Debt Sustainability Depends on Interest, Growth and the Primary Balance

Public debt sustainability depends partly on the relationship between borrowing costs and economic growth. When the economy's nominal income grows faster than the effective nominal interest rate on debt, existing debt can become smaller relative to that income even while its dollar amount increases. This arithmetic is useful, but it does not make the primary budget balance or refinancing needs irrelevant.

The shorthand r minus g compares an interest rate with a growth rate. The comparison must use consistent definitions and periods. A nominal interest rate should be paired with nominal GDP growth in a nominal calculation, not casually compared with real growth that excludes inflation. The effective rate on the outstanding debt stock also differs from the rate quoted today on a newly issued bond.

Start with an explicit debt and GDP path

Take a hypothetical government with debt of 100 units and annual GDP of 100 units. Its starting debt-to-GDP ratio is 100%. Suppose the effective nominal interest rate is 4% and nominal GDP grows 5%. With no primary deficit or surplus and no other debt-creating adjustments, debt becomes 104 and GDP becomes 105. The debt ratio falls to approximately 99.05%.

Debt increased in nominal units while declining relative to the economy. That is not a contradiction: the denominator grew faster than the numerator. The example isolates one year's arithmetic and assumes the interest is financed through additional debt. It does not establish that the same growth and financing conditions will continue, or that creditors will ignore the government's near-term payment schedule.

A primary deficit can overwhelm the favorable gap

Keep the same starting debt, interest rate and growth, but add a primary deficit of two units. End-period debt becomes 106 while GDP is 105, so the debt ratio rises to approximately 100.95%. The interest rate is still below growth. That favorable relationship was simply insufficient to offset the additional noninterest borrowing in this example.

With a primary deficit of one unit instead, end-period debt would be 105 against GDP of 105, leaving the ratio at 100%. Under those assumptions, one unit is the debt-stabilizing primary deficit for the year. This is a calculation for a specific starting ratio and growth rate, not a universal allowance. Different initial debt, rates or growth produce a different balance requirement.

A primary surplus can offset an unfavorable gap

Now use a separate hypothetical scenario with debt and GDP again starting at 100, an effective interest rate of 5% and nominal GDP growth of 3%. With a balanced primary budget, debt becomes 105 and GDP 103, producing a ratio of approximately 101.94%. A primary surplus of two units instead leaves debt at 103, matching GDP and stabilizing the ratio at 100%.

The examples show why neither r below g nor r above g provides a complete verdict. The primary balance changes the result in both directions. The explanation of deficits, refinancing and the debt stock distinguishes noninterest borrowing from the total deficit. A meaningful sustainability account needs those budget measures alongside the interest-growth comparison.

Effective interest costs adjust over time

A rise in current market yields does not immediately reprice every fixed-rate security already outstanding. Maturing debt and new borrowing gradually change the effective cost, while floating-rate or inflation-linked obligations behave differently. CBO's interest-cost primer explains why the maturity structure affects the timing. Using today's marginal yield as though it applied instantly to the whole stock can overstate the immediate budget impact.

The delay is not permanent protection. If higher rates persist, more obligations can be refinanced at those terms. Suppose an illustrative 20 units of debt must be replaced at a rate two percentage points higher. The annualized additional interest on that portion is 0.4 unit before considering issuance dates and other changes. The cash-flow schedule explains when the burden arrives rather than eliminating it.

Risks outside the simple equation can change the result

Exchange-rate movements can increase the domestic-currency value of foreign-currency debt. Guarantees or other contingent obligations can become actual liabilities. An IMF working paper on emerging and developing economies finds that a favorable interest-growth gap alone did not eliminate vulnerabilities from deficits, currency exposure and hidden debts. That research is evidence about its studied economies, not a forecast for every sovereign borrower.

A government can also face a large near-term refinancing requirement even when a longer-run debt ratio looks manageable. Sustainability and immediate market access are connected but different questions. A useful assessment states the debt measure, consistent rate and growth assumptions, primary balance and maturity profile, then tests weaker outcomes. Debt arithmetic helps identify the pressure points; it cannot certify a safe path without examining the assumptions and obligations behind it.