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Corporate Governance and Capital Structure Dynamics:
Evidence from Structural Estimation ∗
Erwan Morellec† Boris Nikolov‡ Norman Schurhoff§
July 2010
∗We thank an anonymous referee, the associate editor, the editor (Campbell Harvey), and DarrellDuffie for many valuable comments and Julien Hugonnier for suggesting an elegant approach to thecalculation of conditional densities in our setting. We also thank Tony Berrada, Peter Bossaerts, BernardDumas, Michael Lemmon, Marco Pagano, Michael Roberts, Rene Stulz, Toni Whited, Marc Yor, JeffZwiebel, and seminar participants at Boston College, Carnegie Mellon University, HEC Paris, the LondonSchool of Economics, the University of Colorado at Boulder, the University of Lausanne, the Universityof Rochester, the 2008 American Finance Association meetings, 2008 North American Summer Meetingsof the Econometric Society, and the conference on “Understanding Corporate Governance” organized bythe Fundacion Ramon Aceres in Madrid for helpful comments. The three authors acknowledge financialsupport from the Swiss Finance Institute and from NCCR FINRISK of the Swiss National ScienceFoundation.
†Swiss Finance Institute, Ecole Polytechnique Federale de Lausanne (EPFL), and CEPR. E-mail:erwan.morellec@epfl.ch. Postal: Ecole Polytechnique Federale de Lausanne, Extranef 210, QuartierUNIL-Dorigny, CH-1015 Lausanne, Switzerland.
‡William E. Simon Graduate School of Business Administration, University of Rochester. E-mail:boris.nikolov@simon.rochester.edu. Postal: Simon School of Business, University of Rochester, NY 14627Rochester, USA.
§Swiss Finance Institute, University of Lausanne, and CEPR. E-mail: norman.schuerhoff@unil.ch.Postal: Ecole des HEC, University of Lausanne, Extranef 239, CH-1015 Lausanne, Switzerland.
Abstract
We estimate a dynamic capital structure model to ascertain whether agency conflicts canexplain corporate financing decisions. The model features corporate and personal taxes, refi-nancing and liquidation costs, costly debt renegotiation, and allows managers to capture partof the firm’s cash flows as private benefits within the limits imposed by shareholder protec-tion. The analysis demonstrates that private benefits of control lead managers to issue lessdebt and rebalance capital structure less often than optimal for shareholders. Using data onfinancing choices and the model’s predictions for different moments of leverage, we find thatprivate benefits or agency costs of 1.02% of equity value on average (0.23% at median) are suf-ficient to resolve the conservative debt policy puzzle and to explain the time series of observedleverage ratios. We also find that the variation in agency costs across firms is sizeable and thatgovernance mechanisms significantly affect the value of control and firms’ financing decisions.
JEL Classification Numbers: G12; G31; G32; G34.
A central theme in financial economics is that incentive conflicts within the firm lead to dis-
tortions in corporate policy choices and, as a result, to lower corporate valuations. Because
debt limits managerial flexibility (Jensen, 1986), a particular focus of the theoretical research
has been on the importance of managerial objectives in the workings of financing decisions. A
prevalent view in the literature is that managers do not always make capital structure decisions
that maximize shareholder wealth. The capital structure of a firm should then be determined
not only by real market frictions, such as taxes, bankruptcy costs, or refinancing costs, as in
the seminal work of Fisher, Heinkel, and Zechner (1989), but also by the severity of incentive
conflicts between managers and shareholders. A variety of empirical evidence lends support to
this view.1 However, after more than two decades of research, how much do we really know
about the magnitude of manager-shareholder conflicts? In addition, how much do we know
about their effects on the dynamics and cross section of corporate capital structure?
The goal of this paper is to address these and related questions by exploiting the structural
restrictions from a dynamic capital structure model. To do this, we begin by formulating a
dynamic tradeoff model that emphasizes the role of agency conflicts in shaping firms’ financing
decisions. The model features corporate and personal taxes, refinancing costs, liquidation costs,
and costly renegotiation of debt in distress. In the model, each firm is run by a manager who
sets the firm’s financing, restructuring, and default policies. Managers act in their own interests
and can capture part of the firm’s cash flows as private benefits within the limits imposed by
shareholder protection. In this environment, we determine the optimal leveraging decision of
managers and characterize the effects of incentive conflicts between managers and shareholders
on financing decisions. We then use panel data on observed leverage choices and the model’s
predictions for different statistical moments of financial leverage to obtain firm-specific estimates
of unobserved private benefits of control.
Several important results follow from this analysis. First, we show how various capital
market imperfections interact with firms’ incentives structures to determine financing deci-
sions. This allows us to derive testable implications relating manager-shareholder conflicts to
a firm’s target leverage as well as the pace and size of capital structure changes. Second, we
infer the magnitude of agency conflicts from data on leverage choices. Specifically, we provide
1For example, Jung, Kim, and Stulz (1996) identify security issue decisions that seem inconsistent withshareholder value maximization. Friend and Lang (1988), Mehran (1992), Berger, Ofek, and Yermak (1997), andKayhan (2008) find that leverage levels are lower when CEOs do not face pressure from the market for corporatecontrol. Berger, Ofek, and Yermak also find that leverage increases in the aftermath of shocks reducing managerialentrenchment. Garvey and Hanka (1999) find that firms protected by “second generation” state antitakeoverlaws substantially reduce their use of debt, and that unprotected firms do the reverse.
1
firm-specific estimates of agency costs and relate these estimates to the firms’ governance struc-
ture. The agency conflicts identified from the data have an economically significant order of
magnitude, exhibit sizeable variation across firms, and vary with various proxies for corporate
governance. Third, we show that by accounting for agency conflicts in dynamic tradeoff mod-
els, and giving the manager control of the leverage decision, one can obtain capital structure
dynamics consistent with the data. Specifically, manager-shareholder conflicts can explain why
some firms issue little debt despite the known tax benefits of debt—the conservative debt policy
puzzle (see Graham, 2000), and why leverage ratios exhibit inertia and other robust time-series
patterns (see Fama and French, 2002, Welch, 2004, or Flannery and Rangan, 2006).
As in prior dynamic tradeoff models, our analysis emphasizes the role of external financing
costs in affecting the time series of leverage ratios. Due to capital market frictions, firms are not
able to keep their leverage at the target at all times. As a result, leverage is best described not
just by a number, the target, but by its entire distribution—including target and refinancing
boundaries. The model also reflects the interaction between real market frictions and manager-
shareholder conflicts, allowing us to generate a number of novel predictions relating agency
conflicts to the firm’s target leverage, the frequency and size of capital structure changes, and
the likelihood of default. Notably, our model predicts that incentive conflicts between managers
and shareholders lower the firm’s target leverage and raise the refinancing cash-flow trigger. As a
consequence, the range of leverage ratios widens and financial inertia becomes more pronounced
as agency conflicts increase. The intuition behind these results is that managers choose capital
structure to maximize the sum of their equity stake and the present value of private benefits.
Since debt constrains managers by limiting the cash flows available as private benefits (as in
Jensen, 1986, Zwiebel, 1996, or Morellec, 2004), managers issue less debt (lower target and
default cash-flow trigger) and restructure less frequently (higher refinancing cash-flow trigger)
than optimal for shareholders.
The paper also provides new evidence on the relation between governance mechanisms and
capital structure dynamics. Specifically, we use observed financing choices to provide firm-
specific estimates of manager-shareholder conflicts. We exploit not only the conditional mean
of leverage (as in a regression) but also the variation, persistence and distributional tails—in
short, the conditional moments of the time-series distribution of leverage. Using structural
econometrics, we find that agency costs of 1.02% of equity value for the average firm are
sufficient to resolve the conservative debt policy puzzle and explain the time series of observed
leverage ratios. We also find that the variation in agency costs across firms is substantial. Thus,
2
while leverage ratios tend to revert to the (manager’s) target leverage over time, the variation
in agency conflicts leads to persistent cross-sectional differences in leverage ratios, in line with
Lemmon, Roberts, and Zender (2008).
To make the analysis of capital structure determinants complete, we also introduce shareholder-
debtholder conflicts in our setting. In the model, shareholders can renegotiate outstanding
claims in default as in Fan and Sundaresan (2000). Our structural estimates reveal that the
bargaining power of shareholders in default is close to the Nash solution for the average firm.
Hence, shareholders can extract substantial concessions from debtholders in default. However,
while shareholder-debtholder conflicts reduce leverage, we find that they have little effect on
the cross-sectional variation and on the dynamics of leverage ratios.
The analysis in the present paper relates to the literature that analyzes the relation between
manager-shareholder conflicts and firms’ financing decisions.2 The paper that is closest to ours
is Zwiebel (1996) in that it also builds a dynamic capital structure model in which financing
policy is selected by a partially-entrenched manager. However, while firms are always at their
target leverage in Zwiebel’s model, refinancing costs create inertia and persistence in capital
structure in our model. Second, this paper relates to the dynamic contingent claims models of
Fisher, Heinkel, and Zechner (1989), Goldstein, Ju, and Leland (2001), or Strebulaev (2007).
In this literature, conflicts of interest between managers and shareholders have been largely
ignored (see however the static models of Morellec, 2004, or Lambrecht and Myers, 2008).
Our model also relates to the tradeoff models of Hennessy and Whited (HW 2005, 2007).
Their models consider the role of internally generated funds. However they do not allow for
default (HW, 2005) and ignore manager-shareholder conflicts. Another important difference is
that our closed-form expression for the time-series distribution of leverage ratios allows us to
look at all statistical moments of the leverage distribution (including target leverage, refinanc-
ing frequency, and default probability) instead of focusing on a limited number of moments.
Finally, our paper is related to the analysis in Lemmon et al. (2008), who find that traditional
determinants of leverage account for relatively little of the variation in capital structure. In-
stead they show that the majority of the cross-sectional variation in capital structures is driven
by an unexplained firm-specific determinant. Our analysis reveals that the heterogeneity in
capital structure can be structurally related to a number of corporate governance mechanisms,
providing an economic interpretation for their results.
2See Stulz (1990), Chang (1993), Hart and Moore (1994, 1995), Zwiebel (1996), Morellec (2004), or Barclay,Morellec, and Smith (2006). This literature has provided a rich intuition on the effects of managerial discretionon financing decisions, it has been so far mostly qualitative, focusing on directional effects.
3
This paper advances the literature on financing decisions in two important dimensions.
First, we develop the first dynamic model of capital structure decisions that includes taxes,
bankruptcy costs, refinancing costs, and agency conflicts. This allows us to derive clear testable
predictions regarding the effects of these various determinants of financing policies on target
leverage and the pace and size of capital structure changes. Second, and more importantly, our
analysis adds to the literature by providing firm-specific estimates of agency conflicts, and by
showing that the separation between ownership and control can explain the conservative debt
policy puzzle as well as the dynamics of leverage ratios.
The remainder of the paper is organized as follows. Section I describes the model. Section II
discusses the data and our empirical methodology. Section III provides firm-specific estimates of
manager-shareholder conflicts and shareholder bargaining power in default. Section IV explores
how well the model fits the time series and cross section of financial leverage. Section V
relates the estimates of agency conflict to various corporate governance mechanisms. Section VI
concludes. Technical developments are gathered in an Appendix.
I. The Model
Most capital structure models make the simplifying assumption that managers choose capital
structure in the interests of shareholders. Recently, however, research into capital structure
has explicitly recognized that managers’ self interest can lead to financial policies that do not
maximize shareholder wealth. This section presents a model of firms’ financing decisions that
extends the contingent claims framework to incorporate manager-shareholder conflicts. In the
following sections, we use this model to obtain firm-specific estimates of agency conflicts.
A. Assumptions
The model closely follows Leland (1998) and Strebulaev (2007). Throughout the paper, assets
are continuously traded in complete and arbitrage-free markets. The default-free term structure
is flat with an after-tax risk-free rate r, at which investors may lend and borrow freely.
We consider an economy with a large number of heterogeneous firms, indexed by i =
1, . . . , N . Firms are infinitely lived and have monopoly access to a set of assets, that are
operated in continuous time. The firm-specific state variable is the cash flow generated by the
4
operation of the firm’s assets, denoted by Xi. This operating cash flow is independent of capital
structure choices and governed, under the risk neutral probability measure Q, by the process:3
dXit = µiXit dt + σiXit dBit , Xi0 = xi0 > 0, (1)
where µi < r and σi > 0 are constants and (Bit)t≥0 is a standard Brownian motion. Equation
(1) implies that the growth rate of cash flows is Normally distributed with mean µi∆t and
variance σ2i ∆t over the time interval ∆t under the risk-neutral probability measure. It also
implies that the mean growth rate of cash flows is mi∆t = (µi + βiψ)∆t under the physical
probability measure, where βi is the unlevered cash-flow beta and ψ is the market risk premium.
Cash flows from operations are taxed at a constant rate τ c. As a result, firms may have an
incentive to issue debt to shield profits from taxation. To stay in a simple time-homogeneous
setting, we consider debt contracts that are characterized by a perpetual flow of coupon pay-
ments c and a principal P . Debt is callable and issued at par. The proceeds from the debt issue
are distributed on a pro rata basis to shareholders at the time of flotation. We consider that
firms can adjust their capital structure upwards at any point in time by incurring a proportional
cost λ, but that they can reduce their indebtedness only in default.4 Under this assumption,
the firm’s initial debt structure remains fixed until either the firm goes into default or the firm
calls its debt and restructures with newly issued debt. The personal tax rate on dividends
τd and on coupon payments τ i are identical for all investors. These features are shared with
numerous other capital structure models, including Leland (1998), Goldstein, Ju, and Leland
(2001), Hackbarth, Miao, and Morellec (2006), or Strebulaev (2007).
We are interested in building a model in which financing choices reflect not only the tradeoff
between the tax benefits of debt and contracting costs, but also agency conflicts. Agency
3This corresponds to a reduced-form specification of a model in which the firm is allowed to invest in newassets at any time t ∈ (0,∞) and investment is perfectly reversible. To see this, assume that the firm’s assetsproduce output with the production function F : R+ → R+, F (kt) = kγ
t , where γ ∈ (0, 1) and that capitaldepreciates at a constant rate δ > 0. Define the firm’s after tax profit function fit by
fit = maxk≥0
[(1 − τ ci )(Xitk
γt − δkt) − rkt].
Solving this maximization problem for kt and replacing kt by its expression in the firm’s after-tax profit functiongives fit = (1 − τ c
i )Yit where (Yit)t≥0is a (capacity-adjusted cash flow) shock governed by
dYit = µY Yitdt + σY YitdWt, Yi0 = AXi0 > 0.
where µY = ϑµi + ϑ(ϑ − 1)σ2i /2, σY = ϑσi, and (A,ϑ) ∈ R
2++ are constant parameters.
4While in principle management can both increase and decrease future debt levels, Gilson (1997) finds thattransaction costs discourage debt reductions outside of renegotiation.
5
conflicts between the manager and shareholders are introduced by considering that each firm
is run by a manager who can capture a fraction φ ∈ [0, 1) of free cash flow to equity as private
benefits (as in La Porta, Lopez-de Silanes, Shleifer, and Vishny (2002), Lambrecht and Myers
(2008), or Albuquerque and Wang (2008)). That is, the unadjusted cash flows to equity are
(1− τ c)(Xt − c), of which shareholders receive a fraction (1−φ) and management appropriates
a fraction φ. This cash diversion or tunneling of funds toward socially inefficient usage may
take a variety of forms such as excessive salary, transfer pricing, employing relatives and friends
who are not qualified for the jobs in the firm, and perquisites, just to name a few. In the model,
we take φ as a fixed, exogenous parameter that reflects the severity of manager-shareholder
conflicts. When φ = 0 there is no agency conflict and managers and shareholders agree about
corporate policies. Our objective in the empirical section is to estimate the magnitude of φi,
i = 1, . . . , N , and to relate our estimates to corporate governance mechanisms.
