Strategic Interaction of Capital Structures:
A Spatial Econometric Approach
Zhengyu Zhang
Center for Econometric Study
Shanghai Academy of Social Sciences
[email protected]
This Version: December 2011
Abstract
In this article, we suggest an alternative setting for empirically examining firms’
strategic interaction in choosing their capital structure. Following Lyandres (2006)’s
theoretical model, this article explicitly focuses on how the competitive interaction in
output market may induce a firm to take the rival firms’ capital structure into account in
deciding its own capital structure. It is also shown that the direction of such strategic
response depends on whether the output market competition is in strategic substitutes or
in strategic complements. A spatial regression model is introduced to test the relationship
between firms’ financial choices and their product market strategies. The empirical
evidence suggests that inclusion of the spatially lagged term of a firm’s leverage could be
empirically significant in explaining the optimal choice of a firm’s financial structure.
Key words： Capital structure; Output market competition; Spatial regression;
JEL: C21; G32; L13;
1. Introduction
A relatively new literature, dating back to the seminal work of Brander and Lewis
(1986), is examining the effects of the interaction among firms in output market on their
financial and operating decisions. Generally, this strand of research argues that debt
allows the firm to commit to a certain strategy to its rivals in the output market. Almost all
models in these studies can be boiled down to two main theories. One theory, developed
by Brander and Lewis (1986) and Maksimovic (1988), establishes that due to the effect of
limited liability, the leverage will cause firm to behave aggressively, which makes
competition tougher. The other class of predatory model, represented by Bolton and
Scharfstein (1990), argues that where leveraged firms decrease output, the unleveraged
rival has the incentive to increase output or cut prices to drive the leveraged firm out of
market and as a result, debt commits leveraged firms to behave less aggressively, which
makes competition softer. One undesirable feature of the limited liability effect models is
that the theoretical predictions they derive may heavily rely on the specific form of product
market competition. For example, the models that are based on the choice of debt in the
first stage as a commitment to the subsequent product market strategy in the second stage,
have traditionally been developed in a Cournot type quantity competition setting (Brander
1
and Lewis, 1986; Maksimovic, 1988; Glazer, 1994). In this competition setting, debt
commits firms to a choice of higher quantity than in the absence of debt benefits. However,
these results could change dramatically if alternative frameworks of oligopolistic
competition are adopted. Showalter (1995) finds that the optimal strategic debt choice of
Bertrand competitors depends on the type of uncertainty of the output market. When costs
are uncertain, price competing firms will not use debt and the use of debt is strategically
advantageous only if demand conditions are uncertain. Interestingly, Schuhmacher (2002)
comes up with the opposite results. He shows that the capacity-price competitors, by
committing to capacity levels prior to setting prices, will use no debt when there is demand
uncertainty and will use high debt levels when there is cost uncertainty.
As an attempt to mitigate the weakness that the derived results rely on certain
competition type, Lyandres (2006) develops a model where firms are not necessarily
required to compete against each other by quantity or by price. Lyandres shows that,
regardless of whether firms’ product market choices are strategic substitutes or strategic
complements, 1the stronger the extent of competitive interaction among rival firms in
output market, the larger the strategic benefit of debt.
Although the theoretical link between firms’ financial choices and product market
strategies has been investigated by numerous aforementioned models, none of them
explicitly answers the following question: as a strategic response to the rival firms
increasing leverage to commit a more aggressive market strategy, will a firm have the
incentive to raise or reduce its own debt accordingly? If so, how the direction and
magnitude of such strategic adjustment is determined? This paper extends the existing
literature by theoretically and empirically examining how the competition among firms in
output market may induce strategic interaction among these firms’ financial structures.
Specifically, the current study contributes to the exiting literature from the two
dimensions that follow:
Theoretically, by revisiting Lyandres (2006)’s model, we explicitly show how the
competitive interaction in output markets may induce a firm to take its rival firms’ capital
structures into calculus in deciding its own one. Although the basic setting of our
theoretical analysis looks similar to Lyandres’, it should be pointed out that our major
interest and the consequent insight focus on the strategic financial decision-making
among competing firms instead of the relationship between the extent of competition and
the optimal leverage. Most research on determination of corporate capital structure
mainly builds on traditional hypotheses, such as tradeoff or pecking order theory, which
largely ignore interactions among firms' financial policies. However, as it has been well
recognized by the literature that interactions in the product markets can generate
interactions among financial policies, it might be expected that firms do not make
financing decisions in isolation of one another. Being interested in off-equilibrium
According to Bulow et al. (1985), strategic substitutes and strategic complements are defined by
whether a firm’s more aggressive strategy lowers or raises its rivals’ marginal profits.
1
2
outcome by focusing on firms' best response in their financial decision making instead of
equilibrium itself, our analysis provides an initial and intuitive bridge between the
corporate finance of capital structure and the industrial organization structure in which
the firm operates. Consequently, such off-equilibrium analysis contributes to further
understanding the factors that could be responsible for determining a firm's leverage ratio.
Recall that in Lyandres (2006), the debt level is shown to be positively correlated to the
extent of competition regardless of whether firms’ product market choices are in strategic
substitutes or complements. In other words, the explicit role played by the firms’ product
strategy type remains silent there. By contrast, the main theoretical insight here is that the
direction of such strategic leverage adjustment depends on whether the output market
competition is in strategic substitutes or in strategic complements. Furthermore, it can be
shown that the magnitude of such adjustment monotonically relies on the extent of
competition in output market.
Empirically, we relate the theoretical predictions to a spatial autoregressive model
and show that the resulting empirical implications can be tested within this spatial
econometric framework. We run a series of spatial panel data model regressions to
estimate the response slope of a firm’s leverage ratio with respect to its rivals within the
same industry for a broad sample of manufacturing firms. The empirical results suggest
that inclusion of the spatially lagged term of a firm’s leverage could be empirically
significant in explaining the optimal choice of a firm’s financial structure.
Many existing studies aimed to empirically examining the link between the extent of
competition and a firm’s financial decisions such as IPO timing (Chod and Lyandres, 2011),
leverage choice (Lyandres, 2006), payout policy (Grullon and Michaely, 2006) and
repurchasing (Massa et al., 2007) often require proxies for the degree of competitive
interaction among product market rivals, given the degree of product market competition
not being straightforwardly observed. The proxies usually employed in these studies
include the number of rival firms in the same industry, estimated effect of firms’ actions
on their rivals’ marginal profits, Herfindahl index and among others. These empirical
studies, however, share two common features that should be noted. First, the proxies, in
entering the regression equation, are treated as one of the exogenous determinants of
optimal leverage like firm size and profitability, among others. Second, the regression
model is often estimated by a OLS-based method. Intuitively, the proxying method is
appropriate only if the number of competing firms is substantially large and the influence
of any one firm is too limited to affect the entire competition structure in output market.
