Testing the Nominal-to-Real Transformation

Nominal-to-real data transformations are routinely used in empirical work. A common example is the transformation of nominal money and prices to real money and the rate of inflation. This paper establishes the necessary and sufficient condition for a transformation to reduce the order of integration of an I(2) vector process while retaining the cointegrating relations among the variables. A particular direction in which the condition potentially fails is often treated 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 is invalidated. An easy-to-implement sequential test of the transformation based on I(1) cointegration methods is suggested. It demonstrates good size and power properties in a small-scale simulation experiment. An empirical example illustrates the need to test the nominal-to-real transformation.