Firms whose conditions deteriorate sufficiently may default on their debt obligations. In
the model, default can lead either to liquidation or to renegotiation. At the time of default,
a fraction of assets are lost as a frictional cost, leading to a reduction in operating cash flows.
Specifically, we consider that if the instant of default is T , then XT = (1 − α)XT− in case of
liquidation and XT = (1−κ)XT− in case of reorganization, with 0 ≤ κ < α. We assume that in
case of reorganization, manager-shareholder conflicts are unaffected by default. Because liqui-
dation is more costly than reorganization, there exists a surplus associated with renegotiation.
This surplus represents a fraction (α − κ) of cash flows after default. Following Fan and Sun-
daresan (2000), we consider a Nash bargaining game in default that leads to a debt-equity swap.
We denote the bargaining power of shareholders by η ∈ [0, 1]. Assuming that the renegotiation
surplus is shared according to a sharing rule , the generalized Nash bargaining solution is
simply given by = η, so that the shareholders get a fraction η (α− κ) of cash flows after
default. In addition to the estimates of φi, the paper provides estimates of ηi, i = 1, . . . , N .
Agency costs of managerial discretion typically depend on the allocation of control rights
within the firm. In this paper, we follow Zwiebel (1996), Morellec (2004), and Lambrecht and
Myers (2008) by considering that the manager owns a fraction ϕ of the firm’s equity and has
decision rights over the firm’s initial debt structure and the firm’s restructuring and default
policies. When making policy choices, managers act in their own interests to maximize the
present value of the total expected cash flows (managerial rents and equity stake) that they will
take from the firm’s operations. As in Leland (1998) and Strebulaev (2007), the firm’s initial
debt structure remains fixed until either the firm’s cash flows reach a low level that the firm
6
goes into default or the cash flows rise to a sufficiently high level that the manager calls the debt
and restructures with newly issued debt. In the analysis below, we will denote by xD (< x0)
the default threshold and by xU (> x0) the restructuring threshold selected by the manager.
We can thus view the manager’s policy choices as determining the initial coupon payment c,
the restructuring threshold xU , and the default boundary xD.
B. Model Solution
Before solving the manager’s optimization problem, it will be useful to derive explicit expressions
for the value of corporate securities. In the model, the cash flow accruing to the manager at each
time t is given by [φ+ ϕ(1 − φ)] (1−τ)(Xt−c), where the tax rate τ = 1−(1−τ c)(1−τd) reflects
corporate and personal taxes. Shareholders’ cash flows are in turn given by (1−φ)(1−τ)(Xt−c).That is, shareholders receive the cash flows from operations minus the coupon payment c, the
cash flows captured by the manager, and the taxes paid on corporate and personal income.
Since managers and shareholders are entitled to a cash flow stream that is proportional to the
firm’s net income (1 − τ)(Xt − c), we start by deriving the value of a claim on net income at
time t, denoted by N(x, c) for Xt = x.
Let n (x, c) denote the present value of the firm’s net income over one financing cycle, i.e.,
for the period over which neither the default threshold xD nor the restructuring threshold xU
are hit and the firm does not change its debt policy. This value is given by
n(x, c) = EQ[ ∫ T
te−r(s−t) (1 − τ) (Xs − c) ds|Xt = x
], (2)
where T is the first time that the firm changes its debt policy, defined by T = inf {TU , TD} with
Ts = inf {t ≥ 0 : Xt = xs}, s = U,D. This expression gives the value of a claim to the firm’s
net income until either the firm increases its debt level to shield more profits from taxation or
the firm defaults on its debt obligations. This value does not incorporate any of the cash flows
that accrue to claimholders after a restructuring. These cash flows belong to the next financing
cycle and will be incorporated in the total value of the claim to net income, N(x, c).
Denote by pU (x) the present value of $1 to be received at the time of refinancing, contingent
on refinancing occurring before default, and by pD (x) the present value of $1 to be received at
7
the time of default, contingent on default occurring before refinancing. Using this notation, we
can write the solution to equation (2) as:
n(x, c) = (1 − τ)
[x
r − µ− c
r− pU (x)
(xU
r − µ− c
r
)− pD (x)
(xD
r − µ− c
r
)], (3)
where [see Revuz and Yor (1999, pp. 72)]
pD (x) =xξ − xνxξ−ν
U
xξD − xν
Dxξ−νU
and pU (x) =xξ − xνxξ−ν
D
xξU − xν
Uxξ−νD
and ξ and ν are the positive and negative roots of the equation 12σ
2β (β − 1) + µβ − r = 0.
The first two terms in the square bracket of equation (3) represent the value of a perpetual
entitlement to net income. The other terms reflect the fact that payments are stopped after
either a restructuring (third term) or a default (fourth term).
Consider next the total value N (x, c) of a claim to the firm’s net income. We show in the
Internet Appendix that in the static model in which the firm cannot restructure, the default
threshold xD is linear in the coupon payment c. In addition, the selected coupon rate c is linear
in x. This implies that if two firms i and j are identical except that xi0 = Λxj
0, then the selected
coupon rate and default threshold satisfy ci = Λcj and xiD = Λxj
D, respectively, and every claim
will be scaled by the same factor Λ.
For the dynamic model, this scaling feature implies that at the first restructuring point, all
claims are scaled up by the same proportion ρ ≡ xU/x0 as asset value has increased (i.e., it is
optimal to choose c1 = ρc0, x1D = ρx0
D, x1U = ρx0
U ). Subsequent restructurings scale up these
variables again by the same ratio. If default occurs prior to restructuring, firm value is reduced
by a constant factor η (α− κ) γ with γ ≡ xD/x0, new debt is issued, and all claims are scaled
down by the same proportion η(α− κ)γ. As a result, we have for xD ≤ x ≤ xU :
N (x, c) = n (x, c)︸ ︷︷ ︸ + pU (x) ρN (x0, c)︸ ︷︷ ︸ + pD (x) η (α− κ) γN (x0, c)︸ ︷︷ ︸ .
Total value Value over PV of claim on net PV of claim on net
of the claim one cycle income at a restructuring income in default
(4)
This equation shows that the value of a claim to the firm’s net income over all financing cycles
is equal to the cash flows claimholders receive over one financing cycle plus the value of the
cash flows they get after the restructuring or in default. Using this expression, we can express
8
the total value of a claim to the firm’s net income at the initial date as:
N (x0, c) =n (x0, c)
1 − pU (x0) ρ− pD (x0) η (α− κ) γ≡ n (x0, c) S(x0, ρ, γ), (5)
where S(x0, ρ, γ) is a scaling factor that transforms the value of a claim to cash flows over one
financing cycle at a restructuring point into the value of this claim over all financing cycles.
The same arguments apply to the valuation of corporate debt. Consider first the value
d (x, c) of the debt issued at time t = 0. Since the issue is called at par if the firm’s cash flows
reach xU before xD, the current value of corporate debt satisfies at any time t ≥ 0:
d (x, c) = b (x, c)︸ ︷︷ ︸ + pU (x) d (x0, c)︸ ︷︷ ︸ .
Value of debt over one cycle PV of cash flow at a restructuring(6)
where b(x, c) represents the value of corporate debt over one refinancing cycle, i.e., ignoring the
value of the debt issued after a restructuring or after default, and is given by
b (x, c) =
(1 − τ i
)c
r[1 − pU (x) − pD (x)] + pD (x) [1 − (κ+ η (α− κ))]
(1 − τ
r − µ
)xD . (7)
The first term on the right-hand side of this equation represents the present value of the coupon
payments until the firm defaults or restructures (i.e., until time T ). The second term represents
the present value of the cash flow to initial debtholders in default.
As in the case of the claim to net income, the total value of corporate debt includes not
only the cash flows accruing to debtholders over one refinancing cycle, b(x, c), but also the
new debt that will be issued in default or at the time of a restructuring. As a result, the
value of the total debt claim over all the financing cycles is given by b(x0, c)S(x0, ρ, γ), where
S(x0, ρ, γ) is defined in equation (5). Because flotation costs are incurred each time the firm
adjusts its capital structure, the total value of adjustment costs at time t = 0 is in turn given
by λd (x0, c) S(x0, ρ, γ). We can then write the value of the firm at the restructuring date as
the sum of the present value of a claim on net income plus the value of all debt issues minus
the present value of issuance costs and the present value of managerial rents, or
V (x0, c) = S(x0, ρ, γ) {n (x0, c) + b (x0, c) − λd (x0, c) − φn (x0, c) } . (8)
We are now in a position to determine the manager’s policy choices. Denote the present
value of the manager’s cash flows for a current value of the cash-flow shock x by M(x, c). This
9
value is the sum of the manager’s equity stake and the value of private benefits. The value of
equity at the time of debt issuance is equal to total firm value, V(x, c), because debt is fairly
priced. Assuming that managers stay in control after default,5 we can then express the total
value of the manager’s claims as:
M(x, c) = ϕV(x, c)︸ ︷︷ ︸ + φN(x, c)︸ ︷︷ ︸ ,
Equity stake PV of managerial rents(9)
where ϕ represents the fraction of the firm’s equity owned by the manager and φ represents the
fraction of the firm’s net income that can be captured by the manager.
When choosing financing policy, the objective of the manager is to maximize the ex-ante
value of his claims by selecting the coupon payment c and the scaling factor ρ = xU/x0. Thus,
the manager solves
supc,ρ
M(x, c) = supc,ρ
{ϕV(x, c) + φN(x, c)} . (10)
Since N(x, c) decreases with c, equation (9) implies that the efficient choice of debt (optimal
for shareholders) differs from the manager’s choice of debt whenever φ > 0. In particular, the
model predicts that the coupon payment decreases with φ and that the debt level selected by
the manager is lower than the debt level that maximizes firm value.
In a rational expectations model, the solution to the problem (10) reflects the fact that
following the flotation of corporate debt, the manager chooses a default policy that maximizes
the value of his claim after debt has been issued. As in Leland (1998) or Strebulaev (2007), the
selected default threshold results from a tradeoff between continuation value outside of default
and the value of claims in default. Since all claims are scaled down by the same factor in default,
the manager and shareholders agree on the firm’s default policy. The value of equity at the
time of default satisfies V(x, c) − d (x, c) = η (α− κ) γV(x, c) (value-matching). The default
threshold can then be determined by solving the smooth-pasting condition:
∂ [V(x, c) − d (x, c)]
∂x
∣∣∣∣x=xD
=∂η (α− κ) γV(x, c)
∂x
∣∣∣∣x=xD
. (11)
The full problem of managers thus consists of solving (10) subject to (11). A closed-form
solution to this problem does not exist and thus standard numerical procedures are used.
5This assumption reflects the fact that managers usually stay in control after debt is renegotiated privatelyor after court supervised debt renegotiation (see e.g. Gilson, 1989, for empirical evidence).
10
II. Empirical Analysis
In this section, we estimate the model derived in Section I using data on financial leverage. Our
objective is to ascertain whether agency conflicts can explain the debt conservatism puzzle as
well as the time-series patterns in observed leverage ratios. To do so, we exploit the structural
restrictions of the model and estimate from panel data on financing decisions the level of agency
conflicts that best explain observed financing behavior (a similar approach is used in Hennessy
and Whited, 2007). In a second stage, we examine whether these estimates are related to
variables reflecting the quality of a firm’s governance structure.
A. Data
Estimating the model derived in Section I requires merging data from various standard sources.
We collect financial statements from Compustat, managerial compensation data from Execu-
Comp, stock price data from CRSP, analyst forecasts from I/B/E/S, governance data from
IRRC, and institutional ownership data from Thomson Reuters. Following the literature, we
remove all regulated (SIC 4900−4999) and financial firms (SIC 6000−6999). Observations with
missing SIC code, total assets, market value, sales, long-term debt, debt in current liabilities are
also excluded. In addition, we restrict our sample to firms that have total assets over $10 mil-
lion. As a result of these selection criteria, we obtain a panel dataset with 13, 159 observations
for N = 809 firms, for the time period from 1992 to 2004 at the quarterly frequency. Tables I
and II provide detailed definitions and descriptive statistics for the variables of interest.
Insert Tables I and II Here
In the analysis, each firm i = 1, . . . , N is characterized by a set of parameters θi =
(mi, µi, σi, βi, αi, κi, ϕi, λi, τc, τ i, τd, ψ, r, φi, ηi) ∈ Θ. The subscript i indicates that the pa-
rameter values are firm-specific. Otherwise the parameter takes a single, economy-wide value.
The different parameters determine the growth rate mi (µi under the risk-neutral measure)
and volatility σi of the firm’s cash flows, the liquidation and reorganization costs (αi, κi), the
manager’s equity stake ϕi, the refinancing cost λi, and the tax environment (τ c, τ i, τd). The
parameters of interest—capturing different sources of agency conflicts—are the fraction of cash
flows captured by the manager φi and the bargaining power of shareholders in default ηi.
11
Estimating the entire parameter vector θi for each firm i = 1, . . . , N using solely data on
financial leverage is unnecessary and practically infeasible. We therefore split the parameter
vector into two parts: nuisance parameters and deep (agency) parameters that we estimate
structurally. Given the dimensionality of the empirical estimation problem, we first determine
the nuisance parameters θ⋆i = (mi, µi, σi, βi, αi, κi, ϕi, λi, τ
c, τ i, τd, ψ, r) using the above data
sources. We then keep the nuisance parameters θ⋆i fixed when estimating the deep parameters
(φi, ηi) from data on financial leverage. Since the estimators of θ⋆i are
√n-consistent for a
sample of size n, consistency of our estimates of the structural parameters is unaffected by
assuming we can estimate or construct proxies for the true values of θ⋆i . We investigate the
effect of sampling error in θ⋆i on our estimates of agency cost parameters in Section III.B below.
We construct the estimates of the nuisance parameters as follows. In our base case esti-
mation, we first compute period-by-period estimates for each firm. Since the model is writ-
ten in terms of constant firm level parameters, we then average the time-specific estimates
(mit, µit, σit, αit, βit, ϕit) over the sample period for each firm to obtain the set the parameters
(mi, µi, σi, αi, βi, ϕi) (i.e., θ⋆i = 1
ni
∑ni
t=1 θ⋆it for i = 1, . . . , N , where ni is the number of observa-
tions). In Section III.C, we check whether our estimation results depend on this assumption.
We proxy the growth rate of cash flows, m, by an affine function of the mean long-term
growth rate per industry, m, where we use SIC level 2 to define industries. The Institutional
Brokers’ Estimate System (IBES) provides analysts’ forecasts for the long-term growth rate.
It is generally agreed, however, that IBES consensus long-term growth rates are too optimistic
compared to realized growth. In addition, Chan, Karceski, and Lakonishok (CKL, 2003) show
that IBES predicts too much cross-sectional variation in growth rates. Following CKL (2003),
we adjust for these two biases by using the following least-squares predictor for the cash-flow
growth rate: mit = 0.007264043+0.408605737× mit . We then estimate the growth rate of firm
i by the time-series average mi = 1ni
∑ni
t=1mit. Using data on IBES consensus forecasts in our
sample, we can predict the actual growth rates reasonably well with this linear specification;
our estimates are in line with the values reported in CKL (2003).
Next, we use the Capital Asset Pricing Model (CAPM) to estimate the risk-neutral growth
rate of cash flows: µit = mit − βitψt, where ψt is the market risk premium and βit is the
leverage-adjusted cash-flow beta. We estimate market betas from monthly equity returns and
unlever them using the model-implied relations. Similarly, we estimate cash-flow volatility σit
using the standard deviation of monthly equity returns and the following relation (implied by
12
It’s lemma): σit = σEit/(
∂E(x,c)∂x
xE(x,c)), where σE
it is the volatility of stock returns and E(x, c) ≡V(x, c) − d (x, c) is the stock price derived from the model. In these estimations, we use stock
returns from the Center for Research in Security Prices (CRSP) database.
