Testing the nominal-to-real transformation

This paper establishes the necessary and sufficient condition for nominal-to-real data transformations routinely used in empirical work to reduce the order of integration of an I(2) vector process while retaining the cointegrating relations among the variables. The condition potentially fails in a direction which is often dealt with by assumption in applied work. In this case, the transformed process satisfies a well-specified vector equilibrium model, yet I(1) inference and interpretation based on the real transformed system are invalidated. An easy-to-implement sequential test of the transformation based on I(1) cointegration methods demonstrates good size and power properties. An empirical example illustrates the need to test the nominal-to-real transformation.