Only under this circumstance should the proxies for the extent of competition be regarded
approximately exogenous. Otherwise, when the number of competing firms is moderate
and a single firm’s operating strategy may have significant impact on the rest, exogeneity
of the proxying variable and justifiability of the resulting OLS-based estimation method
seems to be debatable. By contrast, the spatial econometric framework manages to
circumvent the dilemma like this: on the one hand, it accommodates possible endogeneity
3
of intra-industry competition explicitly in the model specification; on the other hand, there
have already existed numerous well-developed estimation methods to cope with such
endogeneity. In this sense, this paper supplements the existing literature by providing an
alternative empirical approach to examining the relation between firms’ financial choices
and output market competition.
The remainder of this paper is organized as follows: Section 2 revisits Lyandres
(2006)’s model and presents our theoretical predictions. Section 3 lays down the empirical
framework and summarizes the empirical implications of the model. Section 4 includes
the empirical evidence in support of the theoretical results and Section 5 concludes.
Technical details are relegated to the Appendix.
2. Theoretical Motivations
While Lyandres (2006) concentrates on the equilibrium relation between the degree of
competitive interaction on output market and the debt levels chosen by its participants,
our subsequent analysis explicitly highlights the strategic interaction of firms’ financial
choices induced by their competition in output market. To save space while keep our
expositions complete, the rest of this section will be organized like this: we briefly
re-introduce the key elements of Lyandres’ model in Section 2.1. Our main theoretical
prediction is summarized in a proposition with some discussions coming in order in
Section 2.2. The proof is relegated to the Appendix.
2.1 The Model
Lyandres (2006)’s model has two stages. In the first stage,
enter the market and simultaneously choose their debt level
firms,
,
’s. In the second stage,
information concerning the financial structures of these firms is disclosed and
shareholders of each firm choose their aggressiveness of market strategy
’s to compete
against each other in the product market.
A firm’s market strategy is assumed to affect its expected value from three aspects.
First, a more aggressive strategy, corresponding to greater
, generates higher cash flows
once it succeeds. We assume that the cash flows generated by the project are proportional
to the aggressiveness chosen by the firm through a parameter
aggressiveness
.1 Second, the greater
is, the more likely the project is to fail. Third, the probability of project
success relies not only on the operating decisions made by the firm itself but also on the
strategies chosen by its rivals. All the three aspects are incorporated into the following
shareholders’ expected payoff function:
(1)
where
,
is the expected value of firm ’s equity,
and
denote the aggressiveness
In Lyandres’ model, the marginal benefit of aggressiveness
is standardized to one. It is relaxed in
Eqn.(1) since we intend to emphasize that the strategic response among firms’ financial choices is shown
to rely only on the extent of market competition while independent of this parameter . See Proposition 1
in Section 2.2.
1
4
and debt level chosen by firm ,
reflects the marginal cash flow generated by an
aggressive strategy. The parameters
determine the extent of impact of a
, then
firm’s strategy upon the probability of another firm’s project’s success. If
and
firms
strategy
compete in strategic substitute. Increasing the aggressiveness of firm
reduces the marginal profit of firm
default. For
, firms
aggressiveness of firm
and
’s strategy
’s
and also increases its probability of
compete in strategic complements. Increasing the
raises the marginal profit of firm
, firms
reduces its probability of default. In the marginal case
and
and also
operate
independently in output market and firm ’s strategy has no impact on the cash flows the
firm
receives. Consequently,
is the probability of success for firm
and this probability decreases with its own aggressiveness and is related to other firms’
operating strategies through
,
. The term
reflects a firm’s equity value
if the project succeeds. It is the residual cash flows generated by a successful project after
the debt obligations are met.
2.2 Theoretical Prediction and Discussion
Similar to Lyandres (2006), we can solve the game using backward induction. To keep
the analysis manageable and to highlight the essential characteristics, we make the
following simplifications:
Assumption 1. (i)
’s,
, are equal to each other, namely,
，and they satisfy (ii)
.
Assumption 1 is implicitly maintained in Lyandres (2006)’s model. Assumption 1-(i)
requires the extent of competition is homogenous among firms in output market and
excludes the coexistence of competition both in strategic substitutes and strategic
complements among the firms considered. (ii) implies for any ，
, which
requires that the total extent of competition from all the rival firms should have an upper
bound. As the number of firms becomes larger, the extent of competition from a single
rival firm becomes smaller. Without (ii), the system may have no equilibrium solution as
goes to infinity. Our main theoretical motivation then can be summarized by the
following proposition.
Proposition 1. (i) The slope of the debt level reaction function depends on extent of
market competition
operating aggressiveness
and is independent of the marginal benefit of
. (ii) Under Assumption 1, for any
firms compete in strategic substitutes, namely,
, then
compete in strategic complements, namely,
, then
Assumption 1,
decreases with
as
and
, if the
，; if the firms
. (iii) Under
.
Proposition 1 highlights some new features of the relationships between firms’ financial
choices and their product market competition, and thus supplements the existing
literature in several aspects. First, it explicitly relates how and to what extent a firm
strategically adjusts its financial structure in response to the change of its rival firms’ to
the parameters of competition structure
. Lyandres(2006) derives the
5
relationship between extent of competition in product market and firm’s optimal leverage,
but he does not derive the explicit form of firm’s leverage function in response to other
firms’ leverage change. Second, it clarifies the exact role played by the firms’ product
strategy type, i.e. strategic substitutes or strategic complements, in determining the
direction of strategic interaction of firm’s financial structures. Proposition 1-(ii) should be
interpreted carefully. Essentially, it characterizes how a firm will reacts instantaneously
towards its rivals’ deviation from the equilibrium leverage. Intuitively, consider the firms
compete in strategic substitutes and at time 0, all of them stayed at their equilibrium debt
levels. Assume that at time 1, one firm developed or acquired a new technique. This
positive external shock may induce this firm to raise its debt level and undertake a more
aggressive market strategy, e.g. increase the output. The Proposition then says that for the
rest of the firms, their optimal reactions towards such change are to instantaneously
reduce their leverages, which is consistent with the conclusion of Brander and Lewis
(1986). Third, the monotonic relationship between the extent of market competition and
the magnitude of the strategic adjustment is useful. It allows me in the subsequent
empirical analysis to indirectly compare the extents of market competition across different
industries through the estimated magnitude of strategic adjustment of financial structures.
