We consider a government that aims at reducing the debt-to-gross domestic product

(GDP) ratio of a country. The government observes the level of the debt-to-GDP ratio and an

indicator of the state of the economy, but does not directly observe the development of the underlying

macroeconomic conditions. The government's criterion is to minimize the sum of the total expected

costs of holding debt and of debt's reduction policies. We model this problem as a singular stochastic

control problem under partial observation. The contribution of the paper is twofold. Firstly, we

provide a general formulation of the model in which the level of debt-to-GDP ratio and the value of

the macroeconomic indicator evolve as a diffusion and a jump-diffusion, respectively, with coefficients

depending on the regimes of the economy. These are described through a finite-state continuous-time

Markov chain. We reduce via filtering techniques the original problem to an equivalent one with full

information (the so-called separated problem), and we provide a general verification result in terms of

a related optimal stopping problem under full information. Secondly, we specialize to a case study in

which the economy faces only two regimes, and the macroeconomic indicator has a suitable diffusive

dynamics. In this setting we provide the optimal debt reduction policy. This is given in terms of the

continuous free boundary arising in an auxiliary fully two-dimensional optimal stopping problem.