Inflation Persistence, the Stability of Money Demand, and the Natural Rate of Interest

Evidence since the XIX century shows that whereas the demand for M1 is uniformly stable (Benati, Lucas, Nicolini, and Weber, 2021), the demand for broader aggregates is stable under monetary regimes making inflation strongly mean-reverting–such as the Gold Standard and inflation-targeting–but it became temporarily unstable during the Great Inflation. A simple extension of the Sidrauski model rationalizes these findings. The crucial mechanism hinges on the different impact of inflation on the demand for broad money, compared to that for M1. This implies that when inflation is highly persistent broad money demand becomes disconnected from both the demand for M1, and nominal interest rates. This evidence suggests that the post-Goldfeld (1973, 1976) consensus that money demand is unstable due to velocity shocks and financial innovation is incorrect. In fact, the only thing that matters for the stability of the demand for broad money is inflation persistence. I illustrate several implications of these findings, from identifying shocks to the natural rate of interest to estimating the natural rate and long-horizon inflation expectations, and identifying disequilibria in house and stock prices.