A reappraisal of the evidence on PPP: a systematic investigation into MA roots in panel unit root tests and their implications

Abstract

Abstract:Panel unit root tests of real exchange rates -as opposed to univariate tests -usually reject non-stationarity. These tests, however, could be biased if the real exchange rate contained MA roots. Indeed, two independent arguments claim that the real exchange rate, being a sum of a stationary and a non-stationary component, is possibly an ARIMA (1, 1, 1) process. Monte Carlo simulations show, how systematic changes in the parameters of the components, of the test equation and of the correlation matrix affect the size of first and second generation panel unit root tests. Two components of the real exchange rate, the real exchange rate of a single good and a weighted sum of relative prices, are constructed from the data for a panel of countries. Computation of the relevant parameters reveals that panel unit root tests of the real exchange rate are severely oversized, usually much more so than simple ADF tests. Thus, the evidence for PPP from panel unit root tests may be merely due to extreme size biases. Keywords:panel unit root test, purchasing power parity, real exchange rate, Monte Carlo simulation JEL-Classification: F31, C33 Non Technical SummaryIn the last fifteen years, the empirical validity of purchasing power parity (PPP) over the post-Bretton Woods period has been studied extensively. As regards the methodology, unit root tests have been used to investigate whether the real exchange rate is stationary or not. While panel unit root tests usually confirm purchasing power parity, univariate unit root tests reject the PPP hypothesis in most cases. Since they combine information from several time series, panel unit root tests display greater power than univariate unit root tests. For this reason, the issue of whether purchasing power parity holds is widely held to be settled in favour of PPP.The evidence presented in this study challenges conventional wisdom. It is shown that unit root tests are biased in favour of a rejection of the non-stationarity null if they are applied to a variable that is the sum of two components, one of which is stationary Two arguments from the literature are presented, both of which suggest independently that the real exchange rate consists of two such components. Based on one of the theoretical arguments, the data from the OECD's structural analysis database are used to construct the two components for eleven industrial countries. Consistent with the theory, panel unit root tests show that one of the series can be considered stationary, whereas the other most probably is non-stationary. The parameters of the two component model are estimated. For both this particular parameter constellation as well as one taken from the literature, the bias which occurs when panel unit root tests are applied to real exchange rates is determined by using Monte Carlo simulations.It turns out that panel unit root tests of real exchange rates are biased quite substantially in favour of a rejection of the non-stationarity null if a two-component structure is assumed. The large body of empirica...

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