To get a visual impression of Proposition 1-(iii), we plot the function graphs of
for
in Figure 1. The most important feature of
Figure 1 is that
both
and
always decreases with
and
by looking into
increases with
for
.
Figure 1. Graphs of
with Different
’s.
3. Empirical Framework
In this section, we relate the theoretical results derived in Section 2 to a class of spatial
autoregressive models and establish the framework that can be used to test the theory.
According to Proposition 1, we are interested in both the magnitude and the sign of
. In this position, we argue that spatial econometrics provide us an appropriate
approach to estimating the reaction slope in practice. Specifically, we can estimate the
6
following regression equation to learn about
:
(2)
，
.
Eqn. (2) is termed as spatial autoregressive (SAR) model. As usual, each
，
contains a set of exogenous determinants of firm leverage
, such as firm
，
size and profitability, among others. Generally, the most important component of SAR
model is the spatial weights
, which determine the structure of cross
sectional dependence among cross sectional agents. Parameterized SAR model requires
specification of these spatial weights in line with certain economic theories or practical
principles by the applied researchers.1 The parameter of most interest in model (2) is the
spatial autoregressive coefficient
, whose magnitude measures the extent of the relevant
cross-sectional dependence and whose sign suggests the direction of such dependence. For
our problem, as the cross sectional dependence of firms’ financial structures is caused by
their competition in product market, one may expect the relevant spatial weights
can be defined from the perspective of product market competition. See
Section 4.3 for a detailed description of spatial weighting schemes for this paper.
Within the empirical setting of Eqn. (2), the empirical implications of theoretical
predictions can be summarized as follows: First, the sign of
should be determined by
firms’ product market competition strategy. If they compete in strategic substitutes, one
has
. Second, by Proposition 1-(iii), the absolute value of
is positively related to
the extent of firms’ competition in product market.
As one feature of this SAR model (2), the spatially lagged term
correlated with the error term
is
, and such endogeneity then precludes any OLS-based
estimation methods. To get a consistent estimate of the coefficients, a number of
estimation procedures have been developed for SAR model, including the method of
moments by Kelejian and Prucha (1999, 2010), the method of quasi-maximum likelihood
estimation by Lee (2004), the method of two-stage least squares by Kelejian and Prucha
(1998), Lee (2003), Zhang and Zhu (2010) and the generalized method of moments by Lee
(2007), Lin and Lee (2010), and Liu et al. (2010).
It is instructive to compare the spatial econometric framework with the empirical
setting in the prior literature. The close relationship between firms’ financial choices and
their competition in output market has been recognized by many financial economists.
Empirical test as such requires proxies for the degree of competitive interaction among
product market rivals, given the degree of product market competition not being
straightforwardly observed. The proxies usually employed in these studies include the
number of rival firms in the same industry, estimated effect of firms’ actions on their
rivals’ marginal profits, Herfindahl index and among others. For example, Lyandres(2006)
As one of the recent advances, spatial econometrics has developed models which relax parameterization
of the spatial weights and allow for nonparametrically specified spatial weights (Pinkse and Slade 2002).
But the issue of nonparametric spatial weights will not be explored in this paper.
1
7
regresses the leverage on these proxies and other exogenous determinants of optimal
leverage to empirically explore the relationship between optimal leverage and extent of
competition. In addition, such tactics has been used by Chod and Lyandres (2011) to
examine the relationship between product market competition and firms’ IPO timing and
by Grullon and Michaely (2006) and Massa et al. (2007) to empirically investigate the
relationship between extent of competition and firms’ payout policies and repurchasing
decisions, respectively.
These empirical studies, however, share two common features that should be noted.
First, the proxies, in entering the regression equation, are treated as one of the exogenous
determinants of optimal leverage like firm size and profitability, among others. Second,
the regression model is often estimated by the OLS-based method. Arguably, capital
structure may influence a firm's willingness or ability to compete with its rivals, i.e., its
potential entry/exit decisions, and a firm's position in its competitive environment,
measured by price, output and market share, e.g., the industry's equilibrium Herfindahl
index. Phillips (1995) and Chevalier (1995a, 1995b) empirically investigate the interaction
between product market outcomes and capital structure by examining competitive
responses to sharp increases in leverage. A subsequent group of studies by Khanna and
Tice (2000, 2005) and Campello (2003) analyze shocks to competitive environments,
exploring how differences in ex-ante capital structure are associated with differential
responses and competitive outcomes. Considering possible influence that a firm’s capital
structure may have upon the consequent competitive environment, the proxying method is
appropriate only if the number of competing firms is substantially large and the influence
of any one firm is too limited to affect the entire competition structure in output market.
In other words, only under this circumstance should the proxies for the extent of
competition be regarded approximately exogenous. Otherwise, when the number of
competing firms is moderate and a single firm’s operating strategy may have significant
impact on the rest, exogeneity of the proxying variable and the resulting OLS-based
estimation method seems to be debatable. In other words, the prevalent tactics of proxying
is vulnerable to such a dilemma: On the one hand, applied researchers expect their choice
of proxies to be indisputably exogenous. Such expectation is evidenced by the usual
OLS-based econometric analysis that follows. On the other hand, reasoning above suggests
that the extent of competition might be endogenous. By contrast, the spatial econometric
framework manages to circumvent the dilemma like this: on the one hand, it
accommodates possible endogeneity of intra-industry competition explicitly in the model
specification; on the other hand, there have already existed numerous well-developed
estimation methods (mentioned in the 3rd paragraph of this section) to cope with such
endogeneity. In this sense, this paper supplements the existing literature by providing an
alternative empirical approach to examining the relation between firms’ financial choices
and output market competition.
