The Relationship between Stock Prices and Dividends:
Evidence Based on Taiwan Panel Data Investigation
Corresponding author: Chi-Wei Su, Assistant Professor, Department of Finance,
Providence University, Taichung, Taiwan. TEL: 886-4-2632-8001 ext. 13613. FAX:
886-4-2292-0677. Address: No. 200 Chung-Chi Rd., Shalu, Taichung, Taiwan 43301,
R.O.C., E-Mail:cwsu@pu.edu.tw
Hsuling Chang, Assistant Professor, Department of Accounting and Information, Lin
Tung University, Taichung, Taiwan. E-Mail: hsulingchang@mail.ltu.edu.tw
Chien-Chun Wei, Assistant Professor, Department of Finance, Providence University,
Taichung, Taiwan., E-Mail:cwsu@pu.edu.tw
1
The Relationship between Stock Prices and Dividends:
Evidence Based on Taiwan Panel Data Investigation
Chi-Wei Su*
Department of Finance, Providence University, Taichung, Taiwan
Hsu-Ling Chang
Department of Accounting and Information, Ling Tung University, Taichung,
TAIWAN
Chien-Chun Wei
Department of Finance, Providence University, Taichung, Taiwan
ABSTRACT
In this study, we employ the newly developed panel unit root test and
cointegration technique to determine the long-run relation between stock prices and
dividends in Taiwan’s stock market during June 1991 to February 2005. Panel
methods amplify the power and precision of the estimation procedures, allowing to
concentrating on both the short- and long-run relations. The results indicate that
there exists a significant cointegration relationship between stock prices and dividends.
These findings further support the existence of stock price increases relative to
fundamentals. Different from previous studies, our results reveal that stock prices
adhere to dividends and rational bubbles were nonexistent in the Taiwan’s stock
market.
Keywords: Present Value Model; Panel Unit Root Test; Panel Cointegration Test
*
Corresponding author: Assistant Professor, Department of Finance, Providence University, Taichung,
Taiwan, TEL: 886-4-2632-8001 ext. 13613. FAX: 886-4-2292-0677. E-mail: cwsu@pu.edu.tw.
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1. Introduction
This study investigates whether rational bubbles were present in Taiwan stock
market during June 1991 to February 2005 time period.
Financial theory points out
that in a well-functioning capital market the prices and dividends should be related
(Brealey and Myers, 1986); the present value of the share should be equal to the
dividend stream discounted by the return earned on securities of a comparable risk.
The occurrence of rational bubbles signifies that no long-run relationships exist
between stock prices and dividends.
In pursuit of determining if stock prices and
dividends are cointegrated, empirical studies have, for the most parts, employed
cointegration techniques. According to the present value model, stock prices are
fundamentally determined by the discounted value of their future dividends, which
derive their value from future expected earnings (e.g., see Campbell, Lo, & Mackinlay,
1997; Cochrane, 2001).
Consequently, conventional integration and cointegration methods are not
appropriate because they assume a unit root as the null hypothesis and a linear process
under the alternative.
Yet it cannot be ignored that it has been reported lately that
not only do conventional unit root tests fail to consider information across different
industries, which result in less efficient estimations, but also they have lower power
when compared with near-unit-root but stationary alternatives.
Therefore, it is not
surprising that these shortcomings have cast considerable doubt on many of the earlier
findings that have been based on a unit root in stock prices and dividends.
It has been suggested that one feasible way to increase power when testing a unit
root is to use panel data.
Among the most notable work has been by Levin et al.’s
(2002) and Im et al. (2003) panel-based unit root tests.
Previous empirical research
has investigated whether rational bubbles were existent in Taiwan stock’s market,
which indicates a large part of current debates in Taiwan stock’s price behavior. This
3
experience raises the question of whether stock prices are driven by fundamentals.
Most studies used traditional linear Dickey-Fuller unit root and Engle-Granger
cointegration tests to test the occurrence of the rational bubbles and then concluded
