The 2024 reform of the Stability and Growth Pact was supposed to take the context of individual countries into account and give national governments more flexibility and ownership in how they govern their finances (Janeba and Larch 2025). Instead of the commonly criticised one-size-fits-all approach under the old rules (Weymuller et al. 2022, Reuter and Debrun 2022), the new system allows for individual solutions under a commonly agreed upon framework. However, as Reuter and Debrun (2022) noted, enforceability and flexibility might come at the cost of transparency. 

The central element of the new fiscal rules is the calculation of what primary surplus will be required by the end of a four-to-seven-year ‘adjustment period’ to ensure that the member state gets its debt ratio on a plausibly downward path. To be concrete: Italy chose a seven-year adjustment period (2025-2031). Its required primary balance condition is determined with 2031 as the starting point. We focus on a simple way to determine this future required surplus. 

In the debt sustainability analysis (DSA), this surplus depends on many variables (interest rates, GDP growth, the starting deficit, etc.) in a large, sometimes recursive, set of relationships where any change in an exogenous variable necessitates a full rerun. Thus, the projections and subsequent consolidation requirements are largely a black box, with the Bruegel implementation of these projections running to more than three thousand lines of Python code (Darvas et al. 2024). 

We open the black box and derive a set of simplified conditions that approximate the full debt sustainability analysis. 

A standard (deterministic) debt sustainability analysis just determines the primary balance (b) required to keep the debt ratio constant (the well-known condition b = (r – g) × d; see for example Corsetti and Codogno 2022 or Blanchard 2019). To a first-order approximation, the new fiscal rules are equivalent to requiring that: b ≥ (r – g + 1) × d. 

Our simplification cannot replace the full calculations, but we hope it demystifies the debt rules and provides a shortcut for assessing the impact of policies on debt sustainability. 

The debt sustainability analysis (DSA) in brief: What drives the result

In the Commission’s debt sustainability analysis, ‘plausibly downwards’ is operationalised through two conditions: The debt ratio must be declining, and the primary balance must therefore be chosen such that the debt ratio continues to decline even in the face of a series of pre-determined shocks (deterministic criterion). Moreover, debt must be declining in 70% of 10,000 simulations using the past distribution of growth, interest rates, and other variables (stochastic criterion). These criteria and the 70% threshold are codified in EU acts (European Commission 2024). We now discuss these two criteria in turn. 

Deterministic criterion

The deterministic conditions require the simulated debt ratio to fall every year across the ten-year post-adjustment window under a baseline case and three shock scenarios that in practice imply a buffer relative to the baseline. In Gros and Hofer (2025), we show how, starting from the full debt sustainability analysis and with few assumptions, one can arrive at a simplified rule of thumb. Below, we summarise the derivation and results. 

The Commission’s debt sustainability analysis uses a debt dynamics equation that can be simplified to the well-known law of motion of the debt-to-GDP ratio: the debt ratio changes by the difference between the primary balance (b_t) and the product of the starting debt ratio, d_t, times the difference between the interest rate (r_t) and the GDP growth rate (g_t). As debt must decline every year, and ‘decline’ is approximately ‘not increase’, we can formulate the baseline condition as the familiar constant debt ratio condition at steady state:

b_bl = d_t (r_t – g_t)

A country with a debt ratio of 140% and r-g equal to 1% therefore needs a primary surplus of at least 1.4% of GDP. Importantly, what matters is the maximum r_t – g_t over the ten-year window, so debt declines even in the worst year. For Italy, r_t – g_t is based on the values expected between 2032 and 2041.

The three shocks then add a buffer relative to the baseline: The debt ratio must decline every year for the ten years even under shock scenarios. The buffer then depends on the deterioration of the r – g factor under the shocks: 

• Financial stress: In only the first year after adjustment ends (2032 for Italy), a risk premium is added to the refinancing interest rate. Because only a fraction of the debt stock is refinanced every year (all short-term debt and a fraction of long-term debt), a one-year shock only affects that portion. The risk premium is a function of the debt level itself, producing a quadratic effect of the debt level on interest payments as analysed in Alcidi and Gros (2019). The impact is strongest in the first year. In subsequent years, the short-term rate returns to the pre-shock path and only the small part of long-term debt that had to be refinanced during the shock year increases the interest burden. 
• Adverse r – g shock: Both short- and long-term refinancing rates rise, and GDP growth falls permanently by half a percentage point, increasing the r-g term by one percentage point. However, the full effect materialises only once the entire debt stock has been rolled over at the higher rate, which takes roughly until the end of the ten-year period. The buffer required under this scenario is thus about 1% of the debt ratio, about 1.4% of GDP for Italy, for example.
• Primary balance shock: the primary balance deteriorates by 0.5 percentage points permanently. 

