Fractional Cointegration and the Demand for M1

Using wavelets, the author estimates the fractional order of integration of a common long-run money-demand relationship whose parameters are obtained from a full-information maximum-likelihood procedure. Because the order of integration is found to be significantly higher than zero, a grid-search procedure is used over the local parameter space to isolate the parameters required to lower the fractional order of integration. When Canadian data from 1968–99 are examined, a 25 per cent reduction in the interest semi-elasticity, accompanied by a corresponding increase in the income elasticity, is required to render the equilibrium relationship more stationary. However, given the large standard errors around the estimates of the fractional order of integration, the improvement in the estimate of the cointegration relationship is relatively modest. This suggests that money, output, prices, and interest rates are, at best, fractionally cointegrated.