We document that, across households, the money consumption ratio increases with age and decreases with consumption, and that there has been a large increase in the money consumption ratio during the recent era of very low interest rates. We construct an overlapping generations (OLG) model of money holdings for transaction purposes subject to age (older households use more money), cohort (younger generations are exposed to better transaction technology), and time effects (nominal interest rates affect money holdings). We use the model to measure the role of these different mechanisms in shaping money holdings in recent times. We use our measurements to assess the interest rate elasticity of money demand and to revisit the question of what the welfare cost of inflation is (which depends on how the government uses the windfall gains from the inflation tax). We find that cohort effects are quite important, accounting for half of the increase in money holdings with age. This in turn implies that our measure of the interest rate elasticity of money is -0.6, on the high end of those in the literature. The cost of inflation is lower by one-third in the model and, as a result, lower than previously estimated in the literature that does not account for the secular financial innovation.