In a recent NBER working paper, Luca Benati, Robert E. Lucas, Jr., Juan Pablo Nicolini, and Warren Weber report estimates of long-term money demand. They write:

[U]sing annual data on money (M1, for us), nominal GDP, and short term interest rates from 31 countries over periods that range in some cases to over 100 years. We find remarkable stability in long run money demand behavior in many countries, and an equally surprising sameness across different countries. In some cases of instability, anomalies have straightforward explanations.