Panel Threshold Effect of Debt Ratio on Firm Value in Taiwanese
Listed Companies
Feng-Li Lina
aAssociate Professor, Department of Accounting, Chaoyang University of Technology, Taichung, Taiwan.
Ph.D Candidate, College of Business, Feng Chia University, Taichung, Taiwan, ROC.
Abstract
The goal in this paper is to analyze whether leverage affects firm value for a panel of 272 Taiwanese
listed companies during the nine-year period 1997 to 2005. Advanced panel threshold regression model is
performed to test if there exists an “optimal” debt ratio , which may result in threshold effects and
asymmetrical relationships between debt ratio and firm value. Tobin’s q is adopted as proxy variables for
firm value.
The result in this study shows that there exists two thresholds effect between debt ratio and firm
value. The estimated threshold value ( ˆ1 , ˆ 2 ) are found to be 48.92% and 49.55%. Among three
coefficients ( ̂ 1 , ̂ 2 , ̂ 3 ), the estimate of coefficient ̂1 , ̂ 3 are negative but not significant which means
when the debt ratio is smaller than 48.92% or greater than 49.55% , the relationship between debt ratio
and firm value is unclear. In the second regime, where the debt ratio is between 48.92% and 49.55%, the
estimate of coefficient ̂ 2 is 0.009, which implies Tobin’s q will be increased by 0.009% via 1%
increase of debt ratio. Tobin’s q will also be increased. Thus, this suggests that financial managers should
utilize the relevant financial leverage wisely in order to maximize the firm’s value.
Keywords: Tobin’s q, Panel threshold effect, Debt ratio
1. Introduction
The theory of business finance in a modern sense starts with the Modigliani and Miller (1958)
capital structure irrelevance proposition, showing that the firm value and weighted average cost of capital
is unaffected by the financial structure of the firm. However, Modigliani and Miller’s (1958) perfect
market assumptions: such as no transaction costs, no taxes, symmetric information and identical
borrowing rates, and risk free debt, are contradictory to the operations in the real world. The literature on
capital structure emphasis has been placed on releasing the assumptions made by Modigliani and Miller,
in particular by taking into account corporate taxes (Modigliani and Miller, 1963), personal taxes (Miller,
1977), information asymmetries (Ross, 1977; Myers and Majluf, 1984; Myers, 1984), agency costs
(Jensen and Meckling, 1976; Myers,1977; Kim and Sorensen,1986), and bankruptcy costs(Stiglitz, 1972;
Castanias,1983; Altman,1984). Two main theories currently dominate the capital structure debate: the
trade-off theory and the pecking order theory.
The trade-off theory, developed by Myers (1977), is a static amount of debt leading managers to find
the “optimal capital structure” that maximize firm value when the benefits of debt equal the marginal cost
of debt. The pecking order theory, developed by Myers (1984) and Myers and Majluf (1984), predicts that
information asymmetry between managers and investors creates a preference ranking in firms’ financing
policy. Beginning with internal funds, followed by debt, and then equity, companies work their way up
the pecking order to finance investment in an effort to minimize adverse selection costs. Aggarwal and
Zong (2006) documents that in all four countries (USA, UK, Japan, and Germany), controlling for the
investment opportunity set, investment levels are significantly positively influenced by levels of internal
cash flows, indicating that firms face limitation in access to external finance and may operate using a
pecking order.
Like the pecking order theory, two additional theories of capital structure assert that there is no
reversion to a target capital ratio: the market timing theory and the inertia theory. Unlike the pecking
order theory, the market timing theory argued by Baker and Wurgler (2002), asserts that the most realistic
account of leverage is that it reflects the attempts by managers to time the equity market—issuing equity
when the market is receptive.. The firm’s observed capital structure reflects its cumulative ability to sell
overpriced equity shares. If market timing affects debt and equity issuance decisions, then measures of the
equity market (the market-to-book ratio) and the debt market (the interest rate) ought to have significant
impacts on changes in leverage. The inertia theory suggested by Welch (2004), is that managerial inertia
permits stock price changes to have a main effect on market-valued debt ratios. In Welch’s view, shocks
to the stock market affect capital structure but since firms do not take steps to reestablish a leverage target,
the levels of debt and equity do not influence subsequent leverage adjustments. In contrast, the tradeoff
theory maintains that market imperfections generate a link between leverage and firm value, and firms
take positive steps to offset deviations from their optimal debt ratios. The pecking order, market timing,
and inertia theories of capital structure imply that managers perceive no great leverage effect on firm
value and therefore make no effort to reverse changes in leverage.
Unlike Welch (2004), Flannery and Rangan (2006) find that stock price changes have only transitory
1
effects on capital structure. Their evidence indicates that firms do target a long run capital structure, and
that the typical firm converges toward its long-run target at a rate of more than 30% per year. However,
more than half of the observed changes in capital structures can be attributed to targeting behavior while
market timing and pecking order considerations explain less than 10% each. Frank and Goyal (2004)
found that there is a long-run leverage ratio to which the system reverts. Deviations from that ratio help to
predict debt adjustments, but not equity adjustments. A high ratio of market to book is associated with
subsequent debt reduction, but there is no effect in the equity market.
The relationship between capital structure and firm value has been the subject of considerable
debate throughout the literature. There are two issues to discuss: 1. “Do firms reverse to an optima debt
ratio ?”; 2. “Do leverage effect on firm value ?”. The goal of this study is to test whether application of
financial leverage affects firm value of Taiwanese listed firms, we apply threshold regression model to the
observed “balanced panel data” to test if there exists an optimal debt ratio which may result in threshold
effect and asymmetrical responses of the firm value to the debt ratio. If this “threshold” value of  is
