The Long-Run Relationship between Real GDP, Money Supply, and Price Level: Unit Root and Cointegration Tests with Structual Changes

Many studies have attempted to find a stable money demand function, which is a prerequisite, among other things, for monetary targeting to work effectively as a means of monetary policy. An error correction model has increasingly become popular as a means of finding such a stable function; however, its shortcomings have also been pointed out. This paper examines prerequisites for the application of the traditional unit root and cointegration tests and emphasizes the importance of structural changes in the deterministic trend as well as the distinction between deterministic and stochastic cointegration. It presents a time series model with a deterministic trend consisting of multiple linear and nonlinear parts as the appropriate model for Japan's postwar real GDP, money supply (M1), and the GDP deflator series, which exhibit structural changes. The unit root test of this model produces evidence against the presence of a unit root in the real GDP and the GDP deflator. This indicates that the cointegration between the three variables, which is supported by previous studies on the money demand function, arises from a misspecification of the time series model, and that the instability of the money demand function arises from the non-stationarity of the M1 series.