Study on Capital Structures & Operating Performances of
Credit Cooperatives in Taiwan
—Application of Panel Threshold Method
Kuei-Chiu Lee
Department of Cooperative Economics, Feng Chia University,
Taichung, Taiwan
Chia-Hao Lee
Department of Finance, National Chung Hsing University
Taichung, Taiwan
Submitted to
The 15th Annual Conference on PBFEAM*
held at
the Equatorial Hotel in Ho Chi Minh City, Vietnam
on July 20 and July 21, 2007.
0
Study on Capital Structures & Operating Performances of
Credit Cooperatives in Taiwan
—Application of Panel Threshold Method
Abstract
This paper collects financial data of the credit cooperatives in Taiwan from 1994
through 2005, applies regression model based on panel threshold and explores their
capital structure and operating performance.
This paper uses savings on net worth
value ratio, net worth on loan ratio, net profit margins, current ratio and loan growth
rate as proxy variables.
Overall, the empirical finding is that the credit cooperatives
of Taiwan are under the influence of capital structures.
The threshold variables (net
worth to loan ratio) have two threshold values, 0.16 and 0.212.
When the threshold
value is between 0.16 and 0.212, every unit of growth in loans increases net profit
margins by 2.094 times.
On the contrary, with a poor capital structure, the increase
in loans reduces net profit margins.
The empirical finding also shows that the
growth in loans for the credit cooperatives in northern and central Taiwan affects net
profit margins, especially for those in central Taiwan.
However, threshold
relationship does not exist for the credit cooperatives in southern Taiwan.
Keywords: Credit cooperatives, capital structure, Panel Threshold, performance.
1
Introduction
Credit cooperatives in Taiwan are not only a foundation in the financial system,
but also a member of cooperative enterprises. They have been around for over 90
years. In 1989, the Taiwanese government started to lift its controls over interest rates.
In 1991, the market was open to new banks. After the liberalization of the financial
markets, structural changes have been happening in Taiwan. As banks gradually
expanded their scope of services and operations, credit cooperatives that focus on
small loans in the regions have been heavily hit. Over the past decade, the market
share of credit cooperatives in the deposit market went from 13.28% in 1991 to 4.37%
in December 2000. Their market share in the loan market declined from 10.07% in
1991 to 3.38% at the end of 2000. Return on equity dropped from 18.84% to 1.2%. In
1991, the number of branches of credit cooperatives totaled 572 and accounted for
20.5% of all the branches in the financial market. In 1994, there were still 74 credit
cooperatives. However, the run on the Fourth Credit Cooperative of Changhua in
1995 and continuous transformation of large credit cooperatives into commercial
banks since 1997 have reduced the number of credit cooperatives to only 28 at the end
of 2005, as certain credit cooperatives were taken over or merged into commercial
banks.
At the end of 2005, there were a total of 295 branches of credit cooperatives,
accounting only 3.47%1 of the total branches in the financial market in Taiwan.
In
other words, over the course of the 13 years, 46 credit cooperatives disappeared from
the financial market.
Their competitiveness also declined.
In 1996, the deposits
with credit cooperatives totaled NT$1,620.2 billion and the loans totaled NT$1,286.6
billion.
By the end of 2005, the deposits with credit cooperatives totaled NT$598.3
billion while the loans totaled NT$337.7 billion only.
cooperatives were seriously hit.
This shows that credit
Aiming for a turnaround, many credit cooperatives
started to transform themselves into commercial banks or merged with commercial
banks since 1995, as attempts to improve operating performance.
However, in
addition to mergers with commercial banks or transformations into ones, credit
cooperatives should continue to endeavor to improve their performance and efficiency.
As credit cooperatives operate in the banking market as cooperatives, they need to
strike a balance between keeping up the spirits as cooperatives and operating as banks.
In the fierce competition of the financial market over the past years, how to improve
1
Chang, S.Y., Operating Performance of Credit Cooperatives in Taiwan Over the Past Decade,
Cooperatives Report, Issue 58, Jan. 2006, p.3
2
capital structure and operating efficiency is a critical issue for credit cooperatives.
For any credit cooperatives to strengthen capital structure and improve operating
efficiency, the first task is optimal asset allocations, i.e. the most appropriate mix of
equity and liabilities, in order to minimize cost of capital and to maximize
shareholders’ value.
This is the goal that capital structure theory tries to achieve.
The previous studies on capital structure include Titman and Wessels (1988), who
pointed out the inverse correlation between the short-term debt ratio and scale of
company operations.
Bradley et al. (1984) applied computer simulation analysis,
find that there exists an optimal liabilities ratio for companies and indicate the inverse
correlation between debt ratio and earnings volatility.
Eric (2002) argued that the tax
shields achieved by leverage can effectively increase the value of the firm, but such
benefits get offset by the cost associated with leverage.
Therefore, liability ratio
must be at its optimal level in order to effectively enhance the value of the firm.
Hameeteman and Scholtens (2000) applied Pearson method and a multiple regression
model to examine the correlation between growth rates and capital structures, assets,
changes of pre-tax earnings and scales of the top 100 banks listed by The Banker from
1987 through 1997.
They found that there exists a significant negative correlation
between capital sizes, assets, growth rates and pre-tax earnings.
Also, the growth
rates of large banks decline gradually with the increase of capital, assets and pre-tax
earnings.
The majority of previous studies focus on the operating performances of
