# 6 The debt-ratio in the long-run and the EU’s fiscal rules

In one of the apps of the previous section it was already mentioned in passing that the long-run value of the debt-to-GDP ratio is determined by the ratio of the long-run deficit and the long-run growth rate of GDP. So for a constant deficit (in % of GDP) and a constant growth rate of nominal GDP, the following equation holds true:

$\text{Debt-to-GDP ratio}_\text{ long run} = \frac{\text{Public deficit in %}}{\text{Growth rate of nominal GDP}}$

The next app illustrates this.

The debt-ratio in the long-run: In the following app, you learn that the long run value of the debt-to-GDP ratio, also called the steady-state value, is determined by the ratio of the total deficit in percent of GDP and the growth rate of nominal GDP.

Important assumption: The simulation assumes a constant deficit (in % of nominal GDP) and a constant growth rate of nominal GDP. This implies that over time, the debt-to-GDP ratio will actually converge to the ratio of the deficit and the growth rate.

Of course, thinking about the “long-run debt-to-GDP ratio” raises the question about what the “long run” actually is. In economics, the usage of the the term “long-run” is generally quite vague. In the context of the above equation, it might help to think about it in terms of the debt-ratio of a hypothetical country. For any country, the deficit and the growth rate of GDP are of course not constant at any point in time. They change from year to year. But if we would take the average value of all of these values, the actual debt-to-GDP ratio will have fluctuated in some way around their ratio.

## European fiscal rules: why 3 % and 60 %?

While the long-run concept of the debt-ratio does not necessarily seem particularly relevant for the day-to-day activity of fiscal policy, especially given the historical context of policy with crises and suddenly arising financing needs in a world of uncertainty, it is an important reference point in the fiscal policy debate. The long-term view of the debt ratio, as presented in the equation above, has even been partially invoked as a justification for the specific values of the EU’s fiscal rules from the Maastricht Treaty. According to these rules, the government deficit may not exceed 3% and the debt ratio may not exceed 60% of GDP. Although the exact history of the values of 3 % and 60 % in the treaty is rather obscure, in retrospect, one might imagine that the reasoning could have been roughly as follows: 60 % was close to the average debt ratio of important signature states at the time. In addition, in the mid-90s, a medium-term forecast of the average growth rate of nominal GDP of 5 % also seemed realistic. So the value of the deficit, that would stabilise the debt-ratio at 60 %, according to the equation from above, would need to be 3 % on average.7 Regardless of the actual reasons for the values in the EU fiscal rules, do you think it made sense to include these two numbers in the EU treaties?8

Travel back to 1992: You already know this app from the previous section. Use it to create some counterfactual scenarios for some countries in the context of the EUs fiscal rules. For example, make the simulation start in 1992 and insert the simulation parameters in a way that is compatible with the EU fiscal rules. Compare this to the actual development.

In the next step, we integrate macroeconomic feedback effects of fiscal policy on GDP.