Fractional Cointegration and Aggregate Money Demand Functions

In this paper we examine aggregate money demand relationships in five industrial countries using a two-step strategy for testing the null hypothesis of no cointegration against alternatives that are fractionally cointegrated. Fractional cointegration would imply that, although there exists a long-run relationship, the equilibrium errors exhibit slow reversion to zero, i.e. that the error correction term possesses long memory, and hence deviations from equilibrium are highly persistent. It is found that the null hypothesis of no cointegration cannot be rejected for Japan. In contrast, there is some evidence of fractional cointegration for the remaining countries, i.e. Germany, Canada, the USA and the UK (where, however, the negative income elasticity that is found is not theory-consistent). Consequently, it appears that money targeting might be the appropriate policy framework for monetary authorities in the first three countries, but not in Japan or in the UK