that Taiwan’s stock market existed rational bubbles (Chang, 1990; Lin and Ko, 1993;
Sheng and Chang, 2000).
Moreover, Campbell and Shiller (1987) used the cointegration testing procedure
thus pioneering the testing of the time-series properties of dividends, earnings and
stock prices. Unfortunately, they were unable to find a strong evidence of a long run
relationship.
Therefore, they have conceded that the power of their test of the
present value model for stock is “low”. Their failure of uncovering a long-run
relationship between stock prices and dividends may be due to the test itself rather
than the absence of relationship in practice, so intrinsic to single equation
cointegration may have been the reason.
One possible explanation for this analysis
is that the power of previous tests is relatively low because of long data set needed to
undertake such an analysis, because the underlying character of most companies
varies over such a long time span due to mergers, takeovers and other forms of
corporate restructuring.
One proposed approach to increase power in testing for a unit root involves the
use of panel data.
Using panel methods will assist to improve the power of unit root
test which is known to yield very low discriminatory power if performed on
individual time series.
Through the use of panel data, Levin et al. (2002) and Im et
al. (2003) developed the asymptotic theory and the finite-sample properties of the
ADF tests. Both tests have demonstrated that even relatively small panels could
yield large improvements with respect to power.
Furthermore, we will also apply panel cointegration testing and estimation
methods to determine the long-run relation between stock prices and dividends.
4
Panel methods amplify the power and precision of the estimation procedures that
allowing to concentrating on both the short-run and the long-run relations.
Rather
than focusing on a long-term period, we also examine the present-value model by
pooling individual industries and using panel cointegration estimation methods test
the long-run relation between stock prices and dividends.
Panel methods are
particularly useful when both time periods is relatively short. The increase in power
and precision methods that we gain by using these procedures allows us to apply
recent data and evaluate more accurately with the present-value model.
For all the
causes, we think that the present value model is more suitable with panel data method
provides an empirically valid description of Taiwan’s stock price behavior in the
long-run, while short-run deviations of actual stock prices from present value prices
are driven by rational bubbles.
The framework of the remainder of this paper is as followed.
In section 2, we
provide the theoretical background. Section 3 briefly describes the panel unit root
and panel cointegration test. Section 4 presents the data we use in our study and our
empirical results are shown in Section 5. Finally, Section 6 concludes the paper.
2. Present Value Model
This paper investigates whether a long-run relationship exists between dividends
and prices using a cointegration methodology.
The framework for our study is a
present value model which relates the real stock price, Pt , to its discounted expected
future real dividends, Dt .
In particular it has been applied to test present value
models for stock prices:
Pt 
1
Et ( Pt 1  Dt 1 ) ,
(1  R)
0  (1  R) 1  1
5
(1)
where E t denotes the conditional expectations operator, Pt denotes the real price at
time t, Dt is the time t real dividend, R is the expected real return (assumed
constant), and  denotes first differences.
If the transversality condition holds,
then the real stock price is equal to the fundamental value Pt . Following Campbell
and Shiller (1987), it implies:
Pt 
i
Dt  1     1  
   E t  
  Dt i
R  R   i 1  1  R  
(2)
If both (real) stock prices and dividends are non-stationary then, under a
no-bubbles assumption such that the right-hand-side of (2) is I(0), Pt and Dt will
be cointegrated with the cointegrating vector equal to  1, 1/ R .
Campbell and Shiller (1988a, 1988b) proposed a log-linear approximation of the
present value framework which enables to investigate stock prices behavior under any
model of expected returns.
It leads to the following present value equation:

