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, alexander.stomper@univie.ac.at

‡Department of Economics, University of Vienna, BWZ-Brunnerstr. 72, A-1210 Vienna, Aus-tria, christine.zulehner@univie.ac.at

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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32

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