Why Leverage Distorts Investment

Why Leverage Distorts Investment∗ Alex Stomper†

Christine Zulehner‡

February 25, 2004

Abstract We theoretically and empirically analyze why leverage distorts firms’ output pricing and their implicit investments in market share to generate future profits. We find evidence of two effects. Leverage changes not only the rate at which firms effectively discount future profits but also their marginal rates of substitution between current and future profits. We show that the second effect either counteracts or reinforces the investment distortions due to the first effect. While levered firms never 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, Gregor Hoch, Ron Giammarino, Robert Heinkel, Hans-Georg Kantner, Vojislav Maksimovic, Dennis C. Mueller, Judith Spiegl, Neal Stoughton and Josef Zechner for helpful discussions and suggestions. We thank the ¨ “Osterreichische TourismusBank” for providing us with data. † Department of Business Studies, University of Vienna, BWZ-Br¨ unnerstr. 72, A-1210 Vienna, Austria, [email protected] ‡ Department of Economics, University of Vienna, BWZ-Br¨ unnerstr. 72, A-1210 Vienna, Austria, [email protected]

Why Leverage Distorts Investment Abstract We theoretically and empirically analyze why leverage distorts firms’ output pricing and their implicit investments in market share to generate future profits. We find evidence of two effects. Leverage changes not only the rate at which firms effectively discount future profits but also their marginal rates of substitution between current and future profits. We show that the second effect either counteracts or reinforces the investment distortions due to the first effect. While levered firms never 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.

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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 soon turned 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. Empirically, most studies have found that leverage makes firms less aggressive competitors. However, it remains unknown why this finding is obtained – the empirical 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 open as to why leverage distorts investment, and whether the investment distortions are bound to vary across industries as predicted by Showalter (1995). 1

For surveys of this literature, see Maksimovic (1995) and Grinblatt and Titman (2002).

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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 firms’ objective functions. We find that leverage distorts investment not only due to an increase in the rate at which firms effectively discount future profits, but also due to a change in their marginal rates of substitution between current and future profits. By contrast to the investment distortions themselves, the underlying changes in firms’ objective functions do not depend on whether firms’ investments are strategic substitutes or complements. In this sense, our findings are robust to cross-industry variation in the nature of firms’ investment problems. The paper has a theoretical part and an empirical part. Throughout the paper, we consider an investment decision commonly taken by many firms: investment in market share in order to attract repeat customers. To undertake such investments, firms reduce the price of their output at the cost of a decrease in their current profitability. We consider how leverage distorts 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 is that modeled by Chevalier and Scharfstein (1996) and Dasgupta and Titman (1998): leverage induces under-investment as if firms discount future profits at a higher rate.4 In addition, our model captures a second effect of leverage that has not been analyzed before: leverage increases the cost that a firm’s owners incur if the firm charges less for its 2

This distinguishes our paper from previous empirical studies, like the seminal contributions by Phillips (1995), Chevalier (1995), and Chevalier and Scharfstein (1996). 3 Opler and Titman (1994), Kovenock and Phillips (1997), Zingales (1998), Khanna and Tice (2000) and Campello (2003) analyze how leverage directly affects firms’ market shares. 4 Chevalier and Scharfstein (1996) build on prior work by Bolton and Scharfstein (1990, 1996) and Hart and Moore (1989) in order to analyze how leverage affects firms’ output pricing in a model in which debt financing is optimal. Campello and Fluck (2003) extend the model of Chevalier and Scharfstein (1996) to consider the case in which firms’ customers anticipate that capital market imperfections may drive firms out of business.

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output in order to attract additional customers. This result is obtained since the owners consider the cost of a price reduction 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 output that it can meet its financial obligations. In these states, a price reduction causes a higher shortfall 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. As a result, investment in market share is more costly for the owners of a more highly levered firm. Our model captures this effect as part of a dynamic effect of leverage on firms’ output pricing. We show that a firm’s optimal pricing strategy depends on its relative expected profitability in the non-default states across periods. For the firm’s owners, the first-period non-default states determine the conditional expected cost of investment in market share; the owners’ conditional expected profit from such investment depends on the profitability of the second-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 twoperiod model shows how the DLL-effect changes the marginal rates of substitution firms use in trade-offs between current and future profits. With two effects of leverage on firms’ output pricing, our model generates novel testable predictions. By contrast to the limited 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, this effect can counteract or reinforce the under-investment induced by leverage due to the first of the two effects mentioned above. We analyze the overall effect and find that levered firms never over-invest 5

Showalter (1995) shows that the direction of the limited liability effect is fully determined by underlying assumptions about the nature of firms’ competition (strategic substitutes vs. strategic complements) and the kind of uncertainty they face (cost vs. demand uncertainty). Holding constant these assumptions, the limited liability effect makes firms either more or less aggressive competitors, but only one of these results can be obtained. See Kovenock and Phillips (1995) for a discussion of the limited liability effect in terms of investment in production capacity. FaureGrimaud (2000) extends the analysis by Brander and Lewis (1986) to consider the optimal financial contracts. Glazer (1994) argues that the result of Brander and Lewis depends on the assumption that debt is short-term, Dockner, Elsinger and Gaunersdorfer (2000) respond by pointing out that long-term debt also causes firms to be more aggressive.

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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, we are the first to provide empirical evidence for leverageinduced 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 cannot adequately characterize leverageinduced under-investment since they fail to 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, i.e. hotels close to ski resorts. 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 at 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 modelling profit uncertainty this way, we can identify how shortterm 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. 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.

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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 equilibrium 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 interpreted 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 subscriptions 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 additive uncertainty.7 Leverage affects the pricing choices of the firms in our model 6

Think of telecom firms, newspapers, hotels, etc. In the empirical analysis, we consider hotels close to ski resorts which face the risk of cancellations due to uncertain snow conditions. 7 Chevalier and Scharfstein (1996) and Campello and Fluck (2003) also consider the case of demand uncertainty. However, their models allow for only two states of demand rather than a continuum. Hence, their models are not suited for analyzing how leverage affects firms’ marginal rates of substitution between current and future profits (the DLL-effect).

