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Capital Structure and Interaction among Firms in Output Markets: Theory and Evidence Author(s): Evgeny Lyandres Source: The Journal of Business, Vol. 79, No. 5 (September 2006), pp. 2381-2421 Published by: The University of Chicago Press Stable URL: http://www.jstor.org/stable/10.1086/505239 Accessed: 23-05-2016 16:03 UTC

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(Journal of Business, 2006, vol. 79, no. 5) � 2006 by The University of Chicago. All rights reserved. 0021-9398/2006/7905-0005$10.00

Evgeny Lyandres Rice University

Capital Structure and Interaction among Firms in Output Markets: Theory and Evidence*

I. Introduction

The majority of optimal capital structure models, start- ing with Modigliani and Miller (1958), are developed in a single-firm framework and do not consider the interaction among firms in output markets. The im- plicit assumption that firms’ financial, operating, and investment decisions do not affect and are not affected by those of their rivals precludes strategic capital structure choices.

A growing literature, starting from the work of Tit- man (1984), Brander and Lewis (1986), and Poitevin (1989a), is examining the effects of the interaction among firms in output markets on their financial and operating choices. Because of the limited liability, in- creasing leverage raises firms’ incentives to pursue riskier output strategies, which increase returns in sol- vent states and reduce returns in bankrupt states. The reason is that after the debt is issued, firms’ share- holders do not take the reduction in firms’ returns in bankrupt states into account when choosing their prod-

* I am grateful to Mike Barclay, Erwan Morellec, and Cliff Smith for valuable discussions. I would also like to thank Rui Albuquer- que, Gennaro Bernile, Jim Brickley, Jiri Chod, Gustavo Grullon, Leslie Marx, Sanjog Misra, Ralitsa Petkova, Gordon Phillips, Bill Schwert, Josep Tribo, Ross Watts, Ivo Welch, James Weston, sem- inar participants at the University of Rochester, the European Fi- nance Association (2002), and the Multinational Finance Society (2002), and an anonymous referee for very helpful comments and suggestions. All remaining errors are mine only. Contact the author at [email protected].

I develop a simple model that examines the rela- tions between the extent of competitive interaction among firms in output markets, their capital structures, and the ag- gressiveness of their op- erating strategies. A firm’s optimal leverage is related to the degree to which its operating strat- egy affects its rivals’ value functions and re- sulting optimal output market choices. This rela- tion is positive, regard- less of whether the com- petition in output markets is in strategic substitutes or in strategic comple- ments. I test the model’s prediction using two proxies for the extent of competitive interaction among firms. The empiri- cal evidence provides support for the model.

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2382 Journal of Business

uct market strategies, since the debt holders own all the claims to firms’ assets in those states. Thus, in addition to distorting a firm’s value maximization problem, debt allows the firm to precommit to a certain behavior in output markets, affecting optimal operating strategies of the firm’s rivals. Therefore, debt financing can have a strategic advantage if the distortion of the firm’s product market strategy that it causes influences product market choices of the firm’s rivals in a way that benefits the firm.1

Models that are based on the idea that the choice of debt in the first stage of the game serves as a commitment to subsequent output strategies in the second stage, in which product market competition takes place, have tradi- tionally been developed in a Cournot-type quantity competition setting. These models include the seminal work of Brander and Lewis (1986), as well as studies by Maksimovic (1988) and Glazer (1994). In the framework of Cournot competition, debt commits firms’ shareholders to a more aggressive product market behavior (higher quantity choices), and equilibrium debt levels are positive, even in the presence of agency costs of debt and in the absence of tax-related or other benefits of debt.

Alternative frameworks of oligopolistic competition are Bertrand-type price competition (see, e.g., Showalter 1995; Dasgupta and Titman 1998) and capacity-price competition (see Schuhmacher 2001). Showalter shows that in the case of price competition, firms choose debt in equilibrium if the uncertainty is demand related. In contrast, when costs are uncertain, debt carries a strategic disadvantage and is not chosen in equilibrium. Schu- hmacher demonstrates the opposite result for the case of capacity-price competition. When demand conditions are uncertain, firms do not use debt, while in the case of uncertain costs, firms choose positive debt levels.

The aforementioned limited liability models show the conceptual difference between the optimal choice of debt in a perfectly competitive environment and in an environment where strategic interaction among rivals is present. However, none of the previous studies analyzes the relation between the extent of competitive interaction among output market rivals and their optimal capital structure choices.

This study examines the links between the extent of competitive interaction among firms, their optimal leverage, and the aggressiveness of their operating strategies. The model developed here is not limited to a specific form of product market competition. It shows that, regardless of whether firms’ product market choices are strategic substitutes or complements, as defined in Bulow, Geanakoplos, and Klemperer (1985), the stronger the influence of firms’ strat-

1. In addition to the limited liability effect, firms’ strategies in product markets can be driven by strategic bankruptcy considerations. Firms can make product market choices that raise the chances of driving their competitors into insolvency, and the probability of a firm getting into financial distress depends on its capital structure. Strategic bankruptcy considerations are not analyzed here. Models based on the strategic bankruptcy effect of debt include Brander and Lewis (1988), Poitevin (1989b), Bolton and Scharfstein (1990), and Rotemberg and Scharfstein (1990).

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Firms in Output Markets 2383

egies on their rivals’ value functions and resulting operating strategies, the larger the strategic benefit of debt.2 This corresponds to an intuitive notion that the strategic benefit of debt and optimal leverage should be monotonically decreasing as one moves from a duopoly to perfect competition.3 While this conclusion would not hold under some of the parametrizations of price and capacity-price oligopolistic competition, such as those in Showalter (1995) and Schuhmacher (2001), in which optimal debt levels are zero, the intuition is that whenever an increase in a firm’s debt causes an increase in the optimal aggressiveness of its operating strategy, debt is strategically advantageous, and the extent of strategic interaction among firms is positively related to their equilibrium debt levels and leverage ratios.

The availability of data needed to examine the relations between firms’ financial and operating decisions is limited. As a consequence, there are few empirical studies examining the relation between firms’ capital structures and their product market strategies. Chevalier (1995a, 1995b), Phillips (1995), and Kovenock and Phillips (1997) are notable exceptions. These articles inves- tigate the relation between the intra-industry price variation and firms’ lev- erage. They focus on a small number of industries in which some firms have experienced sharp changes in their capital structures.4 In contrast, I perform a broad cross-sectional analysis of the relation between the extent of com- petitive interaction among firms and their leverage ratios. The empirical anal- ysis of this article is, thus, related to the recent empirical studies of the determinants of firms’ leverage choices by Frank and Goyal (2004), MacKay and Phillips (2005), Barclay, Morellec, and Smith (2006) and to earlier studies by Bradley, Jarrell, and Kim (1984), Titman and Wessels (1988), Smith and Watts (1992), Gaver and Gaver (1993), Barclay, Smith, and Watts (1995), and Rajan and Zingales (1995).

I use two proxies for the extent of competitive interaction among firms. The first proxy is based on the number of rivals competing with a firm in its output market. The second one is based on an estimate of the effect of firms’ actions on their rivals’ marginal profits. The empirical tests support the pre- dictions of the model. There is a strong evidence of a positive relation between the extent of competitive interaction among industry rivals and their leverage ratios.

The remainder of the article is organized as follows. In Section II, the model of strategic financial and operating choices is developed. The empirical proxies for the extent of competitive interaction among firms are discussed in Section III. Section IV discusses the data, variable definitions, and empirical methods.

2. Strategic substitutes and complements are defined by whether a more “aggressive” strategy by a firm lowers or raises its rivals’ marginal profits.

3. There is no strategic benefit to holding debt if a firm is a monopolist in its output market and there are no rivals that can affect the firm’s value.

4. Chevalier (1995a, 1995b) studies the effects of recapitalizations on product market strategies in the supermarket industry. Phillips (1995) and Kovenock and Phillips (1997) investigate four and 10 relatively concentrated industries, respectively, with at least one of the top four firms recapitalizing using a leveraged buyout.

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2384 Journal of Business

Fig. 1.—The sequence of the game

The results of the empirical tests are presented in Section V. Section VI summarizes the theoretical and empirical results of the article. Proofs are provided in the appendix.

II. The Model of Strategic Debt Choices

Similar to most precommitment models (see Shapiro [1989] and Bagwell and Wolinsky [2002] for discussions of such models), the static model developed here has two stages. In the first stage, firms enter the market and simultaneously choose their financial structures. The latter are summarized by the face values of debt maturing at the end of the game. Each firm’s shareholders (or, equiv- alently, managers acting in shareholders’ interests) choose their firm’s debt level with the objective of maximizing the total value of the firm while taking the firm’s own and its rivals’ subsequent output market strategies into account. In the second stage, the shareholders of each firm choose its output market strategy before observing the realization of the shock to the firm’s cash flow. The realization of the shock, together with the output market strategies chosen by the firm and by its rivals, determines whether the firm is solvent or defaults. If the realization of the shock is above the threshold value, the firm is solvent; it repays its debt and distributes the residual cash flow to its shareholders. If the realization of the shock is below the threshold value, the firm’s cash flow equals zero, which leads to default.5 The sequence of the game is presented in figure 1.

5. In a more general setting, where the cash flow in the bad state is positive, a firm may be able to issue risk-free debt with a face value lower than the cash flow in the bad state. However, riskless debt does not affect the firm’s operating strategy and its value. Thus, it cannot serve as a commitment device. As shown below, debt carries a strategic benefit. Therefore, the equilibrium

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Firms in Output Markets 2385

To simplify the exposition, the analysis of strategic debt choices is devel- oped in a duopolistic setting. However, varying the “interaction parameter,” r, which describes the extent to which firms’ choices affect their competitor’s value, enables examining the relation between the extent of competitive in- teraction among firms in output markets and their optimal operating strategies and capital structure choices.6 Examining the interaction between two firms does not lead to a sacrifice of generality. The model can be easily extended to accommodate n firms, in which case the interaction parameter would de- scribe the extent to which each firm’s strategy affects each of its rivals. All the conclusions of the model with respect to relations between the interaction parameter and firms’ optimal financial and operating choices remain intact in an n-firm setting.7 The model’s setup allows examining the effects of the extent of competitive interaction on firms’ financial and operating decisions, as opposed to concentrating on one of the possible determinants of the degree of interaction, specifically the number of firms operating in an industry.

The game will be solved by finding a subgame perfect equilibrium. In the first stage, firms choose the face values of their debt, denoted by for firmFi

i. There are two firms in the model, therefore . The strategic effecti p {1, 2} of debt follows from the fact that after the debt levels have been chosen, firms’ shareholders take only the cash flows in solvent states into account when they choose their operating strategies. Thus, debt serves as a commitment mechanism to choosing a more aggressive operating strategy in the second stage of the game.

