Skip to content

Lesson M21.L02: External Debt Sustainability

Module: M21: Open Economy Macroeconomics Part II Level: intermediate Duration: 30 minutes Learning Objective: Derive the external debt stability condition and apply it to Australia's net foreign liability position. Data as of: 2024 Provenance: RBA Statistical Tables โ€“ Foreign Debt | IMF External Debt Statistics

Explanation

A country can run current account (CA) deficits for extended periods โ€” but not indefinitely. The central question of external debt sustainability is: under what conditions will the ratio of external debt to GDP remain stable rather than explode?

Notation: - D = stock of net external debt (net foreign liabilities) - Y = GDP - d = D/Y = debt-to-GDP ratio - r = real interest rate on external debt - g = real GDP growth rate - CA = current account balance (positive = surplus)

Debt dynamics derivation:

The stock of external debt evolves as:

\[D_{t+1} = (1 + r) D_t - CA_{t+1}\]

Each period, debt grows by interest (rยทD) and falls by the CA surplus (or rises if CA is in deficit).

Dividing both sides by Y_{t+1} = (1+g)ยทY_t:

\[\frac{D_{t+1}}{Y_{t+1}} = \frac{(1+r)}{(1+g)} \cdot \frac{D_t}{Y_t} - \frac{CA_{t+1}}{Y_{t+1}}\]

For small r and g, (1+r)/(1+g) โ‰ˆ 1 + (rโˆ’g). Therefore, the change in the debt ratio is:

\[\Delta d \approx (r - g) \cdot d - \frac{CA}{Y}\]

Stability condition: For d to remain stable (ฮ”d = 0), we need:

\[\frac{CA}{Y} \geq (r - g) \cdot d\]

This is the external debt stability condition. The required CA surplus (as % of GDP) equals the product of (rโˆ’g) and the current debt ratio.

Key intuition: - If r > g: the debt ratio tends to grow on its own (interest compounds faster than GDP); a CA surplus is needed to offset this. - If r < g: the economy "grows out of" its debt and can sustain a small CA deficit. - The higher the debt ratio d, the larger the required CA surplus.

Australia's position (2024): Australia's net foreign liability position is approximately 55% of GDP. Interest rates suggest r โ‰ˆ 4.5% (real) while Australia's trend growth g โ‰ˆ 2.5%. Thus r โˆ’ g โ‰ˆ 2%. Australia's recent CA has been approximately +1โ€“2% of GDP (post-commodity boom), placing it at the margin of sustainability.

Worked Example

Given data:

Variable Value
Net foreign debt ratio d = D/Y 55% = 0.55
Real interest rate r 4.5% = 0.045
Real GDP growth g 2.5% = 0.025
Current account CA/Y (recent) +1.5% = 0.015

Step 1: Calculate the interest-growth differential.

\[r - g = 0.045 - 0.025 = 0.020 \quad (2\%)\]

Step 2: Calculate the required CA surplus to stabilise the debt ratio.

\[\left(\frac{CA}{Y}\right)^* = (r - g) \times d = 0.020 \times 0.55 = 0.011 = 1.1\%\]

Australia needs a CA surplus of at least 1.1% of GDP to keep its debt-to-GDP ratio from rising.

Step 3: Check against actual CA.

\[\frac{CA}{Y} = +1.5\% > \left(\frac{CA}{Y}\right)^* = 1.1\%\]

Conclusion: Australia's actual CA surplus (1.5%) exceeds the required surplus (1.1%), so ฮ”d < 0 โ€” the debt ratio is declining.

Step 4: Calculate the actual change in debt ratio.

\[\Delta d = (r - g) \cdot d - \frac{CA}{Y} = 0.020 \times 0.55 - 0.015 = 0.011 - 0.015 = -0.004\]

The debt ratio falls by approximately 0.4 percentage points per year.

Step 5: How long to reach 50% debt ratio from 55%?

\[\text{Years} = \frac{55\% - 50\%}{0.4\% \text{ per year}} = 12.5 \text{ years}\]

At current settings, Australia would reach a 50% debt ratio in roughly 12โ€“13 years โ€” assuming r, g, and CA remain constant.

Common Misconception

Misconception: As long as a country can pay the interest on its debt, the debt is sustainable.

Correction: Paying interest is necessary but not sufficient. The debt-to-GDP ratio can grow even when interest payments are made, if r > g. Specifically, if the CA surplus is less than (rโˆ’g)ร—d, debt compounds faster than the economy grows. Sustainability requires the CA surplus to be large enough to offset the debt-compounding effect โ€” captured precisely by the condition CA/Y โ‰ฅ (rโˆ’g)ร—d.

Practice Prompts

  1. Conceptual: Why does the interest-growth differential (rโˆ’g) matter so much for debt sustainability? What happens to the required CA surplus if g rises due to a productivity boom? โ†’ Answer: When r > g, interest on external debt compounds faster than GDP grows, pushing the debt ratio upward automatically. The required CA surplus = (rโˆ’g)ร—d must offset this. If g rises (productivity boom), rโˆ’g shrinks, so the required CA surplus falls โ€” the country can "grow its way out of debt" more easily. This is why structural reforms that raise productivity growth are part of debt sustainability strategies.

  2. Numerical: A country has D/Y = 80%, r = 5%, g = 3%, and CA/Y = โˆ’1% (deficit). Calculate (a) the required CA surplus for stability, (b) the actual change in the debt ratio ฮ”d, and (c) whether debt is on a sustainable path. โ†’ Answer: (a) Required CA/Y = (rโˆ’g) ร— d = (0.05 โˆ’ 0.03) ร— 0.80 = 0.02 ร— 0.80 = 1.6% surplus (b) ฮ”d = (rโˆ’g)ร—d โˆ’ CA/Y = 0.016 โˆ’ (โˆ’0.010) = 0.016 + 0.010 = +0.026 = +2.6 pp per year (c) Not sustainable. The debt ratio rises 2.6 pp per year. At this rate, a country at 80% debt could exceed 100% in under 8 years.

  3. Application: Australia's CA moved from a deficit of โˆ’4% GDP (2015) to a surplus of +2% GDP (2022) primarily due to commodity price surges. How does this shift affect external debt sustainability? What risks remain if commodity prices normalise? โ†’ Answer: The shift from โˆ’4% to +2% dramatically changes sustainability. At โˆ’4%, Australia was far below the required threshold of ~1.1%, causing the debt ratio to rise rapidly. At +2%, Australia exceeds the threshold and is slowly reducing d. However, commodity price dependence creates vulnerability: if iron ore, coal, and LNG prices fall toward long-run averages, Australia's CA could return to deficit. Australia's structural CA balance (excluding terms-of-trade effects) remains closer to โˆ’1% to โˆ’2% GDP, suggesting the debt ratio could resume rising once the commodity boom fades โ€” making productivity reform and structural saving improvements important for long-run sustainability.

Further Resources