verified, the financial managers should take steps to increase debt levels in the low debt regime of debt
ratio lower than the  . Conversely, they should take steps to reduce debt levels in the high debt regime of
debt ratio higher than  .
This paper contributes to previous literature in two aspects. First, we apply advanced panel
threshold regression model developed by Hansen (1999) to test if there exists a “threshold” of optimal
debt usage. In contrast with traditional linear model, this nonlinear threshold model can describes the
“trade-off” between the benefits of tax shields of more debts and the disadvantages of costs from
additional debts that may damage the firm value. Second, it’s panel data of Taiwanese listed companies to
be considered for fully examining the financial characteristics of the Taiwanese industry and solving the
short period sample problem.
The remainder of this paper is organized into five sections. Section 2 provides data collection and
Methodology, Section 3 discusses the empirical results, and finally Section 4 concludes the study with
implications of the findings and suggestions for future research.
2. Methodology
2.1 Sample set
This paper explores if there exists an optimal debt ratio, which may result in threshold effect and
asymmetrical responses of the firm value to the debt ratio through employing threshold regression model.
The investigation has been performed via “balanced panel data” for a sample of 272 selected Taiwanese
companies listed on the Taiwan Stock Exchange during 1997 to 2005. Total 2,448 observations are
adopted for each variable considered. Table 1 shows the industry breakdown of the sample. Eighteen
industries are listed in the table 1. Electron and Textiles industries accounted for more than one-thirds of
the sample, and the remaining industries had fewer than ten percent of the sample.
2
2.2 Variables
In order to consider the effect of market valuation of a firm, Tobin’s q, which defined as the ratio of
the market value of a firm to the replacement cost of its assets, is also selected as the proxy variable for
the firm value. The calculation of the approximated q, following the suggestions by Chung and Pruitt
(1994), is defined as follows:
Approximated Tobin’s q = (MV + PS + DEBT)/TA,
where MV is the product of a firm's share price and the number of common stock shares outstanding, PS
is the liquidating value of the firm's outstanding preferred stock, DEBT is the value of the firm's
short-term liabilities net of its short-term assets, plus the book value of the firm's long-term debt, and TA
is the book value of the total assets of the firm.
There are two categories of explanatory variables in our panel data. The first is the threshold variable,
debt to total assets ratio (debt ratio), which is the key variable used to investigate whether there exists an
asymmetric threshold effect of the leverage on firm value. In our examination, four applied control
variables include management ownership ratio, natural log of total assets, ratio of R&D expenses to total
sales, and ratio of advertising expenses to total assets, which are presumed to have influences upon the
firm value. All data sets are obtained from Taiwan Economic Journal (TEJ) Data of Taiwan. Table 2
shows the descriptive statistics of variables for 272 firms
2.3 Research methodology
2.3.1 Panel Unit Root Models
Hansen’s (1999) panel threshold regression model is an extension of the traditional least squared
estimation method, in fact. It requires that variables considered in the model need to be stationary in order
to avoid the so-called spurious regression1. Thus, the unit root test is first processed in this study. Since
the data are all panel in this investigation, both well known LLC (Levin, Lin and Chu, 2001) and IPS (Im,
Pesaran and Shin, 1997) techniques are employed for the panel unit root tests2.
Table 2 presents the descriptive statistics of variables for 272 firms. The result of the stationary test
for each panel (i.e. explained variables, threshold variable, and control variables) shows that all the
variables are most likely to be presumed to carry stationary characteristics since the null of unit root are
mostly rejected, especially in the findings from LLC test3. These stationary findings are available for
further estimations of the panel threshold regression.
1
Spurious regression is argued in Granger and Newbold (1974) that the estimation of the relationship among non-stationary series is easily
getting higher R2 and t statistics.
2 LLC is a modified version of the LL (Levin and Lin, 1992, 1993) panel unit root technique.
3 For saving space, the results are not reported here. However, it will be available upon reader’s request.
3
2.3.2 Threshold Autoregressive Model
Modern dynamic capital structure model proposed an idea of finding the “target” optimal debt ratio
and firms will adjust outstanding debt levels in response to changes in firm value. This paper applies a
newly-developed, alternative method: panel threshold regression model to solve this problem, to strike a
“balance” between the tax benefit and the potential costs that comes along with this benefit. Since Tong
(1978) proposed Threshold Autoregressive model, thereafter, this non-linear time series model has
become very popular for economic and financial research.
When the Threshold Autoregressive Model is estimated, first we should test if there exists threshold
effects. If we can not reject the null hypothesis, the threshold effect doesn’t exist. Again, the existence of
nuisance will make the testing statistic follow non-standard distribution, which was called “Davies’
Problem4”. Hansen (1999) suggested a “bootstrap” method to compute the asymptotic distribution of
testing statistics in order to test the significance of threshold effect. Furthermore, when the null hypothesis
doesn’t hold, which means, the threshold effect does exist, Chan (1993) proved that OLS estimation of
threshold is super consistent, the asymptotic distribution is derived. However, nuisance influences this
distribution and makes it non-standard. Hansen (1999) used simulation likelihood ratio test to derive the
asymptotic distribution of testing statistic for a threshold. Hansen (1999) proposed to use two-stage OLS
method to estimate the panel threshold model. On the first stage, for any given threshold ( ) , compute the
sum of square errors (SSR) separately. On the second stage, try to find the estimation of
 