In the second stage, firms make their product market choices, summarized by a variable for firm which determine the probability distributionc ≥ 0 i,i

of the firms’ cash flows. Higher increases firm i’s cash flow in the solventci

state and also increases the probability of its default. In the remainder of the article will be interpreted as the choice of the aggressiveness of the firm’sci

product market strategy. In addition to affecting the distribution of firm i’s cash flow, affects the default probability of firm i’s competitor, thus influ-ci

encing the competitor’s optimal operating strategy, which indirectly affects firm ’s value. As mentioned in the introduction, the model is not restrictedi to a specific type of oligopolistic competition. While I intentionally define the nature of the interaction among firms in terms of strategic substitutes and complements, it is useful to relate the model’s setup to the common Cournot

face value of the firm’s debt would be higher than the payoff in the bad state. Therefore, assuming that the payoff in the bad state is zero does not result in a loss of generality.

6. This is one of the possible ways of parameterizing oligopolistic competition (see, e.g., Boone 2000).

7. The proof of this statement is available upon request. It is also possible to examine the relation between the number of firms operating in an industry, n, and firms’ financial and operating strategies in a setting where the ability of each firm to affect each of its rivals’ value functions is negatively related to n. This setting results in relations between the number of firms and their financial and operating choices, which are the opposite of the relations between the extent of interaction in output markets and firms’ financial and operating decisions. This is expected since the extent of interaction is negatively related to the number of industry rivals. Thus, the model’s results and empirical predictions are not driven by the modeling choice.

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2386 Journal of Business

quantity competition setting. In the case of quantity competition, higher value of corresponds to a larger production quantity (the larger the quantity, theci

higher the profits when the equilibrium price is above the average cost and the larger the losses when the price is below the average cost).

I assume that a stochastic shock to firms’ cash flows, z, is distributed uniformly between zero and one.8 The choice of determines the thresholdci

of the realization of the shock, above which firm i is solvent and receives cash flow equaling . Firm 1’s default threshold depends on and on . Ic c ci 1 2

assume, for analytical tractability, that firm 1’s default threshold is

T p c � rc ,1 1 2

and similarly for firm 2. The interaction parameter, r, is allowed to vary in the interval . The restriction on the lower and the upper bounds of r(�1, 1) is placed in order to prevent the effect of a change in a firm’s rival’s ag- gressiveness choice on the firm’s probability of default from being stronger than the effect of a similar change in the firm’s own operating choice.9 If

, then firms compete in strategic substitutes. Increasing the aggressivenessr 1 0 of firm 1’s strategy, , reduces the marginal profit of firm 2 and decreasesc1

the optimal aggressiveness of its operating strategy, . In addition, a morec2

aggressive strategy of firm 1 increases the probability of default of firm 2 and reduces its value, and vice versa. For , firms compete in strategic com-r ! 0 plements. Increasing raises the marginal profit of firm 2 and increases thec1

optimal aggressiveness of its strategy. Increasing reduces the probabilityc1

of default of firm 2 and increases its value. Using the assumption of the uniform distribution of the shock, the prob-

ability of firm 1 being solvent is

prob (solvency) p prob(z ≥ T ) p 1 � c � rc , (1)1 1 1 2

and similarly for firm 2. Under the assumption of zero cash flow in the bankrupt state, the combined value of firm 1’s debt and equity, given its own and its rival’s operating choices, is

[ ]V p 1 � c � rc c .1 1 2 1

I assume that the risk-free rate is zero and that all agents are risk neutral. In a one-period setting, zero risk-free rate, risk neutrality, and the assumption of zero cash flow in the bankrupt state imply that the market value of firm

8. In general, the shocks to the cash flows of the two firms do not have to be the same. The only assumption required in order to keep the model symmetric is that the shocks are drawn from the same distribution. The correlation between the shocks to firms’ cash flows does not influence the results because of the single-period setting, which ignores strategic bankruptcy considerations.

9. In addition, it is easy to show that no symmetric equilibria exist for .r ≤ �1

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Firms in Output Markets 2387

1’s debt at the time of issuance (the ex ante value of debt), , equals its faceD1

value times the probability of firm 1 being solvent:

[ ]D p 1 � c � rc F , (2)1 1 2 1

while the ex ante value of firm 1’s equity, , equalsE1

[ ] [ ]E p 1 � c � rc c � F , (3)1 1 2 1 1

and similarly for and .10D E2 2

The distributions of firm 1’s total payoff and its shareholders’ payoff are depicted in figure 2 for two different choices of : and , wherec c c c !1 1 1 1l h l

, for a given level of .11 Choosing results in a lower probability ofc c c1 2 1h l

default and a lower payoff in the solvent state than those corresponding to .c1h

In the remainder of this section, I solve the game using backward induction. I start from determining firms’ optimal operating strategies conditional on debt levels. Then I derive firms’ equilibrium debt levels and leverage ratios.

A. Second Stage—Choices of Operating Strategies

In this stage firms maximize their equity values in equation (3), conditional on previously chosen own and rival’s debt levels. Maximizing equation (3) with respect to , and a similar function for firm 2 with respect to , andc c1 2

solving the resulting system of two equations lead to the following result: Proposition 1. There exists a unique stable equilibrium in firms’ op-

erating choices. The equilibrium aggressiveness of a firm’s operating strategy is increasing in the face value of its debt. If firms’ strategies are substitutes (complements), then the equilibrium aggressiveness of a firm’s operating strat- egy is decreasing (increasing) in the face value of its rival’s debt.

Proof. See the appendix. Because of the limited liability, a higher debt level causes a firm to choose

a more aggressive operating strategy. If firms’ strategies are substitutes, their reaction functions in operating choices are downward sloping. Thus, a higher rival’s debt level, causing the rival to choose a more aggressive strategy, reduces the firm’s own optimal aggressiveness choice. In the case of strategic complements, firms’ reaction functions in operating strategies are upward sloping. A higher level of a competitor’s debt that causes it to choose a more

10. It is never optimal for a firm to raise debt with a face value that is higher than its payoff in the solvent state; if it were to do so, the value of the firm’s equity before the realization of the shock (ex ante) and after the realization of the shock (ex post) would be zero. Thus, a firm’s equilibrium debt-level choice is such that the firm is always able to fulfill its debt obligations in full in the solvent state.

11. Since and are nonnegative by assumption, firm 1 would never choose that is higherc c c1 2 1

than , since such a choice would result in a negative firm value. Similar argument holds1 � rc2

for firm 2. In addition, in a symmetric equilibrium, and for1 � c � rc ! 1 1 � c � rc ! 11 2 2 1

. Thus, the functional form in eq. (1) satisfies the probability function assumptions,�1 ! r ! 1 in the sense that in equilibrium 0 ≤ prob(z ≥ T ) ≤ 1.1

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2388 Journal of Business

Fig. 2.—Distribution of firm 1’s and its shareholders’ payoffs for various operating choices. The top figure depicts firm 1’s total payoff for various realizations of the shock, z. The payoff for the case of operating strategy is represented by the solidc1h

line, while the payoff for the case of strategy is represented by the dotted line. Thec1l

bottom figure depicts firm 1’s shareholders’ payoff. The solid line corresponds to , while the dotted line corresponds to .c c1 1h l

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Firms in Output Markets 2389

aggressive output strategy causes the firm also to choose a more aggressive strategy.

B. First Stage—Debt Level Choices

In this stage, firms choose their debt levels with the objective of maximizing their ex ante values, and , given byV V1 2

∗ ∗ ∗[ ]V p 1 � c (F , F ) � rc (F , F ) c (F , F ), (4)1 1 1 2 2 1 2 1 1 2

for firm 1, and similarly for firm 2, where and are the∗ ∗c (F , F ) c (F , F )1 1 2 2 1 2

optimal second-stage operating choices of firms 1 and 2, given their own and their rival’s debt levels.

As shown in proposition 1, debt has a strategic effect of causing a firm’s rival to choose a less aggressive output strategy in the case of competition in strategic substitutes and of causing a firm’s competitor to adopt a more ag- gressive output stance in the case of competition in strategic complements. Thus, the strategic benefit of firm 1’s debt is in changing its rival’s operating strategy. This observation allows quantifying the value of the strategic benefit of a given debt level. The strategic advantage of firm 1’s debt, , isb (F , F )1 1 2

the difference between firm 1’s value given its own and its rival’s debt levels, , and its value corresponding to a competitor’s oper-∗ ∗V (c (F , F ), c (F , F ))1 1 1 2 2 1 2

ating strategy that would have been chosen had firm 1 been entirely equity financed, :∗ ∗V (c (F , F ), c (0, F ))1 1 1 2 2 2

∗ ∗ ∗ ∗b (F ,F ) p V (c (F , F ), c (F , F )) � V (c (F , F ), c (0, F ))1 1 2 1 1 1 2 2 1 2 1 1 1 2 2 2

∗ ∗ ∗p [1 � c (F , F ) � rc (F , F )]c (F , F ) (5)1 1 2 2 1 2 1 1 2

∗ ∗ ∗� [1 � c (F , F ) � rc (0, F )]c (F , F ).1 1 2 2 2 1 1 2

In addition to benefiting a firm by favorably affecting its rival’s operating strategy, debt has a cost. The agency cost of debt is that of distorting the firm’s value maximization problem. Instead of maximizing the total value of the firm, its shareholders are maximizing their expected residual claims. Debt holders anticipate this behavior at the time of debt issuance and, therefore, debt reduces the ex ante firm value. The agency cost of debt is the difference between the firm’s value when its value maximization problem is not distorted (all-equity firm) and the value of the firm when its shareholders maximize the value of their residual claims (partially debt-financed firm), for a given operating strategy of the firm’s rival. Thus, the agency cost of firm 1’s debt,

, is the difference between firm 1’s value had it chosen a zero debtg (F , F )1 1 2

level, , and the firm value corresponding to face value∗ ∗V (c (0, F ), c (0, F ))1 1 2 2 2

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2390 Journal of Business

of debt of and a competitor’s operating strategy had firm 1 chosen to beF1

all-equity financed, :∗ ∗V (c (F , F ), c (0, F ))1 1 1 2 2 2

∗ ∗ ∗ ∗g (F , F ) p V (c (0, F ), c (0, F )) � V (c (F , F ), c (0, F ))1 1 2 1 1 2 2 2 1 1 1 2 2 2

∗ ∗ ∗p [1 � c (0, F ) � rc (0, F )]c (0, F ) (6)1 2 2 2 1 2

∗ ∗ ∗� [1 � c (F , F ) � rc (0, F )]c (F , F ).1 1 2 2 2 1 1 2

The optimal debt level choice incorporates the trade-off between these two effects. Maximizing each firm’s strategic benefit of debt net of the agency cost of debt, for firm 1 with respect to its debt level,b (F , F ) � g (F , F )1 1 2 1 1 2

and similarly for firm 2, results in the following proposition:12

Proposition 2. (1) If firms compete in strategic substitutes (comple- ments), then their debt level reaction functions are downward (upward) slop- ing; (2) the optimal face value of a firm’s debt is positive for all values of its rival’s debt, except when the interaction parameter equals zero, in which case the optimal face value of the firm’s debt is zero.

Proof. See the appendix. For each debt level of a firm’s competitor, there is a unique nonnegative

(positive for all but one extreme case) debt level that maximizes the firm’s value. This result is consistent with the conclusion of Brander and Lewis (1986) for the case of quantity competition. It is also in line with the positive equilibrium debt levels in some of the parametrizations of price competition in Showalter (1995) and capacity-price competition in Schuhmacher (2001).13

The next proposition establishes the relation between firms’ equilibrium fi- nancing choices and the extent of competitive interaction in their industries, which is the main result of the model.

