A non-linear model of public debt with bonds and money finance

In this paper, we study the dynamic relationship between the public debt ratio and the inflation rate. Using a non-linear macroeconomic model of difference equations, we analyze the role of monetary and fiscal policy in influencing the stability of the debt ratio and inflation. We get three main results. First, we find that, in a low inflation scenario, money finance can be helpful in stabilizing the debt ratio. Second, we show that in a dynamic setting, standard Taylor rules may not be sufficient to control inflation. The Central Bank’s credibility in driving inflation expectations is indeed crucial to control price developments and to achieve macroeconomic stability. Finally, an active budget adjustment rule has a stabilizing effect on the debt ratio, even if it may not be enough to avoid explosive patterns. Notably, the stability of the steady state depends on the fine-tuning of the policy mix. One of the novelties of our analysis is the presence of a threshold level for the debt ratio and inflation, beyond which the debt ratio becomes unsustainable following an explosive path. The distance between this threshold and the steady state can be considered a proxy of the robustness of the economy to exogenous shocks.