TY - JOUR

T1 - Explicit formula for the optimal government debt ceiling

AU - Cadenillas, Abel

AU - Huamán-Aguilar, Ricardo

N1 - Publisher Copyright:
© 2015, Springer Science+Business Media New York.

PY - 2016/12/1

Y1 - 2016/12/1

N2 - 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.

AB - 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.

KW - Government debt ceiling

KW - Government debt control

KW - Government debt ratio

KW - Stochastic singular control

UR - http://www.scopus.com/inward/record.url?scp=84947093545&partnerID=8YFLogxK

U2 - 10.1007/s10479-015-2052-9

DO - 10.1007/s10479-015-2052-9

M3 - Article

AN - SCOPUS:84947093545

SN - 0254-5330

VL - 247

SP - 415

EP - 449

JO - Annals of Operations Research

JF - Annals of Operations Research

IS - 2

ER -