by
minimization of the sum of squares. At last, use the estimation of threshold to estimate the coefficient for
every “regime” and do analysis.
2.3.3 Threshold Model Construction
According to the “Tradeoff Theory” of Capital Structure, when debt ratio increases, the interest tax
shield increases; however, on the other side, leverage related costs increase to offset the positive effect of
debt ratio to the firm value. Thus, this paper aims at examining whether threshold effect exists between
the financial leverage and value. We assume that there exists an optimal debt ratio, and try to use
threshold model to estimate this ratio, which can capture the relationship between financial leverage and
firm value as well as help financial managers make decisions.
Thus we set up single threshold model as follows:
    hit  1 dit   it
vit   i
i   hit   2 dit   it
if dit  
(1)
if dit  
  (1 , 2 ,3 , 4 ) , hit  ( sit , mit , git , cit )
4
“Davies’ Problem” is one that testing statistics follow non-standard distribution because of the existence of the nuisance (Davies,
1977,1987). Afterwards, Andrews and Ploberger (1994) and Hansen(1996) tested again to solve the problem.
4
Where v it represents proxy variables of the firm value, which are qit : Tobin’s q; d it , debt ratio,
which is also the threshold variable;  , the specific estimated threshold value. There are four “control
variables”( hit ) that they may have influences upon the firm value, which are sit : natural log of total
assets, mit : management ownership ratio, git : ratio of R&D expenses to total sales, and cit : ratio of
advertising expenses to total assets. Besides,  i , the fixed effect, represents the heterogeneity of
companies under different operating conditions; The errors  it is assumed to be independent and
identically distributed with mean zero and finite variance  2 (  it ~ iid (0,  2 ) ); i represents different
companies; t represents different periods.
Another threshold regression model of (1) is to set:
vit  i   'hit  1 dit I  dit      2 dit I  dit     it
(2)
where I(.) represents indicator function,
vit  i   hit   dit    it
can be written as:
 hit