8
Since our spatial model essentially regresses leverage on the weighted industry mean
leverage and other control variables, this framework looks very similar to the framework of
Frank and Goyal (2009), who regress leverage on the industry median leverage and other
control variables. The differences between the two settings, however, can be argued as
follows. First, the two regression frameworks are differently motivated. Frank and Goyal
(2009)’s motivation for the inclusion of industry median leverage is to employ it as a proxy
for some factors that are common to all firms in the industry but are not captured by
firm-specific variables. By contrast, inclusion of a spatially lagged term in our regression is
to explicitly capture firms’ strategic interaction in their financial decision making. Second,
as will become clear in Section 4, we run each regression on the firms belonging to the
same manufacturing industries but not pooling them together from different industries.
This arrangement makes our framework not conflict with Frank and Goyal (2009)’s
because for the firms in the same industry, they share an identical median leverage and
this common effect will be absorbed into the intercept term or the year dummy variable.
As a result, the spatial coefficient, once the common factors are controlled for by the
intercept or year dummy, exactly captures the strategic response as desired. Third, we
have pointed out that the spatially lagged term (weighted mean of dependent variables) in
the SAR model (2) is endogenous in nature, implying that any OLS-based estimator will
generally produce an inconsistent result. Similar argument applies to Frank and Goyal
(2009)’s regression which assumes the dependent variable (leverage) responds to the
median of its neighboring values (median industry leverage). In this sense, Frank and
Goyal’s estimate remains vulnerable to the dilemma discussed above, that is, given the fact
that the industry median leverage can not be indisputably justified to be exogenous, usual
OLS-based econometric analysis is probably unreliable.
4.
Empirical Evidence
Our empirical implementation essentially builds on the setting of Lyandres (2006) and
Frank and Goyal (2009). But while there already have been a large body of empirical
literature examining various factors that determine a firm’s financial structure, or the
relation between firms’ capital structure and their product market strategies, the
subsequent empirical exercise we will do differs from the previous studies in the three
aspects that follow. First, our empirical exercise serves to explicitly test the theoretical
predictions concerning the strategic interaction of firms’ capital structures derived in
Section 2 while the past researches are directed to examine other aspects of the capital
structure theory. Second, unlike all its past studies, we use the spatial econometric setting
to do the empirical work. This framework, as introduced in Section 3, is developed
specifically for testing the theoretical results derived in this paper and surely, allows us to
learn about something that can not be revealed using the variable proxying method. Third,
unlike the past studies, we run each regression for the sample of the firms from the same
manufacturing industries but not for the firms pooled from different industries. The
rationale for this is twofold. On the one hand, only the firms in the same manufacturing
9
industry are expected to compete against each other in the product market. Regression by
pooling the firms from different firms does not make any financial sense. On the other
hand, since one may expect the capital structure determination takes on some
industry-specific characteristics, the extent of strategic interaction of firms’ financial
choices may also vary from industry to industry. Although pooling the firms from different
industries poses no technical difficulty for estimation, such pooling has nothing to
contribute but blur the industry-related heterogeneities.
4.1 Data and Econometric Model
The data source used in the empirical test is Compustat Annual Industrial Files. To
make our empirical findings robust and credible, the empirical exercises are conducted
with the companies drawn from ten industry groups (composed of firms with identical SIC
codes up to the 3rd or 4th digit) of the manufacturing division. Table 1 lists these industry
groups considered in our empirical test. The sample consists all Compustat firms
belonging to these industries and having a complete record on the variables used in the
analysis from 1998 to 2009.
Table 1：Summary of Industry Groups
Description of Industry
SIC(First 3 or 4 Digits)
Total Observations
Beverages
208x
369
Women’s, Misses’ and Juniors’ Outerwear
233x
179
Household Furniture
251x
201
Paper Mills
262x
182
Motor Vehicles And Motor Vehicle Equipment
371x
922
Pharmaceutical Preparations
2834
2652
In Vitro and In Vivo Diagnostic Substances
2835
835
Biological Products, Except Diagnostic Substances
2836
2205
Printed Circuit Boards
3672
259
Semiconductors and Related Devices
3674
1730
We choose these manufacturing industries for empirical analysis for several reasons.
First, the manufacturing division contains a relatively large number of major groups and
industry groups. Second, each industry group, particularly those which we choose in Table
1, has the number of firms ranging from twenty to over two hundred. Considering the
firms’ number in an industry is expected to be negatively related to the intensity of market
competition, such variation allows us to explore the debt reaction slope within diverse
types of market competition. Third, manufacturing enterprises are expected to intensely
compete against each other in the product market and this competitive feature makes the
sample typical for testing the empirical relevance of the theory.
With a double index
for each observation, the regression model (2) can be
written as
10
(3)
,
where firm
has
observations,
is the number of total observations
in a given industry. Choice of control variables and specification of spatial weights for
model (3) will be discussed in detail below.
4.2 Definition of Variables
Leverage：We use market leverage ratios in the empirical test. A firm’s market leverage is
defined as the ratio of the book value of its debt to the sum of the market value of its equity
and book value of its debt. We also run the regression using book value of leverage ratio,
defined as the ratio of the book value of its debt to the book value of assets and obtain
similar empirical results.
A large body of literature on capital structure has explored a large number of
determinants of firms’ leverage choices. In a recent study, however, Frank and Goyal
(2009) show that only a small number of factors are really empirically robust and
financially significant. Particularly, they identify seven factors that seem to be the most
important in explaining firms’ leverage choices. In line with Lyandres (2006), we use five
of them, namely,
Mix of growth options and assets in place: measured 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.
Collateral: measured as the ratio of the sum of net fixed assets and inventories to assets.
Profitability: measured as the ratio of operating income to assets.
Dividends: a 0-1 dummy, which equals one if the firm has paid cash dividend in a given
year.
Size: defined as the logarithm of its assets.
Year dummy: used to control for macroeconomic changes over time.
See Lyandres (2006) for a brief review of related theories on how these factors explain
the cross sectional variation in firms’ capital structures. The other two factors that were
found by Frank and Goyal (2009) to be influential in explaining firms’ leverage choice are
the median industry leverage and expected inflation. However, since our regression is run
on firms belonging to the same industry, the two factors will be absorbed into the intercept
term and year dummy respectively, and will not appear in the control variables. The
descriptive statistics of the dependent and control variables of several selected industries
are summarized in Table 2.
4.3 Spatial Weighting Schemes
In any empirical implementation using spatial econometric model, choice of
appropriate spatial weights scheme is fairly important. For the current study, specifying
the spatial weights are motivated by the following three considerations. First, as the firms
in the same industry manufacture the products with similar characteristics, any firm is
expected to compete with, in other words, be spatially correlated with the rest of the
industry. Second, as argued, such interdependence of firms’ financial choices, if any, is
11
induced by their competition in product market. Then the extent of the correlation
between two firms is expected to rely on their relative market shares or operating incomes.
