Ghosh and Ostry (1995) show the method for computing restrictions when p = 1. We extend
that method for the VAR with five lags. Using equations (11) and (14) we get the following
-[10000 OOOOO][Ψ/(1 + r)][I-Ψ/(1 + r)]-1 =[00000 10000] (15)
Post-multiplying equation (15) with [I-Ψ/(1 + r)] and adding [0 0 0 00 100 0 0]Ψ/(1 + r)
we get the following
[-10000 10000][Ψ /(1 + r )]=[00000 10000] (16)
For the VAR with five lags, the Ψ matrix can be written as follows
|
a 1 |
a2 |
a3 |
a4 |
a5 |
b1 |
b2 |
b3 |
b4 |
b 5 ’ | ||
|
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 | ||
|
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 | ||
|
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 | ||
|
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 | ||
|
Ψ= |
c 1 |
c2 |
c3 |
c4 |
c5 |
d1 |
d2 |
d3 |
d4 |
d 5 |
(17) |
|
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 | ||
|
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 | ||
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 | ||
|
.0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 _ |
Therefore, from equations (16) and (17) we get the following restrictions
c1 - a1 = 0, c2 - a2 = 0, c3 - a3 = 0, c4 - a4 = 0, c5 - a5 = 0,
(18)
d1 -b1 =1+ r, d2 -b2, d3 -b3, d4 -b4, d5 -b5
We test these restrictions using the VAR coefficients from tables IV and V. The standard
errors for the tests are computed using the Variance-Covariance matrix from the VAR. Results
for the test of equality of the two accounts are provided in table VII. From the results we see that
all but two of the restrictions hold. We therefore weakly support the IBM based on the test of this
implication.
The last implication of the model is the equality of variance of the actual and optimal
consumption smoothing current account. Using the F-test for equality of variance, we find that
16