Proposition 3. There exists a unique stable equilibrium in firms’ debt levels. Firms’ equilibrium leverage ratios are increasing in the absolute value of the interaction parameter, 14 The equilibrium face values of firms’ debtFrF. and their leverage ratios approach zero as r approaches zero.

Proof. See the appendix. The intuition for this result is straightforward. The absolute value of the

interaction parameter determines the degree of influence of a firm’s operating strategy on its competitor’s value function and on its resulting operating

12. This is equivalent to maximizing the total firm value, given in eq. (4), with respect to the face value of debt.

13. It is, however, inconsistent with other parameterizations in Showalter (1995) and in Schuh- macher (2001), in which debt reduces the optimal aggressiveness of a firm’s operating strategy, exhibits a strategic disadvantage, and is not chosen in equilibrium. In the model presented here, I do not analyze the case in which an increase in a firm’s debt level reduces the optimal aggressiveness of its strategy. The setting of the model implicitly assumes that a firm’s own debt increases the firm’s aggressiveness both in the case of competition in strategic substitutes and in the case of competition in complements. (This result, established in proposition 1, follows from examining the first-order conditions of the equity holders’ operating strategy choice.)

14. I define a firm’s leverage as the ratio of the market value of its debt at the time of issuance to the firm’s total value.

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Firms in Output Markets 2391

choice. The higher the absolute value of the interaction parameter, the larger the strategic benefit of debt. Thus, increasing the interaction parameter when it is positive and decreasing it when it is negative results in higher equilibrium debt levels and leverage ratios.

Proposition 3 should be interpreted cautiously. As mentioned above, an implicit assumption of the model is that an increase in a firm’s debt level raises the aggressiveness of its operating strategy both when the firm competes in strategic substitutes and when it competes in complements. Thus, the con- clusions of the model would not hold in the case when an increase in debt reduces the firm’s optimal aggressiveness, as in some parameterizations in Showalter (1995) and Schuhmacher (2001). Therefore, the correct interpre- tation of the model is that whenever an increase in debt causes an increase in the optimal aggressiveness of a firm’s operating strategy, debt carries a strategic benefit, which is increasing in the extent of competitive interaction among product market rivals. If the strategic effect of debt is positive, firms’ optimal leverage ratios are increasing in the extent of interaction among them.15

III. Proxies for the Extent of Competitive Interaction and Empirical Predictions

The model developed in the previous section predicts a positive relation be- tween the extent of competitive interaction among firms in output markets and their leverage ratios. Empirical tests of this prediction require proxies for the degree of competitive interaction among product market rivals. Proxies usually employed in the industrial organization literature are industry con- centration indexes, such as the Herfindahl index, and measures related to cross- price elasticities. Because of the lack of pricing data in the Compustat database, however, the latter measures are difficult to construct.16

The Herfindahl index is arguably the most widely used measure of an industry’s structure. The Herfindahl index, however, can be misleading as a measure of the extent of competitive interaction. High Herfindahl index may be due to the low number of firms operating in the industry and, thus, be positively related to the extent of competitive interaction. However, it might also be due to the high variation in industry participants’ sizes. It follows from Maksimovic and Zechner’s (1991) model and from MacKay and Phil-

15. It may be argued that, while the optimal debt levels are positive in an equilibrium of a static game, in the case of competition in strategic substitutes leverage can generate costs from a collective standpoint and reduce the combined value of industry participants. Therefore, while coordinating on strategic choices may be difficult because of their unobservability/nonverifiability, tacit collusion on debt seems plausible. It is easy to show that in an infinitely repeated game setting, the extent of competitive interaction is positively related to firms’ willingness to deviate from a collusive (no-debt) equilibrium if the firms compete in strategic substitutes. This result reinforces the conclusion from the static model regarding the positive relation between firms’ optimal leverage ratios and the extent of competitive interaction in their industries. The dynamic model is available upon request.

16. As discussed below, the data used in the empirical tests come from the Compustat Annual Industrial files.

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2392 Journal of Business

lips’s (2005) empirical analysis that the larger the differences in firms’ char- acteristics (such as size) are, the smaller is the expected influence of firms’ actions on their rivals’ values. Therefore, the relation between the Herfindahl index and the extent of interaction among firms in product markets is ambiguous.17

Another potential proxy for the extent of competitive interaction is the degree of advertising competition in an industry. Advertising competition is the primary component of firms’ interaction in output markets that is not price or quantity based. Marketing literature shows that a firm’s own advertising, as well as that of its rivals, affects the firm’s sales.18 Advertising may be seen as a proxy for the willingness of firms to engage in costly actions that affect their output market rivals. Thus, advertising expenditures are expected to be positively related to the extent of competitive interaction and, therefore, are expected to positively affect industry participants’ leverage ratios. However, a severe problem with using advertising expenditures as a proxy for the extent of competitive interaction is the possibility of reverse causality. Advertising level may be a result of firms’ leverage choices, which may not be related to the extent of product market competition.19

In what follows, I describe two proxies for the extent of competitive in- teraction that do not seem to suffer from the deficiencies described above. As argued below, neither of the proposed proxies is close to being perfect. The results obtained using each of the two proxies separately should be viewed as complementary to each other.

A. Number of Firms in an Industry

The simplest possible proxy for the extent of competitive interaction in an industry is the number of firms operating in it. If we assume appropriate industry definitions, the number of industry participants can serve as an in- dicator of the degree of influence of firms on their competitors. As the number of firms in an industry increases, one moves from a duopoly, in which firms’ profits and product market strategies are expected to be strongly dependent on their rival’s strategies, to a perfect competition, in which firms are price

17. This relation remains unclear even when the number of industry rivals is controlled for. On one hand, the lower the Herfindahl index, the more similarly sized firms operate in the industry and the higher the extent of competitive interaction in the industry. On the other hand, in highly competitive industries, similarly sized firms cannot significantly affect their rivals’ actions. If, however, an industry consists of a few large firms and numerous fringe firms, then large firms’ choices may affect their large rivals’ values and actions. This may result in a positive relation between the Herfindahl index and the extent of competitive interaction. Thus, the overall relation between the industry’s Herfindahl index and the extent of competitive interaction in the industry is ambiguous.

18. See Grullon, Kanatas, and Kumar (2002) for citations of evidence regarding advertising expenditures being the major component of interfirm rivalry, and regarding the relation between firms’ sales and their own and their rivals’ advertising.

19. Indeed, Grullon et al.’s (2002) findings indicate that it is capital structure that influences firms’ choices of advertising, rather than firms choosing their capital structures that are consistent with the degree of advertising competition.

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Firms in Output Markets 2393

takers and are unable to influence their rivals’ decisions. This is true regardless of whether the competition is in strategic substitutes or complements (or, alternatively, whether firms’ reaction functions are downward or upward sloping).

While the number of firms is a simple and intuitive proxy for the extent of competitive interaction, it has two important deficiencies. First, Compustat covers only public firms, understating the number of firms belonging to each industry. The second difficulty is the classification of firms to industries. Similar to past industrial organization literature, I use four-digit Standard Industrial Classification (SIC) industries in the analysis. This industry clas- sification, however, is far from being perfect. Dunne, Roberts, and Samuelson (1988) discuss the inadequacies of (four-digit) SIC industries as measures of economic markets. For example, firms can produce the same good but compete in different geographic markets. In addition, the SIC industry classification is based on production methods, as opposed to economic markets. It is also known that many firms produce in more than one SIC industry.20

The number of firms operating in an industry is expected to be negatively related to the absolute value of the slope of firms’ reaction functions. There- fore, despite the limitations that follow from the problematic industry defi- nitions and from the heterogeneity of industry participants’ products, pro- duction methods, and sizes, the number of firms in an industry can serve as a proxy for the ability of firms to influence their competitors’ strategies.

This being said, the extent of competitive interaction in an industry is not likely to be linear in the number of firms. (The difference between the degree of competitive interaction in industries consisting of two and 10 firms is likely to be larger than the difference between the extent of interaction in industries consisting of 102 and 110 firms.) Thus, I use the logarithm of the number of firms operating in an industry as an (inverse) proxy for the extent of com- petitive interaction in that industry.

B. Competitive Strategy Measure

According to Bulow et al.’s (1985) definition, firms compete in strategic substitutes whenever a more aggressive play by a firm lowers its rivals’ mar- ginal profits. Likewise, firms are said to compete in strategic complements when a more aggressive strategy by a firm raises its competitor’s marginal profits. More formally, a positive (negative) cross-partial derivative of a firm’s value with respect to its own and its rivals’ operating strategies,

, where is firm 1’s value, and and denote the operating2� V /�c �c V c c1 1 2 1 1 2

choices of a firm and its competitor, corresponds to competition in strategic

20. In order to mitigate these problems, in addition to the four-digit SIC classification, I examine an alternative definition of industries proposed by Fama and French (1997). They map firms to 48 industries, based on their four-digit SIC codes. The results are generally in line with those reported.

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2394 Journal of Business

complements (substitutes). In the remainder of this section, I use the terms “value” and “profit” interchangeably.

There are three potential difficulties in constructing an empirical proxy for the effects of firms’ actions on their rivals. First, firms’ strategies can take different forms. The most common examples of operating strategies are quan- tities and prices. However, Compustat reports neither quantities nor prices. It does report firms’ sales, but sales are not a strategic variable. Thus, in order to base the proxy for the extent of competitive interaction on firms’ sales, one needs to show that regardless of whether the competition is in quantities or prices, the sign of the cross-partial derivative of a firm’s profit with respect to its own and its rival’s sales is the same as the sign of the cross-partial with respect to its own and its rival’s quantities (prices) in the case of quantity (price) competition.

Proposition 4. Regardless of whether firms compete in quantities or prices, the sign of the cross-partial derivative of a firm’s profit with respect to its own quantity (price) and its rival’s quantity (price), 2d p /1

, is the same as the sign of the cross-partial derivative2dq dq (d p /dp dp )1 2 1 1 2

of its profit with respect to its own and its rival’s sales, 2d p /dS dS.1 1 2

Proof. See the appendix. Proposition 4 establishes that the cross-partial derivative of a firm’s profit

with respect to its own and its rival’s sales is a valid measure of the nature of product market competition. If is negative, then firms compete2d p /dS dS1 1 2

in strategic substitutes. If is positive, then firms compete in stra-2d p /dS dS1 1 2

tegic complements. However, there is another difficulty in constructing the empirical proxy for the cross-partial derivative of firms’ values with respect to their own and their rivals’ actions. Compustat does not report firms’ mar- ginal profits and marginal changes in sales. The data contain, however, time- series observations of firms’ profits and sales and firms’ product market rivals’ sales, from which discrete changes in these variables over time can be cal- culated.

