Exchange Rate Economics: Theories and Evidence

136 Empirical evidence on the monetary approach
and on combining (6.2) with (6.5) and (6.6) with the standard UIP condition
(st e = i t ′ ) the following reduced form may be derived:
s t = π 0 + π 1 s t−1 + π 2 m t ′ + π 3m t−1 ′ + π 4p t−1 ′ + π 5y t
′
+ π 6 y t−1 ′ + π 7ε t ′ − π 8ε t−1 ′ ,(6.7)
where the following constraints can be shown to hold on the coefficients:
4 i=1 π i = 1, π 1 < 0, π 2 > 1, π 3 < 0, π 4 < 0, π 5 < 0 and π 6 < 0. The first
constraint says that PPP must hold in the long-run. Note,particularly,the sign
on π 2 which suggests that an increase in the money supply leads to a more than
proportionate rise in the exchange rate,which is a key prediction of the sticky price
monetary model (i.e. that there is exchange rate overshooting). Also note that the
error term in the final reduced form is predicted to follow a first-order moving
average (MA1) process,rather than the random error assumed in equation (6.1).
An interesting feature of the earlier derivation is that by substituting for i ′ we end
up with a reduced-form exchange rate equation purged of the effects of a relative
interest rate term on the exchange rate. Driskell demonstrates that if capital is less
than perfectly mobile an equivalent reduced form to (6.7) may be derived,where
the prediction is that the coefficient on m only needs to be positive (i.e. there does
not need to be overshooting in the less-than-perfect capital mobility version of the
sticky-price model).
6.1.3 The hybrid monetary model, or RID
The hybrid,or real interest differential (RID),model was first popularised by
Frankel (1979),and essentially attempts to combine elements of the sticky-price
model with the flex-price approach in a manner which is amenable to econometric
testing. In particular,and following Frankel (1979),we modify the regressive
expectations formulation to have the following representation:
s e t+1 = ϕ(¯s t − s t ) + p ′ t+1 ,(6.8)
which simply says that in long-run equilibrium,when the actual exchange rate is at
its equilibrium level, ¯s t = s t ,the exchange rate is expected to change by an amount
equal to the long-run inflation differential. The equilibrium short-run exchange
rate may be obtained by substituting (6.8) into the UIP condition (s e t = i ′ t ),and
rearranging to get:
s t =¯s t − ϕ −1 (i t ′ − E tp t+1 ′ ). (6.9)
Equation (6.9) indicates that the current exchange rate, s t ,may be above or below
¯s t depending on the real interest differential. Hence if the domestic real interest
rate is above the foreign real interest rate the currency will appreciate relative to its
equilibrium value; this captures the spirit of overshooting in the sticky-price model.
It is usual to assume that ¯s t in equation (6.9) is determined by the FLMA. Combining