A Bayesian analysis of the PPP puzzle using an unobserved components model

The failure to describe the time series behaviour of most real exchange rates as temporary deviations from fixed long-term means may be due to time variation of the equilibria themselves, see Engel (2000). We implement this idea using an unobserved components model and decompose the observations on real exchange rates in long-term components, which capture the time-variation of the mean and in medium and short-term components which measure temporary deviations. A simulation-based Bayesian analysis is introduced to compute the posterior distribution of (functions) of the model parameters. A stationarity test in this setup indicates that the mean is slowly time-varying. Subsequently, we use our flexible model to derive the implied distributions of some key features of real exchange rates. Most notably, the half-life of deviations from the mean, which is a measure of persistence, is lowered. This provides a possible explanation for the PPP puzzle.