Exchange Rate Economics: Theories and Evidence

we have:
Speculative attack models and contagion 329
p t = p ∗ t + s t + q t ,(13.30)
where,as before,q is the log of the real exchange rate. In the absence of perfect
foresight,the discrete time version of UIP is:
i t = i ∗ t + E t (s t+1 − s t ). (13.31)
Movements in the variables in (13.29) to (13.31) and domestic credit expansion
determine the evolution of foreign exchange reserves and the central bank stops
defending the fixed exchange rate, ¯s,when reserves reach a critical level, ¯R (measured
in foreign currency units). As before, ŝ is the shadow exchange rate which
becomes visible to the researcher at the time of the attack and,therefore,may also
be thought of as the post-devaluation exchange rate. Analagous to the derivation
of (13.5),the flexible exchange rate in this model may be obtained by substituting
(13.30) and (13.31) into (13.29) to get:
˜h t =−αE t ˜s t + (1 + α)˜s t ,(13.32)
where ˜h t ≡ log[D t + ¯R exp(˜s)] −β − y t + αi ∗ t − p ∗ t − u t − w t . Since ˜h t is
unobservable to the researcher,Blanco and Garber assume ˜h t = h t ,the initial
value of ˜h t that would prevail at time t if the floating rate began at time t. The
variable h t is assumed to follow a first-order autoregressive process as:
h t = θ 1 + θ 2 h t−1 + v t ,(13.33)
where v t is a white noise process with a normal density function g(v),with zero
mean and standard deviation σ . The flexible exchange rate solution may be found
by solving the difference equations in (13.32) and (13.33) to obtain:
˜s t = µαθ 1 + µh t ,(13.34)
where µ = 1/[(1 + α) − αθ 2 ]. 5 Rather than use an optimising rule for the determination
of the new exchange rate,Blanco and Garber assume it is given by a
simple linear function:
ŝ t =˜s t + δv t ,(13.35)
where δ is a non-negative parameter. This rule states that after an attack the
central bank will select a new rule equal to the minimum viable rate plus a nonnegative
amount which depends on the magnitude of the disturbance that forced
the collapse. Since when ŝ is greater than ¯s is equivalent to a devaluation at
time t we may use (13.34) and (13.35) to define the probability of devaluation
at time t + 1,based on information at time t as:
pr(µαθ 1 + µh t+1 + δv t+1 > ¯s),(13.36)