Sundaram, John, and John (1996) were the first to notice that one could use these time series to construct a measure of responsiveness of firms’ profits to changes in their competitors’ actions, which is directly related to the cross- partial derivatives of firms’ values with respect to their own and their rivals’ strategies. Sundaram et al.’s competitive strategy measure (CSM) is the cor- relation between the ratio of the change in a firm’s profit and the change in its sales, and the change in the firm’s rivals’ combined sales:

 Dp1 CSM p corr , DS , (7) 1 2

DS 1

where is the change in firm 1’s profit between two consecutive periods,Dp1

is the change in its sales, and is the change in its product marketDS DS1 2

rivals’ combined sales. More generally, the competitive strategy measure in equation (7) can be thought of as the correlation between the ratio of the

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Firms in Output Markets 2395

change in a firm’s value and the change in its operating strategy and the change in the firm’s rivals’ operating strategy, wherecorr [DV /Dc , Dc ] ,1 1 2

and denote a firm’s own and its rival’s operating strategies, respectively.c c1 2

The next proposition shows that within the framework of the model of Section II, as long as a firm’s value function does not change from one period to the next, the covariance between the ratio of the change in the firm’s value and the change in its operating strategy, and the change in its rival’s operating strategy, is directly proportional to the cross-partial derivative of the firm’s value with respect to its own and its rival’s operating choices.

Proposition 5. The covariance between the ratio of the change in a firm’s value and the change in the aggressiveness of its operating strategy, and the change in the aggressiveness of the firm’s rival’s operating strategy, is proportional to the cross-partial derivative of the firm’s value with respect to its own and its rival’s aggressiveness choices.

Proof. See the appendix. Proposition 5 justifies the use of CSM as a measure of competitive inter-

action among product market rivals in the case where the firm’s value function remains constant over time (while shocks to the firm’s rivals’ value functions, resulting in changes in their operating strategies, are allowed). Positive values of CSMcorrespond to competition in strategic complements, while negative values of CSMcorrespond to competition in substitutes.

However, it is not clear whether CSM is a valid measure of the nature of output market competition when the possibility of shocks to a firm’s own value function is taken into account. One example of potential problems caused by a possibility of a change in a firm’s value function is an industry-wide shock to firms competing in strategic substitutes.21 Figure 3 illustrates this point.

Figure 3 depicts firm 1’s value at time t as a function of its operating choice (thick solid line) for a given operating strategy of the firm 2, . Firm 1’sc2, t

value is a function of its own operating choice, , and the value of the shockc1, t

to its value function, . The firm operates at a point at which its marginalzt

profit equals zero (point A in fig. 3). Assume now that two changes occur between times t and . First, the shock to the firm’s value function changest � 1 from to . Also, the strategy of firm 2 changes from to . (Assume,z z c ct t�1 2, t 2, t�1

without loss of generality, that and that firms compete in strategicc 1 c2, t�1 2, t

substitutes.) The thick dotted line depicts firm 1’s profit as a function of its own strategy for the values of the shock and firm 2’s strategy at time ,t � 1

and . Firm 1 adjusts its optimal strategy following the changes in zc z2, t�1 t�1

and , and operates at point B at time , where its marginal profit is zero.c t � 12

Thus, the ingredients of Sundaram et al.’s (1996) CSM, , and areDV /Dc Dc1 1 2

equal to and respectively. However, the ratio(V � V )/(c � c ) c � c1 1 1 1 2, t�1 2, tB A B A

reflects changes in firm 1’s strategy and value that are(V � V )/(c � c )1 1 1 1B A B A

caused both by the change in and the change in z.c2

21. I thank the referee for pointing out this possibility.

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2396 Journal of Business

Fig. 3.—Change in firm’s 1 equilibrium value and operating strategy following a change in firm 2’s operating strategy. The thick solid line represents firm 1’s value as a function of its operating strategy at time t. The thick dotted line represents its value function at time . The solid line represents its implied value function fort � 1 the case when the only change between t and is in the shock to firm 1’s valuet � 1 function, while firm 2’s operating strategy is assumed unchanged.

In order to determine the stand-alone effect of the change in on firm 1’sc2

value and operating strategy, one needs to estimate an “implied value function” of firm 1 that would have been observed under and firm 2’s time t strategy,zt�1

. The solid line depicts firm 1’s implied value as a function of its operatingc2, t

strategy. The firm would have chosen to produce at point D, its optimal strategy being , and its value being . In order to measure that is causedc V DV /Dc1 1 1 1D D

by the change in alone, one needs to obtain the following ratio:c (V �2 1B

. However, in the data, one cannot separate the effects of theV )/(c � c )1 1 1D B D

change in z and the change in on the value and the operating strategy ofc2

firm 1. Empirically, one observes , and this ratio is one(V � V )/(c � c )1 1 1 1AB A B

of the components of Sundaram et al.’s (1996) CSM. In order to mitigate the potential problem described above, I estimate an

implied profit and implied sales for each firm that would have been observed if the only change over time was in the firm’s value function, while the firm’s rivals’ sales were held constant. I assume that the shock to each firm’s prof- itability can be approximated by the average shock to the industry’s profit- ability. I measure the change in the industry’s profitability as a change in the

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Firms in Output Markets 2397

average profit margin of all firms operating in the industry. I then add this change to the firm’s previous year’s profit margin in order to calculate the firm’s implied profit margin, which is used in estimating the firm’s implied sales and implied profit.

In order to estimate the firm’s implied sales, I perform a time-series re- gression for each firm, where the dependent variable is the percentage change in sales over 2 consecutive years, and the independent variable is the change in profit margin over the 2 years:22

 S � S p pi, t�1 i, t i, t�1 i, t p a � b � �e , (8) i i i , tS S S i, t i, t�1 i, t

where and are firm i’s sales in two consecutive years, and andS S pi, t�1 i, t i, t�1

are its profits in these years. I then apply the coefficients of the regressionpi, t

in equation (8) to calculate the firm’s implied sales in each year, :S̃i, t

  ¯ ¯p pt�1 tˆ˜ ˆS p S 1 � a � b � , (9)  i, t i, t i i S S  t�1 t

where and are industry average profit margins in two con-¯ ¯p /S p /St�1 t�1 t t

secutive years, and and are the estimates of the intercept and the slopeˆâ bi i

in equation (8). I then multiply the implied sales in equation (9) by the implied profit margin to get the implied profit, :p̃i t

  ¯ ¯p p pi, t t�1 t˜p̃ p S � � . (10)  i,t i,t S S S  i, t t�1 t

The implied profit and implied sales in equation (10) and equation (9) re- spectively represent an estimate of point D in figure 3. To summarize, the empirical measure of the change in a firm’s sales caused by the change in its rivals’ combined sales is

  ¯ ¯p pt�1 tˆ˜ ˜ ˆDS p S � S p S � S 1 � a � b � , (11)  i i , t�1 i,t i, t�1 i, t i i S S  t�1 t

and the measure of the change in a firm’s profit caused by the change in the firm’s rivals’ sales is

˜ ˜Dp p p � p p p (12)i i , t�1 i,t i, t�1

     ¯ ¯ ¯ ¯p p p p pt�1 t i, t t�1 tˆˆ� S 1 � a � b � � � .     i, t i i S S S S S     t�1 t i, t t�1 t

The adjusted CSMmeasure that I use to estimate the cross-partial derivative

22. This regression is estimated for firms that have at least 10 consecutive observations of profit margin and sales.

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2398 Journal of Business

of firm 1’s value with respect to its strategy and its rivals’ strategy, , is, thus:2� V /�c �c1 1 2

 ˜Dp1 C̃SMp corr , DS , (13) 2˜DS 1

where is the implied change in the firm’s profit between two consecutive˜Dp1

years, is the implied change in its sales between two consecutive years,˜DS1

and is the change in the firm’s product market rivals’ combined salesDS2

between the two years. Following Sundaram et al. (1996), I define a firm’s profit as its operating profit. I define rivals’ sales as the combined annual sales of all other firms in the firm’s four-digit SIC industry.23 I calculate the cor- relation in equation (13) for each firm using all available time-series obser- vations,24 and then obtain mean for each four-digit SIC industry for eachC̃SM year, which is assigned to all firms operating in that industry during that year. This procedure reduces the noise involved in estimating each firm’s andC̃SM also enables time-varying for each firm.25C̃SM

When is positive, it corresponds to firms’ strategies being comple-C̃SM ments, while a negative describes the case of competition in strategicC̃SM substitutes. The prediction of the model is that, regardless of the type of strategic interaction, firms’ leverage is expected to be positively related to the extent of competitive interaction within their industries. Thus, I expect lev- erage to be positively associated with the absolute value of the adjusted com- petitive strategy measure both within a subsample of firms competing in strategic substitutes and within a subsample of those competing in complements.

IV. Data, Variables, and Empirical Methods

The tests in this section build on the results of the empirical work on the cross-sectional determinants of capital structure, most notably by Frank and Goyal (2004), Rajan and Zingales (1995), and Smith and Watts (1992). There are three theories that attempt to explain the cross-sectional variation in firms’ capital structures. The oldest, and the most successful one, is the static trade- off theory, in which the tax advantages of debt are traded off against its agency costs and the deadweight bankruptcy costs. Other theories include the

23. Calculating firms’ using quarterly data provides results similar to those reported.C̃SMs Using quarterly observations reduces the sample size significantly (both because Compustat begins its quarterly coverage in 1962, as opposed to the annual coverage that begins in 1950, and because there are more missing values in the quarterly data than in the annual data).

24. The correlations in eq. (13) are calculated only for firms with at least 10 observations of the changes in implied profit and imlied sales.

25. This procedure is different from that of Sundaram et al. (1996), who calculate only the CSM for one firm in an industry (in their case, the firm announcing a change in research and development expenditures) and assign this CSM to all firms in the industry. Using firm-specific

, following Sundaram et al., instead of industry-wide , provides results that are qual-˜ ˜CSM CSM itatively similar to those reported.

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Firms in Output Markets 2399

pecking order theory, which predicts the order in which firms choose the potential ways of financing their investments, and the market timing theory, which argues that firms’ capital structure choices are explained by managers trying to issue relatively overvalued securities.

While examining the relation between firms’ leverage choices and the extent of competitive interaction in their industries, I control for other factors that were found in past studies to affect firms’ capital structure choices. I follow Frank and Goyal and use factors that they found to exhibit the largest ex- planatory power in leverage regressions. However, I also perform robustness checks of the leverage model by including additional factors that were found important in the past literature, and also by using different definitions of variables that proxy for the factors that are hypothesized to affect firms’ capital structures.

A. Measures of Leverage, Factors Affecting Optimal Leverage, and Their Empirical Proxies

Leverage.—I use both market and book leverage ratios in the empirical tests. Following past empirical literature, I define a firm’s market leverage as the ratio of the book value of its debt to the sum of the market value of its equity and the book value of its debt: (compustat item 9 � item 34)/(item 54 #

. Book leverage is defined as the ratio of theitem 199 � item 9 � item 34) book value of debt to the book value of assets: .26(item 9 � item 34)/item 6

Frank and Goyal (2004) determine seven factors that seem to be the most important in explaining firms’ leverage choices. I use the following five of these factors.

