Ferrari, Giorgio
Giorgio
Ferrari
Controlling public debt without forgetting Inflation
Center for Mathematical Economics
2016
2016-07-21T08:17:07Z
2018-07-24T13:00:39Z
working_paper
https://pub.uni-bielefeld.de/record/2904750
https://pub.uni-bielefeld.de/record/2904750.json
urn:nbn:de:0070-pub-29047501
451378 bytes
application/x-download
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.