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Optimal Maturity of Government Debt without State Contingent Bonds

In this paper we explore the ability of the maturity structure of public debt to replicate the welfare enhancing properties of state contingent debt in dynamic stochastic optimal taxation Ramsey problems. We first study the theoretical conditions under which the complete markets Ramsey allocation can be implemented with non-contingent debt of different maturities. We then solve simple calibrated versions of the model to get a quantitative assessment of the optimal maturity structure.

On the theory side, we show that in a dynamic economy where state contingent bonds cannot be issued, a government may still implement the complete markets Ramsey allocation by issuing risk-free bonds with a rich enough menu of maturities. This result is important because it is well known that state contingent debt is an instrument to smooth distortions across states of the world and enhances welfare, but markets for these assets do not exist.

This theoretical point is very closely related to the problem in finance of producing an asset by a combinations of existing assets. In other words, we synthetically construct state contingent debt using non-contingent debt of different maturities. In particular, we present the Ramsey problem of an infinite period stochastic model where the state has finite support. Then, we show that if the government can issue bonds with as many different maturities as the size of the support of the state, the complete markets allocation can be implemented, subject to a full rank condition on the matrix of returns.

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Optimal Maturity of Government Debt without State Contingent Bonds