Mix of growth options and assets in place.—Smith and Watts (1992) hy- pothesize that the ratio of the value of a firm’s investment opportunities to the value of its assets in place is expected to be negatively related to leverage, because of the contracting arguments of Myers (1977) and Jensen (1986).27

I measure a firm’s mix of investment opportunities and assets in place as the ratio of the sum of the market value of its equity and the book value of its debt to the book value of its assets: (item 54 # item 199 � item 9 � item

.2834)/item 6

26. Alternative definitions of the book value of debt are long-term debt plus debt in current liabilities plus preferred stock; long-term debt plus debt in current liabilities minus capitalized leases; and, finally, long-term debt plus debt in current liabilities plus preferred stock minus capitalized leases. The correlations between the measures of leverage based on these definitions are on the order of 95%. All the results are robust to the choice of the definition of the book value of debt.

27. Myers (1977) suggests that, due to the underinvestment problem, firms with numerous investment opportunities should be financed with less debt than firms with few investment opportunities. Jensen (1986) argues that debt has a benefit of mitigating the free-cash-flow problem and, therefore, firms with more assets in place (generating steady cash flows) should be financed with more debt.

28. An alternative proxy for the mix of investment opportunities and assets in place, discussed in Barclay et al. (2006), is the ratio of research and development expenditures to sales, item

. Using it instead of the market-to-book ratio does not change any of the results.46/item 12

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2400 Journal of Business

Collateral.—Collateral reduces the agency costs of debt and is, thus, ex- pected to be positively related to leverage. Collateral is measured as the ratio of the sum of net fixed assets and inventories to assets: (item 8 � item

293)/item 6. Profitability.—Myers’s (1984) pecking order theory predicts that firms are

likely to raise capital first from retained earnings, second by issuing debt, and then by issuing equity. Thus, more profitable firms with more internal re- sources are less likely to resort to debt financing, and a firm’s profitability should be negatively related to its leverage. Similar to Frank and Goyal (2004) and Barclay et al. (2006), I measure profitability as the ratio of operating income to assets, item 13/item 6.

Dividends and repurchases.—Within the pecking order theory, dividends require funds. Firms with larger internal funds would have lower leverage. Thus, firms that pay out dividends are predicted to have lower leverage. Stock repurchases have become an increasingly important way of distrib- uting cash (see, e.g., Boudoukh et al., forthcoming). Thus, the prediction is that a dividends-and-repurchases dummy, which equals one if the firm has paid dividends or repurchased shares in a given year (item or item21 1 0

) and zero otherwise, is expected to be negatively related to115 1 0 leverage.30

Size.—Larger firms are less prone to bankruptcy. In addition, the evidence in Warner (1977) suggests that direct bankruptcy costs constitute a smaller proportion of a firm’s value as the value increases. Thus, a firm’s size is hypothesized to be positively related to leverage. I define a firm’s size as the logarithm of its assets (item 6). In order to measure assets in constant dollars, I adjust nominal assets by the Consumer Price Index at the end of the respective year.31

The other two factors that were found by Frank and Goyal (2004) to be influential in explaining the cross-sectional variation in firms’ capital structure choices are the median industry leverage and expected inflation. However, since the purpose of the tests of this section is to examine the relation between an industry’s competitive structure and its participants’ leverage ratios, in- cluding an industry dummy variable would defeat the purpose of the tests. Moreover, as Frank and Goyal note, the relation between industry median leverage and firm leverage does not have an agreed-upon interpretation. One of the interpretations is that industry leverage proxies for omitted factors. The competitive structure of the industry might be one of these factors. I do not include expected inflation in the tests, since the predictions of the model are

29. Frank and Goyal (2004) notice that the measure of collateral is highly correlated with tangibility, which is defined as the ratio of fixed assets to total assets, , as in Titmanitem 8/item 6 and Wessels (1988). Replacing collateral with tangibility does not alter any of the results.

30. Dividend payouts and stock repurchases are, of course, endogenous. Thus, using the dividends-and-repurchases dummy in leverage regressions may result in biased coefficients on other explanatory variables. Removing the dividends-and-repurchases dummy from the right-hand side of the regressions does not materially alter the results.

31. Defining size as the logarithm of annual sales (item 12) does not affect any of the results.

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Firms in Output Markets 2401

regarding the cross-sectional variation in firms’ capital structures. In addition, Frank and Goyal report that expected inflation is the least important of the factors affecting leverage. Also, as discussed below, I use year dummy var- iables to control for the changes of macroeconomic factors over time.

Past studies have employed alternative explanatory variables in the leverage regressions. These variables are as follows:

Regulation.—The conflicts between stockholders and debt holders are less severe in regulated industries than in unregulated ones. The reason is that in regulated industries, managers, who are usually thought of as maximizing shareholder value, have less discretion over firms’ actions. Therefore, firms in regulated industries are expected to have higher leverage ratios. I follow Barclay et al. (2006) and define telecommunications (SIC codes 4812 and 4813) before 1983, railroads (SIC code 4011) before 1981, trucking (SIC codes 4210 and 4213) before 1981, airlines (SIC code 4512) before 1979, and gas and electric utilities (SIC codes 4900–4939) as regulated.

Uniqueness.—Bradley et al. (1984) predict a negative relation between the uniqueness of a firm’s products, which is positively related to the expected bankruptcy costs, and leverage. I follow Titman and Wessels (1988) and use a uniqueness dummy variable that takes the value of one if a firm produces machines and equipment (firms with SIC codes 3400–3999) and of zero oth- erwise as an indicator of uniqueness.

Tax advantages of debt.—The tax advantages of debt may vary with a firm’s profitability, the volatility of its earnings, its tax-loss carry forwards and its nondebt tax shields. I use the ratio of investment tax credits to assets as a proxy for nondebt tax shields, , which is expected to beitem 208/item 6 negatively related to the tax advantages of debt.32

Volatility.—Bradley et al. (1984) show that a firm’s optimal leverage is negatively related to the variability of its value. Following Bradley et al. and Titman and Wessels (1988), I use the standard deviation of the percentage change in a firm’s annual operating income (item 13) as a proxy for its volatility.

Past returns.—Welch (2004) finds that firms do not issue or repurchase debt in order to return to their target leverage ratios and, therefore, capital structure is largely determined by past stock returns. I measure past returns for a period of 5 years ending in December of the year preceding the year of the observation.

32. As Graham (1996) notes, indirect proxies for a firm’s tax status can be misleading because of their high correlations with other explanatory variables. Therefore, I also perform regressions using the database of marginal tax rates (MTRs) for Compustat firms, provided by John Graham. Simulated MTRs do not suffer from the deficiencies of other tax proxies. However, Graham’s database includes only a subset of all Compustat firms used in the analysis, thus reducing the size of the sample substantially. Using MTRs does not significantly change the coefficients on the competitive-interaction-related variables.

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2402 Journal of Business

B. Data and Methods

The source of the data used in the empirical tests is the Compustat Annual Industrial Files.33 The sample consists of all Compustat firms belonging to nonmonopolistic four-digit SIC industries, with SIC codes ranging between 1000 and 5999, and having a complete record on the main variables used in the analysis. The reason for excluding financial companies (SIC codes 6000–6799) is Rajan and Zingales’s (1995) observation that banks’ and in- surance companies’ debt liabilities are not directly comparable to debt of nonfinancial firms. The sample period is 1950–2003. In addition, I perform robustness tests using other time periods. I eliminate extreme outliers, which are defined as firms belonging to the top and bottom half percentiles of market- to-book ratios, collateral, and profitability ratios in each year of the sample. Alternative truncation rules do not influence the results materially. The number of firm-years that satisfy the aforementioned criteria is 148,946 for the full sample.

Table 1 presents descriptive statistics of the measures of competitive in- teraction and the control variables used in the empirical tests. Section 1 of table 1 contains summary statistics of the proxies for the degree of interaction among firms, while section 2 contains descriptive statistics of other factors that are expected to affect firms’ leverage choices and summary statistics of the book and market leverage ratios.

The first two rows in section 1 contain the statistics of the number of firms operating in four-digit SIC industries. In the first row, the statistics are cal- culated on an industry level (each industry gets equal weight regardless of the number of firms operating in it), while in the second row the statistics are calculated on a firm level (industries with more firms get higher weights). The number of firms in a four-digit SIC industry ranges between 2 and 351, with a mean of 11.6 and a median of 7 (36.5 and 18 on a firm level). Since the natural logarithm of the number of firms is used as a measure of competitive interaction in the empirical tests, rows 3 and 4 present the statistics for the logarithm of the number of industry participants. Rows 5–6 present the sum- mary statistics for the adjusted competitive strategy measure, . The meanC̃SM and median are positive, but not very high in absolute value when theC̃SM statistics are calculated both on a firm level and on an industry level, indicating that the number of firms competing in strategic complements is somewhat larger than the number of firms competing in strategic substitutes. This finding is generally consistent with Sundaram et al. (1996), who estimate that firms in about half of the industries in their sample compete in strategic substitutes, while the rest compete in complements. There is a large variation in the values of across industries. Broad industry groups (according to the Fama-C̃SM French [1997] classification) with the highest average over the yearsC̃SM include entertainment (0.042) and alcoholic beverages (0.036). The lowest

33. Stock returns used in robustness checks are from the Center for Research in Security Prices.

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F irm

s in

O utput

M arkets

2403

TABLE 1 Summary Statistics of Measures of Competitive Interaction and Firm Characteristics

Mean SD Lower Quartile Median Upper Quartile Minimum Maximum N

A. Proxies for the Degree of Intersection

Number of firms 11.58 17.12 4 7 13 2 351 13,244 36.47 51.27 9 18 39 2 351 148,946

Log (number of firms) 1.99 .89 1.39 1.95 2.56 .69 5.86 13,244 2.97 1.09 2.2 2.89 3.66 .69 5.86 148,946

Adjusted CSM .987% 12.673% �5.511% 1.586% 7.755% �71.978% 58.182% 13,005 1.184% 9.227% �3.539% 2.053% 6.156% �71.978% 58.182% 148,322

Absolute adjusted CSM 9.281% 8.686% 3.168% 6.867% 12.570% .000% 71.978% 13,005 6.828% 6.318% 2.503% 5.025% 9.281% .000% 71.978% 148,322

B. Other Factors Related to Leverage

Market leverage .285 .249 .062 .232 .459 .000 1.000 148,946 Book leverage .251 .194 .088 .234 .375 .000 1.000 148,946 Market-to-book 1.461 1.190 .687 .957 1.541 .048 65.352 148,946 Log (assets) 3.694 2.171 2.197 3.581 5.116 �6.535 11.579 148,946 Profit margin .077 .259 .057 .123 .181 �7.598 .601 148,946 Collateral .547 .217 .409 .574 .705 .000 .970 148,946 Dividends-and-repurchases

dummy .473 .499 .000 .000 1.000 .000 1.000 148,946

Note.—The sample period is 1950–2003. Each firm-year included in the sample satisfies the following criteria: (1) a firm’s SIC code is between 1000 and 5999, and (2) a firm’s market- to-book ratio, collateral ratio, and operating profit margin do not belong to the top and the bottom half percentiles annually. In rows 1, 3, 5, and 7 the statistics are calculated on an industry level. In the rest of the table, the statistics are calculated on a firm level. The construction of the adjusted competitive strategy measure ( ) is described in Sec. III. The absolute adjustedC̃SM CSM is the absolute value of . Market leverage is the ratio of book value of debt to the sum of book value of debt and market value of equity. Book leverage is the ratio of book valueC̃SM of debt to the book value of assets. Market-to-book is the ratio of the sum of book value of debt and market value of equity to book value of assets. Log (assets) is the natural logarithm of assets, deflated by the Consumer Price Index. Collateral is the ratio of the sum of net fixed assets and inventories to assets. Profit margin is the ratio of operating profit to assets. Dividends- and-repurchases dummy equals one if a firm paid dividends or repurchased shares in a given year.

