Principles of Macroeconomics / Unit 14 MAC 1307 worked example, 60 to 90 seconds
The Debt Ratio Can Fall While Debt Rises
The idea
Compute the debt-to-GDP ratio across years and see what governs it. The ratio has a numerator and a denominator, and both move. A country can run a deficit every year and still watch the ratio fall, provided output grows faster than the debt does.
In practice
Take a debt of 720 billion against GDP of 3,000 billion, a ratio of 24 percent. Next year the government runs a deficit of 60, so the debt becomes 780. If GDP grows 5 percent to 3,150, the ratio is 780 divided by 3,150, about 24.8 percent, and it has risen. Now take the same deficit with GDP growing 10 percent to 3,300. The ratio is 780 divided by 3,300, about 23.6 percent, and it has fallen. The borrowing was identical in both cases; growth decided the direction.
Where people slip
This is why growth appears in every serious discussion of debt, and it cuts both ways. Growth is not a policy lever that can be pulled at will, and a recession moves both terms the wrong way at once: the deficit widens automatically while output falls, so the ratio jumps for two reasons rather than one.
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