 i

pt 
 Et   ((1   )d t i  rt i )
1 
 i 1

(3)
where p t denotes the log of real stock price, d t the log of the dividend payment,
and rt the discount rate.
 and  are linearizatiom parameters.
Rewriting Eq. (3) in terms of the log dividend-price ratio, we yield:
d t  pt  



 Et  i (d t i  rt i )
1 
 i 1

6
(4)
Given that changes in the log dividend and the discount rate follow process, then the
log stock price and the log dividends are cointegrated with the cointegrating vector
1,  1
and the log dividend-price ratio is a stationary process (see Cochrane &
Sbordone, 1988; Craine, 1993).
When expected returns vary overtime the present value model does not generally
imply the existence of a stationary relationship between the integrated level variables
Pt and Dt .
In contrast, cointegration tests that rely on the log dividend-price ratio
are valid in the presence of expected returns.
If there is no long-run relationships
between stock prices and dividends, it means Taiwan stock market exists rational
bubbles.
3. Testing for Panel Data Method
3.1 Panel Unit Root Tests
In order to ensure robustness of our results we conduct a set of panel unit root
tests and cointegration tests.
Inference on cointegration depends on the stationarity
properties of the individual time series.
From a methodological point of view, if we
apply panel cointegration tests, we should first use panel integration tests. Thus, in
this section we will describe different panel unit root tests before focusing ourselves
on cointegration tests.
3.1.1 Levin, Lin and Chu (L-L-C, 2002) Panel Unit Root Test
The conventional ADF test for single-equation is based on the following
regression equation:
k
X it  i  i X i ,t 1   it   ij X i ,t  j   it ,
j 1
7
(5)
where  is the first difference operator, X it is the stock prices and dividends,  it is
a white-noise disturbance with a variance of  2 , and t = 1, 2,…., T indexes time.
The unit root null hypothesis of  i  0 is tested against the one-side alternative
hypothesis of i  0 , which corresponds to X it being stationary. The test is based
on the test statistic t  i  ˆi / se( ˆi ) (where ̂ i is the OLS estimate of  i in
Equation (5) and se( ˆi ) is its standard error) since the single-equation ADF test
may have low power when the data are generated by a near-unit-root but stationary
process.
Levin, Lin and Chu (2002) found that the panel approach substantially
increases power in finite samples when compared with the single-equation ADF test,
proposed a panel-based version of Equation (5) that restricts ̂ i by keeping it
identical across cross- industries as follows:
k
X it  i   X i ,t 1   it    ij X i ,t  j   it ,
(6)
j 1
where i =1,2,…N indexes across cross-industries.
Levin-Lin-Chu tested the null
hypothesis of 1  2  ....    0 against the alternative of 1  2  ....    0 ,
with the test based on the test statistic t   ˆ / se( ˆ ) (where ̂ is the OLS
estimate of  in Equation (6), and se( ˆ ) is its standard error).
3.1.2 Im, Pesaran and Shin (IPS, 2003) Panel Unit Root Test
While the Levin-Lin-Chu panel-based unit root test has become increasingly
8
popular in applied work, one drawback is that  is restricted by being kept identical
across regions under both null and alternative hypotheses.
Im et al., (2003, hereafter
Im-Pesaran-Shin) relaxed the assumption of the identical first-order autoregressive
coefficients of the Levin-Lin-Chu test and developed a panel-based unit root test that
allows  to vary across regions under the alternative hypothesis.
Im-Pesaran-Shin tested the null hypothesis of
In addition,
1  2  ....  0 against the
alternative of  i  0, for some i .
The Im-Pesaran-Shin test is based on the mean group approach. They use the
average of the t  i statistics from Equation (6) to perform the following t-bar statistic:
Z  N [t  E(t )] / Var(t )
(7)
N
where t  (1 / N ) t  i , E(t ) and Var (t ) are respectively the mean and variance of
i 1
each t  i statistic, and they are generated by simulations (for further details, see Im et
al., 2003).
This Z converges a standard normal distribution. Based on Monte
Carlo experiment results, Im et al., (2003) demonstrated their test is even more
powerful than the Levin-Lin-Chu panel test in finite samples.
3.1.3 Maddala and Wu (MW, 1999) Panel Unit Root Test
An alternative approach to panel unit root tests uses Fisher's (1932) results to
derive tests that combine the p-values from individual unit root tests. This idea was
proposed by Maddala and Wu (1999).
If we define  i as the p-value from any
individual unit root test for cross-section, then under the null of unit root for all
9
cross-sections, we have the asymptotic result that
N
 2 l o g( i )  x 22N
(8)
i 1
In addition, it demonstrates that:
Z
N
1

