Exchange Rate Economics: Theories and Evidence

210 Real exchange rate determination
8.2.4 Tests of the EERM
Based on the EERM model of Mussa (1984),discussed earlier,Faruqee (1995) uses
the cointegration methods of Johansen to estimate equilibrium real exchange rate
equations for the US and Japan. The real exchange rate used is the CPI-based real
effective exchange rate and the conditioning variables are net foreign assets as a
proportion of GNP,an index of the terms of trade. Two measures of productivity
were additionally used as conditioning variables. They are the relative price of
traded to non-traded goods,TNT,and comparative measure of labour productivity,PROD.
Clear evidence of at least on cointegration is reported for both the US
and Japanese systems. Focusing on the first significant vector the following result
is obtained for the US:
REER t = 1.47nfa t + 0.91tnt t − 0.30,(8.26)
and,similarly,for Japan
REER t = 0.66PROD t ,(8.27)
these results were obtained by implementing exclusion restrictions on the full set
of variables,indicated above.
MacDonald (1999b) tests the EERM using the methods of Johansen. In particular,expression
(8.3) is rearranged into one which is analytically equivalent,
namely:
s t = (1/(γ + η)) ·
∞∑
(η/(γ + η)) j · E t [m t+j − k t+j ],(8.28)
j=0
where we have set t = n and
k = K + α 1 p ∗ − α 5 (i ∗ + λ) + (α 4 + σα 1 )q + α 2 A.
Expression (8.28) is useful from an estimation perspective for two key reasons. First,
in the context of a present value model such as (8.28) if the dependent variable and
the right hand side variables are integrated of order 1, I (1),then it follows (see,for
example,Campbell and Shiller (1987) and MacDonald and Taylor (1993)) that
for the model to be valid s must be cointegrated with the right hand side variables.
Second,the existence of cointegration facilitates the construction of a dynamic
error correction model of the short-run exchange rate and its dynamic adjustment
to the long-run equilibrium.
The long-run equilibrium relationship,or cointegrating vector,implied by (8.28)
is given as:
¯s = β 0 ¯m + β 1 ȳ + β 2 ¯ p ∗ + β 3 ( ¯ i ∗ + ¯λ) + β 4 ¯ tnt + β 5 ¯ tot + β 6 Ā,(8.29)