378 The Long Swings Puzzle
- Changes in the nominal exchange rate either do not seem to have been signif-
icantly responding to movements in relative inflation rates or, if they have, in
an equilibrium increasing manner. - The US inflation rate does not seem to have been responding to this “adverse”
behavior of the change in the Dmk–$ rate.
8.9.3 The estimated driving forces
The scenario in section 8.8 can now be directly assessed based on the estimates
of the MA representation in Table 8.7. The results clearly show that the empirical
reality has deviated quite substantially from the assumed theoretical scenario. For
example, the estimated loadings to theI( 2 )trend,β⊥ 2 , show that the price coeffi-
cients are not even close to being equal, as assumed by the long-run homogeneity
hypothesis. Given the previous rejection of long-run price homogeneity, this result
should, of course, not come as a big surprise. However, what is more surprising is
that the coefficient to the Dmk–$ rate is not even close to zero, suggesting thats12,t
is empiricallyI( 2 ), rather thanI( 1 )as assumed in the scenario. Another surprising
result is that, given the estimates ofβ⊥ 2 , theI( 2 )trend does not seem to cancel
inppp=p 1 −p 2 −s 12. For this to be the case, the coefficients would need to be
proportional toβ′⊥ 2 =[a,−a,2a].
That the real exchange rate is empiricallyI( 2 )would be hard to reconcile with
standard theories. However, the theory of imperfect knowledge economics (Fry-
dman and Goldberg, 2007) does in fact explain such a result. Frydmanet al.
(2008) demonstrate that, under highly plausible assumptions on agents’ behav-
ior, speculative transactions in the foreign exchange market are likely to generate
pronounced persistence in nominal exchange rates that would be hard to distin-
guish from a nearI( 2 )process. Johansenet al.(2008) find strong evidence for
this to be the case based on the same US–German (2008) data analyzed here, but
extended with short- and long-term interest rates. They also find that theppptrans-
formed variable exhibits highly persistent behavior that can be considered either
Table 8.7 The common stochastic trends and their
loadings
⎡
⎣p 1 t
p2,t
s12,t⎤
⎦=⎡
⎣0. 04
0. 09
0. 16⎤
⎦[
α′⊥2,1
∑∑
ˆεs]+⎡
⎣c 11 c 12
c 21 c 22
c 31 c 32⎤
⎦[
α′⊥2,1
∑
εˆi
α′⊥1,1
∑
εˆi]
+⎡
⎣b 11 b 12
b 21 b 22
b 31 b 32⎤
⎦[
t91.1
t]where:α′⊥2,1εˆt=− 0. 57
[−4.03]ˆεp 1 ,t+1.0ˆεp 2 ,t− 0. 09
[−2.32]ˆεs 12 ,t
α′⊥1,1εˆt= 0. 25
[6.79]εˆp 1 ,t+ 0. 14
[2.52]ˆεp 2 ,t− 0. 04
[−1.82]ˆεs 12 ,t