Testing Hypotheses in an I(2) Model with Applications to the Persistent Long Swings in the Dmk/$ Rate

Table 3: The trace test statistics for cointegration rank indices

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 = [ppp_t, ∆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.

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.

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