Table 2：Summary of Statistics of Firm Characteristics
Industry
Market
Stat
SIC
M/B
Profitability
Collateral
Dividend
Size
Leverage
Ratio
Dummy
Mean
0.215
4.729
1.169
0.145
0.461
0.456
SD
0.210
3.485
1.471
0.422
0.237
0.435
Max
1
10.79
74.37
0.723
0.987
1
Min
0
-5.809
0.163
-4.342
0
0
Mean
0.245
6.234
2.342
0.214
0.431
0.571
SD
0.145
4.231
1.843
0.634
0.214
0.345
Max
1
13.34
56.34
0.832
0.891
1
Min
0
-2.635
0.496
-5.345
0
0
Mean
0.278
4.576
3.234
0.174
0.573
0543
SD
0.261
2.346
2.242
0.564
0.424
0.442
Max
1
9.42
65.73
0.674
0.967
1
Min
0
-1.451
0.345
-2.342
0
0
Mean
0.381
5.325
4.578
0.262
0.427
0.527
SD
0.264
3.432
2.563
0.632
0.372
0.362
Max
1
8.272
85.57
0.894
0.941
1
Min
0
-4.562
1.527
-3.458
0
0
Mean
0.344
6.344
2.169
0.184
0.452
0.436
SD
0.242
3.905
1.548
0.274
0.354
0453
Max
1
7.36
102.45
0.824
0.923
1
Min
0
-6.238
0.546
-2.345
0
0
208x
233x
251x
262x
371x
Note: The sample consists all Compustat firms belonging to these industries and having a complete record on the variables
used in the analysis from 1998 to 2009. A firm’s market leverage is defined as the ratio of the book value of its debt to the sum
of the market value of its equity and book value of its debt. M/B ration is measured 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. Collateral is the ratio of the sum of net fixed assets
and inventories to assets. Profitability is the ratio of operating income to assets. Dividend indicator is a 0-1 dummy, which
equals one if the firm has paid cash dividend in a given year. Size: defined as the logarithm of its assets.
Third, as a matter of fact, prior to the current paper, spatial econometrics has already
been applied to a number of branches of economics such as regional, urban and
environmental economics. Therefore, it is useful to refer to some practical criteria of
specifying spatial weights that have already been well recognized in other application
fields of spatial econometrics. For example, Fredriksson and Millimet(2002), in analyzing
the strategic environmental policymaking of U.S. states, define the following population
12
weighted spatial weights matrix
, with
,
(4)
denotes the population of state ,
where
is the set of states that share a common
boundary with state . Moreover, Case et al. (1993) in examining the budget spillover and
fiscal interdependence among U.S. states, argue that states may regard as neighbors other
states that are similar to them economically or demographically, regardless of
geographical proximity. For example, they construct the following spatial weights based on
states’ economic similarity:
，
(5)
where
is the income per capital of state
averaged over the sample period.
All these considerations suggest that we explore the following two criteria in specifying
the spatial weights matrix for the current study. Let
upon firm
at year . (a) The spatial weight
be the spatial weight put by firm
is equal to the proportion of firm
total sales to the sum of total sales of all other firms in the industry than firm
’s
at year .
Equivalently, we have
(6)
，
where
or
is the total sales of firm
, let
at year . If firm
has no observation at year ,
. Since for each industry in our sample, there are always more
than two firms observed at a given year, a weighting scheme like (6) is always feasible.
Moreover, unlike operating incomes and net profits, total sales are always nonnegative,
thus avoiding some unnecessary troubles in constructing the weights and interpreting the
results. (b) Following Case et al. (1993), for any
，firm ’s weight given by firm
is
proportional to the reciprocal of the absolute value of their sales difference at year ,
namely,
(7)
，
.
Both schemes introduced above imply different interaction patterns among firms. By
definition, scheme (a) assumes a firm is more likely to be influenced by firms with larger
sales than with smaller ones in the same market while scheme (b) assumes that a firm is
likely to interact with peer firms with comparable sales. A close look into both further
suggests a significant difference between them. The row elements of
summed to be one, but it is not so for
are always
. Actually, there are two merits for such row
normalization. First, row normalization facilitates interpretation of spatially lagged term
of cross sectional unit as weighted average of its neighbors. Second, it can make different
spatial autoregressive parameters comparable.1By row normalization, the elements of
can be redefined as
As the magnitude of the spatial interaction parameters are to be compared across industries, the second
merit is of much importance to the subsequent analysis.
1
13
(8)
.
，
4.4 Empirical Results
We employ the quasi-maximum likelihood method (Lee 2004) and two-stage least
squares (2SLS, Kelejian and Prucha 1998) to estimate model (3) under the weighting
schemes as defined above. The 2SLS estimator employs
as the instrument
for the endogenous spatially lagged term while the maximum likelihood program can be
downloaded from http://www.spatial-econometrics.com. According to Lee (2007), for a
spatial autoregressive model like (3), both MLE and 2SLSE are consistent but the former
will be more efficient than the latter. The regression results using market leverage as the
dependent variable are reported in Table 3. 1 The main findings from Table 3 are
summarized as follows.
