Controlling public debt without forgetting Inflation
Ferrari, Giorgio
debt-to-GDP ratio
inflation rate
debt ceiling
singular stochastic control
optimal stopping
free-boundary
nonlinear integral equation
ddc:330
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.
Center for Mathematical Economics
2016
info:eu-repo/semantics/workingPaper
doc-type:workingPaper
text
https://pub.uni-bielefeld.de/record/2904750
https://pub.uni-bielefeld.de/download/2904750/2904751
Ferrari G. <em>Controlling public debt without forgetting Inflation</em>. Center for Mathematical Economics Working Papers. Vol 564. Bielefeld: Center for Mathematical Economics; 2016.
eng
info:eu-repo/semantics/altIdentifier/issn/0931-6558
info:eu-repo/semantics/openAccess