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Why Leverage Distorts Investment∗
Alex Stomper† Christine Zulehner‡
March 2, 2004
Abstract
We analyze theoretically and empirically why leverage distorts firms’ out-put pricing, and thus their implicit investments in market share. We findevidence of two effects. By raising the probability of insolvency, leverage ef-fectively increases the rate at which profits from investments are discounted.In addition, leverage determines the costs and benefits of investments in mar-ket share, conditional on firms being solvent. The optimal investment policyshifts profits to those periods in which a firm must generate especially highearnings to repay its debt. This effect may either counteract or reinforceinvestment distortions due to the first effect. We show that levered firmsnever over-invest in market share; the magnitude of leverage-induced under-investment depends on the debt maturity structure.Keywords: capital structure, financial and product market interactions.JEL Classifications: D43, G31, L83.
∗We would like to thank Michael Brennan, Jesus Crespo-Cuaresma, Ron Giammarino, MichaelHalling, Robert Heinkel, Gregor Hoch, Markus Hochradl, Hans-Georg Kantner, Vojislav Maksi-movic, Dennis C. Mueller, Pegaret Pichler, Judith Spiegl, Neal Stoughton and Josef Zechner forhelpful discussions and suggestions. We thank the “Osterreichische TourismusBank” for providingus with data.
†Department of Business Studies, University of Vienna, BWZ-Brunnerstr. 72, A-1210 Vienna,Austria, [email protected]
‡Department of Economics, University of Vienna, BWZ-Brunnerstr. 72, A-1210 Vienna, Aus-tria, [email protected]
Why Leverage Distorts Investment
Abstract
We analyze theoretically and empirically why leverage distorts firms’ out-put pricing, and thus their implicit investments in market share. We findevidence of two effects. By raising the probability of insolvency, leverage ef-fectively increases the rate at which profits from investments are discounted.In addition, leverage determines the costs and benefits of investments in mar-ket share, conditional on firms being solvent. The optimal investment policyshifts profits to those periods in which a firm must generate especially highearnings to repay its debt. This effect may either counteract or reinforceinvestment distortions due to the first effect. We show that levered firmsnever over-invest in market share; the magnitude of leverage-induced under-investment depends on the debt maturity structure.Keywords: capital structure, financial and product market interactions.JEL Classifications: D43, G31, L83.
1 Introduction
Many contributions to the theory of optimal capital structure seek to explain firms’
financing choices as resulting from trade-offs between costs and benefits of leverage.
One commonly considered cost of debt financing arises from conflicts of interests
between firms’ owners and their creditors. As Jensen and Meckling (1976) and
Myers (1977) have shown, such conflicts of interests can distort firms’ investment
decisions since leverage changes their objective functions. Rather than maximizing
firm value, management chooses an investment policy which maximizes equity value;
with limited liability of firms’ owners, too much or too little is invested.
In analyzing investment distortions induced by leverage, corporate finance theory
typically considers a firm in isolation. However, such investment distortions may also
affect a firm’s competitors. Within a more general analytical framework, leverage
can therefore be viewed as part of corporate strategy. The analysis of strategic
effects of leverage is the subject of a growing literature with early contributions
by Titman (1984), Fudenberg and Tirole (1986), Brander and Lewis (1986) and
Maksimovic (1986).1 While these early papers clarified some of the reasons why
leverage affects corporate strategy, it turns out that the direction of the effects can
depend on the nature of firms’ interactions in oligopolistic settings, as determined
by firms’ industry affiliations. For the seminal model of Brander and Lewis (1986),
Showalter (1995) shows that leverage can make firms either more or less aggressive
competitors contingent on whether their investments are strategic substitutes or
strategic complements.
Most empirical studies have found that leverage makes firms less aggressive com-
petitors. However, the economic reasons for these findings remain opaque – the
evidence is consistent with a number of explanations. Chevalier and Scharfstein
(1996) and Dasgupta and Titman (1998) propose models in which leverage affects
investment the same way as an increase in the rate at which firms discount future
profits. Showalter (1995) shows that similar investment distortions can arise due to
the strategic effect of leverage proposed by Brander and Lewis (1986). Hence, it is
still an open question why leverage distorts investment, and whether the investment
distortions are bound to vary across industries as predicted by Showalter (1995).
1For surveys of this literature, see Maksimovic (1995) and Grinblatt and Titman (2002).
1
In this paper, we address the first of these questions and also take a step towards
answering the second question. The focus of our analysis differs from that of previous
studies: rather than directly analyzing investment distortions induced by leverage,
we investigate how leverage affects firms’ objective functions. We do not regard
leverage itself as the central explanatory variable of our analysis.2 Instead, we test
for two different effects of leverage on firms’ investment decisions that are due to two
specific changes in their objective functions. First, leverage raises the probability
with which a firm defaults, thus discouraging investment as if future profits are
discounted at a higher rate. Second, the investment policy of a levered firm depends
on the debt maturity structure – such a firm shifts profits to those periods in which
its earnings must be especially high to cover debt repayment. This is optimal since
leverage changes the firm’s marginal rate of substitution between current and future
profits, conditional on the firm remaining solvent.
The paper has a theoretical and an empirical part. Throughout the paper, we
consider a common investment decision of many firms: investment in market share
to attract repeat customers. To undertake such investments, firms cut their prices
at the cost of a decrease in their current profits. We consider how leverage dis-
torts firms’ investments in market share implicit in their pricing strategies.3 In
the theoretical section, we analyze a two-period model of imperfect competition
between owner-managed firms facing demand uncertainty. The model incorporates
the two effects of leverage mentioned above. The first effect has been modeled by
Chevalier and Scharfstein (1996) and Dasgupta and Titman (1998): leverage induces
under-investment as if a firm discounts future profits at a higher rate.4 Besides this
“under-investment effect” of leverage, our model captures a second effect: leverage
changes the marginal rate of substitution between current and future profits that
firms use in investment decisions to maximize equity value in the non-default states.
To see this, consider a firm which cuts the price of its output to attract additional
2This distinguishes our paper from previous empirical studies, like the contributions by Phillips(1995), Chevalier (1995), and Chevalier and Scharfstein (1996).
3Opler and Titman (1994), Kovenock and Phillips (1997), Zingales (1998), Khanna and Tice(2000) and Campello (2003) analyze how leverage directly affects firms’ market shares.
4Chevalier and Scharfstein (1996) build on work by Bolton and Scharfstein (1990, 1996) andHart and Moore (1989) to analyze how leverage affects firms’ output pricing in a model in whichdebt financing is optimal. Campello and Fluck (2003) extend the model of Chevalier and Scharfstein(1996) to consider the case in which capital market imperfections may drive firms out of business.
2
customers, thus investing in market share. The firm’s owners consider the cost of
the price cut only for the states in which the firm does not default in the first period,
i.e. the high-demand states where sufficiently many customers buy the firm’s out-
put that it can meet its financial obligations. In these states, the price cut causes a
higher reduction in the firm’s conditional expected profit than in low-demand states
in which fewer customers buy the firm’s output at the reduced price. From the
perspective of the firm’s owners, leverage therefore raises the cost of investment in
market share.
We show that a levered firm’s optimal pricing strategy depends on its relative
expected profitability in the non-default states across periods, as determined by the
maturity structure of the firm’s debt. For the firm’s owners, the first-period non-
default states determine the conditional expected cost of investment in market share,
as discussed above. The owners’ conditional expected profit from such investment
depends on the profitability of the second-period non-default states. Holding con-
stant the probability of default, investment in market share is more attractive for a
firm whose second-period non-default states are more profitable than its first-period
non-default states. We refer to this effect as “dynamic limited liability effect” or
DLL-effect since it is a dynamic version of the “limited liability effect” proposed by
Brander and Lewis (1986) and Maksimovic (1986) and further analyzed by Showalter
(1995). By contrast to the one-period models of these authors, our two-period model
reveals that the DLL-effect distorts firms’ investments by changing their marginal
rates of substitution between current and future profits.
The theoretical analysis yields novel testable predictions. By contrast to the lim-
ited liability effect, the DLL-effect can distort firms’ investments in market share
towards over- and under-investment, even when holding constant all assumptions
about the nature of firms’ competition and the kind of uncertainty they face.5 Hence,
5Showalter (1995) shows that the direction of the limited liability effect is fully determined byunderlying assumptions about the nature of firms’ competition (strategic substitutes vs. strategiccomplements) and the kind of uncertainty they face (cost vs. demand uncertainty). Holdingconstant these assumptions, the limited liability effect makes firms either more or less aggressivecompetitors, but only one of these results can be obtained. See Kovenock and Phillips (1995) fora discussion of the limited liability effect in terms of investment in production capacity. Faure-Grimaud (2000) extends the analysis by Brander and Lewis (1986) to consider the optimal financialcontracts. Glazer (1994) argues that the result of Brander and Lewis depends on the assumptionthat debt is short-term, Dockner, Elsinger and Gaunersdorfer (2000) respond by pointing out thatlong-term debt also causes firms to be more aggressive.
3
this effect may either counteract or reinforce the under-investment induced by lever-
age due to the first of the two effects mentioned above. We analyze the overall
effect and find that levered firms never over-invest in market share. However, the
magnitude of leverage-induced under-investment depends on debt maturity. In our
model, a firm invests more in market share, the smaller the average maturity of its
debt tranches, holding constant debt value.
In the empirical part of our paper, we test our hypotheses and find evidence
consistent with both of the two effects of leverage in our theoretical model. To
the best of our knowledge, this is the first paper to provide empirical evidence for
leverage-induced changes in firms’ objective functions like in the one-period models
of Brander and Lewis (1986), Maksimovic (1986) and Showalter (1995). However,
the resulting investment distortions can only be captured by means of a multi-period
model: consistent with the DLL-effect of leverage on firms’ investment decisions, we
find that a firm’s optimal strategy depends on its relative expected profitability in
the non-default states across periods. In addition, we find evidence consistent with
the models of Chevalier and Scharfstein (1996) and Dasgupta and Titman (1998).
However, we also show that these models fail to adequately characterize leverage-
induced under-investment since they do not capture the DLL-effect.
By contrast to previous studies, our analysis reveals why leverage distorts firms’
investments in market share. We can separately test for two kinds of investment
distortions since our model specifies not only how firms’ output prices depend on
leverage, but also how they depend on debt maturity. Moreover, we use data on a
sample of firms that is particularly suited for testing the theory: hotels close to ski
resorts in the Austrian Alps. As assumed in the theoretical analysis, these hotels
are managed by their owners. Also, market shares are major determinants of the
hotels’ future profits since tourists tend to return to hotels in which they stayed
before. Finally, the hotels face exogenous but quantifiable uncertainty in that their
revenues depend on snowfall as a risk factor with a distribution determined by the
altitude of nearby ski resorts. By modeling profit uncertainty this way, we can
identify how short-term and long-term leverage affect a hotel’s pricing strategy in
different ways since its expected profitability in the non-default states varies over
different planning horizons. This identification strategy is central to our empirical
analysis.
4
The remainder of the paper is structured as follows. In Section 2, we present our
theoretical model. Section 3 describes the empirical analysis. Section 4 concludes.
2 Theory
In this section, we present a model to analyze the pricing decisions of firms which
compete with other firms producing similar but differentiated products. This model
captures why a firm’s financial structure affects its optimal strategy in a Nash equi-
librium in prices. As in the model by Klemperer (1995), there are two periods and
a firm’s first-period market share is positively related to its second-period profits.
This is the case since customers are not only sensitive to price, but also tend to
favor the firm whose product they purchased before which allows the firms to raise
their prices in the second period. In setting their first-period prices, firms strike a
trade-off between their profits in the first and the second period: by raising its price
today, a firm can increase its first-period profits at the expense of a loss in market
share, and hence a reduction in its second-period profits.
We consider two firms, A and B. These firms set their prices to maximize the
expected payoff of their equityholders. This expected payoff depends on the firms’
capital structures, characterized by two parameters: Di,1 and Di,2 denote short-run
and long-run debt of firm i, due at the end of period one and period two, respectively.
