Fiscal policy/Tutorials

Overview
The ultimate limit upon the size of the national debt is reached when more money is required for its repayment than the government can raise from taxation - at which point,  the only alternative to a default amounting to national insolvency is by creating money for the purpose of repayment. Money creation aside, national insolvency is, in fact,  an inevitable long-term outcome if  national debt persistently grows faster than gdp. That is known as the debt trap, and its avoidance is the economic policy objective known as "fiscal sustainability". Under stable conditions, fiscal sustainability normally requires the maintenance of a surplus  of  tax revenue over public expenditure, when expressed as fraction of the national debt,  has to average a percentage of gdp least equal to the difference between the interest rate payable and the gdp growth rate.

Although that identity-based criterion would ensure fiscal sustainability in a stable, risk-free environment, it is generally accepted that a more stringent criterion is needed in order to guard against operating risks.

The debt trap identity
According to the debt trap identity (proved in the appendix below), the increase, Δd, in national debt in any given year, as a percentage of GDP is given by:


 * Δd =  f + d(r - g)

where d is the amount of the accumulated debt as a percentage of GDP at the beginning of the year, and f is the primary budget balance for the year (shown with a negative negative sign if a surplus) as a percentage of GDP, r is the interest rate payable on the debt, and g is the then current GDP growth rate.

So that if Δd = 0


 * f = -d(r - g)

- which is to say that to avoid an increase in public debt in the course of any year, the budget balance during that year must not be greater than the opening level of debt multiplied by the difference between the interest rate on the debt and the GDP growth rate in that year (and that means a budget surplus if the interest rate is greater than the growth rate).

If, for example, r were 5% and g were 2% then a debt of 50% of gdp would require a surplus of 1.5% of GDP, a debt of 100% of GDP would require a surplus of 3% of gdp,  and so forth.

Steady state analysis
It is a necessary  condition for long-term sustainability that budget surpluses do not continue indefinitely  - because that would  lead  eventually to the logically impossible outcome of  an interest payment greater than the national income -  and the debt trap identity establishes the means of satisfying that condition. But that does not, in practice, amount to a sufficient condition. The further condition that has to be met is that the national debt must not rise above the maximum level that can be financed by taxation - and that is is a condition  that cannot be derived  objectively, but only by subjective judgement. It follows that claims that a fiscal stance is sustainable (or unsustainable) is a statement, not of fact, but of opinion.

In any case the debt trap identity applies only on the unrealistic steady-state assumption that there are no changes in its variables of  growth rate, debt level and discount rate. The following paragraph considers the problem of maintaining sustainability on more realistic assumptions.

Cyclical influences
During periods of economic stability, and when liquidity is plentiful and domestic interest rates are low,  investors tend to seek profit opportunities abroad, as a result of which debtor governments find it easy to borrow at modest rates of interest. However, an international economic downturn, or a credit crunch, or discount rate increase in their creditors' countries can threaten the  fiscal sustainability, even of countries with relatively modest levels of national debt. The economic downturn may be transmitted to their economies and raise their budget deficits through the operation of their automatic stabilisers. A credit crunch or discount rate increase may make investors reluctant to roll-over their short-term debt, and the resulting fall in demand may raise the interest rate necessary to continue borrowing. In some cases the resulting reduction in their fiscal sustainability may prompt investors to demand the addition of a risk premium to the interest rate that they would otherwise accept - thus detracting further from their fiscal sustainability. And in extreme cases rumours of of impending sovereign default spread by a government's critics can generate a herding response that leads to a rapid escalation of their risk premium and a precipitous loss of sustainability.

The fiscal dilemma
Fiscal policy often poses a choice between the growth objective and the sustainability objective, but a more pressing dilemma can arise concerning the conduct of fiscal policy during a recession. The operation of automatic stabilisers during a recession necessarily increases a country's budget deficit - sometimes to the extent of raising fears of possible sovereign default. The dilemma is posed by the choice whether to increase that deficit in order to mitigate the depression, or to reduce it in order to avert the danger of an investor panic. That choice is complicated by the fact that in the absence of effective action to counter the recession, its increasing severity might in any case raise the national debt to an unsustainable level. The consensus choice before 2008 had been to refrain from fiscal expansion and to counter the recession solely by an expansionary monetary policy. But in face of the threat posed by the international crash of 2008, most of the G20 governments considered it necessary to use discretionary fiscal policy to augment the diminishing effects of monetary expansion. The recession came to to an end in 2009, but in view of the perceived fragility of the recovery, the dilemma remained: whether to implement immediate tax increases or public expenditure cuts, or to postpone such action pending signs of a sufficiently robust recovery.

Previous post-war experience of that dilemma had been confined to the developing countries. Panics among investors and anticipations of default by speculators had been such a frequent  cause of sovereign default among them that  the International Monetary Fund had  made its assistance conditional upon  the avoidance of deficits, even during recessions ).

Appendix: proof of the debt trap identity
Let D and Y be the levels of public debt and GDP at the beginning of a year; and, let F be the primary, or discretionary budget deficit (the total deficit excluding interest payments) and, let r be the annual rate of interest payable on the public debt; and assume that F, r, and g are all mutually independent.

- then the public debt at the end of the year is D1 = D + F +Dr; the GDP at the end of the year is   Y1 = Y(1 + g); and the ratio of public debt to GDP has risen from  D/Y to  (D + F + Dr)/{Y(1 + g);

- thus the increase in the ratio of public debt to GDP in the course of a year is:


 * Δ(D/Y) = (D + F + Dr)/{Y(1 + g)} - D/Y

Let 1/{Y(1;+ g)} = A andso that AY = 1/(1 + g) ,and  1/AY = 1 + g - then:
 * Δ(D/Y) = A(D + F + Dr) - D/Y
 * = A( D + F + Dr  - D/AY)

- and substituting 1 + g for 1/AY:
 * = A( D + F + Dr - D - Dg)

substituting for A:
 * Δ(D/Y) = {F + D(r - g)}/{Y(1 + g)}

or, approximately:-
 * Δ(D/Y) = {F + D(r - g)}/Y
 * = F/Y + (r - g)D/Y

Let f = F/Y ,and d = D/Y

- then                Δd  =  f + d(r - g)

where f is the primary budget deficit as a percentage of GDP, and d is public debt as a percentage of GDP