# How Much Debt Can We Bear?

In a recent Bloomberg post, I argued that small federal budget deficits were infinitely sustainable. That seemed to give a lot of people an intellectual heart attack. It really shouldn't. This is basic stuff.

To prove it, I built a simulator which allows you to plug in a few basic inputs -- the original debt, the annual rate of inflation, the annual real interest rate, the total or primary deficit as a share of GDP, and the annual rate of real GDP growth -- and it will plot back for you the trajectory of debt for the next 100 years.

I even included two optional features, one that assigns a penalty on real GDP growth if there is a high debt-to-GDP ratio, and another that boosts GDP according to the deficit.

You can play with the model online here. Download an Excel spreadsheet version here. I hope this is a useful tool for people who want to think about government debt. (Please, if you adjust the online settings, which I encourage you to do, set it back when you are done.)

A few thoughts which come from the model:

(1) People who worry about the sustainability of the debt, well, shouldn't. Sustainability problems only become problems in and of themselves because of the effects of compound interest, so they take a while to generate and can be nipped in the bud by a prudent readjustment of policy. Basically, the only way to have it become a problem is to have policymakers behave per the simulation -- that is, zero change in the budget for a century. That's not a realistic historical expectation, though it makes for fun graphs. The lesson here is that the exponential increases of debt you see in fiscal projections are entirely a function of interest payments.

(2) Here's a much better thing for the debt-sustainability crowd to worry about: interest payments crowding out other spending. My model shows that you can make almost any total deficit sustainable -- but that doesn't mean you should. In fact, it's much harder to make primary deficits sustainable. That tells us that our ability to run long-term deficits exists in a trade off with interest as a share of government spending.

(3) Inflation is a pretty weak tool to reduce government debts. Yes, it depresses the real value of the current debt, but the increase in interest rates offsets that considerably.

(4) One likely condition for a very-long-run debt sustainability issue is that the real interest rate must exceed the real growth rate of GDP. This hasn't been historically true.

(5) I do think the idea of a "growth trap" from debt is legitimate. There are a pretty wide set of specifications you can enter into my model in which the debt is sustainable when you turn off the growth effects and unsustainable when you turn them on.

(6) We can sustain some pretty big deficits. My default specs for the model are a 2 percent inflation rate, a 2 percent real interest rate, a 5 percent-of-GDP deficit, and a 2.2 percent real GDP growth rate. Over the long run, debt stabilizes at approximately 120 percent of GDP.