalized Recovery Claim (Model 1)
The dependent variable is capital expenditures normalized by the capital stock. The explanatory
variables are: Q; dummy for bond rating above investment grade; separate cash f low variables for
firms above and below investment grade; R/K , which is the the imputed market value of lenders’
recovery claim in default normalized by the capital stock; and R/K interacted with the indicator
for bond rating above investment grade. We report minimum distance estimates corresponding to
the four types of crosssection estimators: OLS, GMM3, GMM4, and GMM5. The sample consists
of the 278 firms with bond ratings included in Erickson and Whited (2000) data during the period
1992 to 1995. Standard errors are reported in parentheses. For OLS, White standard errors are
reported.
OLS
Intercept
Average Q
DUM = 1 if rating above BB+
R/K
DUM ∗ (R/K )
Cash f low: Rating at/below BB+
Cash f low: Rating above BB+
R2 GMM3 GMM4 0.025∗∗∗ 0.030∗∗∗ 0.031∗∗∗ (0.008)
0.013∗∗∗
(0.003)
0.007
(0.013)
−0.174∗∗∗
(0.053)
−0.200
(0.214)
0.441∗∗∗
(0.040)
0.483∗∗∗
(0.094)
0.391 (0.008)
0.041∗∗∗
(0.011)
−0.005
(0.018)
−0.312∗∗∗
(0.094)
0.039
(0.399)
−0.004
(0.125)
−0.123
(0.253)
0.642 (0.008)
0.037∗∗∗
(0.002)
0.004
(0.015)
−0.125∗∗
(0.052)
−0.170
(0.197)
0.251∗∗∗
(0.043)
0.054
(0.131)
0.651 GMM5
0.031∗∗∗
(0.008)
0.052∗∗∗
(0.003)
0.003
(0.015)
−0.173∗∗∗
(0.059)
−0.090
(0.212)
0.208∗∗∗
(0.047)
−0.152
(0.144)
0.602 The symbols ∗∗∗ , ∗∗ , and ∗ indicate statistical significance at the 1, 5, and 10% levels, respectively. respectively. The estimated coefficients on R/K are well in excess of typical estimates of the Q coefficient. The insignificant coefficients on the dummy variable
for HIGH status and the interaction term between HIGH and R/K indicate that
issuance of additional secured debt does not mitigate the overhang effect for
firms with high debt ratings.
Table IV contains parameter estimates from Model 2, where lagged R/K is
used as a regressor in order to deal with potential endogeneity concerns. The
parameter estimates from Model 2 are similar to those from Model 1, with the
coefficients on Q and R/K always significant at the 1% level. Once again, we
find no evidence that the overhang effect is mitigated for higherrated firms,
with the indicator for HIGH status and the interaction term insignificant across
all specifications.
The parameter estimates from Models 3 and 4, which use recovery ratios as
the basis for assigning firms HIGH status, are contained in Tables V and VI. The
results are similar to those for Models 1 and 2. Average Q and R/K are always
significant at the 1% level. The insignificance of the HIGH dummy variable Tobin’s Q, Debt Overhang, and Investment 1735 Table IV Test of Overhang Effect by Bond Rating Using the Lagged Value
of the Normalized Recovery Claim (Model 2)
The dependent variable is capital expenditures normalized by the capital stock. The explanatory
variables are: Q; dummy for bond rating above investment grade; separate cash f low variables
for firms above and below investment grade; lagged R/K , which is the imputed market value
of lenders’ recovery claim in default normalized by the capital stock; and lagged R/K interacted
with the indicator for bond rating above investment grade. We report minimum distance estimates
corresponding to the four types of crosssection estimators: OLS, GMM3, GMM4, and GMM5. The
sample consists of the 278 firms with bond ratings included in Erickson and Whited (2000) data
during the period 1993 to 1995. Standard errors are reported in parentheses. For OLS, White
standard errors are reported.