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2404 Journal of Business

values of belong to the defense industry (�0.071), coal (-0.070), andC̃SM mining (�0.045). The prediction of the model is regarding the relation between capital structure and the absolute value of , the statistics for which areC̃SM reported in rows 7–8. Mean absolute value of the is generally on theC̃SM same order of magnitude as the comparable measures reported in Sundaram et al.

Descriptive statistics of firms’ leverage ratios and factors affecting firms’ leverage choices, reported in section 2 of table 1, are similar to the statistics reported in recent studies by Frank and Goyal (2004) and Barclay et al. (2006). Mean book and market leverage ratios range between 25% and 30%, mean market-to-book ratio is about 1.5, while the median is substantially lower, at about one. Median firm in the sample is profitable, although operating profit margin has a high variation. Slightly more than half of the median firm’s assets are collateralizable, and slightly less than half of the firms in the sample pay dividends or repurchase shares.

Pearson correlation coefficients among the proxies for the extent of com- petitive interaction and the factors that are expected to affect leverage are presented in table 2. In addition to the correlations for the full sample, I report the correlations between the two measures of the extent of competitive in- teraction and all other variables for the subsample of firms competing in strategic substitutes (rows 2 and 5) and the subsample of firms competing in strategic complements (rows 3 and 6), as indicated by the sign of their in- dustries’ .C̃SM

The most important finding in table 2 is that the correlations between the logarithm of the number of industry participants and the absolute value of

are negative and relatively high in absolute value (�0.24 for the caseC̃SM of strategic substitutes and �0.37 for the case of strategic complements).34

This is expected, since the first measure is expected to be negatively associated with the extent of competitive interaction, while the second measure is ex- pected to be positively related to the degree of interaction. In general, the competitive interaction measures are not strongly correlated with other factors. (Most correlation coefficients reported in table 2 are, however, statistically significant at common levels.)

To test the relation between the extent of competitive interaction and lev- erage, I estimate regressions of the following type:

¯L p b � b I � b C � e , (14)i ,t 0 1 i, t j i , t i, t

where i and t are firm and time subscripts, respectively, is a measure ofLi, t

leverage, is a proxy for the extent of competitive interaction, and isI Ci, t i, t

the vector of control variables, discussed in the previous subsection. Most of the existing empirical tests of optimal capital structure (see, e.g.,

Smith and Watts 1992; Rajan and Zingales 1995; Frank and Goyal 2004;

34. These correlations are statistically signifiant at a 1% level.

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TABLE 2 Correlations among Measures of Competitive Interaction and Firm Characteristics

Log (No. Firms) Absolute CSM Market

Leverage Book Leverage Market-to-Book Log (Assets) Profit Margin Collateral Dividend Dummy

Log (number of firms): All firms 1.000 �.323 �.083 �.024 .147 �.083 �.177 �.055 �.210 Substitutes 1.000 �.240 .018 .030 .100 .007 �.155 .013 �.103 Complements 1.000 �.371 �.134 �.051 .167 �.132 �.187 �.084 �.265

Absolute adjusted CSM: All firms 1.000 .048 .028 �.043 .011 .023 .012 �.002 Substitutes 1.000 .044 .039 �.020 .010 �.002 .039 �.027 Complements 1.000 .047 .019 �.056 .010 .038 �.012 .010

Market leverage 1.000 .797 �.350 .195 .030 .309 �.011 Book leverage 1.000 �.146 .148 �.027 .263 �.071 Market-to-book 1.000 �.211 �.337 �.234 �.154 Log (assets) 1.000 .361 .236 .521 Profit margin 1.000 .237 .302 Collateral 1.000 .272 Dividends-and-repurchases

dummy 1.000

Note.—This table presents Pearson correlation coefficients among proxies for the extent of competitive interaction, leverage measures and firm characteristics, presented in table 1. The upper value in each cell in the first two rows is the correlation estimated using all firms satisfying the sample selection criteria. The middle and the lower value in each cell in the first two rows are the correlations estimated for firms competing in strategic substitutes and complements, respectively, as evidenced by the sign of their industries’ .C̃SM

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2406 Journal of Business

Barclay et al. 2006) pool cross-sectional and time-series observations and estimate the regressions using ordinary least squares (OLS). Given the large variation in firms’ capital structures over time, documented in Frank and Goyal, I add annual fixed effects by adding year dummy variables (the co- efficient estimates on which are not reported).35 The next section presents the results of the main tests.

V. Empirical Tests

As discussed above, I employ two proxies for the extent of competitive in- teraction among firms. Table 3 presents the results of the regressions of firms’ market and book leverage ratios on the number-of-firms-based proxy for the extent of competitive interaction and on the control variables discussed above, while table 4 presents the results using the proxy for the extent of interaction based on the absolute value of the adjusted competitive strategy measure,

. The first three columns of tables 3 and 4 present the results of regressionsC̃SM with market leverage as a dependent variable, while columns 4–6 present the results of regressions with book leverage. Columns 1 and 4 contain the results of regressions performed using the full sample, columns 2 and 5 present the results for the subsample of firms operating in industries characterized by competition in strategic substitutes, as indicated by negative industry ,C̃SM while columns 3 and 6 contain the results of regressions performed on the subsample of firms operating in industries with positive . The predictedC̃SM sign column shows the expected sign on each of the explanatory variables following from the discussion in the previous section.

Most of the coefficient estimates on noncompetitive-interaction-related fac- tors support the underlying theories. Consistent with the agency theories, the coefficients on the market-to-book ratio are significantly negative in all spec- ifications. Firm size, as proxied by the logarithm of assets, is found to be positively and significantly related to leverage. The coefficients on collateral are significantly positive. Consistent with the pecking order theory, the co- efficients on profitability are negative and significant. Similar to Frank and Goyal (2004), dividend-paying firms have significantly lower leverage than nonpayers.

The coefficients on the natural logarithm of the number of firms are negative and highly significant in both market leverage and book leverage regressions. This is true for the regressions estimated using the full sample, as well as for those estimated using the subsample of firms operating in industries charac- terized by competition in strategic substitutes and the subsample of firms competing in strategic complements. The economic effect of the number of industry rivals on firms’ capital structure choices is also significant. The ex- pected difference between the market leverage ratio of a firm operating in an

35. T-statistics are calculated using White heteroskedasticity-consistent variance-covariance matrices of the coefficient estimates.

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TABLE 3 Regressions of Leverage on the Logarithm of the Number of Industry Rivals

Predicted Sign

Market Leverage Book Leverage

All Firms Substitutes Complements All Firms Substitutes Complements

Intercept .160* .117* .191* .118* .098* .135* Market-to-book � �.038* �.044* �.035* �.010* �.012* �.009* Log (assets) � .030* .030* .029* .023* .023* .022* Collateral � .297* .307* .287* .248* .247* .248* Profit margin � �.171* �.205* �.151* �.114* �.136* �.102* Dividends and repurchases

dummy � �.118* �.113* �.122* �.098* �.089* �.104* Log (number of firms) � �.025* �.009* �.033* �.014* �.008* �.018* Number of observations 148,946 57,799 91,147 148,946 57,799 91,147

Adjusted 2R .225 .314 .233 .167 .132 .161

Note.—This table presents regressions of firms’ leverage ratios on their characteristics and on the natural logarithm of the number of firms operating in their industries, according to eq. (14). Industries are defined according to four-digit SIC classification. The variables are discussed in table 1. The predicted sign is a sign of the regression coefficient following from the discussion in Sec. IV. Pooled regressions are estimated using all time-series and cross-sectional observations using OLS with year dummy variables (the coefficients on which are not reported). Asterisk indicates statistical significance at 1% level.

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TABLE 4 Regressions of Leverage on the Absolute Value of the Adjusted Competitive Strategy Measure

Predicted Sign

Market Leverage Book Leverage

All Firms Substitutes Complements All Firms Substitutes Complements

Intercept .075* .087* .069* .070* .071* .070* Market-to-book � �.039* �.045* �.036* �.011* �.013* �.010* Log (assets) � .029* .030* .029* .023* .023* .022* Collateral � .287* .305* .276* .243* .244* .242* Profit margin � �.164* �.203* �.145* �.109* �.132* �.099* Dividends-and-repurchases

dummy � �.111* �.112* �.112* �.094* �.089* �.098* Absolute adjusted CSM � .174* .090* .225* .084* .052* .105* Number of observations 148,322 57,175 91,147 148,322 57,175 91,147

Adjusted 2R .233 .317 .273 .167 .133 .153

Note.—This table presents regressions of firms’ leverage ratios on their characteristics and on the absolute value of their industries’ , according to eq. (14). Industries are definedC̃SM according to four-digit SIC classification. The variables are discussed in table 1. The predicted sign is a sign of the regression coefficient following from the discussion in Sec. IV. Pooled regressions are estimated using all time-series and cross-sectional observations using OLS with year dummy variables (the coefficients on which are not reported). Asterisk indicates statistical significance at 1% level.

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Firms in Output Markets 2409

industry with 3 firms (log [number firms] ) and a firm competing in an≈ 1 industry with 20 firms (log [number firms] ranges between two percentage≈ 3) points for firms competing in substitutes and six and a half percentage points for the subsample of firms competing in complements.

Table 4 reports the regressions estimated according to equation (14), with the proxy for the extent of competitive interaction being the absolute value of the competitive strategy measure. The layout of table 4 is identical to that of table 3.

The coefficients on the control variables are, again, supportive of the un- derlying theories. Consistent with the prediction of the model, the coefficient estimates on the absolute value of are positive and highly significantC̃SM within the full sample and within the subsamples of firms competing in stra- tegic substitutes and complements. In order to access the economic significance of the relation between the absolute value of and leverage, note thatC̃SM moving from the 25th percentile of absolute (3.17%; see table 1) to theC̃SM 75th percentile (12.57%) causes an increase in market leverage that ranges between one and two percentage points, depending on the subsample.

Overall, the results in tables 3 and 4 strongly support the model’s predic- tions. The relation between the extent of competitive interaction and firms’ leverage ratios is positive for both proxies for the degree of interaction among product market rivals and for both subsamples of firms competing in strategic substitutes and those competing in complements. This relation is statistically significant in all the specifications and economically important in most of them. In what follows, I perform various robustness checks of the results in tables 3 and 4.