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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 customer base. The first-period profit of firm i ∈ A, B depends on both firms’ firstperiod prices, pA,1 and pB,1 , as well as on a random factor denoted as α ˜ i,1 : x˜i,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 firstperiod profit.8 Firm i’s second-period profit depends similarly on a random factor, α ˜ i,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: x˜i,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 ].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 α ˜ i,1 and α ˜ i,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. 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 8

Throughout this paper, we use a tilde to denote random variables and use the same variable names without the tilde to denote realizations of random variables. A star is used to mark latent variables that cannot be observed directly. 9 For 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.

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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 α ˜ i,1 and α ˜ i,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 α ˜ i,2 is too small such that the firm’s profit falls short of the required payment to its creditors: xi,2 = αi,2 x∗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: Z

Di,1 − αi,1 x∗i,1 [pA,1 , pB,1 ] >

αi,2 [Di,2 ]

(αi,2 x∗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 α ˜ i,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 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. 10

As discussed below, this assumption is appropriate for the firms considered in our empirical analysis. The assumption is relaxed in Campello and Fluck (2003). 11 To see this, suppose that firm i defaults in the second period if αi,2 < α. Then, the firm sets its second period price according to the first-order condition (1 − F[α])∂x∗i,2 /∂pi,2 = 0 the solution of which does not depend on α. 12 Alternatively, we could allow for the firms issuing junior debt at date t = 1. This would not change our results.

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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 αi,2 |˜ αi,2 ≥ αi,2 ]x∗i,2 − Di,2 )). + (1 − F[αi,2 ])(E[˜

(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 firstorder condition:14 (1 − F[αi,1 ])(E[˜ αi,1 |˜ αi,1 ≥ αi,1 ]

∂x∗i,1 ∂x∗ + (1 − F[αi,2 ])E[˜ αi,2 |˜ αi,2 ≥ αi,2 ] i,2 ) = 0, ∂pi,1 ∂pi,1

(5)

where the first-period non-default probability (1 − F[αi,1 ]) cancels out. Rearranging this equation yields the following equivalent condition: 

∂x∗i,1 ∂pi,1 DLL[Di,1 , Di,2 ]  − ∂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 (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 13

Dasgupta and Titman (1998) obtain a similar result. See equation (6) of their paper. Besides 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 definitions of αi,1 (stated in the proof of Lemma 1) and αi,2 = Di,2 /x∗i,2 . 14

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probability F[αi,2 ] with which the firm defaults on its long-term debt. 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 substitution 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 structure (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 DLLeffect 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. 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 ad9

justment factor, DLL[Di,1 , Di,2 ], given by expression (7). This marginal rate of substitution 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 discussed 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 overor 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 α ˜ i,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. 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 10

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 ² < 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. To ensure reaction function stability and a positive slope of reaction functions, we impose the following standard assumptions: ∂ 2 Πi ∂ 2 Πi ∂ 2 Πj ∂ 2 Πi ∂ 2 Πj > 0 and − > 0 for i, j ∈ {A, B}, i 6= j. (9) ∂pi,1 ∂pj,1 ∂p2i,1 ∂p2j,1 ∂pi,1 ∂pj,1 ∂pj,1 ∂pi,1 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 15

In this respect, our analysis confirms the main result of Chevalier and Scharfstein (1996) and Dasgupta and Titman (1998) whose models do not capture the DLL-effect.

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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.

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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 maturity. 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 therefore 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 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 16

Family-owned hotels are the norm in Austrian rural areas – there are no hotel-chains since the chain stores specialize in city tourism and business travel. 17 In a recent survey by the Austrian National Tourist Office, more than 40% of all respondents said that they already stayed at the same hotel at least once in the past. The survey titled ¨ “G¨astebefragung Osterreich” is available at http://tourism.wu-wien.ac.at. 18 In 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 hotels

12

exogenous but quantifiable uncertainty in that the demand for accommodation depends 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 markets are very underdeveloped, it is virtually impossible for hotels to obtain equity financing in order to re-capitalize. Hence, hotels’ capital structures are mostly exogenously 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 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 Austrian 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 customers 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 changed the number of beds during the sample period. Also, hotels’ opening and closing dates are mostly determined by the ski season; in many cases, the hotels simply match the period during which nearby ski resorts are in operation. 19 Recently, artificial snow is being used on ski pistes. However, this is only possible if the temperature is sufficiently low. The altitude of a ski resort determines the temperature distribution, and hence whether artificial snow can be used. 20 See BMWA (2000), pp. 33. 21 ¨ Of course, the OHT cannot issue a state-backed guarantee for its own loans.

13

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, described 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 companies, none of which have entered a formal bankruptcy procedure 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 variable 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 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 22

The meteorological stations are usually located in ski resorts in order to facilitate maintenance.

14

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 accommodation, 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 standard 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 structures. 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 characterized 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 firstorder condition (5) as a starting point. By rearranging this condition, we obtain an equation suitable for econometric implementation. For hotel i = 1, . . . , n and year t = 1, . . . , T , this equation is given by: ∂x∗i,t ∂x∗i,t+1 + (1 − Fi,t+1 [αi,t+1 ])(1 + tDLLi,t ) = 0, ∂pi,t ∂pi,t

(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 23

Even though quality of accommodation is usually measured in terms of five categories, we ¨ could not obtain finer data from the OHT. 24 We cannot use market values since our sample contains only non-listed firms. 25 While 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 a formal bankruptcy procedure.

