A stable money demand: Looking for the right monetary aggregate

The stability of a money demand relationship has been a major concern in monetary economics for the last 50 years. It is conventional to call the relationship between real money, a nominal interest rate, and a measure of economic activity a money demand relationship. A stable relationship between these variables helps answer important questions such as the following: What is the average growth rate of money that is consistent with price stability, given the average growth of the economy and a stable nominal interest rate? Knowledge about the response of money demand to changes in the nominal interest rate may also help quantify the welfare gains from a low average inflation rate.