commercial banks.
As credit cooperatives are similar to commercial banks in nature,
this study attempts to analyze operating performances of credit cooperatives in order
to identify the optimal capital structure.
Meanwhile, as credit cooperatives are
highly regional, this paper divides the credit cooperatives into three groups in
northern, central and southern Taiwan, in order to explore whether capital structures
have differing effects on operating performances in different regions.
Therefore, this
paper adopts Panel Threshold model proposed by Hansen (1999) to conduct analysis
so as to explore whether there is an optimal debt ratio for credit cooperatives.
If the
debt ratio of a credit cooperative is smaller than the threshold of optimal debt ratio,
capital structure and operating performance is positive correlated.
In other words,
the increase of loans within this scope may effectively increase efficiency.
On the
contrary, if the debt ratio is higher than the threshold of optimal debt ratio, the
increase of financial risks may reduce operating performances for credit cooperatives.
3
This paper studies on the 28 credit cooperatives from 1994 through 2005 and uses
proxy variables to construct Panel Threshold model to explore the relationship
between their capital structures and operating performances.
Data description
The major businesses of credit cooperatives are to take deposits and offer loans.
Therefore, this paper uses deposits, share capital, operating expenses, loans, operating
income, assets and net worth as relevant proxy variables.
Operating expenses are the
costs dedicated to the taking of deposits and offering of loans.
Operating income is
mainly the interest income from loans, but also includes fee incomes, gains from the
money markets and other investments.
Customers for loans and deposits include
members, associate members and non-members, while loans are mainly offered to
members or associate members.
Share capital paid by members is the major source
of equity and equity is paid-up based on the legal requirements for a number of
businesses of credit cooperatives.
This paper converts all the relevant variables into
proxy variables, such as capital adequacy, capital structure, profitability, liquidity and
business growth.
The definitions of all the relevant proxy variables in this paper are
as follows:
1. Capital Adequacy:
In order to measure the adequacy of their own capital for credit cooperatives, this
paper uses deposit to net worth ratio as the proxy variable for capital adequacy.
The higher the deposit to net worth ratio means the lower the capital.
Deposit to net worth ratio = deposit/net value
2. Capital Structure
This variable measures business risks of credit cooperatives.
This paper uses net
worth to loan ratio as the proxy variable for capital structure.
The lower the net
worth to loan ratio, the higher the business risks are.
The inability to recover
loans may trigger an operational crisis.
Net worth to loan ratio = net value / loans
3. Operating Performance
Profitability is a measurement for operating performance for credit cooperatives.
Net profit margin is used as the proxy variable for operating performance.
Net
profit margin measures the pre-tax earnings as a percentage of operating income.
The highest the margin, the better profitability is.
4
Net profit margin = pretax earnings/revenue
4. Liquidity
Liquidity measures the ability of credit cooperatives to convert assets into cash to
pay back debts within one year.
liquidity ratio should be over 2.
It is also debt repayment ability.
In principle,
The higher the ratio, the more likely credit
cooperatives are to pay back current liabilities.
If current ratio is smaller than 1,
it means there are liquidity risks in the short term.
Current ratio = deposits/loans
5. Business Growth
As loans are the main driver of profitability, the growth in loans is an indicator of
business growth and capital utilization for credit cooperatives.
Loan growth rate = loans (t) – loans (t-1) / loans (t-1)
As capital structure affects loans offered by credit cooperatives, a strong balance
sheet is able to allow growth in loans and hence to boost profitability and overall
operating performance.
Empirical Model - Single Threshold Model
This model uses balance panel data  yit , qit , xit :1  i  n,1  t  T  , where i
indicates the number of cross-section samples, t indicates the length of interval, yit
dependent variable, qit threshold variable, xit independent variable.
The Formula
is as follows:
yit  ui  1 xit I (qit   )   2 xit I (qit   )  eit
(1)
where I ( ) is an objective function. Therefore, the above formula may also be
expressed as follows:
u    x  e , if q  
i
1 it
it
it
yit  
ui   2 xit  eit , if qit  
Assume   ( 1  2 ) , Eq.(1) can also be expressed as :
yit  ui   xit ( )  eit
(2)
From the above formula, we know that when threshold variable qit is bigger or
smaller than threshold value  , the samples can be divided into two groups, which can
be expressed in different slopes 1 and  2 . To tell 1 from  2 , independent
5
variable xit has to be time invariant.
Meanwhile, it is also assumed that threshold
variable qit is time invariant. Error item eit must comply with the iid assumptions ,
where the average is 0, and variance is  2 . The extended model allows the existence
of heterogeneous variables.
When T remains constant, and n   , this model
derives similar conclusions.
The purpose of this paper is to use known data yit , qit and xit , to estimate
known parameters  ,  and  2 .
Therefore, it uses the balance threshold model
proposed by Hansen (1999) to validate the asymptotic distributions of threshold
values. Example for single-threshold models that do not contain controlled variables
are as follows:
(A) Estimates
The traditional method to eliminate individual effect ( ui ) is to cross out
individual averages, i.e. de-mean.
This method is easy to understand in linear
models, but requires extra cautions in non-linear models.
Therefore, this paper
derives the average of Eq.(1):
yi  ui   xi ( )  ei
(3)
Where yi  T 1 t 1 yit , ei  T 1 t 1 eit
T
T
 T 1  T xit I (qit   ) 
t 1

