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Time-Inconsistent Optimal Quantity of Debt

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Abstract

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 dominant incentive to issue plenty of debt such that all households are fully self-insured against idiosyncratic risk. 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.

Suggested Citation

  • YiLi Chien & Yi Wen, 2020. "Time-Inconsistent Optimal Quantity of Debt," Working Papers 2020-037, Federal Reserve Bank of St. Louis, revised 02 Sep 2021.
  • Handle: RePEc:fip:fedlwp:88991
    DOI: 10.20955/wp.2020.037
    Note: Publisher DOI: https://doi.org/10.1016/j.euroecorev.2021.103913
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    Cited by:

    1. Chien, YiLi & Wen, Yi, 2022. "The determination of public debt under both aggregate and idiosyncratic uncertainty," Journal of Economic Theory, Elsevier, vol. 203(C).
    2. YiLi Chien & Yi Wen, 2022. "The Ramsey Steady-State Conundrum in Heterogeneous-Agent Economies," Working Papers 2022-009, Federal Reserve Bank of St. Louis, revised 29 May 2024.

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    More about this item

    Keywords

    Time Inconsistency; Optimal Debt; Ramsey Problem; Incomplete Markets;
    All these keywords.

    JEL classification:

    • E13 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Neoclassical
    • E62 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - Fiscal Policy; Modern Monetary Theory
    • H21 - Public Economics - - Taxation, Subsidies, and Revenue - - - Efficiency; Optimal Taxation
    • H30 - Public Economics - - Fiscal Policies and Behavior of Economic Agents - - - General

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