Exchange Rate Economics: Theories and Evidence

54 Purchasing power parity and the PPP puzzle
Table 2.1 Engle–Granger two-step cointegration tests
CPI
WPI
α 0 α 1 ADF α 0 α 1 ADF
Canada −0.00001 0.223 −2.400 0.783 −0.672 2.100
France 3.157 −3.662 −2.260 1.709 −1.192 −2.350
Germany 5.552 −3.266 −1.620 3.144 −2.250 −1.420
Italy 1.916 −2.892 −2.050 0.668 −0.365 −1.470
Japan 1.088 −1.390 −2.670 2.161 −1.621 −2.920
Netherlands 1.681 −1.275 −2.150 2.111 −1.593 −1.310
Sweden −0.318 0.921 −1.950 0.929 −0.809 −1.180
Switzerland 0.382 −0.758 −2.360 2.254 −1.355 −1.650
United Kingdom 0.614 −0.579 −2.350 0.517 −0.478 −2.060
Notes
The countries in the first column denote the home currency component of the nominal exchange
rate used in the Engle–Granger two-step regression (in all cases the foreign currency is the US
dollar). The entries in the columns labelled α 0 and α 1 denote estimated coefficients and ADF
denotes the augmented Dickey–Fuller statistic calculated from the residuals of the cointegration
regression. The critical value for the latter is −2.98. The labels CPI and WPI indicate the use of
a consumer or wholesale price measure in the cointegrating regression.
of the estimated augmented Dickey–Fuller statistics are significant at the 5% level
(indeed,none are significant at even the 10% level). Taylor and McMahon (1988)
use the Engle–Granger two-step test to evaluate the PPP hypothesis for inter-war
exchange rates; however,see Ahking (1990) for a critique of this work.
However,as is now well known the two-step method of Engle and Granger
suffers from a number of deficiencies,such as having poor small sample properties
and,in the presence of endogeneity and serial correlation,the asymptotic
distribution of the estimates will depend on nuisance parameters (see,for example,Banerjee
et al. 1986). Since Johansen’s (1988,1995) full information maximum
likelihood method produces asymptotically optimal estimates (because it has a parametric
correction for serial correlation and endogeneity) a number of researchers
have applied this method to testing the PPP hypothesis. Thus,Cheung and Lai
(1993),Kugler and Lenz (1993),MacDonald (1993,1995a) and MacDonald and
Marsh (1994a) all report strong evidence of cointegration,and therefore support
for weak-form PPP,but little evidence in favour of strong-form PPP when US
dollar bilateral exchange rates are used,since homogeneity restrictions are usually
strongly rejected. MacDonald (1993,1995a) reports more evidence in favour of
strong-form PPP when DM-based bilaterals are used.
For illustrative purposes,we present Table 2.2 which contains a representative
set of Johansen-based PPP results from MacDonald (1995a) (these estimates are
constructed using the same data sets underlying the numbers in Table 2.1 for the
Engle–Granger tests,discussed earlier).
Table 2.2 should be read in the following way. The numbers in the column
labelled ‘Trace’ are estimates of Johansen’s Trace test for the hypothesis that there
are at most r distinct cointegrating vectors. The estimates of the normalised cointegrating
vectors are contained in the two columns under α 0 and α 1 ,the entries