xi ( )  T  t 1 xit ( )  
T

1
T

  t 1 xit I (qit   ) 
1
T
Eq.(2) subtracts Eq.(3) can derive:
yit*   xit* ( )  eit*
(4)
Where yit*  yit  yi , xit* ( )  xit ( )  xi ( ) 及 eit*  eit  ei .
All the data and errors of the second phase and the following get stacked up and
can be defined as follows:
 yi*2 
 xi*2 ( ) ' 
ei*2 
 

 *  
yi*    , xi* ( )  
 , ei   
 y* 
 x* ( ) ' 
e* 
 iT 
 iT

 iT 
Based on the above definition, Y *  yi* , X * ( )  xi* ( ) , e*  ei* , therefore, Eq.(4)
can be rewritten into the following:
Y *  X * ( )   e*
(5)
6
When  is known, ordinary least squares estimator (OLS) can be used to estimate
the slope parameter  .
The estimation is as follows:
ˆ ( )  ( X * ( ) X * ( )) 1 X * ( )Y *
(6)
The residual of the regression vector, e *  Y *  X * ( ) ˆ ( ) .
Meanwhile, sum
square error can be derived:
S1 ( )  e * ( )e * ( )
(7)
 Y *  I  X * ( )( X * ( ) X * ( )) 1 X * ( )  Y *
Chan (1993) and Hansen (2000) suggested the use of ordinary least squares
estimator should be used to estimate threshold value  .
This derives the minimum
residual sum of square so that the estimation of the minimum squares of  should
be:
ˆ  arg min S1 ( )
(8)