Figure 1 presents the time line. Firms set prices at the start of each period. These
pricing decisions determine firms’ cash flows at the end of each period, and hence
whether they are able to repay their debt. Both firms are liquidated at the end of
the second period.
We assume that the firms are exposed to uncertainty such that their profits are
random multiples of expected profit levels. This form of uncertainty can be inter-
preted as demand uncertainty but can also be taken literally. For example, a firm’s
customers may “subscribe” to its product, and a random fraction of these subscrip-
tions may be cancelled early, resulting in a profit shortfall on the part of the firm.6
In any case, this assumption constitutes an important difference between our paper
and other analyses, such as Dasgupta and Titman (1998) who consider the case of
6Think of telecom firms, newspapers, hotels, etc. In the empirical analysis, we consider hotelsclose to ski resorts which face the risk of cancellations due to uncertain snow conditions.
5
additive uncertainty.7 Leverage affects the pricing choices of the firms in our model
not only like an increase in the rate at which future profits are discounted. Instead,
there is also a second effect, the dynamic limited liability effect defined below.
We assume that both firms start into the first period with an exogenous cus-
tomer base. The first-period profit of firm i ∈ {A,B} depends on both firms’
first-period prices, pA,1 and pB,1, as well as on a random factor denoted as αi,1:
xi,1 = x∗i,1[pA,1, pB,1]αi,1, where x∗
i,1[pA,1, pB,1] can be interpreted as firm i’s expected
first-period profit.8 Firm i’s second-period profit depends similarly on a random
factor, αi,2, but also on the firm’s first-period market share, σi,1[pA,1, pB,1]. Since
market shares also determine the firms’ optimal pricing strategies in the second
period, we can write firm i’s second-period profit as a function of the first-period
prices: xi,2 = x∗i,2[pA,1, pB,1]αi,2, where x∗
i,2 depends on the first-period prices pA,1
and pB,1 through σi,1[pA,1, pB,1] and through firm i’s optimal second period price.9
To compute the value of firm i as of date t = 0, we impose some simplifying
assumptions. First, we assume that the risk-free interest rate is zero and that all
players are risk-neutral. Second, we assume that the state variables αi,1 and αi,2 are
independently and identically distributed according to a distribution F[·] with mean
α. Under these assumptions, the value of firm i is given by the sum of its expected
first-period and second-period profits:
Vi = x∗i,1[pA,1, pB,1]α+ x∗
i,2[pA,1, pB,1]α. (1)
For future reference, we wish to point out that the value of firm i is being maximized
if the firm sets its first-period price such that the marginal rate of substitution
between current and future profits equals the discount factor:
−∂x∗
i,1
∂pi,1
∂x∗i,2
∂pi,1
= 1, (2)
where the discount factor is equal to one since the risk-free interest rate equals zero.
7Chevalier and Scharfstein (1996) and Campello and Fluck (2003) also consider the case ofdemand uncertainty. However, their models allow for only two states of demand rather than acontinuum, as in our model. Hence, their models are not suited for analyzing the DLL-effect.
8Throughout this paper, we use a tilde to denote random variables and use the same variablenames without the tilde to denote realizations of random variables. A star is used to mark latentvariables that cannot be observed directly.
9For example, (∂x∗i,2/∂pi,1) = (∂x∗i,2/∂σi,1 + (∂x∗i,2/∂pi,2) (∂ρi,2/∂σi,1))∂σi,1/∂pi,1 where ρi,2
denotes firm i’s optimal second-period price.
6
Next, we analyze the effects of short-term and long-term debt on the pricing
strategy of firm i ∈ {A,B} at date t = 0. Thereby, we assume that neither firm can
induce the other to exit from the industry; a firm’s default merely causes a transfer
of ownership from its equityholders to its creditors.10 For the sake of brevity, we
focus on the firms’ first-period pricing strategies. Dasgupta and Titman (1998) show
that, given firms’ first-period market shares, debt has no effect on their second-period
pricing strategies. A similar result holds also for our model.11
To derive the first-period pricing strategy of firm i, we need an expression for the
firm’s equity value that must be maximized under the optimal strategy. We start
by analyzing for which realizations of the state variables αi,1 and αi,2 firm i’s owners
receive zero payoff since the firm defaults on its debt. Consider date t = 2. At
this date, firm i defaults on its long-term debt Di,2 if the realization of αi,2 is too
small such that the firm’s profit falls short of the required payment to its creditors:
αi,2x∗i,2[pA,1, pB,1] < Di,2 ⇔ αi,2 < αi,2[Di,2], for αi,2 = Di,2/x
∗i,2[pA,1, pB,1]. Next,
consider date t = 1. We assume that a firm defaults due to a profit shortfall in the
first period if its owners fail to meet the firm’s financial obligations out of their own
pockets as they would have to do in order to retain their equity stakes.12 Therefore,
firm i defaults at date t = 1 if its first-period profit falls short of Di,1 and this profit
shortfall exceeds the expected payoff that the firm’s owners would receive at date
t = 2:
Di,1 − αi,1x∗i,1[pA,1, pB,1] >
∫αi,2[Di,2]
(αi,2x∗i,2[pA,1, pB,1]−Di,2)dF[αi,2], (3)
where the right-hand side is the firm’s conditional expected cash flow after debt
repayment that its owners receive in the second-period non-default states (in which
αi,2 > αi,2[Di,2]). Rearranging the above stated inequality shows that default occurs
if the realization of αi,1 is too small: αi,1 < αi,1[Di1 , Di,2] for αi,1 as defined in the
proof of Lemma 1.
In the remainder, we drop the arguments of the functions αi,1, αi,2, x∗i,1 and x∗
i,2 in
10As discussed below, this assumption is appropriate for the firms considered in our empiricalanalysis. The assumption is relaxed in Campello and Fluck (2003).
11To see this, suppose that firm i defaults in the second period if αi,2 < α. Then, the firm setsits second period price according to the first-order condition (1−F[α])∂x∗i,2/∂pi,2 = 0 the solutionof which does not depend on α.
12Alternatively, we could allow for the firms issuing junior debt at date t = 1. This would notchange our results.
7
order to simplify the notation. Based on the above-stated results, we can compute
the equity value of firm i at date t = 0. The result is stated in Lemma 1.
Lemma 1: At date t = 0, the value of firm i’s equity is given by:
Πi = (1− F[αi,1])(E[αi,1|αi,1 ≥ αi,1]x∗i,1 −Di,1
+ (1− F[αi,2])(E[αi,2|αi,2 ≥ αi,2]x∗i,2 −Di,2)). (4)
Proof: See Appendix A.
The result in Lemma 1 is very intuitive. At date t = 0, firm i’s equity value equals
the sum of its expected cash flows net of the payments to creditors scheduled for
dates t = 1, 2, weighted by the probability with which the firm will repay its debt.13
At date t = 0, firm i chooses its first-period price pi,1 to maximize its equity
value. Differentiating expression (4) with respect to pi,1 yields the following first-
order condition:14
(1− F[αi,1])(E[αi,1|αi,1 ≥ αi,1]∂x∗
i,1
∂pi,1
+ (1− F[αi,2])E[αi,2|αi,2 ≥ αi,2]∂x∗
i,2
∂pi,1
) = 0, (5)
where the first-period non-default probability (1−F[αi,1]) cancels out. Rearranging
this equation yields the following equivalent condition:
DLL[Di,1, Di,2]
−
∂x∗i,1
∂pi,1
∂x∗i,2
∂pi,1
= 1− F[αi,2], (6)
where DLL[Di,1, Di,2] depends on firm i’s debt structure through αi,1 and αi,2:
DLL[Di,1, Di,2] =E[αi,1|αi,1 ≥ αi,1]
E[αi,2|αi,2 ≥ αi,2]. (7)
We now discuss how condition (6) can be interpreted in the same way as condition
(2), i.e. as an equation between a marginal rate of substitution and a discount
factor. The two conditions differ due to two effects of leverage on firms’ objective
functions. First, consider the term on the right-hand side of condition (6). This
term differs from the discount factor on the right-hand side of condition (2) due
to the “under-investment effect” of leverage modeled by Chevalier and Scharfstein
13Dasgupta and Titman (1998) obtain a similar result. See equation (6) of their paper.14Besides the terms stated in equation (5), the first-order condition contains also the terms
∂αi,1/∂pi,1 and ∂αi,2/∂pi,1 but these terms are multiplied by terms which vanish by the definitionsof αi,1 (stated in the proof of Lemma 1) and αi,2 = Di,2/x
∗i,2.
8
(1996) and Dasgupta and Titman (1998) – leverage affects firms’ pricing strategies
similar to a change in the discount factor used to value second-period profits. In
condition (6), the “discount factor” depends on firm i’s capital structure through the
probability F[αi,2] with which the firm defaults on its long-term debt if it does not
default in the first period. The higher this probability, the smaller firm i’s incentive
to invest in market share because the firm’s owners benefit from such an investment
only with a probability of 1− F[αi,2].
The left-hand side of condition (6) can be interpreted as a marginal rate of sub-
stitution between firm i’s first- and second-period expected profits. This marginal
rate of substitution is the product of that stated on the left-hand side of condition
(2) and an adjustment factor denoted as DLL which depends on firm i’s debt struc-
ture (Di,1, Di,2). This adjustment factor captures the relative expected profitability
of the states of nature at dates t = 1 and t = 2 in which the firm can repay its
short-term and long-term debt, respectively. From the perspective of the owners
of firm i, only these non-default states are relevant since the owners receive zero
payoff if firm i defaults on its debt. The higher the DLL-factor, the more biased
towards raising current profits is the optimal strategy of firm i relative to that of an
unlevered firm, holding constant the right-hand side of condition (6). To see this,
consider a change in the first-period price dpi,1 which results in a transfer of one
dollar of expected profits from period one to period two: −dx∗i,1 = dx∗
i,2 = 1, (for
dx∗i,t = ∂x∗
i,t/∂pi,1 dpi,1 and t = 1, 2). The owners of firm i consider the effects of
such a price change on the profitability of the firm in the non-default states. From
their perspective, the price change would cost them E[αi,1|αi,1 ≥ αi,1] dollars in the
first period and yield E[αi,2|αi,2 ≥ αi,2] dollars in the second period. Relative to the
owners of an unlevered firm, those of firm i therefore benefit more (less) from the
price change if DLL[Di,1, Di,2] < 1 (DLL[Di,1, Di,2] > 1).
In the remainder, we refer to the effect captured by the factor DLL[Di,1, Di,2] as
“dynamic limited liability effect” or DLL-effect. By contrast to the “limited liability
effect” of leverage in the one-period model of Brander and Lewis (1986), the DLL-
effect induces investment distortions that depend on the maturity structure of a
firm’s debt, as determinant of its marginal rate of substitution between current and
future profits. Proposition 1 characterizes how the DLL-effect depends on firm i’s
debt structure.
9
Proposition 1: The dynamic limited liability effect For any pair of first-
period prices pA,1 and pB,1, firm i’s marginal rate of substitution between first- and
second-period expected profits equals that of a similar unlevered firm times an ad-
justment factor, DLL[Di,1, Di,2], given by expression (7). This marginal rate of sub-
stitution increases in firm i’s short-term debt level Di,1 and increases or decreases
in firm i’s long-term debt level Di,2.
Proof: See Appendix A.
Next, we analyze the effect of firm i’s debt structure on its optimal first-period
pricing strategy. In the optimum, the firm faces a trade-off between current and
future profits; this trade-off depends on firm i’s debt structure as it has been dis-
cussed below condition (6). There are two effects, i.e. the under-investment effect
and the DLL-effect which can distort the firm’s optimal strategy towards either over-
or under-investment. The two effects counteract or reinforce each other, depending
on whether DLL[Di,1, Di,2] < 1 or DLL[Di,1, Di,2] > 1, respectively. Proposition 2
characterizes the overall effect.
