The natural interest rate is of great relevance to central banks, but it is difficult to measure. We show that in a standard microfounded monetary model, the natural interest rate co-moves with a transformation of the money demand that can be computed from actual data. The co-movement is of a considerable magnitude and independent of monetary policy. An optimizing central bank that does not observe the natural interest rate can take advantage of this co-movement by incorporating the transformed money demand, in addition to the observed output gap and inflation, into a simple but optimal interest rate rule. Combining the transformed money demand and the observed output gap provides the best information about the natural interest rate.