The money-age distribution: Empirical facts and economic modelling

The money-age distribution is found to be hump-shaped for the US economy. The variation (inequality) of cash holdings within generations increases (declines) with age. Furthermore, cash holdings are found to be only weakly correlated with both income and wealth. We analyze three motives for money demand in an overlapping generations model in order to explain this effect: 1) money in the utility, 2) an economy with costly credit service, and 3) limited participation. Both the simple money-in-the-utility model and the economy with the cash-credit goods are able to replicate the hump-shape profiles of cash holdings and its variation, but not the decreasing inequality within generations over age. In addition, we discuss the optimality of the Friedman rule in heterogeneous-agent economies. In the first two models, the optimal inflation rate is above zero.