I was at an interesting Conference a few days ago. Speaking was an official from the European Commission who put on some nice public debt to GDP arithmetic: 1 – m ε – m b.

Wow. What is it? It is a key number for our debate. It tells us nothing less than the impact of a certain restrictive fiscal package on the number one “European Mantra”, the public debt to GDP ratio. If its value is positive, then a certain fiscal restriction reduces the public debt ratio, as many conservatives are recommending.

If its value is negative … then a fiscal restriction gets into a territory that my EC friend calls “perverse”. Perverse indeed, we agree. It is the territory where higher fiscal consolidation (higher taxes, lower expenditures) drive an increase and not a decrease in the public debt to GDP ratio. Wow. How might this occur? Well, quite easy. Listen to the EC guy.

Let’s look at the formula again. That “1” is quite clear: you do raise taxes by 100 euro, or lower expenditure by the same amount and what happens next is that your deficit and your debt go down by the same amount, 1 for 1. OK. So this component tells you: restrict fiscal policy if you want to lower your debt to GDP ratio.

Now however. Let us keep in mind that raising taxes or lowering expenditures decreases growth and GDP (the extraordinary fact here is that even the European Commission is willing to recognize that, or maybe it is just my friend, who might be considered a weirdo in Brussels. Just kidding). So here comes “M b”. M is the level of the of the impact of the fiscal package on growth, the M stands for the usual multiplier: more taxes, less spending, less growth. Notice however that this negative impact is greater the larger the level of debt to gdp to begin with. [* You may want to skip this if it is already clear to you why*: Imagine you have two ratios: one, call it Joseph, is equal to 4 divided by 2 (equal 2!) and the other one, call it Frank, is 100 divided by two (equal 50!). Now imagine that that number 2 which divides both ratios becomes number 1, i.e it halves. What will happen to Joseph and Frank? Well Frank goes up from 2 to 4 (4 divided by 1) and Joseph to 100 (100 divided by 1). Frank goes up by 2 and Joseph by 50. I am just having some fun.]. So Italy, for example, which has a very high public debt to GDP ratio will see the negative impact on growth of a given fiscal package increase the public debt ratio by more than other countries with lesser debt.

Tough luck, you might say. Hold on, it’s not over. There is a third effect, the one that too increases debt because, as we know, when growth declines, automatic stabilizers (lower tax revenues, higher expenditures) kick-in, enlarging the deficit, the level of debt and the public-debt to GDP ratio. That is what is given by m ε, which measures the reaction of the deficit to a worsening of growth.

So imagine that Italy does a restrictive maneuver of 1% of GDP (sounds familiar?). It is sufficient for the multiplier to be 0,65 to make this maneuver perverse: debt over GDP is going to increase and not decrease. For a country like Germany, everything else equal, with a debt GDP ratio around 70%, the negative impact on the economy should be much larger (multiplier equal to 1) to create the same perverse effect. This is maybe why Germans seem to come from Venus and Italians from Mars.

Now. Imagine the following. Had Monti done an expansive fiscal package and increased the deficit. Debt would have gone high. But growth would have increased. And the deficit with that growth would have declined. Lowering in all likelihood the Debt/GDP ratio. Imagine this. Now make it reality and markets will see the light at the end of the tunnel.