considered another highly persistent trend. It may not be exactly I(2), but persistent
enough for the trace test not to reject it as a double unit root.8
Unfortunately, the assumption of two stochastic I(2) trends seems to introduce an
inconsistency in the analysis. If ppt and s12,t are the only near I(2) variables then they
will be long-run excludable from τ given two common stochastic I(2) trends. Thus, to
maintain the assumption of two I(2) trends, there must be other variables in the system
which exhibit approximately the same persistency profile. Figure 1, lower panel, clearly
suggests that the real interest rate spread is a likely candidate because it is closely co-
moving with the ppp, the long swings of which are associated with nominal exchange
rate.
The graphs of the data in the Appendix C show a number of outlier observations.
Most of them belong to the short-term interest rates in the period 1980-1982 which
coincide with the period of monetary targeting. This was a very volatile period which
does not seem representative for the rest of the sample. The hypothesis that the
parameters of the VAR model are unchanged in this period was tested in Hansen and
Johansen (1999) and clearly rejected. Because of this we have excluded the observations
from 1980:2-1982:3 from the model analysis.
The properties of the VAR estimates have been shown to be reasonably robust to
moderate excess kurtosis (long tails) as long as the error distribution is symmetrical
(Gonzalo, 1994). Therefore, among the remaining outliers only those being extra-
ordinarily large and those producing skewed residuals have been corrected for9. The
dummies and their estimated effects are reported in Table 1, which shows that the very
large shocks were associated with large and unexplainable changes (given our data and
our model) in the short-term interest rates and the US bond rate. The dummy vari-
able, Dtax, measures the impact on German prices from a number of excise taxes in
1991:7, 1991:1, and 1993:1 to finance the re-unification. All dummy variables, except
the one in 1984:1 which is a transitory dummy (...,0,1,-1,0,..), are impulse dummies
(..., ^l, 1, ^i,...).
Thus, provided that we are willing to consider broken linear trends in the variables,
but no quadratic or cubic trends, we need to restrict the trend, t, and the broken linear
trend, təi:i, to exclusively enter the β'xt-1 relations, and the constant and the shift
dummy Ps91 : lt to exclusively enter the δ'∆xt~1 and τ,∆xt~1 relations, whereas the
permanent blip dummy, can enter the VAR model unrestrictedly. See the specification
in (13).
Given this specification, Table 2 shows that the model passes most of the specifica-
tion tests, though there are still some problems with the normality of the short-term
interest rates and nominal exchange rates due to excess kurtosis and with residual
ARCH for the two bond rates. However, the cointegrated VAR results are reasonably
8The nonlinear adjustment process in Bec and Rahbek (2004) might even provide a better approx-
imation, but testing for this possibility is outside the scope of this paper.
9As a sensitivity check, the model has been estimated without the hole in 1980-1982 and without
correcting for outliers. The main conclusions hold, but the statistical interpretation of the results is
less reliable.
14