Proposition 2: Given the first-period price charged by the other firm, firm i’s
optimal first-period price increases in its short-term debt level Di,1 as well as in its
long-term debt level Di,2. Holding constant the value of firm i’s debt, its optimal
first-period price increases in the average time to maturity of its two debt tranches.
Proof: See Appendix A.
Proposition 2 shows that increasing firm i’s leverage increases its first-period price,
irrespective of the maturity structure of the firm’s debt. For short-term debt, this
result is a consequence of the DLL-effect characterized in Proposition 1. The higher
firm i’s short-term debt-level Di,1, the higher the firm sets its first-period price since
this price is chosen to maximize equity value. Due to equityholders’ limited liability,
only those states of nature are taken into account in which the equityholders receive
a non-zero payoff since firm i repays its debt. The higher the firm’s short-term debt
level, the more profitable must be the non-default states of nature at date t = 1
in that αi,1 takes a higher conditional expected value: E[αi,1|αi,1 ≥ αi,1] increases
in Di,1, and so does the variable DLL[Di,1, Di,2] which captures the DLL-effect in
condition (6). As discussed above Proposition 1, this implies that firm i sets its
price with more of a bias towards increasing its expected profit in the first period.
10
Hence, a higher first-period price is optimal.
For long-term debt, the result in Proposition 2 corresponds to the effect of such
debt on a firm’s pricing strategy in the model of Dasgupta and Titman (1998). The
higher firm i’s long-term debt Di,2, the higher the probability with which it defaults
on such debt at date t = 2. This implies that the firm faces a stronger incentive
to under-invest in market share since its owners benefit from such investment with
a smaller probability. As a consequence, the optimal first-period price increases.
Surprisingly, this clear-cut result is obtained even though long-term debt has an
ambiguous effect in Proposition 1 which characterizes the DLL-effect.15 Hence,
Proposition 2 has an important corollary: while the DLL-effect alleviates a levered
firm’s under-investment in market share if DLL[Di,1, Di,2] < 1, such a firm never
aims for a higher market share than an unlevered firm. Instead, leverage always
causes under-investment in market share, even in the presence of the DLL-effect.
In Proposition 2, we also characterize the effect of debt maturity on the first-period
price set by firm i. Thereby, we consider changes in the firm’s capital structure for
which the total value of the firm’s debt remains constant. With no discounting, the
value of the marginal dollar to be repaid at time t = 2 equals the value of (1−F[αi,2])
dollars to be repaid at time t = 1 since firm i defaults with a probability of F[αi,2]
between time t = 1 and time t = 2. Hence, the total value of firm i’s debt remains
constant for changes in the firm’s capital structure of the form:
dDi,1 = (1− F[αi,2])ε, dDi,2 = −ε, (8)
where ε denotes an infinitesimally small positive or negative number. Proposition 2
states that firm i should set a higher first-period price if ε < 0, i.e. dDi,1 < 0 and
dDi,2 > 0 such that the average time to maturity of the firm’s debt increases.
In Proposition 3, we characterize the effect of firm i’s debt structure on both firms’
equilibrium pricing strategies. In doing this, we extend and combine the analyses of
Dasgupta and Titman (1998) and Showalter (1995) to a two-period duopoly model
in which the firms have short- and long-term debt. Like Dasgupta and Titman
(1998), we impose the following standard assumptions that ensure reaction function
15In this respect, our analysis confirms the main result of Chevalier and Scharfstein (1996) andDasgupta and Titman (1998) whose models do not capture the DLL-effect.
11
stability and a positive slope of reaction functions:
∂2Πi
∂pi,1∂pj,1
> 0 and∂2Πi
∂p2i,1
∂2Πj
∂p2j,1
− ∂2Πi
∂pi,1∂pj,1
∂2Πj
∂pj,1∂pi,1
> 0 for i, j ∈ {A,B}, i �= j. (9)
Proposition 3: In equilibrium, firm i’s first-period price increases in its short-
term debt level Di,1 as well as in its long-term debt level Di,2. Firm j’s first-period
price also increases in Di,1 and Di,2. Holding constant the value of firm i’s debt,
both firms’ first-period prices increase in the average time to maturity of firm i’s two
debt tranches.
Proof: See Appendix A.
The results in Proposition 3 follow rather directly from those in Proposition 2.
An increase in firm i’s short- or long-term debt level shifts its reaction function
such that the firm chooses a higher first-period price given the price chosen by firm
j. With both firms’ reaction functions being upward-sloping, they both set higher
first-period prices in equilibrium.
3 Empirical evidence
In this section, we build on our theoretical analysis to develop an econometric model
that specifies how firms price their output as a function of leverage and debt matu-
rity. Then, we proceed to test the theory using data on family-owned hotels located
in rural areas in Austria which predominantly attract ski tourism. As mentioned
in the Introduction, these hotels represent an ideal testing ground for the theory
since the underlying assumptions are satisfied. First, the hotels are managed by
their owners and, hence, in the owners’ interest.16 Second, the hotels are rarely shut
down in the event of default since they are located in rural areas where it is hard
to find a profitable alternative use for hotels’ fixed assets. A hotel’s default there-
fore merely causes a transfer of ownership from its equityholders to its creditors,
as assumed in the theoretical analysis above. Third, market shares are important
determinants of hotels’ future profits since repeat customers make up for a sizeable
part of room sales.17 As in the theoretical model, hotels’ market shares are in turn
16Family-owned hotels are the norm in Austrian rural areas – there are no hotel-chains since thechain stores specialize in city tourism and business travel.
17In a recent survey by the Austrian National Tourist Office, more than 40% of all respondentssaid that they already stayed at the same hotel at least once in the past. The survey titled
12
mainly determined by their pricing decisions; in recent years, there has been little
real investment in accommodation capacity since the Austrian hotel industry is a
very mature industry with quite substantial overcapacity.18 Fourth, the hotels face
exogenous but quantifiable uncertainty in that the demand for accommodation de-
pends on the weather and, in particular, on the snow levels in nearby ski resorts.
Hence, we can use data on the altitude of ski resorts in order to derive proxies for
hotels’ profit distributions induced by the resorts’ snowfall distributions.19 Finally,
we can obtain control variables for possible effects of leverage on product quality,
as in Maksimovic and Titman (1991). Hotels are rated according to the quality of
accommodation; such data can be used to control for effects of product quality on
pricing.
Besides industry characteristics, also the financing of the Austrian hotel industry
makes it especially suited for testing the theory. Since the Austrian financial mar-
kets are very underdeveloped, it is virtually impossible for hotels to obtain equity
financing in order to re-capitalize. Hence, hotels’ capital structures are mostly ex-
ogenously determined by the weather conditions in past years as determinants of
hotels’ past profits. Many hotels exhibit strikingly high levels of indebtedness – for
the year 1999, a study of the Austrian Federal Ministry of Economic Affairs and
Labor (BMWA) found that the average Austrian hotel owes debt with a book value
equal to more than thirteen times its cash flow.20 To resolve this problem, an Aus-
trian bank has been granted a charter to issue state-backed guarantees for the debts
of hotels which meet certain criteria. Receiving such a guarantee enables a hotel to
renegotiate the interest rates of its bank loans and to eventually repay some of its
debts. This bank, the “Osterreichische TourismusBank” (OHT), has been founded
as joint subsidiary of the three biggest Austrian banks. Besides issuing guarantees,
it also specializes in lending to hotels in rural areas, most of which are former cus-
“Gastebefragung Osterreich” is available at http://tourism.wu-wien.ac.at.18In our empirical analysis, we define a hotel’s accommodation capacity as the product of the
number of beds and the number of days during which a hotel stays open for business. Hotels’accommodation capacities are mainly exogenously determined. In our sample, none of the hotelschanged the number of beds during the sample period. Also, hotels’ opening and closing dates aremostly determined by the ski season; in many cases, the hotels simply match the period duringwhich nearby ski resorts are in operation.
19Recently, artificial snow is being used on ski pistes. However, this is only possible if thetemperature is sufficiently low. The altitude of a ski resort determines the temperature distribution,and hence whether artificial snow can be used.
20See BMWA (2000), pp. 33.
13
tomers of OHT’s owners.21 The OHT typically starts to deal with these hotels after
they get into financial distress but well before they would have to enter a formal
bankruptcy procedure. These business relationships usually continue after the hotels
are re-capitalized. Hence, the OHT’s clientele comprises hotels which differ widely
in their leverage, including a sizable number of very highly levered hotels. We will
base our empirical analysis on a representative sample of clients of the OHT, de-
scribed in the next section. With this sample, we can measure distortions of levered
hotels’ pricing strategies across the entire range of possible levels of leverage.
3.1 Data
The sample comprises 100 family-owned hotels incorporated as limited-liability com-
panies, none of which have entered a formal bankruptcy procedure before or during
the sample period. For all hotels, we have data for the years 1999 and 2000; for
20 hotels we also have data for the year 2001. The data comprise balance sheet
data as well as data on hotels’ quality ratings, the average prices they charge for
accommodation per night (where the average is taken across all overnight stays sold
in a hotel-year), room sales (in overnight stays sold), and accommodation capacities,
i.e. the number of beds times the number of days during which a hotel stays open
for business. For 20 hotels, we lack data on their accommodation capacities. While
these hotels are included in our estimations, we use a dummy variable to control for
differences between these and the other observations.
We know for each hotel the postal code of the village in which the hotel is located.
Using this information, we can identify the meteorological station that is used to
monitor the weather in the area surrounding the hotel. Since these meteorological
stations are usually located in ski resorts, we use data on their altitude as a proxy
for the altitude of the resorts; for hotel i, the altitude of the closest meteorological
station is denoted as Alti.22 Besides this variable, we will use several other variables
to describe the nature of a hotel’s business. The second variable is an indicator vari-
able IAlti>1000 that equals one for any hotel i for which the closest meteorological
station is at an altitude Alti of more than one thousand meters, and zero otherwise.
This variable indicates whether a hotel is located in an area especially suited for ski
21Of course, the OHT cannot issue a state-backed guarantee for its own loans.22The meteorological stations are usually located in ski resorts in order to facilitate maintenance.
14
tourism, nearby a ski resort in which the snow conditions are fairly certain to be
good. The third variable is the ratio of seats in a hotel’s restaurant to the number
of beds of the hotel, denoted as SBRi,t. This variable captures to which extent the
profit of hotel i depends not only on room sales, but also on the profitability of
the hotel restaurant. We use this variable together with another indicator variable
denoted as ISBRi,t>2 that equals one for hotels with a relatively sizable restaurant,
and zero otherwise. The fourth variable is a measure for quality of accommodation:
Cati is an indicator variable that equals one if hotel i offers high quality accommo-
dation, rated four or five stars out of five.23 Finally, a hotel is characterized by its
capacity Capi,t, the number of beds times the number of days the hotel stays open.
Table 1 describes the data set. In Panel A, we report the mean and the stan-
dard deviation of any variable used in the econometric analysis. These variables are
defined below, when we discuss the econometric implementation of our theoretical
model. In Panel B, we present descriptive statistics concerning hotels’ capital struc-
tures. Thereby, we measure debt levels and equity values in terms of book values.24
Leverage is defined the usual way as the fraction of total capital that is debt capital.
In addition, we report descriptive statistics for the debt maturity structure charac-
terized by the ratio of short-term to long-term debt, defined as debt to be repaid
within and after one year, respectively. As discussed above, our sample contains a
number of very highly levered firms: the average leverage is 85 percent and there
are 39 hotel-years with a book leverage of almost one.25
3.2 Econometric implementation
We now present the econometric implementation of our theoretical model and state
the main hypotheses to be tested. We assume that each period of the theoretical
model corresponds to one year. To develop the econometric model, we use the first-
order condition (5) as a starting point. By rearranging this condition, we obtain an
equation suitable for econometric implementation. For firm i = 1, . . . , n and year
23Even though quality of accommodation is usually measured in terms of five categories, wecould not obtain finer data from the OHT.