ExecuComp provides data on managerial compensation schemes, allowing us to measure the
extent to which managerial incentives are aligned with shareholders’ interests (as reflected by ϕi
in our model). We construct several firm-specific measures of managerial ownership. Following
Core and Guay (1999), we construct the managerial delta, defined as the sensitivity of option
value to a one percent change in the stock price, for each manager and then aggregate over the
five highest-paid executives. In addition, following Jensen and Murphy (1990), we construct
a managerial incentives measure as the change in managerial wealth per dollar change in the
wealth of shareholders (see Appendix B for details):
ϕit = ϕEit + deltait
Shares represented by options awardsit
Shares outstandingit
. (12)
This incentives measure accounts for both a direct component, managerial share ownership ϕE ,
and an indirect component, the pay-performance sensitivity due to options awards.
The remaining parameters are standard. The risk-free rate r is based on the yield curve
of Treasury bonds during the sample period (r = 4.21%). The risk premium is set to the
consensus value of 6%. The relevant tax rates are based on estimates in Graham (1996). We
use the mean over the sample period for the tax rate on dividends and interest income, τd and
τ i, respectively. The tax rate on corporate income, τ c, is set to 35%. Gilson and Lang (1990)
find that renegotiation costs represent a small fraction of firm value. We thus fix renegotiation
costs κ to zero in our base case estimation (and to 15% in a robustness check). Following
Berger, Ofek, and Swary (1996), we estimate firm-specific liquidation costs, αit, as:
αit = 1 − (Tangibilityit + Cashit)/Total Assetsit. (13)
In equation (13), Berger, Ofek, and Swary (1996) estimate tangibility as Tangibilityit = 0.715
∗Receivablesit + 0.547∗Inventoryit + 0.535∗Capitalit.
Last, several studies provide estimates for issuance costs as a function of the amount of debt
being issued. The model, however, is written in terms of debt issuance cost λ as a fraction of
the total debt outstanding. The cost of debt issuance as a fraction of the issue size is given in
the model by ρρ−1λ, where ρ is the restructuring threshold multiplier. Since our estimates yield
13
a mean value of 2 for ρ, we set λ = 1%. This produces a cost of debt issuance representing
2% of the issue size on average, corresponding to the upper range of the values found in the
empirical literature (see e.g. Altinkilic and Hansen, 2000, and Kim, Palia, and Saunders, 2007).
B. Estimation Strategy and Empirical Specification
Our structural estimation of the deep parameters of the model uses simulated maximum likeli-
hood (SML) and exploits the panel nature of the data and the model’s predictions for different
moments of leverage. For an individual firm, the model implies a specific time-series behavior
of the firm’s leverage ratio. The policy predictions include the target leverage, the refinancing
frequency, and the default probability. In addition to the time-series predictions, the model
yields comparative statics that describe how financial policies and financial leverage vary in the
cross-section of firms. We exploit both types of predictions to identify the structural parame-
ters in the data and to disentangle cross-sectional heterogeneity from the impact of transaction
cost-driven inertia on financial leverage.
The main focus of inference is on the firm-specific private benefits of control φi and share-
holders’ bargaining power in default ηi. In the structural estimation, we treat these agency
parameters as random coefficients to reduce the dimensionality of the problem. Specifically, the
structural parameters characterizing agency conflicts are defined as:
φi = h(αφ + ǫφi ) and ηi = h(αη + ǫηi ), (14)
where h : R → [0, 1] is a transformation that guarantees that the parameters stay in their
natural domain6 and the ǫi = (ǫφi , ǫηi ) are bivariate random variables capturing the firm-specific
unobserved heterogeneity. As in linear dynamic random-effects models, the firm-specific random
effects ǫi are assumed independent across firms and, for all firms i = 1, . . . , N , are normally
distributed: ǫφi
ǫηi
∼ N
0,
σ2
φ σφη
σφη σ2η
. (15)
This setup is sufficiently flexible to capture cross-sectional variation in the parameter values
while imposing the model-implied structural restrictions on the domains of the parameters. In
summary, the set of structural parameters we need to estimate is θ = (αφ, αη , σφ, ση , σφη).
6In the base case, we use the standard normal cumulative distribution function Φ for h. Alternatively, we usethe inverse logit transformation. The results are similar and summarized in the section on robustness tests.
14
The likelihood function L of the parameters θ given the data and nuisance parameters θ⋆ is
based on the probability of observing the leverage ratio yit for firm i at date t. Assume that there
are N firms in the sample and let ni be the number of observations for firm i. The observations
for the same firm are correlated due to autocorrelation in the cash-flow process. Given these
assumptions, the joint probability of observing the leverage ratios yi = (yi1, . . . , yini)′ for firm
i and the firm-specific unobserved effects ǫi = (ǫφi , ǫηi ) is given by
f (yi, ǫi|θ) = f (yi|ǫi; θ) f (ǫi|θ)
=
(f(yi1|ǫi; θ)
ni∏
t=2
f(yit|yit−1, ǫi; θ)
)f (ǫi|θ) , (16)
where f(ǫi|θ) is the bivariate normal density corresponding to (15). Integrating out the ran-
dom effects from the joint likelihood f (y, ǫ|θ) =∏N
i=1 f (yi, ǫi|θ), we obtain the marginal log-
likelihood function (since the ǫi are drawn independently across firms from f(ǫi|θ)) as
lnL (θ; y) =
N∑
i=1
ln
∫
ǫi
(f(yi1|ǫi; θ)
ni∏
t=2
f(yit|yit−1, ǫi; θ)
)f (ǫi|θ) dǫi. (17)
For the model described in Section I, explicit expressions for the stationary density of
leverage f(yit|ǫi; θ) and conditional density f(yit|yit−1, ǫi; θ) can be derived (see Appendix A.1).
We evaluate the integral in equation (17) using Monte-Carlo simulations. When implementing
this procedure, we use the empirical analog to the log-likelihood function, which is given by
lnL (θ; y) =
N∑
i=1
ln1
K
K∑
ki=1
(f(yi1|ǫki
i ; θ)
ni∏
t=2
f(yit|yit−1, ǫki
i ; θ)
). (18)
In this equation, K is the number of random draws per firm, and ǫki
i is the realization in draw
ki for firm i. In Appendix C, we investigate how the precision and accuracy of the Monte-Carlo
simulations performed as part of the estimation depends on the number of random draws K
and how this affects the finite simulation sample bias in estimated coefficients. Figure 1 plots
the magnitude of the Monte-Carlo simulation error (Panel A) and its impact on the precision
and accuracy of the simulated log-likelihood (Panel B) as functions of K. We find that 1,000
random draws are sufficient to make the simulation error negligible. We thus set K = 1, 000 in
the estimations.
Insert Figure 1 Here
15
The SML estimator is now defined as: θ = arg maxθ lnL(θ; y). This estimator answers the
question: What magnitude of agency costs best explain observed financing patterns?
C. Model Predictions and Identification
Before proceeding to the empirical analysis, it will be useful to better understand how we iden-
tify in the data the parameters describing the (unobserved) agency conflicts. Our identification
strategy uses data on observable variables—corporate financing decisions—to infer properties
of unobserved variables—private benefits of control and shareholders’ bargaining power in de-
fault. In the following, we first illustrate the predictions of the model linking unobservables to
observables for a specific set of input parameter values. We then discuss more formally how
identification is obtained in our setting.
C.1. Model Predictions
In order to build intuition for the identification strategy, we start by reviewing the predictions of
the model with respect to firms’ financing decisions. Table III reports the firm’s target leverage,
the refinancing and default thresholds, the recovery rate in default, the corporate bond yield
spread at the leverage target, and the percentage increase in firm value due to tax savings
(the tax benefit of debt). Input parameter values for our base case are set as follows: the
risk-free interest rate r = 4.21%, the initial value of the cash flow shock x0 = 1 (normalized),
the growth rate and volatility of the cash flow shock µ = 1% and σ = 25%, the corporate
tax rate τ c = 35%, the tax rate on dividends τd = 11.6%, the tax rate on interest income
τ i = 29.3%, liquidation costs α = 50%, renegotiation costs κ = 0%, refinancing costs λ = 0.5%,
shareholders’ bargaining power η = 50%, managerial ownership ϕ = 7%, and private benefits
of control φ = 1%. These parameter values are used for illustrative purposes and are either
taken from the literature or estimated following the procedure discussed in Section II.A.
Insert Table III Here
Table III shows that the effects of corporate taxes, default costs, and cash flow volatility on
the various quantities of interest are similar to those reported previously in the literature (see
e.g. Strebulaev, 2007). In addition, the table reveals that incentive conflicts between managers
16
and shareholders affect the selected debt level and the refinancing and default triggers and,
hence, the frequency and size of capital structure changes. Specifically, high (low) agency costs
lead to low (high) leverage and fewer (more) capital structure rebalancings.
Figure 2 provides comparative statics for the model-implied time-series distribution of lever-
age depending on various firm characteristics. Panel A plots the distribution function of leverage
for different parameter values. Panel B depicts the median (solid line), the 5% and 95% quan-
tiles of leverage (dashed lines), and the low and high of leverage (dotted lines) as functions of
the parameters.
Insert Figure 2 Here
The figure shows that an increase in manager-shareholder conflicts, as measured by φ, lowers
both the target leverage and the debt issuance trigger and raises the default trigger. As a
result, the range of leverage ratios widens as agency costs increase and the speed of mean
reversion declines (autocorrelation rises). The intuition underlying this result is that cash
distributions are made on a pro-rata basis to shareholders, so that management gets a fraction
of the distributions when new debt is issued. Management’s stake in the firm, however, exceeds
its direct ownership due to the private benefits of control. Since debt constrains managers
by limiting the cash flows available as private benefits (as in Jensen, 1986, Zwiebel, 1996, or
Morellec, 2004), managers issue less debt (lower target leverage and higher default trigger) and
restructure less frequently (lower refinancing trigger) than optimal for shareholders.
The figure also reveals that an increase in the bargaining power η leads to accelerated
default, as shareholders capture a larger fraction of the surplus in default. Higher bargaining
power results in costlier debt as bondholders anticipate shareholders’ strategic action in default
and require a higher risk premium on corporate debt. An increase in the bargaining power of
shareholders therefore decreases target leverage and the low and high restructuring bounds. As
a result, the leverage distribution shifts to the left and the speed of mean reversion increases
(autocorrelation drops). However, the quantitative effect is limited.
To aid the intuition of the identification, Table III and Figure 2 also plot the leverage
distribution as a function of the cost of debt issuance λ. The table and the figure show that
the cost of debt issuance affects predominantly the low leverage tail and, for realistic parameter
values, leaves the target leverage ratio largely unaffected. By contrast, the target leverage
ratio is very sensitive to managerial entrenchment. Overall, refinancing costs have similar
directional effects as manager-shareholder conflicts on the distribution of leverage. The main
17
difference is that refinancing costs have a much smaller quantitative impact on target leverage
than manager-shareholder conflicts.
C.2. Identification
It is necessary for consistent inference that the structural parameters θ = (αφ, αη , σφ, ση, σφη)
can be identified in the data. In our setting, identification requires that the model parameters
(φi, ηi) have a distinct effect on financing choices which, in turn, determine the intertemporal
evolution of the firms’ financial leverage.7 A sufficient condition for identification is a one-to-one
mapping between the structural parameters and a set of data moments of the same dimension.
To gain intuition, we focus in this section on moments that are a-priori informative about the
agency-conflict parameters we seek to estimate—much like in method-of-moments estimation
(In the simulated maximum likelihood estimation we perform, these moments are then chosen
optimally). Heuristically, a moment m is informative about an unknown parameter θ if that
moment is sensitive to changes in the parameter and the sensitivity differs across parameters. In
formal terms, local identification requires the Jacobian determinant, det(∂m/∂θ), to be nonzero.
Insert Table IV Here
The first column of Table IV lists a broad choice of data moments. The main moments
to consider are the mean, standard deviation, range, and mean reversion of leverage and the
quarterly changes in leverage. The mean reversion in leverage is captured by β in the time-
series regression yt − yt−1 = α + β(yt − yt−1) + εt. We also report the median, skew, kurtosis,
min, max, interquartile range, and persistence in leverage measured by quarterly and annual
autocorrelation. In addition, we list default and issuance probabilities and the size of debt
issues as a fraction of firm value. Not all of these moments are required for identification; a few
low-order moments are sufficient to identify the structural parameters. For comparison with
the standard dynamic tradeoff theory without agency conflicts, we also discuss identification of
the restructuring costs λ. The baseline parameter values are set to (λ, φ, η) = (.005, 0, 0).8
7Formally, identification obtains when, for a given true parameter vector, no other value of the parametervector exists that defines the same true population distribution of the observations. In this case, the parametervector uniquely defines the distribution and, hence, can be consistently estimated.
8A concern with the standard approach is that local identification may not guarantee identification globally.We have therefore simulated the model moments and computed sensitivities in two ways, as marginal effect atdifferent sets of baseline parameters and as average effect over a range of parameter values. Table IV reports
18
Table IV reveals that the model moments exhibit significant sensitivity to the model pa-
rameters. More importantly for identification, the sensitivities differ across parameters, such
that one can find moments with det(∂m/∂θ) 6= 0. While the qualitative effect on mean leverage
is comparable across parameters, the measures of variation and mean reversion depend very
differently on the parameters. Bargaining power tends to decrease the variation in leverage
and to increase autocorrelation; the cost of refinancing and private benefits of control have the
opposite effect. In turn, the leverage skew and kurtosis increase with shareholders’ bargaining
power and private benefits of control, and decrease with the refinancing cost—because of a
different interplay between issuance frequency and issue size. Overall, the different sensitivi-
ties reveal that the structural parameters can be identified by combining time-series data on
financial leverage (pinning down αφ and αη) with cross-sectional information on variation in
leverage dynamics across firms (pinning down σφ, ση, and σφη).
III. Estimation Results
A. The Benchmark: Dynamic Capital Structure without Agency Conflicts
The dynamic tradeoff theory proposed by Fischer, Heinkel, and Zechner (1989) and Goldstein,
Ju, and Leland (GJL, 2001) forms the benchmark for our analysis. We thus start by estimating
the key structural parameter(s) of this model. Since the benchmark model by GJL is nested in
ours (if we set φi = 0 and ηi = 0), we can estimate the level of refinancing costs λi necessary to
explain observed leverage choices using the methodology described in Section II. As illustrated
by Figure 2, an increase in refinancing costs has similar impact on the time-series distribution
of leverage than an increase in agency costs. In this section we are interested in answering the
question: What magnitude of refinancing costs best explains observed financing patterns?
We estimate the benchmark model using an SML estimation in which we constrain φi = 0,
ηi = 0, and allow λi to vary across firms as follows:
λi = h(αλ + ǫλi ), (19)
the sensitivity (∂m/∂θ)/m in the baseline. Alternatively, we have computed the differential effect as the averagesensitivity over the range of parameter values generating non-zero leverage and normalized by the average effecton the mean. The marginal effect captures local identification, while the average effect across (λ,φ, η) ∈ [0, λ]×[0, φ] × [0, η] gives an idea of which moments yield global identification and which parameters have strongnonlinear impact on the model moments. We find that average sensitivities are, not surprisingly, more similaracross parameters than marginal effects in the baseline. Importantly, however, the quantitative differences intheir impact on the model moments remain, warranting identification.
19
where h = Φ is the standard normal cumulative distribution function (Φ ∈ [0, 1] guarantees
that cost estimates are between zero and 100% of firm value) and ǫλi is a firm-specific i.i.d. un-
observed determinant of λi. Panel A of Table V reports the point estimates. Cluster-robust
t-statistics that adjust for cross-sectional correlation in each time period and, respectively, in-
dustry clustered t-statistics are reported in parentheses. Both the estimate of the mean, αλ,
and the variance estimate for the random effect are statistically significant.
Insert Table V Here
Table V, Panel B reports descriptive statistics for the predicted cost of debt issuance,
λi = E(λi|yi; θ), in the dynamic capital structure model without agency conflicts (the hat
indicates fitted values). Appendix A.2 shows how to compute this conditional expectation.
