This paper studies the possibility of using the broad monetary aggregate M2 to target the quarterly rate of growth of nominal GDP. Our findings indicate that the Federal Reserve could probably guide M2 in a way that reduces not only the long-term average rate of inflation but also the variance of the annual rate of growth of nominal GDP. An optimal M2 rule, derived from a simple VAR, reduces the mean ten-year standard deviation of annual GDP growth by over 20 percent. Although there is uncertainty about this value because of both parameter uncertainty and stochastic shocks to the economy, we estimate that the probability that the annual variance would be reduced over a ten year period exceeds 85 percent. A much simpler policy based on a single equation linking M2 and GDP is shown to be almost as successful in reducing this annual GDP variance. Additional statistical tests indicate that M2 is a useful predictor of nominal GDP. Moreover, a battery of recently developed tests for parameter stability fails to reject the hypothesis that the M2 - GDP link is stable, but the MI - GDP and monetary base - GDP relations are found to be highly unstable. This evidence contradicts those who have argued that the M2 - GDP relation is so unstable in the short run that it cannot be used to reduce the variance of nominal GDP growth.