Explicit formula for the optimal government debt ceiling

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• 作者：Abel Cadenillas ; Ricardo Huamán-Aguilar
• 关键词：Government debt control ; Government debt ceiling ; Government debt ratio ; Stochastic singular control
• 刊名：Annals of Operations Research
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：247
• 期：2
• 页码：415-449
• 全文大小：
• 刊物类别：Business and Economics
• 刊物主题：Operation Research/Decision Theory; Combinatorics; Theory of Computation;
• 出版者：Springer US
• ISSN：1572-9338
• 卷排序：247

文摘

Motivated by the current debt crisis in the world, we develop a stochastic debt control model to study the optimal government debt ceiling, or equivalently the optimal ceiling for government debt. We consider a government that wants to control its debt by imposing an upper bound or ceiling on its debt-to-GDP ratio. We assume that debt generates a cost for the country, and this cost is an increasing and convex function of debt ratio. The government can intervene to reduce its debt ratio, but there is a cost generated by this reduction. The goal of the government is to find the optimal control that minimizes the expected total cost. We obtain an explicit solution for the government debt problem, that gives an explicit formula for optimal government debt ceiling. Moreover, we derive a rule for optimal debt policy in terms of the optimal government debt ceiling. In an extension of the model, we find that countries with a strong positive link between debt and economic growth should have a high optimal debt ceiling. This paper provides the first theoretical model for the optimal government debt ceiling.