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 sustainabil-

ity 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.