Exchange Rate Economics: Theories and Evidence

230 Equilibrium exchange rates
A number of researchers (see,for example,Brigden et al. 1997) have used this
expression to calculate a measure of the (short- to medium-run) equilibrium
exchange rate. For example,absent a risk premium,if the interest rate in the
home country is x% above that in its trading partner its currency will be expected
to depreciate by x% over the maturity of the bonds used to define i and i ∗ . On the
basis of this relationship it should therefore be possible to say where an exchange
rate will be in period k (the maturity period). However,as we noted in Chapter 1
(and as is discussed again in Chapter 15) there is little empirical support for this
relationship on its own and therefore drawing inferences purely on the basis of
(9.8) is hazardous.
A related approach to explaining the persistence in real exchange rates,and
also in obtaining well-defined measures of the equilibrium exchange rate,involves
combining an interest differential with PPP. This approach has been popularised by
Johansen and Juselius (1990),Juselius (1995),MacDonald and Marsh (1997,1999)
and Juselius and MacDonald (2004,2007). We refer to this approach as a capital
enhanced equilibrium exchange rate,or CHEER. The approach captures the basic
Casselian view of PPP,discussed in Chapter 6,that an exchange rate may be away
from its PPP determined rate because of non-zero interest differentials. In terms
of expression (9.1),therefore,the approach focuses on the interaction between the
real exchange rate and the capital account items; it ignores the relative output
terms and net foreign assets (and indeed any other ‘real’ determinants). Unlike
the pure form of Casselian PPP,in which non-zero interest differentials only have
a transitory impact on the real exchange rate,here the interest rates can have a
medium-run,or business cycle,effect. The essential proposition of this approach is
that the long-term persistence in the real exchange rate is mirrored in the interest
differential. We consider the CHEERs approach first from a statistical perspective
and then from an economic perspective.
Since interest differentials are usually empirically found to be I (1) processes
(see,for example,Juselius and MacDonald 2004,2007) some combination of an
appropriate interest differential and the real exchange rate may cointegrate down
to a stationary process. More specifically,if the expected exchange rate in (9.8) is
used to determine the relative prices,as in an absolute PPP condition,we may use
(9.8) to derive the following relationship:
(i t − i ∗ t ) = ω 2(p t − p ∗ t ) − s t,(9.9)
or,less restrictively,as:
[ω 1 (i t − i ∗ t ) − ω 2(p t − p ∗ t ) + s t]∼I (0). (9.10)
The reason why an appropriate interest differential and real exchange rate may
cointegrate is as follows. For a period such as the recent float we know that there
have been large current account imbalances (this is especially clear when the US
dollar is the bilateral numeraire) and these have been driven in large measure by
national savings imbalances,such as fiscal imbalances. The fact that real exchange