Exchange market participants constantly shift funds around the
globe such that yields of international assets with similar risk
should be equalized. However, sometimes we do observe substantial
differences in interest rates across different countries. To get a
more complete picture we have to take exchange rates into account.
This is done by the theory of uncovered interest parity (UIP). A
typical macroeconomic textbook model of the UIP
(e.g. Burda and Wyplosz; 1993)
has the following form: Let us
denote the domestic interest rate as , the foreign interest
rate as
and the nominal exchange rate as
. At time
we
can write the UIP as
Following MacDonald and Nagayasu (1999) we modify equation (12.2).
First, we use real exchange rates and real interest rates. Second,
since it is not clear whether the UIP holds for short or long term
interest rates, we include a short and a long term interest rate.
The panel dataset contains observations
countries
and at
time periods. Therefore, the log
exchange rate of country
at time
is written as
.
Since we are interested in the change of the exchange rate we
calculate first differences as
. Then
is interpreted as the growth
rate of the exchange rate. It is impossible to include the
expected exchange rate growth in the empirical analysis because it
is unobservable. Instead we use the observable growth rate denoted
as
as a proxy for the expectations formed at time
. In doing so we assume economic agents have static
expectations, i. e.
.
Although this assumption can be problematic too, we proceed in
order to make empirical analysis feasible.
Furthermore, let
be the long-term interest
rate differential, where
and
denote the domestic and
foreign long-term rates respectively. Finally, we use
to denote the short-term interest differential. At
best, economic theory predicts that UIP holds in the long-run (see
Burda and Wyplosz (1993)). We test this assumption by including
short and long-term interest rate differentials in the estimated
equation. If the UIP holds in the long-run, we expect
to
be positive and close to unity and
.
Now, we can estimate an equation of the following form: