Exchange Rate Economics: Theories and Evidence

where
Real exchange rate determination 211
β 0 , β 3 > 0, β 1 , β 2 , β 4 , β 5 , β 6 < 0
and,for expository purposes,we have used a bar to denote a long-run equilibrium
value, y,real income,has been substituted for K , tnt,the relative price of non-traded
goods,and tot,the terms of trade,have been substituted for the real exchange rate
and the β’s are reduced form coefficients. In testing relationship (8.29) MacDonald
used the multivariate cointegration methods of Johansen (1995) and finds clear evidence
of cointegration in systems for the effective exchange rates of the US dollar,
German mark and Japanese yen,over the period 1973 to 1993. In particular,the
US dollar exhibited one cointegrating vector,the German mark two cointegrating
vectors and the Japanese yen four cointegrating vectors. MacDonald attempted
to interpret these vectors using the approach of Johansen and Juselius (1992).
In particular,for a system with four cointegrating relationships this identification
procedure amounts to the joint selection of four stationary relationships of the form:
β ={H 1 φ 1 , H 2 φ 2 , H 3 φ 3 , H 4 φ 4 },(8.30)
where H 1 to H 2 represent the specific hypothesis implemented on each of the
cointegrating vectors and this can be interpreted as the joint selection of four
stationary relationships which are fully specified and identified (in terms of the
Johansen (1995) rank condition). The restricted vectors for Japan are reported
in Table 8.1.
The idea underlying the identification in Table 8.1 is that the first vector is
interpreted as an exchange rate relationship,the second as a money market system,
the third as an expression for net foreign assets and the final vector represents the
interaction between the terms of trade and the relative price of non-traded to
traded prices. Imposing this structure across the four vectors produced a Wald
statistic of 17.46 and a p-value of 0.06.
Table 8.1 Restricted cointegrating vectors for the Japanese yen effective exchange rate
S y P ∗ i ∗ tnt tot nfa M
−1 0 −1.47 0.06 −1.08 0 0 0
(0.08) (0.004) (0.16)
0 2.13 0.11 0 0 0 0 −1
(0.03) (0.02)
0 0 0 0 0 5.26 −1 0
(0.29)
0 0 0 0 −1 0.34 0 0
(0.02)
Source: MacDonald (1999b). Check coefficient on p in second coin vector of EERM.
Note
Standard errors in parenthesis.