*By Karl Smith*

In a speech this morning, Tim Geithner said:

We need to cut the annual deficits, now roughly 10 percent of GDP, to the point where the overall debt burden begins to fall as a share of the economy .… For the United States, this means a deficit below 3 percent of GDP.

Which reminds me of a point I often try to help policy makers understand: For every deficit, there is some long-term debt level that matches it.

So suppose that the US has a permanent deficit of 3% of GDP. What does that mean for our long-term debt? Won’t we grow ever deeper into the whole?

No. The deficit-debt balance equation looks like this:

(US-Deficit-Percentage)/(US-Growth-Rate) = (US-Debt-Ratio)

Geithner wants a 3% deficit. The long-term growth rate of the US economy is somewhere around 5% nominal. All of this is in nominal, not real terms. That gives a Debt-Ratio of 3%/5% = 60%.

In other words, if the deficit falls to 3%, then the national debt will trend towards 60% of GDP. This happens to be true whether you are above or below your deficit target. Imagine that we had a balanced budget and we raised the deficit to 3% of GDP. The Debt-to-GDP ratio would still trend towards 60%.

There are a couple of interesting corollaries to this:

- Even for huge deficits, there is some long-run balance. So, for example, a deficit of 10% gives a long-run balance of 10%/5% = 200%.
- A deficit of zero gives a long-run balance of zero. That is, you don’t actually have to run a surplus in order to run down the debt. If you stop borrowing completely, you will grow out of the debt.
- This also works for negative deficits. Negative deficits are of course surpluses. So if the US government ran a 5% surplus, then its Asset-to-GDP ratio would tend towards 5%/5% = 100% of GDP. In modern terms, we would say the US Sovereign Wealth Fund would stabilize at around 100% of GDP.
- Lastly, changes in the denominator matter as well. Let's say the US increased its growth rate by 1% through a policy of slow but sustained immigration. Let's also presume that the deficit as a percentage of GDP did not fall. This means more absolute borrowing, since GDP is higher and specifically more borrowing for entitlements since military spending does not rise with increased immigration. Then we have 3%/6% = 50% of GDP.

Notice that we haven’t reformed anything about our finances. The per-person savings on military spending are presumed to be balanced out by increased per-person entitlement spending on immigrants and we are not counting on importing any new Sergey Brin’s to revolutionize our technology. We are just steadily increasing the population.

Nonetheless, debt-to-GDP falls.