Exchange Rate Economics: Theories and Evidence

Real exchange rate determination 209
all of the low frequency information from the data,some of which may be useful
for tying down a desirable relationship. Moreover,from a theoretical perspective
transforming the data using a first difference operator presupposes that the effect
of real interest rates on the real exchange rate is permanent; however,to the extent
that (8.21) represents a reduced form representation of the sticky price monetary
model the relationship between the two variables would only be expected to be
transitory.
In order to better understand the RERI model Baxter (1994) proposes an alternative
specification to (8.21),namely one which relates the transitory component
of the real exchange rate to the real interest differential (she assumes real interest
rates are stationary). In regression equation form this is given as:
q T t = α + β k ( k r − k r ∗ t ) + u kt. (8.24)
Such a relationship can be derived by assuming the real rate comprises permanent
(q P t ) and transitory (q T t ) components and that the permanent component follows
a random process. Using,alternatively,univariate and multivariate Beveridge–
Nelson decompositions to derive q T t ,and ex post and ex ante measures of the real
interest differential,Baxter estimates (8.24) for a number of bilateral country pairings.
The majority of her estimates of β turn out to be significantly negative,the
only exception being those for the UK. Further,the majority of point estimates
reported by Baxter are above unity,which (her version of) the model predicts,
and it is noteworthy that this is the only paper on the RERI which establishes this
result. MacDonald and Swagel (1998) use band pass filters to extract the business
cycle component from both real exchange rates and real interest rates for bilateral
and real effective exchange rates. They find very strong evidence of the real interest
rate/real exchange rate relationship in the sense that coefficients are correctly
signed and statistically significant.
Hoffman and MacDonald (2005) propose a correlation-based approach to estimating
the RERI. This may be illustrated in the following way. Rewrite equation
(8.15) as:
lim E(q t+k − q t ) =−α k ( k r t − k rt ∗ ). (8.25)
k→∞
This equation indicates that the current real interest differential contains sufficient
information for forecasting the expected long-run change in the real exchange rate.
Hence although an econometrician may not have access to all of the information
used by economic agents in their forecasting process,equation (8.25) indicates that
current real interest rates should embody all of that information. Hoffman and
MacDonald therefore extract two measures of the expected change in the real
exchange rate from a VAR system comprising the real interest differential and the
real exchange rate. For a selection of six currencies over the period 1978 quarter 1,
to 1997 quarter 4,they report clear evidence that the real interest differential is
closely correlated with the real interest differential.