Exchange Rate Economics: Theories and Evidence

The new open economy macroeconomics part 1 257
By subtracting (10.19) from (10.18) and making use of the PPP relationship for the
overall price series the following relative output relationship may be derived:
ŷ t −ŷ ∗ t = θ[Ŝ t + ˆp ∗ t (f ) − ˆp t (h)]. (10.20)
The log-linear versions of the home and foreign counterpart to (10.13) are:
(θ + 1)ŷ t =−θĈ t + Ĉ w
t ,(10.21)
(θ + 1)ŷ ∗ t =−θĈ ∗
t
+ Ĉ w
t ,(10.22)
and on subtracting (10.22) from (10.21) we obtain an alternative measure of relative
income,which we use later:
ŷ t −ŷt ∗ =−
θ
1 + θ (ĉ t −ĉt ∗ ),(10.23)
In sum equations (10.3a ′′ ),(10.3b ′′ ),(10.14),(10.15),(10.16),(10.17),(10.18),
(10.19),(10.21) and (10.22) define the model. Before presenting a solution of the
model we must first discuss the wealth interactions and the current account.
10.1.3 Wealth transfers and the current account
A crucial aspect of the model,as we shall see in more detail later,is the effect
that wealth transfers,through the current account,can have on the steady state.
Because of this,the model contains important similarities with the portfolio-balance
and currency substitution models discussed in Chapter 7 and the eclectic exchange
rate model in Chapter 8. In both countries steady-state consumption must equal
steady-state real income:
¯C = δ ¯F + ¯p(h)ȳ
¯P ,(10.24)
( ) n
¯C ∗ =− δ ¯F + ˆp ∗ − (f )ȳ ∗
1 − n
¯P ∗ ,(10.25)
where the log-linearised counterparts of (10.24) and (10.25) are:
ć = δ ´F + ṕ(h) +ý − Ṕ,(10.26)
( ) n
ć ∗ =− δ ´F + ṕ ∗ (f ) +ý ∗ − Ṕ ∗ ,(10.27)
1 − n
where the over prime denotes the percentage change in the steady-state values;
that is, ´X = d ¯X / ¯X 0 . On subtracting (10.27) from (10.26) we obtain:
( ) 1
Ć − Ć ∗ = δ ´F +ý −ý ∗ −[Ś + ṕ ∗ (f ) − ṕ(h)]. (10.28)
1 − n