The data reveal that the cost of debt issuance should be in the order of 15.5% of the total
debt outstanding (or 31% of the issue size), with median value at around 11.2% (or 22% of the
issue size), to explain observed financing choices and the dynamics of leverage ratios.9 These
numbers are unreasonably high and inconsistent with empirically observed values. Thus, while
dynamic capital structure theories that ignore agency conflicts can reproduce qualitatively the
financing patterns observed in the data (see Strebulaev, 2007), they do not provide a reasonable
quantitative explanation for firms’ financing policies. In that respect, our results are in line with
the recent study by LRZ (2008), who find that the traditional determinants of capital structure
explain little of the observed variation in leverage ratios.
B. The Estimated Agency Conflicts
We now turn to the estimation of the model with agency conflicts and transaction costs using
the procedure described in Section II.B . In the estimation, we allow the structural parameters
characterizing agency conflicts to vary accross firms as follows:
φi = h(αφ + ǫφi ) and ηi = h(αη + ǫηi ), (20)
where, in our base specification, h is set to the standard normal cumulative distribution function
Φ ∈ [0, 1] and ǫφi and ǫηi are firm-specific i.i.d. unobserved determinants of φi and ηi.
9The cost estimates are robust to different specifications of the link function in expression (19). We havealternatively used the inverse logit transformation and obtained similar results.
20
Panel A of Table VI summarizes the maximum likelihood estimates of the structural pa-
rameters θ = (αφ, αη, σφ, ση, σφη). Cluster-robust t-statistics that adjust for cross-sectional
correlation in each time period and, respectively, industry clustered t-statistics are reported
in parentheses. The parameters capturing the private benefits of control and the bargaining
power of shareholders in default are well-identified in the data, yet not all point estimates
are statistically significantly different from zero. For instance, the estimate αη is negative but
insignificant—suggesting that shareholder bargaining power is close to the Nash solution on
average (since η = Φ(αη + ǫη) ≈ 0.5 when αη ≈ 0 and ǫη = 0). The fact that the estimates
for the variances of the random effects are economically and statistically significant indicates
sizeable variation in manager-shareholder conflicts and in shareholder bargaining power across
firms. The cross-sectional covariation between the private benefits of control and shareholders’
bargaining power is negative (though, insignificant). This suggests that shareholders can ex-
tract a greater surplus from bondholders in default when managers’ and shareholders’ interests
are more aligned.
Insert Table VI Here
Using the structural parameter estimates reported in Table VI, we can construct firm-
specific measures of the manager’s private benefits of control φi and of shareholders’ bargaining
power in default ηi. Appendix A.2 derives expressions for the best predictors, E[φi|yi; θ] and
E[ηi|yi; θ], of these two quantities given the data yi = (yit). We evaluate these expressions using
Monte-Carlo integration.
Insert Figure 3 and Table VII Here
Figure 3 plots histograms of the predicted private benefits of control, φi = E[φi|yi; θ], and
the predicted bargaining power of shareholders in default, ηi = E[ηi|yi; θ] (the hat indicates
fitted values). The figure shows that the variation in agency costs across firms is sizeable.
Hence, while our dynamic capital structure model suggests that leverage ratios should revert
to the (manager’s) target leverage over time, the differences in agency conflicts observed in
Figure 3 imply persistent cross-sectional differences in leverage ratios.
Table VII reports summary statistics for the fitted values φi and ηi, i, . . . ,N , in the base
specification. We also report in brackets the private benefits of control expressed as a fraction
of equity value. Table VII reveals that the cost of managerial discretion is 1.02% of equity
21
value for the average firm, and 0.23% for the median firm. The distribution across firms peaks
at zero, is positively skewed, and exhibits sizeable variance and kurtosis—suggesting that most
firms manage to limit managerial entrenchment. For a number of firms, however, inefficiencies
arising from agency conflicts within the firm constitute a substantial portion of equity value.
The mean and median bargaining power of shareholders are 43% and 46%, respectively—
close to the Nash solution. Given the magnitude of bankruptcy and renegotiation costs, this
implies that shareholders can capture around 20% of firm value on average by renegotiating
outstanding claims in default. The distribution of shareholders’ bargaining power is bimodal
with η concentrated at zero and around 50%, and exhibits lower kurtosis than that of φi.
Together with Table III and Figure 2, this suggests that shareholders’ bargaining power in
default η has a smaller impact than private benefits of control φ on the cross-sectional variation
and the dynamics of leverage ratios.
Overall the results imply that small conflicts of interest between managers and shareholders
are sufficient to resolve the leverage puzzles identified in the empirical literature and explain
the time series of observed leverage ratios. Hence, the tradeoff theory augmented with agency
conflicts performs orders of magnitude better than the standard explanations based exclusively
on financing frictions. Before assessing the fit of the model in Section IV, we examine in the
next section the robustness of the parameter estimates we have obtained.
C. Robustness Checks
In the previous section, we have made a number of assumptions when implementing the empiri-
cal estimation of the parameters governing agency conflicts. One may thus be concerned about
the robustness of our estimates. To address this issue, we perform in this section a number of
robustness checks. First, we vary the calibrated parameters. We set the cost of debt issuance
to 0.5% (or 1% of the issue size) and re-estimate the model. Then we set managerial incentives,
ϕ, equal to management’s equity ownership net of option compensation. Last, we increase the
cost of renegotiating debt to 15%. The results of these robustness checks are summarized in
panels two to four of Table VI. Panels two to four of Table VII report the predicted private
benefits of control, E[φi|yi; θ], and the predicted bargaining power of shareholders, E[ηi|yi; θ],
under these alternative specifications.
22
The estimates reported in Tables VI and VII are broadly consistent with the base case.
Private benefits of control are around 0.7-1.2% of equity value on average and 0.1-0.3% for the
median firm. As one would expect, the estimates of the private benefits of control are larger
under smaller restructuring costs. The estimates of private benefits are lower under the alter-
native ownership definition ϕE and under larger renegotiation costs, since a smaller ownership
share and less surplus for shareholders in distress both diminish the manager’s incentives to
take on leverage. These effects are compensated for in the model by lower private benefits.
The bargaining power of shareholders is around 40% on average in all cases. These estimates
are slightly lower than in the base case. Nonetheless, the cross-sectional variation, skewness,
and kurtosis in both agency cost measures remain about the same across all specifications. The
correlation between the two agency cost parameters is negative in all environments except when
κ = 15%. Overall, the variation across specifications is limited. The likelihood is the highest
in the base case, corroborating our choice of parameters.
Another potential issue with our results is that we set the parameters (mi, µi, σi, αi, βi, ϕi)
for each firm equal to the average of the time-specific values (mit, µit, σit, αit, βit, ϕit) over the
sample period (i.e., θ⋆i = 1
ni
∑ni
t=1 θ⋆it for i = 1, . . . , N). We check in two ways whether our results
depend on this assumption. First, we set the nuisance parameters θ⋆i to their corresponding
value in the first period for which we have data (i.e., θ⋆i = θ⋆
i1, ∀i). Second, we allow the
parameters to vary period by period, assuming managers are myopic about the time variation
in parameters.10 The coefficient estimates in panels five and six of Table VI and VII are again
very similar to the base case.
In the last two robustness checks, we change the link function h to the inverse logit and
use the alternative definition of leverage described in Table III. The estimates in the remaining
two panels of Table VI and VII yield similar distributional characteristics across specifications.
The inverse logit generates lower stealing and lower bargaining power estimates (in conjunction
with lower likelihood)—suggesting a non-parametric estimation of h may be a promising route.
The alternative definition of leverage (which produces lower leverage ratios) predicts more
stealing and about the same bargaining power for the firms in our sample. Overall, the main
conclusions from the estimation seem resilient to the specific parametric assumptions, and the
observed deviations have an intuitive justification.
10We thank the referee for pointing out this interpretation of the specification.
23
IV. Moment tests and specification analysis
As shown in Section III, the model performs well in the sense that the estimated agency conflicts
are of reasonable magnitude. In this section we are interested in the following two questions.
First, how well does the model fit the data? Second, along which dimensions does the model
fail? A natural approach to answer these questions is to compare various model moments to
their empirical analog. The maximum likelihood estimator in Section II.B is just-identified and
efficient; that is, it picks in an optimal fashion as many moments as there are parameters. As
a result, there are many conditional moments that the estimation does not match explicitly.
Conditional moment (CM) tests exploit these additional moment restrictions and allow to
statistically test for model fit. An alternative is to construct likelihood-based statistical tests
of goodness-of-fit, which allows comparing nested and non-nested model specifications. We
explore both routes in the following.
A. Moment Tests
Table VIII lists an extensive set of leverage moments. These include the mean, median, stan-
dard deviation, and higher-order moments of leverage and of changes in leverage. We also
compare various dispersion measures (range, inter-quartile range, minimum, maximum) and
the persistence in leverage at quarterly and annual frequency (“inertia puzzle”). The empirical
moments reported in the table are computed analogously to the simulated model moments.11
We obtain the model moments by simulating artificial economies as described in Appendix D.1.
Insert Table VIII Here
Conditional moment tests allow to test the hypothesis that the distance between empirical
and simulated data moment is zero [see Newey (1985) and Pagan and Vella (1989)]. Let the
distance for observation i between J data moments and the corresponding (simulated) model
moments be ri ∈ R1×J . Then the hypothesis is that for the true θ, Eθ[ri] = 0. Let n be the
sample size and m the number of parameters in the SML estimation. Denote by R the n × J
11The numbers reported in Table VIII are measured as the time-series average of all observations per firm,averaged across firms. These numbers can differ from the pooled averages reported in Table II.
24
matrix whose ith row is ri and by G the n × m gradient matrix of the log-likelihood. The
sample moment can be written r ≡ 1n
∑ni=1 ri. The Wald statistic is defined by:
nr′Σ−1r −→ χ2(J), (21)
where the degrees of freedom J are the number of moment restrictions being tested and Σ is
defined by Σ = 1n [R′R −R′G(G′
G)−1G′R].
In Table VIII, we report test statistics and p-values for the goodness-of-fit of each individual
moment and assess overall fit by testing the joint hypothesis using (21) (reported in the last
row). The model performs well along moments that the literature has identified to be of first-
order importance. The average and median level of leverage are matched reasonably well. The
CM test cannot reject the hypothesis that empirical and simulated moments are the same. The
same holds true for leverage persistence at quarterly frequency, though the model is rejected over
the longer horizon. The model is also statistically rejected for higher-order leverage moments
and dispersion measures, though the numerical values are economically quite close. We also find
that, while the model can match the median as well as large changes in leverage (that is, the
kurtosis in leverage changes), it does not replicate well some other basic features of quarterly
leverage changes. This may tell us that there is more going on in the actual data than the
model is able to capture by focusing on major capital restructurings.
Table IX further characterizes the cross-sectional properties of leverage ratios in our dy-
namic economy with agency conflicts and assesses the model fit. To do so, we first simulate a
number of dynamic economies as described in Appendix D.1. We then replicate the empirical
analysis in several cross-sectional capital structure studies. We start by investigating the link
between capital structure and stock returns as in Welch (2004). We also examine the speed of
mean reversion to the target as in Fama and French (2002) and Flannery and Rangan (2006).
Appendix D.2 provides a detailed description of the approach used to replicate the empirical
tests of these studies.
Insert Table IX Here
The regressions results reported in Table IX are consistent with those reported in the em-
pirical literature. In Panel A of Table IX, the estimates based on the simulated data from
our model closely match Welch’s estimates based on real data. For a one-year time horizon,
the ADR coefficient is close to one. For longer time horizons, this coefficient is monotonically
25
declining, consistent with the data. Panel B of Table IX yields that leverage is mean reverting
at a speed of 9% per year, which roughly corresponds to the average mean-reversion coefficient
reported by Fama-French (2002) (7% for dividend payers and 15% for non-dividend payers).
As in Fama and French, the average slopes on lagged leverage are similar in absolute value to
those on target leverage and are consistent with the partial-adjustment model.
B. Specification Analysis
In the following we conduct a specification analysis to diagnose which modeling assumptions
are crucial in fitting the data. Table X summarizes the statistical test results for alternative
model specifications. We consider a total of nine models. In addition to the base specification
given in (14) and (15), we estimate six additional nested models and two non-nested models:
(1) φi and ηi with uncorrelated random effects: φi = h(αφ + ǫφi ), ηi = h(αη + ǫηi ), σφη = 0
(2) no shareholder bargaining power: φi = h(αφ + ǫφi ), ηi = 0
(3) no manager-shareholder conflicts: φi = 0, ηi = h(αη + ǫηi )
(4) φ and η constant: φi = h(αφ), ηi = h(αη)
(5) no shareholder bargaining power and φ constant: φi = h(αφ), ηi = 0
(6) no manager-shareholder conflicts and η constant: φi = 0, ηi = h(αη)
(7) λ with random effects (non-nested): λi = h(αλ + ǫλi ), φi = 0, ηi = 0
(8) λ constant (non-nested): λi = h(αλ), φi = 0, ηi = 0
We use two types of likelihood-based hypothesis tests to discriminate between models. For
nested models, we use a standard likelihood-ratio test. For non-nested models, we use the
approach proposed by Vuong (1989). Details on the construction of the test statistics are
summarized in Appendix E.
Insert Table X Here
Table X reveals that our base specification dominates all alternatives. Specifications that do
not account for cross-sectional heterogeneity (φ, η, and λ defined as constants) perform poorly.
In our setup, incorporating firm-specific heterogeneity in the estimation helps dramatically in
matching observed leverage ratios. Our base specification also performs significantly better
26
than specifications assuming perfect corporate governance. Last, the specification analysis
in Table X (specifically, hypothesis tests against alternatives (7) and (8)) provides statistical
confirmation—complementing the economic intuition from Table V—that a dynamic tradeoff
model with agency costs yields better goodness-of-fit than the classic dynamic tradeoff theory
based solely on transaction costs.
V. Governance Mechanisms and Agency Conflicts
Many studies have identified factors that purport to explain variation in corporate capital struc-
tures. However, as shown by LRZ (2008), little of the variation in observed capital structures
is captured by traditional determinants of financing decisions (such as size, market-to-book,
profitability). Instead, LRZ find that the majority of the variation in leverage ratios is driven
by an unobserved firm-specific effect. The present paper argues that a potential explanation
for these findings is that managers have discretion over financing decisions, so that leverage
ratios should be determined not only by real market frictions but also by manager-shareholder
conflicts. In this section, we examine which factors affect the estimates of agency conflicts
obtained from the structural estimation.
To relate our estimates of the manager-shareholder conflicts to the firms’ governance struc-
ture, we employ data on various governance mechanisms provided by the Investor Responsibil-
ity Research Center (IRRC), Thomson Reuters, and ExecuComp. We use the IRRC data to
construct the entrenchment index of Bebchuk, Cohen and Farell (2009), E-index. IRRC also
provides data on blockholder ownership. In the analysis, we use both the total holdings of block-
holders and the holdings of independent blockholders as governance indicators. Institutional
ownership is another important governance mechanism. We collect data on the institutional
ownership share from Thomson Reuters’s database of 13f filings.
We build two proxies for internal board governance—board independence and board com-
mittees. These two measures are motivated by the SOX Act. Board independence represents
the proportion of independent directors reported in IRRC. Board committees is the sum of
four dummy variables capturing the existence and independence (more than 50% of commit-
tee directors are independent) of audit, compensation, nominating, and corporate governance
committees. In addition to these corporate governance variables, we include in our regressions
standard control variables for other firm attributes. Last, a natural proxy for CEO entrench-
ment and power is the tenure of the CEO. We obtain data on this measure from ExecuComp.
27
The definition and construction of the dependent and explanatory variables is summarized in
Table I. Table II provides descriptive statistics for these variables.
