B. Cha, S. Oh International Review of Economics and Finance 9 2000 299–322 307
and Taiwan, which have had relatively more restrictions on international capital flows than other AEMs, the return rates exhibited only weak correlation with those in the
U.S. and Japan before the Asian financial crisis. Since the crisis, however, the correla- tion has become much greater.
3. Method
3.1. Vector autoregression VAR In general, a k-th order vector autoregression VAR model for an n31 vector Y
is written as shown in Eq. 1, Y
t
5 D
t
1
o
k s
5
1
B
s
Y
t
2
s
1 e
t
, t 5
1, . . ., T 1
where D
t
is an n31 deterministic vector, and e
t
is an n31 serially uncorrelated residual vector with E[e
t
] 5 0 and E[e
t
e
t
9] 5 S , ∞
.
5
Here, the residual vector e is said to be the innovation shock in Y because it is the component in Y that cannot be predicted
from past values of variables in the system.
6
Then, either by a polynomial lag division or by a successive substitution, the corresponding moving average representation
MAR is derived from Eq. 2, Y
t
5 F
t
1
o
∞ s
5
A
s
e
t
2
s
, t 5
1, . . ., T 2
where F
t
is the corresponding deterministic part and A 5 I
n
. In this paper, for each of the four AEMs, Y
t
is defined as a 331 vector such as given in Eq. 3,
Y
t
5 [Y
U ,t
, Y
J ,t
, Y
A ,t
]9 3
where Y
U ,t
, Y
J ,t
, Y
A ,t
are the stock return series for the U.S. market, the Japanese market, and the AEM in concern, respectively. Thus, the VAR system [Eq. 1] for
an AEM is written as given in Eq. 4, Y
U ,t
5 b
U ,0
1
o
k s
5
1
b
U U
,S
Y
U ,t
2
s
1
o
k s
5
1
b
J U
,S
Y
J ,t
2
s
1
o
k s
5
1
b
A U
,S
Y
A ,t
2
s
1 e
U ,t
Y
J ,t
5 b
J ,0
1
o
k s
5
1
b
U J
,S
Y
U ,t
2
s
1
o
k s
5
1
b
J J
,S
Y
J ,t
2
s
1
o
k s
5
1
b
A J
,S
Y
A ,t
2
s
1 e
J ,t
Y
A ,t
5 b
A ,0
1
o
k s
5
1
b
U A
,S
Y
U ,t
2
s
1
o
k s
5
1
b
J A
,S
Y
J ,t
2
s
1
o
k s
5
1
b
A A
,S
Y
A ,t
2
s
1 e
A ,t
4 where b
m n
,s
is the coefficient of Y
m ,t
2
s
in the equation for Y
n
and e
U ,t
, e
J ,t
, e
A ,t
are the residual series for Y
U ,t
, Y
J ,t
, Y
A ,t
, respectively. While the estimated coefficients b
m n
,s
in the VAR system [Eq. 4] provide little insight into the dynamic interactions among the three stock return rates, the MAR
[Eq. 2] presents information equivalent to that contained in the original estimates,
308 B. Cha, S. Oh International Review of Economics and Finance 9 2000 299–322
but in a form which is relatively easy to understand. In this paper, the MAR was used in two ways. First, it was used to compute the proportion of the forecasting error
variance of the AEM’s return rate that can be attributed to shocks in the U.S. and Japan, and the AEM’s own domestic shocks, in a process known as variance decomposi-
tion. This variance decomposition method provides useful econometric evidence for explaining the relative importance of the U.S. and Japanese markets to the AEMs.
Second, it was used to compute the dynamic responses of the AEM’s return rate to random shocks in the U.S. and Japanese markets. The dynamic impulse responses
investigate how unexpected changes in U.S. and Japanese return rates change the return rates of the Asian emerging markets over time.
3.2. VAR with autoregressive conditional heteroscedasticity ARCH For Hong Kong, Korea, Singapore, and Taiwan, and for each subsample period,
Eq. 1 was initially estimated with four lags and a constant term for the deterministic part.
7
An important assumption underlying the usual unrestricted VAR is that the residu- als are not serially correlated. The trends of the stock return rates in Fig. 2, however,
clearly question the presence of autoregressive conditional heteroscedasticity ARCH. In this context, an attempt was made to test the ARCH effect by modeling
the residual series as ARCH processes such as shown in Eq. 5:
Var e
U ,t
5 a
U ,0
1 a
U ,1
e
2 U
,t
2
1
1 a
U ,2
e
2 U
,t
2
2
1 . . . 1 a
U ,p
e
2 U
,t
2
p
Var e
J ,t
5 a
J ,0
1 a
J ,1
e
2 J
,t
2
1
1 a
J ,2
e
2 J
,t
2
2
1 . . . 1 a
J ,q
e
2 J
,t
2
q
Var e
A ,t
5 a
A ,0
1 a
A ,1
e
2 A
,t
2
1
1 a
A ,2
e
2 A
,t
2
2
1 . . . 1 a
A ,r
e
2 A
,t
2
r
5 Eq. 5 indicates that different orders of lags were allowed for residual series within
each VAR system. Applying the test proposed by Engle 1982 with one to 12 lags for each residual series has confirmed that the ARCH effect is indeed present.
8
In order to generate the correct residuals that will be used in variance decomposition and impulse response functions in the presence of the ARCH effect, the optimal lag
length of each ARCH process in Eq. 5 should be determined first. We applied the Schwarz 1978 information criterion SIC to determine the optimal lags; that is,
p 5 pˆ , q 5 qˆ, r 5 rˆ in Eq. 5.
9
Table 3 presents the results of the optimal lags and the chi-square statistics for each equation in the four VAR systems. It is shown in
Table 3 that the numbers of optimal lags in the ARCH process for the residual series are one and five for the U.S. and the Japanese return rates, respectively, in all four
VAR systems. But, those for the AEMs’ return rates were different across the VAR systems; that is, one for the Hong Kong and the Singaporean return rates, eight for
the Korean return rate, and three for the Taiwanese return rate.
Finally, with the optimal lags in Table 3, Eqs. 4 and 5 were jointly estimated by the pseudo-maximum likelihood method using the BHHH algorithm and the residu-
als were saved.
10
In the next section, these residuals were used to form the MAR, which was utilized in variance decomposition and impulse response functions.
B. Cha, S. Oh International Review of Economics and Finance 9 2000 299–322 309
Table 3 Optimal lag length for the autoregressive conditional heteroscedasticity ARCH process for residual
series VAR
Country Lags
x
2
Statistics HONG KONG
US 1
81.40 JAPAN
5 94.26
HONG KONG 1
1.03 KOREA
US 1
80.12 JAPAN
5 84.02
KOREA 8
188.45 SINGAPORE
US 1
74.52 JAPAN
5 93.78
SINGAPORE 1
5.12 TAIWAN
US 1
73.55 JAPAN
5 92.67
TAIWAN 3
227.09 Notes:
1 denotes statistical significance of the ARCH effect at the 5 level. 2 The lag length was determined by the Schwarz Information Criterion SIC.
4. Empirical results
