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 comoves 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.