At the recent U.S. Monetary Policy Forum I presented the paper Crunch Time: Fiscal Crises and the Role of Monetary Policy, along with co-authors David Greenlaw (Managing Director and Chief U.S. Fixed Income Economist for Morgan Stanley), Peter Hooper (Managing Director and Chief Economist for Deutsche Bank Securities Inc.), and Frederic Mishkin (professor at Columbia University and former governor of the Federal Reserve). One of the goals of our research was to try to understand the events that can lead a country to a tipping point in which it faces rapid increases in the interest rate on its sovereign debt, as a result of which the country finds itself with an unmanageable fiscal burden.

One can characterize the essentials of debt dynamics with a simple equation. A key parameter is what we call the net interest rate (*r _{t}*), which can be thought of as the difference between the average nominal interest rate on outstanding government debt (

*R*) and the nominal GDP growth rate (

_{t}*g*):

_{t}*r*=

_{t}*R*–

_{t}*g*

_{t}Let

*b*denote debt as a fraction of GDP as of the beginning of year

_{t}*t*and let

*s*denote the government’s primary surplus during that year, that is,

_{t}*s*is government revenues minus government spending on all items other than interest costs, again expressed as a fraction of GDP. The above variables then determine what the level of government debt will be in the following year (

_{t}*t*+ 1):

If we know the country’s interest rate and long-run growth rate, then we can calculate its long-run net interest cost

*r*

^{*}. Given any debt level

*b*

^{*}, it is then straightforward to calculate the value for the primary surplus

*s*

^{*}that would be required in order to keep debt from growing as a proportion to GDP:

Basically equation (2) says that the primary surplus must be big enough to cover the interest costs on the debt once one takes account of the contribution of economic growth. For example, if the nominal interest rate is

*R*= 3%, growth rate is

_{t}*g*= 2%, and debt load is

_{t}*b*= 100% of GDP, then revenues will need to permanently exceed non-interest spending by about 1% of GDP in order to keep debt from growing relative to GDP. If the interest rate is less than the growth rate (so that

_{t}*r*

^{*}is negative), the government could permanently run a primary deficit (that is, maintain a negative value for

*s*) without increasing debt relative to GDP.

What happens if the primary surplus *s*^{*} that would be needed to stabilize the debt/GDP ratio is larger than the current surplus? Then debt next year will be a larger fraction of GDP than it is now. If *r*^{*} is positive, the underlying dynamic equation (1) is unstable– debt would grow to an infinite multiple of GDP if something doesn’t change. One possibility is fiscal reform (tax increases or spending cuts). Another possibility is improvement in the economic growth rate. And a third possibility is that the government either partially defaults on the debt or reduces its value with an unanticipated inflation in order to bring *b* back down to a level that the country realistically could afford to service. Reinhart and Rogoff (2009) have reminded us that the third option has been taken by many different countries many different times.

Of course, if the would-be buyers of the government’s debt assign some nonzero probability to this third possibility, they will require a higher interest rate *R _{t}* as compensation. But from equation (1), that just makes the debt grow even bigger, and the treadmill starts moving faster. The result can be a tipping point in which the government faces a fiscal crisis as a result of rapidly rising interest expenses.

To study these dynamics, we assembled a data set of 20 different advanced economies over the last decade. Our goal was to identify the factors in year *t* – 1 that would help statistically to predict the interest rate on 10-year sovereign debt that different countries faced in year *t*. We looked at both gross government debt and net government debt (the latter subtracts off sums that are owed to government trust funds) as possible predictors. Many economists might prefer to use the net debt series, reasoning that there is no burden associated with money that the government promises to pay itself. On the other hand, these trust funds may themselves entail significant off-balance sheet liabilities and commitments that matter for the government’s long-term ability to service its publicly-held debt. Our approach was to treat it as an empirical question which measure, net or gross debt, was most useful for predicting sovereign interest rates. We found similar results using either measure, but a better statistical fit is obtained when we used the gross debt. Another reason this may work better than net debt is that the gross numbers are less subject to discretionary accounting decisions.

We also found that the country’s current-account balance is very useful for predicting its interest rate. The more public or private debt that is owed to foreigners, the greater the burden the country may face in making its interest payments, the greater the incentive to default, and the more subject the country is to international capital flight.