When threshold value ( ˆ ) is determined, it is possible that the number of
observations in certain section are too few or null.
Therefore, in the selection of the
optimal threshold value ( ˆ ), limits can be added that 1% or 5% (or any percentage)
observations should be included in-between two sections.
As soon as the optimal threshold value ˆ is derived, the estimation of slope
should be    (ˆ) , and residual vector should be ê  eˆ* (ˆ ) .
The estimation of
residual variances should be:
ˆ 2 
1
1
S1 (ˆ )
eˆ* eˆ* 
n(T  1)
n(T  1)
(9)
(B) Testing
It is very important to test whether threshold effects exist.
Based on the linear
limitations of Eq.(1), the null hypothesis that threshold effects do not exist can be
expressed as H 0 : 1   2 .
Under the null hypothesis, threshold value  cannot be
derived and there exist nuisance parameters.
This type of testing yields non-standard
distributions so these questions are generally described as Davies Problem2.
Hansen
(1996) suggests that the approximations derived from bootstrapping simulations that
are similar to distributions are more effective than testing.
2
Please refer to Davies (1977,1987).
7
Therefore, under the null
hypothesis that there is no threshold effect, the model can be modified into the
following:
yit  ui  1 xit  eit
(10)
After conversion to eliminate fixed-effect, we derive:
yit*  1 xit*  eit*
(11)
Where regression coefficient 1 can be estimated with ordinary least squares,
therefore, it is possible to derive ̂1 , residual ( eˆit* ) and sum of residual squares
( S 0  eˆ* ê* ). At this point, the likelihood ratio of null hypothesis is as follows:
F1 
S0  S1 (ˆ )
ˆ 2
(12)
Where asymptotical distribution of F1 is not standard distribution.
Hansen
(1996) derives a first-order asymptotic distribution by bootstrapping, and finds that
p-value constructed during bootstrapping is effective.
Therefore, the asymptotical
distribution of F1 using bootstrapping under the null hypothesis is close to p-value.
When p-value is smaller than threshold value, the null hypothesis is rejected.
(C) Estimations of Asymptotical Distribution of Threshold Value
According to Chan (1993) and Hansen (2000), the threshold effects of the
regressions do exist.
In other words, when coefficient 1   2 , the estimated
threshold value ˆ and the actual threshold value  0 will be consistent.
At this time,
due to the presence of nuisance parameter, asymptotic distribution exhibits a highly
non-standard pattern.
Hansen (1997) suggested that it is necessary to construct a
no-rejection region of confidence interval to test  .
When the value of LR1 ( 0 ) is
big enough so that p value falls outside the confidence intervals, it means that we can
significantly reject null hypothesis H 0 .
This means that threshold estimated value
 does not equal to the actual threshold value  0 . The testing method is as follows.
The first step is to test the null hypothesis H 0 :    0 , and the maximum
approximation of estimates is :
LR1 ( ) 
S1 ( )  S (ˆ )
ˆ 2
(13)
8
LR1 ( 0 ) is to test whether H 0 :    0 .
Eq.(12) and Eq.(13) are different.
In other
words, it is to test whether threshold estimate value equal to the actual threshold value.
F1 is to test whether H 0 : 1   2 .
In other words, it is to test whether threshold
effects exist.
Hansen (1999) pointed out that when null hypothesis H 0 :    0 stands and
meets with the assumptions3, LR1 ( )  d  , when n   ,  is a random variable
of a probability distribution:
P(  x)  (1  exp( x 2)) 2
(14)
If there are no nuisance parameters, according to Eq.(14), the asymptotical
distribution of likelihood ration statistic is not standard.
When n   ,  2  1  0 ;
this implies that the larger the sample size, the smaller the variances becomes between
the slopes of the two sections.
However, if the threshold effects are significant,
threshold values (regardless of the levels) can be accurately estimated.
asymptotic distribution derived from Eq.(14) is critical.
The
Approximate confidence
intervals can be derived from Eq.(14). The inverse function of Eq.(14) can derive
the following:
C ( )  2 log(1  1   )
(15)
Eq.(15) can derive the threshold value.
When the confidence interval is 
and LR1 ( 0 )  C ( ) , we can reject H 0 :    0 , i.e. the actual threshold value not
equal to threshold estimate value.
(D) Asymptotical Distribution of Slope Parameters
Estimate formula ˆ  ˆ (ˆ ) is under the influence of threshold estimate value.
This makes it even more difficult to determine  .
Chan (1993) and Hansen (2000)
indicate that when threshold estimate is equal to the actual threshold value, ˆ  ˆ (ˆ ) .
Therefore, ˆ is close to normal distribution and its covariance matrix is as follows:
 n T

Vˆ    xit* (ˆ ) xit* (ˆ ) 
 i 1 t 1

1
ˆ 2
(16)
In estimating the confidence interval for  , errors should meet with the iid
3
Please refer to Hansen (1999) in the attachments regarding the assumptions 1 to 8 on P.363.
9
assumptions; however, in estimating slope parameters, the assumptions can be
broadened.
If the allowed error exists conditional heterogeneous variances, the
covariance matrix of ˆ is as follows:
1
1
 n T
  n T
 n T

Vˆh    xit* (ˆ ) xit* (ˆ )    xit* (ˆ ) xit* (ˆ)(eˆit* ) 2   xit* (ˆ) xit* (ˆ)  (17)
 i 1 t 1
  i 1 t 1
 i 1 t 1