vit  i   ,  
   it
d
(

)
 it 
vit  i   xit    it
(3)
 d I  d it   
dit     i t

 dit I  dit    




where   1 , 2 ,    ' ,  ' , xit   hit' , dit' ( )  .
'
'
'
The observations are divided into two “regimes” depending on whether the threshold variable d it
is smaller or larger than the threshold value (  ). The regimes are distinguished by differing regression
slopes,  1 and  2 . We will use known v it and d it to estimate the parameters (  ,  ,  , and  2 ).
2.3.4 Estimation
Note that taking averages of (3) over the time index t to derive:
vit  i   ' dit    it
where vi 
1
T
T
 vit ，  i 
t 1
(4)
1
T
T

t 1
it
, and
5
1 T

 T  d it I (d it   ) 
T
1
t 1

d i     d it ( )   T
T t 1
1

 T  d it I (d it   )
 t 1

Taking the difference between (3) and (4) yields:
vit*   d it* ( )   it*
(5)
where vit*  vit  vi ， d it* ( )  d it ( )  d i ( ) ， and  it*   it   i
Let
vi*2 
d i*2 ( ) 
 i*2 


 
 
*
vi*    ， d i* ( )  
 ，  i   
d * ( )
 * 
v * 
 iT

 iT 
 iT 
Denote the stacked data and errors for an individual , with one time period deleted. Then let V  , D  ( )
and e  denote the data stacked over all individuals.
v1* 
d1* ( )
 1* 
 


 
 


 
*
*
*
*
*
V  vi  ， D ( )  d i ( ) , e   i* 
 


 
 


 
 *
 * 
 *
 n 
vn 
d n ( )
Use this notation, (5) is equivalent to
Vit*  Dit* ( )  eit*
(6)
The equation (6) represents the major estimation model of threshold effect. For any given  , the
slope coefficient  can be estimated by ordinary least squares (OLS). That is,
ˆ     D* ( )D* ( )  D* ( )V *
1
(7)
The vector of regression residuals is
eˆ* ( )  V *  D* ( )ˆ ( )
(8)
and the sum of squared errors, SSE is
SSE1 ( )  eˆ* ( )eˆ* ( )  V * ( I  D* ( )( D* ( )D* ( )) 1 D* ( ))V *
(9)
Chan (1993) and Hansen (1999) recommend estimation of  by lease squares. This is easier to
6
achieve by minimization of the concentrated sum of squared errors (9). Hence the least squares estimators
of  is
ˆ  arg min SSE1 ( )
(10)
Once ˆ is obtained, the slope coefficient estimate is ˆ  ˆ ˆ  . The residual vector is eˆ*  eˆ* ˆ ， and the
estimator of residual variance is
1
1
ˆ 2  ˆ 2 (ˆ ) 
eˆ * (ˆ )eˆ * (ˆ ) 
SSE1 (ˆ )
n(T  1)
n(T  1)
(11)
where n indexes the number of sample, T indexed the periods of sample.
2.3.5 Testing for a threshold
This paper hypothesizes that there exists threshold effect between the debt ratio and firm value. It is
important to determine whether the threshold effect is statistically significant. The null hypothesis and
alternative hypothesis can be represented as follows:
H 0 : 1   2

H 1 : 1   2
When the null hypothesis holds, the coefficient 1 =  2 the threshold effect doesn’t exist. When the
alternative hypothesis holds, the coefficient 1 ≠  2 the threshold effect exists between the debt ratio and
firm value.
Under the null hypothesis of no threshold, the model is
vit  ui   hit   dit    it
(12)
After the fixed-effect transformation is made, we have
Vit *  1H it *  eit *
(13)
The regression parameter is estimated by OLS, yielding estimate 1 , residuals e~ * and sum of squared
e* ~
e*.
errors SSE 0  ~
/
Hansen (1999) suggests that the relevant F Test Approach and the sup-Wald statistic are used to test
the existence of threshold effect and to test the null hypothesis, respectively.
F  sup F ( )
(14)
( SSE0  SSE1 ˆ ) / 1 SSE0  SSE1 ˆ 
F   

(15)
SSE1 ˆ  / n(T  1)
ˆ 2
Under the null hypothesis, some coefficients (e.g. the pre-specified threshold,  ) do not exist,
therefore, the nuisance exists. According to “Davies’ problem” (1977, 1987), the F statistic becomes
non-standard distribution. Hansen (1996) showed that a bootstrap procedure attains the first-order
7
asymptotic distribution, so p-values constructed from the bootstrap are asymptotically valid. Treat the
regressors x it and threshold variable d it as given, holding their values fixed in repeated bootstrap samples.
Take the regression residuals eˆit* , and group them by individual: eˆi*  (eˆi1 , eˆi2 ,, eˆiT ) . Treat the sample
eˆ , eˆ ,eˆ 

