1 Short-Memory and the PPP-Hypothesis Mahmoud A. El-Gamal and Deockhyun Ryu * January 2003 Abstract 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 label short-memory in distribution (SMD, which is similar to the notion of φ -mixing), and short-memory in mean (SMM, c.f. Granger (1995)). We show that focusing on a simple notion such as "half-life" can be very misleading. In particular, we show that it is possible to match desired "half-lives" for any of the most popular non-linear models recently proposed in the literature, at the expense of matching their more general dynamic structure. We conclude that depending on the models and criteria selected for investigating the PPP-puzzle, the puzzle may be in the eye of the beholder. Keywords: PPP-puzzle; half-life; SMD; SMM; φ -mixing; persistence measures; cross- validation; non-parametric time series analysis; Markov models. * El-Gamal is a Professor of Economics and Statistics at Rice University, where Ryu is a Ph.D candidate in the Economics Department. Contact: Mahmoud A. El-Gamal, Economics MS 22, Rice University, 6100 Main Street, Houston, TX 77005. Emails: elgamal@rice.edu , dhryu@rice.edu .