Public Debt Dynamics and Religion

by George Hatjoullis

There is a great deal of media discussion about ‘sustainable’ public debt levels. George Osborne has made a big song and dance about legislating to target budget surpluses which would seem to imply at least not increasing debt levels. Greece is being vilified by all and sundry for accumulating an unsustainable level of debt. For the average voter all this is meaningless and there is a tendency to extrapolate from the individual to the state in a way that is intuitive but quite wrong. The state and the individual are not the same and the dynamics of debt do not work in the same way. I touched on this in my series of Economics lessons (1-19) which is still published on this blog but these need to be read as a block to make sense. In this blog I want to try to clarify some of the basic arithmetic to enable a better understanding of what is being discussed by the media.

The IMF have published technical papers covering the maths and the FT has set up an interactive that can be used to play around with the arithmetic. The basic equation is:


where Dt=debt to GDP ratio

Rt=real interest rate

Gt=real GDP growth rate

PBt= primary balance as % of GDP

Dt-1 is just last years debt to GDP ratio. The primary balance is net government expenditure ignoring interest expenses.

The first term to look at is [1+Rt]/[1+Gt]. If the real interest rate is 4% and the growth rate is 2% then this term is 1.04/1.02=1.02, with a bit of rounding. It is greater than one so the debt to GDP ratio tends to grow. At the moment real interest rates are negative to zero whilst growth rates are positive so debt to GDP ratios are not inclined to grow owing to this component. Debt dynamics are generally quite healthy. If governments do nothing the debt to GDP ratio is biased to decline at the moment. So why all the fuss?

The second term, the primary balance, may be negative and minus a negative is of course a positive. Negative primary balances are added to Dt and thus increase debt to GDP. If there is a primary deficit (a negative primary balance), debt tends to increase as a % of GDP. Running a primary surplus ( a positive primary balance) reduces debt to GDP.

Putting the two together it is clear that running a primary surplus is not necessary in order to reduce debt to GDP at the moment because of the relationship between real interest rates and real growth. A primary balance of zero will suffice. The question is does it reduce the debt to GDP ratio sufficiently quickly. Perhaps a better question is quickly enough for what?

There is a clear view in the economic literature and among policy makers that certain levels of debt are bad and unsustainable. Underlying this view are beliefs of the ‘natural order of things’. One important belief is that real interest rates typically exceed growth rates and debt levels will tend to grow unless kept in check through primary balance fiscal prudence. No one to my knowledge has unequivocally demonstrated that real interest rates must typically exceed growth rates. The present situation may persist. Moreover, if real interest rates are less than growth rates why exactly does the level of debt matter? It is evidently not inhibiting growth and the level of debt is inclined to fall. A primary balance of zero will suffice for fiscal prudence.

Fiscal prudence and the associated austerity has taken on a religious significance. It has become an act of faith that seems to ignore the facts on the ground. Real interest rates presently are less than growth rates, typically, and thus debt levels are biased to decline, ceteris paribus. In this situation growth is clearly not being inhibited by debt so why worry about the level of debt. A primary balance of zero or even a small deficit will not increase debt levels and is consistent with declining levels of debt. Chill out and focus on ensuring the economy is growing not too far below potential.