Table 3：Regression Results
Industry
Div
Size
M/B
Profitability
Adjusted
Collateral
SIC
Dummy
MLE
0.127*
0.027**
-0.014
-0.021*
0.268**
-0.083**
0.346
2SLS
0.144*
0.026**
-0.010
-0.026*
0.246**
-0.080**
0.325
MLE
0.099*
0.025*
-0.015
-0.030*
0.233**
-0.077**
0.330
2SLS
0.104*
0.028**
-0.018
-0.027*
0.242**
-0.079**
0.321
MLE
0.146**
0.019*
-0.008
-0.016*
0.366**
-0.066*
0.425
2SLS
0.158**
0.016*
-0.006
-0.017*
0.347**
-0.054*
0.419
MLE
0.117*
0.015*
-0.006
-0.012*
0.329**
-0.074**
0.410
2SLS
0.123*
0.018*
-0.007
-0.016*
0.384**
-0.076**
0.402
MLE
0.091*
0.024*
-0.010
-0.033*
0.336**
-0.098**
0.376
2SLS
0.078*
0.022*
-0.008
-0.036*
0.314**
-0.100**
0.367
MLE
0.066
0.019*
-0.009
-0.037*
0.366**
-0.097**
0.343
2SLS
0.068
0.022*
-0.009
-0.035*
0.345**
-0.098**
0.338
MLE
0.218**
0.037**
-0.024*
-0.024*
0.375**
-0.086**
0.465
2SLS
0.222**
0.038**
-0.022*
-0.025*
0.386**
-0.085**
0.456
MLE
0.229**
0.034**
-0.021*
-0.020*
0.401**
-0.086**
0.451
2SLS
0.236**
0.032**
-0.026*
-0.026*
0.392**
-0.087**
0457
MLE
0.157**
0.045**
-0.021*
-0.032*
0.328**
-0.106**
0.376
2SLS
0.156**
0.046**
-0.022*
-0.033*
0.314**
-0.132**
0.334
MLE
0.131*
0.043**
-0.022*
-0.030*
0.324**
-0.118**
0.379
2SLS
0.127*
0.047**
-0.019*
-0.034*
0.313**
-0.114**
0.340
(a)
208x
(b)
(a)
233x
(b)
(a)
251x
(b)
(a)
262x
(b)
(a)
371x
(b)
Note: The regression results are computed using market leverage ratio as the dependent variable. Double asterisk (**)
1
Regression results using book leverage ratio as the dependent variable are available upon request.
14
indicates statistical significance at 95% level while single asterisk (*) indicates statistical significant at 90% level. The spatial
weighting schemes (a) and (b) are defined according to (6) and (8), respectively.
Table 3：(Continued)
Industry
Div
Size
M/B
Profitability
Adjusted
Collateral
SIC
Dummy
MLE
0.069
0.031**
-0.027*
-0.032*
0.311**
-0.075*
0.255
2SLSE
0.068
0.032**
-0.030*
-0.034*
0.312**
-0.078**
0.244
MLE
0.066
0.036*
-0.026*
-0.033*
0.316**
-0.074*
0.247
2SLSE
0.065
0.037**
-0.028*
-0.032*
0.312**
-0.078**
0.241
MLE
0.112*
0.025*
-0.012
-0.025*
0.280**
-0.095**
0.326
2SLS
0.108*
0.024*
-0.010
-0.026*
0.273**
-0.099**
0.318
MLE
0.088*
0.027*
-0.008
-0.025*
0.277**
-0.092**
0.313
2SLS
0.080
0.028*
-0.011
-0.024*
0.283**
-0.096**
0.310
MLE
0.127*
0.035**
-0.037**
-0.023*
0.425**
-0.087**
0.395
2SLS
0.126*
0.038**
-0.036**
-0.025*
0.427**
-0.085**
0.397
MLE
0.113*
0.033**
-0.032**
-0.022*
0.473**
-0.088**
0.387
2SLS
0.098*
0.037**
-0.038**
-0.024*
0478**
-0.084**
0.379
MLE
0.264**
0.042**
-0.015
-0.033*
0.395**
-0.095**
0.347
2SLE
0.280**
0.045**
-0.013
-0.034*
0.394**
-0.099**
0.348
MLE
0.229**
0.046**
-0.012
-0.030*
0.384**
-0.096**
0.339
2SLS
0.238**
0.048**
-0.011
-0.036*
0.389**
-0.101**
0.336
MLE
0.188**
0.039**
-0.011
-0.040*
0.366**
-0.115**
0.327
2SLS
0.199**
0.041**
-0.010
-0.040*
0.365**
-0.116*
0.325
MLE
0.148*
0.037**
-0.009
-0.045*
0.349**
-0.118**
0.318
2SLS
0.135*
0.042**
-0.008
-0.043*
0.359**
-0.115**
0.316
(a)
2834
(b)
(a)
2835
(b)
(a)
2836
(b)
(a)
3672
(b)
(a)
3674
(b)
Note: The regression results are computed using market leverage ratio as the dependent variable. Double asterisk (**)
indicates statistical significance at 95% level while single asterisk (*) indicates statistical significant at 90% level. The spatial
weighting schemes (a) and (b) are defined according to (6) and (8), respectively.
First, in most cases, both MLE and 2SLSE of the spatial autoregressive parameter
have significantly positive signs across the industries based on both spatial weighting
schemes, implying that firms are engaged in strategic interaction with their rivals in
choosing financial structures. Moreover, positive the spatial coefficient suggests that firms
tend to react in the same direction to leverage adjustment of their rivals and they compete
against each in strategic substitutes.
Second, we see significant variation of the extent of strategic interaction across the
industries. Among the selected industries, the extent of strategic interaction varies from
0.06 to 0.28, implying certain heterogeneity of competition intensity from one product
market to another. Among them, firms in the industries of paper mills or printed circuit
15
boards are expected to adjust their financial structures by a larger margin in response to
rivals’ change, suggesting more intense competition in these markets. Furthermore,
Lyandres (2006) show that the extent of market competition is expected to be negatively
related to the firms’ number in the market. Our estimation results seem to be consistent
with this prediction.
Third, in most cases, the estimates associated with weighting scheme (b) have smaller
magnitude than those with scheme (a). It seems to us that scheme (a) would be a more
appropriate criterion relative to scheme (b) in characterizing firms’ cross-sectional
correlation in their output market in terms of the magnitude of both the estimates and the
adjusted R square. Considering the different patterns implied by two weighting schemes,
this may indicate that a firm would be likely to mimic the larger firms or just follow the
industry leaders rather than interact with its comparable peers.
Fourth, coefficient signs of the control variables are consistent with prior literature.
For example, firm size and collateral are positively correlated with the leverage while M/B
ratio, dividend dummy and profit margin are negatively correlated with the leverage.
Finally, estimated coefficients of these controls are robust to the choice of spatial
weighting scheme, suggesting that firm-level characteristics are not strongly correlated
with rivals' leverage ratios.
4.5 Robustness Check
To check the robustness, first we run a pooled regression on the sample from several
industries which have been estimated to have relatively significant extent of strategic
interaction. That is, we put the firms from seven industries (excluding SIC 251x, 2834 and
2835) together and run the regression (3) by adding an industry dummy. It should be
noted that in this regression the spatial matrix will be a block-diagonal matrix, i.e.,
, where
are the spatial weight matrices for
,
each industry in the previous regressions. The regression results are summarized in Table
4. We find that the results have the same sign and comparable magnitude to those
reported in Table 3.