N
1
i 1
( i )  N (0,1)
(9)
where  1 is the inverse of the standard normal cumulative distribution function.
It reports both asymptotic x 2 and standard normal statistics using ADF and
Phillips-Perron individual unit root tests. The null and alternative hypotheses are the
same as for the as IPS.
3.1.4 Hadri Panel Unit Root Test
The Hadri (2001) panel unit root test is similar to the KPSS unit root test, and it
has a null hypothesis of no unit root in any of the series in the panel.
Like the KPSS
test, the Hadri test is based on the residuals from the individual OLS regressions of on
a constant, or on a constant and a trend.
If we include both the constant and a trend,
we derive estimates from:
yit   i  i t   it
(10)
Given the residuals ˆ from the individual regressions, we form the LM statistic:
LM 1 

1 N 

 i 1   S i (t ) 2 / T 2  / fˆ0 
N
 t


(11)
where S i (t ) is the cumulative sum of the residuals,
t
S i (t )   ˆit
(12)
s 1
10
and fˆ0 is the average of the individual estimators of the residual spectrum at
frequency zero:
N
fˆ0   f i 0 / N
(13)
s 1
An alternative form of the LM statistic allows for heteroscedasticity across i:
LM 2 

1 N 

 i 1   S i (t ) 2 / T 2  / f i 0 
N
 t


(14)
Hadri shows his idea under mild assumptions,
Z
N ( LM   )

