# The Kiel Institute Barometer of Public Debt

*David Benček*

*16 February, 2015*

### Current Assessment

The Kiel Institute Barometer of Public Debt assesses the long-run debt sustainability of EU countries. It displays the respective necessary primary balances and takes into account an interval of likely growth scenarios for each country. For the point estimate we assume a median growth rate (from the past 20 years); the upper and lower boundaries represent a 95% interval of the mean growth rate. Necessary primary balances below the critical threshold of 5% are considered sustainable.

For the largest part of the EU debt levels are entirely sustainable even when including the downside risk of low growth. Cyprus is slowly recovering from its financial sector breakdown and the ensuing ESM/IMF rescue package. Independent financing through capital markets has not been restored yet.

A look at Greece is more of theoretic interest, as nearly all of its debt is held by Europe’s public sector and credit conditions do not currently adhere to financial market rules. Nevertheless an assessment of Greece’s long-run ability to finance its debt (assuming it will at some point in the future return to independent financing through capital markets) may prove useful, as it mirrors the market opinion on the country’s prospects of recovery. The turbuluence and political uncertainty ensuing January’s parliamentary elections has driven up interest rates so that only growth rates far above average could restore debt sustainability, even taking into account that market interest rates on bonds would fall in the process.

### Necessary Primary Surplus – The Concept

The debt barometer uses the primary surplus concept to determine the sustainability of a country’s revenue and expenditure policies. The basic idea involved is that we do not know what the maximum limit to a particular country’s debt ratio is, but we do know that its debt to GDP ratio cannot keep rising forever – at some point the country would go bankrupt. We therefore determine the critical level of primary surplus that is necessary to keep a country’s debt to GDP ratio constant. This first requires expressing the relationship between current and future debt (\(d_t\) and \(d_{t+1}\)) as \[d_{t+1} = \frac{1+i}{1+\gamma} d_t + c_t - \tau_t,\] where \(i\) and \(\gamma\) are the nominal rate of interest on government debt and the nominal growth rate, respectively. By definition the difference of revenue and spending \(\tau_t - c_t\) is the primary surplus \(p_t\). Using this and rearranging the above equation we see that the change in debt to GDP can be written as \[d_{t+1} - d_{t} = \frac{i-\gamma}{1+\gamma} d_{t} - p_{t}.\] A constant debt ratio requires the left-hand side to be zero and gives us the debt-stabilizing primary surplus: \[p^{*} = \frac{i-\gamma}{1+\gamma} d_{t}\]

This necessary primary surplus is only useful in determining the limits of a country’s debt if it is coupled with criteria of which levels of the primary surplus ratio are realistic and how large the gap between the necessary primary surplus and the feasible primary surplus can become before the country will no longer be able to deal with its debt.

Our empirical assessment of historical developments in numerous countries leads to the conclusion that it is extremely difficult for a country to prevent its debt from increasing infinitely when the necessary primary surplus ratio reaches a critical level of more than 5%. When this level is exceeded for some time, it is almost impossible for a country to service its debt without receiving outside help (see Bencek and Klodt (2011)).

Since the ability of a country to service its debt is heavily dependent on its economic growth outlook and since predicting growth is fraught with lots of uncertainties, the debt barometer utilises a country’s past growth rates to derive an interval of likely medium-term rates.

### Calculation

#### Data Sources

**Interest Rates:**As the current average interest rate on governement debt we use secondary market rates for long-term government bonds provided on a monthly basis by the ECB.**Debt to GDP Ratios:**From the IMF Economic Outlook database we can retrieve data on past, present and future projected debt of all countries. An estimate of Europe’s current debt sustainabilty only requires a look at the latest debt projection for 2014.**Growth Rates:**Instead of assuming the same growth rate for all EU countries we derive estimates of the growth potential in each country from past growth rates. For this purpose we retrieve time series of real growth rates from Eurostat. However, we only use data from the past 20 years to avoid distortions from the collapse of the Soviet Union, parts of the Yugoslav Wars and the general economic development in countries catching up with globalization. Based on the mean and standard deviation of a country’s past real growth rates we then determine upper and lower bounds: Assuming an underlying normal distribution we construct a 95% confidence interval: \[g_{j}^{\text{low}} = \bar{g}_{j} - 1.96 \sigma(g_j) \quad \text{and} \quad g_{j}^{\text{high}} = \bar{g}_{j} + 1.96 \sigma(g_j)\] Since these growth limits are real values, we also require the current level of inflation \(\pi_j\) so that we can run our calculations using the nominal market interest rates. Eurostat offers monthly estimates of the rate of inflation that we can use.

\[(1+\gamma) = (1+g) (1+\pi)\]

#### Barometer

Combining these data sources we can determine the necessary primary balance for each country and month according to \[\text{p}^{*}_{jt}=\frac{(i_{jt}-\gamma_{jt}^{r})}{1 + \gamma_{jt}^{r}} d_{jt},\] where \(\gamma_{j}^{r}=\gamma_{j}^{\text{med}}\) for the median growth scenario and \(\gamma_{j}^{\text{low}}\) and \(\gamma_{j}^{\text{high}}\) are used for the upper and lower bound, respectively.

The underlying real growth rates for all countries are shown in the following table:

Country | Lower Bound | Median | Upper Bound |
---|---|---|---|

Austria | -1.38 | 2.40 | 5.40 |

Belgium | -6.94 | 1.85 | 12.58 |

Bulgaria | -6.10 | 4.45 | 11.30 |

Croatia | -4.97 | 3.75 | 9.33 |

Cyprus | -3.54 | 2.95 | 7.97 |

Czech Republic | -3.23 | 3.00 | 8.49 |

Denmark | -2.96 | 1.90 | 5.98 |

Finland | -3.91 | 3.50 | 8.92 |

France | -1.43 | 1.90 | 4.56 |

Germany | -2.47 | 1.60 | 5.27 |

Greece | -7.36 | 3.40 | 9.61 |

Hungary | -3.65 | 3.15 | 7.64 |

Ireland | -5.36 | 5.00 | 14.11 |

Italy | -3.40 | 1.45 | 4.87 |

Latvia | -8.43 | 5.30 | 16.81 |

Lithuania | -6.49 | 6.35 | 15.69 |

Luxembourg | -3.44 | 3.60 | 10.19 |

Malta | -2.24 | 2.40 | 5.92 |

Netherlands | -2.29 | 2.10 | 6.15 |

Poland | 0.39 | 4.40 | 7.85 |

Portugal | -3.64 | 1.50 | 6.13 |

Romania | -5.32 | 3.70 | 11.13 |

Slovenia | -3.98 | 3.70 | 9.89 |

Spain | -2.53 | 3.20 | 7.15 |

Sweden | -2.09 | 3.05 | 7.40 |

United Kingdom | -2.11 | 3.05 | 6.82 |