•M1 velocity is, approximately, the permanent component of the short-term rate.•Agents-in deciding how much wealth to allocate to non interest-bearing M1, as opposed to interest-bearing assets-almost uniquely react to permanent shocks to the opportunity cost, ignoring transitory shocks.•Money-demand models must be modified to allow for such distinct reaction to permanent and transitory shocks to the opportunity cost.•Under monetary regimes making inflation stationary, permanent fluctuations in velocity uniquely reflect, to a close approximation, permanent shifts in the natural rate of interest. M1 velocity is, approximately, the permanent component of the short-term rate. This implies that agents—in deciding how much wealth to allocate to non interest-bearing M1, as opposed to interest-bearing assets—almost uniquely react to permanent shocks to the opportunity cost, essentially ignoring transitory shocks. This suggests that money-demand models must be modified to allow for such distinct reaction to permanent and transitory variation in the opportunity cost of holding M1. Under monetary regimes making inflation stationary, permanent fluctuations in M1 velocity uniquely reflect, to a close approximation, permanent shifts in the natural rate of interest.