Efthymios G. Pavlidis, Ivan Paya and David A. Peel 1047Krugman, cast in continuous time, is based on the log-linear monetary model with
instantaneous purchasing power parity so that the reduced form for the logarithm
of the exchange rates(t)is given by:
s(t)=f(t)+α
E[ds(t)]
dt, (22.56)wheref(t)is the logarithm of the fundamental andαrepresents the interest rate
semi-elasticity of money demand. The fundamental is assumed equal to:
f(t)=m(t)+v(t), (22.57)wherem(t)represents the policy instrument andv(t), which is assumed to fol-
low a Brownian motion without drift, contains all the other determinants of the
exchange rate which impact through the termf(t). Krugman assumes a credible
target zone exists so thatsl≤s≤su, whereslandsuare the lower and upper
bounds respectively. The authorities are assumed to intervene by movements inm
when the exchange rate reaches either boundary valueslorsu. The formal solution
of the model given by Krugman (1991) or Taylor (1995) has the form:
s(t)=m(t)+v(t)+A[exp(θ(m+v))−exp(−θ(m+v))], (22.58)whereθ=
√
2 /(ασ^2 ).Ais uniquely determined by the “smooth-pasting” condi-
tions (see, e.g., Taylor, 1995). The formal solution to the basic (symmetric) target
zone model is an S-shaped function. The S shape illustrates the “honeymoon
effect” and the “smooth-pasting conditions.” Ifsis close tosuthen the probability
that the exchange rate will fall is higher than that it will rise as the authorities
intervene to stop the exchange rate breaching the upper band. Consequently,
the exchange rate will be lower than if the exchange rate was freely floating.
Similar considerations apply near the lower bound. This behavior implies that
variation in the exchange rate will be smaller, for any variation in the fundamen-
tal, than under a freely floating regime. This is called the “honeymoon effect.” The
so-called “smooth-pasting” conditions ensure the absence of riskless speculative
gains.
There have been numerous empirical tests of the target zone model with various
refinements to the basic model.^53 We will consider the models of Iannizzotto and
Taylor (1999), Taylor and Iannizzotto (2001) and Lundbergh and Teräsvirta (2006),
which are empirical tests assuming that the zone is credible. Suitable data points
are therefore chosen by them for the analysis given this assumption.
22.4.1 Method of simulated moments (MSM)
Iannizzotto and Taylor (1999) and Taylor and Iannizzotto (2001) employ the MSM.
This method is based on work by Lee and Ingram (1991) and Duffie and Singleton
(1993). The essential idea is to simulate data from the chosen target zone model for
a range of parameter values and compare the statistical moments of the simulated
data with the statistical moments of the real data. A loss function which penalizes
the deviation between the actual and simulated moments is minimized over the