Money velocity and the natural rate of interest

Since World War I, M1 velocity has been, to a close approximation, the permanent component of the short-term nominal rate. This logically implies that, under monetary regimes which cause inflation to be I(0), permanent fluctuations in M1 velocity uniquely reflect, to a close approximation, permanent shifts in the natural rate of interest. Evidence from the Euro area and several inflation-targeting countries is compatible with this notion, with velocity fluctuations being systematically strongly correlated with a Stock and Watson (1996, 1998) estimate of trend real GDP growth. I exploit this insight to estimate the natural rate of interest for the United Kingdom and Canada under inflation targeting: In either country, the natural rate has been consistently declining since the early 1990s.