ECO2004S
TUTORIAL 7
Question 1:
Given the nominal exchange rate between the rand and the dollar at time t, E
t,R/$
, show that the
uncovered interest rate parity condition:
(1+i
t
SA
)=[(1+i
t
US
)E
e
t+1,R/$
]/E
t,R/$
Is
approximately
equal to:
i
t
SA
≈ i
t
US
+ [(E
e
t+1,R/$
- E
t,R/$
)]/E
t,R/$
Where
i
t
SA
,
i
t
US
and E
e
t+1,R/$
denote the nominal interest rate in South Africa, the nominal interest rate
in US and the expected nominal rand-dollar exchange rate at time t+1, respectively.
Question 2:
Given that the purchasing power parity holds between the rand and the dollar, using the following
facts:
•
(1+i
t
SA
)=[(1+i
t
US
)E
e
t+1,$/R
]/E
t,$/R
Uncovered interest rate parity condition
•
Π
e
t,SA
= (P
e
t+1,SA
– P
t, SA
)/P
t,SA
Expected inflation rate in SA
•
Π
e
t,US
= (P
e
t+1,US
– P
t, US
)/P
t,US
Expected inflation rate in US
Show that the uncovered interest parity condition approximates to:
i
t
SA
- Π
e
t,SA
≈ i
t
US
- Π
e
t,US
(Fisher Equation)
Where i
t