OLS
Intercept
Average Q
DUM = 1 if rating above BB+
Lagged (R/K )
DUM ∗ Lagged (R/K )
Cash f low: Rating at/below BB+
Cash f low: Rating above BB+
R2 GMM3 GMM4 0.019∗∗ 0.033∗∗∗ 0.030∗∗∗ (0.009)
0.012∗∗∗
(0.003)
0.006
(0.014)
−0.220∗∗∗
(0.068)
−0.011
(0.225)
0.520∗∗∗
(0.046)
0.477∗∗∗
(0.100)
0.408 (0.009)
0.043∗∗∗
(0.010)
−0.008
(0.018)
−0.333∗∗∗
(0.096)
0.120
(0.443)
−0.059
(0.112)
−0.162
(0.251)
0.627 (0.008)
0.063∗∗∗
(0.004)
0.006
(0.016)
−0.215∗∗∗
(0.074)
−0.085
(0.264)
0.142∗∗
(0.068)
−0.009
(0.156)
0.636 GMM5
0.030∗∗∗
(0.008)
0.066∗∗∗
(0.004)
0.005
(0.016)
−0.272∗∗∗
(0.082)
−0.089
(0.309)
0.143∗
(0.073)
−0.270
(0.179)
0.591 The symbols ∗∗∗ , ∗∗ , and ∗ indicate statistical significance at the 1, 5, and 10% levels, respectively. and the interaction term indicate that there is no evidence for mitigation of the
overhang effect for firms expected to have superior ability in issuing additional
secured debt.
Table VII reports pvalues for the J statistics of the alternative models. The
results are consistent with the overidentifying restrictions, given that we fail
to reject at the 5% level, while finding only three rejections at the 10% level.
Taken together, these results provide strong evidence in favor of the existence
of debt overhang and against the notion that firms utilize additional secured
debt issuance as a device for mitigating the problem. Although this second
finding runs counter to standard theory, a number of potential explanations are
possible. First, incremental investment may take the form of assets that are
inherently difficult to pledge as collateral. Second, existing covenant protections
may be sufficient to give senior lenders inviolable collateral. Finally, even in
the absence of binding credit constraints, firms may be reluctant to expropriate
existing lenders due to reputational concerns.
The data suggest a potential puzzle, however. Note that in the absence of a collateral channel, the basic structural model implies that coefficients on average 1736 The Journal of Finance
Table V Test of Overhang Effect by Recovery Ratio Using the Current Value
of the Normalized Recovery Claim (Model 3)
The dependent variable is capital expenditures normalized by the capital stock. The explanatory
variables are: Q; dummy for recovery ratio at/above the sample median of 41.5%; separate cash f low
variables for firms above and below investment grade; R/K which is the imputed market value
of lenders’ recovery claim in default normalized by the capital stock; and R/K interacted with the
indicator for recovery ratio at/above the sample median. We report minimum distance estimates
corresponding to the four types of crosssection estimators: OLS, GMM3, GMM4, and GMM5. The
sample consists of the 278 firms with bond ratings included in the Erickson and Whited (2000)
data during the period 1992 to 1995. Standard errors are reported in parentheses. For OLS, White
standard errors are reported.