1

2

n
as the empirical distribution to be used for bootstrapping. Draw a sample of size n from
the empirical distribution and use these errors to create a bootstrap sample under H 0 . Using the bootstrap
sample, estimate the model under the null (13) and alternative (5) and calculate the bootstrap value of the
likelihood ratio statistic F ( ) (15). Repeat this procedure a large number of times and calculate the
percentage of draws for which the simulated statistic exceeds the actual. This is the bootstrap estimate of
the asymptotic p-value for F ( ) under H 0 . The null of no threshold effect is rejected if the p-value is
smaller than the desired critical value.
~
P  P( F ( )  F ( )  )
(16)
~
where  is the conditional mean of F    F   .
2.3.6 Asymptotic distribution of threshold estimate
Chan (1993) and Hansen (1999) showed that when there is a threshold effect 1   2 , ˆ is
consistent for  0 , and that the asymptotic distribution is highly non-standard. Hansen (1999) argued that
the best way to form confidence intervals for  is to form the ‘no-rejection region’ using the likelihood
ratio statistic for tests on  . To test the hypothesis
H 0 :    0

H1 :    0
We construct the testing model:
SSE1 ( )  SSE1 (ˆ )
(17)
ˆ 2
Hansen (1999) pointed out that when LR1 ( 0 ) is too large and the p-value exceeds the confidence
LR1 ( ) 
interval, the null hypothesis is rejected5. Besides, Hansen (1999) indicated that under some specific
assumptions6 and H 0 :    0 ,
LR1 ( )  d
as n   , where  is a random variable with distribution function
P(  x)  (1  exp(  x )) 2
2
(18)
(19)
The asymptotic p-value can be estimated under the likelihood ratio. According to the proof of Hansen
5
Note that the statistic (17) is testing a different hypothesis from the statistic (15) introduced in the previous section.
H0 :   0
6
while
F ( ) is testing H 0 : 1   2 .
Refer to Hansen (1999) Appendix: Assumptions 1-8.
8
LR1 ( 0 ) is testing
(1999), the distribution function (18) has the inverse
c( )  2 log( 1  1   )
(20)
from which it is easy to calculate critical values. For a given asymptotic level  , the null hypothesis
   0 rejects if LR1 ( ) exceeds c( ) .
2.3.7 Multiple thresholds Model
If there exist double thresholds, the model is modified as:
    'h   d  
it
1 it
it
 i
vit   i   ' hit   2 dit   it

'
 i   hit   3 dit   it
if dit   1
if  1  dit   2
(21)
if  2  dit
where threshold value  1   2 . This can be extended to multiple thresholds model （  1 ,  2 ,  3 , n ）.
3. Empirical Results
It’s applied in this paper that the threshold theory is proposed by Hansen (1999) and the assumption
that debt ratio and corporate performance have asymmetric nonlinear relationship is made. First, if there
exists threshold effect, then test double threshold and single threshold effect are tested, respectively, and
the relevant formulas for both models are as follows:
    'h   d  
it
1 it
it
 i
vit   i   ' hit   2 dit   it

'
 i   hit   3 dit   it
    ' hit  1 dit   it
vit   i
'
i   hit   2 dit   it
if dit   1
if  1  dit   2 for double threshold effect
if  2  dit
if dit  
for single threshold effect
if dit  
The dependent variable v it represents firm value, which uses Tobin’s q as proxies. The
independent variable d it represents debt ratio, which is indeed the threshold variable. hit is a control
variable vector that contains four variables of natural log of total assets, management ownership ratio,
R&D expenses to total sales ratio, and advertising expenses to total assets ratio. Besides,  i , the fixed
effect, represents the heterogeneity of companies under different operating conditions. The errors  it is
assumed
to
be
independent
and
identically
distributed
with
mean
zero
and
finite
variance  2 (  it ~ iid (0,  2 ) ). i and t are symbols for firms and time periods.
This paper follows the bootstrap method to get the approximation of F statistic and then calculate the
p-value. After repeating bootstrap procedure 1,000 times for each of the three panel threshold tests, Table
9
3 presents the empirical results of test for single threshold, double threshold, and triple threshold effects.
we find that the test for a single threshold and a triple threshold are insignificant with a bootstrap p-value
of 0.896 and 0.78 respectively, the significant finding at the 1% level with a bootstrap p-value of 0.004
occurs only in the test for a double threshold. We thus conclude that there exists a double threshold effect
of the debt ratio on firm value. For the remainder of the analysis we work with this double threshold
model.
When there exists a double threshold effect of the debt ratios on firm value, all observations are
split into three regimes. Table 4 represents the regression slope estimates together with the conventional
OLS standard errors and White-corrected standard errors for two regimes. Figure 1 shows the single
threshold. Figure 2 and Figure 3 presents the double threshold.
The estimated model from our empirical result is represented as follows:
 i  0.001d it   it  if d it  48.92

