Exchange Rate Economics: Theories and Evidence

Real exchange rate determination 217
which indicates that the flex-price real exchange rate depreciates with respect to
a supply disturbance and appreciates in response to a demand disturbance. With
γ>0,the expectation that the demand disturbance will be partially offset in the
future produces the expectation of real depreciation which in turn dampens the
magnitude of the appreciation in the present.
From the definition of the real exchange rate and (8.35) the equilibrium
price that would prevail in the flexible price rational expectation equilibrium, p e′
must satisfy:
(1 + λ)p e′
t
= m ′ t − ys′ t + λ(E t q e t+1 − qe t ) + λE tp e′
t+1 . (8.42)
On using (8.38) to (8.40) and (8.41) in (8.42) we can obtain:
p e′
t
= m ′ t − ys′ t + λ(1 + λ) −1 (η + σ) −1 λδ t . (8.43)
From (8.43) we see that the flexible price relative price level rises in proportion to the
monetary shocks,declines in proportion to the supply shock and rises in response to
the temporary component in the demand shock. In contrast a permanent demand
shock will have no effect on pt e′ . This follows because by driving up the common
level of both real and nominal interest rates,it must drive up home and foreign
prices in proportion. The flexible price solution to the model may therefore be
characterised by (8.41),(8.43) and:
y e′
t = y s′
t . (8.44)
This characterisation makes clear that in the flexible price equilibrium the levels of
relative output,the real exchange rate and relative national price levels are driven
by three shocks: a supply shock, z,a demand shock,δ and a monetary shock, v.
A comparable sticky price equilibrium may be derived in the following way. By
substituting (8.43) into (8.36) the following expression for the evolution of the price
level may be derived:
p ′ t = p e′
t − (1 − θ)(v t − z t + αγδ t ),(8.45)
where α ≡ λ(1 + λ) −1 (η + σ) −1 . A positive money or demand shock produces
a rise in the relative price level which is less than the flexible price case, p e′ . With
a positive supply shock the price level falls but by less than the flexible price case.
An expression for the real exchange rate may be derived by substituting (8.34) and
(8.37) into (8.35) and using (8.43),the following expression may be obtained:
q t = q e t + v(1 − θ)(v t − z t + αγδ t ),(8.46)
where v ≡ (1 + λ)(λ + σ + η) −1 . We note that as in the non-stochastic version
of the MFD model the existence of sticky price adjustment means that the real