Empirical research on the validity of the purchasing power parity (PPP) condition is generally based on real exchange rates built using the consumer price index (CPI), but fails to provide clear support to PPP. In this paper we show theoretically that, even if the law of one price (LOP) holds for traded goods, CPI-based real exchange rates are not mean reverting, and are neither stationary nor integrated. Therefore, both unit root and stationarity tests should reject their null. Our theoretical results are validated both by simulations and an empirical application.