  0.009d it   it  if 48.92  d it  49.55
vit   i
 i  0.002d it   it  if d it  49.55


ˆ1 and ˆ 2 plit the observations into three regimes depending on whether the threshold variable d it
is smaller or larger than the threshold value ( ˆ ).The regimes are distinguished by differing regression
slopes, ̂1 , ̂ 2 and ̂ 3 . In the first regime, where the debt ratio is below 48.92%, the estimate of
coefficient ̂1 is -0.001, but insignificant. In the second regime, where the debt ratio is above 48.92%%
but below 49.55%, the estimate of coefficient ̂ 2 is 0.009 , significant at the 1% level, which implies,
Tobin’s q will be increased by 0.009% via 1% increase of debt ratio. In the third regime, where the debt
ratio is above 49.55%, the estimate of coefficient ̂ 3 is -0.002, but insignificant. The estimate of
coefficient ̂1 , ̂ 3 are negative but not significant, which means, when the debt ratio is smaller than
48.92% or greater than 49.55% , We thus conclude that there exists an optimal debt ratio above
48.92%% but below 49.55% that increase firm value. These results are consistent with the trade-off
theory, for which we may search a “balance” that the interest tax shield is equal to the incremental costs
through debt financing.
This paper further investigates the influences of four control variables upon the firm value. The
estimation of coefficients of control variables shown in Table 5, which shows that natural log of total
assets and R&D expenses to total sales ratio have significant negative impact on firm value. It means that
the negative relationship between firm size and firm value and the negative relationship between R&D
expenses and firm value.此段再加 Hansen P361Tale4 圖
4. Conclusion
Two main theories currently dominate the capital structure debate: the trade-off theory and the
pecking order theory. The trade-off theory (Myers, 1977), is a static amount of debt leading managers to
10
find the “optimal capital structure” that maximize firm value when the benefits of debt equal the marginal
cost of debt. The pecking order theory ( Myers, 1984; Myers and Majluf, 1984), predicts that information
asymmetry between managers and investors creates a preference ranking in companies’ financing policy.
Beginning with internal funds, followed by debt, and then equity, firms work their way up the pecking
order to finance investment in an effort to minimize adverse selection costs.
The goal of this paper is to investigate whether leverage affects firm value for a panel of 272
Taiwanese listed companies during the nine-year period 1997to 2005. Advanced panel threshold
regression model is performed to test if there exists an “optimal” debt ratio, which may result in threshold
effects and asymmetrical relationships between debt ratio and firm value. Tobin s’ q are adopted as proxy
variables for firm value.
The result shows that there exists double thresholds effect between debt ratio and firm value. The
estimated threshold value ( ˆ1 , ˆ 2 ) are found to be 48.92% and 49.55%. Among three coefficients
( ̂ 1 , ̂ 2 , ̂ 3 ), the estimate of coefficient ̂1 , ̂ 3 are negative but not significant, which means when the
debt ratio is smaller than 48.92% or greater than 49.55% , the relationship between debt ratio and firm
value is unclear. In the second regime, where the debt ratio is between 48.92% and 49.55%, the estimate
of coefficient ̂ 2 is 0.009, which implies Tobin’s q will be increased by 0.009% via 1% increase of debt
ratio. Thus, it’s concluded that there exists an optimal debt ratio between 48.92% and 49.55% that
increases firm value. These results are more consistent with the trade-off theory (Modigliani and Miller,
1963; Myers, 1977, and Ross, 1977) for which firm may search a “balance” that the interest tax shield is
equal to the incremental costs through debt financing. This suggests that financial managers should use
