IDEAS home Printed from https://ideas.repec.org/p/bie/wpaper/564.html
   My bibliography  Save this paper

Controlling public debt without forgetting Inflation

Author

Listed:
  • Ferrari, Giorgio

    (Center for Mathematical Economics, Bielefeld University)

Abstract

Consider the problem of a government that wants to control its debt-to-GDP (gross domestic product) ratio, while taking into consideration the evolution of the inflation rate of the country. The uncontrolled inflation rate follows an Ornstein-Uhlenbeck dynamics and affects the growth rate of the debt ratio. The level of the latter can be reduced by the government through fiscal interventions. The government aims at choosing a debt reduction policy which minimises the total expected cost of having debt, plus the total expected cost of interventions on debt ratio. We model such problem as a two-dimensional singular stochastic control problem over an infinite time-horizon. We show that it is optimal for the government to adopt a policy that keeps the debt-to-GDP ratio under an inflation-dependent ceiling. This curve is the free-boundary of an associated fully two-dimensional optimal stopping problem, and it is shown to be the unique solution of a nonlinear integral equation.

Suggested Citation

  • Ferrari, Giorgio, 2016. "Controlling public debt without forgetting Inflation," Center for Mathematical Economics Working Papers 564, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:564
    as

    Download full text from publisher

    File URL: https://pub.uni-bielefeld.de/download/2904750/2904751
    File Function: First Version, 2016
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Frank Riedel & Xia Su, 2011. "On irreversible investment," Finance and Stochastics, Springer, vol. 15(4), pages 607-633, December.
    2. Ioannis Karatzas & Fridrik M. Baldursson, 1996. "Irreversible investment and industry equilibrium (*)," Finance and Stochastics, Springer, vol. 1(1), pages 69-89.
    3. Carmen M. Reinhart & Kenneth S. Rogoff, 2010. "Growth in a Time of Debt," American Economic Review, American Economic Association, vol. 100(2), pages 573-578, May.
    4. Carmen M. Reinhart & Vincent R. Reinhart & Kenneth S. Rogoff, 2012. "Public Debt Overhangs: Advanced-Economy Episodes since 1800," Journal of Economic Perspectives, American Economic Association, vol. 26(3), pages 69-86, Summer.
    5. Giorgio Ferrari, 2012. "On an integral equation for the free-boundary of stochastic, irreversible investment problems," Papers 1211.0412, arXiv.org, revised Jan 2015.
    6. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    7. Lee, Hsiu-Yun & Wu, Jyh-Lin, 2001. "Mean Reversion of Inflation Rates: Evidence from 13 OECD Countries," Journal of Macroeconomics, Elsevier, vol. 23(3), pages 477-487, July.
    8. Tiziano De Angelis & Salvatore Federico & Giorgio Ferrari, 2014. "Optimal Boundary Surface for Irreversible Investment with Stochastic Costs," Papers 1406.4297, arXiv.org, revised Jan 2017.
    9. Hindy, Ayman & Huang, Chi-fu & Kreps, David, 1992. "On intertemporal preferences in continuous time : The case of certainty," Journal of Mathematical Economics, Elsevier, vol. 21(5), pages 401-440.
    10. Jaejoon Woo & Manmohan S. Kumar, 2015. "Public Debt and Growth," Economica, London School of Economics and Political Science, vol. 82(328), pages 705-739, October.
    11. Stephen Cecchetti & Madhusudan Mohanty & Fabrizio Zampolli, 2011. "The real effects of debt," BIS Working Papers 352, Bank for International Settlements.
    12. Hindy, Ayman & Huang, Chi-fu, 1993. "Optimal Consumption and Portfolio Rules with Durability and Local Substitution," Econometrica, Econometric Society, vol. 61(1), pages 85-121, January.
    13. Olivier Jean Blanchard & Stanley Fischer, 1989. "Lectures on Macroeconomics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262022834, 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. Giorgio Ferrari, 2016. "On the Optimal Management of Public Debt: a Singular Stochastic Control Problem," Papers 1607.04153, arXiv.org, revised Dec 2017.
    2. David Greenlaw & James D. Hamilton & Peter Hooper & Frederic S. Mishkin, 2013. "Crunch Time: Fiscal Crises and the Role of Monetary Policy," NBER Working Papers 19297, National Bureau of Economic Research, Inc.