Finally, we found very strong nonlinearities in the data– high debt levels matter more than low debt levels, and they matter more when the current account is running a big deficit. The regression below captures these nonlinearities by allowing the interest rate to depend not just on the level of debt, but also the square of the level of debt and the product of the debt level with the current-account balance. As seen from the *t* statistics in parentheses, these nonlinear terms are highly significant.

We also include what are known as country fixed effects in this regression (the coefficients α

*), which allow each country*

_{i}*i*to have its own special characteristics, as well as year fixed effects (the coefficients γ

*), which allow for the possibility that something unusual was happening globally in each different year*

_{t}*t*of the sample.

The figure below gives one perspective on the above regression. On the horizontal axis are different possible values for debt as a percentage of GDP. On the vertical axis is how much higher the 10-year yield would be predicted to be if the country had that level of debt compared to if it had no debt. The different colors correspond to different assumptions about the country’s average current-account balance as a percent of GDP. For example, for a country like the United States with gross debt currently about 100% of GDP and with a current-account deficit that hopefully will be no higher than 2.5% of GDP over the next 5 years, each one-percentage-point increment in debt/GDP would be expected to increase the 10-year yield by 6 basis points (that is, by 0.06 percentage points).

The above regression summarizes the broad correlations across different countries and different years. Our paper also looked at the specific week-to-week news events that seemed to produce sudden changes in interest rates in a number of different countries. In the case of Greece, as of the fall of 2008 the country was reporting debt at 100% of GDP and anticipating a deficit around 2% of GDP, as indicated by the black line in the figure below. With a growth rate of

*g*= 6.6% and a borrowing cost of

*R*= 5%, the situation would have appeared to be sustainable.

Unfortunately, the recession produced a huge increase in the budget deficit, and the historical budget turned out to have been significantly misreported. In our paper we review the particular news developments associated with the upward lurch in Greek yields as debt eventually soared to 165% of GDP, well past the tipping point. We also review the various policy measures that were announced with great fanfare but all proved to be of only temporary value. The primary event that made a significant difference was the PSI default on March 8 of last year, which brought Greek’s debt burden back down to more manageable levels.

Ireland is a very different case. The country entered the financial crisis with a low debt load but at the peak of a property-price bubble. The government responded to concerns about the banking system by guaranteeing all the liabilities of its six major banks. As property prices collapsed, the banks’ losses proved to be enormous, leading to an explosion of Irish sovereign debt and moving the country to the tipping point. Stabilization of real-estate prices and fiscal reform have in our assessment likely been successful in pulling Ireland back from the brink.

Spain’s situation is similar to Ireland’s, although it remains unclear who will ultimately bear the losses of falling real-estate prices there. Portugal involves a mix of the problems faced by both Spain and Greece.

Another very interesting case is Italy. Twenty years ago, the country had a debt load of 120% of GDP, with which creditors seemed to have no problem. Why when debt recently returned to those same historical levels should Italy now be in danger of passing the fiscal tipping point?

Our answer is that Italy’s growth rate is much slower today than it was then. The graph below plots an exponentially smoothed average of Italy’s nominal GDP growth over the previous decade as of each date over the sample. Italy was growing at a 7.5% annual rate in 1995; today its growth rate is down to 2%.

One can feed these growth rates into equation (2) above to calculate the primary surplus that Italy would need to stabilize its debt/GDP at the level seen on any historical date if it faced a nominal borrowing cost of 5%. That series for the necessary surplus is plotted as the dashed red line in the graph below, to be compared with the actual surplus in black. The actual surplus was higher than necessary in 1995 (which was why debt/GDP was falling back then), but is lower than necessary in 2012 (which is why debt/GDP is rising again). Thus Italy was short of its tipping point in 1995, but dangerously close today.

What about Japan? This has the highest gross debt/GDP of any country in our sample but one of the lowest borrowing costs. In terms of our regression (3), this is explained by the fact that Japan has been running a current-account surplus rather than a deficit and that Japan has unusually favorable country-specific characteristics (that is, a big negative value for α

*). Hoshi and Ito (2012) argue that Japan’s special privilege is a result of its very high domestic saving rate coupled with extreme home bias. Notwithstanding, they calculate that with Japan’s aging population, their saving rate will decline and the government will soon be forced to borrow on international markets, at which point the sovereign yield will be more subject to the same forces as other countries. We share the pessimism of Hoshi and Ito (as well as many others who have studied Japan’s situation) about the sustainability of current Japanese fiscal policy.*

_{Japan}Another very interesting case is the United States. I will take this up in a subsequent post.

*This piece is cross-posted from Econbrowser with permission.*