A Bayesian Analysis of the PPP Puzzle using an Unobserved Components Model

The failure to describe the time series behaviour of most realexchange rates as temporary deviations from fixedlong-term means may be due to time variation of the equilibriathemselves, see Engel (2000). We implement thisidea using an unobserved components model and decompose theobservations on real exchange rates in long-termcomponents, which capture the time-variation of the mean and inmedium and short-term components whichmeasure temporary deviations. A simulation-based Bayesian analysis isintroduced to compute the posteriordistribution of (functions) of the model parameters. A stationaritytest in this setup indicates that the mean isslowly time-varying. Subsequently, we use our flexible model toderive the implied distributions of some keyfeatures of real exchange rates. Most notably, the half-life ofdeviations from the mean, which is a measure ofpersistence, is lowered. This provides a possible explanation for thePPP puzzle.