Debt Sustainability Analysis (DSA)
A country’s sovereign debt sustainability is dictated by the relationship between the real interest rate ($r$) and the real GDP growth rate ($g$). The change in the debt-to-GDP ratio ($d_t$) is governed by the following law of motion:
$$ \Delta d_t = \frac{r – g}{1 + g} d_{t-1} – pb_t $$
Where $pb_t$ is the primary fiscal balance (as a % of GDP). If $r > g$, the debt ratio will explode exponentially unless the government runs sufficiently large primary surpluses (austerity).
The Debt Overhang Hypothesis
Debt overhang occurs when a nation’s existing debt is so massive that all future economic growth is immediately absorbed by creditors to service the debt. This disincentivizes domestic investment and structural reforms, leading to macroeconomic stagnation.