The reluctant defaulter: A tale of high government debt

Fabrice Collard, Habib Michel, Jean-Charles Rochet

13 July 2016



Recent years have seen an explosion in sovereign debt levels, in the case of many OECD countries at least. Thus, at end 2015, the (sovereign) debt-to-GDP ratio stood at 243% in Japan, 105% in the US, 92% in the Eurozone and 90% in the UK. Are such levels sustainable? How high can they get?

In a series of papers made all the more prescient by their predating the recent explosion in sovereign debt levels, Bohn (1991, 1998, 2008) appraises debt sustainability through the response of fiscal policy to government debt. He observes that primary surpluses in the US respond positively to increases in the debt-to-GDP ratio, a finding he deems “credible evidence in favour of sustainability.” Ghosh et al. (2011) extend Bohn’s ‘weak sustainability criterion’ to rule out reliance for debt service on ever-increasing debt-to-GDP ratios. They develop a measure of maximum debt that depends both on a country’s ‘fiscal response function’ – how strongly its primary surplus responds to changes in the debt-to-GDP ratio – and on the country’s ability to roll over its debt (i.e. to service old debt that has become due by issuing new debt). They allow for ‘fiscal fatigue’, that is, at high levels of debt, the primary surplus ceases to respond to changes in the debt-to-GDP level. They use their results to obtain a measure of the ‘fiscal space’ available to 23 OECD countries – what scope, if any, is there for these countries to further increase debt levels before reaching their respective maximum debt levels beyond which default is certain?

New research

That default is certain beyond maximum debt makes Ghosh et al.’s (2011) debt truly maximal, but hardly sustainable – absent fiscal response, any shortfall in growth results in default. In recent work, we develop a measure of maximum sustainable debt, one that sees a shortfall in growth naturally increase the probability of default, without however implying certain default (Collard et al. 2015).

As in Ghosh et al. (2011), a country’s maximum sustainable debt depends on its maximum primary surplus and on its ability to roll over its debt. Since newly issued debt ultimately will be repaid out of future primary surpluses, rollover effectively serves to make future MPS available already at present. This increases governments’ maximum borrowing proceeds, from 16% to 88% of GDP in the case of Switzerland, for example, if debt were to be rolled over every four years, but it also provides a very strong incentive for governments to choose debt levels that present very little risk of default – default would preclude rollover, in turn precluding the bringing forward of the future maximum primary surplus.

The relation between future payment promised and present payment received, the latter adjusting the former for the probability of default, therefore has the form of a ‘Laffer curve’ (Figure 1). The payment received initially increases in payment promised, eventually to collapse as default precludes reliance on new debt issuance for old debt service. Maximum sustainable debt is the level of debt that corresponds to the apex of the Laffer curve. It is constant over time when expressed as a fraction of GDP; the alternative would imply reliance on ever-growing debt ratios, that is, on a borrowing bubble.

Figure 1. Present payment received and future payment promised

Since maximum sustainable debt depends on the future maximum primary surplus, which represents claims on future output, a country’s maximum sustainable debt clearly depends on that country’s output growth. Figure 2 shows the relationship between 23 OECD countries’ maximum sustainable debt and these countries’ growth rates over the period 1980-2010. The strong positive relation is to be expected – countries that grow more can afford to borrow more, for they can count on faster-growing output to service their higher borrowing. Whether these countries’ governments actually wish to borrow more is a question we turn to below.

Sovereign debt sustainability has generally been appraised by comparing a country’s primary surplus to the country’s interest payments deflated by growth (Aaron 1966). Tanner (2013) rearranges this condition to obtain a measure of maximum debt that equals the present value of all future maximum primary surpluses. We show that Tanner’s measure is not so much a measure of maximum debt as one of maximum equity; it has a government issue not debt but GDP-linked securities (Collard et al. 2015). This is because it assumes there can never be default and, consequently, that there can always be rollover. The no-default assumption is difficult to reconcile with the reality of debt financing at the very high levels of debt Tanner’s measure implies – Switzerland’s maximum borrowing proceeds rise to 189% of GDP absent the possibility of default. Our measure of maximum sustainable debt therefore lies between the measure that would obtain if rollover never were possible and that which would obtain if rollover always were possible; it allows for rollover, but it also allows for default to preclude rollover.