15

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 α ˜ i,t and α ˜ i,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: ∗ ∗ x˜i,t = α ˜ i,t x∗i,t = (pi,t − mci,t ) q˜i,t , for x∗i,t = (pi,t − mci,t )qi,t and q˜i,t = α ˜ i,t qi,t ,

(13)

where mci,t denotes the marginal cost of firm i and q˜i,t denotes output, a random ∗ multiple of a latent output level denoted as qi,t . For hotels, this latent output level

can be interpreted as the number of overnight stays booked; some of these bookings are randomly cancelled, resulting in an actual output of q˜i,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 M ati,t + γ3 Servi,t , 26

(14)

Hence, we test for the DLL-effect as a distinguishing feature of our model relative to a model that 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

where M ati,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 F Ci,t for firm i and period t. Firm i defaults in period t if its profit xi,t falls short of Di,t + F Ci,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 + F Ci,t+1 − xi,t+1 > ei,t+1 ⇔ xi,t+1 < Di,t+1 + F Ci,t+1 − ei,t+1 ⇔ αi,t+1 < αi,t+1 ,

(15)

where the second equivalence follows from xi,t+1 = αi,t+1 x∗i,t+1 for αi,t+1 = (Di,t+1 + F Ci,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 α ˜ i,t+1 . Equivalently, we could also work with the profit distribution induced by the distribution Fi,t+1 . If this profit distribution is denoted as Gi,t+1 , then Fi,t+1 [αi,t+1 ] = Gi,t+1 [Di,t+1 + F Ci,t+1 − ei,t+1 ] by 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 + F Ci,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 . 27

We re-define the critical values αi,t and αi,t+1 in order to take into account hotel i’s fixed costs and its equity value at the end of period t + 1. 28 Corresponding to the definition of Fi,t below condition (10), we define Gi,t [.] = G[.|Zi,t ].

17

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 + µm i,t ,

(16)

where µm i,t denotes an error term which exhibits multiplicative heteroscedasticity: ln[Var[ln[xi,t ]]] = β20 + β21 Alti + β22 IAlti >1000 + β23 SBRi,t + β24 ISBRi,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 ˆ i,t and let the standard deviation be denoted as sd ˆ i,t . Then, we can be denoted as lx define the following measure of the default probability Gi,t+1 [Di,t+1 +F Ci,t+1 −ei,t+1 ]: Gi,t+1 [Di,t+1 + F Ci,t+1 − ei,t+1 ] ≈ Φ[

ˆ i,t+1 ln[Di,t+1 + F Ci,t+1 − ei,t+1 ] − lx ], ˆ i,t+1 sd

(18)

where Φ denotes the standard normal distribution, the fixed cost F Ci,t+1 is defined as the sum of wages, costs of marketing, administrative expenses, costs of heating, 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 29

Using a Shapiro-Wilk Test we cannot reject the null hypothesis of a log-normal distribution. We 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 dummy variables IAlti >1000 and ISBRi,t >2 were significantly related to hotels’ profits, except as proxies for profit uncertainty in (17). Furthermore, we allowed for time fixed effects which also turned out to be insignificant. 31 We cannot choose the period t equity value ei,t as instrument for ei,t+1 since both of these variables depend on hotel i’s price in period t. 30

18

substituting the instrument for ei,t+1 in the above-stated argument of Φ[.], we obtain ˆ i,t+1 as exogenous measure of the default probability Gi,t+1 [Di,t+1 + a probability DP F Ci,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: x∗

tDLLi,t = ≈

Ei,t+1 [˜ xi,t+1 |˜ xi,t+1 ≥αi,t+1 x∗i,t+1 ] x∗ i,t −Ei,t [˜ xi,t |˜ xi,t ≥αi,t x∗i,t ] i,t+1

Ei,t [˜ xi,t |˜ xi,t ≥αi,t x∗i,t ] Ei,t+1 [˜ xi,t+1 |˜ xi,t+1 ≥αi,t+1 x∗i,t+1 ]−Ei,t [˜ xi,t |˜ xi,t ≥αi,t x∗i,t ] , ∗ Ei,t [˜ xi,t |˜ xi,t ≥αi,t xi,t ]

(19)

for αi,t and αi,t+1 re-defined as follows:27 αi,t+1 = αi,t =

Di,t+1 +F Ci,t+1 −ei,t+1 , x∗i,t+1 ˆ Di,t +F Ci,t −(1−DPi,t+1 )(Ei,t+1 [˜ xi,t+1 |˜ xi,t+1 ≥αi,t+1 x∗i,t+1 ]−(Di,t+1 +F Ci,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 approximate 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 ˆ i,t , we estimate the model (16)-(17) and derive estimates variable, denoted as tDLL for Ei,t+1 [˜ xi,t+1 |˜ xi,t+1 ≥ αi,t+1 x∗i,t+1 ] and Ei,t [˜ xi,t |˜ xi,t ≥ αi,t x∗i,t ] as functions of the explanatory variables of this model and the variables Di,t , F Ci,t , and ei,t−1 as instrument for ei,t+1 . Thereby, Di,t is the book value of debt to be repaid within one year, F Ci,t denotes the sum of (current period) fixed costs, and ei,t denotes the book value of equity at the end of period t. 32 While we cannot observe hotels’ expected profits, we can test whether the ratio of their actual profits has a mean of one. We cannot reject this hypothesis. 33 To see this, notice that the expected profits x∗i,t and x∗i,t+1 cancel out since they appear not only in the products αi,t x∗i,t and αi,t+1 x∗i,t+1 but also in the denominators of the terms for αi,t and αi,t+1 , respectively.