The binding constraint is whichever scenario requires the highest primary balance. The primary balance shock can be neglected because it requires generally a smaller buffer than the adverse  r – g scenario if the debt ratio is above 50%.

A priori it is unclear whether the adverse r – g or the financial stress shock is binding. Gros and Hofer (2025) show that given the low shares of short-term debt of most countries in the euro area the financial stress scenario requires a higher buffer only if the debt ratio is above 140% of GDP, i.e. the value of Italy. Whether by coincidence, or by design, the adverse r-g shock thus determines the required buffer for all countries. Until recently, Greece’s debt ratio was above this threshold, but it has so little debt to be refinanced that the financial shock is not binding.  

So, the r-g scenario of a one percentage point deterioration should be the binding constraint normally. Gros and Hofer (2025) verify this by running a set of simulations of the full debt sustainability analysis using Bruegel’s implementation (Darvas et al. 2024). 

The debt sustainability analysis – simplified II: Stochastic criterion

The stochastic part mandates that at least 70% of debt ratio paths must have declined by the end of a five-year window following the end of the adjustment period, out of 10,000 baseline scenario projections with random shocks to key variables. Cottarelli (2024) offers a simplification. If the distribution of the debt ratio in year five is approximately normal, the 70% threshold translates into a simple requirement: the mean debt path must decline each year by at least 0.1 times the standard deviation of the debt ratio (over a five-year period). 

The key variable then becomes the standard deviation, which can be gauged from deciles of the 90/10 percentiles of the distribution of the shocks published by the European Commission (2024). This standard deviation is rather low, on average around 12%, thus reducing the importance of the stochastic criterion.

The standard deviation is low because the Commission winsorises the data from past shocks that form the basis for the simulations. This has been criticised by Cottarelli (2024), noting that if reality is characterised by ‘fat tails’, there is little sense in removing them. 

One could argue that the deterministic scenarios (e.g. r – g) deal with large persistent shocks, and the stochastic scenario is designed to capture the ‘normal’ uncertainty and not tail events. We note that when the winsorisation is turned off, we find that the stochastic scenario tends to dominate, unlike in the simulations with winsorised data (Gros and Hofer forthcoming), the deterministic shocks constitute thus only a partial compensation for the elimination of the extreme events. 

Conclusion

The debt sustainability analysis underpinning the new fiscal rules is complex and largely a black box. The stochastic element is rarely relevant given that winsorisation eliminates the largest shocks from the data used to perform the simulations. 

We show that the new rules boil down to requiring a buffer in addition to the standard requirement that the primary balance must be large enough to offset the interest – growth effect. The required buffer is equal to one percent of the debt ratio, i.e. about 1.4% of GDP for a country like Italy.

References

Alcidi, C and D Gros (2019), “Public Debt and the Risk Premium“, CEPS Policy Insights 2019–06, May.

Blanchard, O (2019), “Public Debt and Low Interest Rates”, American Economic Review 109(4): 1197–229.

Corsetti, G and L Codogno (2022), “Shifts in Expectations May Undermine Debt Sustainability”, VoxEU.org, 3 November.

Cottarelli, C (2024), “Economic Governance and EMU Scrutiny Unit (EGOV) Directorate-General for Internal Policies”, SSRN Electronic Journal, ahead of print, November.

Darvas, Z, L Welslau and J Zettelmeyer (2024), “The Implications of the European Union’s New Fiscal  Rules”, Breugel, October.

European Commission (2024), Debt Sustainability Monitor: 2023, Publications Office. 

Gros, D and S M Hofer (2025), “Readiness 2030 and the New Fiscal Framework”, Paper presented at Seventh Annual Conference of the European Fiscal Board (EFB), 14 November. 

Gros, D and S M Hofer (forthcoming), “Questioning two key assumptions of the DSA: short financial shock and winsorising data in the stochastic analysis”, Paper presented at Seventh Annual Conference of the European Fiscal Board (EFB). 

Janeba, E and M Larch (2025), “The European Union’s New Fiscal Rules: A Fine Line between Brilliant Masterpiece and Another Chapter of Déjà Vu”, VoxEU.org, 14 November. 

Reuter, H and X Debrun (2022), “Fiscal Is Local: EU Standards for National Fiscal Frameworks”, VoxEU.org, 24 January. 

Weymuller, C-H, G Lorenzoni, F Giavazzi, V Guerrieri and L D’Amico (2022), “Revising the European Fiscal Framework, Part 1: Rules”, VoxEU.org, 14 January.