24We cannot use market values since our sample contains only non-listed firms.25While a book leverage of one clearly indicates a very high leverage, this does not imply that
a hotel with such leverage necessarily defaults. None of the hotels in our sample has entered aformal bankruptcy procedure.
15
t = 1, . . . , T , this equation is given by:
∂x∗i,t
∂pi,t
+ (1− Fi,t+1[αi,t+1])(1 + tDLLi,t)∂x∗
i,t+1
∂pi,t
= 0, (10)
where Fi,t[.] = F[.|Zi,t] is the firm-specific distribution of the state of demand, Zi,t
denotes a vector of firm characteristics defined below, and tDLLi,t is a transformed
version of expression (7),
tDLLi,t =1
DLL[Di,t, Di,t+1]− 1, (11)
where we omit firm i’s debt structure (Di,t, Di,t+1) as an argument of the function
tDLLi,t. The transformation (11) is required in order to test for the DLL-effect as
a deviation of firms’ output pricing from the optimal pricing strategies in a model
without the DLL-effect.26 By expressions (7) and (11), tDLLi,t is given by:
tDLLi,t =Ei,t+1[αi,t+1|αi,t+1 ≥ αi,t+1]− Ei,t[αi,t|αi,t ≥ αi,t]
Ei,t[αi,t|αi,t ≥ αi,t], (12)
where we use subscripts to capture that the conditional expected values of the
state variables αi,t and αi,t+1 may depend on cross-firm and in-time variation in the
distribution Fi,t.
In the following paragraphs, we convert condition (10) into a regression model with
the price pi,t as the dependent variable. Moreover, we will discuss how to estimate
this model in spite of two explanatory variables being endogenously determined by
firms’ pricing strategies, i.e. the default probability Fi,t+1[αi,t+1] and the variable
tDLLi,t. As in the theory section, we assume that hotels’ financial structures are
determined exogenously; effects of possible capital structure endogeneity will be
tested by means of instrumental variables, as discussed below.
Marginal profits and marginal costs: We use the following profit function:
xi,t = αi,tx∗i,t = (pi,t −mci,t) qi,t, for x∗
i,t = (pi,t −mci,t)q∗i,t and qi,t = αi,tq
∗i,t, (13)
where mci,t denotes the marginal cost of firm i and qi,t denotes output, a random
multiple of a latent output level denoted as q∗i,t. For hotels, this latent output level
26Hence, we test for the DLL-effect as a distinguishing feature of our model relative to a modelthat is nested in ours. This nested model corresponds to the first-order condition ∂x∗i,t/∂pi,t +(1 − Fi,t+1[αi,t+1]) ∂x
∗i,t+1/∂pi,t = 0 which can be regarded as an econometric implementation of
a model like that by Dasgupta and Titman (1998).
16
can be interpreted as the number of overnight stays booked; some of these bookings
are randomly cancelled, resulting in an actual output of qi,t.
In computing the marginal cost mci,t, we allow for the total cost function to be
quadratic in the output realization, qi,t. Hence, we specify the following marginal
cost function for hotels:
mci,t = γ0 + γ1 qi,t + γ2 Mati,t + γ3 Servi,t, (14)
where Mati,t is the cost of “raw materials” such as supplies for cooking, cleaning,
etc., while Servi,t denotes the marginal cost of services that the hotels offer to their
guests. To obtain these variables, we take the total of the relevant variable costs
stated in a hotel’s profits&loss account and divide by the number of overnight stays
sold.
The default probability Fi,t+1[αi,t+1]: By inspection of condition (10), we need
a measure for the probability with which a firm defaults on its debt due at the end
of period t+ 1. In order to obtain such a measure, we start by specifying a default
condition. Corresponding to the theory section, we assume that a firm defaults due
to a profit shortfall if its owners fail to meet the firm’s financial obligations out of
their own pockets. In the empirical model, we consider not only firms’ financial
obligations towards creditors but also fixed costs, denoted as FCi,t for firm i and
period t. Firm i defaults in period t if its profit xi,t falls short of Di,t + FCi,t and
the profit shortfall exceeds the value of the firm’s equity, denoted as ei,t. For the
period t+ 1, we therefore obtain the following default condition:
Di,t+1 + FCi,t+1 − xi,t+1 > ei,t+1 ⇔ xi,t+1 < Di,t+1 + FCi,t+1 − ei,t+1
⇔ αi,t+1 < αi,t+1,(15)
where the second equivalence follows from xi,t+1 = αi,t+1x∗i,t+1 for αi,t+1 = (Di,t+1 +
FCi,t+1 − ei,t+1)/x∗i,t+1.
27
To directly compute the default probability Fi,t+1[αi,t+1], we would need to know
the distribution Fi,t+1 of the state variable αi,t+1. Equivalently, we could also work
with the profit distribution induced by the distribution Fi,t+1. If this profit distri-
bution is denoted as Gi,t+1, then Fi,t+1[αi,t+1] = Gi,t+1[Di,t+1 + FCi,t+1 − ei,t+1] by
27We re-define the critical values αi,t and αi,t+1 in order to take into account hotel i’s fixed costsand its equity value at the end of period t+ 1.
17
the second equivalence relation in (15).28 Since profits are directly observable, we
choose the latter approach. Thereby, we must take into account that the default
probability Gi,t+1[Di,t+1+FCi,t+1−ei,t+1] is endogenously determined because hotel
i’s profit distribution depends on its pricing strategy. Hence, we specify a first-stage
regression explaining hotels’ profits as functions of exogenous variables included in
the vector Zi,t+1 which determines the distributions Fi,t+1 and Gi,t+1.
We assume that the profits of each hotel i are log-normally distributed with a mean
determined by its capacity Capi,t, and its category Cati.29 Profit uncertainty will be
specified as a function of the altitude Alti of the meteorological station located the
closest to hotel i and the seat-to-bed ratio SBRi,t of the hotel. By using the first of
these variables, we intend to capture location-related demand uncertainty, say due
to uncertain snow conditions in nearby ski resorts. The second variable captures the
extent to which hotels’ profits depend not only on the demand for accommodation
but also on the success of the hotels’ restaurants. To summarize, we will use the
following specification:30
ln[xi,t] = β10 + β11 Cati + β12 ln[Capi,t] + β13 ln[Capi,t] ∗ Cati + µmi,t, (16)
where µmi,t denotes an error term which exhibits multiplicative heteroscedasticity:
ln[Var[ln[xi,t]]] = β20 + β21Alti + β22IAlti>1000 + β23SBRi,t + β24ISBRi,t>2 + µvi,t. (17)
Based on the above model, we can compute an estimate of the mean and the standard
deviation of the logarithmic profit for each hotel i and year t. Let the estimated mean
be denoted as lxi,t and let the standard deviation be denoted as sdi,t. Then, we can
define the following measure of the default probability Gi,t+1[Di,t+1+FCi,t+1−ei,t+1]:
Gi,t+1[Di,t+1 + FCi,t+1 − ei,t+1] ≈ Φ[ln[Di,t+1 + FCi,t+1 − ei,t+1]− lxi,t+1
sdi,t+1
], (18)
where Φ denotes the standard normal distribution, the fixed cost FCi,t+1 is defined
as the sum of wages, costs of marketing, administrative expenses, costs of heating,
28Corresponding to the definition of Fi,t below condition (10), we define Gi,t[.] = G[.|Zi,t].29Using a Shapiro-Wilk Test we cannot reject the null hypothesis of a log-normal distribution.30We tried a number of alternative specifications such as allowing in (16) for a relation between
E[ln[xi,t]] and Alti or SBRi,t. However, we found that neither these variables nor the dummyvariables IAlti>1000 and ISBRi,t>2 were significantly related to hotels’ profits, except as proxies forprofit uncertainty in (17). Furthermore, we allowed for time fixed effects which also turned out tobe insignificant.
18
energy and maintenance, Di,t+1 is the book value of debt to be repaid next year,
and ei,t+1 is the book value of equity at the end of the next year. Of these variables,
only the book value of equity ei,t+1 is endogenously determined by hotel i’s pricing
decision in period t. Hence, we can use the probability Φ[.] as explanatory variable
if we compute this probability based on an instrument for ei,t+1. We choose as
instrument the book value of hotel i’s equity at the end of period t− 1, ei,t−1.31 By
substituting the instrument for ei,t+1 in the above-stated argument of Φ[.], we obtain
a probability DPi,t+1 as exogenous measure of the default probability Gi,t+1[Di,t+1+
FCi,t+1 − ei,t+1].
The dynamic limited liability effect tDLLi,t: We need a measure for the
variable tDLLi,t, given by expression (12). To obtain such a measure, we use the
following approximation:
tDLLi,t =Ei,t+1[xi,t+1|xi,t+1≥αi,t+1x∗
i,t+1]x∗
i,tx∗
i,t+1−Ei,t[xi,t|xi,t≥αi,tx
∗i,t]
Ei,t[xi,t|xi,t≥αi,tx∗i,t]
≈ Ei,t+1[xi,t+1|xi,t+1≥αi,t+1x∗i,t+1]−Ei,t[xi,t|xi,t≥αi,tx
∗i,t]
Ei,t[xi,t|xi,t≥αi,tx∗i,t]
,
(19)
for αi,t and αi,t+1 re-defined as follows:27
αi,t+1 = Di,t+1+FCi,t+1−ei,t+1
x∗i,t+1
,
αi,t =Di,t+FCi,t−(1−DPi,t+1)(Ei,t+1[xi,t+1|xi,t+1≥αi,t+1x∗
i,t+1]−(Di,t+1+FCi,t+1−ei,t+1))
x∗i,t
,
The expression in the first line of (19) follows from the ratio in expression (12) if
both the denominator and the numerator of this ratio are multiplied by x∗i,t. To
obtain the approximation in the second line, we set to one the ratio x∗i,t/x
∗i,t+1 of
hotel i’s expected profits in periods t and t + 1 which appears in the numerator
of the fraction stated in the first line of (19). This approximation is reasonable
since this ratio is likely to be close to one.32 Moreover, we can obtain an approxi-
mate expression for tDLLi,t that does not depend on hotel i’s first-period price pi,t
and can therefore be used as exogenous explanatory variable.33 To compute this
31We cannot choose the period t equity value ei,t as instrument for ei,t+1 since both of thesevariables depend on hotel i’s price in period t.
32While we cannot observe hotels’ expected profits, we can test whether the ratio of their actualprofits has a mean of one. We cannot reject this hypothesis.
33To see this, notice that the expected profits x∗i,t and x∗i,t+1 cancel out since they appear notonly in the products αi,tx
∗i,t and αi,t+1x
∗i,t+1 but also in the denominators of the terms for αi,t and
αi,t+1, respectively.
19
variable, denoted as ˆtDLLi,t, we estimate the model (16)-(17) and derive estimates
for Ei,t+1[xi,t+1|xi,t+1 ≥ αi,t+1x∗i,t+1] and Ei,t[xi,t|xi,t ≥ αi,tx
∗i,t] as functions of the
explanatory variables of this model and the variables Di,t, FCi,t, and ei,t−1 as in-
strument for ei,t+1. Thereby, Di,t is the book value of debt to be repaid within one
year, FCi,t denotes the sum of (current period) fixed costs, and ei,t denotes the book
value of equity at the end of period t.
Pricing equation: To convert equation (10) into a regression model, we substitute
for the derivative ∂x∗i,t/∂pi,t determined by the profit function (13) and the marginal
cost function (14). Upon rearranging the resulting equation, we obtain an expression
for the price pi,t, the dependent variable of our regressions. We will regress this price
on the explanatory variables specified by our theoretical model as well as a number of
control variables. The first two control variables, IAlti>1000 and Cati, capture how a
hotel’s pricing depends on location and the quality of accommodation, respectively.
