Persistence of the Sovereign Debt Components and Debt Sustainability: Some Evidence for the US and Europe

This paper analyses the persistence and mean reversion properties of sovereign debt and its components by applying fractional integration methods to long runs of annual data starting in 1831 for the UK and the US, in 1862 for Italy and in 1881 for France and Germany, and ending in all cases in 2022. The empirical results provide evidence of a high degree of persistence in all debt/GDP series, which appear to be I(1). However, cross-country differences emerge when analysing the properties of the individual components of debt. Specifically, in countries with a relatively large debt/GDP ratio, such as France and Italy, the primary balance is more persistent (0.5<d<1) than the snowball term in the budget constraint equation, while in those with lower debt, such as Germany and the US, it is stationary but bond yields are persistent (0.5<d<1). In all cases, the other financial transactions series is stationary and peaking in the war periods, while GDP growth exhibits low persistence and mean reversion (0<d<0.5). We also assess debt sustainability by analysing the stochastic properties of the differential between interest payments and primary deficits. The empirical findings (0.4<d< 0.6) support sustainability in all countries (both over the full sample and the most recent period from 1950), although mean reversion appears to be rather slow and a sizeable GDP growth might be needed to keep the debt/GDP ratio on a sustainable path.