What drives the federal government's near-term fiscal outlook is, to a surprising extent, interest payments rather than Medicare and Medicaid. They are set to grow faster than mandatory or discretionary spending over the next decade, from 1.3 percent of GDP to 2.6 percent of GDP.

The difference between rising debt over the next decade and keeping debt stable as a percentage of GDP is just one percentage point in the average interest rate on the U.S. public debt.

Paul Krugman has argued recently that the Congressional Budget Office's forecast for interest rates is too high -- and inconsistent with the odds that the economy remains somewhat depressed for some time to come. I figured it would be useful to do some math and test some of the assumptions in the latest CBO forecast.

First, I backed out its forecast for the average interest rate on U.S. public debt -- you can do this by dividing interest payments as a percentage of GDP by debt as a percentage of GDP. What you find is that the CBO expects this rate to reach 4.2 percent by 2024.

Is that reasonable? Well, it's hard to know without having a good sense of how the average interest rate on U.S. public debt behaves. It turns out that you can proxy for it very closely with the 10-year Treasury. I added the forecast line in green. The public debt interest rate in blue is estimated by taking the annual federal expenditure on interest payments and dividing it by the stock of total public debt.

That doesn't seem to be an impossible path for the average interest rate on public debt. In fact, we can use the 20-year Treasury and the 10-year Treasury to back out the 10-year, 10-year-forward rate -- the expected interest rate on the 10-year Treasury note in 2024. Given a current 10-year rate of 2.63 percent and a current 20-year rate of 3.35 percent, the 10, 10 forward rate is 4.08 percent.

But what if you assume that the interest rate will be 3 percent rather than 4.2 percent? How does the debt outlook change? Well, at that rate, debt stays constant for the next decade as a share of GDP, given the CBO's forecast for primary balance (the deficit ex-interest). Here's the graph comparing the two assumptions for the interest rate:

And here's the graph showing how this change in interest rates has a big impact on the near-term outlook for the federal debt:

I'm not making any claim that three percent is the correct assumption for the interest rate. In fact, I've presented some evidence as to why four percent is closer to market expectations. But it's always interesting to see how sensitive debt forecasts are to small changes in parameters like the interest rate. I guess this does illustrate Carmen Reinhart's view that highly-indebted governments almost always turn to financial repression.

You should also account for the correlation between the 10 year treasury yield and GDP growth expectations. For the 10 year yield to fall growth expectations should also fall which would cause Treasury revenue to fall.

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