Table 4：Robustness Check: Pooled Regression
Div
Size
M/B
Profitability
Adjusted
Collateral
Dummy
MLE
0.117*
0.033**
-0.024*
-0.030*
0.380**
-0.098**
0.247
2SLSE
0.105*
0.032**
-0.022*
-0.034*
0.357**
-0.096**
0.239
MLE
0.094*
0.035**
-0.023*
-0.032*
0.371**
-0.099**
0.227
2SLSE
0.096*
0.033**
-0.023*
-0.033*
0379**
-0.094**
0.225
(a)
(b)
Note: The regression pools the firms from seven industries (excluding SIC 251x, 2834 and 2835) together and run the
regression (3) by adding an industry results. Double asterisk (**) indicates statistical significance at 95% level while single
asterisk (*) indicates statistical significant at 90% level.
Although Table 3 has indicated certain robustness of our results to the choice of spatial
16
weighting schemes, a naïve weighting scheme is used here to check the robustness further.
We assign equal weight to each firm in the same industry, regardless of their
heterogeneous market shares, that is, we let
(9)
,
where
,
,
is the number of firms observed at year . This weighting scheme makes our
regression resemble Frank and Goyal (2009)’s regression setting where the industry
median leverage is replaced by the sample mean leverage here, although both are
differently motivated. The estimation results are reported in Table 5. Under equally
weighting scheme, the spatial coefficient is less significant than under scheme (a) and (b),
which might be regarded as evidence for asymmetry of the strategic interaction among
firms. Such asymmetry is also consistent with the observation in Section 4.4 that the data
are in favor of weighting scheme (a) (that puts more weight on larger firms) relative to
scheme (b) (that puts more weight on comparable peers). Since the fundamental purpose
of this paper is to empirically test for the strategic effect, exploring the exact strategic
pattern and distinguishing between several conflicting patterns of interaction seem to be
beyond the scope of this paper. It may be the topic for future research.
Table 5：Robustness Check: Equally Weighting Scheme
Industry
Div
Size
M/B
Profitability
Adjusted
Collateral
SIC
Dummy
MLE
0.054
0.026**
-0.012
-0.023*
0.263**
-0.083**
0.308
2SLSE
0.050
0.024**
-0.011
-0.027*
0.248**
-0.078**
0.299
MLE
0.078*
0.019*
-0.009
-0.015*
0.358**
-0.065*
0.378
2SLSE
0.075
0.020*
-0.006
-0.013*
0.343**
-0.055*
0.372
MLE
0.043
0.025*
-0.011
-0.036*
0.337**
-0.094**
0.316
2SLSE
0.042
0.023*
-0.009
-0.032*
0.323**
-0.094**
0.320
MLE
0.104*
0.035**
-0.025*
-0.021*
0.367**
-0.087**
0.419
2SLSE
0.115*
0.036**
-0.025*
-0.023*
0.373**
-0.085**
0.423
MLE
0.082*
0.042**
-0.023*
-0.030*
0.330**
-0.102**
0.353
2SLSE
0.083*
0.040**
-0.024*
-0.032*
0.315**
-0.126**
0.348
MLE
0.035
0.028**
-0.026*
-0.037*
0.307**
-0.077*
0.230
2SLSE
0.038
0.029**
-0.029*
-0.036*
0.312**
-0.078**
0.228
MLE
0.062
0.025*
-0.015
-0.024*
0.274**
-0.090**
0.286
2SLSE
0.066
0.027*
-0.012
-0.022*
0.268**
-0.095**
0.291
MLE
0.074*
0.037**
-0.035**
-0.025*
0.428**
-0.087**
0.367
2SLSE
0.072*
0.034**
-0.032**
-0.027*
0.430**
-0.084**
0.361
MLE
0.135*
0.040**
-0.013
-0.034*
0.396**
-0.094**
0.319
2SLSE
0.132*
0.041**
-0.012
-0.032*
0.391**
-0.100**
0.312
MLE
0.094*
0.043**
-0.013
-0.040*
0.367**
-0.114**
0297
2SLSE
0.098*
0.045**
-0.010
-0.043*
0.365**
-0.117*
0.285
208x
233x
251x
262x
371x
2834
2835
2836
3672
3674
17
Note: The regression uses an equally weighting scheme, as defined by (9). Double asterisk (**) indicates statistical significance
at 95% level while single asterisk (*) indicates statistical significant at 90% level.
Finally, instead of using the first order spatial lag of the exogenous regressors
as the instrument for the endogenous part, we can use second order or higher order spatial
lags
as the instruments. The regression results are quite similar to the
2SLSE in Table 3 and are not reported here.
4.6 Further Analysis
Although our prior analysis seems to support the strategic interaction hypothesis, we
provide further evidence in this subsection. To distinguish the interpretation of our
empirical result from other competing theoretical alternatives, particularly Frank and
Goyal (2009)’s, we regress the time
changes in firms leverage on time
changes of
weighted average leverage of other firms in the same industry and other controls, that is,
(10)
，
where
。The basic intuition behind such regression
,
is that even if the industry median leverage in Frank and Goyal (2009)'s is empirically
significant in explaining a firm’s leverage, it will be eliminated by first-order differencing
while our weighted mean leverage is not. Consequently, the spatial coefficient
remains
identifiable from (10). Although regression (10) can eliminate the industry-specific
common effect, it is by no means the only way to achieve this. We have also explored two
alternative specifications for robustness consideration. One regresses the time
in firms leverage on time
changes
changes of weighted average leverage of other firms in the
same industry and other controls, namely,
(11)
.
Note that the interpretation of the two regressions (10)-(11) differs in that the latter
indicates a simultaneous strategic reaction of firm’s leverage adjustment while the former
implies that such strategic effect is one period lagged. The third regression then is aimed
to nesting both above, that is, we regress the time
time
and
changes in firms leverage on both
changes of weighted average leverage of other firms in the same
industry and other controls, namely,
(12)
.
We use the two-stage least squares method (Kelejian and Prucha, 1998) to estimate Eqn.
(10)-(12) under weighting scheme (a)-(b) and both the spatial coefficients and R squared
are presented in Table 6.
