Economic Models - Convex Optimization

Credit and Income 217
Y i = Y i + Y i−1
W i = W i + W i−1
u i = Y i − 0.289613W i − 0.0036218t i .
(19)
It may be useful to note that there are three identities in the system
and the only exogenous variable present in the system is the trend. We may
obtain dynamic simulation results from the ECVAR specified in Eq. (19),
in order to obtain predictions for Y i and W i and at the same time to verify
the validity of the co-integration vector used. This can be achieved by first
formulating the following deterministic system.
K 0 y i = K 1 y i−1 + K 2 y i−2 + K 3 y i−3 + ˜Dq i (20)
where y i = [ϒ i W i u i Y i W i ] ′ , q i = [t i 1] ′
⎡
K 0 =
⎢
⎣
1 0 0 0 0
0 1 0 0 0
0 0 1 −1 0.289613
−1 0 0 1 0
0 −1 0 0 1
⎤
⎥
⎦ ,
⎡
⎤
0.2618 0.0273 −0.0879 0 0
0.0977 0.4864 −0.03852 0 0
K 1 =
⎢ 0 0 0 0 0
⎥
⎣ 0 0 0 1 0⎦ ,
0 0 0 0 1
⎡
⎤
0.161 0.0487 0 0 0
0.2256 0.0123 0 0 0
K 2 =
⎢ 0 0 0 0 0
⎥
⎣ 0 0 0 0 0⎦ ,
0 0 0 0 0
⎡
⎤
−0.00432 0.076 0 0 0
0.199 −0.068 0 0 0
K 3 =
⎢ 0 0 0 0 0
⎥
⎣ 0 0 0 0 0⎦ ,
0 0 0 0 0