Quantifying Uncertainty in France’s Debt Trajectory: A VAR Based Analysis

Non-Technical Summary

This paper develops a simple, transparent method to quantify the uncertainty around forecasts of public debt. Rather than producing a single “best guess” debt path, the approach generates a range of plausible futures and associates probabilities with different outcomes. This probabilistic view is intended to give policymakers and analysts a clearer sense of fiscal risk and the likelihood that particular policies will succeed in stabilizing public debt. Based on 2023 vintage data, this analysis does not reflect recent fiscal developments and is therefore not intended to inform the current public debate on public debt. Its purpose is to improve SDSA methodologies.
Our approach models the joint behavior of the key drivers of the debt to GDP ratio — namely, the primary balance (revenues minus expenditures, excluding interest), nominal GDP growth, and short and long term nominal interest rates — using a standard Vector Auto-Regression (VAR) estimated on quarterly French data from 1990 through 2023. We implement two variants of this model: a conventional (frequentist) specification and a Bayesian version that incorporates mild prior information. They are used to simulate a large number (10,000) of future paths for these drivers, drawing shocks that reflect their historical volatility and interdependence. Combining these simulated paths with the familiar debt accounting identity produces a “fan chart” for the debt to GDP ratio: a visual and quantitative representation of the range of outcomes and their probabilities.
The median debt trajectories produced by both model variants closely track the deterministic baseline projection for 2024–2028, which follows the deterministic debt sustainability analysis framework of Bouabdallah et al. (2017). Crucially, that baseline lies comfortably within the middle of the distribution produced by our simulations, suggesting the baseline is a plausible central scenario given known historical dynamics. The Bayesian model yields slightly wider uncertainty bands than the frequentist model for the horizon we study; for example, the Bayesian 10–90 percent fan cone for 2028 is modestly larger than its frequentist counterpart. The two model variants also assign high probabilities that the 2028 debt ratio will remain above its 2023 level, although the Bayesian model produces a somewhat lower probability than the frequentist model. Overall, the magnitude of our uncertainty bands falls between the measures reported by the European Commission and the European Central Bank, lending further credibility to the quantitative scale of the results.
The probabilistic framework makes it straightforward to ask policy relevant questions such as: what is the probability that a given fiscal path will stabilize debt within a target horizon? Applied to France (see Figure 1) our simulations indicate that an earlier and larger consolidation than in the baseline would meaningfully improve the odds of bringing debt dynamics onto a stable path.
The proposed method deliberately favors parsimony and transparency over structural complexity: it quantifies risk conditional on historical relationships among the main drivers. An important extension is to embed the analysis within the European Union’s new fiscal framework (the Economic Governance Review adopted in February 2024), which will alter both baseline trajectories and the policy metrics used to judge sustainability.
By converting deterministic projections into probabilistic assessments, the approach offers a practical, replicable complement to standard institutional debt projections and helps clarify the degree of policy effort needed to change the odds of stabilizing public debt.