Don’t expect easy answers or simple rules. Projecting growth, deficits, and interest rates is just the beginning

When does the level of debt become unsafe?

To answer this question, we need a definition of “unsafe.” I propose the following: Debt becomes unsafe when there is a non-negligible risk that, under existing and likely future policies, the ratio of debt to GDP will steadily increase, leading to default at some point.

The natural way to proceed is then straightforward.

The dynamics of the debt ratio depend on the evolution of three variables: primary budget balances (that is, spending net of interest payments minus revenues); the real interest rate (the nominal rate minus the rate of inflation); and the real rate of economic growth.

###### A two-step approach

The first step must be to form forecasts of those three variables under existing policies and work out the implications for the dynamics of the debt-to-GDP ratio. Forecasts of these levels for the next decade or so are likely to be available. But such forecasts are not enough; we need to assess the uncertainty associated with those forecasts, which means coming up with a range of possible outcomes for each variable.

That is much harder, and it involves answering some tricky questions. For example, what is the risk of a recession and its likely magnitude? What is the risk that real interest rates will rise? If they do, how does the maturity of the debt affect interest payments?

If debt is partly in foreign currency—often the case for emerging market economies—what is the likely distribution of the exchange rate? What is the probability that some of the implicit liabilities transform themselves into actual liabilities; that, for example, the social security system runs a large deficit which must be financed by a transfer from the government? What is the distribution of the underlying potential growth rate?

Going through this step delivers a distribution of the debt ratio, say, a decade from now. If the probability that the ratio steadily increases at the end of the horizon is small enough, we can conclude that the debt is safe. If not, we must move to the second step and answer the next set of questions: Will the government do something about it? And if the government announces new policies or commitments, what is the probability that it will deliver on those?

This second step is even harder than the first. The answers depend on the nature of the government: a coalition government may be less likely to take tough measures than one with a large legislative majority. The outcome depends not just on the current government, but on those in the future, and thus the results of future elections. It depends on the reputation of the country, and on whether, when, and why it has defaulted in the past.

If all this sounds difficult, that’s because it is. If it sounds like it depends on many assumptions that can be challenged, that’s because it does. This is not a defect of the approach but a reflection of the complexity of the world. But the exercise must be done. Indeed, it is what credit-rating agencies do, whether they use the same terms to describe the process, and whether or not their criterion for a less than perfect rating depends on the same definition as mine. With a lower rating comes the effective punishment; namely, a government will have to compensate investors for taking on the higher risk of default by paying a higher rate of interest.

###### The problem with rules

Now let me go back to the original question. When does the level of debt become unsafe?

The process I have described makes it obvious that the answer is not going to be some universal magic number. Nor will there be a combination of two magic numbers, one for debt and one for the deficit.

This is particularly obvious if we think of changes in the underlying interest rates. Suppose, as has been the case in the United States since the early 1990s, that the real interest rate falls by 4 percentage points. That implies a decrease in the real cost of servicing the debt of 4 percent of the debt ratio; so if debt is 100 percent of GDP, debt service falls by 4 percent of GDP. Quite obviously, lower rates imply much more favorable debt dynamics. A debt ratio that may have been unsafe in the early 1990s is much less likely to be unsafe now. We might conclude from this that the magic variable therefore should not be the ratio of debt to GDP, but rather the ratio of debt service to GDP. This would indeed be an improvement, but it comes with its own problems: the variability of debt-service costs depends on the variability of real interest rates, which can be substantial. An increase in the real rate from 1 percent to 2 percent will double the debt-service cost. The cost may be low but it is also uncertain, and the uncertainty will affect whether the debt is safe or not.

The long decrease in real interest rates is in part what has triggered the current discussion on the appropriateness of magic numbers and the reforms of EU budget rules. But the point is much broader: take two countries with the same high debt ratio but with different types of governments, or debt denominated in different currencies. One’s debt might be safe, while the other’s might not.

So my answer to the question is, I do not know what level of debt, in general, is safe. Give me a specific country and a specific time, and I will use the approach above to give you my answer. Then we can discuss whether my assumptions are reasonable.

But don’t ask me for a simple rule. Any simple rule will be too simple. For sure, Maastricht criteria or so-called Black Zero (balanced budget) rules will, if they are respected, ensure sustainability. But they will do so at the cost of constraining fiscal policy when it should not be constrained. Most observers agree for example that fiscal consolidation in the European Union in the wake of the global financial crisis, a consolidation triggered by the rules, was too strong and delayed the EU recovery.

And do not ask me for a complex rule. It will never be complex enough. The history of the EU rules, and the addition of more and more conditions to the point where the rules have become incomprehensible but are still considered inadequate, proves the point.

Opinions expressed in articles and other materials are those of the authors; they do not necessarily reflect IMF policy.