Testing for PPP: the erratic behaviour of unit root tests

In this article we argue that the type of stationarity exhibited by the real exchange rate cannot be accommodated by the fixed-parameter autoregressive homoscedastic models normally employed in the literature. Using a dataset including 39 countries and spanning a period of up to two centuries, we analyse the behaviour of both WPI- and CPI-based measures of the real exchange rate. In particular, we compute a recursive t-statistic, and show that it has an erratic behaviour, suggesting the presence of endemic instability. It appears that the type of non-stationarity present in the data is more complex than the unit root one. This explains the contradictory results of previous studies using standard unit root tests for establishing whether PPP holds.