financial leverage wisely in order to maximize the firm’s value and investors should refer to the debt ratio
to make investment decisions.
11
References
Aggarwal, R. and S. Zong (2006), “The cash flow–investment relationship: International evidence of
limited access to external finance,”Journal of Multinational Financial Management, 16, 89–104.
Altman, E. I. (1984), “A Further Empirical Investigation of the Bankruptcy Cost Question,” The Journal
of Finance, 39(4), 1067-1090.
Baker, M., Wurgler, J., 2002. Market timing and capital structure. The Journal of Finance 57, 1–32.
Castanias, R. (1983), “Bankruptcy Risk and Optimal Capital Structure,” The Journal of Finance, 38(5),
1617-1636.
Chan, K.S. (1993), “Consistency and Limiting Distribution of the Least Squares Estimator of a
Continuous Threshold Autoregressive Model,” The Annals of Statistics, 21, 520-533.
Chung, K. H. and S. W. Pruitt (1994), “A Simple Approximation of Tobin’s q,” Financial Management,
23(3), 70-74.
Davies, R. B. (1977), “Hypothesis testing when a nuisance parameter is present only under the
alternative,” Biometrika, 64, 247-254.
______ (1987), “Hypothesis testing when a nuisance parameter is present only under the alternative,”
Biometrika, 74, 33-43.
Flannery, Mark Jand Kasturi P. Rangan (2006), “ Partial adjustment toward target capital structures,”
Journal of Financial Economics 79 (2006) 469–506.
Frank,M.Z. and V.K. Goyal(2004), “The effect of market conditions on capital structure adjustment,”
Finance Research Letters, 1, 47–55.
Hansen, B. E. (1996), “Inference when a nuisance parameter is not identified under the null hypothesis,”
Econometrica, 64, 413-430.
______ (1999), “Threshold effects in non-dynamic panels: Estimation, testing and inference,” Journal of
Econometrics, 93, 345-368.
______ (2000), “Sample splitting and threshold estimation,” Econometrica, 68, 575-603.
Jensen, M.C. and W. H. Meckling(1976), “Theory of the firm: Managerial Behavior, agency cost and
ownership structure,” Journal of Financial Economics,3, 305-360.
Kim, W. S. and E. H. Sorensen (1986), “Evidence on the Impact of the Agency Costs of Debt on
Corporate Debt Policy,” Journal of Financial and Quantitative Analysis, 21( 2), 131-145.
Miller, M. H. (1977), “Debt and Taxes,” Journal of Finance, 32, 261-275.
Modigliani, F. and M. H. Miller (1958), “The cost of capital, corporate finance, and the theory of
investment,” American Economic Review, 48, 261-297.
______ (1963), “Corporate income taxes and the cost of capital: A correction,” American Economics
Review, 53, 433-443.
Myers, S. C. (1977), “The Determinants of Corporate Borrowing,” Journal of Financial Economics, 5,
147-175.
______ (1984), “The Capital Structure Puzzle,” Journal of Finance, 39, 575-592.
Myers, S. C. and N. S. Majluf (1984), “Corporate Financing and Investment Decisions When Firms Have
12
Information That Investors Do Not Have,” Journal of Financial Economics, 13(2), 187-222.
Ross, S. A. (1977), “The Determination of Financial Structure: the Incentive Signaling Approach,” Bell
Journal of Economics and Management Science, 8(1), 23-40.
Stiglitz, J. E., ‘Some aspects of the pure theory of corporate finance: bankruptcies and takeovers’,Bell
Journal of Economics and Management Science, Vol. 3, 1972, pp. 458–482.
Tong, H. (1978), “On a Threshold Model, in C.H. Chen (ed.), Pattern Recognition and Signal Processing,
Amsterdam: Sijthoff & Noordhoff, 101-141.
Welch, I., 2004. Capital structure and stock returns. Journal of Political Economy 112, 106–131.
13
Table 1 Distribution of Sample
Industry
Number of the sample
Proportion of the samples
Cement
7
2.57%
Food
13
4.78%
Plastics
16
5.88%
Textiles
34
12.50%
Electric, Machinery
14
5.15%
Appliance, Cable
10
3.68%
Chemical
18
6.62%
Class, Ceramics
6
2.21%
Paper, Pulp
7
2.57%
Steel, Iron
18
6.62%
Rubber
7
2.57%
Automobile
2
0.74%
