The claim that volatility of money leads people to increase their demand for money is tested using recently developed cointegration techniques and error-correction modeling. This approach offers an alternative to the standard Granger-causality test for establishing the long-run relation of velocity and money growth variability. In this paper, we employ these procedures on quarterly data from Japan over the 1973:1-1992:1 flexible exchange rate period. Our findings are supportive of the Friedman hypothesis for both the short and long runs. These results are important empirical additions to the new classical theory of economics which suggests that unanticipated movements in the money supply are non-neutral.