The arithmetic of Debt/GDP ratio in no way justifies concerns for a budget deficit of 2.4%
The prospect of an Italian budget deficit of 2.4% of GDP has unleashed extraordinarily strong adverse comment by EU officials and politicians, from Draghi to Juncker, from Dombrovskys to Mattarella, to former ministers like Moscovici and Berlusconi (of all people!) who in their days in government have been among the worst offenders of EU austerity constraints: they actually claimed that the very existence of the Euro was under threat. They should have remained silent at least until greater details of the budget were unveiled, in order not to cause the market upset and rise in the spread between the yield on Italian and German bonds, that they ostensibly feared but in truth whipped up and welcomed with great enthusiasm. They were aided and abetted by the media hysteria of Italian and European press and television; deputy premier Di Maio rightly spoke of “media terrorism”.
Concern was generally expressed about the sustainability of Italian debt, presumed to be reversing its recent course of slow but steady decline as a proportion of GDP. Yet the arithmetic of Debt/GDP ratio evolution over time is very simple and well known, and in no way justifies concerns for a budget deficit of 2.4%, nowhere near the sustainability limits. The point has been made only by Senator Alberto Bagnai, president of the th permanent Commission for Finances of the Italian Senate, in various posts on his bloghttp://goofynomics.blogspot.com/, and is well worth a reminder.
The budget balance f* that stabilizes the debt/GDP ratio in year t is given by following relationship:
f* = d(t-1)*g/(1+g) where d(t-1) is the debt/GDP ratio at the end of the previous year (t -1), and g is the nominal growth rate of GDP in period t. A budget balance lower than f* will necessarily involve a decline of the Debt/GDP ratio in the course of the same year t. This is not a controversial theory, nor rocket science or high mathematics, it is an incontrovertible relationship of simple arithmetic.
To calculate this critical magnitude of the budget balance that will stabilise the debt/GDP ratio in 2019, we need two values, both unknown in 2018 (i.e. today): the value of the debt/GDP ratio at end-year 2018, and the nominal growth rate in 2019. The IMF estimates that Italy’s Debt/GDP ratio at the end of 2018 will be 129.7% of GDP, while GDP nominal growth in 2019 would be 2.5%, made up of 1.13% growth, and about 1.4% inflation (IMF World Economic Outlook, April 2018). Subsequent updates lowered real growth by about one-tenth of a percent. Thus we can assume conservatively a 2019 real growth of 1% and 1.4% inflation, i.e. a nominal growth rate of 2.4%.
By the relationship mentioned above, the value of Deficit/GDP ratio f* sufficient to stabilize the Debt/GDP ratio is therefore:f* = 1.297(0.024/1.024)=3.03% (more precisely, 3.0398 i.e. almost 3.04%). The prospect of a 2.4% budget deficit amply satisfies this constraint, leaving considerable room for contingencies; as it happens, the 2.4% deficit target also happens to amply satisfy the Maastricht ceiling for the budget deficit (which no one proposed to violate). Indeed a deficit rise with respect to the level embodied in earlier growth estimates is bound to raise nominal growth as well above earlier estimates, something that Ministers Tria and Savona were quick to point out, but this is a minor additional argument in favour of current policies, with respect to the powerful implications of 2.4%<f*.
Loose and reckless talk is unbecoming of respectable officials and reporters. Regardless of whether it is due to incompetence or malice, it breeds distrust and contempt, though fortunately it also, in the end, raises popular support for the government.