Exchange Rate Economics: Theories and Evidence

Spot and forward exchange rates 385
The empirical evidence which exploits a risk premium to explain the forward
premium puzzle is evidently not clear-cut with respect to the significance of a risk
premium in explaining the forward premium puzzle. Indeed the preponderance of
estimates reported in this section does not support the risk premium interpretation.
Can the puzzle therefore be explained by some form of expectational failure? We
now consider the evidence on such an interpretation.
15.4 Expectational explanations for the forward
premium puzzle: learning, peso effects and
irrationality
In this section we return to the question of whether expectational failures
explain the forward premium puzzle and,in particular,consider three aspects
of expectational failure,namely: learning,peso effects and irrationality. 3
15.4.1 Rational learning
With rational learning,agents are fully rational but they take time to understand
a once-and-for-all shift in the underlying distribution of the economy – due,say,
to a change in the monetary regime which produces an exchange rate appreciation
– and this can explain the forward rate biasedness result. This may be
demonstrated more formally in the following way. Define the term E t (s t+1 /O) as
the expected future exchange rate conditional on the old regime,and E t (s t+1 /N )
as the expected future exchange rate conditional on the new regime and assume
that E t (s t+1 /O) >E t (s t+1 /N ). In this case the expected future exchange rate at
time t will be a probability weighted average of the two expected values:
E t s t+1 = (1 − φ t )E t (s t+1 /N ) + φ t E t (s t+1 /O),(15.47)
where φ t is the markets’ assessed probability at time t that monetary policy is based
on the old regime. The evolution of φ t is assumed to be based on a rational learning
process – as new information on the regime becomes available (i.e. as the currency
appreciates after the regime change) φ t decreases over time and the plim of φ t
goes to zero as the time dimension goes to ∞. During the learning period this
will generate persistent forecast errors,which can be demonstrated by subtracting
(15.47) from the realised exchange rate to obtain:
and
s N t+1 − E ts t+1 = η t+1 = s N t+1 − E t(s t+1 /N ) − φ t [E t (s t+1 /N ) − φ t E t (s t+1 /O)],
(15.48)
η t+1 = η N t+1 − φ tκ t+1 ,
where s N t+1 indicates a realisation of the exchange rate from process N , ηN t+1 ≡
[s N t+1 − E t(s t+1 /N )] and κ =[E t (s t+1 /O) − E t (s t+1 /N )], 4 which is the difference
between the expected future exchange rate changes,conditional on each