Government Debt Sustainability – a simple equation

The distinction between insolvency and illiquidity is an important one. It usually comes up when thinking about banks that are in financial trouble and suffering a drain on deposits. Before a central bank will intervene with a lender of last resort loan, it normally asks “is it the drain on deposits that is causing the financial problems for the bank, or is the drain on deposits because the bank has made bad lending decisions and got itself into trouble?”

The issue is just as important for governments, but it has not one that has gotten a lot of attention until the euro crisis came along. In future posts, we’ll look at whether governments can suffer a run like a bank (we thinks they can) and if lender of last resort lending could solve it (again, he thinks it could). But before going around advocating lots of LOLR lending (which TH is not 100% convinced about just yet), he wants to discuss a more fundamental problem – what determines whether a government is solvent or not and the relationship between solvency and credibility.

long run debt to GDP ratio*= (primary deficit*)/(nominal growth rate of GDP*-nominal interest rate on government debt*)

Where a * denotes the expected long-run equilibrium value and the primary deficit is the government’s budget deficit excluding interest payments.

The formula is easy to use. Suppose, for example, that the primary deficit was 2% of GDP, the nominal growth rate was 6% and the nominal yield was 5%, then the long-run debt to GDP ratio would be (2/1=) 200% of GDP.

To determine whether this is sustainable or not, one thing you need to think about the tax burden that this stock of debt implies. Based on our calculations, just paying the interest would amount to (0.05×200=) 10% of GDP. That is high, but a country with this level of debt could quite plausibly be solvent. It seems reasonable to think that a government could easily collect, say, thirty percent of a nation’s GDP in taxes and that one third of that could be used to pay bond holders, leaving 22 percent of the nation’s GDP for government provided goods and services (such as roads, schools, hospitals and TV –like the ABC in Australia, BBC in the UK or CBC in Canada).

The ability to service a high debt seems even more likely if the debt is held by domestic residents. Then the debt payments are just a transfer from those in the country who earn income and pay taxes to those who earn an income from holding the government’s bonds (quite often those who have retired and are living on pension income). In this regard, domestically held debt represents a redistribution of income of sorts and doesn’t necessarily cause a significant reduction in the resources available for the economy as a whole to spend on consumption or investment.

Nevertheless, raising taxes to redistribute income can still be a challenge for governments, and there are limits to how much and how effectively governments can tax, which might make high debt levels unsustainable. And of course, if all this debt was foreign owned, then there is much more of an issue – domestic voters might not like seeing their taxes redistributed to foreign bond holders. This is one reason why periphery countries like Spain and Greece face problems – substantial amounts of their government debt is held by foreigners (Germans and other European current account surplus countries). So while Europe owes money to itself as a whole, individual country governments are heavily indebted to residents in others.

It is also important to note that the expected debt level that the formula generates can be quite sensitive to the assumptions (i.e. what people expect the country’s growth rate, interest rate and primary deficit to be). Every time the primary deficit doubles, so does the long term debt and the tax burden required to service it. So, if the primary deficit was 4% of GDP instead of 2% (assuming other assumptions stay the same), then the equilibrium stock of debt would end up at 400% of GDP and the tax bill for interest alone would be 20% of GDP. And, if the interest rate rose to something over 6% or the nominal long-run nominal growth rate dropped to below 5%, then the debt would never stabilise – it, along with the tax burden required to service it, would eventually go to infinity.

That is not to say that residents of this economy, which we assumed would  achieve nominal growth rates of 6% and pay a nominal yield of 5% over the long term, could not tolerate primary deficits that were temporarily much higher than 6% of GDP, just that they would have to be temporary. But it does suggest that the expected long-run solvency of a country can be very sensitive to what assumptions people make.

This sensitivity to the assumptions problem has also affected the Euro area periphery countries – markets have substantially changed their assumptions about these countries fundamentals. For the periphery in general, markets have lowered growth expectations as the previous assumptions about the growth benefits from being a member of a common currency union have proven to be wrong. And that, in turn, has raised the risk premium on government debt.

On top of that there are concerns about the ability of governments to adhere to budget commitments. In Greece for example, markets doubt the credibility of government commitments to budget targets (after all the Greek repeatedly deceived the public about its true budget position); and Europe as a whole has a track record of violating its own treaty on avoiding excessive budget deficits. Last, Europe already has a very high level of taxation – governments in the Euro area collect almost 50% of GDP in taxes – it’s hard to see how they could increase that further without it damaging the capacity of their economies to grow.

So where does that leave us: On the whole Europe, is OK – the debts of some countries are simply a mechanism to redistribute taxes to residents elsewhere in Europe. But Europe doesn’t have a pan-European federal fiscal policy to redistribute funds back to heavily indebted governments, whose debts are held by residents elsewhere in Europe. So periphery governments must tax their residents to pay the residents of the core surplus countries like Germany. This in turn raises discussions about fairness and makes the political commitment to avoid default more challenging to sell to voters. The heavily indebted governments are also part of a monetary union that has proven to be a constraint on rather than a source of growth for the periphery, which has also reduced the capacity of these governments to sustain and service their debts. Furthermore, a poor track record in Europe to meet budget targets despite a high level of taxation, combined with the failure of policy makers to decisively deal with the crisis has reduced government credibility. As a result, markets doubt the ability of governments to meet budget targets.

Thus, while in principle, periphery governments (such as Spain and Greece) could potentially be solvent and able to cut spending and raise taxes required to stabilise debts at reasonable levels; in practice, it seems unlikely that markets would consider these commitments to be credible. Unfortunately for the  European periphery, unless something changes to bolster credibility or growth potential, market expectations are unlikely to be consistent with what is required to make debts sustainable.

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