Cointegration tests of PPP: do they also exhibit erratic behaviour?

We analyse whether tests of PPP exhibit erratic behaviour (as previously reported by Caporale et al., 2003) even when (possibly unwarranted) homogeneity and proportionality restrictions are not imposed, and trivariate cointegration (stage-three) tests between the nominal exchange rate, domestic and foreign price levels are carried out (instead of stationarity tests on the real exchange rate, as in stage-two tests). We examine the US dollar real exchange rate vis-a-vis 21 other currencies over a period of more than a century, and find that stage-three test statistics are also somewhat erratic, though less than stage-two ones.