Optimal Management of Debt-To-GDP Ratio with Regime-Switching Interest Rate

Giorgio Ferrari and Neofytos Rodosthenous
Additional contact information
Giorgio Ferrari: Center for Mathematical Economics, Bielefeld University
Neofytos Rodosthenous: Center for Mathematical Economics, Bielefeld University

No 589, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

Abstract: We consider the problem of a government that wants to manage the country's debt-to- GDP (gross domestic product) ratio. The latter evolves stochastically in continuous time, and its drift is given by the interest rate on government debt, net of the growth rate of GDP. We further allow the interest rate to be affected by an exogenous macroeconomic risk process modelled by a continuous-time Markov chain with *N* states. The debt-to-GDP ratio level can be reduced by the government, e.g. through austerity policies in the form of spending cuts, or increased, e.g. by public investments. The aim of the government is to choose a policy which minimises the total expected cost of having debt plus the total expected cost of austerity policies, counterbalanced by the total expected gain from public investments. We model this as a bounded-variation stochastic control problem over an infinite time-horizon with regime switching, and we provide its explicit solution. To the best of our knowledge, such a problem has not been previously solved in the literature. We show that it is optimal for the government to adopt a policy that keeps the debt-to-GDP ratio in an interval, whose boundaries are depending on the states of the risk process, and are given through a zero-sum optimal stopping game with regime switching. We completely characterise these boundaries as solutions to a system of nonlinear algebraic equations with constraints. Finally, we put in practice our methodology in a case study of a Markov chain with *N* = 2 states; we provide a thorough analysis and we complement our theoretical results by a detailed numerical study on the sensitivity of the optimal debt ratio management policy with respect to the model's parameters.

Keywords: Debt-to-GDP ratio; government debt ratio management; regime switching; singular stochastic control; zero-sum optimal stopping game; free-boundary problem (search for similar items in EconPapers)
Pages: 30
Date: 2018-08-15
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
https://pub.uni-bielefeld.de/download/2930425/2930451 First Version, 2018 (application/pdf)
Our link check indicates that this URL is bad, the error code is: 403 Forbidden

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bie:wpaper:589

Access Statistics for this paper

More papers in Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University Contact information at EDIRC.
Bibliographic data for series maintained by Bettina Weingarten (bettina.weingarten@uni-bielefeld.de).