Debt, Growth and Interest Rate

Warning: this is a model.

A note on the relationship of federal debt, GDP growth and interest rate.

The Formulas

1. In the long run, the steady debt to GDP ratio is

Debt/GDP=Rdef/g

where Rdef is the rate of deficit (including interest payment) to GDP; g is the growth rate of GDP

2. In the long run, the ratio of deficit less interest to GDP is

(Def-Int)/GDP=Rdef(1-Rint/g)

where Rdef is the rate of deficit (including interest payment) to GDP; g is the growth rate of GDP; Rint is the interest rate.

What It Says

• The beginning debt to GDP ratio doesn’t matter in the long run
• If there’s GDP growth, debt to GDP ratio always stabilizes in the long run
• The net deficit (i.e., deficit less interest payment) depends on whether interest rate exceeds GDP growth
• If they equal, the net deficit is zero
• if interest rate is higher than growth, the net deficit is negative, or federal spending would have to be less than tax revenue
• The GDP growth rate here is nominal, so that inflation helps

An Example

Suppose the beginning Debt/GDP ratio is 80%, GDP growth 4%, interest rate 3%, deficit/GDP 2%:

Long-term Debt to GDP approaches 50%.

Net deficit would be 0.5% of GDP.

 

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