Plans by the Italian government for a deficit of 2.4 % instead of pursuing the adjustment path agreed with the EU have led to a sharp increase in the yields on Italian debt, with the yields on ten-year bonds rising above 3%.

Today’s rates represent a sharp deterioration from only 6 months ago, but they should be bearable, given that it is only slightly above the present growth rate of nominal GDP of between 2.5 and 3%.  With only a minimal difference between growth and interest rates a small primary surplus should be sufficient to stabilize the debt to GDP ratio.

But there remains a latent risk. What has come to the fore over recent months is the crucial importance of the level of debt and its interaction with risk premia. Experience shows that that the risk premium, and thus (market) interest rate on public debt, depends on the level of debt as a percentage of GDP. This introduces a significant self-reinforcing mechanism that can easily lead to widely divergent results, even if the initial conditions change only marginally.

For example, in their Debt Sustainability Analysis, the IMF and the Commission use a simple rule of thumb: the risk premium increases by 3-4 basis points for every percentage point increase in the debt-to-GDP ratio above 60 %.

For Italy, with a debt-to-GDP ratio 70 points above the 60 % threshold, the ‘normal’ risk premium should thus fall between 210 basis points (Commission estimate) and 240 basis points (IMF). This is less than the value observed recently, but much higher than the minimum of around 100-150 basis points achieved before the formation of the new government in May/June of this year.

A key implication of the empirical regularity that the risk premium depends on the level of debt is that there exists an ‘amplifier’ effect: higher debt implies higher interest expenditure not only because the debt is higher, but also because higher debt leads to increases in the interest rate.

This means that debt can easily enter into an unstable regime under which a higher debt-to-GDP ratio leads to much higher interest rate expenditure, which then in turn leads to even higher levels of debt. Of course, a responsible government would avoid such a spiral by running a prudent fiscal policy to set the debt on a declining path, thus anchoring expectations about future debt-to-GDP ratios.

Italy seems to be only one step away from such an explosive feedback loop.

With current market rates, the average interest service cost, now around 3%, will simply no longer fall. This is not so much due to the long term rate being above 3%, but rather the fact that even the rate on short and medium term debt has increased considerably. With the two-year rate now at around 1.5-2.0 %, debt service costs are rising rapidly. The explosive loop has not started.

But given its high debt, Italy inevitably remains on the brink of the precipice. Any further small deterioration of the situation (either in terms of growth, the risk-free interest rate, or risk aversion in financial markets) could lead to an increase in debt service costs and start a spiral of higher debt levels and ever-increasing interest rate costs.

Figure 1 below demonstrates this ‘knife-edge’ characteristic by presenting two simulations, both of which go over 20 periods (years), using the same set of basic parameters (primary surplus equal to 3% of GDP, risk-free rate equal to the growth rate, same starting debt ratio), but two different assumptions about the parameter linking the debt level to the risk premium, which constitutes a measure of the risk sensitivity in financial markets. The lower line shows that an initial ratio of 1.3 (debt = 130 % of GDP) would be sustainable if the degree of risk aversion is low, as is usually assumed by the European Commission in its debt sustainability analysis. However, if the degree of risk aversion were to increase (such that every percentage point increase in the debt-to-GDP ratio above the 60% threshold leads to an increase in the risk premium of 4 basis points –the IMF assumption in its debt sustainability analysis) an initial debt-to-GDP ratio of 130% would no longer be sustainable.

Italy’s public finances are thus in a precarious situation. The current constellation of deficits, interest and growth rates is border-line sustainable. But any small increase in risk aversion could start a vicious circle of higher debt and higher risk premia. Moreover, the policy of spending today with the promise of saving tomorrow increases the burden for the country, since accumulating higher debt now will necessarily make future adjustments more costly. This is of course not lost on the markets.