 N (0,1)
(15)
where   1 / 6 and   1 / 45 , if the model only includes constants ( i is set to 0
for all i), and   1 / 15 and   11 / 6300 , otherwise.
The Hadri panel unit root tests require only the specification of the form of the
OLS regressions: whether to include only individual specific constant terms or both
constant and trend terms.
The results will have two Z-statistic values, one based on
LM1 with the associated homoscedasticity assumption, and the other using LM 2 ,
which is heteroscedasticity consistent.
3.2 Panel Cointegration Test
To test for the existence of a long run relationship among stock prices and
dividends, a common practice to test for integration is Johansen’s procedure.
However, the power of the Johansen test in multivariate systems with small sample
size can be severely distorted. To this end, we need to combine information from
time series as well as cross-section data.
employed.
Then, panel cointegration tests are
Kao (1999) and Pedroni (1997, 1999) developed several tests to examine
11
the existence of cointegration in a multivariate framework.
They proposed statistics
test the null hypothesis of no cointegration versus the alternative of cointegration.
However, pooling time series has resulted in a substantial sacrifice in terms of the
permissible heterogeneity of the individual time series.
It is important in the process
of pooling time series to permit as much heterogeneity as possible among individual
time series.
Testing for cointegration among the variables should permit for as much
heterogeneity as possible among the individual countries of the panel.
If pooled
results rely on homogeneous panel cointegration theory, then common slope
coefficients are imposed.
Pesaran and Smith (1995) showed that if a common
estimator is used due to differences among the individual industries, then the stock
prices and dividends are not cointegrated.
3.2.1 Kao (1999) Homogeneous Panel Cointegration Tests with the null of
non-cointegration
The various tests summarized in this section are based on the OLS estimators,
and study the null hypothesis of non-cointegration, being residual-based tests.
Those
tests are based on regressing a non-stationary variable on a vector of non-stationary
variables and may suffer the spurious regression problem.
However, after
appropriate normalizations, these tests converge in distribution to random variables
with normal distributions.
Kao (1999) proposed two sets of specifications for the DF test statistics.
The first
set depends on consistent estimation of the long-run parameters, while the second one
does not.
Under the null hypothesis of no cointegration, the residual series eit
should be non-stationary.
The model has varying intercepts across the cross-sections
(the fixed effects specification) and common slopes across i.
The DF test can be calculated from the estimated residuals as:
12
eˆit  eˆit 1  vit
(16)
The null hypothesis of non-stationarity can be written as H 0 :   1 .
Kao
constructed new statistics whose limiting distributions, N 0,1 , are not dependent on
the nuisance parameters, that are called DF* and DFt* (where it is assumed that
both regressors and errors are endogenous).
Alternatively, he defines a
bias-corrected serial correlation coefficient estimate and, consequently, the
bias-corrected test statistics and calls them DF and DFt .
In this case, the
assumption is the strong exogeneity regressors and the errors. Finally, Kao (1999)
also proposed an ADF type of regression and an associated ADF statistic.
3.2.2 Pedroni (1997, 1999) Heterogeneity Panel Cointegration Tests for the null of
non-cointegration with multiple variables
Pedroni (1997,1999) developed a number of statistics based on the residuals of the
Engle and Granger (1987) cointegration regression.
The tests proposed in Pedroni
(1997, 1999) allow for heterogeneity among individual members of the panel,
including heterogeneity in both the long-run cointegrating vectors and in the
dynamics.
Consequently, Pedroni (1997, 1999) allows for varying intercepts and
varying slopes.
Assuming a panel of N industries each with m regressors (Xm) and T
observations, the long run model is written as:
Yit   i  i t  1i X 1,it   2i X 2,it     mi X m,it   it
t  1, , T
i  1,  N
(17)
Equation (17) implies that all coefficients, and, hence, the cointegrating vector,
vary across industries, thus allow full heterogeneity across individual members of the
panel.
In these tests, the null hypothesis is for each member of the panel the
variables involved are not cointegrated, and the alternative that for each member of
13
the panel exists a single cointegrating vector.
same in all cases.
Moreover, this vector needs not be the
This fact makes the tests special interesting, since frequently the
cointegrating vectors are not strictly homogeneous.
Pedroni (1997, 1999) also developed seven panel cointegration statistics.
Four
of these statistics, called panel cointegration statistics, are within-dimension based
statistics. The other three statistics, called Group mean panel cointegration statistics,
are between-dimension panel statistics.
The asymptotic distributions of these
statistics are derived in Pedroni (1997).
Thus, the former statistics pool the
autoregressive coefficients across different members for the unit root tests on the
estimated residuals, while the later on are based on estimators that simply average the
individually estimated coefficients for each member i.
The distinction is reflected in
the autoregressive coefficient,  i , of the estimated residuals under the alternative of
cointegration: in the within-dimension statistics, the tests presume a common value for
 , whereas in the between-dimension statistics, they don’t.
Thus, the
between-dimension introduces an additional source of heterogeneity across the
individual members of the panel.
Following Pedroni (1995, 1997), the
heterogeneous panel and heterogeneous group mean panel of rho(  ), parametric
(ADF) and non-parametric (PP) statistics are calculated as follows.
Panel v-Statistic
 N T 2 2 
ˆ
Z v    Lˆ11
i ei ,t 1 
 i 1 t 1

1
(18)
Panel  -Statistic
 N T 2 2 
ˆ
Z     Lˆ11
i ei ,t 1 
 i 1 t 1

1 N
T
 Lˆ
i 1 t 1
11i
eˆ
i ,t 1
eˆi ,t  ˆi
14

(19)
Panel non-parametric (PP) t-Statistic
Z pp
 2 N T ˆ 2 2 
   L11i eˆi ,t 1 
 i 1 t 1

