Public Debt under Limited Private Credit

There is a conventional wisdom in economics that public debt can serve as a substitute for private credit if private borrowing is limited. The purpose of this paper is to show that, while a government could in principle use such a policy to fully relax borrowing limits, this is not generally optimal. In our economy, agents invest in a short term asset, a long term asset, and government bonds. Agents are subject to idiosyncratic liquidity shocks prior to the maturity of the long term asset. We show that a high public debt policy fully relaxes private borrowing limits and is suboptimal. This is because agents expecting such a policy respond by investing less than is socially optimal in the short asset which can protect them in the event of a liquidity shock. The optimal policy is more constrained and it induces a wedge between the technological rate of return on the long asset and the rate of return on bonds. In such a regime, agents subject to liquidity shocks are also borrowing constrained, and this expectation of being borrowing constrained induces them to invest the optimal level in the short asset.