Consider a government with a positive stock of debt,and suppose the real interest rate on government bonds equals the rate of growth of real GDP.In this case,the government's debt-to-GDP ratio will rise only if

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In this case, the government's debt-to-GDP ratio will only rise if there is a primary budget deficit. This is because the real interest rate on the government bonds is equal to the rate of growth of real GDP, so the debt will not increase if the government runs an overall budget deficit. However, if there is a primary budget deficit (i.e. the government is spending more on goods and services than it is collecting in taxes), then the government will need to borrow more to finance its spending, and the debt-to-GDP ratio will rise.

Consider a Government with a Positive Stock of Debt,and Suppose