Feedback covariates unit root tests : an application to the sustainability of fiscal policy

Sustainability tests often ignore the joint dynamics of stock and flow variables. This paper shows that such a practice leads to inappropriate statistical inference, and that taking into account this joint dynamics when testing for unit root induces large power gains. This paper introduces a new statistics denoted FADF (Feedback augmented Dickey Fuller), which fully combines feedback effects and covariates. The paper derives the limit distribution of the test statistic and comments on the asymptotic power functions. A simulation study and an empirical application based on US public debt sustainability illustrate the potential of this approach.