Optimal Public Debt with Life Cycle Motives

William B. Peterman and Erick Sager

Abstract

This paper shows that accounting for life cycle behavior substantially affects optimal public debt in the presence of incomplete markets. In a calibrated model, we find that the life cycle changes optimal policy from public debt equal to 24% of output to public savings equal to 61% of output because it introduces two features that are observed in the data: (i) young individuals have little wealth and accumulate savings during their lifetimes, and (ii) average consumption and hours worked vary over individuals’ lifetimes. Public debt affects welfare by crowding out productive capital and increasing the interest rate, which encourages more self-insurance against labor market risk through private saving. Without the life cycle, the welfare benefits of public debt are larger since individuals simply have more wealth on average. With the life cycle, the welfare benefit is smaller because even though public debt leads to more private savings, individuals must accumulate this savings over their lifetimes. Instead, public savings improves welfare by yielding a lower interest rate that encourages a flatter allocation of consumption and leisure over individuals’ lifetimes. Additionally, the life cycle makes optimal policy far less sensitive to wealth inequality because wealth is now correlated not only with income, but also with age.