19

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 ˆ i,t+1 and tDLL ˆ i,t . Thereby, we use as control those captured by the variables DP 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: ˆ i,t+1 ) pi,t = γ0 + γ1 qi,t + γ2 M ati,t + γ3 Servi,t + γ4 (1 − DP ˆ i,t+1 ) tDLL ˆ i,t + γ6 IAlt >1000 + γ7 Cati + γ8 Levi,t+1 + µpi,t , (20) +γ5 (1 − DP i for i = 1, . . . , n and t = 1, . . . , T . The price of an overnight stay in hotel i is a funcˆ i,t+1 , the variable tion of the hotel’s marginal costs, the non-default probability DP ˆ i,t which captures the DLL-effect, and three control variables, IAlt >1000 , Cati tDLL i 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 a model 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 ˆ i,t+1 and tDLL ˆ i,t that capture effects of hotels’ instrument also the variables DP 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. 20

Hypotheses: Our main hypothesis concerns the coefficients of the non-default ˆ i,t+1 ) and the product of this probability and the (transformed) probability (1 − DP ˆ i,t , denoted as γ4 and γ5 respectively. By equadynamic limited liability effect, tDLL 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 )/(∂qi,t /∂pi,t ) = ∗ ∗ −∂x∗i,t+1 /∂qi,t , where ∂x∗i,t+1 /∂qi,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 alternative 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 /∂qi,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 coefficient 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 predictions 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 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 21

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 ˆ i,t+1 ); Panel B distribution of our estimates for the non-default probability (1 − DP ˆ i,t measuring the (transformed) DLLstates similar statistics for the variable tDLL 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 (0.225). These values are very high but this is perhaps not surprising given the substantial leverage of many hotels in our sample. ˆ i,t characterizes the transformed DLL-effect The distribution of the variable tDLL 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 ˆ i,t < 0, then the respective hotel has an t + 1. If this difference is negative, tDLL incentive to raise its price in the current period in order to increase its short-term ˆ i,t > 0, the DLL-effect profits, thus under-investing in market share.34 For tDLL 34

To see this, recall the discussion above Proposition 1. As stated there, the DLL-effect distorts ˆ i,t < 0, a firm’s optimal strategy towards raising its current profits if DLL[Di,t , Di,t+1 ] > 1 ⇔ tDLL

22

induces the opposite incentive; this is the case for 75% of the hotels in our sample.

Table 3 about here Finally, we discuss the estimation results for the pricing equation (20); the estimates 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 specification, with the restriction γ4 = γ5 imposed in the first column (since these two coefficients 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 ˆ i,t+1 and tDLL ˆ i,t ; column (4) reports estimates obtained by inby the variables DP ˆ i,t+1 and tDLL ˆ i,t in order to remove a possible bias strumenting the variables DP 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 M ati,t 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 where the equivalence follows from definition (11).

23

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 ˆ i,t+1 ), and via affects output pricing both via the non-default probability (1 − DP ˆ i,t which captures the DLL-effect. Ceteris paribus, the price pi,t the variable tDLL ˆ i,t+1 . This is consistent with the hypothesis increases in the default probability DP 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 depend ˆ i,t which measures the DLL-effect. As discussed significantly on the variable tDLL above Proposition 1, this effect can be interpreted as leverage-induced change in the way firms define the marginal rate of substitution between profits in the current and the next period. Since only the non-default states are taken into account, the optimal pricing strategy depends on the relative expected profitability of the nonˆ i,t+1 , hotels default states across periods. Holding constant the default probability DP ˆ i,t . To interpret this result, recall charge higher prices, the smaller the variable tDLL ˆ i,t is inversely related to the DLL-factor the definition (11): since the variable tDLL 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 above Proposition 1: ceteris paribus, the higher the DLL-factor, the more biased towards 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 column (3), we control for effects of leverage on hotels’ pricing strategies beyond those ˆ i,t+1 ) and tDLL ˆ i,t . We include as control varicaptured by the variables (1 − DP 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 24

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 structures being endogenously determined. This column reports instrumental variables estimates, based on instruments not only for the demand for accommodation qi,t but ˆ i,t+1 ) and tDLL ˆ i,t . As stated above, regional fixed also for the two variables (1 − DP effects are used as instruments for the demand for accommodation, qi,t . For the nonˆ i,t+1 ), we use as identifying instrument the (next period) default probability (1 − DP fixed cost F Ci,t+1 . For the transformed dynamic liability effect we use a two-group ˆ i,t exceeds its median instrument, i.e. a variable which takes the value of one if tDLL value, and equals minus one otherwise.35 To obtain an identified model, we impose ˆ i,t is three exclusion restrictions. The identifying instrument for the variable tDLL 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 ˆ i,t+1 ) and with an R2 of 69% for the the case of the non-default probability (1 − DP ˆ i,t . In both cases, the F-statistics take values higher than 10; tDLL-variable tDLL hence, the respective instruments are strong, corresponding to the recommendations of Staiger and Stock (1997). The second-stage estimates are consistent with those 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 35

For further discussion of grouping methods, see Johnston (1991), pp. 430-432. We also tried to use other instruments, for example the change in fixed costs (F Ci,t+1 − F Ci,t )/F Ci,t which would be a natural choice. However, none of these other instruments was significantly related to ˆ i,t . the variable tDLL

25

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 DLLeffect 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 up to twice as high as that of an unlevered hotel. 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, 36

Hence, Figure 3 plots equation (20) with γ4 = −24.46 (as in column (1) of Table 4) and γ5 = 0.

26

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 depend on their current market shares. To invest in market share, firms must cut their prices in order to attract additional customers. Leverage distorts firms’ optimal 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 profits. Second, leverage changes firms’ marginal rates of substitution between current and future profits. For a levered firm, this marginal rate of substitution depends on the firm’s relative expected profitability in the non-default states across periods. We refer to this effect as the “dynamic limited liability effect” or DLL-effect. 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 37

Hence, Figure 4 plots equation (20) with γ4 = γ5 = −24.46 (as in column (1) of Table 4).