Multiple Threshold Models
Model (1) is a single threshold model.
thresholds may appear.
However, in practice, multiple
Below is an explanation of double threshold model:
yit  ui  1xit I (qit   1 )   2 xit I ( 1  qit   2 )  3xit I ( 2  qit )  eit
where threshold value  1   2 .
(18)
It is possible to extend the method of double
threshold model into multiple threshold models.
(A) Estimates
When ( 1 ,  2 ) is known, the linear slope parameters ( 1 , 2 , 3 ) can estimated
with ordinary least square to computer sum square of errors S ( 1 ,  2 ) .
However,
the process is highly complex and it requires approximate N 2  (nT )2 to gradually
identify by grid search.
Chong (1994), Bai (1997) and Bai-Perron (1998) found that in the multiple
change point model, the continuous estimates are fixed.
applicable to the multiple threshold models.
Some of the logic seems
The process is as follows.
The first
step is to let S1 ( ) in Eq.(7) be the residual sum of squares of single threshold
models.
Also, let the minimum value of S1 ( ) equal to the optimal threshold
value ˆ1 .
Chong and Bai suggest that ˆ1 will be consistent with either  1 or  2
in the double threshold model (depending which one has stronger effects).
After fixing the first stage, the estimation is ˆ1 .
The selection criteria of
thresholds in the second stage are as follows:

 S ( ,  ) if  1   2
S2r ( 2 )   1 2

 S ( 2 ,  1 ) if  1   2
(19)
Where the threshold estimate of the second stage is as follows:
ˆ2r  arg min S2r ( 2 )
(20)
2
10
The estimate cannot accept too few observations within any interval.
Therefore,
in Eq.(20), a condition to limit the number of minimal observations in the three
intervals is added.
does not.
Bai (1997) finds that ˆ2 boasts gradual efficiency while ˆ1
This is because ˆ1 is derived by computing the residual sum of squares in
the single threshold model.
Therefore, due to the fact that effects of one threshold
are neglected and ˆ2 boasts gradual efficiency, it is possible to further modify ˆ1
through the estimate of the third step.
estimate ˆ2 of the second stage.
The third step is to first fix the threshold
At this point, the selection criteria of thresholds in
the third step are as follows:
 S ( ,   ) if    

2
2
1
S1r ( 1 )   1

 S ( 2 ,  1 ) if  1   2
(21)
Further refined threshold estimate are as follows:
ˆ1r  arg min S1r ( 1 )
(22)
1
Bai (1997) pointed out that refined threshold estimate ˆ1r boasts gradual
efficiency at change point estimation.
(B) Determination on the Number of Thresholds
According to the previous mentioned model Eq.(18), it is possible that there may
be no threshold, only one threshold or two thresholds.
In the single threshold model,
it is suggested that F1 stats are used to test whether there is one single threshold or
no threshold.
value.
Bootstrapping method should be applied to estimate the gradual p
If F1 stats reject the null hypothesis, it should be further tested whether
there is one threshold or two thresholds.
It is possible to derive, in the estimates of
the second stage, minimum residual sums of squares S 2r ( 2 ) and variance
estimate ˆ 2  S2 (ˆ2 ) / n(T  1) .
Therefore, the likelihood ratio stats to test single or
double thresholds are as follows:
F2 
S1 ( 1 )  S 2 ( 2 )
ˆ 2
(23)
When F2 stats reject the null hypothesis, it means double thresholds exist.
11
(C) Construction of Confidence Intervals
It is necessary to construct a confidence interval for the two threshold
parameters { 1 ,  2 } .
Bai (1997) uses change point models and finds that the refined
threshold estimates and that of single threshold model share the same asymptotic
distribution.
Therefore, it is suggested that confidence interval should be
constructed in the same way that single threshold model is constructed.
LR2 ( ) 
Therefore,
S2 ( )  S2 (ˆ2 )
S1 ( )  S1 (ˆ1 )

and
LR
(

)

