Exchange Rate Economics: Theories and Evidence

Purchasing power parity and the PPP puzzle 49
from Frenkel (1981) for the dollar–franc rate over the period June 1973–July 1979:
s t = 1.521 + 0.184(p
t − pt ∗ ),SER = 0.029,DW = 2.30. (2.20)
(0.027) (0.37)
This kind of result led Frenkel (1981) to refer to ‘the collapse of purchasing
power parities during the 1970s’. Krugman (1978) also presents estimates of (2.17)
and (2.18) for both the inter-war and recent floating periods and his results are
unfavourable to PPP in both periods. He concludes,‘There is some evidence then
that there is more to exchange rates than PPP. This evidence is that the deviations
from PPP are large,fairly persistent and seen to be larger in countries with unstable
monetary policy.’
However,two early studies estimated (2.17) and (2.18) using panel methods,
that is,pooled time series – cross-section estimators,and report results which are
favourable to PPP even for the 1970s period. Panel estimates of PPP rely on the
following framework:
s it = α i + β ′ (p it − p ∗ it ) + { ∑
i
} { ∑
γ i D i +
t
δ t D t
}
+ u it ,(2.21)
where the i subscript indicates that the data has a cross-sectional dimension (running
from 1 to N ), D i and D t denote,respectively,country-specific and time-specific
fixed effect dummy variables (although not noted here it is straightforward to
incorporate random effects into (2.21)). In a standard panel setting a number of
modelling strategies are available for the disturbance term,ranging from a purely
random term to autoregressive processes (with either common autoregressive terms
across individual panel members or different autoregressive terms across members),
or it may be spatially correlated,or some combination of these assumptions may
be used.
One clear advantage to using panel methods to estimate PPP has been noted
by Frankel and Rose (1995). Their argument is as follows. Since PPP is unlikely to
hold continuously,deviations from PPP – that is,the error term in equation (2.17) –
will be correlated with relative prices,that is,Cov (φ, p− p ∗ ) ̸= 0. If this covariance
is non-zero it will introduce a standard errors-in-variable bias producing
biased and inconsistent estimates of the αs. However,this bias will vanish in circumstances
where u becomes sufficiently small relative to the total variation in
the data (see also Davutyan and Pippenger 1985). In the context of a PPP study,
Frankel and Rose (1995) demonstrate that for panel data sets defined for the recent
floating period the cross-sectional variability dominates the time series variability.
Therefore Cov (φ, p − p ∗ ) is likely to go to zero in a panel framework.
The earliest application of panel methods to testing PPP was that of Hakkio
(1986),who used a monthly data set for the period March 1973–April 1982 to
estimate equation (2.16) for the UK pound,French franc,Canadian dollar and
Japanese yen (all against the US dollar). A systems estimator was used which
incorporated the correlation of the error term across countries and Hakkio found