Table XI reports regression coefficients of the predicted private benefits of control, E[φit|yit; θ],
expressed in basis points, on the various explanatory variables. As robustness check, we vary
the sample and regression specification across the different columns in Table XI. Most of the
control variables have signs in line with accepted theories and, to conserve space, we confine our
discussion to those variables related to the hypothesis about the relation between managerial
discretion and financial leverage. The general pattern, which is robust across specification, is
that the coefficients on governance variables are significant and have sign that are consistent
with economic intuition. This suggests that our structural estimates indeed measure agency
conflicts within the firm.
Insert Table XI Here
The estimates in Table XI show that external governance mechanisms, represented by in-
stitutional ownership and outside blockholder ownership, are negatively related to managerial
entrenchment, suggesting that independent outside monitoring of management is effective. The
coefficients suggest that a one standard deviation increase in institutional (outside blockholder)
ownership is associated with a decrease of 66-88 (75-100) basis points in private benefits of con-
trol. Anti-takeover provisions are another important mechanism in governing corporate control.
The coefficient on “E-index - Dictatorship” is positive.12 This is consistent with the notion that
anti-takeover provisions lead to greater entrenchment and to more private benefits.
Internal governance mechanisms are captured in Table XI by managerial characteristics
and characteristics of the board of directors. CEO tenure intuitively proxies for CEO en-
trenchment and, hence, for managerial discretion. Across specifications, we consistently find
a positive relation of CEO tenure with private benefits of control. Not surprisingly, board
independence—proxied by the number of independent directors or by the existence of indepen-
dent audit, compensation, nominating, and corporate governance committees—is negatively
related to private benefits of control. This is consistent with the idea that a more independent
board of directors is a stronger monitor of management.
12Following Heckman’s (1979) approach to address endogeneity, we add the Inverse Mill’s Ratio to the re-gression specification. The coefficient is negative and statistically significant throughout, suggesting that anti-takeover provisions are endogenously determined.
28
The relation between private benefits of control and managerial delta, a proxy for managerial
incentive alignment, is U-shaped and on average positive.13 This is consistent with the incentives
versus entrenchment literature (see Claessens, Djankov, Fan, and Lang, 2002). The positive
relation on average suggests that executive pay and managerial entrenchment (hidden pay) are
complementary compensation mechanisms (see Kuhnen and Zwiebel, 2008). Not surprisingly,
the proportion of diverted cash flows decreases with firm size.
In summary, our estimates of agency conflicts are related to a number of corporate gover-
nance mechanisms. Variables associated with stronger monitoring have negative connections
with our estimates of agency conflicts. Institutional ownership, anti-takeover provisions, and
CEO tenure have the largest impact on agency conflicts and, hence, on financing decisions.
The sizeable explanatory power of governance variables (R2 is 35-37%) highlights further the
importance of accounting for governance in empirical capital structure tests.
VI. Conclusion
This paper develops a structural model to estimate the magnitude of conflicts of interests
between managers, shareholders, and bondholders and their effects on financing decisions. We
build a dynamic contingent claims model in which financing policy results from a tradeoff
between tax shields, contracting frictions, and agency conflicts. In the model, each firm is
run by a manager who sets the firm’s financing policy. Managers act in their own interests to
maximize the present value of their rents. Our analysis demonstrates that entrenched managers
issue less debt and rebalance capital structure less often than optimal for shareholders.
We estimate the model using simulated maximum likelihood and provide firm-specific esti-
mates of agency conflicts. Using observed financing choices, we find that manager-shareholder
conflicts of 1% of equity value on average are sufficient to resolve the low–leverage puzzle and
explain the time series of observed leverage ratios. Our estimates of the agency costs vary with
variables that one expects to determine managerial incentives. External and internal governance
mechanisms significantly affect the value of control and firms’ financing decisions. Our struc-
tural estimation also reveals that while shareholders can extract substantial concessions from
13One would expect leverage ratios to increase with managerial ownership so long as debt increases shareholderwealth. However, to the extent that managerial ownership protects management against outside pressures andincreases managerial discretion (Stulz, 1988), one expects leverage to decrease with ownership.
29
debtholders in default, shareholder-debtholder conflicts have little effect on the cross-sectional
variation and on the dynamics of leverage ratios.
Finally, our analysis also shows that costs of debt issuance would have to be in the order
of 30% of the amount issued to explain observed financing choices. Thus, while dynamic
capital structure theories that ignore agency conflicts can qualitatively reproduce the financing
patterns observed in the data, they do not provide a reasonable quantitative explanation for
firms’ financing policies. Overall the evidence suggests that part of the heterogeneity in capital
structures documented in Lemmon, Roberts, and Zender (2008) may be driven by the observed
variation in the governance structure of firms.
30
Appendix A. Proofs
A.1. Time-Series Distribution of Leverage
In the following we derive the time-series distribution of the leverage ratio yt. The leverage ratio
yt being a monotonic function of the interest coverage ratio zt ≡ Xt/ct, we can write yt = L (zt)
with L : R+ → R
+ and L′ < 0. The process for zt follows a Brownian Motion with drift µ
and volatility σ, that is regulated at both the lower boundary zD and the upper boundary zU .
The process zt is reset to the target level zS ∈ (zD, zU ) whenever it reaches either zD or zU .
The target leverage ratio can be expressed as L (zS). Denote the restructuring date by ι =
min (ιB , ιU ), where for i = B,U the random variable ιi is defined by ιi = inf {t ≥ 0 : zxt = zi}.Let fz (z) be the density of the interest coverage ratio. The density of leverage can be written
in terms of fz and the Jacobian of L−1 as follows:
fy (y) = fz
(L−1 (y)
) ∣∣∣∣∂
∂yL−1 (y)
∣∣∣∣ = fz
(L−1 (y)
)∣∣∣∣∣
(∂y
∂L−1 (y)
)−1∣∣∣∣∣ . (22)
To compute the time-series distribution of leverage, we need the functional form of the density
of the interest coverage ratio fz. The latter can be determined as follows.
1. Stationary density
To determine fz we first need to derive the distribution of occupation times of the process ztin closed intervals of the form [zD, z], for any z ∈ [zD, zU ]. For every Borel set A ∈ B(R), we
define the occupation time of A by the Brownian W path up to time t as
Γt (A) ,
∫ t
01A (Ws) ds = meas {0 ≤ s ≤ t : Ws ∈ A}
where meas denotes Lebesgue measure. We will be interested in the occupation time of the
closed interval [zD, z] by the interest coverage ratio given by Γt ([zD, z]). Let G (z, z0), with
initial value z0 equal to the target value zS for the interval [zD, z], be defined by:
G (z, z0) = EQz0
[Γι ([zD, z])].
Using the strong Markov property of Brownian motion, we can write
G (z, z0) = EQz0
[∫ ∞
01[zD ,z] (zs) ds
]−
∑
i,j=U,B,i6=j
EQz0
[1ιi<ιj ] EQzi
[∫ ∞
01[zD,z] (zs) ds
].
To compute G (z, z0), we will use the following lemma (Karatzas and Shreve (1991) pp. 272).
31
Lemma 1 If f : R → R is a piecewise continuous function with
∫ +∞
−∞|f (z + y)| e−|y|√2γdy <∞;∀z ∈ R,
for some constant γ > 0, and (Bt, t ≥ 0) is a standard Brownian motion, then the resolvent
operator of Brownian motion, Kγ (f) ≡ E[∫ +∞0 e−γtf (Bt) dt], equals
Kγ (f) =1√2γ
∫ +∞
−∞f (y) e−|y|√2γdy.
Let b = 1σ (µ − σ2
2 ), ϑ = −2bσ , and h(z, y) = ln(z/y). Using the above Lemma, we obtain
after simple but lengthy calculations the following expression for the occupation time measure
(similar calculations can be found e.g. in Morellec, 2004):
G (z, z0) (23)
=
12b2
[eϑh(z0,z) − eϑh(z0,zD)
]− pB
bσ ln(
zzD
)− pU
2b2
[eϑh(zU ,z) − eϑh(zU ,zD)
], for z ≤ z0,
12b2
[1 − eϑh(z0,zD)
]+ 1
bσ ln(
zz0
)− pB
bσ ln(
zzD
)− pU
2b2
[eϑh(zU ,z) − eϑh(zU ,zD)
], for z > z0,
where
pB =zϑ0 − zϑ
U
zϑD − zϑ
U
and pU =zϑ0 − zϑ
D
zϑU − zϑ
D
. (24)
The stationary density function of the interest coverage ratio zt is now given by
fz(z) =∂∂zG (z, z0)
G (zU , z0). (25)
2. Conditional density
To implement our empirical procedure, we also need to compute the conditional distribution
of leverage at time t given its value at initial date 0 (in the data we observe leverage ratios at
quarterly frequency). To determine this conditional density, we first compute the conditional
density of the interest coverage ratio zt = Xt/ct at time t given its value z0 at time 0, P(zt ∈dz|z0), and then apply the transformation (22). For ease of exposition, introduce the regulated
arithmetic Brownian motion Wt = 1σ ln (zt) with initial value w = 1
σ ln (z0), drift b = 1σ (µ− σ2
2 )
and unit variance, and define the upper and lower boundaries asH = 1σ ln(zU ) and L = 1
σ ln(zD),
respectively. Denote the first exit time of the interval (L,H) by
ιL,H = inf{t ≥ 0 : Wt /∈ (L,H)}.
The conditional distribution Fz of the interest coverage ratio z is then related to that of the
arithmetic Brownian motion W by the following relation:
Fz(z|z0) = P(Wt ≤1
σln(z)|W b
0 = w). (26)
32
Given that the interest coverage ratio is reset to the level zS whenever it reaches the boundaries,
W is regulated at L and H, with reset level at S = 1σ ln(zS) and we can write its dynamics as
dWt = bdt + dZt + 1{Wt−=L} (S − L) + 1{Wt−=H} (S −H) .
We would like to compute the cumulative distribution function of the processW at some horizon
t:
G(w, y, t) ≡ P(Wt ≤ y|w) = Ew[1{Wt≤y}], (w, y, t) ∈ [L,H]2 × (0,∞) . (27)
Rather than trying to compute this probability directly, consider its Laplace transform in time
(for notational convenience we drop the dependence of L on λ):
L(w, y) =
∫ ∞
0e−λtG(w, y, t)dt
=
∫ ∞
0e−λt
Ew[1{Wt≤y}]dt = Ew
[∫ ∞
0e−λt1{Wt≤y}dt
]. (28)
The second equality in (28) follows from the boundedness of the integrand and Fubini’s theorem.
Since the process is instantly set back at S when it reaches either of the barriers, we must have
that
L(H, y) = L(L, y) = L(S, y) for all y. (29)
Now let W 0t = w + bt + Zt denote the unregulated process. Using the Markov property of W
and the fact that W and W 0 coincide up to the first exit time of W 0 from the interval [L,H],
we deduce that the function L satisfies
L(w, y) = Ψ(w, y) + L(S, y)Φ(w), (30)
where we have set
Ψ(w, y) = Ew
[∫ ιL,H
0e−λt1{W 0
t ≤y}dt
]and Φ(w) = Ew[e−λιL,H ].
Setting w = S and solving for L(S, y) we obtain
L(S, y) =Ψ(S, y)
1 − Φ(S). (31)
Plugging this into the equation for L shows that the desired boundary condition is satisfied.
We now have to solve for Φ and Ψ. The Feynman-Kac formula shows that the function Ψ
is the unique bounded and a.e. C1 solution to the second order differential equation
1
2
∂2
(∂w)2Ψ(w, y) + b
∂
∂wΨ(w, y) − λΨ(w, y) + 1{w≤y} = 0 (32)
on the interval (H,L) subject to the boundary condition Ψ(H, y) = Ψ(L, y) = 0. Solving this
33
equation, we find that the function Ψ is given by
Ψ(w, y) =
{Λ(w) +AL(y)∆L(w), if w ∈ [L, y],
AH(y)∆H(w), if w ∈ [y,H],(33)
where we have set
Λ(w) =1
λ[1 − e(υ+b)(L−w)], and ∆L,H(w) = e(υ−b)w[1 − e2υ((L,H)−w)], (34)
with υ = υ(λ) =√b2 + 2λ. Because the function 1{w≤y} is (piecewise) continuous, the function
Ψ(w, y) is piecewise C2 (see Theorem 4.9 pp. 271 in Karatzas and Shreve, 1991). Therefore,
Ψ(w, y) is C0 and C1 and satisfies the continuity and smoothness conditions at the point w = y.
This gives
Λ(y) +AL∆L(y) = AH∆H(y), and Λ′(y) +AL∆′L(y) = AH∆′
H(y).
Solving this system of two linear equations, we obtain the desired constants as
AL = AL(y, λ) =Λ(y)∆′
H(y) − Λ′(y)∆H(y)
∆H(y)∆′L(y) − ∆L(y)∆′
H(y), (35)
AH = AH(y, λ) =Λ(y)∆′
L(y) − Λ′(y)∆L(y)
∆H(y)∆′L(y) − ∆L(y)∆′
H(y). (36)
Let us now turn to the computation of Φ. The Feynman-Kac formula shows that the
function Φ is the unique bounded and a.e. C1 solution to the second order differential equation
1
2Φ′′(w) + bΦ′(w) − λΦ(w) = 0 (37)
on the interval (H,L) subject to the boundary condition Φ(H) = Φ(L) = 1. Solving this
equation, we find that the function Φ is given by
Φ(w) = BL∆L(w) +BH∆H(w), (38)
where
BL = BL(λ) = − e(υ+b)H
e2υL − e2υH, and BH = BH(λ) =
e(υ+b)L
e2υL − e2υH. (39)
The conditional density function g(w, y, t) = ∂∂yG(w, y, t) can be obtained by differentiating
the Laplace transform (28) with respect to y. We obtain
∂
∂yL(w, y) =
∫ ∞
0e−λtg(w, y, t)dt =
∂
∂yΨ(w, y) +
Φ(w)
1 − Φ(S)
∂
∂yΨ(S, y), (40)
where∂
∂yΨ(w, y) =
{A′
L(y)∆L(w), if w ∈ [L, y],
A′H(y)∆H(w), if w ∈ [y,H],
34
and
A′L(y) =
(AH(y)∆′′
H(y) −AL(y)∆′′L(y) − Λ′′(y)
∆H(y)∆′L(y) − ∆L(y)∆′
H(y)
)∆H(y), (41)
A′H(y) =
(AH(y)∆′′
H(y) −AL(y)∆′′L(y) − Λ′′(y)
∆H(y)∆′L(y) − ∆L(y)∆′
H(y)
)∆L(y). (42)
The last step involves the inversion of the Laplace transform (40) for g(w, y, t).