1
ˆ 2
ˆ 2
Where S2 ( ) and S1 ( ) are defined in Eq.(19) and Eq.(21) respectively.
Therefore, the confidence interval of (1   )% of  1 and  2 can be defined as
LR1 ( )  C ( ) and LR2 ( )  C ( ) .
Empirical Result
This paper conducts its research and analysis based on Panel threshold model
proposed by Hansen (1999) to explore whether loans of credit cooperatives in Taiwan
are under the influence of capital structures and whether there exist any threshold
relationship between loans and operating performances so that it is possible to analyze
the optimal capital structures for credit cooperatives in Taiwan.
Meanwhile, this
paper also examines whether there are differences in the impacts of loans to capital
structures for credit cooperatives in northern, central and southern Taiwan.
This
paper studies on the 28 credit cooperatives, including 11 in northern Taiwan (Taipei
First Credit Cooperative, Taipei Fifth Credit Cooperative, Taipei Ninth Credit
Cooperative, Keelung First Credit Cooperative, Keelung Second Credit Cooperative,
Tamshui Credit Cooperative, Tamshui First Credit Cooperative, Ilan Credit
Cooperative, Taoyuan Credit Cooperative, Hsinchu First Credit Cooperative, Hsinchu
Third Credit Cooperative), 9 in central Taiwan (Chunan Credit Cooperative, Taichung
Second Credit Cooperative, Changhua First Credit Cooperative, Changhua Fifth
Credit Cooperative, Changhua Sixth Credit Cooperative, Changhua Tenth Credit
Cooperative, Lugang Credit Cooperative, Chiayi Third Credit Cooperative, Chiayi
Fourth Credit Cooperative) and 8 in souther Taiwan (Tainan Third Credit Cooperative,
Hualien First Credit Cooperative, Hualien Second Credit Cooperative, Penghu First
Credit Cooperative, Penghu Second Credit Cooperative, Kinmen Credit Cooperative,
Kaohsiung Second Credit Cooperative, Kaohsiung Third Credit Cooperative).
12
All
the data regarding credit cooperatives are the annual reports from 1994 through 2005.
Based on the previous operational variable explanations and the research method
proposed by Hansen (1999), the model is defined as follows:
git  i  i hit  i dit （
I qit )   it
Where g it represents net profit margins, hit represents controlled variables
and they are deposit to net wroth ratio and current ratio, respectively, d it represents
loans growth while qit represents net worth to loan ratio.
This study uses net worth to loan ratio as threshold variable to examine whether
loans growth and operating performances of credit cooperatives are under the
influence of capital structure, and whether there exists asymmetric threshold
relationship.
In the process of panel threshold regression, it is necessary to first test
whether threshold effects exist.
Hanen (1999) points out that it is possible to derive
p-value and F-stats using bootstrapping method and test in order to know whether
there exist single-threshold, double-threshold or triple-threshold effects.
This study
first tests the threshold effects for the 28 credit cooperatives in Taiwan.
According
to Table 1, under 5% significant level, both single threshold and double thresholds are
significant.
Their F-stats are 6.851 and 39.134, respectively and double-threshold
effects are more significant.
The empirical research finds that loans growth and
operating performances of credit cooperatives in Taiwan exists double threshold
relationships.
In other words, loans growth and operating performances of credit
cooperatives are influenced by their capital structures. There are asymmetric
double-threshold relationships between them.
Figure 1, Figure 2 and Figure 3 show
the threshold estimates from plots of the concentrated likelihood ratio function
LR1 ( ), LR2r ( ) and LR1r ( ) (details about these three figures see Hansen (1999)).
The empirical finding of Table 2 shows the threshold values and threshold
parameter estimates of these 28 credit cooperatives in Taiwan.
The model can be
expressed as follows:
 i  1hit  1dit   it