Moreover, we control for effects of leverage on a hotel’s pricing strategy beyond
those captured by the variables DPi,t+1 and ˆtDLLi,t. Thereby, we use as control
variable a hotel’s leverage after repayment of any debt due during either the current
or the next year. This variable is denoted as Levi,t+1; it does not depend on the
debt levels Di,t and Di,t+1 since these variables measure debt repayment scheduled
for the current year and the next year, respectively.
We obtain the following model:
pi,t = γ0 + γ1 qi,t + γ2 Mati,t + γ3 Servi,t + γ4 (1− DPi,t+1)
+γ5 (1− DPi,t+1) ˆtDLLi,t + γ6 IAlti>1000 + γ7 Cati + γ8 Levi,t+1 + µpi,t,
(20)
for i = 1, . . . , n and t = 1, . . . , T . The price of an overnight stay in hotel i is a func-
tion of the hotel’s marginal costs, the non-default probability DPi,t+1, the variable
ˆtDLLi,t which captures the DLL-effect, and three control variables, IAlti>1000, Cati
and Levi,t. With this specification at hand, we can test our model as well as some
nested models. For example, both γ4 and γ5 are equal to zero if firms exhibit myopic
behavior; γ5 = 0 corresponds to the model of Dasgupta and Titman (1998).
Estimation: We use two-stage estimation techniques in order to estimate equation
(20) by means of the program STATA (2000). The first-stage regression (16) is
estimated by maximum likelihood. For the second stage, we use both OLS and
20
models with firm-specific effects. In all specifications, we instrument the demand
for accommodation qi,t using regional fixed effects based on the first three digits of
hotels’ postal codes (out of four digits). As a robustness check, we subsequently
instrument also the variables DPi,t+1 and ˆtDLLi,t that capture effects of hotels’
capital structures on their pricing strategies. This robustness check is required
since hotels’ capital structures may be endogenously determined; the instrumenting
strategy will be discussed below.
Hypotheses: Our main hypothesis concerns the coefficients of the non-default
probability (1− DPi,t+1) and the product of this probability and the (transformed)
dynamic limited liability effect, ˆtDLLi,t, denoted as γ4 and γ5 respectively. By equa-
tion (10) and the definition of x∗i,t in expression (13), the signs of these coefficients are
determined by the sign of the following expression: −(∂x∗i,t+1/∂pi,t)/(∂q
∗i,t/∂pi,t) =
−∂x∗i,t+1/∂q
∗i,t, where ∂x∗
i,t+1/∂q∗i,t > 0 if a hotel’s future profitability increases in its
current output.
We will test the null hypothesis that γ4 and γ5 are equal to zero against the alter-
native that these coefficients are negative. These hypotheses are joint hypotheses:
whether or not we can reject the null depends on both (i) whether hotels’ future
profits depend positively on their current outputs, ∂x∗i,t+1/∂q
∗i,t > 0, and (ii) whether
leverage affects hotels’ pricing strategies as predicted by our theoretical model.
We can also specify hypotheses for other coefficients of equation (20). We expect
to obtain positive coefficients for the variables of the marginal cost function (14),
since one would generally anticipate a positive relation between prices and marginal
costs. Furthermore, we predict a positive coefficient for the dummy variable Cati
since a higher price should be charged for high-quality accommodation. Finally,
hotels’ long-term leverage Levi,t+1 should receive a positive coefficient, as predicted
by Dasgupta and Titman (1998), i.e. γ8 > 0. In the pricing equation (20), the co-
efficient γ8 must however be interpreted differently: this coefficient measures effects
of leverage on hotels’ pricing strategies beyond those captured by our two-period
model. Hence, we cannot reject the predictions of Dasgupta and Titman if we find
that the coefficient γ8 is not significantly different from zero. Instead, these predic-
tions are tested in terms of our hypotheses about the coefficients γ4 and γ5. Testing
for the significance of the coefficient γ8 is rather more like a test of the validity of our
21
model. If we obtain an insignificant coefficient, then our two-period model seems
to capture adequately how leverage affects the pricing decisions of the hotels in our
sample.
3.3 Estimation results
Table 2 reports estimation results for the first-stage regression (16). The estimates
in Panel A are consistent with our expectations and significant at the 95% level.
A hotel’s profit is positively related to its capacity Capi,t and to the quality of
accommodation as measured by dummy variable Cati that indicates hotels in the
four or five star category. The estimates for equation (17) show that the profit
variance significantly depends on the altitude of the meteorological station with the
closest location to a hotel (as measured by the variables Alti and IAlti>1000) and on
the seat-to-bed ratio (as measured by the variables SBRi,t and ISBRi,t>2). We find
that profit uncertainty is negatively correlated with the altitude Alti, which proxies
for the certainty of snowfall in ski resorts located close to the hotel. However, the
indicator variable IAlti>1000 has a significantly positive coefficient. Hence, a hotel
close to a meteorological station above 1000 meters experiences significantly higher
profit uncertainty, perhaps since its profits do mostly depend on uncertain snow
conditions in nearby ski resorts because the hotel predominantly attracts ski tourism.
Taking both effects into account we observe a non-monotonic relation between the
altitude of ski resorts located close to a hotel and profit uncertainty. In addition,
profit uncertainty is significantly related to the seat-to-bed ratio as a proxy for the
extent to which a hotel’s profit depends not only on the demand for accommodation
but also on the success of the hotel’s restaurant.
Table 2 about here
Table 3 reports descriptive statistics for the variables which capture the effects of
leverage on hotels’ pricing strategies in our theoretical model. Panel A describes the
distribution of our estimates for the non-default probability (1− DPi,t+1); Panel B
states similar statistics for the variable ˆtDLLi,t measuring the (transformed) DLL-
effect. The distribution of the non-default probability has a mean (median) value
of 0.690 (0.775), corresponding to a mean (median) probability of default of 0.310
22
(0.225). These values are very high but this is perhaps not surprising given the
substantial leverage of many hotels in our sample.
The distribution of the variable ˆtDLLi,t characterizes the transformed DLL-effect
for our sample of hotels. For each hotel i, this variable measures how the expected
profitability of the hotel differs in the non-default states between the periods t and
t + 1. If this difference is negative, ˆtDLLi,t < 0, then the respective hotel has an
incentive to raise its price in the current period in order to increase its short-term
profits, thus under-investing in market share.34 For ˆtDLLi,t > 0, the DLL-effect
induces the opposite incentive; this is the case for 75% of the hotel-years in our
sample.
Table 3 about here
Finally, we discuss the estimation results for the pricing equation (20); the esti-
mates are stated in Tables 4 and 5. In the first table, we report estimates based on
pooled data; in the second table we present further results for specifications where
firm-specific effects are taken into account.
Consider Table 4. Columns (1) and (2) present estimates for the basic specifica-
tion, with the restriction γ4 = γ5 imposed in the first column (since these two coef-
ficients should be equal in theory). In column (3), we include the variable Levi,t+1
to control for effects of leverage on hotels’ pricing strategies beyond those captured
by the variables DPi,t+1 and ˆtDLLi,t; column (4) reports estimates obtained by in-
strumenting the variables DPi,t+1 and ˆtDLLi,t in order to remove a possible bias
due to capital structure endogeneity (as discussed below). In all columns, we use
regional fixed effects (based on the first three of four digits of hotels’ postal codes)
as instruments for the demand for accommodation, qi,t; the first stage regression
explains qi,t with a value of 38% for the R2 and an F-value of 5.19.
All estimation methods deliver similar results and a similar R2 of about 93%; we
therefore focus on the estimates in columns (1) and (2) of Table 4. In both columns,
all of the coefficient estimates have the signs we expected. We find that there is a
significant negative relation between a hotel’s pricing and its output, consistent with
the existence of economies of scale. The coefficient estimates for the variables Mati,t
34To see this, recall the discussion above Proposition 1. As stated there, the DLL-effect distortsa firm’s optimal strategy towards raising its current profits if DLL[Di,t,Di,t+1] > 1 ⇔ ˆtDLLi,t < 0,where the equivalence follows from definition (11).
23
and Servi,t of the marginal cost function are positive and significantly different from
zero. Hence, hotels’ prices depend positively on the costs of raw materials and
services that they offer to their guests. Also, the coefficients of the variables IAlti>1000
and Cati are significantly positive, indicating that a hotel’s pricing depends on its
location and quality of accommodation, respectively.
Table 4 about here
Next, we test our central hypotheses concerning the signs of the coefficients γ4
and γ5. Column (1) reports a test of the null hypothesis that γ4 = γ5 = 0 for a
model where we impose the constraint that γ4 = γ5 since these two coefficients take
the same value in theory. We obtain a significantly negative coefficient estimate,
consistent with the model in Section 3. In column (2), we separately estimate the
coefficients γ4 and γ5. We find that both of these coefficients again take the predicted
signs and we cannot reject the hypothesis that γ4 = γ5 (p = 0.76). Leverage therefore
affects output pricing both via the non-default probability (1 − DPi,t+1), and via
the variable ˆtDLLi,t which captures the DLL-effect. Ceteris paribus, the price pi,t
increases in the default probability DPi,t+1. This is consistent with the hypothesis
that levered firms under-invest in market share (by charging a higher price pi,t than
an unlevered firm) since their owners are not certain to benefit from such investment.
Leverage therefore affects hotels’ pricing strategies like an increase in the discount
rate used to value future profits from gains of market share, as in the models of
Chevalier and Scharfstein (1996) and Dasgupta and Titman (1998).
In addition, the estimates in Table 4 reveal that hotels’ pricing strategies de-
pend significantly on the variable ˆtDLLi,t which measures the DLL-effect. As dis-
cussed above Proposition 1, this effect can be interpreted as leverage-induced change
in the way firms define the marginal rate of substitution between current and fu-
ture profits. Since only the non-default states are taken into account, the optimal
pricing strategy depends on the relative expected profitability of the non-default
states across periods. Holding constant the default probability DPi,t+1, hotels charge
higher prices, the smaller the variable ˆtDLLi,t. To interpret this result, recall the
definition (11): since the variable ˆtDLLi,t is inversely related to the DLL-factor
DLL[Di,t, Di,t+1], the estimates in Table 4 imply a positive relation between the
price pi,t and DLL[Di,t, Di,t+1]. This finding is consistent with the effects discussed
24
above Proposition 1: ceteris paribus, the higher the DLL-factor, the more biased to-
wards raising current profits is the optimal pricing strategy of a levered firm relative
to an unlevered firm.
The estimates in columns (3) and (4) confirm the results in column (2). In col-
umn (3), we control for effects of leverage on hotels’ pricing strategies beyond those
captured by the variables (1 − DPi,t+1) and ˆtDLLi,t. We include as control vari-
able hotels’ leverage after repayment of any debt due during either the current or
the next year, denoted as Levi,t+1. However, our estimate of the coefficient of this
control variable is not significantly different from zero. This result suggests that
the other variables of equation (20) capture adequately how leverage affects hotels’
pricing decisions.
In column (4), we check whether our results are affected by hotels’ capital struc-
tures being endogenously determined. This column reports instrumental variables
estimates, based on instruments not only for the demand for accommodation qi,t but
also for the two variables (1− DPi,t+1) and ˆtDLLi,t. As stated above, regional fixed
effects are used as instruments for the demand for accommodation, qi,t. For the non-
default probability (1− DPi,t+1), we use as identifying instrument the (next period)
fixed cost FCi,t+1. For the transformed dynamic liability effect we use a two-group
instrument, i.e. a variable which takes the value of one if ˆtDLLi,t exceeds its median
value, and equals minus one otherwise.35 To obtain an identified model, we impose
three exclusion restrictions. The identifying instrument for the variable ˆtDLLi,t is
excluded from the other two first-stage regressions; the identifying instrument for
the non-default probability is excluded from the first-stage regression explaining the
demand for accommodation qi,t. This way, we obtain a model which satisfies the
order condition for identification, discussed in Davidson and MacKinnon (1993).
