Specifications (3)-(5) are valid regression equations only if the variables on both sides of
the equations are stationary. Tests of unbiasedness or of CIP above therefore are based on
the assumption that the exchange rate and the forward rate are co-integrated with co-
integration vector (1, -1). Actual tests of stationarity of exchange rates and forward rates
have often found them to be I(1) processes, which makes the LHS of (3) stationary.
Unbiasedness therefore requires that the forward premium be stationary as well.
Although there are good economic reasons to believe that that should be so - when the
CIP holds, the forward premium is simply the interest differentials - results of studies of
forward premium stationarity are mixed [Hutchison and Singh, 1997; Horvath and
Watson, 1994; Evans and Lewis, 1994; Engel, 1996 for a survey]. While unbiasedness
can hold only if the exchange rate and forward rate are co-integrated, the reverse is not
true. Finding co-integration between st+1 and ft does not imply that unbiasedness holds.
The additional requirement that unbiasedness imposes is that this co-integrating vector as
well as the co-integrating vector between st and ft be (1,-1).
Another thing to take into account while estimating an equation such as (4) is the
conditional heteroskedasticity of errors, which will be present in one-period horizon data
if forex markets are characterized by tranquil and turbulent periods. Errors will also be
conditionally heteroskedastic if the data is sampled at a higher frequency than the
forward rate horizon (e.g. using daily data on one-month forward interest rates). This is
typically taken care of by using the GMM estimator proposed by Hansen (1982).
Bulk of the empirical research on interest parities has focused on industrialized
countries. I review some of this literature below.