git   i  1hit   2 dit   it
   h   d  
3 it
it
 i 1 it
if qit  0.16
if 0.16  qit  0.212
if qit >0.212
The threshold parameters in Table 2 show that there are two threshold values for
net worth to loan ratio and these two threshold values are 0.16 and 0.212, respectively.
13
These two threshold values divide observations into three regimes and form a
non-linear asymmetric relationship.
In other words, the corresponding threshold
parameter value of different regimes will have different  i .
These results indicate
that when net worth to loan ratio is either lower than 0.16 or higher than 0.212, loans
growth creates negative impacts on net profit margins of credit cooperatives.
The
poor capital structures of credit cooperatives within this range indicate that increase in
loans will hurt net profit margins.
14
Table 2 further indicates that the optimal net worth to loan ratio of credit cooperatives
should be between 0.16 and 0.212. Within this range, the impacts of loans growth to
net profit margins are obvious and the impact is significant.
In other words, one-unit
increase in loans growth creates 2.094-unit increase in net profit margins.
Meanwhile, this paper also finds that two controlled variables such as the deposit to
net worth ratio and current ratio have significant impacts on net profit margins.
The
deposit to net worth ratio show significant and positive impact on net profit margins,
however, on the other hand, current ratio show significantly but negative impact on
net profit margins.
In sum, this paper finds that there exists an asymmetric
relationship in the effects of loan growth on operating performance of credit
cooperatives in Taiwan.
Table 3 reports the number of firms in each regime by year.
We find that most of the firms are in the lower net worth to loan ratio regime and this
result indicates that most of the credit cooperatives are involved in the higher risk.
As we know that the lower the net worth to loan ratio, the higher the business risks are.
The inability to recover loans may trigger an operational crisis.
Moreover, this paper also examines whether threshold relationships are different
in northern, central and southern Taiwan.
This paper tests the threshold effects for
11 credit cooperatives in northern Taiwan, 9 in central Taiwan and 8 in southern
Taiwan. The empirical finding on Table 4 shows that under 5% significant levels,
there is a double-threshold relationship in northern Taiwan.
15
The F-stats and p-value
of the threshold values in northern Taiwan are 18.282 and 0.028, respectively.
There
exists a triple-threshold relationship in central Taiwan under 10% significant levels.
The F-stats and p-value of the threshold values for central Taiwan are 8.255 and 0.09,
respectively.
However, there seems to be no significant threshold effects in southern
Taiwan. These results indicate that both operating performance and loans growth of
credit cooperatives in northern and central Taiwan are under the influence of net
worth to loan ratio and therefore, there exist threshold relationships.
However, there
is no threshold relationship in southern Taiwan, which means that financial structures
do not create significant effects on operating performances.
This may be explained
by differences between urban and rural areas or management styles.
As only credit cooperatives in northern and central Taiwan experience significant
threshold effects, this paper only evaluates these credit cooperatives.
Table 5 shows
that credit cooperatives in northern Taiwan exists threshold values of 0.106 and 0.115
for their net worth to loan ratio.
The model for northern Taiwan is as follows:
 i  1hit  1dit   it

