Efthymios G. Pavlidis, Ivan Paya and David A. Peel 1041

βthat does not differ significantly from unity does not imply that markets are
efficient or expectations are formed rationally. It is also consistent with a variety
of non-rational expectations processes.
Orthogonality tests are a standard method for testing the rationality of expecta-
tions. Consider the following specifications:

st+n−st = λ+θ(ft−st)+vt+n, (22.36)

st+n−ft = λ+(θ− 1 )(ft−st)+vt+n, (22.37)

wherevt+nis the error term. Given rational expectations and risk-neutrality,
(22.34) implies thatλ=0 andθ=1 and the error term exhibits up to ann−1 order
moving average error. In fact, a vast amount of empirical work has reported esti-
mates ofθthat are not only significantly different from unity but also significantly
negative (see, e.g., Fama, 1984; Hodrick, 1987; Backuset al., 1993). The negative
value ofθimplies that the more the foreign currency is at a premium in the for-
ward market, the less the home currency is predicted to depreciate. In that case
the spot exchange rate next period moves, on average, in the opposite direction
to that currently predicted by the forward premium. This implication has become
the forward bias puzzle in the literature. Of course, one explanation could be the
absence of rational or informed expectations and numerous evidence on the prop-
erties of survey evidence on expectation formation support this view (Frankel and
Froot, 1987). However, the systematic nature of the pattern in empirical estimates
ofθover both the interwar and post-war period rather suggestsa priorithat expec-
tation formation cannot play a major role in the explanation even if one attaches
reasonable weight to the quality of survey data.
Numerous reasons have been set out to explain the puzzle and we now con-
sider some of these. Fama (1984) considers the implications of a time-varying
risk-premium for estimates of (22.36) and (22.37). Assuming rational expectations,
we have as a property that:

st+n−st=Est+n−st+ (^) t+n. (22.38)
Also, from rearrangement of (22.33):
ft−st=Etst+n−st+rpt, (22.39)
and from (22.34):
st+n−ft=−rpt+ (^) t+n. (22.40)
Now the OLS estimate ofθin (22.36) must satisfy asymptotically:
plim(̂θ)=θ=
Cov(Est+n−st+ (^) t+n,Etst+n−st+rpt)
Var(ft−st)

Var(Etst+n−st)+Cov(rpt,Est+n−st)
Var(ft−st)
; (22.41)