OLS
Intercept
Average Q
DUM = 1 if recovery ratio ≥ 41.5%
R/K
DUM ∗ (R/K )
Cash f low: Rating at/below BB+
Cash f low: Rating above BB+
R2 GMM3 GMM4 0.028∗∗∗ 0.030∗∗∗ 0.031∗∗∗ (0.007)
0.013∗∗∗
(0.003)
0.009
(0.008)
−0.226∗∗∗
(0.068)
0.028
(0.080)
0.417∗∗∗
(0.047)
0.445∗∗∗
(0.074)
0.394 (0.011)
0.047∗∗∗
(0.011)
−0.001
(0.011)
−0.318∗∗∗
(0.077)
−0.052
(0.114)
0.012
(0.148)
−0.251
(0.228)
0.654 (0.009)
0.042∗∗∗
(0.003)
0.004
(0.009)
−0.190∗∗∗
(0.063)
−0.070
(0.085)
0.272∗∗∗
(0.061)
−0.074
(0.097)
0.641 GMM5
0.030∗∗∗
(0.009)
0.038∗∗∗
(0.004)
0.005
(0.010)
−0.185∗∗∗
(0.065)
−0.140
(0.093)
0.236∗∗∗
(0.065)
−0.121
(0.111)
0.604 The symbols ∗∗∗ , ∗∗ , and ∗ indicate statistical significance at the 1, 5, and 10% levels, respectively. Q and R/K are equal to η−1 and −η−1 , respectively. However, our point estimates of the coefficients on R/K are roughly 3–5 times that on Q. A reasonable
interpretation of this finding is that the negative effect of debt on investment
is not limited to the overhang channel. For instance, Asquith, Gertner, and
Scharfstein (1994) find that firms encountering distress may cut investment
drastically in an attempt to maintain sufficient liquidity to avoid default. Similarly, it is possible that healthy firms respond to rating downgrades by hoarding
cash and avoiding discretionary capital expenditures. Formal tests of this channel, and others by which debt may reduce investment, offer an interesting area
for future research. IV. Conclusions
As the stock of theoretical models increases, the ability of corporate finance
economists to determine their significance will hinge upon our ability to spell
out precise testable hypotheses. Incorporating debt in a dynamic capital Tobin’s Q, Debt Overhang, and Investment 1737 Table VI Test of Overhang Effect by Recovery Ratio Using the Lagged Value
of the Normalized Recovery Claim (Model 4)
The dependent variable is capital expenditures normalized by the capital stock. The explanatory
variables are: Q; dummy for recovery ratio at/above the sample median of 41.5%; separate cash
f low variables for firms above and below investment grade; lagged R/K , which is the the imputed
market value of lenders’ recovery claim in default normalized by the capital stock; and lagged R/K
interacted with the indicator for recovery ratio at/above the sample median. We report minimum
distance estimates corresponding to the four types of crosssection estimators: OLS, GMM3, GMM4,
and GMM5. The sample consists of the 278 firms with bond ratings included in Erickson and Whited
(2000) data during the period 1993 to 1995. Standard errors are reported in parentheses. For OLS,
White standard errors are reported.
OLS
Intercept
Average Q
DUM = 1 if recovery ratio ≥ 41.5%
Lagged (R/K )
DUM ∗ Lagged (R/K )
Cash f low: Rating at/below BB+
Cash f low: Rating above BB+
R2 GMM3 GMM4 0.030∗∗∗ 0.030∗∗∗ 0.033∗∗∗ (0.007)
0.012∗∗∗
(0.003)
0.005
(0.008)
−0.248∗∗∗
(0.060)
0.184∗∗
(0.083)
0.453∗∗∗
(0.052)
0.477∗∗∗
(0.079)
0.411 (0.011)
0.047∗∗∗
(0.010)
0.002
(0.011)
−0.289∗∗∗
(0.071)
−0.009
(0.145)
−0.005
(0.137)
−0.258
(0.225)
0.641 (0.009)
0.060∗∗∗
(0.004)
0.000
(0.009)
−0.276∗∗∗
(0.063)
0.132
(0.104)
0.263∗∗∗
(0.073)
−0.172
(0.113)
0.624 GMM5
0.031∗∗∗
(0.009)
0.061∗∗∗
(0.006)
0.000
(0.010)
−0.293∗∗∗
(0.069)
0.065
(0.133)
0.209∗∗
(0.099)
−0.398∗∗∗
(0.153)
0.599 The symbols ∗∗∗ , ∗∗ , and ∗ indicate statistical significance at the 1, 5, and 10% levels, respectively. accumulation model, this paper derives an empirical proxy for levered equity’s
marginal Q, generating a direct test for debt overhang and mitigation of the
effect through issuance of additional secured debt. In the empirical section,
we tested the structural model finding that overhang is significant, with no
evidence that the problem is mitigated for firms with superior ability to issue
additional secured debt. In fact, our estimates suggest that the negative effect
of debt on investment is stronger than would be implied by the debt overhang
channel working in isolation.