A.2. Predictions of the Structural Parameters
Denote by yit the financial leverage of firm i at date t, and collect the observations for firm i
in the vector yi. The unobserved characteristics of firm i are captured by ǫi = (ǫφi , ǫηi ). The
parameter vector is θ = (αφ, αη , σφ, ση , σφη). Given the leverage data yi = (yit), the conditional
expectation of shareholders’ bargaining power ηi in firm i satisfies:
E[ηi|yi; θ] = E[h(αη + ǫηi )|yi; θ]
=
∫
ǫηi
∫
ǫφi
h(αη + ǫηi )f(ǫφi , ǫηi |yi; θ)dǫ
φi dǫ
ηi
=
∫
ǫηi
∫
ǫφi
h(αη + ǫηi )f(ǫφi , ǫ
ηi , yi|θ)
f(yi|θ)dǫφi dǫ
ηi
=
∫ǫηi
∫ǫφi
h(αη + ǫηi )f(yi|ǫφi , ǫηi ; θ)f(ǫφi , ǫ
ηi |θ)dǫ
φi dǫ
ηi
∫ǫηi
∫ǫφi
f(yi|ǫφi , ǫηi ; θ)f(ǫφi , ǫ
ηi |θ)dǫ
φi dǫ
ηi
=
∫ǫηi
∫ǫφi
h(αη + ǫηi )f(yi1|ǫφi , ǫηi ; θ)
ni∏t=2
f(yit|yit−1, ǫφi , ǫ
ηi ; θ)f(ǫφi , ǫ
ηi )dǫ
φi dǫ
ηi
∫ǫηi
∫ǫφi
(f(yi1|ǫφi , ǫ
ηi ; θ)
ni∏t=2
f(yit|yit−1, ǫφi , ǫ
ηi ; θ)
)f(ǫφi , ǫ
ηi )dǫ
φi dǫ
ηi
. (43)
In these equations, f(yi1|ǫφi , ǫηi ; θ) and f(yit|yit−1, ǫ
φi , ǫ
ηi ; θ) are the unconditional and, respec-
tively, conditional distribution of leverage implied by the model, given in Appendix A.1. The
term f(ǫφi , ǫηi |θ) represents a bivariate normal density, and θ are the estimated parameters. The
conditional expectation of the manager’s private benefits of control satisfies a similar expression
with η replaced by φ. Given parameter estimates for θ obtained in the SML estimation, the
expression in (43) can be evaluated using Monte-Carlo integration. Last, one can show that
these conditional expectations are unbiased. Let zi be omitted explanatory variables. Then
E[gi|yi, zi; θ] = E[gi|yi; θ] + ei,
where g ∈ {φ, η} with the following moment condition on the error ei:
E(ei|yi; θ) = E(E(gi|yi, zi; θ) − E(gi|yi; θ)|yi, δi; θ)
= E(E(gi|yi, zi; θ)|yi, δi; θ) − E(E(gi|yi; θ)|y; θ) = 0.
35
Appendix B. Data Definitions
B.1. Managerial pay-performance sensitivity delta
We compute the delta—the sensitivity of the option value to a change in the stock price—
based on the Black-Scholes (1973) formula for European call options, as modified to account
for dividend payouts by Merton (1973):
Call = Se−dTN (Z) −Xe−rTN (Z − σT 1/2),
where Z =[ln (S/X) +
(r − d+ σ2/2
)T]/(σT 1/2
), S is the price of the underlying stock, X
the exercise price of the option, T the time-to-maturity of the option in years, r the risk-free
interest rate, d the expected dividend yield on the underlying stock, σ expected stock return
volatility, and N is the standard normal probability distribution function.
We follow the methodology of Core and Guay (1999) to compute delta. There are four type
of securities: new option grants, previous unexercisable options, previous exercisable options
and portfolio of stocks. In order to avoid double counting of the new option grants, the number
and realizable value of previous unexercisable options is reduced by the number and realizable
value of new option grants. If the number of new option grants is greater than the number of
previous unexercisable options, then the number and realizable value of previous exercisable
options is reduced by the difference between the number and realizable value of new option
grants and previous exercisable options.
Managerial delta is computed as the sum of delta of new option grants, delta of previous
unexercisable options, delta of previous exercisable options and delta of portfolio of stock where:
1. New option grants: S, K, T , d, and σ are available from ExecuComp. The risk-free
rate r is obtained from the Federal Reserve, where we use one-year bond yield for T = 1,
two-year bond for 2 ≤ T ≤ 3, five-year bond yield for 4 ≤ T ≤ 5, seven year bond yield
for 6 ≤ T ≤ 8 and ten-year bond yield for T ≥ 9.
2. Previous unexercisable options: S, d, σ and r are obtained as explained above. The
strike price K is estimate as: [stock price - (realizable value/number of options)]. Time-
to-maturity, T , is estimated as one year less than time-to-maturity of new options grants
or nine years if no new grants are made.
3. Previous exercisable options: S, d, σ and r are obtained as explained above. The strike
price K is estimated as: K = [stock price - (realizable value/number of options)]. Time-
to-maturity, T , is estimated as three years less than the time-to-maturity of unexercisable
options or six years if no new grants are made.
4. Portfolio of stocks: delta is estimated by the product of the number of stocks owned
and one percent of stock value.
36
B.2. Managerial incentive alignment ϕ
Managerial incentives are defined as the change in managerial wealth per dollar change in
the wealth of shareholders. Incentives are thus composed of a direct component, managerial
ownership and an indirect component, the pay-performance sensitivity generated by options
awards. Following Jensen and Murphy (1990), we define managerial incentives, ϕ, as:
ϕ = ϕE + deltaShares represented by options awards
Shares outstanding,
where ϕE represents managerial ownership and delta is computed as above.
Appendix C. Monte-Carlo Simulation Error in SML
A natural question in any simulated maximum likelihood estimation is the correct choice the
number of random draws, K, when integrating out the unobserved random effects from the
likelihood function. A known issue in simulation-based estimation is that for finite K, the sim-
ulation error can lead to both imprecise and biased point estimates. In order to assess precision
and accuracy of the simulations performed during the SML estimation and the associated bias
in the SML estimates, we perform the following experiment. We vary the choice of K from small
to large. For a given choice of K, we simulate the log-likelihood a total of 100 times at the same
parameters. In every round, we draw a different set of random numbers for the realizations of
the firm-specific random effects (used to integrate out the unobservable random effects from
the likelihood function). This experiment yields both a measure of how the precision of the
simulated log-likelihood changes with K and how fast the bias in the log-likelihood due to a
finite Monte-Carlo simulation sample shrinks. From this, one can infer how the precision of the
estimated coefficients is expected to change with K and how fast the bias in the ML estimates
shrinks—without having to reestimate the model with different sets of random draws.
Figure 1 reports descriptive statistics for simulation precision and bias. Here we repeatedly
simulate the model with K = 2, 3, 4, 5, 10, 25, 50, 100, 250, 500, 750, 1000 (100 times each). In
all plots, we vary on the horizontal axis the number of random draws K used to evaluate the
log-likelihood. Panel A reports box plots for the simulated values of the log-likelihood across
simulation rounds. Depicted are the lower quartile, median, and upper quartile values as the
lines of the box. Whiskers indicate the adjacent values in the data. Outliers are displayed with
a + sign. The highest simulated log-likelihood value across all simulation rounds is indicated
by a dotted line. Panel B reports descriptive statistics for the precision and accuracy of the
Monte-Carlo simulations. We capture precision by the “variation” in the simulation error across
runs (that is, the variation in the simulated log-likelihood) and accuracy by the “average” in the
simulation error. More precisely, Panel B depicts the magnitude of the simulation imprecision
(left) and the simulation bias (right) as function of K. The simulation imprecision is measured
by the 95% quantile minus the 5% quantile across all simulation rounds for given K and
37
normalized by the highest simulated log-likelihood value across all simulation rounds and all K
(our proxy for the true log-likelihood value). The simulation bias is measured by the median
log-likelihood value across all simulation rounds for given K relative to the highest simulated
log-likelihood value across all simulation rounds.
The impact of simulation error on the precision and accuracy of the log-likelihood (and,
hence, on the SML estimates θ) becomes negligible when both the imprecision and bias do not
drop further (y-axis) when we increase the number of random draws K (x-axis). We find that
K = 1000 draws are sufficient to satisfy both criteria and render the simulation error negligible.
Correspondingly, we set the number of draws to K = 1000 in the estimations.
Appendix D. Simulation Evidence on Leverage Dynamics
In this Appendix, discuss the approach taken to simulate a number of dynamic economies used
in our moment tests and used to replicate the empirical tests conducted by cross-sectional
capital structure studies in the literature.
D.1. Simulation approach
We follow the simulation approach of Berk, Green and Naik (1999) and Strebulaev (2007). We
start by simulating a number of dynamic artificial economies that are inhabited by as many
firms as we have observations in the actual data. At date zero, all firms are assumed to be
at their target leverage. We then simulate 75 years of quarterly data. The first 40 years of
data are dropped in order to eliminate the impact of initial conditions. The resulting dataset
corresponds to a single simulated economy. One important deviation from prior studies is
that we base our simulation on parameter estimates (reported in Section III) instead of using
calibrated parameter values.14 Specifically, based on these estimates, we introduce heterogeneity
in the private benefits of control, φi, and in shareholder bargaining power, ηi, by taking a single
random draw for the unobserved random effects. We simulate a total of M = 1, 000 economies,
each characterized by different draws for the random effects. The results we report are average
values over the M economies.
D.2. Simulation evidence on cross-sectional capital structure studies
In this section, we further assess the fit of our model and the cross-sectional properties of leverage
ratios in our dynamic economy with agency conflicts. To do so, we first simulate a number of
dynamic economies as described in the previous section and then replicate the empirical analysis
conducted by various cross-sectional capital structure studies. We test wether the results of
regressions on our simulated data are consistent with those reported in the empirical literature.
14Strebulaev (2007, pp. 1763) notes that “An important caveat is that for most parameters of interest, thereis little evidence permitting precise estimation of sampling distributions or even their ranges [...] Overall then,the parameters used in the simulations must be regarded as ad hoc and approximate.”
38
Leverage Inertia: We start by investigating the link between capital structure and stock
returns. Welch (2004) documents that firms do not rebalance their capital structure in order
to offset the mechanistic effect of stock price movements on firms’ leverage ratios. He shows
that for short horizons the dynamics of leverage ratios are solely determined by stock returns.
While this effect attenuates with time, Welch argues that it is the main driving force behind
leverage ratio changes.
We investigate to what extent this mechanistic effect is reflected in our model. To do so,
we replicate Welch’s analysis on the simulated data. We run a Fama-MacBeth regression of
leverage on past leverage and the implied debt ratio (IDR). In this regression, IDR is the
implied debt ratio that comes about if the firm does not issue debt or equity (and let leverage
ratios change with stock price movements). More formally, we estimate the following model:
Lt = α0 + α1Lt−k + α2IDRt−k,t + ǫt, (44)
where L is the Leverage ratio and k denotes the time horizon in years. If α1 is equal to 1, firms
perfectly offset stock price movements by issuing debt or equity. If α2 is equal to 1, firms do
not readjust their capital structure at all following stock price movements.
Our results are reported in Panel A of Table IX. We observe that the estimates based on
the simulated data from our model closely match Welch’s estimates based on real data. For
a one year time horizon, the ADR coefficient is close to one. For longer time-horizons, this
coefficient is monotonically decreasing.
Mean Reversion in Leverage: Mean reversion is another well documented pattern in lever-
age ratios [see Fama and French (2002) and Flannery and Rangan (2006)]. Following Fama and
French (2002), we perform a Fama-MacBeth estimation of the partial-adjustment model
Lt − Lt−1 = α+ λ1TLt−1 + λ2Lt−1 + ǫt, (45)
where L is observed leverage and TL is target leverage. If λ1 is equal to 1, firms perfectly
readjust leverage to the target. If λ2 is equal to −1, firms are completely inactive. The partial-
adjustment model predicts that λ1 and λ2 are equal in absolute value, and λ1 measures the
speed of adjustment. In the empirical literature, TL is determined in a preliminary step as the
predicted value from the following reduced-form equation:
Lt = a0 + a1πt + a2σ + a3α+ a4η + a5ϕ+ a6φ+ ǫt, (46)
where πt denotes profitability and the remaining independent variables are the firm-specific
characteristics described in Section II.A. In our setup, profitability is defined as πt = (Xt +
∆At)/At−1, where Xt denotes cash flows from operation and At is the book value of assets.
Following Strebulaev (2007), we assume that the book value of assets and cash flows from
operation have the same drift under the physical measure. Equation (46) is estimated in a first
stage using pooled OLS.
39
Our results are reported in Panel B of Table IX. We observe that leverage is mean-reverting
at a speed of 9% per year which roughly corresponds to the average mean-reversion coefficient
reported by Fama-French (2002) (7% for dividend payers and 15% for non-dividend payers).
As in Fama and French, the average slopes on lagged leverage are similar in absolute value to
those on target leverage and are consistent with the partial adjustment model.
Appendix E. Specification Analysis
E.1. Nested Models
For nested models, we use a standard log-likelihood ratio test to discriminate between model
specifications. The log-likelihood ratio test statistic is appropriate only for nested models.
Denote by lnLu the log-likelihood of the unconstrained model and lnLc the log-likelihood of
the constrained model. The number of parameter constraints is J . The likelihood ratio statistic
in this case is defined as:
LR = 2(lnLu − lnLc) → χ2(J). (47)
The test statistic LR follows a Chi-squared distribution with degrees of freedom equal to the
number of parameter constraints.
E.2. Non-Nested Models
For non-nested models, we follow the approach by Vuong (1989). Vuong proposes to discrimi-
nate between two model families Fθ = {f(y|θ); θ ∈ Θ} and Gγ = {g(y|γ); γ ∈ Γ} based on the
following model selection statistic:
LRV =lnLf (θ; y) − lnLg (γ; y) − (p− q)
ω, (48)
where p and q are the degrees of freedom in model Fθ and Gγ , respectively. The constant ω is
defined as:
ω2 =1
N
N∑
i=1
[log
f(yi|θ)g (yi|γ)
]2
−[
1
N
N∑
i=1
logf(yi|θ)g (yi|γ)
]2
. (49)
Under the null hypothesis,
LRV −→ N (0, 1).
If LRV > c, where c is a critical value from the standard normal distribution, one rejects the
null that the models are equivalent in favor of Fθ. If LRV < c, one rejects the null that the
models are equivalent in favor of Gγ . If |LRV | ≤ c, one cannot discriminate between the two
competing models.
40
Appendix F. Internet Appendix: Scaling property
Consider a model with static debt policy, as in Leland (1994). Denote the values of equity
and corporate debt by E (x) and B (x) respectively. Assuming that the firm has issued debt
with coupon payment c, the cash flow accruing to shareholders over each interval of time of
length dt is: (1 − τ) (1 − φ)(x− c)dt, where the tax rate τ = 1 − (1 − τ c) (1 − τd) reflects both
corporate and personal taxes. In addition to this cash flow, shareholders receive capital gains
of E[dE] over each time interval. The required rate of return for investing in the firm’s equity
is r. Applying Ito’s lemma, it is then immediate to show that the value of equity satisfies for
x > xB :
rE =1
2σ2x2∂
2E
∂x2+ µx
∂E
∂x+ (1 − τ) (1 − φ) (x− c) .
The solution of this equation is
E(x) = Axξ +Bxν + Π(x) − (1 − τ) (1 − φ)c
r,
where
Π(x) = EQ[∫ ∞
te−r(s−t)(1 − τ)(1 − φ)Xs ds|Xt = x
]= (1 − τ)
(1 − φ
r − µ
)x. (50)
and ξ and ν are the positive and negative roots of the equation 12σ
2y(y− 1) +µy− r = 0. This
ordinary differential equation is solved subject to the following two boundary conditions:
E (x)|x=xB= η (α− κ) Π (xB) , and lim
x→∞[E (x) /x] <∞.
The first condition equates the value of equity with the cash flow to shareholders in default.
The second condition is a standard no-bubble condition. In addition to these two conditions,
the value of equity satisfies the smooth pasting condition: ∂E/∂x|x=xB= η (α− κ) Πx (xB) at
the endogenous default threshold (see Leland (1994)). Solving this optimization problem yields
the value of equity in the presence of manager-shareholder conflicts as
E(x, c) = Π (x) − (1 − τ) (1 − φ)c
r−{
[1 − η (α− κ)] Π (xB) − (1 − τ)(1 − φ)c
r
}(x
xB
)ν
In these equations, the default threshold xB satisfies
xB =ν
ν − 1
r − µ
r
c
1 − η (α− κ).
Taking the trigger strategy xB as given, the value of corporate debt satisfies in the region
for the cash flow shock where there is no default
rB =1
2σ2x2∂
2B
∂x2+ µx
∂B
∂x+(1 − τ i
)c.
41
This equation is solved subject to the standard no-bubbles condition limx→∞B(x) = c/r and
the value-matching condition B (x)|x=xB= [1 − κ− η (α− κ)] Π (xB). Solving this valuation
problem gives the value of corporate debt as
B (x, c) =
(1 − τ i
)c
r−{
(1 − τ i)c
r− [1 − κ− η (α− κ)]Π (xB)
}(x
xB
)ν
.
