Economic Models - Convex Optimization

Credit and Income 213
4.4. Essential Remarks
In seminal works about money and income (as for instance in Tobin, 1970),
the analysis is restricted in a pure theoretical consideration. Some authors
(see for instance, Friedman and Kuttner, 1992) write many explanations
about co-integration, co-integrating vectors, and error-correction models,
but I did not trace any attempt to compute either. In a later paper by the
same authors (Friedman and Kuttner, 1993), I read (p. 200) the phrase,
“vector autoregression system,” which in fact is understood as a VAR. The
point is that no VAR model is specified in this work. Besides, the lag length
is determined by simply applying the F-test (p. 191). In this context, the
validity of the results is questionable. In other applications (see for instance,
Arestis and Demetriades, 1997), where a VAR model has been formulated,
nothing is mentioned about the test applied to determine the maximum lag
length. Also, in this paper, the authors are restricted to the use of trace
statistic (l (trace) ) to test for co-integration (p. 787), although this is the
necessary but not the sufficient condition, as pointed out above. From other
research works (see for instance, Arestis et al., 2001), I get the impression
that there is not a clear notion regarding stationarity and/or integration,
since the authors state [p. 22 immediately after Eq. (1)], that “D isaset
of I(0) deterministic variables such as constant, trend and dummies. . . ”.
It is clear that this verification is false. How can a trend, for instance, be
a stationary, I(0), variable? 10 The authors declare (p. 24) that “We then
perform co-integration analysis. . . ”. The point is that apart from some
theoretical issues, I did not trace such an analysis in the way it is applied
here. Besides, nothing is mentioned about any ECVAR, analogous to the one
that is formulated and used in this study. Most essentially, I have not traced,
In case that the disequilibrium errors are computed from:
then the co-integration vector will have the form:
u i = Ŷ i − Y i (13)
[−10.289613 0.003621]. (14)
It is noted also that hat (ˆ) is omitted from the disequilibrium errors u i , for avoiding any
confusion with the OLS disturbances.
It should be emphasized that in such a case, i.e., using the disequilibrium errors computed
from Eq. (13), then the sign of the coefficient of adjustment, as will be seen later, will be
changed.
10 It should be re-called at this point, that if t i is a common trend, then t i = 1(∀ i).