Table 5 presents the results of estimating equation (14) using a different estimation method, different control variables, and different sample periods. To save space, only the coefficients on the measures of competitive interaction are reported. The estimates of the coefficients on the control variables are generally consistent with the underlying theories. Otherwise, the layout of table 5 is similar to that of tables 3 and 4.

There is a problem with pooling time-series and cross-sectional observations and estimating regressions using OLS. When dealing with a panel data set, correlations among disturbances are a concern. Even abstracting from possible autocorrelations, estimating the cross-sectional correlations of disturbances is infeasible given the number of cross sections. A common way to deal with cross-sectional correlations is to add firm fixed effects (e.g., by subtracting a firm-specific time-series mean from each observation). However, while this procedure removes correlations among residuals caused by firm-specific ef- fects and preserves the information from the time-series variation in the sam- ple, it ignores most of the information contained in the variation across firms. Since the prediction of the model in Section II is regarding the relation between the cross-sectional variation in firms’ leverage and the competitive structure of industries firms operate in, information contained in the cross sections is crucial for the tests. Therefore, instead of adding firm fixed effects, I deal

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TABLE 5 Robustness Checks: Fama-MacBeth Estimation, Different Control Variables, Different Sample Periods

Market Leverage Book Leverage

Predicted Sign All Firms Substitutes Complements All Firms Substitutes Complements

Section 1: Fama-MacBeth regressions:

Log (number of firms) � �.016 �.020 �.010 �.011 �.019 �.005 (�8.82) (�4.85) (�2.74) (�8.03) (�5.04) (�2.09)

Proportion of negative coef- ficients on log (number of firms)

.889 (9.01)

.741 (4.00)

.574 (1.09)

.796 (5.35)

.796 (5.35)

.556 (.82)

Absolute adjusted CSM � .155 .112 .162 .099 .101 .085 (6.72) (3.84) (6.84) (4.36) (3.22) (4.03)

Proportion of positive coef- ficients on absolute ad- justed CSM

.778 (4.87)

.722 (3.61)

.796 (5.35)

.685 (2.90)

.611 (1.66)

.685 (2.90)

Section 2: Other control variables:

Log (number of firms) � �.032* �.026* �.036* �.019* �.019* �.020* Absolute adjusted CSM � .168* .076* .242* .078* .046* .111*

Section 3: Years 1965–2003:

Log (number of firms) � �.025* �.008* �.034* �.015* �.007* �.018* Absolute adjusted CSM � .172* .081* .229* .079* .041* .106*

Section 4: Years 1984–2003:

Log (number of firms) � �.031* �.016* �.039* �.020* �.014* �.023* Absolute adjusted CSM � .205* .110* .269* .122* .083* .153*

Note.—This table presents regressions of firms’ leverage ratios on their characteristics, the number of firms in their industries, and the absolute value of their industries’ , accordingC̃SM to eq. (14). The first section presents Fama-MacBeth cross-sectional regressions. T-statistics reported in parentheses are calculated using time-series standard errors of coefficient estimates. Rows 3–4 and 7–8 present the proportions of negative (positive) coefficients on the logarithm of the number of firms (absolute ), and the t-statistics for the differences between theseC̃SM proportions and .5. Sec. 2 presents the results of regressions with added control variables: regulation dummy, uniqueness dummy, tax status, and volatility of earnings. The construction of these variables is discussed in Sec. IV. The third and fourth sections of the table report the results of regressions in eq. (14) estimated for the time periods 1965–2003 and 1984–2003, respectively. Industries are defined according to four-digit SIC classification. The variables are discussed in table 1. Pooled regressions in secs. 2–4 are estimated using all time-series and cross-sectional observations using OLS with year dummy variables (the coefficients on which are not reported). Asterisk indicates statistical significance at 1% level.

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Firms in Output Markets 2411

with possible cross-sectional correlations by using the Fama-MacBeth (1973) method, which relies on a separate estimation of coefficients for each time period, and calculating time-series standard errors of estimates.36 Regardless of the true structure of the variance-covariance matrix of disturbances, period- by-period estimates are unbiased (although not efficient). Therefore, averaging annual coefficients provides unbiased and asymptotically efficient estimates of the true coefficients. The first section of table 5 presents the results of Fama-MacBeth cross-sectional regressions. The first and the second row con- tain the mean annual coefficients on the logarithm on the number of firms and the associated t-statistics. Similar to the results reported in table 3, the coefficients on the logarithm of the number of firms are negative and significant in all specifications.37 The third and the fourth row present the proportion of years in which the coefficient on the number of firms is negative and the t- statistic of the difference between this proportion and 0.5. In most cases, the proportion of negative coefficients on the logarithm of the number of firms is significantly higher than one-half. The next four rows present the results of Fama-MacBeth regressions using the absolute value of as a measureC̃SM of the extent of competitive interaction. Similar to table 4, the coefficients on

are positive and significant both for market and book leverage regres-C̃SM sions, and for all subsamples.

The second section of table 5 contains regressions estimated according to equation (14), where I add control variables discussed in Section IV but omitted from the base specification: regulation dummy, uniqueness dummy, a proxy for the tax advantages of debt, an estimate of the volatility of earnings, and past returns. Inclusion of these variables increases the explanatory power of the regressions but does not affect the sign and the significance of the coefficients on the competitive interaction proxies in any of the subsamples.

In order to make sure that the positive relation between the extent of com- petitive interaction and leverage holds during different time periods, I estimate the leverage regressions for periods 1965–2003 and 1984–2003. The reasons for choosing these periods are that Compustat significantly increased its cov- erage in 1965 and that the assignment of firms to four-digit SIC industries is more precise in the last 20 years of the sample. The results for the shorter subsamples are consistent with the results for the whole sample, and they seem to be slightly more economically and statistically significant than the full-sample results.

Frank and Goyal (2004) note that it is important to examine the robustness of the results for subsamples of firms with different characteristics. Therefore, each year I rank firms by their size, market-to-book ratio, collateral ratio, and profitability, and estimate the leverage regressions for subsamples of firms

36. Performing the tests using two-way fixed effects provides results that are weaker than those reported but still consistent with the model and significant in most cases.

37. Adjusting the time-series standard errors using Newey-West variance-covariance matrix does not materially affect the estimates of standard errors. The coefficient estimates on the competitive interaction measures remain significant in most cases.

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2412 Journal of Business

with the values of these variables above and below their cross-sectional me- dians. The results of the regressions for these subsamples are presented in table 6.

Columns 1–2 present the results of market leverage regressions, while col- umns 3–4 present the results of book leverage regressions. The negative and statistically significant relations between the two measures of leverage and the logarithm of the number of firms persist in all eight samples, as do the positive and significant relations between the measures of leverage and ab- solute .C̃SM

One of the possible criticisms of the competitive interaction measure that is based on the number of firms is that the Compustat database contains only public firms, thus understating the number of firms in each industry. Thus, the logarithm of the number of firms is, at best, an imprecise measure of the extent of competitive interaction. To avoid the “spurious precision” problem, I assign firms to four groups based on the number of industry participants and estimate the regressions in equation (14) using dummy variables assigned to each group. The groups are defined as (1) less than 5 firms in an industry, (2) between 5 and 12 firms, (3) between 13 and 32 firms, and (4) more than 32 firms.38 This assignment of firms to the extent-of-competitive-interaction groups also allows us to examine the monotonicity of the relation between the degree of competitive interaction and leverage. Table 7 presents the results.

The coefficients on the control variables are consistent with the underlying theories. The coefficients on the interaction groups dummies are not important by themselves. What is important is the differences between the coefficients on the dummies of adjacent groups. The results of the Wald tests for these differences are presented in curly brackets. Moving from the group of firms belonging to industries with less than five product market rivals to the group of firms operating in industries with five to twelve rivals results in a decrease of about two percentage points in firms’ market leverage ratios, and of about one percentage point in firms’ book leverage ratios. The difference between the coefficients on the dummies for these two groups of firms is statistically significant in all cases in market leverage regressions and is marginally sig- nificant in most cases in book leverage regressions. Similarly, when one moves to the group of 13–32 industry participants, the average market leverage decreases by about two percentage points, while moving to the group of firms operating in industries with more than 32 rivals (and, presumably, a low degree of competitive interaction) reduces the average market leverage by between 2.5 and 6.5 percentage points depending on the subsample, and reduces the average book leverage by about two percentage points. These differences are, again, statistically significant in most cases. Overall, the results in table 7 indicate that the conclusions obtained using the number-of-firms-based mea- sure of competitive interaction are not likely to be affected by the “spurious

38. The assignments are based on the natural logarithm of the number of firms rounded to the closest integer.

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TABLE 6 Robustness Checks: Regressions for Subsamples of Firms Grouped by Characteristics

Market Leverage Book Leverage

Predicted Sign Above Median Below Median Above Median Below Median

Ranking by asset size: Log (number of firms) � �.011* �.034* �.003* �.021* Absolute adjusted CSM � .084* .223* .028* .113*

Ranking by market-to-book: Log (number of firms) � �.013* �.022* �.017* �.013* Absolute adjusted CSM � .117* .113* .116* .068*

Ranking by profitability: Log (number of firms) � �.010* �.039* �.007* �.020* Absolute adjusted CSM � .082* .246* .047* .104*

Ranking by collateral: Log (number of firms) � �.019* �.035* �.008* �.025* Absolute adjusted CSM � .164* .180* .074* .089*

Note.—This table presents regressions of firms’ leverage ratios on their characteristics and on the natural logarithm of the number of firms operating in their industries, according to eq. (14). Firms are divided into subsamples according to whether their asset size, book-to-market ratio, collateral ratio, and profitability are above or below their respective annual medians. Pooled regressions are estimated using all time-series and cross-sectional observations using OLS with year dummy variables (not reported). Asterisk indicates statistical significance at 1% level.

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TABLE 7 Robustness Checks: Regressions for Groups of Number of Rivals

Market Leverage Book Leverage

Predicted Sign All Firms Substitutes Complements All Firms Substitutes Complements

Market-to-book � �.038* �.044* �.035* �.01* �.012* �.009* Log (assets) � .029* .029* .029* .023* .022* .022* Collateral � .296* .298* .286* .248* .242* .247* Profit margin � �.170* �.200* �.150* �.113* �.133* �.102* Dividend-and-repur-

chases dummy � �.118* �.114* �.121* �.098* �.090* �.103*

Number of firms less than five .112 .109 .129 .085 .036 .036

Number of firms be- tween five and 12 .091 .082 .106 .080 .069 .092

{�3.78} {�3.05} {�2.52} {�1.90} {�2.33} {�.65} Number of firms be-

tween 13 and 32 .075 .062 .032 .063 .067 .057 {�2.82} {�2.06} {�3.34} {�3.54} {�.27} {�5.62}

Number of firms more than 32 .013 .035 .014 .040 .038 .045

{�10.40} {�2.56} {�9.09} {�4.62} {�3.79} {�1.88} Number of

observations 148,946 57,799 91,147 148,946 57,799 91,147

Adjusted 2R .696 .715 .637 .633 .707 .678

Note.—This table presents regressions of firms’ leverage ratios on their characteristics and on the dummy variables indicating whether the firm belongs to a certain group of number of industry rivals. The groups are defined as (1) less than 5 firms in an industry, (2) between 5 and 12 firms, (3) between 13 and 32 firms, and (4) more than 32 firms. The t-statistics of the Wald tests for the differences between the estimates on the dummies on two adjacent number-of-firms groups are reported in curly brackets. The predicted sign is a sign of the regression coefficient following from the discussion in Sec. IV. Pooled regressions are estimated using all time-series and cross-sectional observations using OLS with year dummy variables (the coefficients on which are not reported). Asterisk indicates statistical significance at 1% level.

