Exchange Rate Economics: Theories and Evidence

60 Purchasing power parity and the PPP puzzle
long time spans because their relative price of non-traded goods have changed
dramatically (Froot and Rogoff (1995) have presented some empirical evidence to
suggest that there is some support for this hypothesis). For these reasons attention
has turned from expanding T ,the time series dimension,to extending N ,the
cross-sectional dimension.
2.4.1.2 Increasing NT by increasing N: panel studies
In contrast to the early empirical literature,the more recent panel exchange rate
literature has involved testing for the stationarity of the residual series in (2.21) or
reparameterising the equation into an expression for the real exchange rate and
testing the panel unit root properties of real exchange rates. The first paper to test
mean reversion of the real exchange rate in a panel setting was Abuaf and Jorion
(1990). In particular,using a ZSURE estimator they implement a Dickey–Fuller
style test for 10 US dollar-based real exchange rates for the period 1973–87,and
they are only able to reject the null hypothesis of a unit root using a 10% significance
level. More recent tests of the panel unit properties of real exchange rates have
been conducted using the test(s) proposed by Levin and Lin (1992,1994),who
demonstrated that there are ‘dramatic improvements in statistical power’ from
implementing a unit root test in a panel context,rather than performing separate
tests on the individual series. The panel equivalent of the univariate ADF is:
l−1
∑
q it = γ i + δ i q i,t−1 + β ij q i,t−j + v it ,(2.30)
j=1
where,as before,i denotes the cross-sectional dimension.
The Levin and Lin approach involves testing the null hypothesis that each
individual series is I(1) against the alternative that all of the series as a panel are
stationary. Their approach allows for a range of individual-specific effects and also
for cross-sectional dependence by the subtraction of cross-sectional time dummies.
Frankel and Rose (1995),MacDonald (1995b),Oh (1995),Wu (1995) and Wei and
Parsley (1995) have all implemented variants of the Levin and Lin panel unit root
test on ‘overall’ price measures (such as WPI and CPI) and find evidence of mean
reversion which is very similar to that reported in long time spans of annual data,
namely,half-lives of 4 years. Another feature of these studies,which is quite similar
to the long time span studies,is the finding of price homogeneity when PPP is tested
in a panel context using nominal exchange rates and relative prices. Oh (1996)
and Wei and Parsley (1995) have examined the unit root properties of panel data
for the Summers-Heston data set and tradable sectors,respectively,and report
similar results to those based on aggregate data.
Bayoumi and MacDonald (1998) examine the panel unit root properties of interand
intra-national exchange rates. The former are defined for a panel of CPI
and WPI based real exchange rates for 20 countries,over the period 1973–93,
while the intra-national data sets are constructed from Canadian regional and