Next, we have applied Johansen’s ML approach. The reason for taking this approach
as the benchmark for the comparison with our nonparametric cointegration analysis is
threefold. First, the hypotheses to be tested are about the same. Second, Johansen’s method
seems to be the most popular one in applied macroeconomic cointegration research, due to its
own merits as well as the fact that Johansen has made his approach available in the form of a
RATS program. Third, to the best of our knowledge the only other methods available in the
(published) literature that can test for the number of cointegrating vectors are the Stock-
Watson (1988) and Phillips (1991) methods. The Stock-Watson method, however is closely
related to the Johansen method [see Johansen (1991, p.1566)], and Phillips’ efficient ECM
method has a case-dependent null distribution.
In first instance we have specified the ECM (24) with an intercept, and we have
conducted Johansen’s lambda-max and trace tests for the number of cointegrating vectors, r,
for the cases where: (i) the intercept vector π0, say, is not proportional to γ, (ii) π0 is
proportional to γ, but this restriction is not imposed, and (iii) the restriction that π0 is
proportional to γ is imposed. This restriction implies that the cointegration relation has an
intercept rather than the ECM itself. These three cases lead to different null distributions of
the trace and lambda-max tests. We conducted Johansen’s tests for p = 2, 4, 6. The results (at
the 5% and 10% significance level) indicate that there is one cointegrating vector (r = 1),
provided the order p of the VAR model is chosen equal to 6. For the lower values of p the
test results were inconclusive, in the sense that the results of the tests were either
contradictory or different for the 5% and 10% significance levels. Moreover, the restriction
that π0 is proportional to γ is then rejected at the 5% significance level.
The corresponding estimated standardized cointegrating vector is now (1,-0.75)T.
Again we have conducted a series of LR tests of the null hypothesis that the space of
cointegrating vectors is spanned by the column ofa2×1matrix H = (1,a)T, with the same
range of a as before. The result is that all values of a except the value -.75 are rejected at the
5% significance level. Thus even the nonparametric estimate of a, -.7, is rejected!
In order to analyze the difference between the nonparametric and the parametric
estimates of the cointegrating vector, we have run three cointegration regressions, without and
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