On the empirical failure of purchasing power parity tests

In this paper we show by theoretical arguments that, even if the law of one price holds for all the goods traded in two countries, real exchange rates based on CPI are not mean-reverting and therefore statistical tests based on them should reject the PPP hypothesis. We prove that such real exchange rates are neither stationary nor integrated, and so both unit-root and stationarity tests should reject the null according to their power properties. The performance of the most common unit-root and stationarity tests in situations in which the law of one price holds is studied by means of a simulation experiment, based on real European CPI weights and prices.