Exchange Rate Economics: Theories and Evidence

240 Equilibrium exchange rates
Detken et al. (2000) augment the basic Clarida–Gali model to include a relative
employment term,the difference in the ratio of government consumption over
GDP and the long-term interest differential. They apply this model to the real
effective exchange rate of a synthetic euro for the period 1973–98. They find
that the various shocks have a correctly signed effect on the exchange rate and
around one-half of the contemporaneous forecast errors in the real exchange rate
are accounted for by nominal shocks,although in the long-run,despite having a
relatively rich supply side,real demand shocks dominate the evolution of the real
exchange rate.
9.5.3 Cointegration-based PEER estimates
Clark and MacDonald (2000) also propose using the permanent component calculated
from a VAR system and interpret this as measure of equilibrium,which
is referred to as the permanent equilibrium exchange rate (or PEER). In contrast
to the studies that use SVARS the PEER does not rely on Blanchard–Quah style
restrictions,but it does require the existence of cointegration amongst the variables
entering the VAR. Clark and MacDonald (2000) interpret the PEER as one way of
calibrating a BEER and for reasons that shall become clear,they interpret the misalignment
calculated from the PEER as a total misalignment. The approach may
be illustrated in the following way. Johansen (1995) has demonstrated that a vector
error correction model,such as that used by most of the researchers who have
estimated a BEER,has a vector moving average representation of the following
form:
where
x t = C
t∑
ε i + Cµt + C ∗ (L)(ε t + µ),(9.20)
i=1
( ) )
k−1
−1
∑
C = β ⊥
(α ⊥
′ I − Ɣ i β ⊥ α ⊥ ′ ,
1
and where α ⊥ determines the vectors defining the space of the common stochastic
trends and therefore should be informative about the key ‘driving’ variable(s). The
β ⊥ vector gives the loadings associated with α ⊥ (i.e. the series which are driven by
the common trends).
If the vector X is of reduced rank, r (i.e. if there exists cointegration) then
Granger and Gonzalo (1995) have demonstrated that the elements of X can also
be explained in terms of a smaller number of (n − r) of I (1) variables called common
factors, f t ,plus some I (0) components,the transitory elements:
X t = A 1 f t + ˜X t . (9.21)