Domar Condition for Debt Sustainability

The Domar condition explains when an economy can carry public debt without its debt burden continually rising relative to national income. Its central implication is that when the growth rate of GDP exceeds the interest rate on government debt, growth helps contain the debt-to-GDP ratio. This creates room to sustain borrowing, but it does not make every size of fiscal deficit sustainable.

How growth and interest determine the debt burden

Public debt sustainability concerns the government's ability to service its obligations without requiring an implausibly large fiscal adjustment. The debt-to-GDP ratio matters because GDP provides the economic base from which government revenue can be raised.

• Interest payments add to financing needs, while GDP growth enlarges the denominator against which debt is measured.
• The comparison must use consistent measures: the nominal interest rate should be compared with nominal GDP growth, or the corresponding real rates should be compared.
• The relevant interest rate is the effective average cost of outstanding government debt, rather than simply a policy rate or the rate on new borrowing.

The role of the primary balance

The primary deficit is the fiscal deficit minus interest payments. In a simplified debt-accounting framework, bₜ = [(1 + i)/(1 + g)] × bₜ₋₁ + pₜ, where b is the debt-to-GDP ratio, i is the nominal interest rate, g is nominal GDP growth, and p is the primary deficit as a share of GDP.

• When g > i, the inherited debt ratio tends to shrink through growth, allowing a sufficiently limited primary deficit without increasing the debt ratio.
• When g = i, a primary balance keeps the debt ratio unchanged, while a primary deficit raises it.
• When g < i, a primary surplus is needed to prevent a positive inherited debt ratio from rising.

What the condition does and does not establish

A favourable interest-growth differential supports debt sustainability; it is not an unconditional guarantee. Sustainability depends jointly on this differential, the initial debt ratio and the future path of primary balances.

• Even when growth exceeds interest costs, sufficiently large primary deficits can increase the debt ratio.
• Sustainability does not require eliminating all public debt; a stable debt ratio can coexist with a growing absolute debt stock.
• Assessment must also consider refinancing risk, debt maturity and foreign-currency exposure, since a favourable growth-interest comparison alone does not ensure that payments can be met when due.