Time-Inconsistent Optimal Quantity of Debt

A key property of the Aiyagari-type heterogeneous-agent models is that the equilibrium interest rate of public debt lies below the time discount rate. This fundamental property, however, implies that the Ramsey planner's fiscal policy may be time-inconsistent because the forward-looking planner would have a dominate incentive to issue plenty of debt, such that all households are fully self-insured against idiosyncratic risk whenever the interest rate of government borrowing is lower than the household time discount rate. But such a full self-insurance allocation may be paradoxical because, to achieve it, the optimal labor tax rate may approach 100% and aggregate consumption may approach zero. This is puzzling from an intuitive perspective because near the point of full self-insurance the marginal gains of increasing debt should be less than the marginal costs of financing the debt under distortionary taxes. We show that this puzzling behavior originates from the assumption that the planner must commit to future plans at time zero. Under such a full commitment, the Ramsey planner opts to exploit the low interest cost of borrowing to front load consumption by sacrificing future consumption in the long run because future utilities are heavily discounted compared to the inverse of the interest rate on government bonds. We demonstrate our points analytically using a tractable heterogeneous-agents model featuring non-linear preferences and a well-defined distribution of household wealth