The first-stage regressions explain the endogenous variables with an R2 of 44% in
the case of the non-default probability (1− DPi,t+1) and with an R2 of 69% for the
tDLL-variable ˆtDLLi,t. In both cases, the F-statistics take values higher than 10;
hence, the respective instruments are strong, corresponding to the recommendations
of Staiger and Stock (1997). The second-stage estimates are consistent with those
35For further discussion of grouping methods, see Johnston (1991), pp. 430-432. We also triedto use other instruments, for example the change in fixed costs (FCi,t+1 − FCi,t)/FCi,t whichwould be a natural choice. However, none of these other instruments was significantly related tothe variable ˆtDLLi,t.
25
in the other columns of Table 4.
Table 5 about here
Table 5 reports a further robustness check. While the estimates in Table 4 are
based on pooled data, we control for firm-specific fixed and random effects to obtain
the estimates in Table 5. Columns (1) and (2) report estimates for a specification
with fixed effects; columns (3) and (4) present random effects estimates. For the fixed
effects model, an F-test rejects the significance of the firm-specific effects. However,
a Breusch-Pagan test shows that there are significant random effects. Hence, it is
unclear whether we should test our hypotheses based on the OLS estimates in Table
4 or based on the panel estimates in Table 5. Fortunately, both sets of estimates
are very similar and yield the same qualitative results.
3.4 Numerical Simulations
In this section, we present numerical analyses of how leverage affects hotels’ pricing
strategies. We use the coefficient estimates in column (1) of Table 4 in order to
compute the price charged by the average hotel in our sample as a function of
leverage and debt maturity. Hence, we substitute our estimates for the various
coefficients of equation (20). The coefficient γ8 of the variable Levi,t+1 is set to zero
since our estimate of this coefficient in column (3) of Table 4 is not significantly
different from zero.
The results are shown in Figures 2 - 4. Figure 2 depicts how the DLL-effect
depends on leverage, defined as the ratio of total debt to total capital, and on debt
maturity, characterized by the portion of debt to be repaid within one year. As in
Section 2, we measure the DLL-effect in terms of the variable DLL[Di,t, Di,t+1] =
1/(1+ tDLLi,t), given by expression (7). To interpret the plot, recall that the DLL-
effect changes a firm’s marginal rate of substitution between current and future
profits. For a levered firm, this marginal rate of substitution equals that of an
unlevered firm times the DLL-factor depicted in Figure 2. By inspection, a hotel
with high short-term leverage sets its prices based on a marginal rate of substitution
between current and future profits that is about twice as high as that of an unlevered
hotel.
26
Figures 3 and 4 depict how hotels’ leverage affects their pricing. In Figure 3, we
plot the optimal prices that would be obtained if the DLL-effect were ignored, as in
the models by Chevalier and Scharfstein (1996) and Dasgupta and Titman (1998).36
Holding constant debt maturity, the optimal price increases in leverage – the hotel
under-invests in market share as has been discussed above. However, this effect is
entirely due to changes in long-term leverage; holding leverage constant, a reduction
in debt maturity causes a price decrease since long-term leverage decreases.
In Figure 4, we plot the optimal prices specified by our theoretical model. Hence,
we “add” to the plot in Figure 3 the price changes due to the DLL-effect.37 Now,
also short-term leverage has an economically significant positive effect on a hotel’s
pricing and the magnitude of this effect is quite comparable to that of the effect of
long-term leverage. Moreover, Figure 4 differs from Figure 3 in that we obtain a
different effect of changes in debt maturity. Consistent with the result in Proposition
2, the optimal price decreases if short-term debt accounts for a higher portion of
overall leverage. By inspection of Figure 4, the magnitude of this effect is roughly
comparable to the rate of inflation.
Figures 3 and 4 depict rather conservative estimates of the effects of leverage and
debt maturity on hotels’ pricing strategies. With other values for the coefficients
of the pricing equation (20), much stronger effects are obtained. For the coefficient
values in column (4) of Table 4, changes in debt maturity trigger price changes of
up to 20%, comparable in magnitude to the effect of leverage on hotels’ pricing
strategies. Plots of these effects (like those in Figures 3 and 4) are available from
the authors upon request.
4 Discussion and conclusions
We consider why leverage affects firms’ pricing strategies if their future profits de-
pend on their current market shares. To invest in market share, firms must cut
their prices in order to attract additional customers. Leverage distorts firms’ opti-
mal strategies by changing their objective functions in two ways. First, levered firms
tend to under-invest in market share as if they use a higher rate to discount future
36Hence, Figure 3 plots equation (20) with γ4 = −24.46 (as in column (1) of Table 4) and γ5 = 0.37Hence, Figure 4 plots equation (20) with γ4 = γ5 = −24.46 (as in column (1) of Table 4).
27
profits. Second, leverage changes the marginal rate of substitution between current
and future profits that firms use in investment decisions in order to maximize their
conditional equity value if they can repay their debts. We refer to the second effect
as the “dynamic limited liability effect” or DLL-effect. Due to this effect, the invest-
ment policy of a levered firm depends on the debt maturity structure – such a firm
shifts profits to those periods in which its earnings must be especially high to cover
debt repayment. By contrast to the first effect of leverage mentioned above, the
DLL-effect can induce either under- or over-investment in market share, reinforcing
or alleviating the under-investment due to the first effect.
In the empirical part of the paper, we develop a model that can be used to test
separately for the two effects of leverage discussed above. We find evidence for
both effects and thus provide a direct empirical validation of models that have been
proposed in prior studies, such as Chevalier and Scharfstein (1996) and Dasgupta
and Titman (1998). However, our findings show that leverage distorts investment
also due to an effect that has not been analyzed previously, i.e. the dynamic limited
liability effect.
Unlike it is the case for the investment distortions induced by leverage, the un-
derlying changes in firms’ objective functions do not depend on the nature of their
investment decisions. Hence, our findings show why leverage distorts investment,
irrespective of whether firms’ investments are strategic substitutes or complements.
With this focus, the present paper should provide new insight for future research
on capital structure and corporate strategy. More specifically, three implications
of our results should be taken into account. First, leverage affects firms’ optimal
strategies in other ways than just like an increase in the discount rate they use.
The DLL-effect can induce under- or over-investment, which complicates empirical
analyses of investment distortions due to leverage.
As its second implication, our analysis shows that at least two variables are re-
quired in order to measure leverage-induced investment distortions. Besides lever-
age, the debt maturity structure can also affect firms’ investment decisions. We
expect that the strength and the direction of this effect depend on whether firms’
investments are strategic substitutes or complements. As shown in Showalter (1995),
these two cases differ in the direction of investment distortions due to the limited
liability effect. Since a similar result should hold for the DLL-effect, the effects of
28
debt maturity should vary across industries.
Finally, the present paper has implications for inter-industry analyses of leverage
and corporate strategy. Since firms in different industries face different oligopolis-
tic settings, cross-industry variation in the direction of the DLL-effect should cause
variation in investment distortions induced by leverage. Our findings suggest that
such cross-industry variation may not take the form of a qualitatively different re-
lation between leverage and investment. Rather, the magnitude of leverage-induced
investment distortions should vary across industries, and perhaps also across firms
at different strategic positions within their industries. Hence, it is important to
allow for such variation in empirical analyses, as done in recent studies by Campello
and Fluck (2003) and MacKay and Phillips (2003), respectively.
29
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A Appendix: Proofs
Proof of Lemma 1: Condition (3) implies that firm i defaults on its short-term
debt if αi,1 < αi,1, for
αi,1 =Di,1 − (1− F[αi,2])(E[αi,2|αi,2 ≥ αi,2]x
∗i,2 −Di,2)
x∗i,1
. (21)
At date t = 2, firm i defaults if αi,2 ≤ αi,2 = Di,2/x∗i,2. Hence, the equityholders’
total expected payoff is given by:
Πi =∫
αi,1
(αi,1x∗i,1 −Di,1 +
∫αi,2
(αi,2x∗i,2 −Di,2)dF[αi,2])dF[αi,1].
Proof of Proposition 1: The derivative of ∂DLL[Di,1, Di,2]/∂Di,1 is given by:
∂DLL∂Di,1
= DLL[Di,1, Di,2]∂
∂Di,1E[αi,1|αi,1≥αi,1]
E[αi,1|αi,1≥αi,1]=
f[αi,1]
1−F[αi,1]
E[αi,1|αi,1≥αi,1]−αi,1
E[αi,1|αi,1≥αi,1]
∂αi,1
∂Di,1> 0, (22)
where the inequality follows from ∂αi,1/∂Di,1 > 0 by inspection of expression (21).
The derivative of ∂DLL[Di,1, Di,2]/∂Di,2 is given by:
∂DLL
∂Di,2
= DLL[Di,1, Di,2]
∂∂Di,2
E[αi,1|αi,1 ≥ αi,1]
E[αi,1|αi,1 ≥ αi,1]−
∂∂Di,2
E[αi,2|αi,2 ≥ αi,2]
E[αi,2|αi,2 ≥ αi,2](23)
Proof of Proposition 2: The first-order condition (5) can be written as follows:
FOCi =∂x∗
i,1
∂pi,1
+1− F [αi,2]
DLL[Di,1, Di,2]
∂x∗i,2
∂pi,1
= 0. (24)
To obtain the results in Proposition 2, we totally differentiate the above condition
and rearrange the total derivatives, which yields the following results:
dp∗i,1dDi,1
= −(
∂xi,2
∂pi,1/∂FOCi
∂pi,1
)∂
∂Di,1
(1−F[αi,2]
DLL[Di,1,Di,2]
)
dp∗i,1dDi,2
= −(
∂xi,2
∂pi,1/∂FOCi
∂pi,1
)∂
∂Di,2
(1−F[αi,2]
DLL[Di,1,Di,2]
).
(25)
Thereby, ∂x∗i,2/∂pi,1 < 0 and ∂FOCi/∂pi,1 < 0 for a global maximum of firm i’s
equity value in the solution of condition (24). Hence, the signs of dp∗i,1/dDi,1 and
dp∗i,1/dDi,2 are the opposite of those of the derivatives of (1−F[αi,2])/DLL[Di,1, Di,2]
with respect to Di,1 and Di,2, respectively:
∂∂Di,1
(1−F[αi,2]
DLL[Di,1,Di,2]
)= − 1−F[αi,2]
DLL[Di,1,Di,2]h[αi,1]
E[αi,1|αi,1≥αi,1]−αi,1
E[αi,1|αi,1≥αi,1]
∂αi,1
∂Di,1< 0,
∂∂Di,2
(1−F[αi,2]
DLL[Di,1,Di,2]
)= − f[αi,2]
DLL[Di,1,Di,2]
∂αi,2
∂Di,2
− (1−F[αi,2])
DLL[Di,1,Di,2]
(h[αi,1]
E[αi,1|αi,1≥αi,1]−αi,1
E[αi,1|αi,1≥αi,1]
∂αi,1
∂Di,2−
h[αi,2]αi,2
E[αi,2|αi,2≥αi,2]
∂αi,2
∂Di,2
)< 0,
(26)
33
where h[·] denotes the hazard rate h[x] = f[x]/(1−F[x]). The first derivative follows
from result (22) in the proof of Proposition 1 and the fact that αi,2 = Di,2/x∗i,2
does not depend on Di,1. The second derivative follows also from result (22); the
sign of this derivative can be determined upon substituting for ∂αi,1/∂Di,2 = (1 −F[αi,2])/x
∗i,1 > 0 (by differentiating expression (21) and simplifying the derivative)
and ∂αi,2/∂Di,2 = 1/x∗i,2 > 0.
