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.