    3. Haytham Y.M. Ewaida, 2017. "The Impact of Sovereign Debt on Growth: An Empirical Study on GIIPS versus JUUSD Countries," European Research Studies Journal, European Research Studies Journal, vol. 0(2A), pages 607-633.
    4. Balázs Égert, 2015. "Public debt, economic growth and nonlinear effects: Myth or reality?," Journal of Macroeconomics, Elsevier, vol. 43(C), pages 226-238.
    5. Rebeca Jimenez-Rodriguez & Araceli Rodríguez-López, 2015. "What happens to the relationship between public debt and economic growth in European countries?," Economics and Business Letters, Oviedo University Press, vol. 4(4), pages 151-160.
    6. Balázs Egert, 2013. "The 90% public debt threshold: The rise and fall of a stylised fact," Working Papers hal-04141189, HAL.
    7. Yannis Dafermos, 2015. "The ‘other half’ of the public debt–economic growth relationship: a note on Reinhart and Rogoff," European Journal of Economics and Economic Policies: Intervention, Edward Elgar Publishing, vol. 12(1), pages 20-28, April.
    8. repec:cii:cepiei:2015-q1-141-4 is not listed on IDEAS
    9. De Vita, Glauco & Trachanas, Emmanouil & Luo, Yun, 2018. "Revisiting the bi-directional causality between debt and growth: Evidence from linear and nonlinear tests," Journal of International Money and Finance, Elsevier, vol. 83(C), pages 55-74.
    10. Bitar, Nicholas & Chakrabarti, Avik & Zeaiter, Hussein, 2018. "Were Reinhart and Rogoff right?," International Review of Economics & Finance, Elsevier, vol. 58(C), pages 614-620.
    11. Robert A Buckle & Amy A Cruickshank, 2013. "The Requirements for Long-Run Fiscal Sustainability," Treasury Working Paper Series 13/20, New Zealand Treasury.
    12. Markus Eberhardt & Andrea Filippo Presbitero, 2013. "This Time They're Different: Heterogeneity;and Nonlinearity in the Relationship;between Debt and Growth," Mo.Fi.R. Working Papers 92, Money and Finance Research group (Mo.Fi.R.) - Univ. Politecnica Marche - Dept. Economic and Social Sciences.
    13. Dreger, Christian & Reimers, Hans-Eggert, 2013. "Does euro area membership affect the relation between GDP growth and public debt?," Journal of Macroeconomics, Elsevier, vol. 38(PB), pages 481-486.
    14. Willem Vanlaer & Wim Marneffe & Lode Vereeck & Johan Vanovertveldt, 2015. "Does debt predict growth? An empirical analysis of the relationship between total debt and economic output," European Journal of Government and Economics, Europa Grande, vol. 4(2), pages 79-103, December.
    15. Balẳ Égert, 2015. "The 90% public debt threshold: the rise and fall of a stylized fact," Applied Economics, Taylor & Francis Journals, vol. 47(34-35), pages 3756-3770, July.
    16. Jos Mauricio Gil Le n & John William Rosso Murillo & Edgar Alonso Ramirez Hern ndez, 2019. "Public Debt and Stability in Economic Growth: Evidence for Latin America," International Journal of Economics and Financial Issues, Econjournals, vol. 9(4), pages 137-147.
    17. Swamy, Vighneswara, 2015. "Government Debt and Economic Growth – Decomposing the Cause and Effect Relationship," MPRA Paper 64105, University Library of Munich, Germany.
    18. Swamy, Vighneswara, 2015. "Government Debt and its Macroeconomic Determinants – An Empirical Investigation," MPRA Paper 64106, University Library of Munich, Germany.
    19. Ugo Panizza & Andrea F. Presbitero, 2013. "Public Debt and Economic Growth in Advanced Economies: A Survey," Swiss Journal of Economics and Statistics (SJES), Swiss Society of Economics and Statistics (SSES), vol. 149(II), pages 175-204, June.
    20. Gu, Yanwei & Guo, Jing & Liang, Xiao & Zhao, Yajun, 2022. "Does the debt-growth link differ across private and public debt? Evidence from China," Economic Modelling, Elsevier, vol. 114(C).
    21. Wang Man Cang & Zhou Ming Matt, 2017. "Will Rising Debt in China Lead to a Hard Landing?," International Journal of Economics and Finance, Canadian Center of Science and Education, vol. 9(9), pages 60-69, September.

    More about this item

    Keywords

    debt-to-GDP ratio; inflation rate; debt ceiling; singular stochastic control; optimal stopping; free-boundary; nonlinear integral equation;
    All these 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:564. 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.