Linear or nonlinear cointegration in the purchasing power parity relationship?

We test long-run Purchasing Power Parity (PPP) within a general model of cointegration of linear and nonlinear form. Nonlinear cointegration is tested with rank tests of Breitung (2001). We determine first the order of integration of each variable, using monthly data from the post-Bretton Woods era for G-10 countries. In many cases prices are I(2), whereas all exchange rates are I(1). However, there are several countries that have a price level that linearly cointegrates with the US price level so that this combination is I(1). Overall, we find some, though limited, evidence for nonlinear and also linear cointegration for the weak version of PPP.