Table 2: Estimated cointegrating vectors with price indices at regional (2a) and national (2b) levels
and theoretical restrictions imposed
Specification 2a - Regional price index.
|
w1 |
w2 |
logP1 |
logp2 |
logp3 |
Income |
Intercept | |
|
Vector of cointegration (1) |
-1 |
0 |
0.0106 |
0.0452 |
-0.0558 |
0.0946 |
0.1456 |
|
(0.0022) |
(0.0171) |
(0.0155) |
(0.0454) |
(0.0945) | |||
|
[4.938] |
[ 2.644] |
[-3.594] |
[2.081] |
[1.526] | |||
|
Vector of cointegration (2) |
0 |
-1 |
0.0452 |
0.0368 |
-0.0820 |
-0.0237 |
0.0837 |
|
(0.0171) |
(0.0061) |
(0.0169) |
(0.0561) |
(0.0629) | |||
|
[2.644] |
[5.954] |
[-4.829] |
[-0.422] |
[1.331] | |||
|
Theoretical restrictions: |
LR test |
d.f. |
p-value | ||||
|
Symmetry |
1.3972 |
(1) |
[0.2371] | ||||
|
Symmetry and homogeneity |
10.39 |
(3) |
[0.015] |
Specification 2b - National price index.
|
w1 |
w2 |
logpι |
logp2 |
logp3 |
Income |
Intercept | |
|
Vector of cointegration (1) |
-1 |
0 |
0.0118 |
0.0503 |
-0.0621 |
0.0493 |
0.1245 |
|
(0.0024) |
(0.0108) |
(0.0139) |
(0.0295) |
(0.1045) | |||
|
[4.9089] |
[4.6567] |
[-4.4667] |
[1.6712] |
[1.1919] | |||
|
Vector of cointegration (2) |
0 |
-1 |
0.0503 |
0.0322 |
-0.0825 |
-0.0124 |
0.0237 |
|
(0.0108) |
(0.0056) |
(0.0630) |
(0.0137) |
(0.0562) | |||
|
[4.6567] |
[5.6929] |
[-1.4732] |
[-0.9028] |
[0.4221] |
|
Theoretical restrictions: |
LR test |
d.f. |
p-value |
|
Symmetry |
6.46 |
(1) |
[0.011] |
|
Symmetry and homogeneity |
33.754 |
(3) |
[0.000] |
Notes: Standard errors in round brackets; student’s t-test in square brackets. Degrees of freedom and
p-values of LR tests in round and square brackets, respectively.
Table 3: Residual serial correlation of the vector error correction model in equation (7)
|
VEC Residual Portmanteau Tests |
VEC Residual Serial Correlation LM Tests | ||||||
|
Lags |
Q-Stat |
Prob. |
Adj Q-Stat |
Prob. |
df |
LM-Stat |
Prob |
|
1 |
7.6456 |
- |
7.7191 |
- |
- |
46.424 |
0.1144 |
|
2 |
20.253 |
- |
20.571 |
- |
- |
42.455 |
0.2127 |
|
3 |
42.478 |
0.2120 |
43.451 |
0.1837 |
36 |
37.933 |
0.3812 |
Note: Q-statistics and adjusted Q-statistics are shown with small sample correction for residual serial
correlation up to specified order h (see Liitkepohl, 1991, for details). Also shown: LM test statistics for
residual serial correlation up to specified order (see Johansen, 1995, for details). Under null hypothesis
of no serial correlation, statistic tests are χ2 distributed. Degrees of freedom are k2 (p - h) and k2 ,
respectively, where k is number of endogenous variables of V AR and p is V AR lag order.
39