Exchange Rate Economics: Theories and Evidence

330 Speculative attack models and contagion
where ¯s is the time t value of the fixed rate. The devaluation probability may
alternatively be expressed as:
1 − F (k t ) ≡ pr(v t+1 > k t ),(13.37)
where k t ≡[1/(µ + δ)][¯s − µαθ 1 + θ 2 h t ],and F (k t ) is the cumulative distribution
function associated with g(v). Using this probability,the expected future exchange
rate may be expressed as the weighted average of the current fixed rate and the rate
expected conditional on devaluation,both weighted by the respective probabilities
of occurrence:
Es t+1 = F (k t )¯s +[1 − F (k t )]E(¯s t+1 |v t+1 > k t ). (13.38)
Using (13.35) the conditional expectation can be expressed as:
E(ŝ t+1 |v t+1 > k t ) = µθ 1 (1 + α) + µθ 2 h t + (µ + δ)E(v t+1 |v t+1 > k t ). 6
(13.39)
Since g(v) is assumed to be a normal density function,the unconditional forecast
of the exchange rate for period t + 1 is:
Es t+1 = F (k t )¯s +[1 − F (k t )][µθ 1 (1 + α) + µθ 2 h t ]
+ σ(µ+ δ) exp[−0.5(k t/σ ) 2 ]
√
2π
. (13.40)
On the basis of (13.37),(13.39) and (13.40) Blanco and Garber draw the following
predictions: [1-F (k t )] is expected to peak immediately before a devaluation;
E t s t+1 should be closely correlated with the appropriate forward exchange rate; the
conditional forecast should approximate the exchange rate set when a devaluation
occurs. The forward rate for the peso is assumed to be generated by the following
expression:
f t = Es t+1 + ε t ,(13.41)
where ε t is a zero mean disturbance,orthogonal to the variables in the expression
for Es t+1 .
Blanco and Garber propose estimating the model in the following way. First,
the money market relationship is estimated,along with (13.33),and the estimated
parameters are plugged into (13.40) along with starting values for ¯R and δ. The
values of ¯R and δ are then re-estimated by minimising the sum of squared residuals
from (13.40) and this process is repeated until the values of ¯R and δ converged.
Using this methodology,Blanco and Garber confirm that whenever ŝ is greater
than the fixed rate a devaluation occurs – in the periods 1976:Q3 and 1982:Q2.