Electron
55
20.22%
Construction
22
8.09%
Transportation
10
3.68%
Tourism
5
1.84%
Department Stores
10
3.68%
Other
18
6.62%
Total
272
100.00%
14
Table 2 Descriptive Statistics of Variables for 272 firms
Variables
Statistic
86 年
1.54298 1.17255 1.11566 0.55607 0.63109 0.61516
0.70696 0.67504 0.64153
0.85078
Tobin's Q
Average
Maximum
Minimum
Std. Dev.
7.6233 6.11479 7.90927 3.32177 5.50582 3.5158
3.00755 2.26771 4.97011
7.90927
0.18843 -0.0525 -0.2744 -0.4317 -0.5449 -0.5525
-0.0101 -0.0381 -0.1715
-0.5525
1.00619 0.83048 1.18608 0.53085 0.64544 0.44246
0.45399 0.40252 0.51866
0.78629
Average 39.0678 39.3167 40.9019 42.7617 43.2783 43.9908
94.2 97.26
97.5 98.54
Maximum 104.04 108.04
3.2
4.95
7.22
6.55
7.88
3.54
Minimum
Std. Dev. 15.2508 16.0174 15.6339 15.6559 16.0538 17.1044
43.1507 43.3181 42.0372
41.9804
Average 0.50015 0.63585 0.46926 0.35371 0.38261 0.35665
8.03 11.63 10.54
Management Maximum 12.44 12.33 10.03
0
0
0
0
0
0
Ownership Minimum
Std. Dev. 1.40523 1.70767 1.31003 1.10363 1.30874 1.24282
Debt Ratio
Size
R&D
Expenses
87 年
88 年
89 年
90 年
91 年
92 年
93 年
96.35
2.5
94 年
Total
98.88 112.61
2.08
112.61
1.55
1.55
17.255 17.9874 18.9035
16.7519
0.65 0.63324 0.63048
0.51244
10.07
8.32
9.98
12.44
0
0
0
0
1.42398 1.2976 1.38261
1.36553
15.7921 15.9226 15.9988 16.0634 16.0542 16.0533
16.0696 16.0887 16.0827
16.0139
19.1188 19.1307 19.1679 19.6473 19.6318 19.7291
19.798 20.0049 20.0451
20.0451
13.45 13.4177
13.4347 13.4582 12.6558
12.6558
1.01901 1.01821 1.04626 1.10105 1.11246 1.14413
1.17143 1.19506 1.2493
1.12199
Average 1.29923 1.30871 1.2286 1.22956 1.64923 1.56868
Maximum 14.67 16.05 14.89 15.42 54.59 44.67
1.36846 1.19493 1.27246
1.34665
Average
Maximum
Minimum
Std. Dev.
13.4427 13.3823 13.4416 13.4858
0
0
0
0
0
0
Minimum
Std. Dev. 2.42469 2.43708 2.1355 2.1964 4.46087 3.7292
Average 0.74241 0.8227 0.86541 0.71578 0.64923 0.63743
Advertising Maximum 15.0779 25.8538 23.2652 15.9404 8.16344 9.4443
0
0
0
0
0
0
Expenses
Minimum
Std. Dev. 1.72723 2.3386 2.22231 1.7309 1.46739 1.50514
15
15.6
14.61
18.87
54.59
0
0
0
0
2.52359 2.07807 2.37747
2.81497
0.57062 0.57062 0.57062
0.68276
9.56762 9.56762 9.56762
25.8538
0
0
0
0
1.39547 1.39547 1.39547
1.72108
Table 3 Tests for threshold effects between the debt ratio and Tobin’s Q
Single threshold effect test
Threshold
-value
F
p-value
Double threshold effect test
Threshold
-value
F
p-value
49.55
5.2743447
0.896
Critical Value of F
1%
5%
10%
30.37 20.182157
16.49
notes: 1. F Statistic and
Triple threshold effect test
Threshold 27.97 48.93
-value
49.55
F
6.6421943
p-value
0.78
48.93
49.55
27.732463
0.004***
Critical Value of F
1%
5%
10%
22.26 18.164921
15.69
Critical Value of F
1%
5%
10%
50.66 37.46094 28.97
P-value result from repeating bootstrap procedure 1000 times for each of the
three bootstrap tests.
2. ***, **, and *, represent the significant at 1%, 5%, and 10% levels, respectively.
Table 4 Estimated Coefficients for Tobin’s Q
Coefficient
OLS se
White se
t OLS
estimate
̂ 1
-0.00109 0.001852
-0.59039 0.001682
̂ 2
0.008882 0.002475
3.5894** 0.004744
̂ 3
-0.00193
notes: 1.
̂ 1 , ̂ 2
ˆ1  d it  ˆ 2
and
and
̂ 3
0.001406
-1.37215
0.001294
are the coefficient estimates for regimes of
tW hite
-0.65011
1.872264
-1.49187
d it  ˆ1 ,
d it  ˆ2 .
Table5 Estimation of Coefficients of Control Variables
Coefficient
OLS se
White se
t OLS
estimate
1
0.010792
0.011857
0.9102
0.009048
2
-0.79509
0.040601 -19.5829*** 0.070456
3
-0.01457
0.008076
0.008625
-1.8036*
3
-0.01105
0.012376
-0.8927
0.010309
tW hite
1.1928
-11.2850
-1.6887
-1.0717
notes: 1. ˆ1 、 ˆ2 、 ˆ3 及 ˆ4 represent the estimated coefficients: management ownership ratio,
natural log of total assets, ratio of R&D expenses to total sales, and ratio of advertising
expenses to total assets.
2. ***, **, and *, represent the significant at 1%, 5%, and 10% levels, respectively.
16
Single Threshold
Double Threshold
17
18