27

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. With this paper, we wish to provide new insight for future research on capital structure and corporate strategy. Our findings show why leverage distorts investment for investment problems in which firms take their financial structure as given. By contrast to the leverage-induced investment distortions themselves, the underlying changes in firms’ objective functions should not depend on whether firms’ investments are strategic substitutes or complements. It is in this sense that our findings concern effects of leverage that are robust with respect to the nature of firms’ competitive interactions. More specifically, three implications of our results should be taken into account in future studies. 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 underor 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 required in order to measure leverage-induced investment distortions. Besides leverage, 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 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 oligopolistic 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 relation between leverage and investment. Rather, the magnitude of leverage-induced investment distortions should vary across industries, and perhaps also across firms 28

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

References Patrick Bolton and David S. Scharfstein. A theory of predation based on agency problems in financial contracting. American Economic Review, 80(1):93–106, 1990. Patrick Bolton and David S. Scharfstein. Optimal debt structure and the number of creditors. Journal of Political Economics, 104(1):1–25, 1996. James A. Brander and Tracy R. Lewis. Oligopoly and fincial structure. American Economic Review, 76:956–970, 1986. Murillo Campello. Debt financing: Does it hurt or boost firm performance in product markets? University of Illinois, mimeo, 2003. Murillo Campello and Zsuzsanna Fluck. Market share, financial leverage and the macroeconomy: Theory and empirical evidence. University of Illinois and Michigan State University, mimeo, 2003. Judith A. Chevalier. Do LBO supermarkets charge more? An empirical analysis of the effects of LBOs on supermarket pricing. Journal of Finance, 50(4):1095–1112, 1995. Judith A. Chevalier and David S. Scharfstein. Capital market imperfections and countercyclical markups: Theory and evidence. American Economic Review, 86 (4):703–725, 1996. Sudipto Dasgupta and Sheridan Titman. Pricing strategy and financial policy. The Review of Financial Studies, 11(4):705–737, 1998. Rusell Davidson and James G. MacKinnon. Estimation and Inference in Econometrics. Oxford University Press, New York, 1993. Helmut Elsinger, Engelbert J. Dockner and Andrea Gaunersdorfer. The strategic role of dividends and debt in markets with imperfect competition. University of Vienna, mimeo, 2000. Antoine Faure-Grimaud. Product market competition and optimal debt contracts: The limited liability effect revisited. European Economic Review, 44(10):1823– 1840, 2000. 30

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Vojislav Maksimovic. Optimal capital structure in oligopolies. Ph.D. disseration, Harvard University, unpublished, 1986. Vojislav Maksimovic. Financial structure and product market competition. in: Robert Jarrow, Vojislav Maksimovic and William T. Ziemba, Eds., Handbooks in Operations Research and Management Science, Vol. 9, Elsevier Science B.V., Amsterdam, pages 887–920, 1995. Vojislav Maksimovic and Sherdan Titman. Financial policy and reputation for product quality. Review of Financial Studies, 4(1):175–200, 1991. Steward Myers. Determinants of corporate borrowing. Journal of Financial Economics, 4(1):147–175, 1977. Federal Ministry of Economic Affairs and BMWA Labor. Bericht u ¨ber die Lage der ¨ Tourismus- und Freizeitwirtschaft in Osterreich. http: www.seilbahn.net/aktuell/tourismusanalyse.pdf, 2000, Wien, 2000. Tim Opler and Sheridan Titman. Financial distress and coperate performance. Journal of Finance, 49:1015–1040, 1994. Gordon M. Phillips. Increased debt and industry product markets: An empirical analysis. Journal of Financial Economics, 37:189–238, 1995. Dean M. Showalter. Oligopoly and financial structure: Comment. American Economic Review, 85(3):647–53, 1995. Douglas Staiger and James H. Stock. Instrumental variable regression with weak instruments. Econometrica, 65(3):557–586, 1997. Sheridan Titman. The effect of capital structure on the firm’s liquidation decision. Journal of Financial Economics, 13:137–152, 1984. Luigi Zingales. Survival of the fittest or the fattest? Exit and financing in the trucking industry. Journal of Finance, 53(3):905–938, 1998.

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,2 |˜ αi,2 ≥ αi,2 ]x∗i,2 − Di,2 ) Di,1 − (1 − F[αi,2 ])(E[˜ . x∗i,1

αi,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: Z

Z

Πi =

αi,1

(αi,1 x∗i,1 − Di,1 +

αi,2

(αi,2 x∗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 ]

∂ E[α ˜ i,1 |α ˜ i,1 ≥αi,1 ] ∂Di,1

E[α ˜ i,1 |α ˜ i,1 ≥αi,1 ]

=

f[αi,1 ] E[α ˜ i,1 |α ˜ i,1 ≥αi,1 ]−αi,1 ∂αi,1 1−F[αi,1 ] E[α ˜ i,1 |α ˜ i,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: ∂ E[˜ αi,1 |˜ αi,1 ≥ αi,1 ] ∂DLL ∂Di,2 − = DLL[Di,1 , Di,2 ] ∂Di,2 E[˜ αi,1 |˜ αi,1 ≥ αi,1 ]

∂ E[˜ αi,2 |˜ αi,2 ∂Di,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 1 − F [αi,2 ] ∂x∗i,2 + = 0. ∂pi,1 DLL[Di,1 , Di,2 ] ∂pi,1

(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,1 dDi,1

=−

dp∗i,1 dDi,2

=−

³ ³

∂xi,2 ∂FOCi / ∂pi,1 ∂pi,1 ∂xi,2 ∂FOCi / ∂pi,1 ∂pi,1

´ ´

µ ∂ ∂Di,1

µ

∂ ∂Di,2

1−F[αi,2 ] DLL[Di,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: µ ∂ ∂Di,1 ∂ ∂Di,2

µ

1−F[αi,2 ] DLL[Di,1 ,Di,2 ] 1−F[αi,2 ] DLL[Di,1 ,Di,2 ]

¶ ¶

1−F[α

]

= − DLL[Di,1i,2 ,Di,2 ] f[α

]

i,2 = − DLL[Di,1 ,Di,2 ]

−

(1−F[αi,2 ]) DLL[Di,1 ,Di,2 ]

h[αi,1 ]

E[α ˜ i,1 |α ˜ i,1 ≥αi,1 ]−αi,1 ∂αi,1 E[α ˜ i,1 |α ˜ i,1 ≥αi,1 ] ∂Di,1

< 0,

E[α ˜ i,1 |α ˜ i,1 ≥αi,1 ]−αi,1 ∂αi,1 E[α ˜ i,1 |α ˜ i,1 ≥αi,1 ] ∂Di,2

−

∂αi,2 ∂Di,2

µ

h[αi,1 ]

α

∂αi,2 i,2 ] ∂Di,2

h[αi,2 ] E[α˜ i,2 |α˜i,2 i,2 ≥α 33

¶

< 0,

(26)

