Exchange Rate Economics: Theories and Evidence

Empirical evidence on the monetary approach 147
(the statistic has an approximate χ 2 distribution with 12 degrees of freedom). The
normalised vector with the constraints imposed is:
s t = (m t − m ∗ t ) − (y t − y ∗ t ) + 0.049i t − 0.050i ∗ t . (6.21)
This relationship clearly closely conforms to the flex-price monetary model and
perhaps the success in getting such a tightly defined relationship for the mark
reflects,at least in part,the relative success of the Bundesbank in controlling the
German money supply during the sample period (1976–90). However,as is made
clear in Table 6.2,for other countries where there is evidence of cointegration
the estimated coefficients are often far from their expected values and cannot
be restricted in the way they are in (6.21) (see,for example,MacDonald and
Taylor 1991 and 1994; Sarantis 1994; Kouretas 1997). Cushman et al. (1997)
have argued that the critical values used by MacDonald and Taylor to determine
the number of significant cointegrating vectors are only valid for much larger
samples than those available to MacDonald and Taylor. When Cushman et al.
use a small sample correction the existence of cointegration disappears. However,
given that cointegration tests,such as the Johansen maximum likelihood method,
have relatively low power to reject the null of no cointegration,it may be preferable
to use a lower significance level than the standard 95% level. Indeed,Juselius
(1995) has argued that this is especially relevant if the researcher can interpret the
cointegration vector (s) in an economically meaningful way (see also La Cour and
MacDonald 2000).
Using cointegration-based methods,Chrystal and MacDonald (1996) compare
the properties of divisia money (DIM) to simple sum money (SSM) in the context
of a monetary reduced form (for STG–USD). They find that the DIM outperforms
SSM in the sense of producing sensible long- and short-run relationship.
La Cour and MacDonald (2000) attempt to address the issue of multiple cointegrating
vectors in the monetary model using a ‘specific-to-general’ approach which
also allows for deviations of the nominal exchange rate from PPP. Consider first
the following nine-dimensional vector:
x g′
t
=[s t , p t , p ∗ t , m t, m ∗ t , il t , il∗ t , p t , p ∗ t ],(6.22)
which contains a menu of variables consistent with the monetary approach,broadly
defined (it may also,of course,be consistent with other exchange rate models). 4 The
vector is labelled a ‘gross’ vector since from it a number of sub-systems,discussed
later,may be constructed.
Rather than starting with a reduced form based on (6.22),La Cour and
MacDonald advocate a ‘specific-to-general’ approach. The latter involves starting
with the equilibrium relationships underlying the monetary model conditions and
trying to interpret these in an economic and statistical sense before estimating the
final relationship. A natural starting point in the monetary model is the money market
equilibrium condition. Using a data set for the ECU against the US dollar,and a
sample period of January 1982–December 1994,La Cour and MacDonald (2000)