Different measures in testing absolute purchasing power parity

In popular studies, the theory of purchasing power parity (PPP) is tested for the real exchange rate (RER) that is constructed by price indexes and all variables are logarithmic. In this article, we test the absolute PPP theory for the RER that is constructed by general price levels and is in its original form. Panel unit root and cointegration tests reveal that the RER is stationary and a cointegration relationship exists between nominal exchange rate and PPP rate, which supports the PPP theory. But the RER misalignment is not a normal distribution with zero mean, and the coefficient restriction test also rejects the PPP theory. One reason that leads to the conflicting conclusions is given.