Exchange Rate Economics: Theories and Evidence

The new open economy macroeconomics part 1 271
By combining (10.72) and (10.73) the steady-state change in tradables consumption
as a function of the steady-state change in the relative price of non-traded goods
in terms of traded goods is:
[
]
C T ′ = (σ − θ)γ
θ + (P N ′ 1 + σ
− P T ′ ). (10.74)
In the short-run with sticky prices non-traded production is driven purely by the
level of demand as given by (10.66):
ŷ N = Ĉ N = θ ˆP T + Ĉ T . (10.75)
The short-run and steady-state monetary equilibrium conditions may be derived
from a log-linearised variant of (10.67):
ε(M ′ − ˆp) = θ σ
[
ˆP T − ˆP]
+ 1 σ ĈT − 1 r (P ′ T − ˆP T ),(10.76)
ε(M ′ − P ′ ) = θ σ
[
P
′
T − P ′] + 1 σ C ′ T . (10.77)
Equations (10.70) to (10.77) can be used to solve both the short-run and steady-state
effects of an unanticipated monetary surprise,which are:
ˆp T = β 1 M ′ (10.78)
P ′ T = β 2M ′ ,(10.79)
ŷ N = Ĉ N = β 3 M ′ ,(10.80)
y ′ N = C ′ N =−β 4(σ − θ) 2 M ′ ,(10.81)
Ĉ T = β 5 (σ − θ)M ′ ,(10.82)
C T ′ =−β 6(σ − θ)
M ′ ,(10.83)
r
P N ′ − P T ′ =−β 7(σ − θ)M ′ ,(10.84)
where the reduced form parameters, β 1 , β 2 , β 3 , β 4 , β 5 , β 6 , β 7 > 0,are a function
of the underlying structural parameters. We are now ready to analyse the effect of
divergences in the inter- and intra-elasticities of substitution on the current account.
In the ‘base-line’ case where σ = θ,a positive monetary shock results in an
expansion in the nontraded sector (equation (10.80)) and the price of traded goods
rises in both the short- and long-run (equations (10.78) and (10.79)). With the two
elasticities cancelling out by assumption,there can be no spillover to consumption
in the traded sector (from (10.82) and (10.83)) and so the current account must
stay in balance. As in the base-line case,when σ > θ the monetary stimulus
will raise short-run production of the non-traded good and produce a rise in the
price of the traded good (which by assumption represents a nominal depreciation).