1 / 2 N
T
 Lˆ
i 1 t 1
2
11i
eˆ
i ,t 1
eˆit  ˆi

(20)
Panel parametric (ADF) t-Statistic
N T

 2 *2 
ˆ
Z t   Sˆ *2  Lˆ11
i ei ,t 1 
i 1 t 1


1 / 2 N
T
 Lˆ
eˆ
eˆi ,t  ˆi

i 1 t 1
2 *
11i i ,t 1 i ,t 1
eˆi*,t
(21)
Group  -Statistic
N
 T

~
Z      eˆi2,t 1 
i 1  t 1

1 T
 eˆ
t 1
i ,t 1
(22)
Group non-parametric (PP) t-Statistic
N
T


~
Z pp   ˆ 2  eˆi2,t 1 
i 1 
t 1

1 / 2 T
 eˆ
i ,t 1
t 1
eˆi ,t  ˆi

(23)
Group parametric (ADF) t-Statistic
N
 T

~
Z t     Sˆi2 eˆi*,2t 1 
i 1  t 1

1 / 2 T
 eˆ
t 1
*
i ,t 1
eˆi*,t
(24)
where ˆ 2 is the pooled long-run variance for the non-parametric model given
2
ˆ2 ;
as 1 / N i 1 Lˆ11
i i
N


