How to test for debt sustainability? Some theoretical reflections on an empirical test

Testing the reaction of the primary surplus to variations in public debt, relative to GDP respectively, has been frequently resorted to in order to test for sustainability of a given debt policy. In this contribution, we analyze theoretically under which condition a positive reaction of the primary surplus to variations in debt implies a sustainable debt policy. We demonstrate that the evolution of the debt to GDP ratio plays a decisive role as concerns the validity of the test outcome. In addition, we demonstrate that a positive reaction coefficient does not guarantee sustainability unless it exceeds at least the difference between the interest rate on public debt and the GDP growth grate. Thus, this test allows judgements about sustainability of public debt policies only if the interest rate and the GDP growth rate are known.