Precautionary Saving at the Top: On the Concavity of Consumption in the Perlanent Component of Earnings

Changes in the distribution of permanent income, which is a proxy for human capital, have become a key explainer of wealth accumulation at the top, but we know little about the theoretical relation between permanent income and consumption in economic models. I show that, in a standard model, consumption is concave in the permanent component of income: the marginal propensity to consume out of permanent income decreases with permanent income. The concavity arises because an increase in permanent income corresponds to an increase in uncertain future income. Thus, permanent income raises consumption because it raises total resources but its effect is dampened by the fact that it also raises the need for precautionary saving. Under standard preference assumptions, the increase in precautionary saving is higher at a higher initial level of permanent income, that is, for those who are initially exposed to more income risk. This contrasts with the concavity in accumulated wealth, which arises because precautionary saving decreases with wealth, but less so at a higher level of wealth. This reshapes the view on who engages in precautionary saving: there can be precautionary saving at the top of the income distribution. It also highlights what components of a model are important for fully capturing these concavities and why current frameworks may not capture it.