git   i  1hit   2 dit   it
   h   d  
3 it
it
 i 1 it
if qit  0.106
if 0.106  qit  0.115
if qit >0.115
This paper finds that the two threshold values in northern Taiwan are both
smaller those of all Taiwan (0.16 and 0.212).
The impacts of loans growth to net
profit margins within the range of optimal net worth to loan ratio in northern Taiwan
is (1.539) smaller than that for all Taiwan (of 2.094).
This may be due to the fact
that northern Taiwan is where the competition in the financial market is the fiercest so
that the room for credit cooperatives is squeezed to use financial structures to improve
operating performances.
This paper finds that the threshold values of net worth to loan ratios of credit
cooperatives in central Taiwan are 0.145, 0.16 and 0.214. The three threshold model
for central Taiwan is presented as follows:
 i  1hit
   h
 i 1 it
git  
 i  1hit
 i  1hit
 1dit   it
if qit  0.145
  2 dit   it
if 0.145  qit  0.16
 3dit   it
if 0.16  qit  0.214
  4 dit   it
if qit >0.214
The threshold values for central Taiwan is not far from the average threshold
values for all Taiwan.
However, the effects on net profit margins (3.052) from loans
growth within the range of optimal net worth to loan ratios are far greater than the
16
average (2.084) for all Taiwan.
This implies that credit cooperatives in central
Taiwan may use leverage to improve their operating performances and the effects are
significant.
Conclusion
Although credit cooperatives in Taiwan do not hold high market shares in either
deposits or loans markets, they have made their contributions to the local economies
in Taiwan, due to their historical roles, especially in the society.
The empirical
research of this paper finds that the 28 credit cooperatives from 1994 through 2005 in
general, experienced double threshold effects.
should be 0.16~0.212.
The optimal net worth to loan ratio
This indicates that when loans grow by 1%, it creates 2.094%
growth in net profit margins.
As credit cooperatives expect to write off bad debts to
bring down non-performing loans under the initiatives of the government policies, the
loan growth went from the positive to negative from 1997 to 2002.
Therefore, this
paper finds that 1 unit of increase in loans creates 2 units of increase in net profit
margins.
Also, both loan growth rates and operating performances of credit
cooperatives in northern and central Taiwan are under the influence of net worth to
loan ratio and threshold effects exist; however, there is no significant threshold effect
for credit cooperatives in southern Taiwan.
17
Table 1 Testing of Threshold Effects
F
Threshold Value
P Value
10%
5%
1%
0.088
6.746
8.141
12.576
Double Threshold 39.134***
0.004
13.443
16.884
27.484
Triple Threshold
0.402
4.402
6.591
23.349
Single Threshold
6.851*
2.020
Note: p-value and threshold values are computed after 500 samplings based on
bootstrapping method. The symbols *, ** and *** represent they are statistically
significant under 10%, 5% and 1%. Source: this paper.
18
Table 2 Estimates of Threshold Values & Parameter Values
95% Confidence
Threshold Value
Estimates
1
0.160
0.076
0.229
2
0.212
0.212
0.214
Controlled Variable
Intervals
Estimates
t OLS
OLS se
tW hite
White se
1
0.007
1.909**
0.004
1.759*
0.004
2
-0.037
-1.323
0.028
-1.695*
0.022
Estimates
t OLS
OLS se
tW hite
White se
1
-0.016
-0.148
0.109
-0.210
0.077
2
2.094
6.088***
0.344
2.937***
0.713
3
-0.202
-0.761
0.265
-1.369
0.147
Parameter Estimates
Threshold Variable
Parameter Estimates
Note: OLS se is homogenous standard deviations. White se is heterogeneous
standard deviations. The symbols *, ** and *** represent they are statistically
significant under 10%, 5% and 1%. Source: this paper.
Table 3 Firm of each regime by year
Year
Firm class
1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005
qit  0.16
26
26
26
25
25
25
22
19
20
23
23
0.16  qit  0.212
1
1
1
1
1
0
4
5
5
2
2
qit >0.212
1
1
1
2
2
3
2
4
3
3
3
19
Table 4 Testing of Threshold Effects of All Regions
F
10%
5%
1%
0.586
7.484
9.252
12.049
Double Threshold 18.282***
0.028
9.065
13.57
26.146
Triple Threshold
6.556
0.476
27.779
49.458
90.53
Single Threshold
4.155
0.16
5.158
6.241
8.579
Double Threshold
17.89
0.116
18.838
23.742
34.717
Triple Threshold
8.255*
0.09
7.814
10.039
15.565
Single Threshold
5.102
0.606
19.456
25.493
44.885
Double Threshold
5.432
0.598
33.571
50.885
111.859
Triple Threshold
0.906
0.922
12.243
17.544
55.133
Single Threshold
Northern
Central
Southern
Threshold Value
P Value
1.991
Note: p-value and threshold values are computed after 500 samplings based on
bootstrapping method. The symbols *, ** and *** represent they are statistically
significant under 10%, 5% and 1%. Source: this paper.
20
Table 5 Parameter Estimates for Northern Taiwan
95% Confidence
Threshold Value
Estimates
1
0.106
0.076
0.177
2
0.115
0.115
0.116
Estimates
t OLS
OLS se
tW hite
White se
1
0.0005
0.133
0.004
0.265
0.002
2
0.001
0.031
0.047
0.059
0.024
Estimates
t OLS
OLS se
tW hite
White se
1
-0.096
-0.698
0.138
-1.193
0.081
2
1.539
4.157***
0.37
1.506*
1.022
3
0.031
0.224
0.136
0.343
0.089
Controlled Variable
Parameter Estimates
Threshold Variable
Parameter Estimates
Intervals
Note: OLS se is homogenous standard deviations. White se is heterogeneous
standard deviations. The symbols *, ** and *** represent they are statistically
significant under 10%, 5% and 1%. Source: this paper.
21
Table 6 Parameter Estimates for Central Taiwan
95% Confidence
Threshold Value
Estimates
1
0.145
0.071
0.265
2
0.214
0.214
0.214
3
0.16
0.158
0.167
Estimates
t OLS
OLS se
tW hite
White se
1
0.004
0.501
0.008
0.593
0.007
2
-0.053
-1.044
0.051
-1.554
0.034
Estimates
t OLS
OLS se
tW hite
White se
1
-0.273
-0.869
0.314
-1.5
0.182
2
0.781
1.037
0.754
0.638
1.225
3
3.052
4.728***
0.646
3.03***
1.007
4
-0.292
-0.745
0.391
-1.553
0.188
Controlled Variable
Parameter Estimates
Threshold Variable
Parameter Estimates
Intervals
Note: OLS se is homogenous standard deviations. White se is heterogeneous
standard deviations. The symbols *, ** and *** represent they are statistically
significant under 10%, 5% and 1%. Source: this paper.
22
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