# 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.