To obtain the result on the effect of debt maturity, consider a change in Di,1 and
Di,2 of the form specified in (8); debt maturity decreases for ε > 0. The resulting
change in the optimal first-period price p∗i,1 is given by:
dp∗i,1= −(
∂x∗i,2
∂pi,1/∂FOCi
∂pi,1
) (∂
∂Di,1
(1−F[αi,2]
DLL[Di,1,Di,2]
)dDi,1 +
∂∂Di,2
(1−F[αi,2]
DLL[Di,1,Di,2]
)dDi,2
)
= −(
∂x∗i,2
∂pi,1/∂FOCi
∂pi,1
)f[αi,2]
DLL[Di,1,Di,2]
αi,2
E[αi,2|αi,2≥αi,2]
∂αi,2
∂Di,2ε < 0, for ε > 0,
(27)
since ∂x∗i,2/∂pi,1 < 0, ∂FOCi/∂pi,1 < 0 and ∂αi,2/∂Di,2 = 1/x∗
i,2 > 0.
Proof of Proposition 3: By totally differentiating the first-order condition (24)
and the analogous one for firm j, we obtain the derivatives:
dpei,1
dDi,1=
∂FOCj∂pj,1
∆∂
∂Di,1
(1−F[αi,2]
DLL[Di,1,Di,2]
)
dpej,1
dDi,1= −
∂FOCj∂pi,1
∆∂
∂Di,1
(1−F[αi,2]
DLL[Di,1,Di,2]
)
dpei,1
dDi,2=
∂FOCj∂pj,1
∆∂
∂Di,2
(1−F[αi,2]
DLL[Di,1,Di,2]
)
dpej,1
dDi,2= −
∂FOCj∂pi,1
∆∂
∂Di,2
(1−F[αi,2]
DLL[Di,1,Di,2]
),
(28)
where ∆ = (∂FOCi/∂pi,1)(∂FOCj/∂pj,1) − (∂FOCi/∂pj,1)(∂FOCj/∂pi,1) and pei,1
denotes the first-period price that firm i chooses in equilibrium. The results in
Proposition 3 follow from ∂FOCj/∂pi,1 > 0 and ∆ > 0 (by the assumptions above
Proposition 3), the second-order condition ∂FOCj/∂pj,1 < 0, and the results stated
in expression (26) in the proof of Proposition 2, for∂αi,1
∂Di,1= 1/x∗
i,1,∂αi,1
∂Di,2= (1 −
F[αi,2])/x∗i,1 and
∂αi,2
∂Di,2= 1/x∗
i,2.
The result about the effect of the maturity structure of firm i’s debt follows from
the above-stated results:
dpei,1 =
∂FOCj∂pj,1
∆
(∂
∂Di,1
(1−F[αi,2]
DLL[Di,1,Di,2]
)dDi,1 +
∂∂Di,2
(1−F[αi,2]
DLL[Di,1,Di,2]
)dDi,2
),
dpej,1 = −
∂FOCj∂pi,1
∆
(∂
∂Di,1
(1−F[αi,2]
DLL[Di,1,Di,2]
)dDi,1 +
∂∂Di,2
(1−F[αi,2]
DLL[Di,1,Di,2]
)dDi,2
),
(29)
for dDi,1 and dDi,2 of the form specified in (8). For ε > 0, we obtain dpei,1 < 0 and
dpej,1 < 0 as a consequence of ∂FOCj/∂pi,1 > 0, ∆ > 0, the second-order condition
∂FOCj/∂pj,1 < 0, and the results stated in expression (26).
34
B Appendix: Tables and figures
Table 1: Descriptive statisticsTable 1 gives descriptive statistics for a sample of 100 Austrian hotels for 120 firm-years during theperiod 1999-2001. Panel A reports descriptive statistics for the variables used in our econometricanalysis, i.e. the average price pi,t that hotels charge for accommodation per night (where theaverage is taken across all overnight stays sold by a hotel in one year), the number of overnightstays sold, qi,t, hotels’ marginal costs Mati,t, and Servi,t, hotels’ fixed costs FCi,t, the book valueof hotels’ equity, ei,t, the book values of debt to be repaid within the current and the next year,Di,t and Di,t+1 respectively, hotels’ leverage remaining at the end of the next year, Levi,t+1, adummy variable Cati which equals one for any hotel i that offers high quality accommodationrated four or five stars (out of five), hotels’ capacities Capi,t (number of beds × days during whicha hotel stays open for business), the altitude Alti of the closest meteorologic station, a dummyvariable IAlti>1000 which equals one for hotels for which Alti exceeds 1000 meters, the ratio ofthe number of hotels’ beds to the number of seats in the hotel restaurant, SBRi,t, and a dummyvariable ISBRi,t>2 which equals one for hotels with a relatively sizeable restaurant for which SBRi,t
exceeds two. All prices and costs are in constant Euros, as of 1999. Panel B reports summarystatistics for two variables that describe hotels’ capital structures in terms of book values, i.e. theratio of total debt to total assets, and the ratio of hotels’ short-term to long-term debt, defined asdebt to be repaid within and after one year, respectively.
Panel A.Variable Description Nobs. Mean Std.dev.pi,t Price per night in Euros 120 82.99 72.59qi,t Number of overnight stays sold 120 15534 12169.91Mati,t Cost of materials in Euros 120 17.13 21.96Servi,t Cost of services in Euros 120 0.63 0.97FCi,t Total of fixed costs in Euros 120 740939 816240ei,t Book value of equity in Euros 120 421984 1003846Di,t Short-term debt in Euros 120 394781 828089Di,t+1 Long-term debt in Euros 120 433542 949317Levi,t+1 Leverage after repayment 120 0.89 0.685
of Di,t and Di,t+1
Cati Dummy for high quality hotels 120 0.60 0.49Capi,t Capacity (beds×days open) 100 28516 35693Alti Altitude of the closest 120 815 330
meteorological station in metersIAlti>1000 Altitude dummy variable 120 0.27 0.45SBRi,t Seat to bed ratio 120 1.84 1.43ISBRi,t>2 Seat to bed dummy variable 120 0.61 0.49Panel B.Variable Nobs. Mean Std.dev.Total debt to total assets 120 0.85 0.20Short-term to long-term debt 120 0.98 0.33
35
Table 2: First-stage estimation results for the relation between profits and exogenousvariables
Table 2 reports first-stage estimation results for the relation between hotels’ profits and exogenousvariables based on a sample of 100 Austrian hotels for 120 firm-years during the period 1999-2001. Profits are assumed to be log-normally distributed with multiplicative heteroscedasticity.Panel A states how the expected profit depends on a hotel’s capacity, Capi,t, and the qualityof accommodation, as measured by the dummy variable Cati that indicates hotels in the four orfive star category. For 20 hotels, we lack data on their capacities. We set these hotels’ capacitiesto 0.001 (in order to be able to take logs) and use a dummy variable to control for differencesbetween these hotels and the others in the estimations. We do not report the estimated coefficientfor this dummy variable. Panel B states how profit uncertainty depends on a hotel’s locationand the relative size of the hotel restaurant. Thereby, Alti is the altitude of the meteorologicalstation located the closest to hotel i and IAlti>1000 is a dummy variable indicating whether Altiexceeds 1000 meters. The relative size of a hotel’s restaurant is measured in terms of the ratio ofthe number of seats in the restaurant and the number of beds of the hotel, denoted as SBRi,t;ISBRi,t>2 denotes a dummy variable indicating hotels with relatively sizeable restaurants. Theabsolute values of the z-statistics are stated in parentheses. ∗∗(∗) denotes a 95% (90%) level ofsignificance.
Panel A.Dependent variable: ln[profit xi,t]
Variable Description Coefficient EstimateConstant Constant β10 2.651
(1.35)Cati Dummy for high quality hotels β11 9.408
(4.79)∗∗
ln[Capi,t] ln[Capacity=beds×days open] β12 1.067(5.26)∗∗
ln[Capi,t] ∗ Cati ln[Capacity] times category β13 - 0.888(4.34)∗∗
Panel B.Dependent variable: ln[Var[ln[xi,t]]]
Variable Description Coefficient EstimateConstant Constant β20 1.510
(2.14)∗∗
Alti/1000 Altitude of closest β20 -0.839meteorological station (1.67)∗
IAlti>1000 Altitude dummy variable β21 0.629(2.01)∗∗
SBRi,t Seat to bed ratio β22 -0.507(3.35)∗∗
ISBRi,t>2 Seat to bed dummy variable β23 - 0.608(1.89)∗
Number of observations 120Wald-test 713.15
36
Table 3: Distribution of central explanatory variables
Table 3 states the distributions of the two variables which capture the effects of leverage on hotels’pricing strategies in the theoretical model. The sample covers 100 Austrian hotels for 120 firm-yearsduring the period 1999-2001. Panel A reports descriptive statistics for the estimated non-defaultprobability, (1 − DPi,t+1). Panel B states the same statistics for the variable ˆtDLLi,t whichcaptures the dynamic limited liability effect of leverage on hotels’ pricing strategies.
Panel A: Non-default probability (1 − DPi,t+1)Percentiles Smallest
1% 0.0040273 0.00010065% 0.1394295 0.004027310% 0.2120851 0.020972925% 0.4503981 0.078958150% 0.7752711
Largest Mean 0.69075% 0.9902213 1 Std. Dev. 0.30790% 1 1 Variance 0.09495% 1 1 Skewness -0.64599% 1 1 Kurtosis 2.120
Panel B: (Transformed) dynamic limited liability effect ˆtDLLi,t
Percentiles Smallest1% -0.4812593 -0.53129515% -0.3301545 -0.481259310% -0.2500812 -0.444715125% 0.00 -0.402594250% 0.0142116
Largest Mean 0.20575% 0.1954983 0.8573666 Std. Dev. 0.45590% 0.5662895 1.309377 Variance 0.20795% 0.7783068 1.736596 Skewness 1.23199% 1.736596 1.846478 Kurtosis 6.513
37
Table4:
Estimationresultsforthepricingequationbased
onpooled
data
Tab
le4
repo
rtsth
ees
tim
atio
nsre
sultsfo
rth
epr
icin
geq
uation
base
don
pool
edda
ta.The
sam
ple
cove
rs10
0A
ustr
ian
hote
lsfo
r12
0fir
m-y
ears
during
the
period
1999
-200
1.The
depe
nden
tva
riab
leis
the
aver
age
pricep
i,tth
ata
hote
lch
arge
spe
rni
ght
(whe
reth
eav
erag
eis
take
nac
ross
allov
erni
ght
stay
sso
ldby
aho
teli
non
eye
ar).
The
expl
anat
ory
variab
lesin
clud
eth
enu
mbe
rof
over
nigh
tst
aysso
ld,q
i,t,h
otels’
mar
gina
lcos
tsMat i
,tan
dServ i
,t,
the
non-
defa
ult
prob
abili
ty(1
−D
Pi,
t+1),
the
variab
leˆ
tDLL
i,tth
atca
ptur
esth
edy
nam
iclim
ited
liabi
lity
effec
t,a
dum
my
variab
leI A
lti>
1000
whi
cheq
uals
one
forho
tels
forwhi
chth
eclos
estm
eteo
rolo
gic
stat
ion
islo
cate
dat
anal
titu
deof
mor
eth
an10
00m
eter
s,a
dum
my
variab
leCat i
whi
cheq
uals
one
for
any
hote
li
that
offer
shi
ghqu
ality
acco
mm
odat
ion
rate
dfo
uror
five
star
s(o
utof
five)
,an
dLev
i,t+
1de
fined
asa
hote
li’s
leve
rage
atth
een
dof
the
yeart+
1.A
llco
lum
nsre
port
inst
rum
enta
lva
riab
lees
tim
ates
.In
colu
mns
(1)-(3
)we
use
inst
rum
ents
for
the
dem
and
for
acco
mm
odat
ion,
q i,t;i
nco
lum
n(4
)we
addi
tion
ally
cont
rolf
oreff
ects
ofca
pita
lstr
uctu
reen
doge
neity
byus
ing
inst
rum
ents
forth
eva
riab
les(1
−D
Pi,
t+1)an
dˆ
tDLL
i,t
whi
chca
ptur
eeff
ects
ofleve
rage
onho
tels’p
ricing
stra
tegi
es.In
colu
mn
(1),
we
impo
seth
eco
nstr
aintγ4
=γ5.In
colu
mn
(3),
we
includ
eth
eva
riab
leLev
i,t+
1to
cont
rolf
oreff
ects
ofleve
rage
onho
tels’p
ricing
stra
tegi
esbe
yond
thos
eca
ptur
edby
the
variab
lesD
Pi,
t+1
and
ˆtD
LL
i,t.A
llpr
ices
and
cost
sar
ein
cons
tant
Eur
os,a
sof
1999
.The
abso
lute
valu
esof
the
t-st
atistics
,res
pect
ively
z-st
atistics
,are
stat
edin
pare
nthe
ses.
