Exchange Rate Economics: Theories and Evidence

Empirical evidence on the monetary approach 159
Since,as we have seen,there is considerable evidence to support cointegration in
the context of the monetary model,MacDonald and Taylor (1993) propose using
a vector error correction methodology,first proposed in the context of a present
value stock pricing formula by Campbell and Shiller (1987),to test the forwardlooking
model in the presence of cointegration. We now present a description of
the methods of MacDonald and Taylor and this first involves some manipulation of
the basic relationships. Consider again the basic equation of the monetary model:
s t = x t + β 1 E t (s t+1 ). (6.39)
On subtracting x t from both sides of this expression we may obtain
s t − x t = β 1 E t (s t+1 ). (6.40)
Since s t is an I (1) process, s t must be stationary and,if the monetary model is
valid,it must follow that the left hand side of (6.40) is also stationary; that is,s and
x are cointegrated, CI (1,1). Using the forward-looking monetary equation with
the transversality condition imposed,we may write the expected change in the
exchange rate as:
⎡
⎤
∞∑
∞∑
β 1 E t (s t+1 ) = β 1
⎣(1 − θ) θ j E t x t+1+j −(1 − θ) θ j E t x t+j
⎦ ,
=
j=0
∞∑
θ j E t x t+j ,(6.41)
j=1
(where note that θ = β 1 (1 − θ)). Following Campbell and Shiller (1987),
MacDonald and Taylor label s − x as the spread, ζ t ,and therefore (6.40) and
(6.41) imply:
∞∑
ζ t = s t − x t = θ j E t x t+j . (6.42)
j=1
That is to say if the model fundamentals are I (1) processes (they need to be
differenced to achieve stationarity) the model implies that the spot exchange rate
should be cointegrated with the fundamentals. This could be regarded as a first test
of the present value model – if these variables are not cointegrated then it suggests
that there is an additional explosive term on the right hand side of (6.39) due,say,
to a speculative bubble. Expression (6.42) may be rewritten as:
where:
ζ t = E t ˆζ t ,(6.43)
ˆζ t =
∞∑
θ j x t+j ,
j=1
j=0