456 Fractional Integration and Cointegration
where fractional cointegration has attracted attention is the analysis of the link-
age between political opinions and economic indicators. Box-Steffensmeier and
Tomlinson (2000) analyzed the relation between congressional approval and eco-
nomic expectations in the US, using quarterly data from 1974 to 1993. They
estimated parametrically the integration orders of both series (0.72 and 0.86
respectively), computed by OLS the relationship between them, and estimated
parametrically the memory of the cointegrating error (0.40). They considered their
results to be inconclusive about the existence of cointegration because of large
standard errors.
Similarly, Davidson (2003), using quarterly data from 1955 to 1996, examined
the relation between political opinion (measured as the end-of-quarter difference
between support for the governing party and that for the opposition) and economic
indicators in the UK by means of bootstrap methods. The author provides support
for the non-stationary, but mean-reverting, nature of the political opinion variable,
concluding that there is little or no evidence of linkages between political and
economic cycles.
Another interesting issue is the relationship between governing party and prime
ministerial support. In principle, it seems plausible that both variables are co-
integrated, and different studies have provided support for this conjecture. Clarke
and Lebo (2003), using monthly data from 1979 to 1996, linked governing party
support, prime ministerial approval and four subjective economic evaluations.
Using different methods, the authors concluded that the series are non-stationary
but mean-reverting, suggesting the possibility of cointegration between govern-
ing party support and prime ministerial approval. Additionally, they found that,
whereas personal economic evaluations were influential, national ones are not sig-
nificant. Similarly, Davidson, Peel and Byers (2006) proposed two variants of a
fractionally integrated vector error correction model and applied them to the rela-
tionship between the respective performances of prime minister and government
in the UK. Evidence of cointegration was provided.
Finally, a different issue was addressed by Lebo and Moore (2003), who analyzed
an action–reaction model of foreign policy behavior for different pairs of countries,
including Egypt–Israel and US–Russia. They provided strong evidence that those
foreign policy series are fractionally integrated (mainly stationary and in all cases
mean-reverting), and suggested the possibility of cointegration in the Egypt–Israel
relation during the period 1948–76.
10.4 The empirical investigation: the PPP hypothesis
Numerous empirical studies have cast significant doubt on the PPP hypothesis
with respect to the short run, but have yielded mixed evidence with respect to the
long run (see, for example, Corbae and Ouliaris, 1988; Enders, 1988; Kim, 1990;
Taylor, 1988). As mentioned earlier, Cheung and Lai (1993) proposed a fractional
version of the PPP specification, essentially (10.5)–(10.6) withxtrepresenting the
domestic price index andytthe foreign price index, converted to domestic currency
units. The coefficientνin (10.5) is unity according to the absolute or homogeneous