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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
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    References listed on IDEAS

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    Keywords

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