IDEAS home Printed from https://ideas.repec.org/p/bie/wpaper/730.html

A Stochastic Non-Zero-Sum Game of Controlling the Debt-to-GDP Ratio

Author

Listed:
  • Dammann, Felix

    (Center for Mathematical Economics, Bielefeld University)

  • Rodosthenous, Neofytos

    (Center for Mathematical Economics, Bielefeld University)

  • Villeneuve, Stéphane

    (Center for Mathematical Economics, Bielefeld University)

Abstract

We introduce a non-zero-sum game between a government and a legislative body to study the optimal level of debt. Each player, with different time preferences, can intervene on the stochastic dynamics of the debt-to-GDP ratio via singular stochastic controls, in view of minimiz- ing non-continuously differentiable running costs. We completely characterise Nash equilibria in the class of Skorokhod-reflection-type policies. We highlight the importance of different time preferences resulting in qualitatively different type of equilibria. In particular, we show that, while it is always optimal for the government to devise an appropriate debt issuance policy, the legislator should opti- mally impose a debt ceiling only under relatively low discount rates and a laissez-faire policy can be optimal for high values of the legislator’s discount rate.

Suggested Citation

  • Dammann, Felix & Rodosthenous, Neofytos & Villeneuve, Stéphane, 2025. "A Stochastic Non-Zero-Sum Game of Controlling the Debt-to-GDP Ratio," Center for Mathematical Economics Working Papers 730, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:730
    as

    Download full text from publisher

    File URL: https://pub.uni-bielefeld.de/download/3006152/3006153
    File Function: First Version, 2024
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Olivier Jean Blanchard & Stanley Fischer, 1989. "Lectures on Macroeconomics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262022834, December.
    2. Olivier J Blanchard, 2019. "Public Debt: Fiscal and Welfare Costs in a Time of Low Interest Rates," Policy Briefs PB19-2, Peterson Institute for International Economics.
    3. Barro, Robert J, 1989. "The Ricardian Approach to Budget Deficits," Journal of Economic Perspectives, American Economic Association, vol. 3(2), pages 37-54, Spring.
    4. Olivier Blanchard, 2019. "Public Debt and Low Interest Rates," American Economic Review, American Economic Association, vol. 109(4), pages 1197-1229, April.
    5. Abel Cadenillas & Ricardo Huamán-Aguilar, 2018. "On the Failure to Reach the Optimal Government Debt Ceiling," Risks, MDPI, vol. 6(4), pages 1-28, December.
    6. H. Dharma Kwon & Hongzhong Zhang, 2015. "Game of Singular Stochastic Control and Strategic Exit," Mathematics of Operations Research, INFORMS, vol. 40(4), pages 869-887, October.
    7. Abel Cadenillas & Ricardo Huamán-Aguilar, 2016. "Explicit formula for the optimal government debt ceiling," Annals of Operations Research, Springer, vol. 247(2), pages 415-449, December.
    8. M. Brachetta & C. Ceci, 2022. "A stochastic control approach to public debt management," Mathematics and Financial Economics, Springer, volume 16, number 5, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Felix Dammann & Néofytos Rodosthenous & Stéphane Villeneuve, 2024. "A stochastic non-zero-sum game of controlling the debt-to-GDP ratio," Post-Print hal-04810508, HAL.
    2. Dammann, Felix & Rodosthenous, Néofytos & Villeneuve, Stéphane, 2024. "A Stochastic Non-Zero-Sum Game of Controlling the Debt-to-GDP Ratio," TSE Working Papers 24-1481, Toulouse School of Economics (TSE).
    3. Dammann, Felix & Rodosthenous, Néofytos & Villeneuve, Stéphane, 2023. "Debt management game and debt ceiling," TSE Working Papers 23-1430, Toulouse School of Economics (TSE).
    4. Barbara Annicchiarico & Fabio Di Dio & Stefano Patrì, 2023. "Optimal correction of the public debt and measures of fiscal soundness," Metroeconomica, Wiley Blackwell, vol. 74(1), pages 138-162, February.
    5. Sardoni, Claudio, 2021. "The public debt and the Ricardian equivalence: Some critical remarks," Structural Change and Economic Dynamics, Elsevier, vol. 58(C), pages 153-160.
    6. Jussi Lindgren, 2021. "Examination of Interest-Growth Differentials and the Risk of Sovereign Insolvency," Risks, MDPI, vol. 9(4), pages 1-14, April.
    7. Thia, Jang Ping, 2020. "Deficits and crowding out through private loan spreads," The Quarterly Review of Economics and Finance, Elsevier, vol. 77(C), pages 98-107.
    8. Wei-han Liu, 2023. "Attaining stochastic optimal control over debt ratios in U.S. markets," Review of Quantitative Finance and Accounting, Springer, vol. 61(3), pages 967-993, October.
    9. Malley, James & Philippopoulos, Apostolis, 2023. "The macroeconomic effects of funding U.S. infrastructure," European Economic Review, Elsevier, vol. 152(C).
    10. Checherita-Westphal, Cristina & Domingues Semeano, João, 2020. "Interest rate-growth differentials on government debt: an empirical investigation for the euro area," Working Paper Series 2486, European Central Bank.
    11. Sweder van Wijnbergen & Stan Olijslagers & Nander de Vette, 2020. "Debt sustainability when r - g smaller than 0: no free lunch after all," Tinbergen Institute Discussion Papers 20-079/VI, Tinbergen Institute.
    12. Economides, George & Koliousi, Giota & Miaouli, Natasha & Philippopoulos, Apostolis, 2025. "From debt arithmetic to fiscal sustainability and fiscal rules: Taking stock and policy lessons," The Journal of Economic Asymmetries, Elsevier, vol. 31(C).
    13. George Economides & Giota Koliousi & Natasha Miaouli & Apostolis Philippopoulos, 2024. "From debt arithmetic to fiscal sustainability and fiscal rules: taking stock and policy lessons," GreeSE – Hellenic Observatory Papers on Greece and Southeast Europe 194, Hellenic Observatory, LSE.
    14. Stefano di Bucchianico, 2019. "A bit of Keynesian debt-to-GDP arithmetic for deficit-capped countries," Bulletin of Political Economy, Bulletin of Political Economy, vol. 13(1), pages 55-83, June.
    15. Jan Priewe, 2020. "Why 60 and 3 percent? European debt and deficit rules - critique and alternatives," IMK Studies 66-2020, IMK at the Hans Boeckler Foundation, Macroeconomic Policy Institute.
    16. van Wijnbergen, Sweder & Olijslagers, Stan & de Vette, Nander, 2020. "Debt sustainability when r - g," CEPR Discussion Papers 15478, C.E.P.R. Discussion Papers.
    17. Claudio Sardoni, 2020. "Budget deficits, public debt and the Ricardian Equivalence," Working Papers 18/20, Sapienza University of Rome, DISS.
    18. Luca Metelli & Kevin Pallara, 2020. "Fiscal space and the size of the fiscal multiplier," Temi di discussione (Economic working papers) 1293, Bank of Italy, Economic Research and International Relations Area.
    19. Das, Piyali & Ghate, Chetan, 2022. "Debt decomposition and the role of inflation: A security level analysis for India," Economic Modelling, Elsevier, vol. 113(C).
    20. Peppel-Srebrny, Jemima, 2021. "Not all government budget deficits are created equal: Evidence from advanced economies' sovereign bond markets," Journal of International Money and Finance, Elsevier, vol. 118(C).

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;
    ;

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bie:wpaper:730. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Bettina Weingarten (email available below). General contact details of provider: https://edirc.repec.org/data/imbiede.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.