∗∗(∗
)de
note
sa
95%
(90%
)leve
lof
sign
ifica
nce.
Dep
ende
ntva
riab
le:
Pricep
i,t
(1)
(2)
(3)
(4)
Var
iabl
eD
escr
iption
Coe
fficien
tγ4
=γ5
Constant
Con
stan
tγ0
39.6
4538
.250
41.7
0769
.328
(5.3
9)∗∗
(4.4
0)∗∗
(4.6
4)∗∗
(7.3
0)∗∗
ˆq i,t/1
000
Inst
rum
ent
forq i
,t,th
enu
mbe
rof
γ1
-0.5
16-0
.499
-0.4
81-0
.683
over
nigh
tst
ays
sold
,di
vide
dby
1000
(1.9
9)∗∗
(1.8
8)∗
(1.8
2)∗
(2.9
2)∗∗
Mat i
,tCos
tof
mat
eria
lsγ2
3.07
93.
085
3.09
63.
048
(35.
68)∗
∗(3
4.74
)∗∗
(34.
88)∗
∗(3
9.25
)∗∗
Serv i
,tCos
tof
serv
ices
γ3
3.39
73.
480
3.45
01.
970
(1.7
6)∗
(1.7
8)∗
(1.7
7)∗
(1.1
3)(1
−D
Pi,
t)
Non
-def
ault
prob
abili
tyγ4
-24
.460
-23.
127
-22.
686
-(4
.85)
∗∗(3
.46)
∗∗(3
.40)
∗∗-
(1−
ˆ DP
i,t)
Inst
rum
ent
for
(1−
DP
i,t)
γ4
--
--5
3.96
5-
--
(6.1
0)∗∗
(1−
DP
i,t)∗
ˆtD
LL
i,t
(1−
DP
i,t)*
(tra
nsfo
rmed
)D
LL-e
ffect
γ5
-24.
460
-26.
607
-24.
235
-(4
.85)
∗∗(3
.07)
∗∗(2
.76)
∗∗-
(1−
ˆ DP
i,t)∗
ˆtD
LL
i,t
Inst
rum
ent
for(
1−
DP
i,t)∗
ˆtD
LL
i,t
γ5
--
--4
0.17
0-
--
(2.8
8)∗∗
I Alt
i>
1000
Altitud
edu
mm
yva
riab
leγ6
9.65
99.
834
10.1
138.
728
(2.3
1)∗∗
(2.3
2)∗∗
(2.3
9)∗∗
(2.3
2)∗∗
Cat i
,tD
umm
yfo
rhi
ghqu
ality
hote
lsγ7
21.7
5922
.054
21.2
2916
.019
(5.4
5)∗∗
(5.3
4)∗∗
(5.1
2)∗∗
(4.1
8)∗∗
Lev
i,t+
1Lev
erag
eat
the
end
ofpe
riod
t+
1γ8
--
-4.1
03-
--
(1.4
1)-
Num
ber
ofob
serv
atio
ns12
012
012
012
0A
djus
ted
R2
0.93
0.93
0.93
0.94
38
Table5:
Estim
ationresultsforthepricingequationwithfirm
-specificfixed
andfirm
-specificrandom
effects
Tab
le5
repo
rtsth
ees
tim
atio
nsre
sultsfo
rth
epr
icin
geq
uation
base
don
am
odel
with
firm
-spe
cific
fixed
and
firm
-spe
cific
rand
omeff
ects
.The
sam
ple
cove
rs10
0A
ustr
ian
hote
lsfo
r12
0fir
m-y
ears
during
the
period
1999
-200
1.The
depe
nden
tva
riab
leis
the
aver
age
pricep
i,t
that
aho
telch
arge
spe
rni
ght
(whe
reth
eav
erag
eis
take
nac
ross
allov
erni
ght
stay
sso
ldby
aho
telin
one
year
).The
expl
anat
ory
variab
les
includ
eth
enu
mbe
rof
over
nigh
tst
ays
sold
,q i
,t,ho
tels’m
argi
nalco
stsMat i
,tan
dServ i
,t,th
eno
n-de
faul
tpr
obab
ility
(1−
DP
i,t+
1),
the
variab
leˆ
tDLL
i,t
that
capt
ures
the
dyna
mic
limited
liabi
lity
effec
t,a
dum
my
variab
leI A
lti>
1000
whi
cheq
uals
one
for
hote
lsfo
rwhi
chth
eclos
est
met
eoro
logi
cst
atio
nis
loca
ted
atan
altitu
deof
mor
eth
an10
00m
eter
s,a
dum
my
variab
leCat i
whi
cheq
uals
one
for
any
hote
li
that
offer
shi
ghqu
ality
acco
mm
odat
ion
rate
dfo
uror
five
star
s(o
utof
five)
,an
dfir
m-s
pecific
effec
ts.
Col
umns
(1)
and
(2)
repo
rtth
ees
tim
ates
with
firm
-spe
cific
fixed
effec
ts,co
lum
ns(3
)an
d(4
)re
port
estim
ates
with
firm
-spe
cific
rand
omeff
ects
.A
llco
lum
nsre
port
inst
rum
enta
lva
riab
lees
tim
ates
.In
colu
mns
(1)
and
(3)
we
use
inst
rum
ents
for
the
dem
and
for
acco
mm
odat
ion,q i
,t;in
colu
mns
(2)
and
(4)
we
addi
tion
ally
cont
rolfo
reff
ects
ofca
pita
lst
ruct
ure
endo
gene
ity
byus
ing
inst
rum
ents
for
the
variab
les
(1−
DP
i,t+
1)
and
ˆtD
LL
i,twhi
chca
ptur
eeff
ects
ofleve
rage
onho
tels’pr
icin
gst
rate
gies
.A
llpr
ices
and
cost
sar
ein
cons
tant
Eur
os,as
of19
99.
The
abso
lute
valu
esof
the
t-st
atistics
,re
spec
tive
lyz-
stat
istics
,ar
est
ated
inpa
rent
hese
s.∗∗
(∗)de
note
sa
95%
(90%
)leve
lof
sign
ifica
nce.
Dep
ende
ntva
riab
le:
Pricep
i,t
(1)
(2)
(3)
(4)
Var
iabl
eD
escr
iption
Coe
fficien
tFix
edeff
ects
Ran
dom
effec
tsConstant
Con
stan
tγ0
42.2
7971
.028
39.7
54pp
70.7
63(4
.09)
∗∗(6
.62)
∗∗(4
.61)
∗∗(7
.57)
∗∗
ˆq i,t/1
000
Inst
rum
ent
forq i
,t;
γ1
-0.
864
-1.0
26-0
.589
-0.7
72O
vern
ight
stay
sso
ld,di
vide
dby
1000
(2.7
2)∗∗
(3.7
1)∗∗
(2.2
2)∗∗
(3.3
0)∗∗
Mat i
,tCos
tof
mat
eria
lsγ2
3.29
93.
251
3.11
63.
076
(20.
76)∗
∗(2
3.56
)∗∗
(32.
49)∗
∗(3
6.27
)∗∗
Serv i
,tCos
tof
serv
ices
γ3
3.33
12.
099
3.40
91.
963
(1.5
7)(1
.12)
(1.8
2)∗
(1.1
7)(1
−D
Pi,
t)
Non
-def
ault
prob
abili
tyγ4
-25
.875
--2
3.93
3-
(3.4
3)∗∗
-(3
.61)
∗∗-
(1−
ˆ DP
i,t)
Inst
rum
ent
for
(1−
DP
i,t)
γ4
--5
4.63
9-
-55
.065
-(5
.94)
∗∗-
(6.4
0)∗∗
(1−
DP
i,t)∗
ˆtD
LL
i,t
(1−
DP
i,t)*
(tra
nsfo
rmed
)D
LL-e
ffect
γ5
-33.
196
--2
8.36
4-
(2.3
6)∗∗
-(3
.11)
∗∗-
(1−
ˆ DP
i,t)∗
ˆtD
LL
i,t
Inst
rum
ent
for(
1−
DP
i,t)∗
ˆtD
LL
i,t
γ5
--3
6.46
9-
-34.
535
-(2
.32)
∗∗-
(2.6
8)∗∗
I Alt
i>
1000
Altitud
edu
mm
yva
riab
leγ6
10.2
3411
.203
9.95
69.
202
(2.0
6)∗∗
(2.5
9)∗∗
(2.3
5)∗∗
(2.4
3)∗∗
Cat i
,tD
umm
yfo
rhi
ghqu
ality
hote
lsγ7
23.7
6416
.148
22.4
9615
.614
(4.7
0)∗∗
(3.5
4)∗∗
(5.3
6)∗∗
(4.0
3)∗∗
Firm
-spe
cific
effec
tsN
oN
oYes
Yes
Num
ber
ofob
serv
atio
ns12
012
012
012
0A
djus
ted
R2
0.94
0.95
0.94
0.93
39
Figure
1:Timeline
firm
sset
prices
firm
sset
prices
profits
realized
short-term
profits
realized
long-term
✲✛
✲✛
period1
t=0
t=1
t=2
period2
debtrepaid
debtrepaid
40
Figure 2: The dynamic limited liability effect
Figure 2 depicts how the dynamic limited liability effect (DLL-effect) depends on lever-age, defined as the ratio of total debt to total capital, and on debt maturity, charac-terized by the portion of debt to be repaid within one year. For a levered firm, themarginal rate of substitution between current and future profits equals that of an un-levered firm times the DLL-factor depicted in Figure 2. The plot is based on esti-mates for a sample of 100 Austrian hotels for 120 firm-years during the period 1999-2001.
0
0.2
0.4
0.6
0.8
1
Fractionof short-term debt
0
0.2
0.4
0.6
0.81
Leverage
0
1
2
DLL0
0.2
0.4
0.6
0.8
1
Fractionof short-term debt
0
1
2
DLL
41
Figure 3: Firms’ optimal pricing strategies without the dynamic limited liabilityeffect
Figure 3 depicts how hotels’ optimal pricing strategies depend on leverage and debt maturityif the dynamic limited liability effect is ignored. The plot is based on estimates for a sampleof 100 Austrian hotels for 120 firm-years during the period 1999-2001. The Euro price of oneovernight stay is depicted as a function of (i) leverage, defined as the ratio of total debt to totalcapital, and (ii) debt maturity, characterized by the portion of debt to be repaid within one year.
0
0.2
0.4
0.6
0.8
1
Fraction of short-term debt
0
0.2
0.4
0.6
0.81
Leverage
85
90
95
100
Price0
0.2
0.4
0.6
0.8
1
Fraction of short-term debt
85
90
95
100
Price
42
Figure 4: Firms’ optimal pricing strategies with the dynamic limited liability effect
Figure 4 depicts how firms’ optimal pricing strategies depend on leverage and debt maturity ac-cording to the model put forward in this paper. The plot is based on estimates for a sampleof 100 Austrian hotels for 120 firm-years during the period 1999-2001. The Euro price of oneovernight stay is depicted as a function of (i) leverage, defined as the ratio of total debt to totalcapital, and (ii) debt maturity, characterized by the portion of debt to be repaid within one year.
0
0.2
0.4
0.6
0.8
1
Fraction of short-term debt
0
0.2
0.4
0.6
0.81
Leverage
80
85
90
95
Price0
0.2
0.4
0.6
0.8
1
Fraction of short-term debt
80
85
90
95
Price
43