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 ² > 0. The resulting change in the optimal first-period price p∗i,1 is given by: µ

dp∗i,1 =

−

µ

∂x∗i,2 ∂FOCi / ∂pi,1 ∂pi,1 ∂x∗i,2

¶µ ¶

1−F[αi,2 ] DLL[Di,1 ,Di,2 ]

¶

µ

∂ ∂Di,2

dDi,1 +

αi,2 ∂αi,2 f[αi,2 ] DLL[Di,1 ,Di,2 ] E[α ˜ i,2 |α ˜ i,2 ≥αi,2 ] ∂Di,2

i / ∂FOC ∂pi,1 ∂pi,1

=−

µ

∂ ∂Di,1

1−F[αi,2 ] DLL[Di,1 ,Di,2 ]

¶

¶

dDi,2

² < 0, for ² > 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 dpej,1 dDi,1 dpei,1 dDi,2 dpej,1 dDi,2

∂FOCj ∂pj,1

=

∆

=

−

∂FOCj ∂pi,1

∆ ∂FOCj ∂pj,1

=

∆

= −

∂FOCj ∂pi,1

∆

µ ∂ ∂Di,1 ∂ ∂Di,1

µ µ

∂ ∂Di,2

µ

∂ ∂Di,2

1−F[αi,2 ] DLL[Di,1 ,Di,2 ] 1−F[αi,2 ] DLL[Di,1 ,Di,2 ] 1−F[αi,2 ] DLL[Di,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 ∂α

∂αi,1 ∂Di,1

= 1/x∗i,1 ,

∂αi,1 ∂Di,2

= (1 −

= 1/x∗i,2 . F[αi,2 ])/x∗i,1 and ∂Di,2 i,2 The result about the effect of the maturity structure of firm i’s debt follows from the above-stated results: dpei,1 dpej,1

=

∂FOCj ∂pj,1

=−

µ

∆ ∂FOCj ∂pi,1

∆

µ ∂ ∂Di,1

µ

∂ ∂Di,1

1−F[αi,2 ] DLL[Di,1 ,Di,2 ]

µ

¶

1−F[αi,2 ] DLL[Di,1 ,Di,2 ]

µ

dDi,1 + ¶

∂ ∂Di,2

dDi,1 +

∂ ∂Di,2

1−F[αi,2 ] DLL[Di,1 ,Di,2 ]

µ

¶

¶

1−F[αi,2 ] DLL[Di,1 ,Di,2 ]

dDi,2 , ¶

¶

(29)

dDi,2 ,

for dDi,1 and dDi,2 of the form specified in (8). For ² > 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

35

Table 1: Descriptive statistics Table 1 gives descriptive statistics for a sample of 100 Austrian hotels for 120 firm-years during the period 1999-2001. Panel A reports descriptive statistics for the variables used in our econometric analysis, i.e. the average price pi,t that hotels charge for accommodation per night (where the average is taken across all overnight stays sold by a hotel in one year), the number of overnight stays sold, qi,t , hotels’ marginal costs M ati,t , and Servi,t , hotels’ fixed costs F Ci,t , the book value of 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 , a dummy variable Cati which equals one for any hotel i that offers high quality accommodation rated four or five stars (out of five), hotels’ capacities Capi,t (number of beds × days during which a hotel stays open for business), the altitude Alti of the closest meteorologic station, a dummy variable IAlti >1000 which equals one for hotels for which Alti exceeds 1000 meters, the ratio of the number of hotels’ beds to the number of seats in the hotel restaurant, SBRi,t , and a dummy variable 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 summary statistics for two variables that describe hotels’ capital structures in terms of book values, i.e. the ratio of total debt to total assets, and the ratio of hotels’ short-term to long-term debt, defined as debt to be repaid within and after one year, respectively. Panel A. Variable pi,t qi,t M ati,t Servi,t F Ci,t ei,t Di,t Di,t+1 Levi,t+1 Cati Capi,t Alti

Description Price per night in Euros Number of overnight stays sold Cost of materials in Euros Cost of services in Euros Total of fixed costs in Euros Book value of equity in Euros Short-term debt in Euros Long-term debt in Euros Leverage after repayment of Di,t and Di,t+1 Dummy for high quality hotels Capacity (beds×days open) Altitude of the closest meteorological station in meters Altitude dummy variable Seat to bed ratio Seat to bed dummy variable

IAlti >1000 SBRi,t ISBRi,t >2 Panel B. Variable Total debt to total assets Short-term to long-term debt

36

Nobs. 120 120 120 120 120 120 120 120 120

Mean 82.99 15534 17.13 0.63 740939 421984 394781 433542 0.89

Std.dev. 72.59 12169.91 21.96 0.97 816240 1003846 828089 949317 0.685

120 100 120

0.60 28516 815

0.49 35693 330

120 120 120

0.27 1.84 0.61

0.45 1.43 0.49

Nobs. 120 120

Mean 0.85 0.98

Std.dev. 0.20 0.33

Table 2: First-stage estimation results for the relation between profits and exogenous variables Table 2 reports first-stage estimation results for the relation between hotels’ profits and exogenous variables based on a sample of 100 Austrian hotels for 120 firm-years during the period 19992001. 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 quality of accommodation, as measured by the dummy variable Cati that indicates hotels in the four or five star category. For 20 hotels, we lack data on their capacities. We set these hotels’ capacities to 0.001 (in order to be able to take logs) and use a dummy variable to control for differences between these hotels and the others in the estimations. We do not report the estimated coefficient for this dummy variable. Panel B states how profit uncertainty depends on a hotel’s location and the relative size of the hotel restaurant. Thereby, Alti is the altitude of the meteorological station located the closest to hotel i and IAlti >1000 is a dummy variable indicating whether Alti exceeds 1000 meters. The relative size of a hotel’s restaurant is measured in terms of the ratio of the 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. The absolute values of the z-statistics are stated in parentheses. ∗∗ (∗ ) denotes a 95% (90%) level of significance.

