The betting markets now believe that Greece will vote “no”, but nobody really knows even now. So let me take some time to do a calculation that I should have done a while ago. Here’s the question: Even if you ignore everything else, can austerity policies really improve the debt position of a country in Greece’s situation? If so, how long will that take?

Suppose, to be concrete, that we talk about permanently raising the primary surplus by one percent of GDP. As I’ve written before, and as Simon Wren-Lewis notes, given the lack of an independent monetary policy achieving a primary surplus requires a lot more than one-for-one austerity. In fact, a good guess is that you’d have to slash spending by 2 percent of GDP, because austerity shrinks the economy and reduces tax receipts. This in turn means that you’d shrink the economy by around 3 percent. So, a 3 percent hit to GDP to raise the primary surplus by 1.

But a smaller economy means that the debt/GDP ratio goes up initially. In fact, given Greece’s starting point, with debt at 170 percent of GDP, the adverse effects of austerity mean that trying to raise the primary surplus by 1 point quickly causes the debt-GDP ratio to rise by 5 points (.03*170). So this might suggest that it would take 5 years of austerity just to get the debt ratio back to where it would have been in the absence of austerity.

But wait, there’s more. Let’s bring Irving Fisher into the discussion. A weaker economy will mean lower inflation (or faster deflation), which also tends to raise the debt/GDP ratio. The chart shows a scatterplot of Greece’s output gap (as estimated by the IMF — a dubious measure, but stay with it) versus the rate of change of the GDP deflator.

Photo

Yes, it’s a crude Phillips curve, but it sort of works. And it suggests that a 1 point rise in the primary surplus, which requires austerity that causes a 3-point fall in real GDP, will reduce inflation by about 0.7 percentage points (3*0.23). And if you start with debt of 170 percent of GDP, this raises the debt ratio by more than a percentage point each year. That is, the attempt to reduce debt by slashing spending actually raises the ratio of debt to GDP, not just in the short run, but indefinitely.

OK, we can soften this result by bringing in the effect of falling Greek prices on exports, which should boost economic growth. I’m still working this one out, but at best it makes austerity successful at reducing the debt ratio in the very long run — think decades, not years. Austerity for a country in Greece’s position appears to be an unworkable solution even if debt is all you care about.

And just to be clear, I’m basically doing textbook macroeconomics here, nothing exotic. It’s the austerians who are inventing new economic doctrines on the fly to justify their policies, which appear to imply not temporary sacrifice but permanent failure.