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A fiscal policy is sustainable if the debt-to-GDP ratio converges to a stable level. The debt dynamics equation is d_{t+1} = (1+r-g)d_t + (primary deficit ratio), where r is the real interest rate and g is growth. Fiscal policy is sustainable if primary balances and growth are consistent with stable debt levels.
From your understanding of government budgets and debt, you know that governments can spend more than they collect in taxes by borrowing, and that this borrowing accumulates as public debt. The question of fiscal sustainability asks: can a government keep doing this indefinitely, or will the debt eventually spiral out of control? The answer depends on a surprisingly simple relationship between just a few variables — the interest rate on debt, the growth rate of the economy, and the government's primary budget balance (revenues minus non-interest spending).
The key equation is the debt dynamics identity: next period's debt-to-GDP ratio equals the current ratio multiplied by (1 + r − g), plus the primary deficit as a share of GDP. The term (r − g) is the critical pivot. When the real interest rate r exceeds the economy's growth rate g, existing debt grows faster than the economy, meaning the debt-to-GDP ratio rises automatically even if the government runs a balanced primary budget. The government must run a primary surplus (spending less than it collects, before interest payments) just to keep the ratio stable. Conversely, when g exceeds r, growth erodes the debt ratio naturally, and the government can sustain modest primary deficits without debt exploding.
Consider a concrete example. Suppose a country has debt equal to 100% of GDP, a real interest rate of 3%, and real GDP growth of 2%. The gap r − g = 1% means debt grows 1 percentage point of GDP faster than the economy each year, purely from interest accumulation. To stabilize the debt ratio at 100%, the government needs a primary surplus of at least 1% of GDP. If it runs a primary deficit instead, debt-to-GDP rises each year, requiring ever-larger interest payments, which widen the deficit further, creating a snowball effect. This is the mechanism behind debt crises: once markets doubt a government's ability to generate the required primary surpluses, they demand higher interest rates, which raises r, which makes the required surplus even larger — a vicious cycle.
The intertemporal government budget constraint formalizes sustainability more rigorously: a government is solvent if the present discounted value of all future primary surpluses equals (or exceeds) the current stock of debt. This does not require the government to ever fully repay its debt — it only requires that debt not grow faster than the economy forever. In practice, sustainability assessments examine whether projected primary balances under current policy, combined with reasonable assumptions about r and g, imply a stable or declining debt trajectory. When they do not, the arithmetic of the debt dynamics equation tells you exactly how large the fiscal adjustment must be — and whether it is politically feasible is a question the equation cannot answer.