Panel A. Dependent variable: ln[profit xi,t ] Variable Constant

Description Constant

Coefficient β10

Cati

Dummy for high quality hotels

β11

ln[Capi,t ]

ln[Capacity=beds×days open]

β12

ln[Capi,t ] ∗ Cati

ln[Capacity] times category

β13

Estimate 2.651 (1.35) 9.408 (4.79)∗∗ 1.067 (5.26)∗∗ - 0.888 (4.34)∗∗

Panel B. Dependent variable: ln[Var[ln[xi,t ]]] Variable Constant

Description Constant

Coefficient β20

Alti /1000 IAlti >1000

Altitude of closest meteorological station Altitude dummy variable

β21

SBRi,t

Seat to bed ratio

β22

ISBRi,t >2

Seat to bed dummy variable

β23

Number of observations Wald-test

37

β20

Estimate 1.510 (2.14)∗∗ -0.839 (1.67)∗ 0.629 (2.01)∗∗ -0.507 (3.35)∗∗ - 0.608 (1.89)∗ 120 713.15

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-years during the period 1999-2001. Panel A reports descriptive statistics for the estimated non-default ˆ i,t+1 ). Panel B states the same statistics for the variable tDLL ˆ i,t which probability, (1 − DP captures the dynamic limited liability effect of leverage on hotels’ pricing strategies.

Panel A: Non-default probability Percentiles Smallest 1% 0.0040273 0.0001006 5% 0.1394295 0.0040273 10% 0.2120851 0.0209729 25% 0.4503981 0.0789581 50% 0.7752711 Largest 75% 0.9902213 1 90% 1 1 95% 1 1 99% 1 1 Panel B: (Transformed) dynamic Percentiles Smallest 1% -0.4812593 -0.5312951 5% -0.3301545 -0.4812593 10% -0.2500812 -0.4447151 25% 0.00 -0.4025942 50% 0.0142116 Largest 75% 0.1954983 0.8573666 90% 0.5662895 1.309377 95% 0.7783068 1.736596 99% 1.736596 1.846478

38

ˆ i,t+1 ) (1 − DP

Mean Std. Dev. Variance Skewness Kurtosis

0.690 0.307 0.094 -0.645 2.120

ˆ i,t limited liability effect tDLL

Mean Std. Dev. Variance Skewness Kurtosis

0.205 0.455 0.207 1.231 6.513

39 Non-default probability ˆ i,t ) Instrument for (1 − DP ˆ i,t )*(transformed) DLL-effect (1 − DP ˆ i,t ) ∗ tDLL ˆ i,t Instrument for(1 − DP Altitude dummy variable Dummy for high quality hotels Leverage at the end of period t + 1

ˆ i,t ) (1 − DP

ˆˆ (1 − DP i,t )

ˆ i,t ) ∗ tDLL ˆ i,t (1 − DP

ˆˆ ˆˆ (1 − DP i,t ) ∗ tDLLi,t

IAlti >1000

Cati,t

Levi,t+1

Number of observations Adjusted R2

Cost of services

Instrument for qi,t , the number of overnight stays sold, divided by 1000 Cost of materials

Servi,t

M ati,t

qˆi,t /1000

Dependent variable: Price pi,t Variable Description Constant Constant

γ8

γ7

γ6

γ5

γ5

γ4

γ4

γ3

γ2

γ1

Coefficient γ0

9.659 (2.31)∗∗ 21.759 (5.45)∗∗ 120 0.93

-24.460 (4.85)∗∗

(1) γ4 = γ5 39.645 (5.39)∗∗ -0.516 (1.99)∗∗ 3.079 (35.68)∗∗ 3.397 (1.76)∗ - 24.460 (4.85)∗∗

9.834 (2.32)∗∗ 22.054 (5.34)∗∗ 120 0.93

-26.607 (3.07)∗∗

38.250 (4.40)∗∗ -0.499 (1.88)∗ 3.085 (34.74)∗∗ 3.480 (1.78)∗ -23.127 (3.46)∗∗

(2)

10.113 (2.39)∗∗ 21.229 (5.12)∗∗ -4.103 (1.41) 120 0.93

-24.235 (2.76)∗∗

41.707 (4.64)∗∗ -0.481 (1.82)∗ 3.096 (34.88)∗∗ 3.450 (1.77)∗ -22.686 (3.40)∗∗

(3)

-40.170 (2.88)∗∗ 8.728 (2.32)∗∗ 16.019 (4.18)∗∗ 120 0.94

-53.965 (6.10)∗∗ -

69.328 (7.30)∗∗ -0.683 (2.92)∗∗ 3.048 (39.25)∗∗ 1.970 (1.13) -

(4)

Table 4 reports the estimations results for the pricing equation based on pooled data. The sample covers 100 Austrian hotels for 120 firm-years during the period 1999-2001. The dependent variable is the average price pi,t that a hotel charges per night (where the average is taken across all overnight stays sold by a hotel in one year). The explanatory variables include the number of overnight stays sold, qi,t , hotels’ marginal costs M ati,t and Servi,t , ˆ i,t+1 ), the variable tDLL ˆ i,t that captures the dynamic limited liability effect, a dummy variable IAlt >1000 which the non-default probability (1 − DP i equals one for hotels for which the closest meteorologic station is located at an altitude of more than 1000 meters, a dummy variable Cati which equals one for any hotel i that offers high quality accommodation rated four or five stars (out of five), and Levi,t+1 defined as a hotel i’s leverage at the end of the year t + 1. All columns report instrumental variable estimates. In columns (1)-(3) we use instruments for the demand for accommodation, ˆ i,t+1 ) and tDLL ˆ i,t qi,t ; in column (4) we additionally control for effects of capital structure endogeneity by using instruments for the variables (1 − DP which capture effects of leverage on hotels’ pricing strategies. In column (1), we impose the constraint γ4 = γ5 . In column (3), we include the variable ˆ i,t+1 and tDLL ˆ i,t . All prices and costs Levi,t+1 to control for effects of leverage on hotels’ pricing strategies beyond those captured by the variables DP are in constant Euros, as of 1999. The absolute values of the t-statistics, respectively z-statistics, are stated in parentheses. ∗∗ (∗ ) denotes a 95% (90%) level of significance.

