The money-age distribution is hump-shaped for the US post-war economy. There is no clear cut relation between the variation of money holdings within generations and age. Furthermore, money is 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 these observations: 1) money in the utility, 2) an economy with costly credit service, and 3) limited participation. All three models are consistent with the hump-shaped relation between average money holdings and age, yet they predict a much closer association between money holdings, income, wealth, and age than we find in the data. Only the limitedparticipation model partly replicates the low bivariate correlation between money and income as well as between money and interest bearing assets. None of the three models satisfactorily explains these stylized facts.