As we continue seeing interest rate spreads increasing in the euro area, we keep asking the question of whether this is a crisis of solvency or liquidity. The fact that interest rates keep increasing makes it more difficult for governments to meet interest payments, and solvency becomes the more likely culprit. If default happens we might never find out what type of crisis we had. Were governments insolvent? Or did the high interest rates and lack of funding push them into default? And if we cannot tell ex-post, how can we tell ex-ante (now!)?

Let's look at some historical facts to understand the potential scenarios these countries are facing. After my previous post on Italy, let's look at Spain, one of the countries that is also seeing spreads rapidly increasing.

The way we normally look at the question of solvency is by asking what type of effort the government needs to make to keep the debt under control. The typical benchmark is to look at the current ratio of government debt to GDP and think of scenarios where this ratio remains constant. In the case of Spain, this ratio is 60-67% measured in gross terms and 48-56% in net terms. The range corresponds to the number for 2010 and the forecast by the end of 2011. Let's just use 65% as the relevant ratio.

To keep this ratio constant, the Spanish government has to deliver a **primary** balance which is equal to the difference between the interest rate it pays on the debt (r) and the growth rate of GDP (g) multiplied by the debt to GDP ratio [Note: the primary balance is the difference between revenues and spending excluding interest payment on the debt].

With a simple formula: to maintain a stable debt-to-GDP ratio you need a primary surplus of (r-g) Debt/GDP.

Interest rates and growth rates have to be measured in the same units so we either measure them in nominal or real terms. Let me choose nominal rates.

Some facts: In the period 2000-2011, average nominal growth in Spain has been equal to 5.23% (out of which 2.17% was real growth). If we exclude the crisis years (2008-2001), average nominal growth was as high as 7.46%.

I am focusing on the post-euro years as we want to avoid looking at a different monetary policy framework, but just for the sake of understanding history, in the previous decade (1988-99) Spain grew at a rate of 7.73 in nominal terms and 3.11 in real terms.

What about interest rates? Currently the Spanish government is paying about 4% on average (even if on the margin they are facing rates closer to 6%). If Spain managed to maintain rates at 4%, the required primary balance is: (4% - 5.23%) x 65% = -0.74%.

So a deficit of 0.74% will do it. This does not look that different from the actual numbers. Over the period 1999-2011, the government's primary balance in Spain was -0.57%. If we exclude the years of the crisis and focus on the expansion 1999-2007, the primary balance was +2.24%, a significant surplus.

In other words, if Spain faced an interest rate of 4%, and even if within the next decade they experienced another massive crisis with four really bad years (as bad as 2008-2011) in terms of low growth and large deficits, the debt to GDP ratio would still remain at 65% ten years from now. "Business as usual" would do it. This is a very conservative scenario where we are asking no change in policies to the Spanish government.

Is 4% a reasonable interest rate? No, if you look at markets today. But here is where the self-fulfilling nature of the crisis comes in. The relevant question to me is whether can we build a scenario for Spain that is conservative in terms of growth and fiscal efforts coupled with rates which are not too far to a risk-free rate, and where we feel that we can guarantee with almost 100% confidence that the debt will remain stable. If this scenario is possible, then the interest rate of 4% is justified because we are looking at a world of no default.

Of course, if we start with an interest rate of 15%, then all the calculations above will send you in the direction of default, which would justify the high interest rate we started with.

But if both scenarios seem plausible then we are facing multiple equilibria and we need to find a way to coordinate to the good one, the one without default. Looking at last week, it seems that we are going in the opposite direction. So it looks like the only way out is for all of us suddenly become optimistic, or that the ECB steps in and helps us coordinate to the good equilibrium.

Update: And Paul Krugman is also puzzled about interest rates in euro countries when you compare them with fiscal policy outcomes in those countries. He cannot understand how interest rates for Austrian government debt remain so high giving its low debt, low unemployment and a current account surplus.