Table 4: Estimation results for the pricing equation based on pooled data

40 Non-default probability ˆ i,t ) Instrument for (1 − DP ˆ i,t )*(transformed) DLL-effect (1 − DP ˆ i,t ) ∗ tDLL ˆ i,t Instrument for(1 − DP Altitude dummy variable Dummy for high quality hotels

ˆ i,t ) (1 − DP

ˆˆ (1 − DP i,t )

ˆ i,t ) ∗ tDLL ˆ i,t (1 − DP

ˆˆ ˆˆ (1 − DP i,t ) ∗ tDLLi,t

IAlti >1000

Cati,t

Firm-specific effects Number of observations Adjusted R2

Cost of services

Instrument for qi,t ; Overnight stays sold, divided by 1000 Cost of materials

Servi,t

M ati,t

qˆi,t /1000

Dependent variable: Price pi,t Variable Description Constant Constant

γ7

γ6

γ5

γ5

γ4

γ4

γ3

γ2

γ1

Coefficient γ0

10.234 (2.06)∗∗ 23.764 (4.70)∗∗ No 120 0.94

-33.196 (2.36)∗∗

-36.469 (2.32)∗∗ 11.203 (2.59)∗∗ 16.148 (3.54)∗∗ No 120 0.95

-54.639 (5.94)∗∗ -

(1) (2) Fixed effects 42.279 71.028 (4.09)∗∗ (6.62)∗∗ - 0.864 -1.026 (2.72)∗∗ (3.71)∗∗ 3.299 3.251 (20.76)∗∗ (23.56)∗∗ 3.331 2.099 (1.57) (1.12) - 25.875 (3.43)∗∗ -

9.956 (2.35)∗∗ 22.496 (5.36)∗∗ Yes 120 0.94

-28.364 (3.11)∗∗

-34.535 (2.68)∗∗ 9.202 (2.43)∗∗ 15.614 (4.03)∗∗ Yes 120 0.93

- 55.065 (6.40)∗∗ -

(3) (4) Random effects 39.754 pp 70.763 (4.61)∗∗ (7.57)∗∗ -0.589 -0.772 (2.22)∗∗ (3.30)∗∗ 3.116 3.076 (32.49)∗∗ (36.27)∗∗ 3.409 1.963 (1.82)∗ (1.17) -23.933 (3.61)∗∗ -

Table 5 reports the estimations results for the pricing equation based on a model with firm-specific fixed and firm-specific random effects. The sample covers 100 Austrian hotels for 120 firm-years during the period 1999-2001. The dependent variable is the average price pi,t that a hotel charges per night (where the average is taken across all overnight stays sold by a hotel in one year). The explanatory variables include the number of overnight ˆ i,t+1 ), the variable tDLL ˆ i,t that captures the dynamic stays sold, qi,t , hotels’ marginal costs M ati,t and Servi,t , the non-default probability (1 − DP limited liability effect, a dummy variable IAlti >1000 which equals one for hotels for which the closest meteorologic station is located at an altitude of more than 1000 meters, a dummy variable Cati which equals one for any hotel i that offers high quality accommodation rated four or five stars (out of five), and firm-specific effects. Columns (1) and (2) report the estimates with firm-specific fixed effects, columns (3) and (4) report estimates with firm-specific random effects. All columns report instrumental variable estimates. In columns (1) and (3) we use instruments for the demand for accommodation, qi,t ; in columns (2) and (4) we additionally control for effects of capital structure endogeneity by using instruments for the variables ˆ i,t+1 ) and tDLL ˆ i,t which capture effects of leverage on hotels’ pricing strategies. All prices and costs are in constant Euros, as of 1999. The (1 − DP absolute values of the t-statistics, respectively z-statistics, are stated in parentheses. ∗∗ (∗ ) denotes a 95% (90%) level of significance.

Table 5: Estimation results for the pricing equation with firm-specific fixed and firm-specific random effects

41

realized

prices

debt repaid

short-term

profits

period 1

firms set

¾

t=0

prices

firms set

- ¾

t=1

Figure 1: Timeline

realized

profits

period 2

debt repaid

long-term

-

t=2

Figure 2: The dynamic limited liability effect Figure 2 depicts how the dynamic limited liability effect (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. For a levered firm, the marginal rate of substitution between current and future profits equals that of an unlevered firm times the DLL-factor depicted in Figure 2. The plot is based on estimates for a sample of 100 Austrian hotels for 120 firm-years during the period 1999-2001.

2 1 0 0.2

10 0.8

0.4 0.6

Fraction of short- term debt 0.6 0.4 0.8

0.2 1 0

42

Leverage

DLL

Figure 3: Firms’ optimal pricing strategies without the dynamic limited liability effect Figure 3 depicts how hotels’ optimal pricing strategies depend on leverage and debt maturity if the dynamic limited liability effect is ignored. The plot is based on estimates for a sample of 100 Austrian hotels for 120 firm-years during the period 1999-2001. The Euro price of one overnight stay is depicted as a function of (i) leverage, defined as the ratio of total debt to total capital, and (ii) debt maturity, characterized by the portion of debt to be repaid within one year.

100 95 90 85

0 0.2

1 0.8

0.4 0.6

Fraction of short- term debt 0.6 0.4 0.8

0.2 10

43

Leverage

Price

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 according to the model put forward in this paper. The plot is based on estimates for a sample of 100 Austrian hotels for 120 firm-years during the period 1999-2001. The Euro price of one overnight stay is depicted as a function of (i) leverage, defined as the ratio of total debt to total capital, and (ii) debt maturity, characterized by the portion of debt to be repaid within one year.

95 90 85 Price 80 1

0 0.2 0.8

0.4 0.6

Fraction of short- term debt 0.6 0.4 0.8

0.2 10

44

Leverage