Fundamental character of the risk premium to influence the sustainability of the public debt

Traditionally, conditions of sustainability of the public debt have long been related quite exclusively to fiscal policy and to budgetary parameters. However, the interaction between fiscal and monetary policies regarding the fixation of the interest rate is fundamental. Indeed, a simple analytical modelling shows that if the nominal interest rate increases exponentially with the public debt, because of a default (credit) risk premium, if the confidence of investors is fundamental, conditions of sustainability of the public debt could be much more difficult to comply with. Indeed, if the interest rate is risk-free, values for which the public debt can be sustainable are less constraining if the long-term GDP growth rate is high, or if the long-term risk-free nominal interest rate is small. They are also less constraining if the country decides to turn to a non-negligible primary budget surplus in case of a high public debt. However, if the interest rate exponentially increases with the public debt level, in case of a significant importance of the default (credit) risk premium, these parameters have very limited consequences on sustainable and equilibrium public debt levels. The sustainable public debt that a government should target is then much smaller than in absence of this risk premium.