The major finding from Table 6 is that the spatial coefficients for regression (10)-(11)
are estimated to be significantly positive across most industries and these coefficients have
comparable magnitude to those obtained in prior regressions, suggesting that the
18
hypothesized strategic effect is empirically distinguishable from Frank and Goyal (2009)’s
common effect hypothesis. Moreover, it is also noted that the coefficient for lagged
strategic interaction is essentially insignificant given the presence of simultaneous
strategic effect. These results indicate that such interaction is likely to take place
simultaneously instead of having a dynamic pattern.
Table 6：Further Analysis: Regression by Differencing
Eqn. (10)
Industry
SIC
Eqn.(11)
Adjusted
Eqn.(12)
Adjusted
Adjusted
(a)
0.125*
0.298
0.130*
0.317
0.047
0.117*
0.326
(b)
0.094*
0.289
0.103*
0.312
0.039
0.092*
0.325
(a)
0.136*
0.395
0.151**
0.405
0.059
0.138*
0.417
(b)
0.107*
0.374
0.120*
0.389
0.043
0.105*
0.396
(a)
0.068
0.337
0.080
0.359
0.032
0.073
0.372
(b)
0.043
0.329
0.051
0.336
0.029
0.038
0.345
(a)
0.198**
0.427
0.217**
0.447
0.094*
0.187**
0.457
(b)
0.189**
0.414
0.203**
0.441
0.086*
0.174**
0.449
(a)
0.136*
0.319
0.150**
0.332
0.059
0.128*
0.339
(b)
0.121*
0.328
0.128*
0.353
0.052
0.124*
0.359
(a)
0.058
0.229
0.065
0.247
0.034
0.052
0.258
(b)
0.051
0.212
0.058
0.236
0.028
0.045
0.241
(a)
0.094*
0.302
0.101*
0.324
0.046
0.083*
0.338
(b)
0.079*
0.287
0.085*
0.305
0.042
0.073
0.326
(a)
0.103*
0.363
0.124*
0.384
0.049
0.094*
0.393
(b)
0.094*
0.349
0.104*
0.363
0.041
0.089*
0.375
(a)
0.227**
0.328
0.253**
0.345
0.102*
0.202**
0.367
(b)
0.219**
0.314
0.236**
0.332
0.094*
0.198**
0.343
(a)
0.162**
0.305
0.162**
0.328
0.072
0.136*
0.335
(b)
0.136*
0.289
0.136*
0.314
0.058
0.118*
0.324
208x
233x
251x
262x
371x
2834
2835
2836
3672
3674
Note: The regression results are computed using the two-stage least squares method. Double asterisk (**) indicates statistical
significance at 95% level while single asterisk (*) indicates statistical significant at 90% level. The spatial weighting schemes (a)
and (b) are defined according to (6) and (8), respectively.
5. Conclusion
Modern capital structure theory is marked by systematically examining the interaction
between firms’ financial decisions in capital market and their industrial competition in
output market. Focusing on the strategic interaction of firms’ financial choices induced by
their competition in product market, this paper provides several new results that have not
appeared or have not been explicitly investigated in the past literature:
19
Theoretically, we show how the competition in output market may induce a firm to
take its rival firms’ capital structures into calculus in deciding its own one. Furthermore,
the direction of such strategic interaction is related to firms’ competitive strategy type and
a monotonic correspondence is established between the magnitude of such strategic
adjustment and the extent of competition in output market. Empirically, a spatial
econometric model is introduced to test the relation between firms’ financial choices and
their market strategies. We lay down the empirical framework, interpret the empirical
relevance of the parameters and evaluate the proposed setting in contrast with variable
proxying method employed by the prior literature. We also elaborate on the specification
of spatial weights by borrowing from some practical criteria that have already been well
recognized in other application fields of spatial econometrics. Based on a board sample of
U.S. firms from several manufacturing industries, the empirical facts tell us that inclusion
of the spatially lagged term of a firm’s leverage could be significant in explaining the
optimal choice of firm’s financial structure, at least empirically.
Appendix: Proof of Proposition 1.
Proof of (i): We solve the game by backward induction. In the second stage of the game,
the management chooses the operating strategy to maximize the expected wealth of the
firm’s shareholders, conditional on firms’ financial structures disclosed after the first stage.
Differentiate the right-hand side of Eqn (1) with respect to
, it gives
.
(A.1)
with
Introduce the following notations,
,
,
,
. Then Eqn. (A.1) can be written as
,
(A.2)
where
is an
identity matrix. For the moment assume
Then firm ’s aggressiveness
leverage
,
can be represented as the linear combination of firms’
, namely,
.
(A.3)
By defining
(A.4)
is invertible.
, the following identities always hold,
,
，
.
Let’s return to the first stage of the game. In the first stage, firms choose their debt levels,
with the objective of maximizing their ex ante values of both debtholders and shareholders,
given by
(A.5)
.
Substituting Eqn. (A.3) into (A.5) and using the identities in (A.4), we have
(A.6)
20
,
where
and
row of
and
denote the
column vector composed of the elements in the th
, respectively. Each
is
column vector with th
component being one and others being zero. The first order condition for the firms to
choose their optimal debt levels is then given by
(A.7)
,
to be the unique solution to the
For now denote
.
equations in (A.7).
For our purpose, it is of interest to learn something about how a firm’s equilibrium debt
level changes in response to the change of the other firm’s equilibrium debt level, that is,
. To this end, it is unnecessary to solve explicitly the
in attempt to work out the response slope
as a function of
equations for
. Instead, in view of
implicitly determined by Eqn. (A.7), we can
with some given
differentiate the right-hand side of (A.7) with respect to
, which
gives
.
(A.8)
Then Proposition 1-(i) follows since the right-hand side of Eqn. (A.8) is independent of
.
Proof
as
of
(ii):
Starting
from
Eqn.(A.4),
one
. For any
-dimensional column vector
may
write
nonsingular matrix
and some
, applying the formula
, where
gives
for
. Then one has
and
. It suffices to verify that under Assumption 1, there
and
holds
always has contrary sign to
follows from both
follows from both
and
. If
and
. If
,
,
. Whenever
, there always holds
or
,
, (b)
because (a)
(c)
,
and (d)
.
Proof of (iii): The right-side hand of Eqn. (A.8) can be represented as
, where
and
,
,
. Then it suffices to verify the first order derivative of
with reference to
first order derivative of
has negative sign. It can be verified as follows: the
has the same sign as
21
.
By some computation, one has
,
and
, because
,
,
.
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