Exchange Rate Economics: Theories and Evidence

Equilibrium exchange rates 231
rates have been so persistent,and therefore any adjustment of the current account
to relative prices is painfully slow (see Juselius and MacDonald 2004,2007),means
that the current account imbalances have to be financed through the capital
account of the balance of payments. This,in turn,means that the persistence
observed in real exchange rates should get transferred through into persistence
in a nominal interest differential (in particular,an interest differential with a similar
maturity to the evident persistence in real exchange rates). The CHEERs
approach,therefore,involves exploiting the following vector:
x t ′ =[s t , p t , pt ∗ , i t, it ∗ ]. (9.11)
In MacDonald and Marsh (1999) equation (9.11) is estimated using the methods of
Johansen for the US dollar bilateral rates of the DM,pound sterling and Japanese
yen over the period January 1974 through to December 1992. For each country
evidence of two significant cointegrating vectors is found and in each case the first
vector can be identified to have a similar form to that of the German mark–US
dollar exchange rate:
s t = p t − p ∗ t − 7.33(i t − i ∗ t ),(9.12)
which indicates that the coefficient on relative prices can be constrained to have a
coefficient of plus and minus unity and the coefficient on the interest differential has
a traditional capital flow interpretation. Potentially then this relationship could be
used as a measure of the equilibrium exchange rate. However,one problem with
this initial approach is that the second significant cointegrating vector could not
be identified. This issue was solved in MacDonald and Marsh (2004) where it was
argued that to be able to identify both vectors in a system like (9.11) the close linkages
in currency markets should be recognised in any econometric exercise by modelling
currencies and their determinants jointly. Taking the tripolar relationship between
Germany,the US and Japan as an example,this means modelling the following
vector:
x ′ t = [ s ger
t
, s jap
t
, p ger
t
, p jap
t , p us
t , i ger
t
, i jap
t
, i us ]
. (9.13)
MacDonald and Marsh (2004) demonstrate that two significant cointegrating vectors
exist amongst the variables in (9.11) and by testing hypotheses on this vector
they demonstrate how it may be partitioned into two stationary relationships for
Germany and Japan of the form:
t
β ger x =[ω 1 (i ger − i us ) − ω 2 (p ger − p us ) + s ger ],
β jap x =[ω 3 (i jap − i us ) − ω 4 (p jap − p us ) + s jap ],
(9.14)
where ω 2 and ω 4 could be restricted to unity in both equations and ω 1 and
ω 3 were estimated significantly positive (i.e. significantly negative in equation
form). These relationships indicate that although no direct spillovers appear in the