Explicit formula for the optimal government debt ceiling

Cadenillas, Abel; Huamán-Aguilar, Ricardo

doi:10.1007/s10479-015-2052-9

Cited by 25 publications

(61 citation statements)

References 33 publications

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“…Although the government cost functional we consider in this paper is similar to the one in [6], the Markovian formulation of our singular control problem is fully two-dimensional, whereas that of [6] is one-dimensional. This implies that our optimal debt ceiling is a curve, whereas that of [6] is a constant.…”

Section: Introductionmentioning

confidence: 99%

On the Optimal Management of Public Debt: a Singular Stochastic Control Problem

Ferrari¹

2018

SIAM J. Control Optim.

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Consider the problem of a government that wants to reduce the debt-to-GDP (gross domestic product) ratio of a country. 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 the debt ratio. We model this problem as a singular stochastic control problem over an infinite time-horizon. In a general not necessarily Markovian framework, we first show by probabilistic arguments that the optimal debt reduction policy can be expressed in terms of the optimal stopping rule of an auxiliary optimal stopping problem. We then exploit such link to characterise the optimal control in a two-dimensional Markovian setting in which the state variables are the level of the debt-to-GDP ratio and the current inflation rate of the country. The latter follows uncontrolled Ornstein-Uhlenbeck dynamics and affects the growth rate of the debt ratio. 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 given in terms of the solution of a nonlinear integral equation arising in the study of a fully two-dimensional optimal stopping problem.Public Debt Control 2 of a crisis. This negative effect on economic growth from high debt levels has been observed in 18 different advanced economies (see [8]).In this paper we propose a continuous-time stochastic model for the control of the debtto-GDP ratio. The problem we have in mind is that of a government aiming to answer the question: How much is too much? 1 Following classical macroeconomic theory (see, e.g., [5]), in any given period the debt ratio stock grows by the existing debt stock multiplied by the difference between real interest rate and GDP growth, less the primary budget balance 2 . We assume that the government can reduce the level of the debt-to-GDP ratio by adjusting the primary budget balance, e.g. through fiscal interventions like raising taxes or reducing expenses. We therefore interpret the cumulative interventions on the debt ratio as the government's control variable, and we model it as a nonnegative and nondecreasing stochastic process. Uncertainty in our model comes through the GDP growth rate of the country, and its inflation and nominal interest rate which, by Fisher law [21], directly affect the growth rate of the debt ratio. We first assume that they are general not necessarily Markovian stochastic processes whose dynamics is not under government control. Indeed, the level of these macroeconomic variables is usually regulated by an autonomous Central Bank, whose action, however, is not modelled in this paper (see, e.g., [10] and [25] for problems related to the optimal control of inflation).Since high debt-to-GDP ratios can constrain economic growth making it more difficult to break the burden of the debt, we assume that debt ratio generates an instantaneous cost/penalty. This is a general nonnegative convex function of the debt ratio level, that the government would like to k...

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Section: Introductionmentioning

confidence: 99%

On the Optimal Management of Public Debt: a Singular Stochastic Control Problem

Ferrari¹

2018

SIAM J. Control Optim.

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“…In this study, we adopted a theoretical model proposed by [3]. In the model, they developed an explicit formula for determining optimal public debt ceiling for a given country.…”

Section: Background Of the Studymentioning

confidence: 99%

“…Despite the existing debt ceilings in various jurisdictions, the debt ceilings have not been previously developed using a theoretical framework. Hence, the recent framework for developing an Optimal debt Ceiling Formula is is a ground breaking research in stochastic control methods for public debt management [3]. Our contribution to Optimal debt ceiling literature is application of Stochastic control to determine the optimal debt ceiling for Kenya with an aim of advising the public debt policy.…”

Section: Background Of the Studymentioning

confidence: 99%

“…As a result, if a country's debt ratio is above that level, it is prudent for the government to take intervention measures to regulate the debt. However, if the debt ratio is below the debt ceiling, the debt is under control hence no need for fiscal adjustments [3].…”

Section: Literature Reviewmentioning

confidence: 99%

“…Due to recent debt crises in countries such as Portugal, Italy, Ireland, Greece and Spain, debt control has become a key important fiscal policy of every government. In this study, we applied a Public debt ceiling explicit formula to find out the optimal public debt ceiling for Kenya [3]. We made modification to subjective variables in the explicit formula and used the formula to find the optimal public debt ceiling for Kenya.…”

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Determination of Optimal Public Debt Ceiling for Kenya Using Stochastic Control

Kithinji¹,

Muthoni²

2018

SJAMS

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Public debt is a key economic variable. It is the totality of public and publicly guaranteed debt owed by any level of government to either citizens or foreigners or both. Due to recent debt crises in countries such as Portugal, Italy, Ireland, Greece and Spain, debt control has become a key important fiscal policy of every government. In this study, we applied a Public debt ceiling explicit formula to find out the optimal public debt ceiling for Kenya [3]. We made modification to subjective variables in the explicit formula and used the formula to find the optimal public debt ceiling for Kenya. We illustrate that it is prudent for that government to use a fiscal policy that maintains the debt ratio under an optimal debt ceiling.

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Optimal reduction of public debt under partial observation of the economic growth

2020

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We consider a government that aims at reducing the debt-to-(gross domestic product) (GDP) ratio of a country. The government observes the level of the debt-to-GDP ratio and an indicator of the state of the economy, but does not directly observe the development of the underlying macroeconomic conditions. The government’s criterion is to minimise the sum of the total expected costs of holding debt and of debt reduction policies. We model this problem as a singular stochastic control problem under partial observation. The contribution of the paper is twofold. Firstly, we provide a general formulation of the model in which the level of the debt-to-GDP ratio and the value of the macroeconomic indicator evolve as a diffusion and a jump-diffusion, respectively, with coefficients depending on the regimes of the economy. The latter are described through a finite-state continuous-time Markov chain. We reduce the original problem via filtering techniques to an equivalent one with full information (the so-called separated problem), and we provide a general verification result in terms of a related optimal stopping problem under full information. Secondly, we specialise to a case study in which the economy faces only two regimes and the macroeconomic indicator has a suitable diffusive dynamics. In this setting, we provide the optimal debt reduction policy. This is given in terms of the continuous free boundary arising in an auxiliary fully two-dimensional optimal stopping problem.

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Explicit formula for the optimal government debt ceiling

Cited by 25 publications

References 33 publications

On the Optimal Management of Public Debt: a Singular Stochastic Control Problem

On the Optimal Management of Public Debt: a Singular Stochastic Control Problem

Determination of Optimal Public Debt Ceiling for Kenya Using Stochastic Control

Optimal reduction of public debt under partial observation of the economic growth

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