# Decide when debt becomes unsafe

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

When does debt become uncertain?

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

The natural approach is then simple.

The dynamics of the debt ratio depend on the development of three variables: primary budget balances (ie expenditures minus interest payments minus receipts); the real interest rate (the nominal interest rate minus the rate of inflation); and the real rate of economic growth.

###### A two-step approach

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

This is much more difficult and involves answering some tricky questions. For example, what is the risk of a recession and its likely magnitude? What is the risk of real interest rates rising? If so, how does the maturity of the debt affect interest payments?

If part of the debt is denominated in foreign currency – which is often the case in emerging markets – what is the likely exchange rate distribution? What is the probability that some of the implied liabilities will turn into actual liabilities; that, for example, the social security system has a high deficit that has to be financed by a transfer from the state? What is the distribution of the underlying potential growth rate?

Going through this step gives you a distribution of the debt ratio, say in a decade. If the probability of the ratio rising steadily at the end of the horizon is low enough, we can conclude that guilt is certain. If not, we need to move on to the second step and answer the next questions: Will the government do anything about it? And if the government announces new guidelines or commitments, what are the chances that they will comply?

This second step is even more difficult than the first. The answers depend on the type of government: a coalition government may take less harsh action than one with a large parliamentary majority. The result depends not only on the current but also on the future government and thus on the results of future elections. It depends on the country’s reputation and whether, when and why it has defaulted in the past.

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

###### The problem with rules

Now let me come back to the original question. When does debt become uncertain?

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

This is particularly evident when we think about changes in 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. This implies a reduction in the real cost of debt service by 4 percent of the debt ratio; So if debt is 100 percent of GDP, debt service falls by 4 percent of GDP. Clearly, lower interest rates imply much more benign debt dynamics. A debt ratio that may have been uncertain in the early 1990s is much less likely to be uncertain today. From this we might conclude that the magic variable should therefore not be debt-to-GDP ratio, but debt service-to-GDP ratio. That would indeed be an improvement, but it comes with its own set of problems: Debt service cost variability depends on real interest rate variability, which can be significant. Raising the real interest rate from 1 percent to 2 percent will double debt servicing costs. The costs may be low, but they are also uncertain, and the uncertainty will affect whether or not the debt is certain.

The answer will not be a universal magic number.

The long fall in real interest rates has in part prompted the current debate over the appropriateness of magic numbers and reforms to EU fiscal 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 debts may be safe, and the other’s may not.

So my answer to the question is: I don’t know what level of debt is generally safe. Give me a specific country and time and I will use the above approach 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. Certainly Maastricht criteria or so-called Black Zero (balanced budget) rules, if adhered to, will ensure sustainability. But they will do so at the cost of constraining fiscal policy when it should not be constrained. For example, most observers agree that fiscal consolidation in the European Union in the wake of the global financial crisis, a rules-triggered consolidation, was too severe and delayed the EU’s recovery.

And don’t ask me about a complicated rule. It will never be complex enough. The history of EU regulations and the addition of more and more conditions to the point where the regulations have become incomprehensible but are still considered insufficient proves this.

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

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