The empirical analysis presented in this paper is necessarily limited to testing a subset of the testable hypotheses generated by the model, leaving open for
future research the following predictions regarding the relationship between asset life and endogenous leverage and investment determination. First, within
a given firm, debt overhang distorts investment composition and not simply
its level. In particular, overhang creates a greater relative bias against investments in longlived assets, such as land and physical plant, as opposed to
shortlived assets such as desktop computers. Second, the bias against 1738 The Journal of Finance
Table VII pValues for J Tests of Overidentifying Restrictions
The null hypothesis is that the overidentifying restrictions are valid. The abbreviation GMM4
refers to the generalized method of moments estimator based on moments up to the fourth order,
while GMM5 exploits moments up to the fifth order. Model 1 uses the following regressors: Q;
dummy for bond rating above investment grade; separate cash f low variables for firms above and
below investment grade; R/K, which is the imputed market value of lenders’ recovery claim in
default normalized by the capital stock; and R/K interacted with the indicator for bond rating
above investment grade. Model 2 is identical to Model 1, with the exception that the lagged value
of R/K is used instead of the current value. Model 3 uses the following regressors: Q; dummy for
recovery ratio at/or above sample median of 41.5%; separate cash f low variables for firms above
and below investment grade; R/K ; and R/K interacted with the indicator for recovery ratio above
the sample median. Model 4 is identical to Model 3, with the exception that the lagged value of
R/K is used instead of the current value. The sample consists of the 278 firms with bond ratings
included in Erickson and Whited (2000) data during the period 1992 to 1995.
Model 1 Model 2 Model 3 Model 4 0.444
0.523
0.209
0.112 NA
0.526
0.214
0.121 0.651
0.690
0.116
0.222 NA
0.665
0.122
0.226 GMM4
1992
1993
1994
1995 0.484
0.512
0.185
0.096 NA
0.505
0.204
0.115
GMM5 1992
1993
1994
1995 0.652
0.684
0.073
0.117 NA
0.691
0.063
0.170 particular asset classes is mitigated the greater their collateral value with respect to incremental debt finance. Finally, endogenous leverage determination
depends on the asset life of growth options held by the firm, and not simply
their standalone value. This casts doubt on the practice of treating average Q
as a sufficient statistic for the effect of growth options on optimal leverage.
Appendix A
We derive all the results for the extended model with new secured debt,
since the results for the basic model follow by setting λ = 0. For simplicity, we
introduce the infinitesimal generator A. For an arbitrary C2 function h of (K , ε),
Ito’s lemma implies:
E [d h] 1
1
≡ A(h) = ( I − δ K )h K + µ(ε)hε + σ 2 (ε )hεε .
dt
2 Proof of Propositions 2 and 4: The Bellman equation is
r S ( K , ε ) = max π ( K , ε ) − c( I , K ) + λ I − b + A( S ).
I (A1) Tobin’s Q, Debt Overhang, and Investment 1739 The Bellman equation holds identically in K for all (K , ε ), implying that the
derivatives with respect to K of the left and right sides of (A1) must match.
Differentiating with respect to K yields
r S K = π K − c K − δ S K + ( I − δ K ) S K K + µ(ε ) S K ε + 1 σ 2 (ε ) S K εε .