ˆi  1 / 2 ˆ i2  Sˆi2 , where
L̂i
is used to adjust for
autocorrelation in panel parametric model, ˆ i2 and Sˆi2 are the log-run and
contemporaneous variances for individual I, and Ŝ 2 are obtained from individual
ADF-test of ei ,t   i ei ,t 1  vi ,t ; S *2 is the individual contemporaneous variance
from the parametric model, eˆi ,t the estimated residual from the parametric
15
cointegration, while eˆi*,t the estimated residual from the parametric model and Lˆ11i
the estimated log-run covariance matrix for eˆi ,t , and Li is the ith component of the
lower-triangular Cholesky decomposition of matrix
i
for eˆi ,t
with the
appropriate lag length determined by the Newy-West method.
Given that the alternative statistics might yield conflicting evidence, it’s
important to have some information on the properties of these statistics.
First, there
is a difference between panel and group statistics in terms of alternative hypothesis.
For the within-dimension statistics, the test for the null of cointegration is
implemented as a residual based test of the null hypothesis H 0 :  i  1 for all i’s,
versus H 1 :  i    1 for all i, so that it presumes a common value for the first order
autocorrelation coefficient.
By contrast, the statistics between then do not presume a
common value for ρi under the alternative.
Second, the small sample size and power
properties of all the seven statistics are examined in Pedroni (1997).
In general, the
size distortion tends to be minor and the power is very high for all statistics when the
time span is long (T>100).
But for shorter panels, the evidence is more varied.
In
terms of power, Pedroni showed that the group-ADF statistic generally performs best,
followed by the panel-ADF statistic, while the panel-variance and the group-rho
statistic do poorly.
4. Data
We analyze the monthly data for stock price index ( Pt ) and dividends ( Dt ) taken
from Taiwan Economic Journal (TEJ) database during the June 1991 to February
2005 period. The data begin from June 1991 since dividend data are available from
this period.
Our empirical analysis focuses on Taiwan’s group stock price indices,
which are TAIEX, Cement, Food, Plastics & Chemicals, Textile, Electric &
16
Machinery, Construction and Finance.
Otherwise, we use Consumer Price Index (CPI)
to deflate stock price index and dividends. The purpose is that we can get real price
and dividends.
Table 1 provides summary statistics for the stock price index and
dividends data.
As shown in Table 1, the Jarque-Bera tests shown that the
distribution of all stock price indices are non-normal.
The outcome is in dividends
also the same, except for Textile and Finance price indices.
<Insert Table 1>
5. Empirical Results
Time series unit root tests along with panel unit root tests are used to examine the
stationarity properties of the data.
The use of panel data statistics is necessary
because the power of standard time-series unit root tests may be quite low when given
the sample sizes and time spans typically available in economics.
For comparison,
in the present study, several panel-based unit root tests are first applied to examine the
null of a unit root in the real stock prices and real dividends.
The critical values
based on Monte Carlo Simulations using 10,000 replications for each test are given in
Table 8 and Table 9, and it is clear that all Levin-Lin-Chu (Levin et al., 2002),
Im-Pesaran-Shin (Im et al., 2003) and MW (Maddala and Wu, 1999) tests fail to reject
the null of non-stationary real stock prices and real dividends for both TAIEX and 7
industries.
The Hadri (2001) test rejects the null of stationary real stock prices and
real dividends. Five panel unit root tests yields the same results.
<Insert Table 2 and Table 3>
17
Since all the variables in the panel data are integrated of the same order, it is
appropriate to look for a relationship among variables.
Next, we will use
cointegration test to verify the relationship between stock prices and dividends.
The
drawback of the previously mentioned cointegration test is their failure to consider
information across industries. Recently developed techniques allow us to deal with
nonstationary data in a heterogeneous panel, which yields substantial benefits by
exploiting data from a cross-section. With panel data, we are able to examine the
cointegration between real stock prices and real dividends, and to estimate its
cointegrating coefficients with higher degree of precision. We therefore apply the
panel cointegration test of Kao (1999) and Pedroni (1997, 1999) to investigate the
cointegration between real stock prices and real dividends.
Results from Table 4 indicate the null of no cointegration is rejected by all five
statistics mentioned previously.
structurally related.
Having established, that the variables are
On the basis of these results, the long-run relationship between
real stock prices and real dividends found strongly support in each individual industry
over the sample period under examination.
<Insert Table 4>
We also use Pedroni statistics to test the relationship between the stock prices and