Using the above expressions for the values of corporate securities, it is immediate to show that
the present value M(x) of the cash flows that the manager gets from the firm satisfies:
M (x) =
[ϕ+
φ
1 − φ
]Π(x)
+
{ϕ(1 − τ i
)− (1 − τ) [φ+ ϕ (1 − φ)]
}c
r
[1 −
(x
xB
)ν]
−{ϕκ+ [1 − η (α− κ)]
φ
1 − φ
}Π(xB)
(x
xB
)ν
.
Plugging the expression for the default threshold in the manager’s value function M(x), it is
immediate to show that M (x) is concave in c. As a result, the selected coupon payment can
be derived using the first-order condition: ∂M (x0) /∂c = 0. Solving this FOC yields
c = xr (ν − 1) [1 − η (α− κ)]
ν (r − µ)
1
(1 − ν)−ν (1 − τ)
{ϕ (1 − φ) κ
1−η(α−κ) + φ}
ϕ (1 − τ i) − (1 − τ) [φ+ ϕ (1 − φ)]
1
ν
These expressions demonstrate that in the static model the default threshold xB is linear in c.
In addition, the selected coupon rate c is linear in x. This implies that if two firms i and j are
identical except that xi0 = θxj
0, then the optimal coupon rate and default threshold ci = θcj
and xiB = θxj
B, and every claim will be larger by the same factor θ.
42
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Table I
Data Definitions
Variable (Data Source) Variable Definition
Financial Indicators (Compustat):Book debt Liabilities total (item 181) + Preferred stock (item 10)
- Deferred taxes (item 35)Book debt (alternate) Long term debt (item 9) + Debt in current liabilities (item 34)Book equity Assets total (item 9) - Book debtBook equity (alternate) Assets total (item 6) - Book debt (alternate)Leverage Book Debt/(Assets total (item 6) - Book equity
+ Market value (item 25 * item 6))Leverage (alternate) Book Debt (alternate)/(Assets total (item 6) - Book equity (alternate)
+ Market value (item 25 * item 6))Return on assets (EBIT (item 18) + Depreciation (item 14))/Assets total (item 6)Market-to-Book (Market value (item 25 * item 6) + Book debt)/Assets total (item 6)Tangibility Property, plant and equipment total net (item 8)/Assets total (item 6)Size log(Sales net (item 12))R&D Research and development expenses (item 46)/Assets total (item 6)
Earnings Growth (I/B/E/S):EBIT growth rate Mean analysts forecast for long-term growth rate per SIC-2 industry
Volatility and Beta (CRSP):Equity volatility Standard deviation of monthly equity returns over past 5 yearsMarket model beta Market model regression beta on monthly equity returns over past 5 years
Executive Compensation (ExecuComp):Managerial incentives see Appendix BManagerial ownership Shares owned/Shares outstanding for the 5 highest paid executivesManagerial delta see Appendix BCEO tenure Current year - year became CEOEBIT growth rate (alternate) 5-year least squares annual growth rate of
operating income before depreciation
Blockholders (IRRC blockholders):Blockholder ownership Fraction of stock owned by outside blockholders
Directors (IRRC directors):Board independence Number of independent directors/Total number of directorsBoard committees Sum of 4 dummy variables for existence of independent (more that 50% of
committee directors are Independent) audit, compensation, nominatingand corporate governance committee
Anti-Takeover Provisions (IRRC governance):E-index 6 anti-takeover provisions index by Bebchuk, Cohen, and Farell (2004)G-index 24 anti-takeover provisions index by Gompers, Ishii, and Metrick (2003)
Institutional Ownership (Thompson Financial):Institutional ownership Fraction of stock owned by institutional investors
Economy indicators (FED):Term Premium Difference between 10 year and 1 year Government bond yieldDefault Premium Difference between corporate yield spread (all industries)
of Moody’s BAA and AAA rating
47
Table II
Descriptive Statistics
The table presents descriptive statistics for the main variables used in the estimation. Thesample is based on Compustat quarterly Industrial files, ExecuComp, CRSP, I/B/E/S, IRRCgovernance, IRRC blockholders, IRRC directors, and Thompson Financial. Table I provides adetailed definition of the variables.
Mean S.D. 25% 50% 75% Obs
Leverage (y) 0.32 0.20 0.16 0.29 0.46 13,159Leverage (alternate) 0.20 0.19 0.04 0.16 0.31 13,159
EBIT Growth Rate (m) 0.20 0.06 0.15 0.19 0.23 13,159EBIT Volatility (σ) 0.29 0.13 0.19 0.26 0.35 13,159CAPM Beta (β) 1.06 0.51 0.70 1.01 1.34 13,159Liquidation Costs (α) 0.51 0.12 0.45 0.50 0.58 13,159
Financial Characteristics:Return on Assets 4.47 2.41 2.93 4.19 5.69 13,159Market-to-Book 2.05 1.27 1.23 1.64 2.39 13,159Tangibility 0.34 0.22 0.16 0.28 0.47 13,159Firm Size 5.58 1.20 4.74 5.50 6.35 13,159R&D 0.22 0.80 0.00 0.00 0.00 13,159
Ownership Structure:Institutional Ownership 0.60 0.17 0.49 0.62 0.73 11,727Blockholder Ownership 0.09 0.13 0.00 0.00 0.16 13,159
Managerial Characteristics:Managerial Incentives (ϕ) 0.07 0.09 0.02 0.04 0.08 13,159Managerial Ownership (ϕE) 0.05 0.08 0.00 0.01 0.05 13,159Managerial Delta 7.13 13.00 1.11 2.88 7.20 10,895CEO Tenure 8.67 8.78 2.42 5.92 11.90 13,159
Anti-Takeover Provisions:E-index 2.35 1.35 1.00 2.00 3.00 10,828G-index 9.31 2.77 7.00 9.00 11.00 10,853
Board Structure:Board Independence 0.61 0.18 0.50 0.63 0.75 8,665Board Committees 2.49 1.10 2.00 2.00 3.00 6,504
Macro Indicators:Term Premium 0.01 0.01 0.00 0.01 0.02 13,159Default Premium 0.01 0.00 0.01 0.01 0.01 13,159
48
Table III
Comparative Statics for the Dynamic Model
The table reports the main comparative statics of the dynamic model regarding the firm’sfinancing and default policies, the recovery rate in default, corporate spreads (in basis points)and the tax benefit of debt. The tax benefit of debt is defined as the percentage increase in firmvalue due to the tax savings associated with debt financing. Input parameter values for thebase case environment are set as follows: the risk-free interest rate r = 4.21%, the initial valueof the cash flow shock x0 = 1 (normalized), the growth rate and volatility of the cash flow shockµ = 1% and σ = 25%, the corporate tax rate τ c = 35%, the tax rate on dividends τd = 11.6%,the tax rate on interest income τ i = 29.3%, liquidation costs α = 50%, renegotiation costsκ = 0%, refinancing costs λ = 0.5%, shareholders’ bargaining power η = 50%, managerialownership ϕ = 7%, and private benefits of control φ = 1%.
Quasi-Market Leverage (%) at Target Credit Recovery Tax Benefit
Restructuring Target Default Spread (bp) Rate (%) of Debt (%)
Base 15.02 31.81 85.39 151.33 46.44 10.53
Cost of debt issuance (Base: λ = 0.005)λ = 0.0025 17.41 31.09 85.26 158.02 46.64 11.25λ = 0.0075 13.29 32.04 85.51 145.38 46.24 9.90
Managerial entrenchment (Base: φ = 0.01)φ = 0.005 23.14 40.80 83.86 247.78 50.91 13.44φ = 0.015 3.38 12.41 87.82 42.75 40.60 2.52
Shareholder bargaining power (Base: η = 0.5)η = 0.25 17.46 36.94 93.14 152.95 45.85 12.41η = 0.75 12.57 26.66 76.53 149.79 47.04 8.64
Managerial ownership (Base: ϕ = 0.07)ϕ = 0.05 5.10 16.13 87.38 58.21 41.53 4.35ϕ = 0.10 20.70 38.37 84.33 216.05 49.45 12.75
Renegotiation costs (Base: κ = 0.00)κ = 0.05 12.85 27.80 87.53 125.23 42.22 8.77κ = 0.10 11.41 25.01 89.36 109.13 38.72 7.62
Liquidation costs (Base: α = 0.5)α = 0.45 15.51 32.84 87.02 151.65 46.32 10.90α = 0.55 14.53 30.78 83.71 151.02 46.56 10.15
Cash flow growth rate (Base: µ = 0.01)µ = 0.005 15.00 31.76 85.67 161.97 45.93 9.29µ = 0.015 15.04 31.85 85.11 141.67 46.77 12.26
Cash flow volatility (Base: σ = 0.25)σ = 0.20 18.07 35.42 84.03 96.83 51.55 10.57σ = 0.30 12.90 29.12 86.45 217.70 42.44 10.77
Corporate tax rate (Base: τc = 0.35)τc = 0.30 1.43 8.05 87.56 26.78 42.36 0.59τc = 0.40 22.48 38.55 84.52 235.27 46.10 19.23
49
Table IV
Model Identification: Sensitivity of Model Moments to Parameters
The table presents sensitivities of data moments with respect to the model parameters. Weobtain the model-implied moments and sensitivities by Monte-Carlo simulation. The baselineparameter values are (λ, φ, η) = (.005, 0, 0). The column titled ‘Baseline Moments’ reports themodel moment at the baseline parameter values, and the columns titled ‘Sensitivity’ report(∂m/∂θ)/m for each of the structural parameters.
Baseline Sensitivity
moments λ φ η
Leverage:Mean 0.53 -4.59 -11.42 -0.39Median 0.49 -3.20 -13.86 -0.41S.D. 0.19 7.27 4.54 -0.34Skew 0.71 -21.84 21.32 0.31Kurtosis 2.58 -2.83 11.86 0.17Range 0.74 3.69 8.47 -0.23IQR 0.27 5.26 -2.44 -0.41Min 0.26 -10.62 -24.36 -0.36Max 1.00 0.00 0.00 -0.26Autocorrelation 1qtr 0.93 0.78 1.88 -0.01Autocorrelation 1yr 0.75 3.19 6.66 -0.02
Changes in leverage:Mean 0.00 -24.72 -23.95 -0.03Median 0.00 624.58 149.46 -1.34S.D. 0.06 6.34 -7.88 -0.34Skew 0.17 252.65 54.03 -0.58Kurtosis 3.30 16.46 6.59 -0.05Range 0.66 -1.56 11.91 -0.31IQR 0.08 -1.62 -11.75 -0.31Min -0.34 -2.85 16.74 -0.47Max 0.33 -0.23 6.36 -0.14Autocorrelation 1qtr -0.05 -16.47 -52.94 0.02Autocorrelation 1yr -0.03 14.93 -3.32 0.26
Event frequencies:Pr(Default) 0.32 -10.10 -35.03 0.14Pr(Issuance) 2.62 -142.06 -26.60 0.15Issue size (%) 0.13 122.00 12.11 -0.59
50
Table V
Refinancing Cost Estimates in the Model without Agency Conflicts
The table presents estimation results of the cost of refinancing in a dynamic capital structuremodel without agency conflicts (φi = 0 and ηi = 0). The structural parameters characterizingthe cost of refinancing, λ, are defined as:
λi = h(αλ + ǫλi ),
where h = Φ ∈ [0, 1] is the standard normal cumulative distribution function and ǫi ∼ N (0, σ2λ),
i = 1, . . . , N . Panel A reports the parameter estimates. Cluster-robust t-statistics that ad-just for cross-sectional correlation in each time period and, respectively, industry clusteredt-statistics are reported in parentheses. Panel B reports distributional characteristics of thepredicted, model-implied cost of refinancing, λi = E(λi|yi; θ). The refinancing cost estimatesacross firms are expressed in percent. The number of observations is 13,159.
Panel A: Parameter estimates
αλ σλ lnL
Coef. −1.40 1.39 16,566Time clustered t-stat (−14.26) (29.74)Industry clustered t-stat (−6.12) (12.31)
Panel B: Refinancing cost estimates across firms (%)
Mean S.D. Skewness Kurtosis 5% 25% 50% 75% 95%
λi 15.48 15.06 1.74 6.65 0.92 4.46 11.15 20.60 46.39
51
Table VI
Structural Parameter Estimates in the Model with Agency Conflicts
The table presents estimation results of the structural parameters in the dynamic capital struc-ture model with agency conflicts. The structural parameters characterizing the managerialentrenchment, φ, and the bargaining power of shareholders, η, are defined by:
φi = h(αφ + ǫφi ),
ηi = h(αη + ǫηi ),
where h = Φ ∈ [0, 1] is the standard normal cumulative distribution function and ǫi,i = 1, . . . , N , is a bivariate normal random variable capturing firm-specific unobserved het-erogeneity: (
ǫφiǫηi
)∼ N (0,
[σ2
φ σφη
σφη σ2η
]).
Across firms i, (ǫφi , ǫηi ) are assumed independent. The first panel reports the parameter estimates
in the base specification. Cluster-robust t-statistics that adjust for cross-sectional correlation ineach time period and, respectively, industry clustered t-statistics are reported in parentheses.As robustness checks, the remaining panels report the parameter estimates in a number ofalternative specifications. The number of observations is 13,159.
αφ αη σφ ση σφη lnL
Base specificationCoef. −2.79 −0.27 0.94 2.38 −0.15 18,654Time clustered t-stat (−14.57) (−0.46) (44.18) (14.19) (−0.13)Industry clustered t-stat (−44.40) (−0.46) (57.04) (5.55) (−0.12)
Restructuring cost λ = 0.50%Coef. −2.76 −0.70 0.94 2.35 −0.39 18,616Time clustered t-stat (−53.39) (−2.78) (10.81) (2.38) (−0.99)Industry clustered t-stat (−36.11) (−5.67) (5.11) (2.58) (−0.91)
Alternate ownership measure ϕE
Coef. −3.16 −0.73 1.02 2.80 −0.43 18,147Time clustered t-stat (−29.88) (−8.20) (7.33) (8.68) (−0.86)Industry clustered t-stat (−50.65) (−12.85) (13.13) (5.81) (−1.80)
Renegotiation cost κ = 15%Coef. −3.27 −1.29 1.04 5.52 0.88 18,588Time clustered t-stat (−33.19) (−5.40) (67.48) (7.84) (0.68)Industry clustered t-stat (−35.55) (−5.40) (27.42) (4.24) (0.34)
52
Table VI Continued
αφ αη σφ ση σφη lnL
Nuisance parameters set to initial value θ⋆i = θ⋆
i1
Coef. −2.83 −0.48 0.94 3.01 −0.26 18,364Time clustered t-stat (−29.70) (−0.27) (7.18) (0.48) (−0.11)Industry clustered t-stat (−21.76) (−0.41) (6.38) (0.82) (−0.13)
Nuisance parameters set to firm-time specific estimates θ⋆it
Coef. −2.98 −0.39 0.96 2.46 −0.26 -2,741Time clustered t-stat (−12.50) (−3.89) (64.66) (6.52) (−2.09)Industry clustered t-stat (−17.96) (−4.62) (114.23) (5.10) (−3.53)
Logit specification for link function hCoef. −7.16 −1.44 3.21 3.46 −1.09 18,144Time clustered t-stat (−8.88) (−1.69) (2.10) (1.66) (−0.26)Industry clustered t-stat (−12.59) (−1.96) (3.02) (2.54) (−0.68)
Alternate definition of leverageCoef. −2.24 −0.48 0.93 1.90 −0.13 -58,396Time clustered t-stat (−17.30) (−1.24) (146.15) (2.34) (−0.94)Industry clustered t-stat (−26.87) (−2.14) (185.95) (3.37) (−0.65)
53
Table VII
Managerial Entrenchment and Shareholder Bargaining Power Across Firms
The table summarizes distributional characteristics of the fitted managerial entrenchment, φi =E(φi|yi; θ), and bargaining power of shareholders, ηi = E(ηi|yi; θ), i = 1, . . . , N . Appendix A.2derives explicit expressions for φi and ηi. In brackets we report managerial entrenchmentexpressed as a fraction of equity value, E(φiF
∗i /Ei|yi; θ). The managerial entrenchment cost
estimates across firms are expressed in percent. The first panel reports the fitted values inthe base specification. As robustness checks, the remaining panels report the fitted values in anumber of alternative specifications.
