Short-memory and the PPP hypothesis

Over the past decade, the purchasing-power parity (PPP) puzzle has taken two forms. Its early form arose from early tests of unit roots in real exchange rates, which failed to reject the null hypothesis, thus casting doubts on the long-term PPP hypothesis of real exchange rates ' mean reversion. Following the development of more powerful tests that resulted in rejections of unit roots, the PPP-puzzle re-surfaced in the form of surprisingly slow rates of convergence of real exchange rates to their long-run means. Rogoff (1996) expressed this puzzle in terms of the estimated "half-life " of real exchange rate shocks being 3 to 5 years. Recent research has attempted to solve that second form of the puzzle by adopting non-linear stochastic models of real exchange rates. Despite this introduction of non-linearities, the literature has continued to focus on the notion of "half-life " as a measure of persistence. We argue that the half-life measure is only appropriate in linear settings, failing to capture the richness of non-linear dynamics introduced in the more recent literature. We propose operational measures of persistence in such non-linear models, which we labe