Exchange Rate Economics: Theories and Evidence

304 Target zone models
for the DM–lira,Smith and Spencer find evidence against the target zone model
in the sense that the simulated moments did not match the observed moments
(in particular,the model predicted greater skewness and kurtosis in exchange rate
levels and significantly less kurtosis). Other applications of the MSM estimator to
target zone exchange rates are Koedijk et al. (1992),who find evidence against the
target zone model for a number of currencies,and Lindberg and Soderlind (1991)
who find evidence in favour of the model.
12.2 Extensions of the base-line target zone model
As we have seen,the base-line model does not fare very well for the ERM target
zone experience. It is perhaps not surprising therefore that a number of modifications
have been proposed to the basic Krugman model in order to make it better
suited to explaining exchange rate behaviour during this period.
12.2.1 Credibility issues
Perhaps the most obvious extension is that which addresses the evident lack of
credibility of the ERM target zone experience. Bertola and Svensson (1993) propose
the following modification to allow for a lack of credibility. First,the central
parity, c,is assumed to jump at the time of the realignment and stays constant
between realignments and,second,investors are assumed to be uncertain about
the timing and size of realignments. Consider (12.23) again:
E t [ds t ]/dt = E t [dc t ]/dt + E t [dx t ]/dt,(12.28)
where E[dc]/dt is now a product of two factors: the probability of realignment and
the expected size of realignment. If it is assumed that the rate of realignment is
exogenous and does not depend directly on the exchange rate,then on subtracting
c t from both sides of (12.1) and on using (12.28) we have:
where
x t = h t + α E tdx t
,(12.29)
dt
h t ≡ f t − c t + α E tdc t
. (12.30)
dt
The first upshot of this modified version of the model is that any relationship
between the interest differential and the exchange rate within the band is possible
depending on how the expected rate of realignment fluctuates over time and how
it is correlated with the exchange rate. Second,new linear exchange rate function
is now defined for x, h and the expected rate of realignment in the band instead
of s, f and the expected total change in the exchange rate,as in the original
model. These two relationships are formally the same and if it is further assumed
that E t dc t /dt follows a Brownian motion process the new exchange rate function