Foundations · F9 · 9 min

Fiscal policy, debt and bond supply

Explain deficits and debt, project debt against GDP, and say why heavy government borrowing pushes up long-term interest rates.

In the news: Budgets and government borrowing plans: the news that moves long-term interest rates.

The essentials

Deficit and debt: The is one year’s gap between spending and tax revenue, covered mostly by selling bonds; the debt is all the borrowing still owed. Tax cuts and extra spending are expansionary and usually mean more borrowing.
Debt against GDP: Debt is judged against yearly output: £2,000bn of debt with GDP of £2,500bn is 80%. The is the budget before interest on past debt.
Interest rate against growth: When the average rate on the debt exceeds nominal growth, debt/GDP rises on its own: at 100% of GDP, a rate of 4% against growth of 3% adds about 1 point a year, even with a balanced primary budget.
Supply and term premium: The sells . Selling many more long-dated ones makes investors ask a higher to hold them, the , while short yields follow the .
Autumn 2022: After the September 2022 tax-cut package, 30-year gilt yields rose more than 0.8 points in two trading days. Forced selling by funds pushed them higher until the Bank of England bought long gilts from 28 September.

Debt dynamics

Δd ≈ (r − g) × d − pb

d: government debt as a share of GDP
r: average interest rate on the debt (nominal)
g: nominal GDP growth
pb: primary balance, % of GDP: a surplus is positive, a deficit negative

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How it works

1. Governments borrow too

Like a household spending more than it earns, a government that spends more than it collects in taxes in a year runs a . It covers the gap by borrowing, mostly by selling bonds. All the borrowing it still owes is its debt.

2. Looser and tighter budgets

Tax cuts or extra spending put more money into the economy: that is expansionary. Tax rises or spending cuts take money out: it is contractionary. Expansionary budgets usually mean more borrowing.

3. Debt against the economy

£2,000bn of debt means little on its own. What matters is its size against the economy’s yearly output, : £2,000bn of debt with GDP of £2,500bn is 80% of GDP. Debt can keep rising while this ratio falls, if the economy grows faster.

4. The budget before interest

Part of spending is interest on old debt. Leave it out and you have the : a surplus if taxes exceed all other spending, a deficit if not. It shows whether today’s choices add to the debt, before the cost of the past.

5. Interest rate against growth

Interest (r) adds to debt/GDP each year, while nominal growth (g) shrinks it by making the economy bigger. Roughly, debt/GDP changes by (r − g) × debt/GDP minus the primary balance. With debt at 100% of GDP, r at 4% and g at 3%, it rises 1 point a year even with a balanced primary budget.

6. Interest bills catch up slowly

When market rates rise, a government pays more only as old bonds mature and are replaced. £2,000bn at an average 3% costs £60bn a year. If a quarter of it is refinanced at 1 point higher, the bill rises £5bn. Short-dated debt passes on higher rates faster.

7. Supply moves long-term rates

In the UK the sells gilts of different lengths. A bond’s yield is the yearly return it pays at today’s price. Sell many more long-dated gilts and investors must hold more of them, so they ask for a higher yield: the extra is the .

8. 2022: when markets pushed back

On 23 September 2022 the UK government announced large tax cuts paid for by borrowing. By the next Monday, 30-year gilt yields were more than 0.8 points higher. Pension funds using borrowed money, funds, had to sell gilts to meet , pushing yields up further, until the Bank of England bought long gilts from 28 September.

Try it

Push the 10-year yield up more than the 2-year, as heavy long-dated borrowing can: long-term rates rise while short-term rates, tied to the policy rate, move less. Illustrative curve.

Bull steepener2s10s +65bp (from 40bp)

2-year move-30bp10-year move-5bp

Dashed: before. Accent: after. Bull = yields fall (prices rise); bear = yields rise. Illustrative curve.

Worked example

A government’s debt is 100% of GDP. It pays an average 3.5% on its debt, nominal GDP grows 3.0%, and it runs a primary deficit of 1.5% of GDP. Higher market rates then push its average rate towards 4.5%. (Illustrative figures.)

Now: (3.5% − 3.0%) × 100 = +0.5 points a year from r − g.
The primary deficit adds 1.5, so debt/GDP rises about 2.0 points a year.
At r = 4.5%: (4.5% − 3.0%) × 100 = +1.5 points.
Add the 1.5 deficit: debt/GDP now rises about 3.0 points a year.
To hold it steady at 4.5%, the primary balance must reach a 1.5% surplus: a 3%-of-GDP tightening.

Debt/GDP rises about 2 points a year now and 3 at the higher rate; holding it steady would take a 3%-of-GDP tightening.

Check yourself

8 quick questions on the explanation above.

Practice

New numbers every set. Misses and guesses go into your review deck.

In the interview

Answer out loud in under a minute, then compare.

What happened to gilts in autumn 2022, and what did markets learn?
Why can a bigger deficit push up long yields even if the central bank holds rates?
What’s term premium, and why has it come back?

Remember

Δ debt/GDP ≈ (r − g) × debt − primary balance

When interest rates exceed growth, debt grows on its own, and the long end of the curve charges for the extra supply.

Next · F10How data moves markets

Sources

Definitions and maths are standard textbook material; dated facts link to the sources above. Worked numbers are illustrative.