Economic Models - Convex Optimization

218 Athanasios Athanasenas
and
⎡
˜D =
⎢
⎣
⎤
0 0.5132
0 0.2241
⎥
⎦ .
−0.003621 0
0 0
0 0
Pre-multiplying Eq. (20) by K0 −1 we get:
y i = Q 1 y i−1 + Q 2 y i−2 + Q 3 y i−3 + Dq i (21)
where Q 1 = K0 −1 K 1, Q 2 = K0 −1 K 2, Q 3 = K0 −1 K 3, and D = K0
−1 ˜D.
The system given in Eq. (21) can be transformed to an equivalent firstorder
dynamic system, in a similar way to the one already described earlier
[see Eqs. (8) and (8a)]. It is noted that in this case matrix à is of dimension
(15 × 15). It is important to mention again that we should avoid using
a dynamic system, for simulation purposes, that is unstable. Thus, from
this system, we can obtain dynamic simulation results for the variables Y i
and W i . These results are graphically presented (Fig. 2).
The very low value of Theil’s inequality coefficient U, for both cases
is a pronounced evidence that, apart from computing the indicated cointegration
vector, we have also formulated the suitable ECVAR so that the
results obtained are undoubtfully robust.
5. Conclusions and Implications
The purpose of this study is to contribute to the empirical investigation of
the co-integration dynamics of the credit-income nexus, within the economic
growth process of the post-war US economy, over the period from
1957 to 2007.
Utilizing advanced and contemporary co-integration analysis and
applying vector ECM estimation, we place special emphasis on forecasting
and system stability analysis. I can say that to the best of my knowledge,
similar system stability and forecasting analysis, as the one applied here,
is very difficult to meet in the relevant literature, after taking into consideration
similar research works. See for example, (Arestis and Demetriades,
1997; Arestis et al., 2001; Demetriades and Hussein, 1996; Friedman and
Kuttner, 1992; 1993; Levine and Zervos, 1998; Rousseau and Wachtel,
1998; 2000).
My results state clearly that there is no short-run causality effect from
credit changes to income changes, but only in the levels, that is in the long