Figure 5. This graph illustrates the projected US DEBT/GDP ratio, based on an annual growth in GDP of 3% and starting in 2012 with this ratio at 100.3%  We have used the model described in the site panel: "The Recursive Problem - II" described subsequently.  The solid line corresponds to the "7% Paradox" level at which rates can produce "unsustainable" deficits.   

(2/2/2012)

For the past ~2.5 years there has been considerable mounting concern over the national debt issues.  Added to this is the increasing focus for its implications here in the US and globally, as individual countries attempt to plan for various possible outcomes.  The overall changes in sovereign debt, for example, are recursive.

In Figure 5, an example of this recursive performance is illustrated for the US parameter case: 3% GDP Growth and initial (2012) DEBT/GDP = 100.3%. The model for this figure is discussed in subsequent panels. It is important to recognize the figure is for the US situation and it is likely the FED will keep interest rates low...leading to the inflation problem.

Typically, in discussions about such problems, an interest rate of 7% is indicated as an “unsustainable” rate for sovereign bonds.  The example above demonstrates that as sovereign yields approach and exceed the rate, things do get “out-of-hand.”