# Deciding when debt becomes dangerous

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

When does the level of debt become dangerous?

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

The natural way to proceed is then simple.

The dynamics of the debt ratio depends on the evolution of three variables: primary budget balances (ie expenditure net of interest payments less revenue); the real interest rate (the nominal rate minus the inflation rate); and the real rate of economic growth.

###### A two-step approach

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

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

If the debt is partly denominated in foreign currencies, which is often the case for emerging market economies, what is the likely distribution of the exchange rate? What is the probability that certain implicit liabilities will turn into real liabilities? that, for example, the social security system shows a large deficit which must be financed by a transfer from the State? What is the distribution of the underlying potential growth rate?

Going through this step gives a distribution of the debt ratio, say, in a decade. If the probability that the ratio increases steadily at the end of the horizon is low enough, we can conclude that the debt is safe. If not, we need to move on to step two and answer the next set of questions: Will the government do anything about it? And if the government announces new policies or commitments, how likely is it to stick to them?

This second stage is even more difficult than the first. The answers depend on the nature of the government: a coalition government may be less likely to take tough action than a government with a large legislative majority. The result depends not only on the current government, but on those of the future, and therefore on the results of future elections. It depends on the reputation of the country and if, when and why it has failed in the past.

If all of this sounds difficult, that’s because it is. If it seems to depend on many assumptions that can be challenged, 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. Indeed, that is what the rating agencies do, whether they use the same terms to describe the process, and whether or not their criterion of a less than perfect rating depends on the same definition as mine. With a lower rating comes effective punishment; that is, a government will have to compensate investors for taking on the higher default risk by paying a higher rate of interest.

###### The rules problem

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

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 the debt and one for the deficit.

This is particularly evident if one thinks of 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 servicing the debt by 4% of the debt ratio; so if the debt is 100% of GDP, debt service decreases by 4% of GDP. Clearly, lower rates imply much more favorable debt dynamics. A debt ratio that might have been dangerous in the early 1990s is much less likely to be so today. One could conclude that the magic variable should therefore not be the debt-to-GDP ratio, but rather the debt-service-to-GDP ratio. This would certainly 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 significant. An increase in the real rate from 1% to 2% will double the cost of servicing the debt. The cost may be low, but it is also uncertain, and the uncertainty will affect whether the debt is safe or not.

The answer will not be a universal magic number.

The long decline in real interest rates is partly what triggered the current discussion about the relevance 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 government, or debts denominated in different currencies. One’s debt may be safe, while another’s may not be.

So my answer to the question is, I don’t know what level of debt, in general, is safe. Give me a specific country and a specific time, and I’ll 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. Admittedly, the Maastricht criteria or the so-called Black Zero rules (balanced budget) will ensure sustainability, if they are respected. But they will do so at the cost of a restrictive budgetary policy when it should not be. Most observers agree, for example, that the fiscal consolidation in the European Union following the global financial crisis, a rules-triggered consolidation, was too strong and delayed the EU’s recovery .

And don’t ask me for a complex rule. It will never be complex enough. The history of 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 this.

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

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