Is Greece's debt really so unsustainable? Yes, it is.

Lorenzo Bini Smaghi, former member of the executive board of the ECB, writes for the Financial Times that Greece's debt might be sustainable.

One of the points he makes is

...the sustainability of the debt depends on the dynamics over time rather than on the overall level. A high debt-to-GDP ratio can be more sustainable than a lower one, if the former component is expected to stabilise and fall over time, while the latter continues to grow unabated. In fact, the sustainability of the debt is inversely related with the level of interest rate paid on the debt, and positively related to the expected growth rate of the economy and the primary budget balance which has been achieved.

I can't argue with that.

He makes assumptions for the four variables that pin down the dynamics of the debt-to-GDP ratio, and concludes that Greece could reduce its debt burden by 40% of GDP by 2019.

I am shocked. If there was one thing I thought I knew about the Greek crisis, it's that Greece's debt is on an explosive path, under any realistic scenario for the relevant variables. But since a simple computation, in this case, can clarify a lot, I decided to check.

The sovereign debt-to-GDP ratio is governed by the familiar GIDDY equation:

$$D_t =  (1+y-g-i) D_{t-1} + d_t $$
where \(g\) is the growth rate of real GDP; \(i\) is the inflation rate; \(D_t\) is the debt ratio at time \(t\); \(d_t\) is the deficit, as a ratio to GDP; and \(y\) is the average interest rate on the debt (yield).

(I'm assuming all debt is in denominated in domestic currency,  in this case euros, so I can ignore changes in the exchange rate.)

Bini Smaghi draws his debt projections out to 2019, although he's not explicit about his assumptions year by year. Suppose, he says, that Greece grows 3% a year through 2019; it runs a primary fiscal surplus of 4.1% of GDP every year (as Bini Smaghi says Greece will do in 2015); and the average interest rate on debt is 4% (Bini Smaghi assumes 4%, because "official creditors have accepted a reduction of the interest rate on their loans to levels comparable to those of the best eurozone borrowers").

It's not clear whether his growth assumption is real or nominal. However, the debt reduction is way too small if his assumption is for nominal GDP. Let's be generous, then, and suppose he's talking about real GDP, and add an inflation rate of 3% a year through 2019.

With all that in place, I get numbers close to Bini Smaghi's. The debt ratio goes down about seven points in 2015, just like he says, and we get to a level of 138.5%, not too far from his claim of 135%.

(You can plug in your own assumptions in this tool by the Financial Times and the IMF. Beware, though, that this calculator assumes the starting debt ratio, in 2014, is 164%, whereas I started with 175%.)

I checked the IMF's projections, as a benchmark, and it turns out he may have been using the IMF's projections all along! The WEO database shows a debt ratio of 174% in 2014, which goes down to 135% by 2019, just like Bini Smaghi says. The primary balance is 3.5% in 2015, and north of 4% after that. Real GDP growth never falls under 3% after 2015, and inflation gradually soars from 0.4% this year, to 1.75% in 2019.

IMF's projections (WEO Oct. 2014)
	2015	2016	2017	2018	2019
Real GDP growth, %	2.9	3.7	3.5	3.3	3.6
Inflation (GDP deflator), %	0.4	1.1	1.3	1.4	1.8
Primary fiscal balance (% of GDP)	3.0	4.5	4.5	4.2	4.2
Debt (% of GDP)	171	161	152	145	135

Lo and behold, however, the heroic assumptions. Three to three-and-a-half percent real growth, year in year out, through 2019? Primary surpluses above 3% for five years in a row? Are we talking about a fiscally hyper-disciplined, pro growth economy? Or are we talking about Greece?

I'm sorry, Mr. Bini Smaghi and economists at the IMF, but these are science-fiction numbers.

Suppose instead that nominal growth (real growth + inflation) is 3%, primary surpluses average 2%, and the cost of debt stays at 4%. (Still generous projections for a country with Greece's situation and track record.) The debt ratio then declines by a modest 1.3% of GDP over five years, to 173.7%.

Bini Smaghi makes a second point in his column: Greece is unlikely to default because its debt is largely held by the EFSF and it has a long average maturity. Refinancing risk, he says, is much lower than for other eurozone countries that borrow in the market.

But he's addressing two different questions here. One is whether Greece's debt is sustainable. The most likely answer is "no," based on realistic assumptions. The other question is whether Greece will default in the short term. Not necessarily (assuming there were no elections soon). A country can be insolvent in the long term and, yet, thanks to temporary arrangements, be able to service its debt in the short term. There is no doubt that Greece's cost of debt would not be 4% today, if it weren't for the EFSF. And Greece's fiscal balance would not be a surplus of 4% if it weren't for pressure from the troika. Greece is on life support, and current conditions will not, and should not, apply in the long term.