Mean S.D. Skewness Kurtosis 5% 25% 50% 75% 95%
Base specification
φi 1.12 2.23 3.83 19.75 0.02 0.09 0.30 1.16 5.58[1.02] [2.23] [4.19] [23.03] [0.01] [0.07] [0.23] [0.91] [4.82]
ηi 0.43 0.25 0.01 2.08 0.03 0.23 0.46 0.61 0.85
Restructuring cost λ = 0.50%
φi 1.28 2.49 3.98 21.55 0.02 0.10 0.38 1.35 5.34[1.19] [2.50] [4.34] [25.20] [0.01] [0.09] [0.29] [1.18] [5.49]
ηi 0.39 0.23 0.38 2.45 0.04 0.22 0.38 0.54 0.83
Alternate ownership measure ϕE
φi 0.76 1.87 4.34 23.77 0.00 0.03 0.14 0.52 3.55[0.70] [1.85] [4.77] [29.03] [0.00] [0.02] [0.11] [0.47] [3.29]
ηi 0.38 0.25 0.35 2.25 0.02 0.17 0.38 0.55 0.85
Renegotiation cost κ = 15%
φi 0.86 1.96 4.32 24.81 0.01 0.05 0.16 0.72 4.38[0.77] [1.85] [4.59] [28.29] [0.01] [0.04] [0.12] [0.62] [4.00]
ηi 0.41 0.29 0.17 1.81 0.01 0.12 0.42 0.66 0.89
Nuisance parameters set to their initial value θ⋆i = θ⋆
i1
φi 1.33 2.67 3.80 19.98 0.02 0.09 0.34 1.32 6.87[1.23] [2.69] [4.19] [23.46] [0.01] [0.07] [0.27] [1.06] [6.10]
ηi 0.45 0.26 -0.02 2.02 0.03 0.23 0.46 0.66 0.88
Nuisance parameters set to firm-time specific estimates θ⋆it
φi 1.33 3.02 4.23 23.47 0.01 0.06 0.25 1.27 7.25[1.26] [3.23] [4.98] [32.54] [0.01] [0.05] [0.20] [1.04] [6.88]
ηi 0.47 0.30 0.13 1.85 0.02 0.20 0.45 0.72 0.97
Logit specification for link function h
φi 0.35 0.77 3.79 19.40 0.01 0.03 0.06 0.25 1.93[0.40] [1.03] [5.54] [46.66] [0.01] [0.02] [0.05] [0.22] [2.06]
ηi 0.30 0.19 0.54 2.80 0.04 0.14 0.29 0.41 0.65
Alternate definition of leverage
φi 3.14 5.48 3.14 13.78 0.04 0.22 0.89 4.70 15.06[3.73] [7.60] [3.78] [19.09] [0.03] [0.17] [0.66] [4.98] [17.17]
ηi 0.42 0.22 0.12 2.64 0.05 0.27 0.42 0.55 0.82
54
Table VIII
Conditional Moment Tests for Goodness-of-Fit
The table reports the results from conditional moment tests. Conditional moment (CM) testsuse conditional moment restrictions for testing goodness-of-fit. Specifically, the CM tests per-formed check whether the difference between the real data moments listed in each row and thesimulated data moments based on our SML estimates is equal to zero. We report momentsbased on both leverage levels and changes. The test statistic for each individual moment isreported in the third column next to the corresponding moment, and the associated p-value isin the last column. The Wald test statistic reported in the last row tests for joint fit of themodel by checking whether the distances between data and simulated moments are jointly zero.
Empirical Simulated CM testmoment model moment statistic p-value
Leverage:Mean 0.322 0.335 (-1.51) [0.13]Median 0.317 0.326 (-0.89) [0.37]S.D. 0.068 0.097 (-16.53) [0.00]Skew 0.220 0.354 (-6.01) [0.00]Kurtosis 2.308 2.515 (-5.31) [0.00]Range 0.216 0.297 (-14.64) [0.00]IQR 0.100 0.140 (-13.45) [0.00]Min 0.224 0.206 (3.41) [0.00]Max 0.440 0.502 (-7.27) [0.00]Autocorrelation 1qtr 0.916 0.882 (0.70) [0.49]Autocorrelation 1yr 0.737 0.602 (2.74) [0.01]
Changes in leverage:Mean 0.005 0.001 (4.95) [0.00]Median 0.003 0.001 (1.72) [0.09]S.D. 0.049 0.110 (-50.63) [0.00]Skewness 0.258 0.013 (8.96) [0.00]Kurtosis 3.071 3.135 (-1.03) [0.30]Range 0.058 0.132 (-48.81) [0.00]IQR -0.076 -0.189 (45.06) [0.00]Min 0.100 0.192 (-33.79) [0.00]Max 0.176 0.381 (-46.44) [0.00]Autocorrelation 1qtr -0.090 -0.035 (-1.45) [0.15]Autocorrelation 1yr -0.033 -0.059 (0.67) [0.50]
Wald test of joint hypothesis H0: All moments equal (0.49) [1.00]
55
Table IX
Simulation Evidence: Leverage Inertia and Mean Reversion
The table provides simulation evidence on leverage inertia and mean reversion. Panel A reportsparameter estimates from Fama-MacBeth regressions on leverage in levels, similar to Welch(2004). The basic specification is as follows:
Lt = α0 + α1Lt−k + α2IDRt−k,t + ǫt,
where L is the leverage ratio, IDR is the implied debt ratio defined in Welch (2004), and kis the time horizon. Coefficients reported are means over 1,000 simulated datasets. Below ourestimated coefficients we report the coefficients on IDR in Welch (2004) and Strebulaev (2007).Panel B reports parameter estimates from Fama-MacBeth regressions on leverage changes,similar to Fama and French (2002). The basic specification is as follows:
Lt − Lt−1 = α+ λ1TLt−1 + λ2Lt−1 + ǫt,
where L is, again, the leverage ratio and TL is the target leverage ratio. In the first specification,TL is determined in a prior stage by running a cross-sectional regression of leverage on variousdeterminants. In the second specification, TL is set to the model-implied target leverage ratio.Coefficients are means over 1,000 simulated datasets.
Panel A: Leverage inertia
Lag k in years
1 3 5 10
Coefficient estimates in simulated dataImplied Debt Ratio, IDRt−k,t 1.02 0.87 0.77 0.59Leverage, Lt−k -0.05 0.07 0.15 0.31Constant 0.01 0.02 0.03 0.04R2 0.97 0.92 0.87 0.80
IDRt−k,t coefficients in the literatureWelch (empirical values) 1.01 0.94 0.87 0.71Strebulaev (calibrated values) 1.03 0.89 0.79 0.59
Panel B: Leverage mean-reversion
Two-stage estimated TL Model-implied TL
Target Leverage, TLt−1 0.09 0.13Leverage, Lt−1 -0.08 -0.16Constant 0.00 0.01R2 0.04 0.08
56
Table X
Specification Analysis
The table reports likelihood ratio tests to select the best model amongst alternative model spec-ifications. We report test statistics for nested and non-nested models as derived in Appendix E.In addition to the base specification given in (14) and (15), we consider six additional nestedmodels and two non-nested models: (1) φi and ηi, i = 1, . . . , N , with uncorrelated random
effects (φi = h(αφ + ǫφi ), ηi = h(αη + ǫηi ), σφη = 0), (2) no shareholder bargaining power
(φi = h(αφ + ǫφi ), ηi = 0), (3) no managerial entrenchment (φi = 0, ηi = h(αη + ǫηi )), (4) φand η constant (φi = h(αφ), ηi = h(αη)), (5) no shareholder bargaining power and φ constant(φi = h(αφ), ηi = 0), (6) no managerial entrenchment and η constant (φi = 0, ηi = h(αη)), andthe two non-nested models (7) λ with random effects (λi = h(αλ + ǫλi ), φi = 0, ηi = 0), (8) λconstant (λi = h(αλ), φi = 0, ηi = 0). Tests for non-nested models are based on Vuong (1989)and indicated by †. p-values are reported in brackets. For the nested models, a p-value of zeroindicates that the null hypothesis that the parameter restrictions are valid is rejected in favorof the model under the alternative. For the non-nested models, a p-value of zero indicates thatthe null hypothesis that the two models are equivalent is rejected in favor of the model underthe alternative.
Alternative Null hypothesis
hypothesis (1) (2) (3) (4) (5) (6) (7) (8)
Base 1,423 6,864 256,001 214,771 209,506 351,529 2.72† 19.60†
[0.00] [0.00] [0.00] [0.00] [0.00] [0.00] [0.00] [0.00]
(1) – 5,441 254,578 213,348 208,083 350,106 1.80† 19.51†
– [0.00] [0.00] [0.00] [0.00] [0.00] [0.04] [0.00]
(2) – – 16.75† 15.22† 202,641 21.68† -1.13† 19.24†
– – [0.00] [0.00] [0.00] [0.00] [0.87] [0.00]
(3) – – – -3.43† -3.71† 95,529 -17.28† 3.30†
– – – [1.00] [1.00] [0.00] [1.00] [0.00]
(4) – – – – -5,265 136,759 -15.27† 5.73†
– – – – [1.00] [0.00] [1.00] [0.00]
(5) – – – – – 10.63† -15.43† 5.99†
– – – – – [0.00] [1.00] [0.00]
(6) – – – – – – -21.92† -1.02†
– – – – – – [1.00] [0.85](7) – – – – – – – 324,602
[0.00]
57
Table XI
The Determinants of Managerial Entrenchment
The table summarizes the determinants of the managerial entrenchment across firms. Thedependent variable is the predicted value of managerial entrenchment, φi = E(φi|yi; θ) fori = 1, . . . , N , where θ are the parameters estimated in Section III.B and the φi are expressedin basis points. In columns (1)-(3) we report estimation results from cross-sectional regres-sions. Specification (1) utilizes the entire sample. Missing values are imputed with zero anddummy variables that take a value of one for missing values are included in the regression.Specifications (2) and (3) use only observations with no missing data items. In specification(2) we drop the variables with the most missing values from the regression. All specificationsare estimated including industry fixed effects. Standard errors are adjusted for sampling errorin the generated regressands (see Handbook of Econometrics IV, p. 2183) and are reported inparentheses. Statistical significance at the 10%, 5% and 1% level is marked with *, **, and ***,respectively.
(1) (2) (3)
Institutional Ownership −88.15** −90.72*** −66.24*(37.79) (34.67) (37.90)
Independent Blockholder Ownership −74.73 −95.37** −99.98**(52.06) (47.52) (49.70)
E-index - Dictatorship 172.72** 137.92* 133.73*(68.84) (75.68) (76.81)
CEO Tenure 3.72*** 4.70*** 4.85***(1.02) (1.15) (1.30)
Board Independence −78.19* − −72.03(40.04) − (45.85)
Board Committees −6.58 − −3.78(6.99) − (6.89)
Managerial Delta (Quartile 1) −8.68 −14.82 −12.22(11.97) (12.10) (11.80)
Managerial Delta (Quartile 4) 3.21*** 3.39*** 3.45***(0.78) (0.81) (0.94)
Returns on Assets 0.95 1.08 −0.38*(4.04) (4.24) (4.92)
M/B 38.11*** 33.28*** 29.84**(9.00) (11.31) (12.22)
Asset Tangibility −25.23 14.23 26.81(34.69) (37.73) (39.37)
Size −39.47*** −39.04*** −39.36***(6.08) (5.97) (6.62)
R&D 1.16 0.35 4.98(8.44) (10.31) (10.27)
Observations 809 634 569R2 0.35 0.35 0.37
58
Figure 1
Monte-Carlo Simulation Precision and Accuracy
The figure depicts the magnitude of Monte-Carlo simulation error and its impact on the precision and
accuracy of the simulated log-likelihood. In all plots, on the horizontal axis we vary the number of
random draws K used to evaluate the log-likelihood. For given K, we evaluate the log-likelihood 100
times at the same parameters and in each round vary the set of random numbers used to integrate
out the firm-specific random effects from the likelihood function. Panel A reports box plots for the
simulated values of the log-likelihood across simulation rounds. Depicted are the lower quartile, median,
and upper quartile values as the lines of the box. Whiskers indicate the adjacent values in the data.
Outliers are displayed with a + sign. The highest simulated log-likelihood value across all simulation
rounds is indicated by a dotted line. Panel B depicts the magnitude of the simulation imprecision (left)
and the simulation bias (right) as function of K. The simulation imprecision is measured by the 95%
quantile minus the 5% quantile across all simulation rounds for given K and normalized by the highest
simulated log-likelihood value across all simulation rounds. The simulation bias is measured by the
median log-likelihood value across all simulation rounds for given K relative to the highest simulated
log-likelihood value across all simulation rounds.
Panel A: Simulated values of the log-likelihood
2 3 4 5 10 25 50 100 250 500 750 1000
−8
−6
−4
−2
0
2
x 104
Sim
ulat
ed lo
g−lik
elih
ood
K
Panel B: Simulation precision and accuracy of the simulated log-likelihood
2 3 4 5 10 25 50 100 250 500 750 1000
100
101
102
Sim
ulat
ion
impr
ecis
ion
(%)
K2 3 4 5 10 25 50 100 250 500 750 1000
100
101
102
103
Sim
ulat
ion
bias
(%
)
K59
Figure 2
Comparative Statics: Firm-Specific Leverage Distribution
The figure shows comparative statics for the time-series distribution of financial leverage. We vary the refinancing cost λ, the degree of
managerial entrenchment φ, and shareholders’ bargaining power η around the baseline values (λ, φ, η) = (.005, .005, .25). Panel A plots the
distribution function of leverage for different parameter values. Panel B depicts the median (solid line), the 5% and 95% quantiles of leverage
(dashed lines), and the low and high of leverage (dotted lines) as functions of the parameters.
Panel A: Leverage density function under alternative parameter values
0 0.2 0.4 0.6 0.8 10
1
2
3
4
5
Leverage
Den
sity
λ = 0.5%λ = 5%
0 0.2 0.4 0.6 0.8 10
1
2
3
4
5
LeverageD
ensi
ty
φ = 0.5%
φ = 1.5%
0 0.2 0.4 0.6 0.8 10
1
2
3
4
5
Leverage
Den
sity η = 25%
η = 75%
Panel B: Moments of leverage distribution as function of parameter values
0 0.05 0.1 0.150
0.2
0.4
0.6
0.8
1
Leve
rage
λ0 0.01 0.02
0
0.2
0.4
0.6
0.8
1
Leve
rage
φ0 0.5 1
0
0.2
0.4
0.6
0.8
1
Leve
rage
η
60
Figure 3
Managerial Entrenchment and Shareholder Bargaining Power Across Firms
The figure shows histograms of the predicted managerial entrenchment, E(φi|yi, xi; θ), and the predicted
shareholders’ bargaining power, E(ηi|yi, xi; θ), for firms i = 1, . . . , N in the dynamic capital structure
model. The prediction is based on a structural estimate of the model’s parameters. The histograms plot
the predicted parameters for each firm-quarter.
Panel A: Distribution of predicted managerial entrenchment φi
0 1 2 3 4 50
100
200
300
400
Managerial entrenchment (%)
Fre
quen
cy
Panel B: Distribution of predicted shareholder bargaining power ηi
0 20 40 60 80 1000
20
40
60
80
100
Shareholder bargaining power (%)
Fre
quen
cy
61
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