Exchange Rate Economics: Theories and Evidence

390 Spot and forward exchange rates
They propose transforming the basic equation using the autocorrelation function
and generalised least squares. They demonstrate that as a result of this transformation
the coefficient is insignificantly different from unity. However,they also
demonstrate that the error term in the estimated version of (15.4) is strongly serially
correlated (they do not use overlapping contracts) which represents a violation of
the basic efficiency hypothesis.
15.6 The advantages of surveydata in unravelling
forward rate bias
As we have seen,a key problem with standard tests of forward rate unbiasedness
is that they are tests of a joint hypothesis that agents are risk neutral and form
their expectations rationally. The existence of survey data bases offers an independent
measure of exchange rate expectations and,in principle,a way round the
joint hypothesis problem and it has now been widely used to unravel the separate
constituents of the joint hypothesis and also to test other hypothesis about the
behaviour of exchange rates and expectations formation.
With access to an independent source of expectations,the rational expectations
assumption can be replaced with:
s t+k = s e t+k + ε t+k,(15.57)
where st+k e is now the (subjective) market expectation. Frankel and Froot (1987,
1989) were the first to take the mean or median value from a survey data
base as their measure of st+k e . The existence of an independent measure of
expectations should allow a different separation of the risk and expectational
parameters/coefficients to that discussed in Section 15.2. For example,as we
have seen the p lim of α 1 is:
α 1 = Cov(fp t, s t+k )
.
Var(fp t )
And on using expression (15.57) in this formulae we can obtain:
α 1 = Cov(se t+k − s t, fp t ) + Cov(ε t+k , fp t )
Var(fp t )
(15.58)
where the terms in the numerator indicate the two potential reasons why α 1 may
differ from unity. Using the definition of the risk premium given in Section 15.1
we have:
α 1 = 1 − α ω − α e ,