real dividends. Table 5 summarizes the results of cointegration analysis among the
two variables using Pedroni statistics. Two of seven statistics(panel  ; panel PP)
provide evidence of cointegration and support the long-run relationship among the
variables.
From Pedroni (1997) point of view, the group-ADF statistic is more
powerful, it is not significant in our result. We just prove the relationship between
the prices and dividends is weak in Taiwan stock market.
18
<Insert Table 5>
6. Conclusions
The purpose of this paper is to investigate whether rational bubbles exist in
Taiwan stock market.
A large part of the current debate on Taiwan stock price
behavior concentrated on the question of whether stock prices are driven by
fundamentals.
The difference is the past empirical researches is Taiwan stock
market exists rational bubbles (Chang, 1990; Lin and Ko, 1993; Sheng and Chang,
2000).
Most of them use traditional linear Dickey-Fuller unit root and
Engle-Granger cointegration test to improve rational bubbles.
Furthermore, we employ the newly developed panel unit root test and
cointegration technique to determine the long-run relation between stock prices and
dividends, and also to test the present-value model which provides a much stronger
test by using time series data. Panel methods amplify the power and precision of the
estimation procedures, allowing to concentrating on both the short- and long-run
relations.
The results indicate that there exists a significant cointegration
relationship between stock prices and dividends.
These findings further support the
existence of stock price increases relative to fundamentals. Different from previous
studies, our results reveal that stock prices adhere to dividends and rational bubbles
were nonexistent in the Taiwan’s stock market during June 1991 to February 2005.
19
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21
Table 1 Summary Statistics of Stock Index and Dividends
Country
Mean
Std
Max.
Min.
Skewness
Kurtosis
J-B
Stock Index
6325.05
1465.10
10268.21
3780.18
0.5529
2.5669
9.6967***
Dividends
210.75
50.33
342.53
121.96
0.1452
1.9697
7.8781**
Stock Index
360.94
140.10
583.61
122.07
-0.1506
1.6369
13.3971***
Dividends
14.41
7.04
26.43
2.54
-0.2737
1.8257
11.5395***
Stock Index
438.77
178.31
981.20
173.39
0.5809
2.9362
9.3072***
Dividends
14.04
4.44
31.77
6.40
0.8257
4.8060
41.1747***
1. TAIEX
2. Cement
3. Foods
4. Plastics & Chemicals
Stock Index
332.58
76.23
471.35
164.09
-0.0149
2.0039
6.8278**
Dividends
10.56
2.82
18.69
5.83
1.1929
4.3205
51.1194***
Stock Index
285.82
86.11
462.18
110.81
-0.0470
2.0831
5.8406*
Dividends
8.23
2.44
13.92
3.91
0.3811
2.7763
4.3380
5. Textile
6. Electric & Machinery
Stock Index
1155.99
595.74
3048.10
366.93
0.7888
3.3046
17.7496***
Dividends
39.98
20.72
79.84
7.38
-0.1988
1.9568
8.5687**
Stock Index
292.59
162.47
557.83
56.49
-0.0514
1.5210
15.1117***
Dividends
11.51
6.68
24.26
1.11
-0.1932
1.6633
13.3109***
Stock Index
1106.50
367.60
1925.09
515.76
0.5140
2.1242
12.5390***
Dividends
31.1584
9.4685
51.19
11.63
-0.0152
2.3499
2.9115
7. Construction
8. Finance
Note: Std denotes standard deviation and J-B denotes the Jarque-Bera Test for Normality. The ***, **, and *
indicate significance at the 0.01, 0.05 and 0.1 levels, respectively.
22
Table 8 Panel Unit Root Test Results on Stock Prices
Critical value
method
Statistics
Levin, Lin & Chu
P-value
1%
5%
10%
-4.679
0.360
-6.991
-6.471
-6.182
0.389
0.651
4.949
3.258
2.423
-0.768
0.779
4.810
3.303
2.549
MW-Fisher Chi-square
7.310
0.922
39.375
29.611
25.115
Hadri (homo)
6.621
0.013**
6.875
3.850
2.562
Hadri (het)
6.112
0.022**
7.048
3.943
2.575
IPS
t
 LM
Note: 1. ***, **, and * indicate significance at the 0.01, 0.05 and 0.1 levels, respectively.
2. Critical values are based on Monte Carlo Simulations using 10,000 replications.
Table 9 Panel Unit Root Test Results on Dividends
Critical value
method
Statistics
Levin, Lin & Chu
P-value
1%
5%
10%
-4.892
0.302
-6.977
-6.416
-6.132
-0.418
0.338
2.994
1.948
1.458
0.239
0.405
3.266
2.219
1.671
MW-Fisher Chi-square
10.858
0.697
30.831
24.458
21.434
Hadri (homo)
9.413
0.000***
5.984
3.299
2.245
Hadri (het)
7.954
0.000***
5.195
2.950
2.034
IPS
t
 LM
Note: 1. ***, **, and * indicate significance at the 0.01, 0.05 and 0.1 levels, respectively.
2. Critical values are based on Monte Carlo Simulations using 10,000 replications.
Table 16 Homogeneous panel cointegration tests Kao (1999) DF and ADF tests
Test
DF
DFt
DF *
DFt*
P-value
-103.6775***
0.0000
-28.5163***
0.0000
-185.5681***
0.0000
-17.2975***
0.0000
ADF
-4.1446***
Note: 1. The triple asterisks (***) denote rejection of the null hypothesis of
2. The test statistics are distributed as N 0,1 .
 
23
0.0000
non-cointegration at 1%.
Table 17 Pedroni (1997, 1999) cointegration tests for heterogeneous panels.
Panel statistics
Panel variance
0.9847
Panel ρ
-2.0093**
Panel PP
-1.6952*
Panel ADF
-1.2297
Group statistics
Group ρ
-1.2183
Group PP
-1.3829
Group ADF
-0.9671
Note: *, **, *** indicate significance levels at 10%, 5% and 1% respectively. The null hypothesis is
non-cointegration. The critical value is according to the normal distribution.
24