On VoxEU, Luca Benati, Robert Lucas, Juan Pablo Nicolini, and Warren Weber argue that long-run money demand in many countries is rather stable.

… using a specific, narrow monetary aggregate, M1, we study a dataset comprising 32 countries since the mid-19th century (Benati et al. 2016). The main finding of this large-scale investigation is that, contrary to conventional wisdom, in most cases statistical tests do identify with high confidence a long-run equilibrium relationship between either M1 velocity and a short-term interest rate, or M1, GDP, and a short rate – that is, a long-run money demand.