It has recently been argued that unanticipated changes in nominal money supply should affect the real demand for money, and empirical results which appear to support this hypothesis have been presented. Unfortunately, the econometric techniques used by previous authors yield severel biased estimates. In this paper we show how valid estimates may easily be obtained, and present some illustrative empirical results using U.S. data. These results do not support the conclusions of earlier authors. We find that unanticipated money supply changes do indeed affect the real demand for money, but with the wrong sign, and that anticipated changes also have a significant effect.A consistency test for all models employing the anticipated-unanticipated distinction is also proposed.