Table 3: The trace test statistics for cointegration rank indices
p — r |
r |
«2 = 7 |
«2 = 6 |
«2 = 5 |
«2 = 4 |
«2 = 3 |
«2 = 2 |
«2 = 1 |
«2 = 0 |
7 |
ɪ |
1737.63 |
1402.12 |
1137.46 |
908.43 |
715.21 |
528.18 |
379.58 |
280.64 |
[0.00] |
[0.00] |
[0.00] |
[0.00] |
[0.00] |
[0.00] |
[0.00] |
[0.00] | ||
6 |
1 |
1115.86 |
885.59 |
659.57 |
470.53 |
319.31 |
190.76 |
160.82 | |
[0.00] |
[0.00] |
[0.00] |
[0.00] |
[0.00] |
[0.00] |
[0.00] | |||
5 |
2 |
646.64 |
455.20 |
271.26 |
141.15 |
94.27 |
93.63 | ||
[0.00] |
[0.00] |
[0.00] |
[0.00] |
[0.19] |
[0.02] | ||||
4 |
3 |
265.40 |
134.94 |
69.81 |
39.63 |
40.67 | |||
[0.00] |
[0.00] |
[0.72] |
[0.99] |
[0.82] | |||||
3 |
4 |
64.60 |
32.60 |
15.58 |
22.18 | ||||
[0.77] |
[1.00] |
[1.00] |
[0.90] | ||||||
2 |
5 |
13.04 |
2.03 |
8.06 | |||||
[1.00] |
[1.00] |
[0.98] | |||||||
1 |
6 |
—0.91 |
0.17 | ||||||
[^A] |
[1.00] |
test the following four hypotheses:
1. H1 : R'1τ = 0, where R1 = [1,1, 0, 0, 0, 0, 0, 0, 0], i.e. we test whether we can
impose the ppp restriction on all τ vectors. If accepted it would imply that the
nominal to real transformation x't = [pppt, ∆p1,t, ∆p2,t, b1,t, b2,t, s1,t, s2,t] would
be econometrically valid (Kongsted, 2005) in the sense of transforming an I(2)
vector to an I(1) without loss of information. The hypothesis is rejected based
on y2(5) = 16.64 [0.01].
2. H2 : R12τ = 0, where R12 = [0, 0, 0, 0, 0, 0, 0,1,0], i.e. we test whether the broken
trend is long-run excludable from τ. The hypothesis was borderline accepted
based y2(5) = 9.99 [0.08] . Thus, there is only weak evidence that the direction of
the trend in relative prices and /or nominal exchange rates changed at the time
of the re-unification of Germany.
3. H3 : R3τ = 0, where R3 = [0, 0, 0, 0, 0, 0, 0, 0,1], i.e. we test whether the
3 3
trend is long-run excludable from τ. The hypothesis was rejected based y2(5) =
13.75 [0.02] . Thus, there is some evidence that the trend is econometrically needed
as a local approximation of the downward sloping trend in relative prices and in
the nominal exchange rate.
4.
H4 : R4τ = 0, where R14
0,0, 0, 0, 0,0, 0, 0,1
0,0, 0, 0, 0,0, 0,1, 0
, i.e. we test whether the
trends can be left out of the long-run relations. The hypothesis was rejected
based y2(10) = 24.50 [0.01] . Thus, the hypothesis that the downward sloping
trend strongly visible in Figure 1 is stochastic rather than deterministic is re-
jected. However, the hypotheses of no such trends were only borderline rejected,
which supports our prior assumption that a deterministic trend should only be
considered a local approximation.
17