What does the intertemporal government budget constraint imply about deficits and the government debt?

• A. Public debt does not affect deficits in present value
• B. The present value of deficits equals the stock of government debt
• C. Deficits today must be funded by future surpluses only if growth is zero
• D. The debt dynamics are independent of interest rates and growth

Answer: (B)

The key idea is that deficits today are financed by borrowing, so the amount the government owes now (the debt) must equal the present value of the deficits it will run in the future. In other words, if you discount all future deficits back to today, their sum equals the current stock of debt. This is the intertemporal budget constraint in action: the debt today is the discounted value of expected deficits over time (ignoring other assets). For example, if you expect deficits of D1 next year and D2 the year after, at an interest rate i the present value would be D1/(1+i) + D2/(1+i)^2, which should equal the current debt. This linkage explains why debt responds to the path of deficits and to interest rates and growth. The other statements misstate this relationship because debt and deficits are not independent of each other and are not determined without considering discounting, rates, or growth.