2 (A2) Using the generator A this may be rewritten as
rq = π K − c K + A(q ) − δ q . (A3) Multiplying by K and using the fact that KA(q) − δ qK = A(qK ) − qI, we have
rq K = π K K − c K K + A(q K ) − q I . (A4) Using the optimality condition (q + λ)I = cI I, and homogeneity of π and c yields
rq K = π − c + λ I + A(q K ). (A5) Subtracting (A5) from (A1) and rearranging terms yields
A( S − q K ) − r ( S − q K ) = b. (A6) Now define the Ito process ξ as
ξ ( K , ε, t ) ≡ e−rt [ S ( K t , εt ) − K t q ( K t , εt )]. (A7) Application of Ito’s lemma to ξ yields
d ξt = e−rt [ A( S − q K ) − r ( S − q K )] d t + e−rt σ (εt )( Sε − K qε ) d Wt . (A8) Substituting in (A6), we may rewrite dξ as
d ξt = e−rt b d t + e−rt σ (εt )( Sε − K qε ) d Wt . (A9) Integrating ξ up to the optimal default date T and taking expectations, we have
E e−rT ( S ( K T , εT ) − K T q ( K T , εT ))
T = S ( K 0 , ε0 ) − K 0 q ( K 0 , ε 0 ) + E e−rt b d t 0
T +E
0 e−rt σ (εt )[ Sε ( K t , εt ) − K t qε ( K t , εt )] d Wt . (A10) Substituting in the value matching and smooth pasting conditions, S(KT , εT ) =
0 and q(KT , εT ) = 0, and noting that the last term in (A10) is a martingale with
expectation zero, (A10) simplifies to
T K 0 q ( K 0 , ε0 ) = S ( K 0 , ε 0 ) + E e−rt b d t . (A11) 0 The last step is to derive the senior debt price, which carries a default claim
on existing capital plus the fraction of future investment not pledged to new 1740 The Journal of Finance lenders. Therefore,
T D ( K 0 , ε0 ) = E e−rt b d t + (1 − α ) 0
T × E e−rT v(εT ) e−δ T K 0 + (1 − γt )e−δ(T −t ) It d t . (A12) 0 From Lemma 1 we know that under the stated homogeneity assumptions
R ( K 0 , ε0 ) = (1 − α ) E e−rT v(εT ) K T . (A13) Additionally, the terminal capital stock is
T K T = e−δ T K 0 + e−δ(T −t ) It d t . (A14) 0 From (A13) and (A14) it follows that (A12) may be restated as
T D ( K 0 , ε0 ) = E e−rt b d t + R ( K 0 , ε0 ) 0
T −E e−rt [(1 − α )γt e−(r +δ)(T −t ) v(εT )] It d t . (A15) 0 Since secured debt carries price λ, we know ∀t < T
λ It d t = (1 − α )γt Et [e−(r +δ)(T −t ) v(εT )] It d t . (A16) From (A16), it follows that
T D ( K 0 , ε0 ) = E T e−rt b d t + R ( K 0 , ε0 ) − λ E 0 e−rt It d t . (A17) 0 Substituting (A17) into (A11) yields the result. Q.E.D. Proof of Propositions 1 and 3: Rearranging (A3) yields
A(q ) − (r + δ )q = −[π K − c K ]. (A18) Redefine the Ito process ξ as ξ (K , ε, t) ≡ e−(r+δ)t q(Kt , εt ) and repeat the procedures in equations (A8)–(A11). Q.E.D. Appendix B
Collections in the event of default are computed as longterm debt multiplied
by industry specific recovery ratios (rr). Recovery ratios by threedigit SIC code
are from Altman and Kishore (1996), who compute averages from 1971 to 1995.
Collections are multiplied by the value of a hitting claim paying one dollar
at default. Default probabilities (φjt ) by bond rating over a 20year horizon
are from Moody’s. Since the hitting claim could have a low or negative beta, Tobin’s Q, Debt Overhang, and Investment 1741 discount factors (dt ) are based on longterm Treasuries. The hitting claim value
is therefore
20 φ j t dt . (B1) t =1 Letting LTD denote the value of longterm debt, the imputation for R/K is
simply the product of recovery ratio, leverage, and the value of the hitting
claim:
R
K = rr j ∗ LT D
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