Nobody likes taxes, so public spending frequently exceeds revenues, leading governments to borrow. These budget deficits are a flow that add to the stock of debt. Since the Great Financial Crisis of 2007-2009, public debt in a number of advanced economies has surged. In the United States. the Congressional Budget Office (CBO) recently projected that―in the absence of policy changes―federal debt held by the public is headed for record highs (as a ratio to GDP) in coming decades.

Importantly, there is a real (inflation-adjusted) limit to how much public debt a government can issue (see Sargent and Wallace). Beyond that limit, the consequences are outright default or, if the debt is in domestic currency bonds that the central bank acquires, inflation that erodes its real value leading to a partial default.

Ultimately, debt sustainability requires that a country’s ratio of public debt to GDP stabilize. Otherwise, debt eventually will rise above the real limit and trigger default or inflation. In this note, we derive and interpret a simple debt-sustainability condition. The condition states that the government primary surplus―the excess of government revenues over noninterest spending—must be at least as large as the stock of outstanding sovereign debt times the difference between the nominal interest rate the government has to pay and the rate of growth of nominal GDP. If it is not, then the ratio of debt to GDP will explode….