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



Table 7: The common stochastic trends and their loadings

PPt
s12,t
ΔP2,t
bit
b2,t
sι,t
s2,t

=

1.56   -0.69 ^

2.43    3.35

-0.00   0.07

-0.01   0.09

-0.03   0.08

0.00    0.16

-0.05   0.12

Γ αl2,ι∑∑iβ 1

t αl2,2∑ ∑^ J +

Table 6. We also note that this adjustment explains a small part of the variation in
the nominal exchange rate.

Finally, Table 7 reports the weights with which the I(2) stochastic trends have
affected the variables of the system. We do not report the weights of the I(I) trends
as these are complicated functions of the estimated matrices. See Section 2.

We note that the first I(2) trend seems to have affected pp and s12 with coefficients
of the same sign, but not the same magnitude, whereas the second I(2) trend appears
to influence these variables with coefficients of opposite signs. Interpreting the first
trend as the long-run downward sloping trend visible in both relative prices and nom-
inal exchange rates suggests that it is associated with twice cumulated shocks to the
bond spread and the German term spread. Interpreting the second trend as capturing
the long swings movements predominantly in nominal exchange rates suggests that it
is predominantly associated with the twice cumulated shocks to the US short- term
interest rate. Moreover, this second trend has affected relative prices with a fairly small
coefficient that is opposite in sign to the one on nominal exchange rates. This reflects,
of course, the tendency of the nominal exchange rate to move away from relative prices
for extended periods of time. Finally, it is notable that nominal interest rates seem to
have been affected in particular by the second I(2) trend which is consistent with the
FG model as discussed in FGJ.

24

c11

C12

C13

c14

C21

c22

c23

c24

C31

c32

c33

c34

+

C41

C42

r'13

C44

ʤi

C52

r3

r⅛1

ɛei

l>2

r63

C64

c71

c72

c73

C74


⅛ι ∑εi
α≈i2,2∑ ɛi
ɑll,l Σ¾
a'l.1,2∑ ɛi

bii

b12

b21

b22

b31

b32

+

b41

b42

b51

b52

b61

b62

b71

b72


b91.1
t




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