PPP May not Hold Afterall: A Further Investigation

In a recent paper, Engel, C. (1999) presents monte-carlo evidence to suggest that unit root tests cannot detect a non-stationary component in the real exchange rate even when this component accounts for almost half of its longhorizon forecast error variance. This hidden non-stationary component led to the conclusion that long run purchasing power parity might not hold afterall. In this note, we first point out some conceptual difficulties with the statistic being used to measure the size of the non-stationary component, and then argue that it bears no systematic relationship with rejection rates in unit root tests. The problems stem from near observational equivalence of the simulated model in not one, but two dimensions. We then discuss the steps a practitioner can take to minimize Type I error in cases when the non-stationary component is hard to detect. Real exchange rate data for 19 countries are examined and estimates are obtained for the duration of the real exchange rate shocks.