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This paper presents a stochastic analysis of the demand for interest-bearing money, such as NOW accounts, when overdrafting is allowed at some penalty rate. It is shown that the short-run interest elasticity of money demand is probably large (in absolute value) and negative, but in the long run this elasticity is much smaller or even positive. It is also argued that current definitions of the monetary aggregates, which exclude unused credit, may spuriously generate instability of money demand. An alternative definition of money stock is suggested and seems to be conceptually more satisfying. Copyright 1990 by American Economic Association.