A panel unit root test approach to PPP exchange rates with non-linear deterministic trends

Abstract

This paper investigates the purchasing power parity (PPP) hypothesis using panel data. Under PPP the real exchange rate is stationary around a constant mean. Recent panel data unit root tests are employed to test the PPP proposition where, under the conventional null hypothesis of a unit root, the real exchange rate is not stationary and PPP does not hold. In this case, as the time period t + n approaches infinity, its variance relative to period t will also approach infinity. The usual alternative in unit root tests is stationarity around a constant mean or a linear trend. The paper brings innovation into the PPP and panel unit root testing literature by allowing for possible nonlinear deterministic trends in the alternative hypothesis (as advanced by Cushman (2004)). If the null hypothesis is rejected in favour of the alternative of a non-linear trend, PPP still does not hold, but does at least revert back to a meaningful, stable long-run equilibrium. Given this non-linear trend, the variance of the real exchange rate as t + n approaches infinity, conditional on that trend, remains finite. Overall, evidence for stationarity in exchange rates is found in four out of six panels under consideration, including both support for stationary processes with no trend or a linear trend as well as for processes following a non-linear deterministic trend, in particular at time orders 5 and 6. The rejections are, in fact, most consistent at the nonlinear orders. Given nonlinear trends, PPP as usually defined does not hold, despite the rejection of unit roots. It is also found that stronger evidence for stable long-run equilibria in real exchange rates appears when the German Deutschmark is chosen as a base currency instead of the US Dollar. Finally, it appears that a very recent panel unit root test that takes account of cross-sectional dependencies delivers more consistent and sensible results.