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precision” problem. In addition, firms’ market and book leverage ratios seem to be monotonically decreasing in the extent of competitive interaction in their industries.

I perform additional robustness checks that are not reported. First, I repeat the analysis while replacing the four-digit SIC classification with Fama and French’s (1997) industry classification. The results are generally consistent with the model, although often weaker than those reported above. Second, Bradley et al. (1984) and Smith and Watts (1992) note that there are potential problems with the regulated subsample. I repeat the analysis while excluding firms in regulated industries and find no material changes in the results. Third, assigning firms to industries based on their SIC codes implicitly assumes that firms operate in only one SIC industry. However, there are many “conglom- erate” firms, operating divisions in multiple industries. The assignment of such firms to an SIC code of one of its divisions is sometimes arbitrary. Thus, I repeat the analysis while eliminating multidivision firms found in the Com- pustat Industry Segment (CIS) database.39 The results of these tests are, again, in line with those for the full sample.

VI. Conclusions

This article presents a stylistic model that demonstrates a positive relation between firms’ optimal leverage and the extent of competitive interaction in their industries. This result can be seen as a generalization of the Brander and Lewis (1986) type of limited liability models that show the conceptual dif- ference between optimal capital structure choices in a duopoly and in a per- fectly competitive industry. An important feature of the model is that, unlike Brander and Lewis and most subsequent studies of the interaction between firms’ financial and operating decisions, it is not limited to a specific type of product market competition (e.g., Cournot). The model demonstrates that, regardless of the type of competition in output markets, the extent of com- petitive interaction among firms positively affects their optimal leverage when- ever debt carries a strategic advantage.

The model’s predictions are tested using 54 years of Compustat data, while employing two proxies for the extent of interaction among firms in product markets. They are based on the number of firms operating in an industry and on an estimate of the effects of firms’ actions on their rivals’ value functions and resulting strategies. The empirical tests demonstrate that the extent of interaction among product market rivals is an important determinant of their market and book leverage ratios. Statistically and economically significant relations between the proxies for the degree of interaction and leverage are

39. CIS database, however, does not report segments’ SIC codes prior to year 1984. In addition, its coverage decreases dramatically in 1999. Thus, I am able to perform the tests on a subsample of single-division firms only for years 1984–98.

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2416 Journal of Business

robust to various time periods, different subsamples, and different regression specifications and estimation methods.

Appendix

Since firms 1 and 2 are symmetric, I present only the proofs for firm 1. Proof of proposition 1.—Differentiating firm 1’s equity value in equation (3) with

respect to and equating the resulting expression to zero givesc1

1 � F � rc1 2∗c (F , c ) p . (A1)1 1 2 2

The expression for is similar. Both firms’ reaction functions in output market∗c (F , c )2 2 1

choices are linear, and therefore, the equilibrium, if it exists, is unique. Since FrF !

, the reaction functions intersect, and the equilibrium exists. The stability condition1 (see Dixit 1984; Tirole 1988) is

2 2 2 2� V � V � V � V1 2 1 2 1 . (A2)2 2 2 2�c �c �c �c1 2 2 1

In this case,

2 2� V � V1 2 p p �2,2 2�c �c1 2

and

2 2� V � V1 2 p p �r.2 2�c �c2 1

Thus, the stability condition in (A2) is satisfied. Solving the system of two equations given in (A1) for and a similar expression for results in∗ ∗c (F , c ) c (F , c )1 1 2 2 2 1

2 � r � 2F � rF1 2∗c (F ,F ) p , (A3)1 1 2 24 � r

and similarly for ; in equation (A3) is clearly increasing in . It∗ ∗c (F , F ) c (F , F ) F2 1 2 1 1 2 1

is decreasing in for , and is increasing in for .F r 1 0 F r ! 02 2

Proof of proposition 2.—Plugging firms’ optimal operating choices given in equation (A3) for firm 1 and a similar expression for firm 2 into the expression for the total value of firm 1 in equation (4) gives

2[ ] [ [ ] ]2 � r � 2F � rF 2 � r � 2 � r F � rF1 2 1 2∗V (F , F ) p . (A4)1 1 2 2 2[ ]4 � r

Differentiating equation (A4) with respect to and equating the resulting expressionF1

to zero gives

2 [ ]r 2 � r � rF21∗F (F ) p . (A5)1 2 24 2 � r

The expression in equation (A5) is decreasing in for (strategic substitutes),F r 1 02

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Firms in Output Markets 2417

and increasing in for (strategic complements). Therefore, debt-level reactionF r ! 02

function of firm 1 is downward sloping for the case of strategic substitutes and is upward sloping for the case of strategic complements. Equation (A5) is positive for all admissible values of r ( ), since in equilibrium . The exception�1 ! r ! 1 0 ≤ F ≤ 12

is the case of , in which case .∗r p 0 F (F ) p 01 2

Proof of proposition 3.—Obtaining the reaction function of firm 2, , similarly∗F (F )2 1

to equation (A5), and solving the resulting system of two equations in and givesF F1 2

the equilibrium debt levels:

2r∗ ∗F p F p . (A6)1 2 24 � 2r � r

The proof of existence, uniqueness, and stability of equilibrium is similar to that in the proof of proposition 1. Plugging equation (A6) into the expression for firms’ equilibrium operating choices in equation (A3) gives the equilibrium operating choices of firms 1 and 2:

2∗ ∗c p c p . (A7)1 2 24 � 2r � r

Plugging equation (A7) into firm 1’s value function in equation (4) results in the equilibrium firm values:

2[ ]2 2 � r ∗ ∗V p V p . (A8)1 2 2 2[ ]4 � 2r � r

Dividing equation (A6) by equation (A8) gives firms’ quasi-market leverage ratios (defined as the face value of debt divided by the market value of the firm):

∗ ∗ 2 2F F 1 r [4 � 2r � r ]1 2 p p . (A9)∗ ∗ 2V V 2 2 � r1 2

Plugging firms’ equilibrium output market choices in equation (A7) into equation (1) results in the equilibrium probabilities of firms 1 and 2 being solvent:

22 � r∗ ∗prob (solvency) p prob (solvency) p . (A10)1 2 24 � 2r � r

Multiplying the expression in equation (A9) by the probability of the solvent state in equation (A10) gives firms’ leverage ratios:

∗ ∗ 2D D r1 2 p p . (A11)∗ ∗V V 21 2

Firms’ equilibrium leverage in (A11) is clearly increasing in and is, thus, increasing2r in . Both equations (A6) and (A11) as .FrF r 0 r r 0

Proof of proposition 4.—Firm 1’s profit can be expressed in a general form as

p p S (q , p ) � C (q ), (A12)1 1 1 1 1 1

where denotes the firm’s sales (revenues) and denotes its total costs, whileS C q1 1 1

and denote its production quantity and price, respectively. I make standard as-p1

sumptions that revenues are twice continuously differentiable with respect to the choice

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2418 Journal of Business

variable and that costs are continuously differentiable with respect to quantity and are increasing in quantity.

Assume first that firms compete à la Cournot and that their choice variable is quantity. Then, firm 1’s profit function in equation (A12) can be rewritten as

p p S (q ,p (q )) � C (q ), (A13)1 1 1 1 1 1 1

for a given . In equilibrium,q2

dp dS �C1 1 1 p � p 0, (A14)

dq dq �q1 1 1

or

dS �C1 1 p 1 0, (A15)

dq �q1 1

and similarly for firm 2. Thus, around equilibrium and, similarly,(dS /dq ) 1 01 1

, and , and . It follows, there-(dS /dq ) 1 0 sign(dS ) p sign(dq ) sign(dS ) p sign(dq )2 2 1 1 2 2

fore, that around equilibrium

2 2d p d p1 1sign p sign . (A16)( ) ( )dq dq dS dS1 2 1 2

Now assume that firms compete in prices. Then firm 1’s profit function in (A12) can be rewritten as

p p S (q (p ),p ) � C (q (p )), (A17)1 1 1 1 1 1 1 1

for a given , where . In equilibrium,q (�q /�p ) ! 02 1 1

dp dS �C �q1 1 1 1 p � p 0. (A18)

dp dp �q �p1 1 1 1

Since and in equilibrium(�C /�q ) 1 0 (�q /�p ) ! 0,1 1 1 1

dS �C �q1 1 1 p ! 0, (A19)

dp �q �p1 1 1

and similarly for firm 2. Thus, around equilibrium, and, similarly,(dS /dp ) ! 01 1

, and , and . Therefore,(dS /dp ) ! 0 sign(dS ) p �sign(dp ) sign(dS ) p �sign(dp )2 2 1 1 2 2

around equilibrium

2 2d p d p1 1sign p sign . (A20)( ) ( )dp dp dS dS1 2 1 2

Proof of proposition 5.—Differentiating firm 1’s value function in equation (4) with respect to firm 1’s strategy and equating the resulting expression to zero gives firm 1’s optimal strategy as a function of firm 2’s strategy:

1 � rc2∗c (c ) p , (A21)1 2 2

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Firms in Output Markets 2419

and the resulting value of firm 1:

2[ ]1 � rc2∗V (c ) p . (A22)1 2 4

Denote the change in firm 2’s operating strategy between times and t byt � 1 . From equation (A21), the resulting change in firm 1’s operatingDc p c � c2 2,t�1 2,t

strategy is

1 � rc � [1 � rc ] rDc2, t�1 2, t 2∗ ∗ ∗c � c p Dc p p � . (A23)1, t�1 1, t 1 2 2

From equation (A22), the resulting change in firm 1’s value is

2 2[ ] [ ]1 � rc � 1 � rc2,t�1 2,t∗ ∗ ∗V � V p DV p1,t�1 1,t 1 4

[1 � rc � 1 � rc ][1 � rc � 1 � rc ]2,t�1 2,t 2,t�1 2,t p (A24)

4

rDc [2 � 2rc � rDc ]2 2,t 2 p � .

4

Dividing equation (A24) by equation (A23) gives

∗DV 2 � 2rc � rDc1 2,t 2 p . (A25)∗Dc 21

Assume that the time-series changes in , , are drawn from an independent andc Dc2 2

identical distribution with mean m and standard deviation j. Then,

∗ 2DV j1Cov , Dc p �r . (A26)2( )∗Dc 21

Also, note that the cross-partial derivative of firm 1’s value function in equation (4) with respect to its own and its rival’s aggressiveness choices gives

2� V1 p �r. (A27)

�c �c1 2

Thus, the cross-partial derivative in equation (A27) is a positive multiple of the co- variance between the ratio of the change in firm 1’s profit to the change in its sales, and the change in firm 2’s sales in equation (A26).

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