# Italy’s public debt, decomposed

Why is Italy’s debt so high?

Is it because the Italian government was fiscally irresponsible, spending too much and taxing too litte? Or is it because investors demand such high interest rates on Italian government bonds? Or is it a consequence of Italy’s dismal economic performance in recent years?

To answer this question, we can take a simple decomposition of the debt-to-GDP ratio. First, remember the government budget constraint: $\displaystyle dB = G - T + rB.$

where B is public debt, G is spending, T is revenue and r is the interest rate. Second, take the time derivative of the debt-to-GDP ratio $\displaystyle d\left(\frac{B}{Y}\right) = \frac{dB}{Y} - \frac{B}{Y}\frac{dY}{Y}.$

Combine the two equations and denote the GDP growth rate dY/Y by g: $\displaystyle d\left(\frac{B}{Y}\right) = \frac{G-T}{Y} + (r-g)\frac{B}{Y}.$

This equation allows us to decompose the total change in the debt-to-GDP ratio into a primary deficit component, an interest component and a growth component. The graph below shows this composition for Italy during the pre-crisis period (2000-2008) and the post-crisis period (2009-now).

In the years between the introduction of the euro and the financial crisis, Italy’s debt ratio decreased slightly by about 2 percent of GDP. During the years after the crisis, it increased by almost 30 percent of GDP.

What changed? As you can see by looking at the yellow and blue areas in the graph, it wasn’t interest payments or the primary surplus. Interest payments were around 5 percent of GDP both before and after the crisis and the Italian actually ran a primary surplus in both periods. What changed was the green area: the recent rise in the debt ratio is almost entirely due to Italy’s shrinking economy.

# Some More on the Crisis Vulnerability of Countries

A couple of weeks back we had a great post by Christoph Zwick on current account rebalancing in the Eurozone. In the comment section I mentioned I had my doubts on what the variables are that we should look at in order to determine which countries are most vulnerable to experiencing “sudden stops” of capital inflows, thus triggering a financial crisis, which is in essence what happened in the southern Eurozone periphery. In particular I found the argument unconvincing that debt ratios are of much use in this discussion, my thoughts on which I attempted to summarize in a follow-up post I did back then.

I don’t mean to pick on this, but I feel it is important since it is a fairly widespread view that excessive debt ratios (both public and private) are a large part of the reason why some countries fared so badly in the financial crisis while others did much better. The subsequent calls for austerity, often based on this flawed analysis, are also what is destroying the future of an entire generation of young people in the affected economies.

I just happened to stumble on some research by Frankel and Saravelos (.pdf) that seems to address specifically this issue, and I thought it would be a useful addition to the conversation. In essence it is a literature overview that tries to summarize the findings regarding which variables proved to be statistically significant as “early warning indicators” for financial crises. The top 5 indicators they found are as follows (Table 1): foreign exchange reserves, the real exchange rate, GDP growth, growth in credit and the current account. Clearly not all of these are applicable to countries in a monetary union, such as the Eurozone, which essentially by definition have no foreign exchange reserves of their own, for instance. But what struck me the most is the indicator at the very bottom of that list: External Debt. In fact, of the 83 studies reviewed, only 3 found external debt to be a statistically significant indicator to predict a financial crisis. “Budget Balance”, the meaning of which is unfortunately not really defined in the paper, was found to be significant in only 9 of the 83 studies surveyed. Both government as well as external debt simply do not seem to be what we should be looking at here.

P.S.: As a side-note, some economists at Well’s Fargo (.pdf) took these indicators to estimate which of the 30 biggest developing economies in the world are more likely to be subject to crises in the near future. Might be interesting to keep an eye open.

Edit: The survey I quoted in the post relates to pre-2008 crises. The authors then conduct some analysis of their own for 2008-2009 episodes, and for some reason do find external debt to be a significant indicator. I’m not sure how that works, but it does of course change the story I tried to tell.