Economic Models - Convex Optimization

Credit and Income 215
We observe that the estimated adjustment coefficient (−0.0879) is
significant and almost identical to the (1, 1) element of matrix A, as seen
in Eq. (9), which is computed by the ML method. According to Hansen
statistics, all coefficients seem to be stable for α = 0.05. The BG test
revealed that no autocorrelation problems exist. In models like the one seen
in Eq. (16), the term u i−1 usually produces the smallest Spearman’s correlation
coefficient (r s ). In this particular case, we have: r s =−0.0979,
t =−1.37, p = 0.172, which means that no heteroscedasticity problems
exist. Finally, the RESET test shows that there is no any specification error.
In Eq. (16), we have an inflated CN due to spurious multicollinearity,
which is verified from the revised CN, having the value of 3.42 and
as Lazaridis (2007) has shown, this means that, in fact, there is not any
serious multicollinearity problem, affecting the reliability of the estimation
results. In many applications, particularly when the variables are in logs,
then usually the value of this statistic (CN) is extremely high, which in most
cases, as stated above, is due to the spurious multicollinearity, which can be
revealed by computing the revised CN, which is not widely known and it
seems that this is the main reason, for not reporting this statistic in relevant
applications.
To test the null, H 0 : β 1 = β 2 = β 3 = 0, where β j are the coefficients of
W i−j (j = 1, 2, 3), we computed the F-statistic that is F (3,189) = 0.533
(p- value = 0.66). Hence, the null is accepted, which means that there is not
any short-run causality effect from W to Y, but only in the levels, i.e., in
the long run, W causes Y. Observing the value of the adjustment coefficient
(−0.0879), I may conclude that it gives a satisfactory percentage, regarding
the money income convergence towards a long-run equilibrium. 11
4.6. Dynamic Forecasting with an ECVAR
To complete the ECVAR model, it is necessary to estimate a short-run relation
for W. Thus, we consider an equation which is similar to Eq. (15) i.e.,
W i = b 0 +
3∑
a j Y i−j +
j=1
3∑
b j W i−j − a W u i−1 + W v i . (17)
j=1
11 It is already mentioned that if the disequilibrium errors are computed from Eq. (13),
instead of Eq. (12), then the estimated coefficient of adjustment will have a positive sign.