Set out the dangers to global economies from high public debt, including how such debt together with other factors can set fiscal and monetary policy against each other.

FRM® Part II · Current Issues in Financial Markets · Monetary and fiscal policy: safeguarding stability and trust · FRM2.CI.5.c

The idea

High public debt is dangerous because it shrinks fiscal space and ties the budget to interest rates. Debt dynamics follow a rule, in which r is the average nominal interest rate, g is nominal growth, and every term is a ratio to GDP. Next period's debt ratio is as follows: Next debt = debt × (1 + r) ÷ (1 + g) − primary balance. The primary surplus that holds the ratio constant follows from it: Surplus = (r − g) ÷ (1 + g) × debt. A rise in r above g, or a larger debt, raises the required surplus sharply, so the gap and the debt both matter. Debt also feeds a sovereign-bank loop. Weaker public finances reduce bond values on bank balance sheets, and weaker banks need public support. Other pressures such as ageing, defence and climate spending add to deficits. When inflation requires higher rates, higher debt service widens the deficit, markets doubt the central bank's resolve, and the two policies work against each other. A favourable r below g is not permanent, and refinancing passes higher rates through gradually, not at once.

Formulas

Public debt dynamics

dₜ₊₁ = dₜ × (1 + r) ÷ (1 + g) − pb

dₜ: the debt-to-GDP ratio this period
r: the average nominal interest rate on the debt
g: nominal GDP growth
pb: the primary balance as a share of GDP, positive for a surplus

r is the average rate on existing debt, so a jump in market yields passes through only as debt is refinanced.

Primary surplus that holds the debt ratio constant

pb = (r − g) ÷ (1 + g) × d

r: the average nominal interest rate on the debt
g: nominal GDP growth
d: the debt-to-GDP ratio

When r exceeds g a surplus is needed just to stop the ratio rising, and the gap and the debt level both scale it. A favourable r below g is not permanent.

A practice question

From the question bank, with the reason each wrong option is wrong.

Which is a danger of a very high public debt ratio?

It guarantees high inflation within a year.Why not: Overstates the link: high debt raises inflation risk but does not guarantee a quick outcome.
It increases the government's room to run counter-cyclical deficits.Why not: Reverses the effect: high debt reduces room to run deficits in downturns.
It lowers debt service because larger bond issues carry lower coupons.Why not: Wrong: larger issues usually require higher yields and do not lower the interest bill.
It leaves less fiscal space to respond to shocks and makes the budget more sensitive to rises in interest rates. - correct

High debt cuts fiscal space for crises and exposes the budget to higher interest rates as debt rolls over. It raises risks but does not guarantee inflation, and it does not reduce debt service.

A harder one

A government has debt of 120% of GDP, an average nominal interest rate of 6% and nominal GDP growth of 2%. Using debt ratio next year = debt ratio x (1 + r) / (1 + g) - primary balance, the primary balance that holds the debt ratio constant is closest to:

A primary deficit of 4.7% of GDP.Why not: Gets the sign wrong: when r exceeds g the government needs a surplus, not a deficit.
A primary surplus of 7.2% of GDP.Why not: Uses r x debt (6% x 120), ignoring that growth offsets part of the interest cost.
A primary surplus of 4.7% of GDP. - correct
A primary surplus of 2.4% of GDP.Why not: Uses g x debt (2% x 120), the growth term only, and drops the interest rate.

Required primary balance = (r - g) / (1 + g) x debt = 0.04 / 1.02 x 120 = 4.7% of GDP surplus. With r above g, a positive primary surplus is needed just to stop the ratio rising.

The hardest tier

A government has debt of 100% of GDP in bonds spread evenly across 3-year maturities, so one third matures each year, all at a 1.5% coupon. Market yields jump permanently to 4.5%, and maturing bonds are refinanced at that yield with the debt ratio kept constant. After two annual refinancing rounds the interest bill is closest to:

3.5% of GDP. - correct
4.5% of GDP.Why not: Assumes the whole stock reprices at once to 4.5%, ignoring that only the maturing share is refinanced.
2.5% of GDP.Why not: Counts only the first refinancing round (1/3 at 4.5%), which gives 2.5%.
3.0% of GDP.Why not: Takes the simple average of the old and new rates, ignoring the share of debt actually repriced.

After two rounds, two thirds of the debt carries 4.5% and one third 1.5%: 2/3 x 4.5 + 1/3 x 1.5 = 3.5% of GDP. Interest costs rise gradually as debt rolls over, a hidden vulnerability of high debt.

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