Figure 2. Maximum sustainable debt and annual growth, 1980-2010

How empirically relevant is our measure of maximum sustainable debt?

One way to answer that question is to determine the extent to which it can account for sovereign borrowing costs. It is interesting, and perhaps surprising, that a country’s borrowing costs often seem to bear little relation to that country’s debt-to-GDP ratio (Dell’Erba et al. 2013). But such a relationship fails to account for different countries’ different maximum sustainable debt and growth rate means and volatilities – a country with lower average growth will, ceteris paribus, present a higher probability of default because its growth rate will be more likely to fall short of the level necessary to make debt service possible; a country with higher maximum sustainable debt will, ceteris paribus, be able to issue more new debt to service old debt. We develop a measure of the probability of default based on the probability that a country’s growth rate falls short of the level necessary to service debt with the sum of the maximum primary surplus and the maximum proceeds from new debt issuance. We empirically establish the statistical significance of our maximum sustainable debt-dependent probability of default for explaining sovereign yield spreads (Collard et al. 2015).  

But how much do governments want to borrow?

So far, we have asked how much governments can borrow. In Collard et al. (2016), we consider a self-interested government that seeks to maximise the utility of its own consumption over its expected time in office; the government expects to fall if it should default. Our government thus differs from the benevolent, social welfare-maximising governments that have thus far generally been assumed (Eaton and Gersovitz 1981, Aguiar and Amador 2014). We find that the level of debt chosen by a self-interested government is very close to maximum sustainable debt – governments, if left unconstrained, want to borrow very nearly as much as they can borrow.  The reason is that both ‘can’ and ‘want’ are very strongly affected by the desire not to jeopardise new debt issuance through default; the fear of losing power proper to ‘want’ therefore has little additional effect. This result implies that, absent political or constitutional constraints on government borrowing, governments in general will choose debt levels that are nearly as high as can be sustained. Put differently, the limitation of sovereign debt to levels well short of the maximum that can be sustained may require the constraining of government discretion in matters of debt policy.


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Bohn, H (1998) “The behavior of US public debt and deficits”, Quarterly Journal of Economics, 113: 949-963.

Bohn, H (2008) “The sustainability of public policy in the United States”, in R Neck and J-E Sturm (eds), Sustainability of Public Debt, MIT Press.

Collard, F, M Habib and J-C Rochet (2015) “Sovereign debt sustainability in advanced economies”, Journal of the European Economic Association, 13: 381-420.

Collard, F, M Habib and J-C Rochet (2016) “The reluctant defaulter: A tale of high government debt”, CEPR Discussion Paper 6037.

Dell’Erba, S, R Hausmann and U Panizza (2013) “Debt levels, debt composition, and sovereign spreads in emerging and advanced economies”, Oxford Review of Economic Policy, 29: 518-547.  

Eaton, J and M Gersovitz (1981) “Debt with potential repudiation: Theoretical and empirical analysis”, Review of Economic Studies, 48: 289-309.  

Ghosh, A R, J I Kim, E G Mendoza, J D Ostry and M S Qureshi (2013) “Fiscal fatigue, fiscal space and debt sustainability in advanced economies”, Economic Journal, 123: F4-F30.

Tanner, E (2013) “Fiscal sustainability: A 21st century guide for the perplexed”, IMF Working Paper No 13/89.



Topics:  Financial markets International finance Macroeconomic policy

Tags:  government debt, sovereign debt, debt sustainability, default, probability of default

Professor and Chair of Applied Macroeconomics, University of Bern

Professor of Finance, University of Zurich

Professor of Economics at the Toulouse School of Economics and Research Director at Institut D’Économie Industrielle