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William Peterman, Ph.D.

Federal Reserve System, USA

Authors: William B. Peterman and Eric Sager

Abstract: In a seminal paper, Aiyagari and McGrattan (1998) find that in a standard incomplete markets model with infinitely lived agents it is optimal for the U.S. government to have a large amount of public debt. Debt is optimal because it induces a higher interest rate, which encourages more household savings and better self-insurance. This paper revisits their result in a life cycle model only to find that public debt’s insurance enhancing mechanism is severely limited. While a higher interest rate encourages higher average savings in both models, the benefits vary.  In a life cycle model, agents enter the economy with no savings but must accumulate the higher level of savings throughout their lifetime, thereby eliminating some of the benefits. In contrast, infinitely lived agents do not accumulate savings over a lifetime and, thus, simply enjoy the benefit of the higher average savings ex ante. Overall, we find that while optimal debt is equal to 24% of output in the infinitely lived agent model, when a life cycle is introduced it is optimal for the government to hold savings equal to 59% of output. Not accounting for life cycle features when computing optimal policy reduces welfare by nearly one-half percent of expected lifetime consumption.

Keywords: Government Debt; Life Cycle; Heterogeneous Agents; Incomplete Markets

JEL Codes: H6, E21, E6

Full Text:  “Optimal Public Debt with Life Cycle Motives”