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How big a haircut to make public debt sustainable?

I saw this infographic from Der Spiegel and have since then been obsessed with the question: “How big a haircut to make public debt sustainable?”

From Der Spiegel

As I do not read German ;) I could not make heads or tails of the Kiel Institute WP. The classical way of ensuring debt sustainability (I’ll get to the concept in a moment) is to run primary surpluses (by bringing in more tax revenues than the public spending you make). An alternative is to grow faster. Yet another alternative - now on the table in countries like Greece - is a restructuring, or a haircut, where creditors (those who bought the Government bonds) take a hit. Obviously by reducing the level of indebtedness the problem becomes less painful in fiscal terms.

There seem to be many operational definitions of debt sustainability: 1) something is sustainable if it can go on indefinitely - so keeping the ratio of public debt to GDP stable is one way of saying it’s sustainable (the problem is that this way of defining it means that the starting level is irrelevant … hummm I don’t like this); 2) bringing the ratio of debt to GDP down to an arbitrary level, say 60% like in the Maastricht Treaty in Europe (arbitrary, why 60%?); or 3) making sure that the present value of all future surpluses is enough to pay off the initial level of public debt (the problem I have with this definition is that it seems immune to the rate of growth in the economy and that can’t be …)

Using the dynamic equation for public debt, $B_t=B_{t-1} (1+i_t)-PS_t$, where $i$ is the nominal interest rate and $PS$ is the primary surplus, I tried to determine what kind of haircut would be needed to ensure a stable debt to GDP ratio, i.e. $b_t=b_{t-1}$.

Using statistics from the European Commission (AMECO), and parameterizing with multi-year averages I failed to come to meaningful numbers … sometimes haircuts greater than 100% are needed!

MY QUESTION THEN IS: Is there a scientifically superior way of computing required haircuts?

(Note that the Kiel Institute assumption of 2% growth rate is simply unrealistic, and current interest rates are way out of line historically - they ought to come down, i.e. revert to the mean in the future.)

Finally, let me just share what I ended up doing: Parameterizing with 2007-2011 averages, how many percentage points would the ratio of debt to GDP rise in 2012. The figure I got is reproduced below. Interesting how UK and US and much worse than Italy and Spain. Ireland has terrible figures because nominal GDP growth during 2007-2011 was negative, something that won’t be repeated in 2012.

From 10envolver

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