Sovereign Default Threshold Analysis

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In a study of the prospects for Canadian provinces, Marc Joffe writes,

This method employs a multi-year fiscal simulation with a default threshold stated in terms of an interest expense to total revenue ratio (or interest bite). Using evidence from our historical survey, the conclusion is that default is likely at a 25% interest bite, so the simulations simply estimate the probability of each province reaching that level.

One way to think of this is that the political system will not tolerate debt payments that absorb more than 25 percent of revenue, and investors know that. So once the interest rate rises to the point where the interest bite hits .25, expect a debt crisis. That is, at that point, the government (in this case, a Canadian province) will consider default. The interest bite, B, is the average interest rate on debt, r, times the amount of debt, D, divided by tax revenue, T.

B = rD/T

Suppose that the ratio of debt to GDP is 50 percent and the ratio of revenue to GDP is 20 percent. Then we have

B = 2.5r

which means that once the average interest rate on debt hits 10 percent we are in crisis territory.

For the U.S. federal government, the ratio of debt to GDP is at least 70 percent (perhaps it is at least 100 percent), and the ratio of tax revenue to GDP tends to max out at 20 percent. At 70 percent, B = 35r. If we stick to the rule of thumb that a 25 percent interest bite is the point at which default becomes thinkable, then it would take an average interest rate of about 7 percent to reach that point. Note that because we have locked in low rates on some of the debt by issuing long-term bonds, it would take an increase in rates well above 7 percent in order to make the average interest rate on our debt reach 7 percent.

Some other thoughts:

1. It is hard to know what the rule of thumb might be for a U.S. default. It’s not like we have historical examples to serve as benchmarks.

2. For U.S. states, or for Canadian provinces for that matter, I wonder if pension payments to government workers should be added in order to estimate an “interest plus pension cost” bite. My thinking is that the political process may be stressed by taxpayers not receiving current services in return for their tax payments, and neither interest payments nor pension payments can be used to purchase current services.

3. Canadian provinces do not have balanced budget amendments, and consequently at least some of them are in more trouble than U.S. states. I am becoming more and more convinced that it is really hard to keep a democratic polity out of a debt trap in the absence of a Constitutional restraint.

4. Also, the Canadian single-payer health care system is run at the provincial level, so rising health care spending is a big driver of provincial fiscal problems.

5. I like the simplicity of Joffe’s rule of thumb. However, my own analysis of crisis triggers warns that the problem is complex and there are limits to what objective analysis can accomplish.

6 thoughts on “Sovereign Default Threshold Analysis”

  1. If you’re going to count pension costs, do you want to count military costs too? Or do you think most of the population imagines military costs are “current services?”

  2. In many US states pensions enjoy similar protections to bond interest. In my California model, I put pension expenses (but not retiree health costs) in the numerator of my default threshold equation, i.e. I use the ratio of interest costs and pension expenses over total revenue).

  3. I think it is a mistake to consider revenue a fixed number. Think of the government as providing services and making transfer payments (which of course includes servicing debt) Presumably there is a way to extract from the economy whatever funds are needed to pay for economically sound services. Transfer payments are a pure burden on economic activity. There is some maximum level of “rent” that can be squeezed out of the economy. If the govt tries to squeeze more, the economy goes into a downward spiral and transfer payments must be cut. What transfer payments will be cut? This becomes a purely political issue which is why the legal status of the social security trust fund vis-a-vis the public debt is irrelevant. Do we trim agricultural subsidies or do we default on the debt? That one is easy. Do we starve grandma or do we stiff the cigar-smoking fat cats in top hats who tricked our govt into taking on too much debt? Not so easy to answer.

    The tipping point then depends on two primary factors, neither of which is easy to assess, the maximum rent that can be extracted and the political environment.that determines who gets stiffed.

  4. Arnold, here is a graph of the interest bite over time for the USA. Note that it seems to have peaked in the late 80s and early 90s at over 0.18, which is surprisingly high for a country that is too big to bail out.

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