A critical question confronting the world economy today is how much fiscal adjustment advanced economies need to restore public debt sustainability and regain some room for fiscal manoeuvre – ‘fiscal space’. Financial bailouts, stimulus spending and lower revenues in the Great Recession have all contributed to produce some of the highest ratios to GDP of public debt and primary deficits seen in advanced economies in the past 40 years (Figure 1). But, while the financial crisis clearly worsened the public debt positions of most advanced economies, the rise in debt ratios was not especially dramatic when viewed against the infinite-horizon intertemporal budget constraint. Nevertheless, in a number of cases such as Greece, Ireland, Italy, Portugal and Spain, borrowing costs have increased sharply, causing these sovereigns severe financing difficulties, and undermining their solvency.1 Understanding why financing costs shoot up rapidly from essentially risk-free rates to prohibitively costly interest rates, and why previously sustainable debt ratios can suddenly look unsustainable, is crucial to both returning these countries to fiscal solvency and to providing early warning to others at risk of exhausting their fiscal space.

In this article, we develop a new framework for assessing debt sustainability in advanced economies. Specifically, we seek to determine a ‘debt limit’ beyond which fiscal solvency is in doubt (with ‘fiscal space’ defined as the distance between the current debt level and this limit). Our model incorporates a sovereign borrower whose behaviour can be represented in reduced form by a fiscal reaction function that describes how the primary balance responds to changes in debt and risk-neutral creditors who arbitrage the expected return on government debt with the safe interest rate, taking account of the possibility that the government may default because it is unable to repay.

Our analysis begins from the premise that governments in advanced economies usually behave responsibly, increasing primary (i.e. non-interest) surpluses in response to rising debt service so as to stabilise the public debt-to-GDP ratio at a reasonable level. This is an empirically relevant premise consistent with the findings of Bohn (2008) for the US, and Mendoza and Ostry (2008) for subsets of industrial and emerging economies. Large shocks – such as wars or the fiscal fallout of financial crises – may cause temporary deviations from this (implicit or explicit) primary balance ‘rule’. As long as the subsequent increase in the primary balance is sufficient to offset the higher interest bill, however, the debt ratio will again converge to its long-run value.

Of course, it cannot literally be true that the primary balance would always increase enough to offset the interest bill, because, at sufficiently high levels of debt, this would require primary balances that exceed GDP.2 If the primary balance (eventually) exhibits ‘fiscal fatigue’ such that it does not keep pace with higher interest payments as debt rises, then – even assuming a constant interest rate so as to abstract from the endogeneity of the risk premium on government debt – there will be a debt level above which the debt dynamics become explosive and the government will necessarily default. In fact, default will occur before this point because the rising risk premium, as default becomes imminent, exacerbates the debt dynamics. In particular, as the probability of default rises, so will the risk premium, making it less likely that the primary surplus will suffice to meet the interest bill and raising the probability of default further.3 Eventually, the ‘fixed point’ problem of a higher probability of default leading to a larger risk premium, in turn leading to a higher probability of default, has no solution at a finite interest rate. At this point (which we term the debt limit), the government loses market access, is unable to rollover its debt and is forced to default. To determine this point, we solve simultaneously for the probability of default, the interest rate faced by the sovereign and the debt limit.

Our theoretical framework, motivated by Bohn (1998, 2008), thus departs fundamentally from earlier work in pinning down the concept of debt limit. While Bohn shows that a sufficient condition for the government to satisfy its intertemporal budget constraint is that the primary balance always reacts positively to lagged debt, this can be thought of as a weak sustainability criterion that does not, for example, rule out an ever-increasing debt-to-GDP ratio (and thus the need for a primary surplus that eventually exceeds GDP).4 A stricter sustainability criterion, which we adopt here, is that public debt should be expected to converge to some finite proportion of GDP. If the primary balance is always a constant proportion of lagged debt, then a sufficient condition for this stricter definition is that the responsiveness of the primary balance be greater than the interest rate–growth rate differential.5 But, once we allow for the possibility of ‘fiscal fatigue’ whereby the primary balance eventually responds more slowly to rising debt than the interest rate–growth rate differential, there will in general be a finite debt limit. Moreover, as debt approaches this debt limit, the cost of financing will shoot up from the risk-free rate to a prohibitively high interest rate within a very narrow range of debt ratios. The model also allows us to analyse the effects of unanticipated fiscal shocks (such as Greece's large revisions to its primary balance), which lower the debt limit, making a previously sustainable level of debt unsustainable.

Applying our framework empirically to a sample of 23 advanced economies over the period 1970–2007, we find strong support for the existence of a non-linear reduced-form relationship between the primary balance and (lagged) public debt that exhibits the fiscal fatigue characteristic. Specifically, the relationship is well approximated by a cubic function: at low levels of debt there is no, or even a slightly negative, relationship between the primary balance and debt. As debt increases, the primary balance also increases but the responsiveness eventually weakens and then actually decreases at very high levels of debt. This relationship is robust to the addition of a long list of conditioning variables and to a variety of estimation techniques.6

Combining the empirical estimates of the primary balance reaction function with actual interest rate data or with endogenous interest rates obtained from the model, we gauge each country's debt limit and corresponding fiscal space. Our results indicate a precarious fiscal situation for several eurozone periphery countries – notably for Greece, Italy and Portugal, with Ireland and Spain also constrained in their available fiscal space. To the extent that our primary balance reaction function is based on pre-global financial crisis data, our estimates provide early warning for the recent fiscal troubles encountered by these countries, and as such, the financing difficulties that they have been experiencing are consistent with our empirical analysis. Among other countries, Japan has in all likelihood exhausted its fiscal space, whereas Iceland, the US and the UK are also constrained in their degree of fiscal manoeuvre. By contrast, Australia, Korea, New Zealand and the Nordic countries appear to have the most fiscal space to deal with unexpected shocks.

Our contribution to the literature is thus three-fold. First, we provide a simple, intuitive definition of a debt limit (and corresponding fiscal space) that has the reasonable properties of increasing in the country's average fiscal effort and decreasing in the interest rate-growth rate differential. Second, our model can help explain why governments can suddenly lose financing access and why revisions to market estimates about the size of possible shocks to the primary balance (even if the shocks are not realised) can abruptly push a country into a situation of unsustainable debt dynamics. Third, we provide empirical estimates of available fiscal space for advanced economies, which provide early warning for them. Moreover, our approach can quantify the extent to which policy and institutional changes could help to increase the fiscal space of these countries.

In what follows, Section 1 develops the theoretical framework and derives the debt limit for a deterministic example, with the general stochastic case covered in Appendix A. Section 2 presents estimation results for the fiscal reaction function, and reports fiscal space estimates for our sample of countries. Section 3 concludes.