Exchange Rate Economics: Theories and Evidence

374 Spot and forward exchange rates
15.2.1 Small sample bias
The earlier discussion assumes a consistent estimate of α 1 and that there is direct
link between α 1 and α 3 . In small samples,however,it may be that a finite sample
bias exists which drives a wedge between these terms. For example,in finite samples
we have:
ˆα 1 = Cov( f̂
t −s t , s t+k )
,
Var ̂(f t −s t )
whereˆagain denotes an estimate and we now have:
where:
ˆα 1 = 1 −ˆα 3 −ˆα ss ,
ˆα ss = Cov(f t − ŝ
t , E t s t+k − s t+k )
,
Var ̂(f t −s t )
which may be thought of as a small sample expectational failure (in large samples
plim α ss = 0). The α ss term can arise for two reasons related to differences in agents’
information sets,relative to that of the econometrician,namely,learning and ‘peso’
effects. With learning there is a change in the stochastic process governing s t which
agents only learn about gradually and in this case the econometrician,who analyses
the data ex post,has more information than agents. This effect generates a positive
correlation between Es and f − s and this implies a positive value of α ss ,which
goes to zero in large samples.
In the peso interpretation,agents have more information than the econometrician
– agents form expectations using the correct distribution of the exchange
rate,but ex post the sample does not contain all of the events that agents think
will occur with the correct frequency of occurrence. The best known example of
this is where agents expect a large depreciation of s,so E t s t+k − s t is high and
correspondingly f t − s t ,is high,but the expected change does not occur in sample
and so α ss is positive. A classic example of this is the behaviour of the Mexican
peso in the early 1970s in which a persistently high home relative interest rate differential
(which with covered interest parity is equivalent to the forward premium)
was combined with a fixed exchange rate and an expected devaluation which did
not actually occur until the late 1970s. So an econometrician testing (15.4),using
data up to before the devaluation,would have found the forward premium to be
biased because of a positive α ss term.
15.2.2 Irrational expectations
Both of the earlier effects should,of course,disappear in large samples. However,
this need not follow if what is driving the result are irrational expectations. In this