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Controlling public debt without forgetting Inflation

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  • 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

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    References listed on IDEAS

    as
    1. 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.
    2. Frank Riedel & Xia Su, 2011. "On irreversible investment," Finance and Stochastics, Springer, vol. 15(4), pages 607-633, December.
    3. 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.
    4. 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.
    5. 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.
    6. Stephen Cecchetti & Madhusudan Mohanty & Fabrizio Zampolli, 2011. "The real effects of debt," BIS Working Papers 352, Bank for International Settlements.
    7. 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.
    8. Ioannis Karatzas & Fridrik M. Baldursson, 1996. "Irreversible investment and industry equilibrium (*)," Finance and Stochastics, Springer, vol. 1(1), pages 69-89.
    9. 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.
    10. 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.
    11. Olivier Jean Blanchard & Stanley Fischer, 1989. "Lectures on Macroeconomics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262022834, April.
    12. Giorgio Ferrari, 2012. "On an integral equation for the free-boundary of stochastic, irreversible investment problems," Papers 1211.0412, arXiv.org, revised Jan 2015.
    13. 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.
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    More about this item

    Keywords

    debt-to-GDP ratio; inflation rate; debt ceiling; singular stochastic control; optimal stopping; free-boundary; nonlinear integral equation;
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