In recent years, the relevance of money growth indicators for the conduct of monetary policy has been questioned in the mainstream academic literature. It is widely argued that monetary policy should directly relate short-term interest rates to inflation and the output gap. The present paper investigates whether the performance of this type of interest rate rule can be significantly improved by adding a policy response to money growth. In contrast to most previous studies, our analysis explicitly takes into account the fact that real-time data on both actual and potential output, and hence the output gap, may be subject to substantial measurement errors. Broadly speaking, we find that the greater the degree of output gap uncertainty, the greater the benefits of incorporating a money growth response are in terms of reducing volatility in output, inflation and interest rates. The main reason is that real-time data on money growth contain valuable information on the true level of current output growth, which is not otherwise known to policy makers in real time with a sufficient degree of precision. Hence, we conclude that policy makers should explicitly account for money growth in the setting of policy rates.