Hawkeye

Hawkeye Play · Chapter 5 · Economic · Political

Interest and growth

A government owes money equal to 60% of its economy’s yearly output. Interest is due every year, and the economy grows. Does the debt ratio rise or fall?

The rules

The debt ratio is debt divided by GDP. Each year it changes by (r − g) / (1 + g) × last year’s ratio, minus the primary balance (tax revenue minus spending before interest, as a share of GDP). Here r is the real interest rate and g is real growth. The starting numbers are made up.

What the model typically shows

Debt ratio over 30 years from 60% of GDP, primary balance zero
03060901200612182430YearDebt, % of GDPr 4%, g 2%r 2%, g 2%r 1%, g 3%
Data table
Debt ratio, % of GDP (every 5th year)
Yearr 4%, g 2%r 2%, g 2%r 1%, g 3%
060.060.060.0
566.160.054.4
1072.960.049.3
1580.360.044.7
2088.560.040.5
2597.560.036.7
30107.460.033.3

Takeaway

In the standard debt-dynamics identity, the change in the debt ratio depends on the gap between the interest rate and the growth rate, and on the primary balance. When the interest rate is above the growth rate, a primary surplus is needed just to hold the ratio steady. When it is below, the ratio can stay level or fall even with a primary deficit, depending on the deficit’s size.

Sources for the model:

What this model leaves out

  • Interest rates here do not react to the level of debt; in reality lenders may demand more as debt rises (Blanchard discusses this risk).
  • Inflation, exchange rates and debt in foreign currency are left out.
  • Growth here does not depend on what the government spends or taxes.

In the real world

Figures already sourced on the Earth page. The game itself uses made-up numbers.