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Optimal Public Debt with Life Cycle Motives

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Abstract
Public debt can be optimal in standard incomplete market models with infinitely lived agents, since the associated capital crowd-out induces a higher interest rate. The higher interest rate encourages individuals to save and, hence, better self-insure against idiosyncratic labor earnings risk. Even though individual savings behavior is a crucial determinant of the optimality of public debt, this class of economies abstracts from empirically observed life cycle savings patterns. Thus, this paper studies how incorporating a life cycle affects optimal public debt. We find that while the infinitely lived agent model's optimal policy is public debt equal to 24\% of output, the life cycle model's optimal policy is public savings equal to 61\% of output. Although public debt also encourages life cycle agents to hold more savings during their lifetimes, the act of accumulating this savings mitigates the potential welfare benefit. Moreover, public savings improves life cycle agents' welfare by encouraging a flatter allocation of consumption and leisure over their lifetimes. Accordingly, abstracting from the life cycle yields an optimal policy that reduces average welfare by more than 0.6% of expected lifetime consumption. Furthermore, ignoring the life cycle overstates the influence of wealth inequality on optimal policy, since optimal policy is far less sensitive to wealth inequality in the life cycle model than in the infinitely lived agent model. These results demonstrate that studying optimal debt policy in an infinitely lived agent model, which abstracts from the realism of a life cycle in order to render models more computationally tractable, is not without loss of generality.

Suggested Citation

  • William B. Peterman & Erick Sager, 2018. "Optimal Public Debt with Life Cycle Motives," Finance and Economics Discussion Series 2018-028, Board of Governors of the Federal Reserve System (U.S.).
    • Handle: RePEc:fip:fedgfe:2018-28
    DOI: 10.17016/FEDS.2018.028
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    2. Patrick Macnamara & Myroslav Pidkuyko & Raffaele Rossi, 2022. "Taxing Consumption in Unequal Economies," Economics Discussion Paper Series 2210, Economics, The University of Manchester.
    3. Bence Bardóczy & Mateo Velásquez-Giraldo, 2024. "HANK Comes of Age," Finance and Economics Discussion Series 2024-052, Board of Governors of the Federal Reserve System (U.S.).
    4. Blandin, Adam & Peterman, William B., 2019. "Taxing capital? The importance of how human capital is accumulated," European Economic Review, Elsevier, vol. 119(C), pages 482-508.
    5. Zuzana Mucka & Ludovit Odor, 2018. "Optimal sovereign debt: Case of Slovakia," Working Papers Working Paper No. 3/2018, Council for Budget Responsibility.
    6. Hedlund, Aaron, 2018. "Credit constraints, house prices, and the impact of life cycle dynamics," Economics Letters, Elsevier, vol. 171(C), pages 202-207.
    7. Bettoni, Luis G. & Santos, Marcelo, 2023. "Optimal fiscal policy in incomplete market business cycle economies," The Quarterly Review of Economics and Finance, Elsevier, vol. 89(C), pages 218-226.
    8. Gale, William G., 2019. "Fiscal policy with high debt and low interest rates," MPRA Paper 99207, University Library of Munich, Germany.
    9. Pedro Brinca & Hans Holter & Miguel Faria-e-Castro & Miguel Ferreira, 2019. "The Nonlinear Effects of Fiscal Policy," 2019 Meeting Papers 934, Society for Economic Dynamics.
    10. Ono, Taiki, 2024. "Bequests and wealth inequality in Japan," Journal of the Japanese and International Economies, Elsevier, vol. 72(C).
    11. Aaron Hedlund, 2018. "Credit Constraints, House Prices, and the Impact of Life Cycle Dynamics," Working Papers 1807, Department of Economics, University of Missouri.

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    More about this item

    Keywords

    Government debt; Heterogeneous agents; Incomplete markets; Life cycle;
    All these keywords.

    JEL classification:

    • H6 - Public Economics - - National Budget, Deficit, and Debt
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth
    • E6 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook

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