## Probabilistic Sustainability of Public Debt: A Vector Autoregression Approach for Brazil, Mexico, and Turkey

_IMF Working Papers, December 1, 2006_

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## Bibliographic details
- Authors: Evan C Tanner, Issouf Samaké
- Published: December 1, 2006
- Series: IMF Working Papers
- DOI: https://doi.org/10.5089/9781451865554.001

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### Summary
- Examines sustainability of fiscal policy under uncertainty in Brazil, Mexico, and Turkey.
- For each country, estimates a vector autoregression (VAR) that includes fiscal and macroeconomic variables.
- Retrospectively uses historical decomposition to attribute debt accumulation to unsustainable policy, adverse shocks, or both.
- Prospectively uses Monte Carlo techniques to identify the primary surplus required to prevent the debt/GDP ratio from rising in all but the worst 50 percent, 25 percent, and 10 percent of circumstances.
- Frames results as a value-at-risk approach that presents a clearer menu of policy options than currently used frameworks.

### Methodology
- Model: Vector Autoregression (VAR) including fiscal and macroeconomic variables.
- Retrospective analysis: Historical decomposition of debt accumulation drivers (policy vs. shocks).
- Prospective analysis: Monte Carlo simulations to generate distributions of debt/GDP outcomes and compute required primary surplus thresholds for specified risk levels (50 percent, 25 percent, 10 percent).

### Key findings and scenarios
- Historical decomposition quantifies the contribution of unsustainable policy and adverse shocks to past debt accumulation for Brazil, Mexico, and Turkey.
- Monte Carlo results provide primary surplus targets that would keep debt/GDP from rising except in the worst:
  - 50 percent of circumstances
  - 25 percent of circumstances
  - 10 percent of circumstances
- The value-at-risk framing offers discrete policy trade-offs tied to explicit probability thresholds.

### Policy implications and recommendations
- Use probabilistic (value-at-risk) metrics to inform fiscal policy choices and communicate trade-offs across explicit risk levels (50 percent, 25 percent, 10 percent).
- Tailor required primary surplus targets to country-specific VAR-based projections and risk tolerances.
- Employ the combination of historical decomposition and Monte Carlo projections to distinguish between debt dynamics driven by policy versus shocks, aiding the design of corrective fiscal measures.

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_Source: https://www.imf.org/en/publications/wp/issues/2016/12/31/probabilistic-sustainability-of-public-debt-a-vector-autoregression-approach-for-brazil-20006_