Exchange Rate Economics: Theories and Evidence

Purchasing power parity and the PPP puzzle 59
the null of a unit root. The span may also be increased by holding T constant and
increasing N . We now consider each of these alternatives.
2.4.1.1 Increasing NT by increasing T: long time span studies
A number of researchers (see,for example,Frankel 1986,1988; Edison 1987;
Abuaf and Jorion 1990; Grilli and Kaminsky 1991; Lothian and Taylor 1995)
have implemented a real exchange rate unit root test using approximately 100
years of annual data. In contrast to comparable tests for the recent floating period,
these tests report evidence of significant mean reversion,with the average half-life
across these studies being around 4 years. Diebold et al. (1991) also use long time
spans of annual data,ranging from 74 to 123 years,to analyse the real exchange
rates of six countries. In contrast to other long time span studies,the authors
use long memory models to capture fractional integration processes. They find
considerable evidence that PPP holds as a long-run concept and report a typical
half-life of 3 years.
As an alternative to examining the time series properties of real exchange rates,
some long-run studies have examined the nominal exchange rate/relative price
relationship and find that homogeneity restrictions hold,although the implied
half-life is longer than that recovered from real exchange rate autoregressions. For
example,Edison (1987) uses annual data on the UK pound–US dollar exchange
rate over the period 1890–1978 and reports the following error correction model:
s t = 0.135
(0.08) + 0.756
(0.17) [(p − p∗ ) t ]−0.086
(0.04) (s − p − p∗ ) t−1 . (2.29)
where standard errors are in parenthesis. The coefficient on the change in relative
prices is insignificantly different from unity and the coefficient on the error correction
term indicates that approximately 9% of the PPP gap is closed each year,
implying a half-life of 7 years.
Although studies which extend the span by increasing T are obviously interesting,they
are not without their own specific problems since the basket used to
construct the price indices is likely to be very different at the beginning and end
of the sample period. This may be viewed as the temporal analogue to the spatial
problem that arises in comparing price indices at a particular point in time and
makes the interpretation of the results difficult. Also,such studies suffer from spanning
both fixed and flexible rate regimes with the inclusion of data from the former
regime making mean reversion more likely. Additionally,Froot and Rogoff (1995)
raise the problem of ‘survivorship’,or sample selection,bias in these studies. Such
bias arises because the countries for which very long spans of data are available are
countries which have been wealthy for relatively long periods of time and are more
likely to produce evidence in favour of PPP because their relative price of nontraded
goods have not changed that much. Countries which only comparatively
recently became wealthy (such as Japan) or countries which were once wealthy but
are no longer (such as Argentina) have not featured in the studies mentioned earlier.
However,such countries are more likely to produce a violation of PPP over