DG ECFIN: Stochastic public debt projections using the historical variance-covariance matrix approach for EU countries

11 April 2013

The specific approach for stochastic projections used here, based on the variance-covariance matrix of historical shocks, further allows defining a "central scenario", around which shocks apply.

Cross-country differences in the variance of the debt-to-GDP ratio distributions (reflecting differences in historical volatility of macro-economic conditions) emerge clearly from the simulations. This shows the importance of allowing for a more comprehensive and country-tailored assessment of downward and upward risks to debt dynamics. This stochastic framework also has the distinctive advantage of allowing for an explicit probabilistic assessment of debt projection results. A closer scrutiny of three EU countries in the case with temporary shocks reveals, for instance, that the most likely outcome for Italy over 2013-17 is a decreasing path for the debt ratio (though this is projected to be still higher than 116 per cent with a 50 per cent probability in 2017). For Spain, simulations show an increasing path over the projection horizon for all shock constellations, with an 80 per cent probability of a debt ratio greater than 100 per cent in 2017. Finally, for Hungary, the authors obtain a 60 per cent probability that the debt ratio stabilises or reaches higher values from 2013 onwards, with a 40 per cent probability of a debt ratio greater than 80 per cent in 2017.

The stochastic framework presented in this paper produces probabilistic outcomes, like the probability that the debt ratio for a certain country is higher than a certain value in a given projection year or the probability that the debt ratio stabilises or decreases over the projection horizon. This improves the transparency of simulation results relative to deterministic projections, which provide single debt trajectories, dependent on the specific macro-economic assumptions made, with no corresponding probabilistic assessment. In the latter case, the reader can only judge about the relevance of the presented debt projection results based on his expectations about the plausibility of the underlying macro-assumptions, while stochastic projections make such a probabilistic assessment explicit.

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