### Description

This is my translation of a *Commentary on Current Affairs* written by François Ecalle on the French blog Fipeco, devoted to analyses of public finance and the economy in France.

In **part I**, Ecalle discussed how one might understand public debt.

In **part II**, he explained why public debt cannot increase ceaselessly and discussed how the stabilizing of the debt-to-GDP ratio is a necessary (though not sufficient) condition for debt sustainability.

In **part III**, he discussed the formula for a debt-stabilizing primary balance and the limits to a stable public debt.

In **part IV**, he discussed a situation in which the interest rate on public debt is lower than the GDP growth rate, this being the present situation in the euro area and France.

Here, in this fifth part, Ecalle discusses the following two questions: if public debt is stable, does that necessarily mean it is sustainable? And what if public expenditure is ever on the increase, how would that impact debt stability and sustainability?

My thanks to François Ecalle for permission to publish this translation on my blog.

### Publication details

French article by François Ecalle

English translation by Urmila Nair.

Website: https://www.fipeco.fr/

Date of publication: November 11, 2020.

To view the original French article, click **HERE**

### The Translation, part V

#### (3) Furthermore, the possibility of stabilizing the public debt-to-GDP ratio is not a sufficient condition for debt sustainability.

As was noted earlier, if the primary deficit is maintained at 5% of GDP, and if the interest rate-growth differential (i – g) remains steady at 0.02, then public debt stabilizes at 250% of GDP.

However, the State’s creditors are likely to start getting worried at a
far lower public debt level, in which case the apparent or implicit
interest rate on the debt (i) would increase. If, in the above example,
the interest rate-growth differential (g – i) became 0.01, the debt
could only be stabilized at 500% of GDP. And, if the State’s creditors
remained worried, this interest rate would increase even more. If the
interest rate-growth differential thus became zero, then the primary
balance would itself have to be zero to stabilize the debt (cf. the
discussion of the equation in **Part III**
of the translation).

Given such self-fulfilling expectations, a country can pass very quickly from a situation in which a primary deficit of 5% of GDP poses no problem—because it permits debt stabilization—to one in which a primary surplus is needed to stabilize debt. If such a surplus is impossible to attain, the debt becomes unsustainable, which is what happened in countries like Greece.

It is, therefore, not sufficient to stabilize debt: the latter must, additionally, be stabilized at a level that allows the State’s creditors to continue to have confidence in the State.

#### (4) Finally, irrespective of what the interest rate may be, debt increases indefinitely if the growth in expenditure remains persistently greater than GDP growth.

To stabilize or reduce public debt, the primary balance must remain equal to or greater than the debt-stabilizing primary balance, be it a surplus or a deficit. This condition for debt stabilization is, of course, easier to fulfil in case of a primary deficit, but the primary deficit must not itself increase indefinitely.

Now, this deficit increases indefinitely if the growth of primary expenditure remains persistently greater than GDP growth, and if the government does not increase mandatory levies. If tax legislation remains unchanged, the increase in public revenue is roughly proportionate to the nominal GDP increase, on an average, over several years. If the deficit to GDP ratio increases indefinitely, public debt will explode no matter what the interest rate.

The condition for debt stabilization may also be written without the apparent or implicit interest rate, as:

(D_{s}/Y) = (g) (D/Y)

where

D_{s} = the debt-stabilizing deficit;

Y = nominal GDP;

g = nominal GDP growth rate;

D = the corresponding debt at this level.

The higher the deficit, the higher the level at which public debt is stabilized.

If the nominal GDP growth rate is 3%, a deficit of 3% of GDP would permit public debt stabilization at 100% of GDP. Similarly, a deficit of 6% would stabilize this debt at 200% of GDP.

Now, the ratio of deficit to GDP is the difference between the ratios of expenditure to GDP and revenue to GDP. The ratio of revenue to GDP is constant if tax legislation remains unchanged. And, if public expenditure increases persistently at a faster rate than GDP, then the ratio of expenditure to GDP increases indefinitely.

Fresh tax increases would not prevent public debt from exploding: the
ratio of revenue to GDP would rise to a higher level, and the ratio of
deficit to GDP would drop a notch but would then return to its
upward trend. *To avoid an explosion of public debt, fresh tax increases
would have to be imposed each year*, so as to ensure that revenue growth
equaled expenditure growth.