Government Debt

Deficit (flow): G − T in one year.

Debt (stock): cumulative past deficits less surpluses; total amount owed by government to creditors.

Debt-to-GDP ratio. Standard measure of debt burden. Allows comparison across countries and over time.

Debt dynamics. The debt-to-GDP ratio EVOLVES according to:

$\Delta \text{(Debt/GDP)} \approx \text{primary deficit ratio} + (r - g) \times \text{Debt/GDP}$

where:

• r = real interest rate on debt.
• g = real growth rate of GDP.
• Primary deficit = G − T excluding interest payments.

Sustainability rule. If g > r AND no primary deficit (balanced primary budget), debt-to-GDP FALLS over time.

If r > g, then even with balanced primary budget, the ratio RISES. Primary surplus needed to stabilise.

Worked example. Country with debt-to-GDP = 100%, r = 3%, g = 2%, primary balance.

• (r − g) × Debt/GDP = (3 − 2) × 100 = +1% per year.
• Even with no primary deficit, ratio rises by 1pp annually.
• To stabilise, government needs primary surplus of 1% of GDP.

Real-world examples.

• USA: persistent deficit + benign rates kept debt below 100% historically; recently rising sharply.
• Japan: debt-to-GDP > 250%, sustained by very low interest rates and domestic holding.
• Eurozone (2010s): Greek and other crises showed how fast confidence can break.

Crowding out. Government borrowing absorbs savings, raising interest rates → reduces private investment.

• Strongest near full employment.
• Weaker in deep recessions (when private investment is anyway low).
• Modern Monetary Theory (controversial) argues crowding out doesn't bind for countries issuing own currency.

Ricardian equivalence. If consumers are perfectly rational, they should anticipate that today's debt-financed tax cut will require higher taxes later. Forward-looking consumers SAVE the tax cut to pay future tax rises → no AD boost.

In reality:

• Liquidity-constrained consumers spend the tax cut.
• Many people are NOT fully forward-looking.
• Effective: typically only partial offset.

Consequences of HIGH debt:

• Higher interest costs → crowd out other spending.
• Vulnerability to confidence shocks.
• Reduced fiscal space for next crisis.
• Inter-generational equity issues.
• Risk of inflation if monetised.

Limits of debt. Where does the debt limit lie?

• Pure economics: as long as r < g, very high debt sustainable.
• Real world: political and market confidence limits matter.
• Reinhart-Rogoff debate: claimed debt > 90% reduces growth; later challenged but raised concerns.