• H0 : P = 11 v.s. H1 : P =12
Chi-Squared(25)= 42.86003 with Significance Level 0.20055
• H0 : P = 10 v.s. H1 : P =11
Chi-Squared(25)= 52.30518 with Significance Level 0.03868
According to these test results we use VAR(12) to represent a general model that should
be an approximation of the DGP. Because in the dynamic system of (1) - (5) the variable
ukbpt is treated as exogenous, we factorize the VAR(12) process into a conditional process
of dwt ,dpt ,Vtl ,Vtc ,rt given ukbpt and the lagged variables, and the marginal process of
ukbpt given the lagged variables:
dwt
dpt
Vtl
Vtc
rt
C ci ∖
c
c2
c*
c3
c4
V5 /
pl
b2
I1
b3
b4
V5
∖
d74 +
)
ai
a2
a3 |
ukpbt |
a4 | |
a5 |
(14)
a ailk
P a2l k
+ ∑ α3ι k
k=1 a41 k
a51 k
al2 k
a22 k
a32 k
a42 k
a52 k
al3 k
a23 k
a33 k
a43 k
a53 k
al4 k
a24 k
a34 k
a44 k
a54 k
al5 k
a25 k
a35 k
a45 k
a55 k
al6k ʌ
a26 k
a36 k
a46 k
a56 k
dwt-k
dpt-k
Vl
Vt-k
Vc
Vt-k
rt-k
elt ʌ
e21
ukbpt-k
e^
e3t
e41
e51 /
P
ukbpt =c6 + a6lk
k=l
a62k
a63k
a64k
a65k
a66k
dwt-k
dpt-k
Vl
Vt-k
Vc
Vt-k
rt-k
ukbpt-k
+ e6t
(15)
Now we examine if ukbpt can be taken as ”exogenous” variable. The partial system (14) is
exactly identified. Hence the variables ut are weakly exogenous for the parameters in the
partial system,7 For the strong exogeneity of ukbpt, we test whether dwt,dpt,Vtl,Vtc,rt
Granger cause ukbpt .
The test is carried out by testing the hypothesis: H0 : aijk =0, (i =6;j =1, 2, 3, 4, 5; k =
1, 2, ..., 12) in (15) based on likelihood ratio
• Chi-Squared(60)= 69.157150 with Significance Level 0.19572294
7For detailed discussion see Chen (2003)
19